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Murljashka [212]
3 years ago
8

4. Twice the larger of two numbers is three more than five times the smaller. The sum of four times the larger and three times t

he smaller is
71. What are the numbers?
Mathematics
1 answer:
Llana [10]3 years ago
5 0

Answer:

Smaller is 5, larger is 14

Step-by-step explanation:

y is larger, x is smaller

2y = 3 + 5x

4y + 3x = 71

Let's solve for y in the first one, then substitute that into the second one.

y = 3/2 + 5/2x

4(3/2 + 5/2x) + 3x = 71

12/2 + 20/2x + 3x = 71

6 + 10x + 3x = 71

13x = 65

x = 5

Substitute that in to the first equation:

2y = 3 + 5(5)

2y = 3 + 25

2y = 28

y = 14

check those answers in the second equation

4y + 3x = 71

4(14) + 3(5)

= 56 + 15 =71

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Vertical angles must
Nutka1998 [239]

Answer:

see below

Step-by-step explanation:

Vertical angles are formed by two lines and are opposite each other

Vertical angles are equal

6 0
3 years ago
Read 2 more answers
The lemonade recipe calls for 4 scoops of lemonade powder for each quart of water. Each quart is equivalent to 4 cups. Let n rep
tia_tia [17]

Answer:

B. 5 ≤ n≤ 8

f. 10 ≤ S ≤ 16

C. c=2n

d. S = c

Step-by-step explanation:

Jada is making lemonade for a get together with her friends. She expects a total of 5 to 8 people to be there (including herself).?

She plans to prepare 2 cups of lemonade for each person. The lemonade recipe calls for 4 scoops of lemonade powder for each quart of water. Each quart is equivalent to 4 cups. Let n represent the number of people at the get together, c the number of cups of water, S the number of scoops of lemonade powder. Select all the mathematical statements that repsent the quantities and constraints in the situation.

A. 5<n<8

B. 5≤ n≤8

C. c=2n

d. S = c

e. 10<c<16

f. 10≤S≤16

Let

n = number of people at the get together,

c = number of cups of water,

S = number of scoops of lemonade powder.

She expects a total of 5 to 8 people to be there (including herself).

B. 5 ≤ n ≤ 8

She plans to prepare 2 cups of lemonade for each person.

With minimum of 5 people and maximum of 8 people

2 × 5 = 10

2 × 8 = 16

f. 10≤S≤16

The number of cups of water is twice the number of people at the party

C. c=2n

Number of scoops of lemonade powder is equivalent to number of cups of water

d. S = c

4 0
2 years ago
How to find the θ in this equation: tan(θ+16°)=1/tan(θ+60°) by using the trigonometric identities?thanks
DedPeter [7]

Answer:

\huge \theta  =7°

Step-by-step explanation:

tan( \theta + 16 \degree) =  \frac{1}{tan( \theta + 60 \degree) }  \\ tan( \theta + 16 \degree) =cot( \theta + 60 \degree) \\ tan( \theta + 16 \degree) = tan \{90 \degree - (\theta + 60\degree) \} \\ \theta + 16 \degree = 90 \degree - \theta  -  60\degree \\ \theta +\theta  = 30 \degree - 16\degree \\2 \theta  = 14 \degree  \\ \theta  =  \frac{14 \degree}{2}   \\   \huge \red{ \boxed{\theta  =7 \degree}}

7 0
3 years ago
Runners in a long distance race start out going 6 kilometers east and then head north for the remainder of the race. The finish
Harrizon [31]

Answer:

Step-by-step explanation:

alright lets get started.

Please refer the diagram I have attached.

the runner traveled, six kilometers east.

Next, they turn to north and suppose they run x kilometers.

The starting and the ending points distance is 10 kilometers.

There will be a right triangle formed, we can find the value of x by using Pythagorean theorem.

a^2+b^2=c^2

6^2+x^2=10^2

36+x^2=100

Subtracting 36 from both sides

x^2=100-36=64

x=8

So, the runners travel 8 kilometers to the north.     :    answer

Hope it will help.  :)

6 0
3 years ago
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stiks02 [169]

Answer:

2) No function

3) Function: y=30x

Domain: x≥0

Range: y≥0

4) Function: y=160

Domain: x≥20

Range: y=160

Step-by-step explanation:

7 0
3 years ago
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