All categories

2 years ago

Given CS=2x+1, SB=6x, CR=7.5, and RA=18. What must the value of x be in order to prove SR || BA? Justify your answer

Mathematics

1 answer:

dangina [55]2 years ago

4 0

The picture in the attached figure

we know that
In similar triangles. The ratio of the lengths of the sides CS and CB must be equal to the ratio of the lengths of sides CR and CA. CS / CB = CR / CA
which can also be written as,
CS / (CS + SB) = CR / (CR + RA)
CS*(CR+RA)=CR*(CS+RA)
CS=2x+1
SB=6x
CR=7.5
RA=18
(2x+1)*[7.5+18]=7.5*[2x+1+18]
(2x+1)*[25.5]=7.5*[2x+19]
(51x+25.5)=15x+142.5
51x-15x=142.5-25.5
36x=117
x=117/36
x=3.25

the answer is
x=3.25

You might be interested in

Five people each working 8 hrs a day can assemble 400 toys in a 5 day work week. what is the average number of toys per person?

wariber [46]

Answer:

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Tim has an after-school delivery service that he provides for several small retailers in town. He uses his bicycle and charges $

nlexa [21]

Answer:

Step-by-step explanation:

Given that

For delivery within $1\frac{1}2$ mi, charges = $1.25

For delivery within $1\frac{1}2$ mi - $1\frac{3}4$ mi, charges = $1.70

For delivery within $1\frac{3}4$ mi - 2 mi, charges = $2.15

and

so on.

i.e.

For delivery within 2 mi - 2 $\frac{1}4$ mi, charges = $2.60

For delivery within 2 $\frac{1}4$ mi - 2 $\frac{1}2$ mi, charges = $3.05

For delivery within 2 $\frac{1}2$ mi - 2 $\frac{3}4$ mi, charges = $3.50

For delivery within 2 $\frac{3}4$ mi - 3 mi, charges = $3.95

For delivery within 3 mi - 3 $\frac{1}4$ mi, charges = $4.40

So, every 0.25 mi or $\frac{1}4$ mi increase in distance, there is an increase of $0.45 in the charges.

It is given that there is increase of 10% in the rates.

i.e. for every 0.25 mi increase in distance, there is an increase of 0.45*1.10 = $0.495 in the charges.

The distance of $3\frac{1}8$ miles lies within the range 3 mi - 3 $\frac{1}4$ mi.

So actual charges after increase of 10%

$\Rightarrow \$4.40 \times \dfrac{110}{100}\\\Rightarrow \$4.40 \times 1.10\\\Rightarrow \bold{\$4.84}$

6 0

2 years ago

OMG PLEASE HELP ME ASAP!!!!!!! A local charity sponsors a 5K race to raise money. It receives $55 per race entry and $10,000 in

Dominik [7]

Start with how much profit they are making off each race entry. People pay $55 to race, but $15 of that is expenses so they are only profiting $40 for each entry. Now write one side of the equality. They start with $10,000 in donations, and then have a $40 profit for each race entry. So 10,000+40x. X will represent the unknown number of race entries. What do we want that expression to be equal to? We want 10000+40x>55000. It can also be greater than or equal to, not just greater than. Solve for x. Subtract 10000 from each side resulting in 40x>45000. Divide each side by 40 to solve for x. X>1125. X needs to bbe greater than or equal to 1125. If there are 1125 race entries, the charity will profit exactly $55000, so the lowest number of race entries is 1125

3 0

2 years ago

Two of Mrs. Garcia's seventh-grade classes are going on a field trip. They plan to take a bus, tour a factory, and

Alex787 [66]

Answer:

35 and communitive property

Step-by-step explanation:

on edg 2021

4 0

2 years ago

Read 2 more answers

There are 648 cows and sheep on the farm. The ratio of the number of Cows to the number if sheep is 5:4. At an auction 2 thirds

GREYUIT [131]

Cows : sheep = 5 : 4

5x + 4x = 648

9x = 648

x = 72

5x = 5 * 72 = 360

4x = 4 * 72 = 288

There are originally 360 cows and 288 sheep.

2/3 of the sheep are sold. That means that 1/3 of the sheep are left.

1/3 * 288 = 96

96 sheep are left.

x cows were sold.

(360 - x)/96 = 3/1

360 - x = 288

-x = -72

x = 72

72 cows were sold

7 0

2 years ago