What is the sum of 4a^2 − 7a − 5 and −8a^2 − 2a + 7?

Answer:

152$

Step-by-step explanation:

160-5%=152

Answer:

$152

Step-by-step explanation:

160 × 5% = 8

160 - 8 = $152

Answer:

718 cubic inches

Step-by-step explanation:

The formula for a sphere is [tex]V=\frac{4}{3} \pi r^{3}[/tex]. A hemisphere is half this value. We will find the volume and then divide it in half. We substitute r=7 inches.

[tex]V=\frac{4}{3} \pi r^{3}\\V=\frac{4}{3} \pi (7^{3})\\V=\frac{4}{3} \pi (343)\\V=1,436 inches^3[/tex]

We divide 1,436 by 2 for the volume of a hemisphere. V= 718 cubic inches

Answer:

[tex](\frac{-8}{9}) /  (\frac{-2}{3}) * (\frac{-4}{1} )\\\\= (\frac{-8}{9}) *  (\frac{3}{-2}) * (\frac{-4}{1} )\\\\= (\frac{4}{3}) *  (\frac{1}{1}) * (\frac{-4}{1} )\\\\= \frac{-16}{3}[/tex]

Answer:

Step-by-step explanation:

1. Divide the numerator by the denominator.

2. Write down the whole number answer.

3. Write down any remainder above the denominator.

To model the population increase, use the formula P = P0 * (1 + r)^t, where P is the final population, P0 is the initial population, r is the annual growth rate, and t is the number of years. The population after 15 years can be found by substituting t = 15 into the function.

To model the population increase, we can use the formula for exponential growth.

The formula is P = P0 * (1 + r)^t, where P is the final population, P0 is the initial population, r is the annual growth rate (as a decimal), and t is the number of years.

In this case, the initial population is 1,500 and the annual growth rate is 15%. So the exponential function to model the population increase is P = 1500 * (1 + 0.15)^t.

To find the population after 15 years, we can substitute t = 15 into the function. P = 1500 * (1 + 0.15)^15

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have

[tex]y-6=-3(x+2)\to y-6=-3(x-(-2))[/tex]

Therefore

------------

2x - y = 4    it's standard form Ax + By = C

y = 2x - 4     it's slope-intercept form y = mx + b

y - x = 4 → x - y = -4  t's standard form Ax + By = C

Answer:

1  x=-2.5  y = -5.5

2.  x=5  y=1

Step-by-step explanation:

1) What is the solution of the given system?

5x-y=-7

3x-y=-2

Multiply the second equation by -1

-1*(3x-y)=-1(-2)

-3x +y = 2

Now add the first equation to the modified second equation

5x-y=-7

-3x +y = 2

------------------

2x = -5

Divide each side by 2

2x/2 = -5/2

x = -2.5

Now we need to find y

-3x+y =2

-3(-2.5) +y =2

7.5 +y =2

Subtract 7.5 from each side

7.5 -7.5 +y =2-7.5

y = -5.5

2) what is the solution of the given system?

5x+7y=32

8x+6y=46

Divide the second equation by 2

8x/2+6y/2=46/2

4x+3y =23

Multiply the first equation by 4

4 (5x+7y)=32*4

20x+28y = 128

Now multiply the modified 2nd equation by -5

-5(4x+3y )=-5(23 )

-20x -15y = -115

Lets add the new equations together to eliminate x

20x+28y = 128

-20x -15y = -115

---------------------

      13y = 13

Divide each side by 13

13y/13 =13/13

y=1

Now substitute back in to find x

5x+7y=32

5x +7(1) =32

5x +7 =32

Subtract 7 from each side

5x+7-7 =32-7

5x =25

Divide by 5

5x/5 =25/5

x=5

Answer:

0.783

Step-by-step explanation:

To find first r and then r square for the data

n statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

correlation coefficient of x and y = Cov (x,y)/std dev x * std dev Y

Cov (x,y) = E(xy) -E(x)E(y)

Hence calculations would be as follows:

x y xy

1 2 2

2 10 20

5 5 25

7 18 126

10 25 250

Mean 5 12 84.6

Cov E(xy)-E(x)E(y)  24.6

r 0.884640297

r^2 0.782588454

so answre is 0.783 after rounding off.

Answer:

0.783

Step-by-step explanation:

Answer:

y = -1/4x - 2

Step-by-step explanation:

Step 1: The y-intercept is on the y-axis line. The y-intercept in this graph is -2.

Step 2: To find the slope. The line is going downwards so that helps us know that the slope is going to be negative. You want to get the bottom point to the top. So move upwards 1 time and move 4 times to the left.

Step 3: Now just put everything together.

Answer: $31.99

Step-by-step explanation:

So, it is originally $39.99, so first we convert 20% to a decimal, which is 0.2.

Then we do 39.99 * 0.2 to find how much money was taken off.

39.99 * 0.2 = 7.998, or $8

Now, we do the original dollar amount, $39.99, minus the discount, $8, which equals $31.99.

Answer:

min = 67, Q1 = 68, median = 70,

Q3 = 76, max = 78

We have 9 observations.

The correct set of data is:

67, 74, 78, 69, 78, 70, 67, 72, 69

When we rearrange this set of data in numerical order, we have:

67, 67, 69, 69, 70, 72, 74, 78, 78

Answer:

2/6

Step-by-step explanation:

Remember to do m equals y2 minus y1 over x2 minus x1

Answer:

1/3

Step-by-step explanation:

To find the slope when we have 2 point, we use the formula

m = (y2-y2)/(x2-x1)

  = (5-3)/(4--2)

  = (5-3)/(4+2)

  = 2/6

 = 1/3

The answer is D. ∠FVI and ∠GVE. An obtuse angle must be wider than 90° (like the corners of a square or rectangle) and less than 180° (literally a straight line).

An obtuse angle in Mathematics is an angle that is greater than 90 degrees but less than 180 degrees. To identify obtuse angles in a figure, you measure the angles with a protractor. An example of an obtuse angle is one that measures 95 degrees.

In the field of Mathematics, specifically geometry, an obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees. To determine which angles in your figure are obtuse, you would need to measure them. You typically do this with a protractor. If the angle measures more than 90 degrees, it is obtuse. For example, if an angle measures 95 degrees, it is considered obtuse. However, providing specifics without an actual figure to reference is difficult.

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Answer:

 -31 = F

Step-by-step explanation:

We need to convert Celsius to Fahrenheit

(C * 9/5) + 32 = F

C= -35

Lets substitute this in

(-35 *9/5) +32 = F

-63 + 32 = F

 -31 = F

Your answer will be -23.75. Please let me know if you need something different or have any questions or concerns. Hope I helped.

Answer:

$26,195.

Step-by-step explanation:

total of new members(1942) - age group 18-24 (587)= new members(1355) to pay $15 each in fees.

1942-587=1355 x$15=20,325

next: take age group 18-24 (587)and multiple by $10 fee

587 x$10=5,870

last add both numbers together:

$20,325+ $5870=$26,195

Answer:

8(5x + 3y -7)

Step-by-step explanation:

A common number in 40x+24y-56 is 8.

40x / 8 = 5x

24y / 8 = 3y

-56 / 8 = -7

We finally get 8 (5x + 3y -7)

Hope this helps!

-sruthi123

Answer:

8 (5x +3y -7)

Step-by-step explanation:

40x+24y-56

40x = 8*5*x = 2*2*2 *5*x

24y = 3*8*y = 3*2*2*2*y

56 = 7*8 = 7 * 2*2*2

As we can see, each of these terms has a greatest common factor of 8, so we can factor it out

8 (5x +3y -7)

Answer:

Hence final answer is 144.

Step-by-step explanation:

Expression is not typed in proper format but as per given instruction "evaluate the exponent", I think it is:

[tex]\left(-12\right)^2[/tex]

So let's simplify that:

[tex]\left(-12\right)^2[/tex]

[tex]=\left(-12\right)\left(-12\right)[/tex]

[tex]=+144[/tex]  {Since product of two negative numbers is always positive.

[tex]=144[/tex]  

Hence final answer is 144.

Answer:

A. 180°+z−w

Step-by-step explanation:

We know that x  + w = 180  because they are same side exterior angles and a and b are parallel.

z=y  because they are alternate interior angles and a and b are parallel.

x  + w = 180

Solve for x by subtracting w from each side

x = 180-w

y =z

Lets find x+y

x+y

(180-w) +z

Rewriting

180+z-w

Answer:

A. 180º + z - w

Step-by-step explanation:

x + w = 180, because they are same side exterior angles, and are on opposite sides.

z = y, because if you move z down, then you will see that they overlap.

From x + w = 180, you can get x = 180 - w.

We are trying to find x + y in terms of w and z, so:

x = 180 - w

y = z

With that, you can assemble the expression, 180 - w + z.

If you re-arrange, you will get 180 + z - w.

Therefore, A is the answer.

To find out how many times greater 6 x 10^-5 is than 5 x 10^-9, you divide the first number by the second number. The result, in standard form, is 12,000,000 or 1.2 x 10^7. Thus, 6 x 10^-5 is 12,000,000 times greater than 5 x 10^-9.

The question is asking us to determine how many times greater 6 x 10^-5 is than 5 x 10^-9. To do this, we need to divide the first number (6 x 10^-5) by the second number (5 x 10^-9).

First, let's express these numbers in standard form. 6 x 10^-5 equals 0.00006 and 5 x 10^-9 equals 0.000000005.

Simply divide 0.00006 by 0.000000005. The result is 12,000,000 or 1.2 x 10^7.

Therefore, 6 x 10^-5 is 12,000,000 times greater than 5 x 10^-9 or 1.2 x 10^7 times greater.

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Answer:

Solve for y

.

Tap for fewer steps...

Subtract 7x

from both sides of the equation.

−4y=−7x+28

Divide each term by −4

and simplify.

Tap for fewer steps...

Divide each term in −4y=−7x+28

by −4

.

−4y−4=−7x−4+28−4

Simplify the left side of the equation

by cancelling the common factors.

Tap for fewer steps...

Reduce the expression by cancelling the common factors.

Tap for fewer steps...

Factor 4

out of 4y

.

−4(y)−4=−7x−4+28−4

Move the negative one from the denominator of y−1

.

−(−1⋅y)=−7x−4+28−4

Simplify the expression.

Tap for fewer steps...

Multiply −1

by y

.

−(−1y)=−7x−4+28−4

Rewrite −1y

as −y

.

y=−7x−4+28−4

Simplify each term.

Tap for fewer steps...

Move the negative in front of the fraction.

y=7x4+28−4

Simplify −−7x4

.

Tap for fewer steps...

Multiply −1

by −1

.

y=1(7x4)+28−4

Multiply 7x4

by 1

.

y=7x4+28−4

Divide 28

by −4

.

y=7x4−7

Use the slope-intercept form to find the slope and y-intercept.

Tap for fewer steps...

The slope-intercept form is y=mx+b

, where m is the slope and b

is the y-intercept.

y=mx+b

Find the values of m

and b using the form y=mx+b

.

m=74

b=−7

The slope of the line is the value of m

, and the y-intercept is the value of b

.

Slope: 74

Y-Intercept: −7

Any line can be graphed using two points. Select two x

values, and plug them into the equation to find the corresponding y

values.

Tap for fewer steps...

Choose 0

to substitute in for x

to find the ordered pair.

Tap for fewer steps...

Replace the variable x

with 0

in the expression.

f(0)=7(0)4−7

Simplify the result.

Tap for fewer steps...

Multiply 7

by 0

.

f(0)=04−7

Divide 0

by 4

.

f(0)=0−7

Subtract 7

from 0

.

f(0)=−7

The final answer is −7

.

−7

The first point is (0,−7)

.

(0,−7)

Choose 1

to substitute in for x

to find the ordered pair.

Tap for fewer steps...

Replace the variable x

with 1

in the expression.

f(1)=7(1)4−7

Simplify the result.

Tap for fewer steps...

Multiply 7

by 1

.

f(1)=74−7

To write −−71

as a fraction with a common denominator, multiply by 44

.

f(1)=74+−71⋅44

Write each expression with a common denominator of 4

, by multiplying each by an appropriate factor of 1

.

Tap for fewer steps...

Combine.

f(1)=74+−7⋅41⋅4

Multiply 4

by 1

.

f(1)=74+−7⋅44

Combine the numerators over the common denominator.

f(1)=7−7⋅44

Simplify the numerator.

Tap for fewer steps...

Multiply −7

by 4

.

f(1)=7−284

Subtract 28

from 7

.

f(1)=−214

Move the negative in front of the fraction.

f(1)=−214

The final answer is −214

.

−214

The second point is (1,−214)

.

(1,−214)

Create a table of the x

and y

values.

xy0−71−214

Graph the line using the slope and the y-intercept, or the points.

Slope: 74

Y-Intercept: −7

xy0−71−214

Step-by-step explanation:

The following picture is how you graph the equation 2x+4y=28

11. Answer: cats = $7.33 or less, dogs = $11 or less

Step-by-step explanation:

Let c represent cats and d represent dogs, then

3c + 2d ≤ $22

If he spends $0 on the dogs, then 3c ≤ $22  ⇒  [tex]c\leq \dfrac{22}{3}[/tex]  ⇒ c ≤ $7.33

If he spends $0 on the cats, then 2d ≤ $22 ⇒ [tex]d\leq \dfrac{22}{2}[/tex]  ⇒ d ≤ $11

Therefore, he can spend a maximum of $7.33 on each cat and a maximum of $11 on each dog.

12. Answer: [tex]\dfrac{2}{5}[/tex]

Step-by-step explanation:

2 pounds of trail mix divided by 5 friends

= 2 pounds trail mix ÷ 5 friends

[tex]= \dfrac{2\text{ pounds trail mix}}{5\text{ friends}}[/tex]

[tex]= \dfrac{2}{5} \text{ pounds trail mix per friend}[/tex]

Answer:

There are 4 quarts in a gallon. 3x4=12. He bought 12 quarts of milk.

Step-by-step explanation:

Answer: 180, 185, & 190

Step-by-step explanation:

1st #: 5x

2nd #: 5(x + 1)

3rd #: 5(x + 2)

1st # + 2nd # + 3rd # = sum

5x + 5(x + 1) + 5(x + 2) = 555

15x + 15 = 555

15x = 540

x = 36

1st #: 5x  = 5(36)  = 180

2nd #: 5(x + 1)  = 5(36 + 1) = 185

3rd #: 5(x + 2)   = 5(36 + 2)  = 190

(a) Company D has the least variability because it has the smallest range.

(b) Company A has the highest salaries, on average, because it has the largest mean salary.

(a) The company with the least variability in salaries is Company A, with a coefficient of variation of approximately 234.62.

(b) The company with the highest average salary is Company A, with a mean salary of $26,000.

(a) Variability of Salaries:

Variability in this context refers to how spread out the salaries are within each company.

Company A has a mean salary of $26,000 and a range of $61,000. Company B has a mean salary of $23,000 and a range of $66,000. Company C has a mean salary of $24,000 and a range of $69,000. Company D has a mean salary of $25,000 and a range of $60,000.

Calculating the coefficient of variation (CV) for each company will provide a clearer picture of the relative variability. The CV is obtained by dividing the standard deviation by the mean and multiplying by 100. Since the standard deviation is not given directly, we can infer that the coefficient of variation will be highest for the company with the largest range.

The CV for each company is as follows:

CV for Company A = (Range of Salaries / Mean Salary) * 100 = (61000 / 26000) * 100 ≈ 234.62

CV for Company B = (66000 / 23000) * 100 ≈ 286.96

CV for Company C = (69000 / 24000) * 100 ≈ 287.50

CV for Company D = (60000 / 25000) * 100 = 240.00

(b) Highest Average Salaries:

To identify the company with the highest average salary, we compare the mean salaries of each company.

Company A: Mean Salary = $26,000

Company B: Mean Salary = $23,000

Company C: Mean Salary = $24,000

Company D: Mean Salary = $25,000

To know more about mean here

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Answer:

2(x-8)=2

Step-by-step explanation:

Answer:

1. [tex]R_{90} (x,y)=(-y,x)[/tex]

2. [tex]R_{180} (x,y)=(-x,-y)[/tex]

3. [tex]R_{270} (x,y)=(y,-x)[/tex].

Step-by-step explanation:

Let us assume a point (x,y) in the co-ordinate plane on which the transformations will be applied.

Now, we know that 'rotation' is a transformation that turns that image to a certain degree about a point.

So, the given transformations gives us the forms as:

1. When we rotate an ( x,y ) by 90° about origin counter-clockwise, the resultant co-ordinate is ( -y,x ).

So, the function form is [tex]R_{90} (x,y)=(-y,x)[/tex].

2. When we rotate an ( x,y ) by 180° about origin counter-clockwise, the resultant co-ordinate is ( -x,-y ).

So, the function form is [tex]R_{180} (x,y)=(-x,-y)[/tex].

3. When we rotate an ( x,y ) by 270° about origin counter-clockwise, the resultant co-ordinate is ( y,-x ).

So, the function form is [tex]R_{270} (x,y)=(y,-x)[/tex].

Final answer:

To write functions for rotations around the origin, one can use the standard rotation matrices. For 90 degrees counterclockwise, the point (x, y) goes to (-y, x); for 180 degrees, it goes to (-x, -y); and for 270 degrees, it goes to (y, -x), keeping the distance to the origin invariant.

Explanation:

To solve the problem of finding a function for a rotation about the origin, O, in a counterclockwise direction, we need to consider the standard rotation matrices. The coordinate system rotates counterclockwise, while a point x, y remains fixed but its coordinates change relative to the new axes.

For a rotation of 90 degrees counterclockwise, the coordinates of a point (x, y) change to (-y, x).

For a rotation of 180 degrees counterclockwise, the coordinates of a point (x, y) change to (-x, -y).

For a rotation of 270 degrees counterclockwise (equivalently 90 degrees clockwise), the coordinates of a point (x, y) change to (y, -x).

These transformations ensure that the distance of point P to the origin remains invariant under the rotations, as can be verified through the Pythagorean theorem showing that the sum of the squares of the coordinates remains unchanged: x² + y².

Answer:

10 km/h  

Step-by-step explanation:

Let s = man's speed and c = speed of current

    s + c = 15

         c = 2.5     Insert value of c

s + 2.5 = 15        Subtract 2.5 from each side

        s = 12.5 km/h

=====

Speed against current

= 12.5 – 2.5

= 10 km/h

Answer:

The sum is 4 i√2

Step-by-step explanation:

Both the numbers √-2 and √-18 are imaginary number and thus can be presented as  

i√2 and i√18  

On simplifying, the i√18  can be written as i√( 9 x 2)

Taking out square root of 9 we get-  

3i√2  

Thus the summation of i√2 and i√18  can be written as  

i√2 + 3i√2  

= 4 i√2

Answer:

The correct answer is  (4 √2) i

Step-by-step explanation:

The sum we are looking is "x"

x= √-2+ √-18

By the Radical Properties of Multiplication ,

x=√-2 +√(-2*9)

x=√-2 +√-2* √9

Considering √-2= √((-1)*2)= √-1 *√2

According to the propriety of complex numbers , we can say

i=√-1

Replacing

x= i √2 + 3 i√2  

The answer is x= (4 √2) i