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iragen
2 months ago
8

It is known that Ray AP bisects angle CAT. If m<CAT = 5x+17 and m<PAT = 3x-4, then determine the value of x.​

Mathematics
1 answer:
tester [12.3K]2 months ago
8 0

Answer:

x = 25

Step-by-step explanation:

Given that ray AP divides angle CAT, it implies that

\angle CAT=\angle CAP+\angle PAT

Also, \angle CAP = \angle PAT

This leads to, \angle CAT=2\angle PAT

As stated,

\angle CAT = 5x+17 \ \text{and}\ \text{PAT}=3x-4

Consequently,

5x+17=2(3x-4)\\\\5x+17=6x-8

Grouping similar terms together,

5x-6x=-8-17\\\\-x=-25\\\\x=25

Thus, x is 25.

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Jada plans to serve milk and healthy cookies for a book club meeting. She is preparing 12 ounces of milk and 4 cookies per perso
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Jada intends to provide milk and nutritious cookies at a gathering for her book club. She has planned to offer 12 ounces of milk and 4 cookies for each participant. With her included, the total number of club members is 15. Each package of cookies has 24 cookies and is priced at $4.50. A gallon of milk has 128 ounces and costs $3. Let n denote the club members, m for the ounces of milk, c for the cookies, and b for Jada's budget in dollars. Identify all equations that could represent the relevant quantities and constraints in this scenario.

â m = 12(15)

n refers to the club members

b. 3m + 4.5c = 6

c. 4n =

m stands for ounces of milk

& 44.50) = C

c indicates the cookies

e b=2(3) + 3(4.50)

b denotes Jada's budget in

currency

The equations applicable for representing the quantities and constraints in this scenario are:

a) m = 12(15)

c)4n = c

e) b = 2(3) + 3(4.50)

Detailed explanation:

Jada is set to provide milk and nutritious cookies for her book club meeting

She plans to prepare 12 ounces of milk and 4 cookies for each individual

She has 15 members in total

A pack of cookies contains 24 cookies and costs $4.50

A gallon of milk has 128 ounces and costs $3

Designate the total members by n

Ounces of milk = m

The number of cookies = c

Jada's budget in dollars = d

y = 12(15)

Each individual will receive 4 cookies

4n = c

As one pack contains 24 cookies

She requires = 15 × 4 = 60 cookies

60 ÷ 24 = 2.5

Thus, she would need to purchase 3 packs of cookies

She needs = 15 × 12 = 180 ounces of milk

A gallon of milk contains 128 ounces

180 ÷ 128 = 1.406

She will need to acquire 2 gallons of milk

It's noted: from the prompt

Each gallon of milk costs $3

Each package of cookies costs $4.50

b serves as Jada's dollar budget

b = 2(3) + 3(4.50)

<pThe relevant equations that could signify the quantities and constraints in this scenario are:

Options a, c and e are valid

3 0
2 months ago
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