Answer:
3.5467 × 10^-16
y varies indirectly as the square of x. if y=8 when x=4, find y when x=8
Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.
What is the value of y when x equal 8?
Indirect variation is expressed as;
y ∝ 1/x
Given that;
y ∝ 1/x²
y = k/x²
Where k is the proportionality constant.
Given that;
y₁ = 8x₁ = 4x₂ = 8y₂ = ?First, we determine the proportionality constant.
y = k/x²
8 = k/4²
8 = k/16
k = 128
Now, we find y when x = 8
y = k/x²
y = 128 / 8²
y = 128 / 64
y = 2
Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.
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The sum of the roots of the quadratic equation x^2 + 1=0 is equal to
Answer:
x² + 1 = 0
a = 1
b = 0
c = 1
[tex]x1.2 = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
[tex]x1.2 = \frac{ - 0 ±\sqrt{ {0}^{2} - (4.1.1) } }{2.1} [/tex]
[tex]x1.2 = \frac{0± \sqrt{0 - 4} }{2} [/tex]
[tex]x1.2 = \frac{± \sqrt{ - 4} }{2} [/tex]
There is no real solution because the discriminant is negative
Note.
Formula diskriminan
√b² - 4ac.
if the diskrimanan is negatif, so the quadratic equatoin dont have solution
A polynomial function g(x) has a positive leading coefficient. Certain values of g(x) are given in the following table. x –4 –1 0 1 5 8 12 g(x) 0 3 1 2 0 –3 0 If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)?
Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Considering the table, the roots are given as follows:
[tex]x_1 = -4, x_2 = 5, x_3 = 12[/tex]
Hence the function is:
f(x) = a(x + 4)(x - 5)(x - 12).
f(x) = a(x² - x - 20)(x - 12)
f(x) = a(x³ - 13x² - 32x + 240).
When x = 0, y = 1, hence the leading coefficient is found as follows:
240a = 1
a = 0.004167
Then:
f(x) = 0.004167(x³ - 13x² - 32x + 240).
The end behavior is given by the limits of f(x) as x goes to infinity, hence:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 0.004167 x^3 = -\infty[/tex].[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 0.004167 x^3 = \infty[/tex].Hence the end behavior is that the function decreases to the left and increases to the right.
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Women appear to marry about 3 years younger than men, but the two distributions are very similar in shape and spread.
The brief report about what the attached data in the box plot shows that: "Women appear to marry around three years younger than males, although the shape and dispersion of the two distributions are extremely comparable."
What is a box plot?A boxplot is a type of graph that shows how the values in the data are distributed.
A boxplot is a standardized technique of representing data distribution based on a five-number summary ("minimum", first quartile (Q1), median, third quartile (Q3), and "maximum").
It can provide information about your outliers and their values.
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Full Question:
In 1975, did men and women marry at the same age? Here are boxplots of the age at first marriage for a sample of U.S. citizens then. Write a brief report discussing what these data show.
The sum of three numbers is 24. If two numbers are 16 and 22, what is the third?
Answer:
X=-14
Step-by-step explanation:
16+22+x=24
38+x=24
x=24-38
x=-14
Complete this activity.
If the first element of the following pairs of numbers is a measure of hours and the second element is a measure of distance in miles, write an equation for D.
B = {(t, D ): (1, 50), (2, 100), (3, 150), . . .}
D =
t /2
50 t
50/ t
Answer:
D = 50t
Step-by-step explanation:
we see, with every additional hour the distance increases by 50.
that means in general that the number of hours are multiplied by 50 to get the distance.
in other words, this just calculates for a vehicle going constantly 50 miles per hour the distance it is traveling.
Can someone answer this for me
The linear equation graphed is given by:
y - 5 = 3(x - 1).
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In point-slope form, considering a point [tex](x_0, y_0)[/tex], the equation is:
[tex]y - y_0 = m(x - x_0)[/tex]
The line goes through points (0,2) and (1,5), hence the slope is:
m = (5 - 2)/(1 - 0) = 3.
Since the line goes through point (1,5), the equation is:
y - 5 = 3(x - 1).
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i) Baraka bought ksh.20,000 worth of shares of a company each month. During the first three months, he bought the shares at a price of ksh.120, ksh.160 and ksh.210.Compute the average price paid by him for the shares after 3 months
The average price paid by him for the shares after 3 months is ksh. 163.33
AverageTotal value of shares bought = ksh.20,000Amount of shares bought in the first three months = ksh.120, ksh.160 and ksh.210Average price paid for the shares after 3 months
= (120 + 160 + 210) / 3
= 490 / 3
= 163.333333333333
Approximately,
ksh. 163.33
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Which equation represents the vertical line passing through (5,-4)?
Answer:
x = 5
Step-by-step explanation:
Since the line is vertical,
the equation of the line then is x = (some value).
Since this particular line passes throught (5,-4), where the x coordinate is 5, we can deduce the equation of this line to be x = 5.
Help would really be needed asap!
Answer:
C
Step-by-step explanation:
For lines AC and EF, line FC is a transversal.
Angles ACF and EFC are same side interior angles.
Since their measures add to 180°, then the lines are parallel.
Answer: Choice C
If 2y=x³ + 2x², find dy/dx when x=2.
Answer:
10
Step-by-step explanation:
[tex]\boxed{\textsf{If }y=x^n,\: \textsf{then }\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}}[/tex]
Given equation:
[tex]2y=x^3+2x^2[/tex]
Isolate y by dividing both sides by 2:
[tex]\implies y=\dfrac{1}{2}x^3+x^2[/tex]
Differentiate with respect to x:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{2}x^{3-1}+2 \cdot x^{2-1}[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{3}{2}x^2+2x[/tex]
Finally, substitute x = 2 into the differentiated equation:
[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{3}{2}(2)^2+2(2)\\\\ & = \dfrac{3}{2}(4)+4\\\\ & = \dfrac{12}{2}+4\\\\ & = 6+4\\\\ & = 10\end{aligned}[/tex]
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Find the value of x. (5x-40) (5x)
the first equation is inside the triangle at the bottom left but "5x" is at the bottom right on the outside of the triangle.
The value of x is 22
How to solve for x?Based on the description in the question,
The angles 5x -40 and 5x are angles on a straight line
So, we have:
5x - 40 + 5x = 180
Evaluate the like terms
10x = 220
Divide by 10
x = 22
Hence, the value of x is 22
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Information about a play took up 1/3 of the pages in the program. Information about the actors took up 1/4 of the remaining pages. Information about the director, the producer, and the designer took up 2 pages, the same number of pages devoted to the actors. How many pages were there in the program?
Answer:
Step-by-step explanation:
Comment
Let the number of pages = x
Play = 1/3x
Actors = 1/4(x - 1/3 x)
Actors = 1/4(2/3x)
Actors = 2/12 x
Producer Director etc = 2 pages
Equation
Actors = 2 pages
2/12 x = 2
Solution
2x/12 = 2 Multiply both sides by 12
12*2x/12 = 2*12 Combine
2x = 24 Divide by 2
2x/2 = 24/2 Combine
x = 12
Answer
The program had 12 pages.
When
a number is
Substracted from 2, the
result equal 4 less
than one-fifth
the
of
number. Find the number
An employer provides two payment options for employees. Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks. Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks. (Score for Question 1: ___ of 2 points)
Based on the information, it can be inferred that payment option A means a payment of $450, while option B means a payment of $300.
How much money does each payment option receive?The payment options contemplated by the employer are distributed as follows:
Option A
First week: $200Second week: $200 + $50 = $250Third week: $250 + $50 = $300Fourth week: $300 + $50 = $350Fifth week: $350 + $50 = $400Sixth week: $400 + $50 = $450Option B
First week: $200Second week: $220Third week: $240Fourth week: $260Fifth week: $280Sixth week: $300Note: This question is incomplete because there is some information missing. Here is the missing information:
Complete the tables to show how much money would be received for both payment options, each week, for 6 weeks.
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I don’t have an answer but by any chance did you complete the assignment?
How many kilometers are equal to 750 meters?
Answer:
[tex]0.75[/tex]
Step-by-step explanation:
750metres÷1000
The diagonals of a rectangle enclose an angle of measure 78 degree
. If the perimeter of the rectangle is 36cm, what is its area?
the area of the rectangle is 80. 1 cm²
What is the area of a rectangle?
From the given information, let's say one side of rectangle = a
The other side = (36 - 2a)/2
= 18 - a cm
The angles between the diagonals of the rectangle is 78°
Then, the angle diagonal has with base will give
= (180° - 78°)/2
= 102/2
= 51°
We have the angle to be 51 degrees, using the tan ratio
Tan θ = opposite/ adjacent
Opposite of angle 51 degrees = a
Adjacent = 18 - a
Thus,
[tex]tan 51 = \frac{a}{18 - a}[/tex]
[tex]1. 2349 = \frac{a}{18-a }[/tex]
cross multiply
[tex]18 -a ( 1. 2349) = a[/tex]
[tex]22. 23 - 1. 2349a = a[/tex]
collect like terms
[tex]a + 1. 2349a = 22. 23[/tex]
[tex]2. 2349 a = 22. 23[/tex]
[tex]a = \frac{22. 23}{2. 2349}[/tex]
a = 9. 95
If a = 9. 95cm
Then, 18 - a = 18 - 9. 95 = 8. 05cm
The formula of area of a rectangle is given as;
Area = width × length
Area = 9.95 x 8.05
Area = 80. 1 cm²
Thus, the area of the rectangle is 80. 1 cm²
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Identify the correct trigonometry formula to solve for x
The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Hence:
sin(62°) = 18 / x
The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x
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The stemplot below represents the number of bite-size snacks grabbed by 10 students in an activity for a statistics class. A stemplot titled number of snacks. The stems are 1, 2, 3, 4. The first column of leaves is 5, 0, 2, 2. Column 2 is 6, 1, blank, blank, Column 3 is 6, 3, blank, blank. Column 4 is 7, blank, blank, blank, Column 5 is 9, blank, blank, blank. Key 2 slash 4 is a student who grabbed 24 snacks. What is the correct set of data for the stemplot? 15, 16, 17, 19, 20, 21, 23, 32, 42 15, 16, 16, 17, 19, 21, 23, 32, 42 15, 16, 16, 17, 19, 20, 21, 23, 32, 42 15, 15, 16, 17, 19, 20, 21, 23, 32, 42
The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.
According to the question
Using the key: 2|4 = 24, the following are the set of data represented by the stem-and-leaf plot showing:
Row one, 1| 5 6 6 7 9 :
This means there are 5 data set for the first row which are:
15, 16, 16, 17, 19
Row two, 2|0 1 3 :
There are 3 data here, which are:
20, 21, 23
Row 3, 3|2: = 32
Row 4, 4|2: = 42
So, The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.
Correct option is C.
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Find parametrization for the tangent line at time t0=13.
Use the equation of the tangent line such that the point of tangency occurs when t=t0 .
(Write your solution using the form (*,*,*). Use t for the parameter that takes all real values. Simplify all trigonometric expressions by evaluating them. Express numbers in exact form. Use symbolic notation and fractions as needed.)
Where will this line intersect the - plane?
(Write your solution using the form (*,*,*). Express numbers in exact form. Use symbolic notation and fractions where needed.)
The parametrization for the tangent line at time [tex]t_{0}[/tex] is (41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)
The point of intersection is (40, -4, 0)
What is the parametrization for the tangent line at time [tex]t_{0}[/tex] and point of intersection?The given curve is defined parametrically by the equations
x = 3t + 2
y = 4 cos t
z = 4 sin t
To find the parametrization for the tangent line at time t0 = 13, we need to find the point of tangency and the direction vector of the tangent line.
The point of tangency is the position of the curve at time t0, which is
(3 * 13 + 2, 4 cos 13, 4 sin 13) = (41, -4/3, 4/3)
The direction vector of the tangent line is the derivative of the curve at time t0, which is
(3, -4 sin 13, 4 cos 13) = (3, -4/3, 4/3)
Therefore, the parametrization for the tangent line is
(41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)
b. To find the point where this line intersects the -plane, we set z = 0 and solve for t. This gives us
4/3 + 4t/3 = 0
t = -1/2
Therefore, the point of intersection is
(41 - 3/2, -2, 0) = (40, -4, 0).
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use geometric shapes to create a logo that will fit in a measuring 15 cm by 15 cm
A geometric shapes that can be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.
What are geometric shapes?It should be noted that geometric shapes are the figure of area that is closed by a boundary.
In this case, a geometric shapes that. an be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.
This is because all the sides in a square are equal.
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Use the equation and type the ordered-pairs. y=3^x
The ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)
How to type the ordered pairs?The equation is given as:
y = 3^x
Let x = 0, 1 and 2
y = 3^0 = 1
y = 3^1 = 3
y = 3^2 = 9
So, we have the following ordered pairs (0,1), (1,3) and (2,9)
Hence, the ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)
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Given f (x) = x2 + 4x + 5, what is f of the quantity 2 plus h end quantity minus f of 2 all over h equal to?
h2 + 8h
2x + h + 4
8 + h
h + 4
By evaluating the quadratic function, we will see that the differential quotient is:
[tex]\frac{f(2 + h) - f(2)}{h} = 8 + h[/tex]
How to get (f(2 + h) - f(2))/h?Here we have the quadratic function:
[tex]f(x) = x^2 + 4x + 5[/tex]
Evaluating the quadratic equation we get:
[tex]\frac{f(2 + h) - f(2)}{h}[/tex]
So we need to replace the x-variable by "2 + h" and "2" respectively.
Replacing the function in the differential quotient:
[tex]\frac{(2 + h)^2 + 4*(2 + h) + 5 - (2)^2 - 4*2 - 5}{h} \\\\\frac{4 + 2*2h + h^2 + 8 + 4h - 4 - 8 }{h} \\\\\frac{ 2*2h + h^2 + 4h }{h} = \frac{8h + h^2}{h}[/tex]
If we simplify that last fraction, we get:
[tex]\frac{8h + h^2}{h} = 8 + h[/tex]
The third option is the correct one, the differential quotient is equal to 8 + 4.
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On a recent trip to the convenience store, you picked up 3 gallons of milk, 6 bottles of water, and 6 snack-size bags of chips. Your total bill (before tax) was $29.10. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.70 more than a bottle of water, how much does each item cost?
Hi
the trick is to define price by referring only to one item.
Here the bootle of water is you reference.
there is 3 gallons of milk
6 bottles of water
6 bags of chips
let's call bottle of water " X"
water cost = X
milk = X+1.7
chips = X/2
So we have :
3 (X+1.7 ) + 6X + 6 ( X/2) = 29.1
3X+ 5.1 + 6X + 6X/2 = 29.1
3X +6X + 3X + 5.1 = 29.1
12X +5.1 = 29.1
12X = 29.1 - 5.1
12 X = 24
X = 24/12
X = 2
price of bottle is 2 dollars
then milk is 2 + 1.7 = 3.7
chips = 2/2 = 1
let's check = 3*3.7 + 6*2 + 6*1 = 11.1+12+ 6 = 29.1
Convert 45 32’ 55” into decimal degrees to the nearest two decimal places
The decimal equivalent of 45⁰ 32’ 55” is 45.55⁰
Converting degrees into decimalThe given degree is:
45⁰ 32' 55''
This can be converted to decimal as shown below
[tex]45+\frac{32}{60} +\frac{55}{3600}[/tex]
This can be simplified further as:
[tex]45^o32'55'' = 45+0.53+0.0153\\\\45^o32'55'' = 45.55^0[/tex]
Therefore, the decimal equivalent of 45⁰ 32’ 55” is 45.55⁰
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Find the ratio of 700m to 2 km
Answer:
7 : 20
Step-by-step explanation:
2km = 2000m
Then the ratio of 700m to 2 km is :
700 / 2000
Then the ratio in simplest form is :
7 / 20
a mother is 25 years older than her son.
Write down the son's age and the mother's age
Answer:
mother age 37
sons age 12
I don’t know the answer for question number 1
The area of QOR from the given diagram is 2π square centimeters
How to calculate the area of a sectorA sector is said to be a part of a circle made of the arc of the circle along with its two radii.
The formula for calculating the area of a sector is expressed as;
A = r²β/2
where
r is the radius of the circle
β is the angle subtended
Given the following parameters
<QOR = 180 - <POQ
<QOR = 180 - 135
<QOR = 45 degrees
Determine the radius
L = rβ
π = r(π/4)
1 = r/4
r = 4
Determine the area of QOR
Area = 4²(π)/8
Area = 2π
Hence the area of QOR from the given diagram is 2π square centimeters
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What is the angle for x
Answer:
X = 90°Step-by-step explanation:
that is a regular rhombus, by definition it has perpendicular diagonals, so in the center there are 4 90 ° angles, so your answer is x = 90 °
Write the expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression.
csc ß- sin ß
Choose the correct answer below.
OA. 1
B. cos ßcot B
OC. sin²B
OD. 1-sin² B
OE. sin² ßtan² ß
OF. cos B
...
Using trigonometric identities, the simplified expression, without quotients, is given as follows:
A. [tex]\cos{\beta}\cot{\beta}[/tex]
Which trigonometric identities are used to solve this question?The cosecant of an angle is given by one divided by the sine of the angle, hence:
[tex]\csc{\beta} = \frac{1}{\sin{\beta}}[/tex]
The sine and the cosine of an angle are related as follows:
[tex]\sin^2{\beta} + \cos^2{\beta} = 1[/tex]
[tex]\cos^2{\beta} = 1 - \sin^2{\beta}[/tex]
The cotangent of an angle is:
[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}[/tex]
Which is the simplified expression?The expression given is:
[tex]\csc{\beta} - \sin{\beta}[/tex]
Simplifying the cosecant:
[tex]\csc{\beta} - \sin{\beta} = \frac{1}{\sin{\beta}} - \sin{\beta} = \frac{1 - \sin^{2}\beta}{\sin{beta}}[/tex]
Then, applying the last two identities in the subsection above to remove the quotient, the simplified expression will be found as follows:
[tex]\frac{1 - \sin^{2}\beta}{\sin{beta}} = \frac{\cos^2{\beta}}{\sin{\beta}} = \frac{\cos{\beta}}{\sin{\beta}} \times \cos{\beta} = \cos{\beta}\cot{\beta}[/tex]
Hence option A is correct.
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