3x - y = 7

A toll collector on a highway receives $8 for trucks and $7 for cars. At the end of a 33-hour period, she collected $296. H

frosja888 [35]

Answer:

The required list is: 0 car and 37 truck; 8 car and 30 truck; 16 car and 23 truck; 24 car and 16 truck; 32 car and 9 truck;

Step-by-step explanation:

Consider the provided information.

A toll collector on a highway receives $8 for trucks and $7 for cars, at the end she collected $296.

Let t represents the number of trucks and c represents the number of cars pass through highway.

$8t+7c=296$

$8t=296-7c$

$t=37-\frac{7c}{8}$

The number of trucks should be natural number.

Substitute c=0 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(0)}{8}$

$t=37$

Substitute c=8 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(8)}{8}$

$t=37-7$

$t=30$

Substitute c=16 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(16)}{8}$

$t=37-14$

$t=23$

Substitute c=24 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(24)}{8}$

$t=37-21$

$t=16$

Substitute c=32 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(32)}{8}$

$t=37-28$

$t=9$

Hence, the required list is: 0 car and 37 truck; 8 car and 30 truck; 16 car and 23 truck; 24 car and 16 truck; 32 car and 9 truck;

8 0

3 years ago

1. Identify whether this equation has a solution that is positive, negative, or zero:

nasty-shy [4]

X=2/3
Which is positive

7 0

3 years ago

PLEASE HELP! I AM VERY CONFUSED

DerKrebs [107]

Answer: I am the saving grace

Step-by-step explanation:

In the attachments :)

Download pdf

3 0

2 years ago

The triangle shown in the diagram is going to be dilated by a scale factor of 1 3 . What is the length of the new side that corr

Rufina [12.5K]

What’s is side AB if I don’t have that I don’t know how to figure out how they correspond

3 0

3 years ago

The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, = 6 centime

Bingel [31]

Answer:

Part A) see the explanation

Part B) see the explanation

Part C) The perimeter of trapezoid ABCD is 32 centimeters and the perimeter of trapezoid EFGH is 48 centimeters

Step-by-step explanation:

<u><em>The complete question is</em></u>

The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC

Part A) Write a similarity statement for each of the four pair of corresponding sides

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

The corresponding sides are

AB and EF

BC and FG

CD and GH

AD and EH

so

$\frac{AB}{EF}=\frac{BC}{FG}=\frac{CD}{GH}=\frac{AD}{EH}$

Part B) Write a congruence statement for each of the four pair of corresponding angles.

we know that

If two figures are similar, then its corresponding angles are congruent

The corresponding angles are

∠A and ∠E

∠B and ∠F

∠C and ∠G

∠D and ∠H

so

∠A ≅ ∠E

∠B ≅ ∠F

∠C ≅ ∠G

∠D ≅ ∠H

Part C) Determine the perimeter for each of the isosceles trapezoids

we have

The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC

step 1

Find the measure of CD

Remember that

The ratio between corresponding sides is proportional and this ratio is the scale factor

Let

z ----> the scale factor

$z=\frac{2}{3}$

so

$\frac{2}{3}=\frac{CD}{GH}}$

we have

$GH=6\ cm$

substitute

$\frac{2}{3}=\frac{CD}{6}}\\\\CD=4\ cm$

step 2

Find the measure of AB

Remember that

AB is three times the length of DC

so

$AB=3DC$

$DC=CD=4\ cm$

substitute

$AB=3(4)=12\ cm$

step 3

Find the measure of BC

Remember that in an isosceles trapezoid, the legs are equal

so

BC=AD

we have

$AD=8\ cm$

therefore

$BC=8\ cm$

step 4

Find the perimeter of trapezoid ABCD

$P=AB+BC+CD+AD$

substitute the values

$P=12+8+4+8=32\ cm$

step 5

Find the perimeter of trapezoid EFGH

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z ---> the scale factor

x ----> the perimeter of trapezoid ABCD

y ----> the perimeter of trapezoid EFGH

so

$z=\frac{x}{y}$

we have

$z=\frac{2}{3}$

$x=32\ cm$

substitute

$\frac{2}{3}=\frac{32}{y}$

$y=32(3)/2=48\ cm$

therefore

The perimeter of trapezoid EFGH is 48 centimeters

3 0

3 years ago