Use this information to find the value of b
c = 25
s = 9

b = 4c - s2

Answer:

y = 6x+9

Step-by-step explanation:

Equations that are parallel have the same slope

y = 6x+7 is written in slope intercept form where the slope is 6 and the y intercept is 7

The lines will have a slope of 6

The point (0,9) is the y intercept because the x value is 0

We can write the equation in slope intercept form y = mx+b

y = 6x+9

Answer:

Hello! The answer is y = 6x + 9.

Step-by-step explanation:

When lines are parallel, they will have the same slope but a different y-intercept.

The y-intercept, in this case, would be (0, 9) since the x-coordinate equals 0. This leaves us with 9 as the y-intercept.

Our slope-intercept form equation will be written as:

y = 6x + 9

Solution

Step 1:

Write the function:

Step 2:

Horizontally compressed is given below:

Final answer

Answer:

2x-3y=2

x=6y-5

2(6y-5)-3y=2

use the distributive property.

2*6y=12y

2*-5=-10

12y-10-3y=2

combine like terms

12y-3y=9y

9y-10=2

add 10 to both sides.

9y-10+10=9y

2+10=12

9y=12

divide both sides by 9

9y/9=y

y=about 1.33

plug in the value of y in the expression equal to the value of x.

x=6(1.33)-5

solve

6*1.33=7.98

x=7.98-5

7.98-5=2.98

Step-by-step explanation:

x=2.98

y=1.33

13 is the range, 17.0 is the population variance, and 4.1 is the population standard deviation.

The range of a collection of data is a measurement of its variability. It is the difference between a set of data's highest and lowest value.

Given ,

11,11,16,17,15,13,9,18,5,7

Highest value = 18

Lowest value = 5

Range = 18-5 = 13

The following formula works well for population variance:

Population Variance = Σ(x-mean)²/N

N is total element in the data = 10

x are the individual data

Calculating the mean is necessary before we can obtain the variance and standard deviation.

mean = Σfx/N

Mean = 122/10

Mean = 12.2

Variance = 170.16/10

Population variance = 17.016

Population variance ≈ 17.0 (to 1 d.p)

Population standard deviation = √Population Variance

Population standard deviation = √17.016 = 4.125

≈ 4.1 (to 1 d.p)

The complete question is:

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 11,11,16,17,15,13,9,18,5,7

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The Solution:

We are required to find the sum of

This also means that we should simplify

Therefore, the correct answer is option 2

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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The length of the rectangle is 19.25 cm when it is 2 more than three times the width of 5.75 cm.

A perimeter is a closed path that encompasses, surrounds, or outlines a two-dimensional shape or length in one dimension. A circle's or an ellipse's circumference is its perimeter. There are several applications for calculating the perimeter. The length of fence required to encircle a yard or garden is known as the calculated perimeter.  

The perimeter (circumference) of a wheel/circle describes how far it can roll in one revolution.  Similarly, the amount of string wound around a spool is proportional to the perimeter of the spool; if the length of the string were exact, it would equal the perimeter.

Given that,

Perimeter = 2(l + b) = 50cm

And also given that,

l = 2 + 3b

Substituting the value of l in perimeter we get

2((2 + 3b) + b) = 50cm

2(2 + 4b) = 50cm

4 + 8b) = 50cm

8b = 50 - 4

b = 46/8

b = 5.75

Substituting the value of b in l, we get

l = 2 + 3(5.75)

l = 19.25

Therefore, the length of the rectangle is 19.25 cm when it is 2 more than three times the width of 5.75 cm.

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Answer:

The answer is A

Step-by-step explanation:

You can use a graphing calculator (geogebra) It works

Solution

Use now the standard Form of the equation of ellipse for Vertical Major Axis.

The first co-vertex is (h , k - b)

The second co-vertex is (h , k + b)

Centre ( h , k)

Answer:

timeline

Step-by-step explanation:

the table shows the same time I don't have your phone you u you y you can get a hold of y have a lot to do it you got a

The domain and range provides a definition for a graph

Part A: The graph represents a function because a vertical line drawn from the horizontal crosses the graph only once

Part B. Domain: 0 ≤ t ≤ 30

Range: 7000 < f(t) ≤ 9,300

Reason:

Part A: The reason why the graph represents a function is that a function is a one to one relationship that maps each element of the set known as the domain to exactly one element of the set which is the range of the function

Therefore, a vertical line drawn on the graph of a function crosses the graph only once, such that one input cannot have two outputs

Which gives that the graph is a function, given that all the vertical lines from the horizontal axis crosses the graph f(t) at exactly one point

Part B

Domain:

The domain of a function are the possible input values of the function

In the graph, the possible values of the time, t are; 0 ≤ t ≤ 30

The domain of the function is 0 ≤ t ≤ 30

Range:

The range of a function are the possible output values of the function

The range of the given function f(t) are; from approximately 7,000 feet to approximately 9,000 feet, which gives;

The range of the function: 7000 < f(t) ≤ 9,300

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Answer:

45 degrees, 135 degrees, 225 degrees, 315 degrees

Step-by-step explanation:

x = 45 degrees + k * 90 degrees

t^3-4t^2-.5t+2=0

t = 4

t = 2^.5/2

cosx=2^.5/2

The midpoint of the line segment with end points as  (5,6) and (6, -8)  is ( 11/2 , -1)

In the above question, It is given that

A line segment has its endpoints as (5,6) and (6, -8)

Let the mid point of the line segment is (x,y)

The formula to find the midpoint is

x = (\(\frac{x1+x2}{2}\)) , y = (\(\frac{y1+y2}{2}\))

Here, we have x1 = 5, x2 = 6, y1 = 6 and y2 = -8

So putting the values in the formula we get,

x = (\(\frac{5+6}{2}\)) = \(\frac{11}{2}\)

y =( \(\frac{6 - 8}{2}\)) = -1

Therefore, the midpoint of the line segment with end points as  (5,6) and (6, -8)  is ( 11/2 , -1)

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Answer:

1st one is true, 2nd is true and 3rd is false

Step-by-step explanation:

A higher credit score reduces your fixed costs because you will pay lower interest rates. That is option A.

A higher credit score is one of the factors that are being considered by banks or lenders before one is being viewed as being legible to borrow money.

This is soo because a higher credit score will reduce the lending interest rates of the individual because it shows such will pay back the borrowed money as soon as possible.

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Answer:

D

Step-by-step explanation:

The others don't work as it would if it was the older men

Answer:

In 5 years Ahab will have $ 5,400.

Step-by-step explanation:

Given that Ahab has a savings account with $ 4,000 in it that earns 7% simple interest per year, to determine how much money, to the nearest penny, will Ahab have in 5 years, the following calculation must be performed:

4,000 + (4,000 x 0.07 x 5) = X

4,000 + (280 x 5) = X

4,000 + 1,400 = X

5,400 = X

Therefore, in 5 years Ahab will have $ 5,400.

Answer:

the volume of the square pyramid is 2430 cubic cm

Answer:

1296 cm³

Step-by-step explanation:

V = a² x [√s²- (a/2)²] / 3

a = 18 cm

s = 15 cm

V = 18² x [√15²-(18/2)²] / 3 = 18² x [√225-81] / 3

V = 324 x (√144/3) = 1296 cm³

To find the axis of symmetry (AOS) for the equation x^2+x-6=0, we can start by completing the square. This involves adding and subtracting the same value to the equation to make it have the form (x + a)^2 = b. In this case, we can add and subtract 9/4 to the equation to get:

\(x^2 + x - 6 = (x + 1/2)^2 - 9/4\)

This equation has the form \((x + a)^2 = b\), where a = 1/2 and b = -9/4. The axis of symmetry (AOS) is the vertical line that passes through the point where the parabola defined by the equation opens. In this case, the AOS is the vertical line that passes through the point (-1/2, 0), which is the point where the parabola defined by the equation x^2 + x - 6 = 0 opens. Therefore, the AOS for this equation is the vertical line x = -1/2.

Answer:

\(x=-\dfrac{1}{2}\)

Step-by-step explanation:

The axis of symmetry of a quadratic equation in the form y = ax² + bx + c, is a vertical line that passes through the vertex of the corresponding parabola, dividing it into two symmetrical halves.

The formula for the axis of symmetry is:

\(\large\boxed{x=-\dfrac{b}{2a}}\)

For the given equation, x² + x - 6 = 0:

Substitute the values of a and b into the formula:

\(x=-\dfrac{1}{2(1)}=-\dfrac{1}{2}\)

Therefore, the axis of symmetry of the given quadratic equation is:

\(\large\boxed{x=-\dfrac{1}{2}}\)

The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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Answer:

\(\large\boxed{\mathtt{9^{8}}}\)

Step-by-step explanation:

\(\textsf{For this problem, we are asked to simplify the given expression.}\)

\(\textsf{Let's begin by understand an important rule for problems like these.}\)

\(\mathtt{9^{3} \times 9^{5} = 9^{?}}\)

\(\large\underline{\textsf{We should remember that;}}\)

\(\textsf{When exponents multiply, they \underline{add}.}\)

\(\large\underline{\textsf{Why?}}\)

\(\textsf{If not, then the answer will be incorrect. Let's identify why in an example.}\)

\(\large\underline{\textsf{Bad Example:}}\)

\(\mathtt{2^{2} \times 2^{5} = 2^{2 \times 5 =10}}\)

\(\textsf{This means that;}\)

\(\mathtt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \neq 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2.}\)

\(\large\underline{\textsf{Good Example:}}\)

\(\mathtt{2^{2} \times 2^{5} = 2^{2+5=7}}\)

\(\textsf{This means that;}\)

\(\mathtt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2.}\)

\(\textsf{Let's follow the good example!}\)

\({\mathtt{9^{3} \times 9^{5} = 9^{3 + 5=8}}\)

\(\textsf{This means that;}\)

\(\mathtt{9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 = 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9.}\)

\(\large\boxed{\mathtt{9^{8}}}\)

\(\huge\text{Hey there!}\)

\(\mathsf{9^3 \times 9^5}\\\mathsf{= 9\times 9 \times 9\ \boxed{\times}\ 9\times 9\times 9 \times 9 \times 9}\\\mathsf{= 81\times 9\ \boxed{\times}\ 81\times81\times9}\\\mathsf{= 729\ \boxed{\times}\ 6,561\times 9}\\\mathsf{= 729\ \boxed{\times}\ 59,049}\\\mathsf{= 43,046,721}\\\mathsf{= 9^3 \times 9^5 \rightarrow 9^{3 + 5}\rightarrow 9^8}\)

\(\huge\text{Therefore your answer should be:}\)

\(\huge\boxed{\mathsf{9^8}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

the line of symmetry is (-1,0) and the vertex is (0,4)

Step-by-step explanation:

I like to plug in all of my coordinates into a graphing calculator in order to find the answer.

Hope this helps...

Assuming supply and demand are linear, the equilibrium price is equal to $252 and the equilibrium quantity is equal to 2,016 items.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

First of all, we would determine a linear function for both supply and demand by finding the slope using this formula as follows:

\(Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Note: price (p) in dollars would be the output and quantity (q) would be the input.

For supply, the points include the following:

Slope, m = (330 - 180)/(2640 - 1440)

Slope, m = 150/1200

Slope, m = 1/8.

Next, we would find the y-intercept at (1,440, 180):

p = qm + c

180 = 1/8(1440) + c

180 = 180 + c

c = 0.

Therefore, the supply equation is p = q/8.

For demand, the points include the following:

Slope, m = (330 - 180)/(1,470 - 2,520)

Slope, m = 150/-1,050

Slope, m = -1/7.

Next, we would find the y-intercept at (2,520, 180):

p = qm + c

180 = -1/7(2,520) + c

180 = -360 + c

c = 180 + 360.

y-intercept, c = 540.

Therefore, the demand equation is p = -q/7 + 540.

In order to find the equilibrium price and quantity, we would set the supply equal to the demand:

q/8 = -q/7 + 540

Multiplying all through by 56, we have:

7q = -8q + 30,240

15q = 30,240

q = 30,240/15

Equilibrium quantity, q = 2,016 items.

For the equilibrium price, we have:

p = q/8

p = 2,016/8

Equilibrium price, p = $252.

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The equation to find out his score is above average is  x = 300 - 187

and it is 113.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Jean Conrad is an amateur bowler with an average score of 187. She recently bowled a perfect 300 score.

Let the score above her average score be x,

∴ x = 300 - 187.

x = 113.

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Answer:

Segment Addition Postulate.

Step-by-step explanation:

The segment addition postulate justifies the statement:

\(AQ+QB=AB\)

To help this make sense, you are namely adding segments on a line in order to achieve a complete line segment.

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

a) The distance of the stone above ground level at any time t is given by h(t) = 950 + 4.9t², where h(t) is measured in meters and t is measured in seconds.

b) It takes approximately 13.93 seconds for the stone to reach the ground.

c) The stone strikes the ground with a velocity of approximately 136.04 m/s.

d) It takes approximately 16.75 seconds for the stone thrown downward with a speed of 6 m/s to reach the ground.

When objects are dropped or thrown from a height, their speed and position can be determined using physics equations. In this problem, we will calculate the distance, time, and velocity of a stone dropped from a tower.

First, we need to determine the equation for the height of the stone above the ground at any given time t. We can use the formula:

h(t) = h0 + vt + 0.5at²

where h0 is the initial height, v is the initial velocity (which is zero for a dropped object), a is the acceleration due to gravity (g = 9.8 m/s^2), and t is the time since the stone was dropped.

Using the given values, we can plug in the numbers and simplify:

h(t) = 950 + 0t + 0.5(9.8)t²

h(t) = 950 + 4.9t²

To find the time it takes for the stone to reach the ground, we need to set h(t) = 0 and solve for t:

0 = 950 + 4.9t^2

t^2 = 193.88

t ≈ 13.93 seconds

To find the velocity at which the stone strikes the ground, we can use the formula:

v = v₀ + at

where v₀ is the initial velocity (which is zero for a dropped object) and a is the acceleration due to gravity (g = 9.8 m/s²). We can plug in the values for t and solve for v:

v = 0 + 9.8(13.93)

v ≈ 136.04 m/s

Finally, if the stone is thrown downward with a speed of 6 m/s, we can use the same formula for h(t) as before, but with an initial velocity of -6 m/s. We can then find the time it takes to reach the ground using the same method as before:

h(t) = 950 - 6t + 0.5(9.8)t²

0 = 950 - 6t + 4.9t²

t² - 1.22t - 193.88 = 0

t ≈ 16.75 seconds

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Answer:

2

Step-by-step explanation:

1+1=2

The diameter of the circle is 8, because the diameter is twice the radius. The circumference of the circle is 25.1327, because the circumference is calculated using the formula C = 2πr, where r is the radius and π is approximately equal to 3.14.