On solving the provided question, we can say that - the percentage value of 12 % of 90 = 10.8
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
12% of 90 = 12/100 X 90
= 0.12 X 90 = 10.8
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find the values of the variable in the following, giving brief reasons:
Therefore , as a result, we may state that the stated trapezoid angles x = 110°, which is the solution to the problem.
Explain the trapezoid.A trapezoid is a quadrilateral that has at least one connected pair of sides. It has the name trapezium. By definition, a trapezoid in Euclidean geometry is a convex quadrilateral. The trapezoid's base is made up of its parallel sides. A closed, flat shape having two neighboring sides and four successive sides is called a trapezoid. The parallel walls and base of the trapezoid are commonly referred as as the parallel sides and the legs, respectively.
Here,
Given : 110°
and 90°
To find the value of x ,
Thus,
The value of angle opposite to x :
=> 110° + y =180°
=>y =180°-110°
=>y = 70°
thus, x value is
=> x + 70° =180°
=> x =110°
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Factor the expression using the GCF.
50+65h=
Greatest common factor (GCF) of 50 and 65 is 5.
How to find the GCF of 50 and 65?We will first find the prime factorization of 50 and 65. After we will calculate the factors of 50 and 65 and find the biggest common factor number .
Step-1: Prime Factorization of 50
Prime factors of 50 are 2, 5. Prime factorization of 50 in exponential form is:
50 = 21 × 52
Step-2: Prime Factorization of 65
Prime factors of 65 are 5, 13. Prime factorization of 65 in exponential form is:
65 = 51 × 131
Step-3: Factors of 50
1, 2, 5, 10, 25
Final Step: Biggest Common Factor Number
We found the factors and prime factorization of 50 and 65. The biggest common factor number is the GCF number.
So the greatest common factor 50 and 65 is 5.
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A bag contains 27 balls. The ratio of red to blue to yellow balls is 6:1:2 find how many red, blue and yellow balls there are
Answer:
18 red balls, 3 blue balls, 6 yellow balls.
Step-by-step explanation:
Ratios:a ratio helps us understand the relationship between two or more values (in this case three values). More specifically it tells us how much of one item is present, for every amount another item is also present.
In this example, the ratio of red:blue:yellow is given to be: 6:1:2, which means, for every 6 red balls, there is one blue ball and two yellow balls.
In some cases, a ratio can be simplified, similar to a fraction, by dividing each number by some common factor, but in this case, the ratio cannot be simplified any further.
Solving the Problem:Instead of directly trying to find how many red, yellow, or blue balls there are first, we can instead try solving for how many group of sixes are there in the total number of red balls. It helps to think of it this way, since for every group of six red balls there are, there is one blue ball and two yellow balls, which means we can just multiply this number by one and two to find the number of blue and yellow balls in their respective orders. For simplicity, let's assign this to the unknown "G".
Using this logic, we can set up the following equation:
[tex]6G+1G+2G=27[/tex]
For every group of six red balls... there is 6 red balls, 1 blue ball, and 2 yellow balls, adding all these together should give us the total number of balls, which was given to be 27 balls. Now we can just combine the stuff on the left into one term, by adding the coefficients.
[tex]9G=27[/tex]
Now divide by 9
[tex]G=3[/tex]
Now that we know the number of group of six red balls there are, we can multiply six, one, and two to find the red, blue, and yellow balls.
[tex]\text{red balls} = 3 * 6 = 18\\\\\text{blue balls} = 3 * 1 = 3\\\\\text{yellow balls} = 3 * 2 = 6[/tex]
and you can all this together, to double check, which gives us 27.
Answer:
18,3,6
Step-by-step explanation:
Given ,
A bag contains 27 ballsThe ratio of red to blue to yellow balls is 6:1:2To Find : The number of red,blue and yellow balls present in the bag
Let us take the variable as 'x' to represent the number of balls in the bag
When we Put the values in a equation,
6x+x+2x = 27
9x = 27
x = [tex]\frac{27}{9}[/tex]
x = 3
Hence the number of,
Red Balls = 6x = 6 x 3 = 18
Blue Balls = x = 3
Yellow Balls = 2x = 2 x 3 = 6
In a equation is it true that when a variable is alone you have to add a number 1 to it?
I’m wondering since I have to add it to my notes.
Consider the composite function g(f(x)) =x√6.
If f(x) = 3x², what is g(x)?
O g(x)=√2x
Og(x)=√x+3
Og(x)=√6x
O g(x)=√9-x
So on solving the provided question, we can say that the function g(x) is equal to g(x) = [tex]\sqrt{2x}[/tex]
A composite function is what?The mathematical procedure known as "function composition" takes two functions, f and g, and creates a function, h = g f, such that h(x) = g. This process involves applying the function g to the outcome of applying the function f to x. When the result of one function is utilized as the input for another, this is known as a composite function. The function f g (x) fg(x) fg(x) fg(x), also known as "f of g of x" or "f g fg fg of x," is the composition of the two functions if we have a function f and another function g.
f(f(x)) = [tex]\frac{x}{\sqrt{6} }[/tex]
f(x) = 3x^2
g(f(x)) = [tex]\frac{3x^2}{\sqrt{6} }[/tex]
g(x) = [tex]\sqrt{2x}[/tex]
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On Saturday, a local hamburger shop sold a combined total of 396 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Let x be the number of hamburgers sold, then the number of cheeseburgers sold can be represented as 2x. The total number of hamburgers and cheeseburgers sold is the sum of these two quantities, so we can write an equation:
x + 2x = 396
To solve for x, we can combine like terms on the left side of the equation:
3x = 396
Then we can divide both sides by 3 to get:
x = 132
So, the number of hamburgers sold on Saturday is 132.
Please help I was sick and missed out on class thank you.
On solving the value of provided question we can say that - the value of the slope intercept y = -3.
what is slope intercept?The point on the y-axis where the slope of the line passes is known as the intersection point in mathematics. the location on a line or curve where the y-axis crosses that point. This is demonstrated by putting y = mx+c as the equation for the straight line, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the slope (m) and y-intercept (b) of the line are highlighted. The slope is m, and the y-intercept is b for equations in the intercept form (y=mx+b). Additionally, certain equations may be recast to seem like slope intercepts. For instance, if y=x is rewritten as y=1x+0, the slope becomes 1 and the y-intercept becomes 0.
as we can see from graph that,
line passes through origin, so x= 0
the, y = -5x - 3
y = -3
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A maple tree grows 1.5 feet each year. The table shows the yearly growth for a pibe tree
Comparing the maple tree and the pine tree growth information, the tree that grows faster is the pine tree.
How to find the tree that grow fasterA mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so on.
Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of 3 main parts
a = the starting or initial value
b = the base function
x = the exponents
Considering the given problem, b for maple is given as 1.5 and we calculate for pine using the data in the table. the equation is derived as follows
f(x) = a(b)ˣ
12 = a(b)¹
24 = a(b)²
dividing 24 = a(b)² by 12 = a(b)¹
b = 2
hence for pine tree the b is 2 which is greater than 1.5
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Complete the two-way frequency table below, which shows the relationship between students who enroll in advanced algebra and physics in a particular high school. From a sample of 40 students, it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both. How many students are enrolled in either algebra or physics?
Algebra Not in Algebra Total
Physics 5 9 14
Not in Physics 24 2 26
Total 29 11 40
it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both using principle of inclusion-exclusion we can say 38 students are enrolled in either algebra or physics.
How to find the number of students enrolled in either algebra or physics?To find how many students are enrolled in either algebra or physics, you can use the principle of inclusion-exclusion, which states that the total number of elements in two sets can be found by adding the number of elements in each set and then subtracting the number of elements that are in both sets.
So, the number of students enrolled in either algebra or physics is:
29 (students enrolled in algebra) + 14 (students enrolled in physics) - 5 (students enrolled in both) = 38
So, 38 students are enrolled in either algebra or physics.
It is important to notice that in the table you provided is a two-way frequency table also known as a contingency table, it shows the relationship between two variables, in this case, Algebra and Physics and the frequencies of each combination.
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-50 POINTS- if you guess you’ll be reported.
If P=(4,7) Find D2 (P)
You will be reported if you guess. The result is -1 if P=(4,7)on D2 (P). Consequently, P=(4,7) in D2 reports -1. (P).
What is the value of D2 (P)?Given p= (4,7)
The answer to 4 p+7 is 4(-2)+7=-8+7=-1
The value of the denominator (d2), a weighting factor, is depends on the control chart's subgroup size, n. Based on a subgroup size of 5, the value of d2 in the case is 2.326. Following is a brief list of the d2 values for other subgroup sizes.
The table of constants below contains the d2 value, which is determined by the subgroup size. The average moving range, or MR-bar, will be used if your subgroup size is one. Model No. The average range is 0.220, and the mean is 0.8057 (X-bar). The D2 function gives the sample range of n independent, normally distributed random variables with the same mean and a standard deviation of 1 the anticipated value.
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triangle has area 16 m ^2
. List all the possible positive integers that could
represent the lengths of its base and height.
Therefore , the solution of the given problem of triangle comes out to be base=4m,16 and height=8m,2m.
Defining a triangleIn a plane, any three points can be joined to form triangles, which have three sides and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.
Here,
Given :
Triangle area = 16[tex]m^{2}[/tex]
Thus,
To find the possible base and height of the triangle.
The base can be given by 4 m,16
and height be = 8m or 2m
vice-versa
height = 4m ,16mand base =8m,2m
Therefore , the solution of the given problem of triangle comes out to be base=4m,16 and height=8m,2m.
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Answer:
see below
Step-by-step explanation:
given that the area of the triangle is 16m² . We need to list all the possible lengths of its base and height. As we know that, the area of triangle is ,
ar(∆) = 1/2 * base* height
substitute the respective values,
16m² = 1/2* b * h
b*h = 32
now here we need to list out all the possible factors of 32 as ,
1 *32
2 *16
4*8
8*4
16 *2
32*1
therefore, all the possible lengths of heights and bases are ,
b = 1m , h = 32m b = 2m , h = 16mb = 4m , h = 8mb = 8m , h = 4mb = 16m , h = 2mb = 32m , h = 1mand we are done!
-Rishabh
Draw the following figure in your note book and find the perimeter or circumference show your solution.
1.) Triangle : s = 6cm ; P=
2.) Square : s = 7 cm ; P =
3.) Rectangle = W = 4cm , L = 8 cm ; P =
4.) Regular Heptagon : s = 3cm ; P =
5.) Circle : r = 12cm ; C =
1)Triangle : s = 6cm ; P= 18 cm
2.) Square : s = 7 cm ; P = 28 cm
3.) Rectangle = W = 4cm , L = 8 cm ; P = 24cm
4.) Regular Heptagon : s = 3cm ; P = 21 cm
5.) Circle : r = 12cm ; C = 24∏ cm.
What is circumference?
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.
Given that the length of each side of a triangle is 6 cm.
The perimeter of an equilateral triangle is 3a, where a is the length of the side of the equilateral triangle.
The perimeter of the triangle is 3 × 6 = 18 cm
The length of side of a square is 7 cm.
The perimeter of a square is 4a, where a is the length of the side of the square.
The perimeter of the square is 4 × 7 = 28 cm.
The length and breadth of a rectangle is W = 4 cm and L = 8 cm.
The perimeter of a rectangle is 2(L+ W)
The perimeter of the rectangle is = 2(8 + 4) = 2 × 12 =24 cm
The perimeter of Regular Heptagon is 7a, where a is the length of the side of the Regular Heptagon.
The perimeter of a Regular Heptagon is (7 × 3) = 21 cm
The perimeter of a circle with a radius r is 2∏r.
The perimeter of the circle is 2∏ × 12 = 24∏ cm.
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Which TWO scenarios can be represented by a ratio of 4 : 5?
I NEED AN ANSWER ASAP PLEASE
The two scenarios that can be represented by a ratio 4:5 are
1. The ratio of fiction books to the non fiction books, if there are 4 fiction books to 5 non fiction books
2. The ratio of marker to crayon , if there are 4 markers and 5 crayons. ( option A and D)
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
For a scenario that will give ratio of 4:5, it means the first entity will be 4 and the second entity will be 5.
Therefore the two statements that obey this in the option are
1. The ratio of fiction books to the non fiction books, if there are 4 fiction books to 5 non fiction books
2. The ratio of marker to crayon , if there are 4 markers and 5 crayons.
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What is the value of the expression below when x=2x=2?
8x^2 +6x-8
8x
2
+6x−8
The value of the expression 8x² + 6x - 8 below when x=2 is 36.
The value of the expression when x = 2The expression can be evaluated by following the steps below:
8x² + 6x - 8 in x = 2 means that the variable x will be replaced by the given number which is 2.
8*2² + 6*2 - 8
8*4 + 12 - 8
32 + 16 - 8 = 36
This therefore means that when x= 2 in 8x² + 6x - 8 , the value gotten will be 36.
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The equations that are true for x = –2 and x = 2 are:
x^2-4=0 and 4x^2 = 16
How can the equation be known?We can determine the equations that are true for x = –2 and x = 2 by testing the given options:
After testing the options option 1 ; x^2-4=0 putting x = 2 or -2 into the equation will give zero.
(2^)2-4=0
(-2)^2-4=0
Then option 4: 4x^2 = 16
4(2)^2 = 16
4(-2)^2 = 16
Therefore, option 1st and 4th are correct.
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X+X+X+Y+Y=
im doing algebra and cant understand the above question
Answer:
3x + 2y
Step-by-step explanation:
X+X+X+Y+Y=
you simply count equal letters and add them x+x+x is 3x and y + y = 2y.
x + x + x + y + y =
3x + 2y
not knowing the value of x or y we stop hereA raffle for 4 prizes is taking place. each person had to purchase a ticket to enter the raffle. If Lebron bought 4 tickets, Kobe 6 tickets, Jordan 7 and Diana Taurasi 7.
Round answer to the nearest thousandths (3 decimal places)
A). If the ticket gets put back into the raffle after each selections, what is the probability that Kobe wins the first prize and Dianna wins the second?
B) If each ticket can only be used once what is the probability that Kenton win first two prizes
C) What is the probability that Oberon wins first prize, Kobe the second, Jordan the 3rd and Diana the 4th, without replacement?
Raffles are chance-based contests in which participants compete to win exciting prizes.
How does a raffle work?To participate, all you need is a ticket with a number on it. Following the sale of all tickets, a drawing is conducted during which a random selection of tickets is made. If you chance to have the winning ticket, congratulations! a lot of engagement.
Raffles elicit a great deal of interest and support because people enjoy playing games of chance, especially when they have the possibility to win a significant prize.
high income. Your organisation has a strong possibility of making some big money from ticket sales if engagement is high!
low price. A virtual free raffle can be found online! A virtual raffle is the most cost-effective type of fundraising because you won't need to print actual tickets, reserve a location for the drawing, or buy refreshments.
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Ms. Lopez goal is to run 25 miles this week.
She runs 3 miles on Tuesday and 4 miles on Wednesday.
What percent of her goal has she accomplished?
Answer: 28%
Step-by-step explanation: First, we need to find how much she runs in total on Tuesday and Wednesday. So, we add 3 + 4 to get 7. With that, we need to determine how much 7 is from 25. So, it'd look like this:
7 * 100 / 25
700 / 25
=28
Therefore, she's done 28% of her goal (within the 2 days) I hope this helped!
Answer:
I think the other person who answered the question is right
Step-by-step explanation:
help with explanation if possible
Answer: 448
Step-by-step explanation: Parallelogram formula base times height
Simplify 3.5m(3m + 1.8) using the distributive property.
10.5m + 6.3m
10.5m + 1.8
10.5m2 + 6.3m
10.5m2 + 1.8
Answer:
3.5m(3m + 1.8)
10.5m^2+6.3m
Step-by-step explanation:
A concave lear of focal length of 20cm forms an image 1/2 the size of the object .The object distance?
Answer:
60cm
Step-by-step explanation:
given:
focal length (f) = 20cm
image height (v) = ½u
object height (u) = ?
(1÷v) + (1÷u) = (1÷20)
(1÷(½u)) + (1÷u) = (1÷20)
(2÷u) + (1÷u) = (1÷20)
(3÷u) = (1÷20)
u = 20 × 3
u = 60cm
The amount Y (in dollars) Of money in your savings account after X months is represented by the equation Y equals 12.5 X +100 a. graph the linear equation b. how many months will it take for you to save a total of $237.50[QUICK ITS HOMEWORK AND ITS LATE]
The graph of the linear equation is attached below. After 11 months, the total savings will be $237.50.
What is a saving account?
An account in a retail bank is a savings account. Common characteristics include having a finite number of withdrawals allowed, not having check or connected debit card facilities, having few transfer choices, and not being able to become overdrawn.
Given equation is
y = 12.5x + 100
To find points on the linear equation, putting x = 0, 1 and 2 in the given equation:
y(0) = (12.5 × 0) + 100
y(0) = 100
y(1) = (12.5 × (1)) + 100
y(1) = 12.5 + 100
y(1) = 112.5
y(2) = (12.5 × 2) + 100
y(2) = 25 + 100
y(2) = 125.
The points on the linear equation are (0,100), (1, 112.5), (2,125).
Plot the points and join the points to draw the line to get graph the linear equation.
Putting y = 237.50 in the given equation y = 12.5x + 100:
237.50 = 12.5x + 100
Subtract 100 from both sides:
237.50 - 100 = 12.5x + 100 - 100
137.50 = 12.5x
Divide both sides by 12.5:
x = 137.50/12.5
x = 11
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Zachary purchased a computer for $1,800 on a payment plan. Three months after he purchased the computer, his balance was 1,350. Five months after he purchased the computer , his balance was 1,050. What is an equation that models the balance B after m Months
Answer: y = -150x + 1800
Step-by-step explanation:
1. Find the linear slope of the line between two points.
(Change in Y)/(Change in X)
2. Write out an equation in point slope form.
(y-y1) = m(x-x1)
y-1800 = -150(x-0)
3. Simplify the equation and turn it into slope-intercept form.
y = -150x + 1800
For the equation f(x)=1.9(0.41)*, state the initial value C, the growth or decay factor a, and percent change R for each unit increase in x.
C=(Type an integer or a decimal.)
Initial value C is 1.9, Decay factor =0.41 and Growth factor = 0.59 when the function f(x)=1.9(0.41)ˣ.
Given that,
The equation f(x)=1.9(0.41)ˣ.
We have to state the initial value C, the growth or decay factor a, and percent change R for each unit increase in x.
We know that,
What is growth and decay?In order to translate their graphs over the 2D coordinate plane, I will offer the vertex form of an exponential equation for both the growth and decay functions.
In the case of growth, f(x) = a(1+r[tex])^{x-h}[/tex]+k, where b = 1+r
Decay is defined as f(x)=a(1-r)(x-h[tex])^{x-h}[/tex]+k, where b=1-r.
Consider the function f(x)=1.9(0.41)ˣ.
We write as
f(x)=1.9(1-0.59)ˣ
So, initial value C is 1.9
Decay factor =0.41
Growth factor = 0.59
Therefore, Initial value C is 1.9, Decay factor =0.41 and Growth factor = 0.59 when the function f(x)=1.9(0.41)ˣ.
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x³ - 10x = 100
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.
Equation : what is it?An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.
Here,
the formula is written as x3 -10x = 100.
We continue testing for the value of x that is valid for x3 -10x = 100 via trial and error.
We've made multiple tries and have:
x = 5.4 (roughly) (approximately)
In x3 -10x = 100, replace x with 5.4.
5.4^3 -10 * 5.4 = 100
Evaluate
103.5 = 100
Approximate
100 = 100
Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.
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Write and solve a system of equations for each of the following problems. You must write two questions for each problem, thank you
1. Ella is a landscape photographer. She sells small prints for $50 each, and large prints for $75
each. One weekend she sold a total of 52 prints for a total of $2975. How many of each size print did
Ella sell?
2. At a hot air balloon festival, Georges's balloon is at an altitude of 40 meters and rises at a rate of
10 meters per minute. William's balloon is at an altitude of 165 meters and descends at a rate of 15
meters per minute. In how many minutes will both balloons be at the same altitude? What is that
altitude?
The system of equations that satisfy the given problems is x + y = 52 and 50x + 75y = 2975, and the value of x = 15 and y= 37.
What is system of equations?A system of linear equations consists of two or more equations and looks for common answers.
1. Let us suppose small prints = x
Large prints = y
Total prints sold can be written as follows:
x + y = 52
The total cost of the prints can be written as follows:
50x + 75y = 2975
The system of equations is:
x + y = 52 . . . equation 1
50x + 75y = 2975 . . .equation 2
Using equation 1 we have:
x = 52 - y
Substituting the value of x in equation 2 we have:
50(52 - y) + 75y = 2975
2600 - 50y + 75y = 2975
25y = 2975 - 2600
25y = 375
y = 15
Now, substituting the value of y in equation 1 we have:
x + 15 = 52
x = 52 - 15
x = 37
Hence, the solution of the system of equations is y = 15 and x = 37.
2. Let us suppose the altitude = x.
The rising balloon can be thus written as:
40 +10x
The descending balloon can be written as:
165 - 15x
Solving the system of equations by substituting the value of x we get x= 5.
Hence, the altitude at which both the balloons are at the same height is 5m.
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Segment
B
D
‾
BD
bisects
∠
A
B
C
∠ABC. Solve for
x
x. Round to the nearest tenth, if necessary. (Image not necessarily to scale.)
The value of x on the line segment and the triangle is 17.3 units
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
A triangle (see attachment for the triangle)
Also from the question, we understand that:
BD bisects ∠ABC
Using the bisector theorem, we have
x/13 = 20/15
Multiply both sides of the equation by 13
So, we have the following representation
13 * x/13 = 20/15 * 13
Evaluate the products
So, we have the following representation
x = 20/15 * 13
Evaluate the other products
So, we have the following representation
x = 52/3
This gives
x = 17.3
Hence, the length x is 17.3 units
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800 miles in 5 hours miles per hour
roxanne needs 134,000 three years from now. How much should she deposit at the beginning of each 3 months in order to accumulate the desired amount if money is worth 4% coumpounded quarterly?
what is the missing in the given question?
The amount that Roxanne should deposit at the beginning of each 3 months to accumulate $134,000 at 4% compounded quarterly for three years is $10,461.13.
How is the quarterly deposit determined?The quarterly deposit can be computed using an online finance calculator with the following parameters.
The quarterly deposit shows the periodic investment that must be made to accumulate a future value of $134,000.
N (# of periods) = 12 quarters (3 x 4)
I/Y (Interest per year) = 4%
PV (Present Value) = $0
FV (Future Value) = $134,000
Results:
PMT (periodic deposits) = $10,461.13
Sum of all periodic deposits = $125,533.56
Total Interest = $8,466.44
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Write a cubic function whose graph passes through the points (-3, 0), (1, 0), (4, 0), and (0,8)
a cubic function whose graph passes through the points (-3, 0), (1, 0), (4, 0), and (0,8) is: f(x) = - 2 (x + 3) (x - 1) (x - 4)
What is a cubic function?A cubic function is a function whose expression contains the cube of the x variable. A function is referred to as a cubic function if its formula is f(x) = ax³ + bx² + cx + d. a, b, c, and d can all be constants in this case, but make sure that a 0. The b, c, or d might all be zeros.
A cubic function has 3 roots.
Let, assume α, β and γ.
So, f(x) = K (x - α). (x - β). (x - γ)
f(x) is defined by values of x where f(x) = 0
0 = K (x - α). (x - β). (x - γ)
x = α, β, γ
The given cubic function graph is cutting x - axis at 3 points: (-3, 1 ,4)
Now, f(x) = K (x - (-3). (x - 1). (x - 4)
f(x) = K (x + 3) (x - 1) (x - 4)
Next, f(x) passes through point (0,8) which means:
f(0) = 8
so, 8 = K (0 + 3) (0 - 1) (0 - 4)
or, k = - 2
Now, f(x) = - 2 (x + 3) (x - 1) (x - 4)
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