The equation of the line that passes through the points (1,3) and (2,2) is y = -x + 4.
To find the equation of the line, we can use the slope-intercept form of a linear equation, y = mx + c, where m is the slope and c is the y-intercept.
First, we need to find the slope of the line. The slope is given by:
m = (y2 - y1)/(x2 - x1)where (x1, y1) and (x2, y2) are the coordinates of the two given points. Plugging in the values, we get:
m = (2 - 3)/(2 - 1) = -1Next, we can use one of the given points and the slope to find the y-intercept. Using the point (1,3), we get:
3 = (-1)(1) + cSimplifying this equation gives us:
c = 4
Therefore, the equation of the line in slope-intercept form is:
y = -x + 4.
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5+T(6-3); T=4 what’s the answer in a hurry
Answer:
17
Step-by-step explanation:
5+T(6-3); T=4
Use order of operations. Parenthesis, multiplying, then add last.
= 5 + 4(6 -3)
= 5 + 4(3)
= 5 + 12
= 17
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
The perimeter is the sum of the lengths of all the sides of a polygon. Thus, the perimeter of this quadrilateral is:
(10a-6) + (7a+4) + (7a+4) + (10a-6)
Simplifying the expression:
= 34a - 4
Therefore, the perimeter of the quadrilateral is 34a - 4.
Solve for a.
Answer: a =
334a 73
=
Submit Answer
a
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a
73
Write the problem as a mathematical expression.
a
=
334
a
73
Subtract
334
a
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from both sides of the equation.
a
−
334
a
73
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0
Factor
a
out of
a
−
334
a
73
.
Tap for more steps...
a
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−
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a
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=
0
If any individual factor on the left side of the equation is equal to
0
, the entire expression will be equal to
0
.
a
=
0
1
−
334
a
72
=
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a
equal to
0
.
a
=
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1
−
334
a
72
equal to
0
and solve for
a
.
Tap for more steps...
a
=
1
72
√
334
,
−
1
72
√
334
The final solution is all the values that make
a
(
1
−
334
a
72
)
=
0
true.
a
=
0
,
1
72
√
334
,
−
1
72
√
334
The result can be shown in multiple forms.
Exact Form:
a
=
0
,
1
72
√
334
,
−
1
72
√
334
The interest rate of an auto
loan is 4%. Express this
number as a decimal.
Answer: 0.04
Step-by-step explanation:
In order to get 4% as a decimal, you must divide 4 by 100.
4/100 = 0.04
Thus, the answer to your question is 0.04
Can someone please help me with this?
The value of the angle m<CED is 100 degrees
What are corresponding angles?Corresponding angles are simply described as those angles that are formed by same corners or corresponding corners with a transversal when two parallel lines are joined by any other line.
Also, corresponding angles are created when two parallel lines are intersected by a transversal.
The different types of corresponding angles are;
Those angles formed by parallel lines and transversals.Those angles formed by non-parallel lines and transversals.Note that corresponding angles are equal.
From the information given, we have that;
m < BHG = m<CED
If m< BHG = 100 degrees
Then, m< CED = 100 degrees
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Helppppppppppp me please
Answer:
Step-by-step explanation:\Write an expression for the sequence of operations describe below Add C and the quotient of 2 and D do not simplify any part of the expression
Please answer the both questions in the photos below ( will mark brainliest if available + 20p )
Answer:
x=0 & x=2
Step-by-step explanation:
To find when f(x)=g(x), then look for a value that is the same for both functions in the table. 0 occurs twice for the same x value. 0 also appear twice for the x value 2. This is when they are equal. The solution is x=0 and x=2
-17.R Using Percents, Homework
Sarted: Mar 10 at 8:30pm
Question 1 of 9
The Quick Slide Skate Shop sells the Ultra 2002 skateboard for a price of $60.20. However, the Quick Slide
Skate Shop is offering a one-day discount rate of 45% on all merchandise. About how much will the Ultra 2002
skateboard cost after the discount?
$33.00
$87.00
$46.20
$27.00
The price after discount is $33 and option 1 is the correct answer.
What is a discount?A discount is a drop in a product's or service's price. Discounts can be provided for a variety of purposes, such as to entice consumers to make larger purchases, to get rid of excess inventory, or to draw in new clients. Discounts can be represented as a set monetary amount or as a %, as in the example above. For instance, a shop may give customers $10 off any purchase of more than $50.
Given that, one-day discount rate of 45% is applied.
Thus,
Discount = 60.20 * 0.45 = 27.09
Price after discount = 60.20 - 27.09 = 33.11
Hence, the price after discount is $33 and option 1 is the correct answer.
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Find a basis for the space of 2x2 lower triangular matrices:
A basis for the space of 2x2 lower triangular matrices is [tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex].
Lower triangular matrices resemble the following:
[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right][/tex]
We can write it like this:
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right][/tex]
This demonstrates the set's
[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]
covers the set of lower triangular matrices with dimensions 2x2. Moreover, these are linearly independent, so attempting to
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
leads to
[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right] =\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
which results in a = b = c = 0 right away. As there is no other way to
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
, these matrices are linearly independent if a = b = c = 0.
Since
[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]
they serve as a foundation by spanning the collection of 2x2 lower triangular matrices and being linearly independent.
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Find a tangent vector of unit length at the point with the given value of the parameter t.r(t) = 2 sin(t)i + 3cos(t)jt= pi/6Please express answer in terms of i + j
A tangent vector of unit length at the point with the given value of the parameter t. r(t) = 2 sin(t)i + 3cos(t)j , t= π/6 is r'(t) = √3 i +3/2 j.
Differentiation:
Differentiation is the rate of change of one quantity relative to another. Velocity is calculated as the rate of change of distance over time. The speed at each instant is different from the calculated average. Speed, like grade, is nothing more than the instantaneous rate of change in distance over a period of time.
The ratio of a small change in one quantity to a small change in another quantity as a function of the first quantity is called differentiation.
An important concept in calculus focuses on the differentiation of functions. The maximum or minimum of a function, the speed and acceleration of a moving object, and the tangent to a curve are all determined by differentiation. If y = f(x) is differentiable, then the differential is expressed by f'(x) or dy/dx.
According to the Question:
Given that:
r(t) = 2sin(t)i + 3 cos(t)j,
and, t =π/6
Now,
Differentiating with respect to t, we get:
r'(t) = [tex]2\frac{d}{dt}sin(t) + 3 \frac{d}{dt} cos(t)[/tex]
⇒ r'(t) = 2cos(t) + 3 sin(t)
Putting t = π/6, we get:
r'(t) = 2cos(π/6) + 3 sin(π/6)
⇒ r'(t) = 2×√3/2 + 3× 1/2
⇒ r'(t) = √3 + 3/2
Writing the equation in the vector form:
r'(t) = √3 i +3/2 j
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Peter had 4 bags which had equal number of mangoes.He sold 8 mangoes and remained with 24 mangoes.How many mangoes were in each bag?
Answer: 8 mangoes
Step-by-step explanation:
1. To find the total number of mangoes Peter had, add 8 and 24 which gives you 32. 8 + 24 = 32.
2. If Peter had an equal number of mangoes in each bag, and a total number of 32 mangoes, then you must divide the total number of mangoes by the number of bags, which is 4. 32 ÷ 4 = 8. Therefore, there were 8 mangoes in each bag.
Answer:
The answer is 8 mangoes
It’s not 1507 please help me
Answer:
Below
Step-by-step explanation:
Mass of bouncies + box = 17342 subtract mass of box from both sides
mass of bouncies = 17342 - 429 = 16913 g
Unit mass per bouncy = 505 g / 45 bouncy
Number of Bouncies = 16913 gm / ( 505 g / 45 bouncy ) = 1507.1 bouncies
With the given info, I am afraid it IS 1507 bouncies in the box
maybe since the question asks for APPROXIMATE number, the answer is 1510 bouncies ( rounded answer) ....or 1500
Which expressions are equivalent to (x−2)2
?
Select the correct choice
The expressions that are equivalent to (x-2)² is x² - 4x + 4. (option B)
Now, let's look at the expression (x-2)². This is a binomial expression that can be simplified by applying the rules of exponents. Specifically, we can expand this expression as follows:
(x-2)² = (x-2) * (x-2)
= x * x - 2 * x - 2 * x + 2 * 2
= x² - 4x + 4
So, the expression (x-2)² is equivalent to x² - 4x + 4.
However, the problem asks us to identify other expressions that are equivalent to (x-2)². To do this, we can use the process of factoring. We know that (x-2)² can be factored as (x-2) * (x-2). Using this factorization, we can rewrite (x-2)² as:
(x-2)² = (x-2) * (x-2)
= (x-2)²
So, (x-2)² is equivalent to itself.
Hence the correct option is (B).
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Complete Question:
Which expressions are equivalent to (x−2)²?
Select the correct choice.
A. (x + 2) (x - 2)
B. x² - 4x + 4
C. x² - 2x + 5
D. x² + x - 2x
- La decisión más difícil que tuve que tomar durante el proceso fue……………………………………………………… Fue difícil porque……………………………………………………………………………………………………………………………. 2. - Si pudiera mejorar algo de mi emprendimiento, mejoraría…………………………………………………………………… 3. - Lo aprendido en esta experiencia lo podré aplicar también en……………………………………………………………
1. The most difficult decision I had to make during the process was whether or not to pursue a higher degree. It was difficult because I had to weigh the financial and time commitment.
2. If I could improve something about my business, it would improve the customer service and communication.
3. What I learned in this experience I can also apply in many other areas of my life such as problem solving, communication, and time management.
1. Throughout the process, choosing whether or not to go for a graduate degree was the hardest choice I had to make. It was challenging since I had to compare the costs and time required to finish the degree against any potential advantages it might have for my job. Ultimately, I decided to pursue a higher degree since I felt that the benefits of doing so would outweigh the costs.
2. I would invest in better tools for customer support, implement a customer feedback system, and create more opportunities for customers to share their feedback and ideas. I would also invest in better training for customer service staff to ensure they are equipped with the necessary skills to handle customer inquiries and complaints effectively.
3. These skills can be used in my work life, personal relationships, and even my studies. By learning how to better manage my time and communicate effectively, I can become more productive and efficient in any task I take on. Additionally, problem solving is a skill that is applicable to many aspects of life, such as finding creative solutions to difficult issues or troubleshooting technical problems.
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The complete question is:
1. The most difficult decision I had to make during the process was …………… It was difficult because ……………. .
2. If I could improve something about my business, it would improve …… .
3. What I learned in this experience I can also apply in …………….
The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 7 cm and the width is 5 cm, how fast is the area of the rectangle increasing (in cm²/s)?
Answer:
Step-by-step explanation: In the problem, they tell us that
dL / dt = 7 cm/s (the rate at which the length is changing) and
dw / dt = 8 cm/s (the rate at which the width is changing)
Want dA/dt (the rate at which the area is changing) when L = 7 cm and w = 5 cm
The equation for the area of a rectangle is:
A = L·w, so will need the product rule when taking the derivative.
dA/dt = L (dw/dt) + w (dL/dt)
Now just plug in all of the given numbers:
dA/dt = (7)(7) + (5)(8) = 49+40 = 89 cm²/s
In this problem you will use variation of parameters to solve the nonhomogeneous equation y" – 4y' + 4y = -6e2t A. Write the characteristic equation for the associated homogeneous equation. (User for your variable.) B. Write the fundamental solutions for the associated homogeneous equation and their Wronskian. y2 = 41 = W(91, y2) = C. Compute the following integrals. ✓ W dt = 929 dt = и D. Write the general solution. (Use c1 and c2 for cy and c2). y= (Note: Your general solution will only be correct if it is a general solution to the differential equation.)
A. The characteristic equation for the associated homogeneous equation is:
r² - 4r + 4 = 0
B. The characteristic equation has a repeated root of 2, so the fundamental solutions for the associated homogeneous equation are:
[tex]y1(t) = e^(2t)[/tex]
[tex]y2(t) = te^(2t)[/tex]
The Wronskian of these solutions is:
[tex]W(y1, y2) = det([y1 y2; y1' y2']) = det([e^(2t) te^(2t); 2e^(2t) (2t+1)e^(2t)]) = 4e^(4t)[/tex]
So,[tex]W(y1, y2) = 4e^(4t)[/tex]
C. We need to compute the following integrals:
[tex]W(t)dt = ∫(2e^(2t))(te^(2t))dt = ∫(2t)e^(4t)dt = (1/4)te^(4t) - (1/8)e^(4t) + C1[/tex]
[tex]W(dt) = ∫(4e^(4t))dt = (1/4)e^(4t) + C2[/tex]
D. The general solution is:
[tex]y(t) = c1 y1(t) + c2 y2(t) + yp(t)[/tex]
To find a particular solution, we assume yp(t) takes the form:
[tex]yp(t) = A e^(2t)[/tex]
where A is a constant to be determined. We substitute this into the nonhomogeneous equation and solve for A:
[tex]y'' - 4y' + 4y = -6e^(2t)[/tex]
[tex](4A - 4A) e^(2t) = -6e^(2t)[/tex]
[tex]0 = -6e^(2t)[/tex]
This equation has no solution, so we need to modify our assumption for yp(t) by multiplying by t:
[tex]yp(t) = A t e^(2t)[/tex]
We substitute this into the nonhomogeneous equation and solve for A:
[tex]y'' - 4y' + 4y = -6e^(2t)[/tex]
[tex](8A - 8A + 4A) te^(2t) = -6e^(2t)[/tex]
[tex]4A = -6[/tex]
[tex]A = \frac{-3}{2}[/tex]
So, a particular solution is:
[tex]yp(t) = (-3/2) t e^(2t)[/tex]
Therefore, the general solution to the nonhomogeneous equation is:
[tex]y(t) = c1 e^(2t) + c2 t e^(2t) - (3/2) t e^(2t)[/tex]
or
[tex]y(t) = (c1 - (3/2) t) e^(2t) + c2 t e^(2t)[/tex]
where c1 and c2 are constants determined by initial conditions.
A non-homogeneous equation is a type of mathematical equation that involves both homogeneous and nonhomogeneous terms. In general, a homogeneous equation is one in which all the terms have the same degree, whereas a nonhomogeneous equation contains terms of different degrees.
In the context of linear algebra, a nonhomogeneous equation is typical of the form Ax = b, where A is a matrix, x is a vector, and b is a non-zero vector. The term "nonhomogeneous" refers to the fact that b is not the zero vector. In differential equations, a nonhomogeneous equation is one that includes a forcing function or input that is not equal to zero. The solution to such an equation can be found by adding the particular solution to the general solution of the corresponding homogeneous equation.
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1. The line segment AB has endpoints A(-5, 3) and B(-1,-5). Find the point that partitions the line segment in
a ratio of 1:3
Answer:
To find the point that partitions the line segment AB in a ratio of 1:3, we can use the following formula:
P = (3B + 1A) / 4
where P is the point that partitions the line segment in a ratio of 1:3, A and B are the endpoints of the line segment, and the coefficients 3 and 1 represent the ratio of the segment we are dividing.
Substituting the values, we get:
P = (3*(-1, -5) + 1*(-5, 3)) / 4
P = (-3, -7)
Therefore, the point that partitions the line segment AB in a ratio of 1:3 is (-3, -7).
Step-by-step explanation:
In a figure skating compotion each skater receives score from eight judges. A skater has a mean (average) score of 7. 25 points. Write an equation to find the skaters total scores s
A skater has a mean score of 7. 25 points. An equation to determine the skaters total scores received from eight judges is equals to the x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ = 58.
Mean is called the average of the values and is calculated by dividing the addition of values by the total number of values. It is denoted by [tex]\bar X[/tex]. That is bar above X represents mean of x number of values. Mathematically, Mean = (Sum of all the values/Total number of values).We have in a skating compotion where each skater receives score from eight judges. Now, Mean or average of score points obtained by a skater = 7.25 points. Let the skater's received score from eight judges be equals to x₁,x₂,x₃,x₄,x₅,x₆,x₇, x₈. Total score received by skater = x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ and we have to write the equation to determine the skaters total scores. Now, in this case mean of scores means the sum of scores received by skaters from eight judges divided by eight (judges).
=> 7.25 = (x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈)/8
=> x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈
= 8× 7.25
=> x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈
= 58
which is equation of 8 variables for total score. Therefore, the required equation is x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ = 58.
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18. En una tienda tienen la siguiente promoción por 1 día:
Gabriel necesita comprar un pantalón y una polera, pero al revisar estos en la tienda también miró calcetines y zapatillas. Escogió los siguientes productos:
Él piensa que si compra más productos aparte de la polera y el pantalón, podría pagar menos que si lleva solo la polera y el pantalón que necesita
According to the information, Gabriel should buy only the products he needs to spend less money.
How to calculate the option in which Gabriel would pay less?To calculate the option in which Gabriel would pay less, we must take into account the options that he has, first of all he has the option of buying only what he needs (pants and shirt). Second, he has the option to buy all the products to get a bigger discount.
If he buys only the pants and the shirt, he will have a 20% discount:
$10,000 + $20,000 = $30,000$30,000 / 100 = $300$300 * 20% = $6,000$30,000 - $6,000 = $24,000If you buy all four products you will have a 40% discount:
$10,000 + $20,000 + $30,000 + $1,000 = $61,000$61,000 / 100 = $610$610 * 40% = $24,400$61,000 - $24,400 = $36,600Based on the information, we can infer that if Gabriel buys all four products, he will get a greater discount of $24,400. However, if you do not want to spend so much money, it is better to only buy the two products you need because you will spend less money.
Note: This question is incomplete. Here is the complete information:
Attached image
Here is the question in English:
18. In a store they have the following promotion for 1 day:
Gabriel needs to buy pants and a shirt, but when checking these in the store he also looked at socks and sneakers. He chose the following products:
He thinks that if he buys more products besides the shirt and pants, he could pay less than if he only takes the shirt and pants he needs.
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Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round your answers to two decimal places.)a. 81stb. 19thc. 76thd. 24the. 10 th
The percentiles for the standard normal distribution
a. 0.93
b. -0.88
c. 0.67
d. -0.65
e. -1.28
To determine the percentiles for the standard normal distribution, use the standard normal distribution table. Percentiles for standard normal distribution are given by the standard normal distribution table.
The standard normal distribution is a special type of normal distribution with a mean of 0 and a variance of 1.
Step 1: Write down the given percentiles as a decimal and round to two decimal places.
For example, for the 81st percentile, 0.81 will be used.
Step 2: Use the standard normal distribution table to find the corresponding z-score.
Step 3: Round off the obtained answer to two decimal places.
a) 81st percentile:
The area to the left of the z-score is 0.81.
The corresponding z-score is 0.93.
Hence, the 81st percentile for the standard normal distribution is 0.93.
b) 19th percentile:
The area to the left of the z-score is 0.19.
The corresponding z-score is -0.88.
Hence, the 19th percentile for the standard normal distribution is -0.88.
c) 76th percentile:
The area to the left of the z-score is 0.76.
The corresponding z-score is 0.67.
Hence, the 76th percentile for the standard normal distribution is 0.67.
d) 24th percentile:
The area to the left of the z-score is 0.24.
The corresponding z-score is -0.65.
Hence, the 24th percentile for the standard normal distribution is -0.65.
e) 10th percentile:
The area to the left of the z-score is 0.10.
The corresponding z-score is -1.28.
Hence, the 10th percentile for the standard normal distribution is -1.28.
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triangle ABD is right angled at B. On AD, there is a point C for which AC=CD and AB=BC. find angle DAB
The measure of the angle DAB for the right angled triangle ABD is found as 45°.
Explain about the angle sum property of the right angled triangle?A right-angled triangle has two acute angles that add up to 90°. The smallest angle is the one that is opposite the smallest side, and the greatest angle is the one that is against the largest side.
In a triangle, the two angles that face the two equivalent sides are also equal. There can only be one right angle and one obtuse angle in a triangle.
For the question-
Triangle ABC is right angled at B.
D point makes: AC = CD
And , AB = BC
Since ∠ABD = 90, given C is mid point.
Then, It is altitude on AD and it bisects the angle ABD into 2 equal halves as: ∠ABC = ∠CBD = 45.
Now, For triangle ABC
∠ABC = 45
∠BCA = 90
Then,
∠BAC + ∠ABC + ∠BCA = 180
∠BAC + 45 + 90 = 180
∠BAC = 180 - 135
∠BAC = 45°
Thus, the measure of the angle DAB for the right angled triangle ABD is found as 45°.
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What is 6/11 as a decimal rounded to 3 decimal places?
Use Lagrange multipliers to find the point on the given plane that is closest to the following point. (Enter your answer as a fraction.)
x-y+z=3 (5,6,2)
To find the point on the given plane that is closest to the given point (5,6,2), we can use Lagrange multipliers.
Let f be the function that represents the plane x-y+z=3 and let g be the function that represents the point (5,6,2). Then, the point on the plane closest to (5,6,2) is the point that minimizes g=x2+y2+z2. We can use the method of Lagrange multipliers to solve this problem.
Let lambda be the Lagrange multiplier. Then, we need to solve the system of equations given by:
x2+y2+z2-2x-2y-2z=0x-y+z-3=0
By solving this system of equations, we obtain the point 13/14x=7/7y=11/7z=5/7, which is the closest point on the plane to the given point (5,6,2).
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PLEASE HELP I'LL GIVE THE BRAINLEST
Select the correct answer from each drop-down menu. The scatter plot shows the amount of water in a tank as measured every few minutes. The initial amount of water in tank was 0, 20, 100, or 120 gallons. The line of best fit shows that about 4/3, 3/4, 2/3, or 1/2 gallon(s) of water were lost per minute. The tank will be empty in about 0, 60, 80, or 90 minutes.
Given that the graph is falling downward, it can be seen that the graph is negative.
Before the tank's water level starts to drop, there are 120 gallons there.
Finding the slope of the graph will give us the amount of water that was lost every minute.
Slope is equal to a climb or a run.
increase = water in gallons
run equals time in minutes.
Slope equals y2 - y1 / x2 - x1
Two points will be chosen from the graph.
( 30, 80) and (60, 40) (60, 40)
Let x1=30, y1=80, x2=60, and y2=40.
Slope = 40 - 80 / 60 - 30
Slope = -40 / 30
Slope = -4/3
The result in the negative represents a loss in gallons of water per minute.
According to the line of best fit, a gallon of water was lost every minute or so.
The graph indicates that the tank will be empty in around 60 minutes.
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what is the messure or the vertex angle of an isosceles triangle if one of its base angle measures 16 degrees
Which of the following are the first four nonzero terms of the Maclaurin series for the function g defined by g (x) = (1+x)e-* ? A 1 + 2x + 3x2 + x3 + ... B 1+ 2x + 3 x2 + x3 + ... с 1-222 + x3 – 124 + ... D 1 - 3x2 + 3x3 – 6:24 + ...
Let x₁ and x₂ be two independent random variabIes, each with a mean of 10 and a variance of 5.y has a mean of 203 and a variance of 85.
What is function ?A function, in mathematics, is a reIationship between a set of possibIe inputs and an equaIIy IikeIy set of outputs, where each input is associated to exactIy one outcome. Functions are commonIy represented as equations or graphs, and they are used to modeI many reaI-worId processes in domains such as physics, engineering, and economics.
Function types incIude Iinear, quadratic, trigonometric, and exponentiaI functions, among others. CaIcuIus, a fieId of mathematics that investigates how quantities change over time or space, heaviIy reIies on functions.
given
The foIIowing is the MacIaurin series for the function g(x) = (1+x)e(-x):
g(x) = ∑[n=0 to ∞] ((-1)ⁿ*xⁿ) / n!
We may simpIify and pIug in the first few vaIues of n to determine the first four nonzero terms of this series:
n = 0: ((-1)⁰*x⁰) / 0! = 1
n = 1: ((-1)¹*x¹) / 1! = -x
n = 2: ((-1)²*x²) / 2! = x²/2
n = 3: ((-1)³*x³) / 3! = -x³/6
The MacIaurin series for g(x) therefore has the foIIowing first four nonzero terms:
1 - x + x²/2 - x³/6
Let x₁ and x₂ be two independent random variabIes, each with a mean of 10 and a variance of 5. y has a mean of 203 and a variance of 85.
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Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree.
The beam is 7.8 feet far away from the base of the house
How to determine how far away from the base of the house is the beam?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
It involves the use of trigonometric functions such as sine, cosine and tangent.
Using the attached image:
Let b represent the distance from the base of the house to the beam. We can say:
cos 71° = b/24 (adjacent/hypotenuse)
b = 24 * cos 71°
b = 7.8 feet
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y=x^2+7x-3
complete the square to re-write the quadratic function in vertex form.
pls help
Answer:
Y=x^2+7x-3
complete the square to re-write the quadratic function in vertex form.
pls help
Step-by-step explanation:
To complete the square, we need to add and subtract a constant term inside the parentheses, which when combined with the quadratic term will give us a perfect square trinomial.
y = x^2 + 7x - 3
y = (x^2 + 7x + ?) - ? - 3 (adding and subtracting the same constant)
y = (x^2 + 7x + (7/2)^2) - (7/2)^2 - 3 (the constant we need to add is half of the coefficient of the x-term squared)
y = (x + 7/2)^2 - 49/4 - 3
y = (x + 7/2)^2 - 61/4
So the quadratic function in vertex form is y = (x + 7/2)^2 - 61/4, which has a vertex at (-7/2, -61/4).
A cylindrical tank is one-fifth full of oil. The cylinder has a base radius of 80 cm. The height of the cylinder is 200 cm. 1 litre 1000 cm3 How many litres of oil are in the tank? Round your answer to the nearest litre
The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).
The volume of any cylinder can be calculated using the formula,
V = πr²h
(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)
As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:
Volume of oil = (1/5) x Total Volume
Substituting the given values, we have:
Total Volume = π(80cm)²(200cm) = 4,031,240 cm³
Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³
Converting cm³ to litres, we have:
1 litre = 1000 cm³
Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres
Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.
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In isosceles △ABC, points D and F are on leg CB while point E is on leg AB so that AC = AD = DE = EF = BF. Find the measures of the angles of △ABC. I WILL MARK BRAINLIEST PLEASE HELP FAST!!!!
The angles of △ABC can be determined by dividing 360 degrees by the number of congruent triangles. Therefore, each angle of △ABC measures 90 degrees as all the sides are congruent.
Since triangle ABC is isosceles, we know that angle BAC is equal to angle BCA. By drawing the perpendicular bisector of AC from point D, we can see that it intersects AC at its midpoint M. Therefore, we have AD = MC, and angle AMD is equal to angle CMD. Similarly, by drawing the perpendicular bisector of AC from point F, we have FC = CE, and angle CFE is equal to angle ECF. Since AD = DE and BF = EF, we have angle ADE = angle DEF and angle BEF = angle BFE. Therefore, we have four congruent triangles: △AMD, △BME, △ECF, and △FBC. Each of these triangles has angles that add up to 180 degrees, so we can find the measures of the angles of △ABC by dividing 360 degrees by the number of congruent triangles. Thus, each angle of △ABC measures 90 degrees.
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