Find the distance<br> P(-2, -7), Q(4,7)

Box D and Box E are made from unit cubes of the same size.

Dominik [7]

Answer:

Box E has a greater volume than Box D.

Step-by-step explanation:

Step 1 : Find the volume of Box D.

The formula for volume of a rectangular prism such as this is

height * width * depth

Knowing this, let's substitute the values.

3 * 5 * 1 = 15

The volume of box d is 15 cubic units.

Step 2 : Find the volume of Box E.

height * width * depth

4 * 4 * 1 = 16

The volume of box e is 16 cubic units. Therefore box E has a greater volume than box D.

8 0

3 years ago

Jenny and her children went to the SeaWorld.She purchased adult ticket for herself and children tickets for her 2 boys. Tickets

dangina [55]

Given:

She purchased adult ticket for herself and children tickets for her 2 boys.

Cost of one adult ticket = $39.99

Cost of one child ticket = $19.99

To find:

The expression to represent the total cost of the tickets Jenny purchased.

Solution:

Let x represent the number of adult ticket purchase

and y represent the number of child tickets purchase.

Cost of one adult ticket = $39.99

Cost of one child ticket = $19.99

Total cost = 39.99x + 19.99y

Therefore, the expression for total cost is 39.99x + 19.99y.

She purchased one adult ticket and 2 child tickets.

Substitute x=1 and y=2 in the above expression.

Total cost = 39.99(1) + 19.99(2)

= 39.99 + 39.98

= 79.97

Therefore, the required expression to represent the total cost of the tickets Jenny purchased is 39.99(1) + 19.99(2) and total cost is $79.97.

3 0

3 years ago

Given the center of the circle (-3,4) and a point on the circle (-6,2), (10,4) is on the circle

Anastasy [175]

Answer:

Part 1) False

Part 2) False

Step-by-step explanation:

we know that

The equation of the circle in standard form is equal to

$(x-h)^{2} +(y-k)^{2}=r^{2}$

where

(h,k) is the center and r is the radius

In this problem the distance between the center and a point on the circle is equal to the radius

The formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Part 1) given the center of the circle (-3,4) and a point on the circle (-6,2), (10,4) is on the circle.

true or false

substitute the center of the circle in the equation in standard form

$(x+3)^{2} +(y-4)^{2}=r^{2}$

Find the distance (radius) between the center (-3,4) and (-6,2)

substitute in the formula of distance

$r=\sqrt{(2-4)^{2}+(-6+3)^{2}}$

$r=\sqrt{(-2)^{2}+(-3)^{2}}$

$r=\sqrt{13}\ units$

The equation of the circle is equal to

$(x+3)^{2} +(y-4)^{2}=(\sqrt{13}){2}$

$(x+3)^{2} +(y-4)^{2}=13$

Verify if the point (10,4) is on the circle

we know that

If a ordered pair is on the circle, then the ordered pair must satisfy the equation of the circle

For x=10,y=4

substitute

$(10+3)^{2} +(4-4)^{2}=13$

$(13)^{2} +(0)^{2}=13$

$169=13$ -----> is not true

therefore

The point is not on the circle

The statement is false

Part 2) given the center of the circle (1,3) and a point on the circle (2,6), (11,5) is on the circle.

true or false

substitute the center of the circle in the equation in standard form

$(x-1)^{2} +(y-3)^{2}=r^{2}$

Find the distance (radius) between the center (1,3) and (2,6)

substitute in the formula of distance

$r=\sqrt{(6-3)^{2}+(2-1)^{2}}$

$r=\sqrt{(3)^{2}+(1)^{2}}$

$r=\sqrt{10}\ units$

The equation of the circle is equal to

$(x-1)^{2} +(y-3)^{2}=(\sqrt{10}){2}$

$(x-1)^{2} +(y-3)^{2}=10$

Verify if the point (11,5) is on the circle

we know that

If a ordered pair is on the circle, then the ordered pair must satisfy the equation of the circle

For x=11,y=5

substitute

$(11-1)^{2} +(5-3)^{2}=10$

$(10)^{2} +(2)^{2}=10$

$104=10$ -----> is not true

therefore

The point is not on the circle

The statement is false

7 0

3 years ago

How fractions and decimal are alike

seraphim [82]

Again, decimals and fractions represent all the values in between integers. Decimals are simply one step more of simplification from fractions.

8 0

3 years ago

Read 2 more answers

What is the value of z in the equation 2(4z − 9 − 7) = 166 − 46?

kumpel [21]

Hi there!

2(4z - 9 - 7) = 166 - 46
let's make this a little more simpler...

2(4z - 16) = 120

use distributive property.
multiply 2 and 4z , 2 and -16.
8z - 32 = 120

add 32 on both sides to isolate the variable

8z = 152

divide both sides by 8...

z = 19

So your answer is A. 19

Hope this helped!! :)

8 0

3 years ago

Read 2 more answers

Find the distance P(-2, -7), Q(4,7)