(Combining Equation)What is the result of subtracting the second equation from the first ?-2x + y = 0 -7x + 3y = 2

The surface area of a sphere is given by

in our case r=10 units ( the radius). By substituting this value into the last formula, we have

which gives

On the other hand, the surface area of a cube is given by

where L is the length of one side, that is, L=10. Then, we have

By comparing both results, we can see that the surface area of our sphere is larger than the surface area of the given cube. So the answer is TRUE.

Answer:

The coordinates of point B is;

Explanation:

Given the attached image;

The coordinate of point A is;

The coordinate of point C is;

If AB is 1/5 of AC;

So; let (x,y) represent the coordinates of B;

The same applies to y coordinate;

So;

Therefore, the coordinates of point B is;

The smaller of two similar balloons has a diameter of 10 inches. If it takes 12 (same sized) breaths to blow up the smaller balloon and 40.5 to blow up the larger, what is the diameter of the larger balloon?​

we have that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube.

so

Find the scale factor

ratio volumes=40.5/12=3.375

3.375=(scale factor)^3

scale factor=1.5

To find out the diameter of the larger balloon multiply the scale factor by the diameter of the smaller balloon

so

1.5*(10)=15 inches

Given the function f(x) defined as:

We need to obtain the graph after performing two shifts: 1 unit up and 2 units left. For the first shift, we do the transformation:

Now, for the second shift:

Combining these transformations:

Explanation:

The set of values are given below as

Mode:

This the data that occurs highest or the dat that has the highest frequency

Range:

The is the difference between the lowest val and the highest value

Hence,

The final answers are

Hence,

The final answer is

Answer:

Explanation:

The surface area of a cone is calculated using the formula:

We want to solve for l.

First, subtract πr² from both sides of the equation:

Next, divide both sides by πr:

The equation solved for l is:

The hours when the prices of the two stocks be the same is 2.38 hours.

From the information, the price of Stock A at 9 A.M. was $12.42 and the price has been increasing at the rate of $0.12 each hour. This will be the expressed as 12.42 + 0.12h.

At noon the price of Stock B was $12.92. It begins to decrease at the rate of $0.09 each hour. This will be:

= 12.92 - 0.09h

where h = number of hours

Equate both equations. This will be:

12.42 + 0.12h = 12.92 - 0.09h

Collect like terms

12.92 - 12.42 = 0.12h + 0.09h

0.21h = 0.50

h = 0.50 / 0.21

h = 2.38 hours.

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Given the inequality:

4m < 24

Let's solve for m.

To solve for m, divide both sides of the inequality by 4:

ANSWER:

m < 6

Answer:

C. 84

Explanation:

First, we will calculate the percentage of left-handed students in the group of 60 that the teacher asked.

So, the percentage is equal to:

Therefore, 30% of the randomly selected students are left-handed.

Now, we can use this percentage to estimate the number of left-handed students in the group of 280.

Then, 30% of 280 is equal to:

So, the answer is C. 84.

we were told that in every 4 songs on the playlist, 3 of the songs are longer than 5

so if in for 4 songs, 3 is longer than 5

for 8 songs,

we divide the the number of songs in the playlist by 4 in other to get the numbers of 4 in it then muliply by the number of songs longer than 5

for 8 songs on the playlist:

= 8/4 X 3

= 2 X 3

= 6

For 32 songs on the playlist

= 32/4 X 3

= 8 X 3

= 24

For 40 songs on the playlist

= 40/4 X 3

= 10 X 3

= 30

For 136 number of songs on the playlist

= 136/4 X 3

= 34 X 3

= 102

so in completing the table:

Total Number of Songs on the Playlis Number of songs longer than 5min.

8 6

32 24

40 30

136 102

Solution:

The Function transformation of f(x) is:

If c > 0, then the graph shift left f(x+c).

If c<0, then the graph shift right f(x-c)

If d > 0, then the graph shift up f(x) +d

If d < 0, then the graph shift down f(x) -d

When the given equation is:

The transformation equation is given:

Then, the graph shifts down 2 units and shifts left 5 units.

Also, the vertical stretch with a scale factor 3.

Therefore, the correct options are B and D.

WE are to solve an inequality, so we proceed to isolate the variable "p" on one side of the inequality symbol:

6 p - 15 < 33

we add 15 to both sides:

6 p < 33 + 15

6 p < 48

now divide both sides by 6 (notice that since 6 is a positive number, the division doesn't change the direction of the inequality)

p < 48/6

p < 8

So we need to highlight on the number line, the line that starts at "8" and goes all the way to the left (to minus infinity), and make sure that at the point "8" you draw an "empty" circle to indicate that the number 8 itself is NOT included in your set of solutions.

In order to determine the amount of brownies left in the refrigerator, subtract 8 from 12.

If Abby bakes 2 -dozen brownies, she baked 24 brownies. There are 12 pieces in 1 dozen, thus if she bakes two dozens, she baked 24 brownies ( 12 x 2).

The amount of brownies left after she takes one dozen to school = amount baked - amount taken for the meeting

24 - 12 = 12

Amount left in the refrigerator : amount left after she took a dozen for the meeting - amount eaten by her family

12 - 8 = 4

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Solution

Using triangle inequality

The triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.

The fence line is the longest size

100, 130 can't be the answer

280 can't be the answer be ause the triangle inequality says it should be less than the sum

Therefore, the correct answer is 220

step 1

The equation of line k is y=-x

The rule of the reflection across the line y=-x is equal to

(x,y) -------> (-y,-x)

so

we have the point (2,5)

Apply the rule

(2,5) -----> (-5,-2)

step 2

Reflection across the x axis

The rule of the reflection across the x axis is

(x,y) ------> (x,-y)

so

Apply the rule to the point (-5,-2)

(-5,-2) ------> (-5,2)

therefore

the answer is

We are going to test all options to see which is true and false.

The one that is true will be the point that is part of the solution.

We will move to the next option and test:

Given the table that shows the number of movies and the corresponding frequency, you can determine that the total frequency is:

By definition:

By definition, the Cumulative Frequency can be obtained by adding the corresponding frequency with the previous frequencies and dividing the sum by the Total Frequency.

Therefore, you can determine that:

- For:

You know:

And:

- Given:

You get:

And:

- Given:

You get:

And:

- Given:

You get:

And:

- Given:

You get:

And:

Hence, the answer is:

ANSWER

88

EXPLANATION

Let x be the miles driven and y be the earnings of the company when they drive for x miles.

If the company charges $0.17 per mile driven plus a flat rate of $85, then the total cost for moving x miles away is,

Now, we have to find for how many miles, x, the company must drive to earn $100 or more,

Subtract 85 from both sides,

And divide both sides by 0.17,

Hence, the company must drive for at least 88 miles to earn at least $100, rounded to the nearest mile.

Step 1

To change word problem to an inequality, you must take the word problem step by step and translate it into an inequality.

Step 2

Take the word problem step by step

The systems of equations which correctly models the situation as described is;

It follows from the task content that the system of equations which models the production process of caffe mocha be determined.

As given in the task content;

Hence, since For each ounce of chocolate syrup, she uses 5 ounces of coffee, the situation can be represented algebraically as;

Also, since she wants to make 48 ounces of caffe mocha; we have;

Therefore, the required system of equations is;

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Sand will be placed under the base of a circular pool with a diameter of 14 feet. 1 bag of sand covers about 5 square feet. the number of bags of sand required is 30bags.

The area of the pool is

 A = πr²

 A = 3.14×(7 ft)² = 153.8 ft²

The number of bags of sand required is ...

 (153.8 ft²)/(5 ft²/bag) ≈ 30.76bags

bags of sand are needed.

The diameter is defined as twice the length of the radius of the circle. The radius is measured from the centre of the circle to one endpoint on the boundary of the circle, while the diameter is the distance  measured from one end of the circle to a point on the other end of the circle that passes through the centre. This is indicated by the letter D. The circumference of  a circle has an infinite number of points, which means that the circle has an infinite number of diameters and each diameter of the circle is the same length.

Ø is the symbol  used in the design to indicate the diameter. This symbol is often used in technical data and drawings.

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The most appropriate choice for equation of line in slope intercept form will be given by-

y = 2x - 8 is the required equation of line

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line

Here,

The given equation of line is y= 2x +3

Slope of this line = 2

Slope of the line parallel to this line = 2

The line passes through (-2, -12)

Equation of the required line = y - (-12) = 2(x - (-2))

                                                = y + 12 = 2x + 4

                                                = y = 2x + 4 - 12

                                                = y = 2x - 8

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Answer

f(x)

domain: all real numbers, range: all real numbers

f⁻¹(x)

domain: all real numbers, range: all real numbers

Step-by-step explanation

Given the function:

This is the equation of a line.

The domain and range of a linear function are all real numbers.

On the other hand, the range of an inverse function is the domain of the original function and the domain of an inverse function is the range of the original function. Then, the domain and range of the inverse of f(x) are all real numbers.

for the given hyperbola

We have the following graph. Visually we can see that this hyperbola does have a transverse axis, however you can do all the calculations to check it

As we can see y = -7 is a line parallel to the x axis, turning the transversal axis horizontal.

That is, this hyperbola does have a horizontal transverse axis and the answer is TRUE

Given

Answer

Central angle

Name XOY

Measure 90

Inscribed angle

name XZY

Measure 45

Arc

name XY

Measure = circumference of circle/4

Recall that given points (a,b) and (c,d) the distance between them would be

In our case we are given a=0,b=0,c=2,d=3. So the distance would be

so the distance between them is the square root of 13.

None of Ari's answer to the question is correct. The right application of the laws of exponents to get the correct answer is explained below.

Some of the laws of exponents can be summarized as follows.

Based on the above laws of exponents, none of Ari's answer is correct. Below are the correct way to solve the questions:

1. [tex]4^2 \times 4^5 = 4^{2 + 5} = 4^7[/tex]

2. [tex](2^{-5})^3 = 2^{-3 \times 5} = 2^{-15} = \frac{1}{2^{15}}[/tex]

3. [tex]\frac{(\frac{1}{4})^4 \times (\frac{1}{4})^5 }{(\frac{1}{4})^3} = \frac{(\frac{1}{4})^{4 + 5} }{(\frac{1}{4})^3} = \frac{(\frac{1}{4})^9 }{(\frac{1}{4})^3} = (\frac{1}{4})^{9 - 3}} = (\frac{1}{4})^6[/tex]

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Answer:

Explanation: We have to find the center of the circle, the equation of the circle is as follows:

Ploting the equation (0) gives the following result:

Therefore the center of the circle has the coordinates (0,4).

Leah, this is the solution:

Variables:

Let x to represent the weight of one Hershey kiss

Let y to represent the weight of one Reese cup

System of equations:

6x + 6y = 82.4

4x + 5y = 63.8

______________

Let's multiply the second equation by - 3/2, therefore:

6x + 6y = 82.4

-6x - 15y/2 = -95.7

________________

-15/2 + 6 = -3/2

_________________

-3y/2 = -13.3

Dividing by -3/2 at both sides:

-3y/2 / -3/2 = -13.3 / -3/2

y = 8.87

______________

Replacing y in the first equation and solving for x:

6x + 6 * 8.87 = 82.4

6x + 53.22 = 82.4

Subtracting 53.22 at both sides:

6x +53.22 - 53.22= 82.4 - 53.22

6x = 29.18

Dividing by 6 at both sides:

6x/6 = 29.18/6

x = 4.86

_________________

In conclusion, one Hershey kiss weights 4.86 ounces and one Reese cup weights 8.87 ounces.