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jek_recluse [69]
3 years ago
6

PLEASE HELP FAST!!!! Fill in the blanks Solve using the elimination method

Mathematics
1 answer:
Rainbow [258]3 years ago
6 0

Answer: Look below

Step-by-step explanation:

1(10x-6y)=-16

3(5x+2y)=66

10x-6y=-16

15x+6y=66

-25x=50

x=-2

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Four time a number r plus half a number s equals 12. Twice the number r plus one fourth of the numbers s equals 8. What are the
Snezhnost [94]

The system of equations have no solution.

Explanation:

The equations are 4r+\frac{1}{2}s=12 and 2r+\frac{1}{4} s=8

To find the two numbers, let us solve the equations using substitution method.

From the equation 2r+\frac{1}{4} s=8, let us determine the value of r,

$\begin{aligned} 2 r+\frac{1}{4} s &=8 \\ 2 r &=8-\frac{1}{4} s \\ r &=\frac{1}{2}\left(8-\frac{1}{4} s\right) \\ r &=4-\frac{1}{8} s \end{aligned}$

Let us substitute the value of r in 4r+\frac{1}{2}s=12, we get,

$\begin{aligned} 4\left(4-\frac{1}{8} s\right)+\frac{1}{2} s &=12 \\ 16-\frac{1}{2} s+\frac{1}{2} s &=12 \\ 16 &=12 \end{aligned}$

which is not possible.

This means that the system has no solution.

6 0
3 years ago
This problem has been solved!See the answerA municipal bond service has three rating categories (A, B, and C). Suppose that in t
mariarad [96]

Answer:

a. \frac{35}{51}

b. \frac{51}{100}

c. \frac{1}{5}

Step-by-step explanation:

Suppose cities represented by C', suburbs represented by S and rural represented by R,

Let x be the total number of bonds issued throughout the US,

According to the question,

n(A) = 70% of x = 0.7x,

n(B) = 10% of x = 0.1x,

n(C) = 20% of x = 0.2x,

n(A∩C') = 50% of n(A) = 0.5 × 0.7x = 0.35x,

n(A∩S) = 20% of n(A) = 0.2 × 0.7x = 0.14x,

n(A∩R) = 30% of n(A) = 0.3 × 0.7x = 0.21x,

n(B∩C') = 40% of n(B) = 0.4 × 0.1x = 0.04x,

n(B∩S) = 30% of n(B) = 0.3 × 0.1x = 0.03x,

n(B∩R) = 30% of n(B) = 0.3 × 0.1x = 0.03x,

n(C∩C') = 60% of n(C) = 0.6 × 0.2x = 0.12x,

n(C∩S) = 15% of n(C) = 0.15 × 0.2x = 0.03x,

n(C∩R) = 25% of n(C) = 0.25 × 0.2x = 0.05x,

n(C') = n(A∩C')  + n(B∩C')  + n(C∩C')  = 0.35x + 0.04x + 0.12x = 0.51x

n(S) = n(A∩S) + n(B∩S) + n(C∩S) = 0.14x + 0.03x + 0.03x = 0.20x

a. The probability that it will receive an A rating, if a new municipal bond is to be issued by a city,

P(\frac{A}{C'})=\frac{P(A\cap C')}{P(C')}=\frac{0.35x/x}{0.51x/x}=\frac{0.35}{0.51}=\frac{35}{51}

b. The proportion of municipal bonds are issued by cities = \frac{n(C')}{x}

=\frac{0.51x}{x}

=\frac{51}{100}

c. The proportion of municipal bonds are issued by suburbs = \frac{n(S)}{x}

=\frac{0.20x}{x}

=\frac{20}{100}

=\frac{1}{5}

3 0
3 years ago
What number is 12% of 315
goldenfox [79]

Answer:

12% of 315 is 37.8 :) Tag me if I'm wrong

6 0
2 years ago
Read 2 more answers
PLSSS HELP ME!!!!!!!!!!! I WILL MARK U!!!!!
max2010maxim [7]

Answer:

a2

Step-by-step explanation:

you're using the pythagorean theorem

8 0
3 years ago
Write a function rule for the area of a triangle whose base is 4 ft more than the height. What is the area of the triangle when
solong [7]

Answer:

A) Area as function of H ,

     F'(a) = 2 +H

B) Area of triangle with height 6ft = 30 ft²      

Step-by-step explanation:

Given as for a triangle ,

Let the height of triangle = H ft

And base = 4 ft + H ft

Now area of triangle = \frac{1}{2} × height  × base

                          F (a) =  \frac{1}{2} × H × ( 4ft + H ft)

Or,                      F (a) =  \frac{1}{2} × ( 4H + H² )

Now,   here Area is function of height ,

So ,                    F'(a) = \frac{1}{2}(4 + 2H)

Hence Area as function of H ,

                          F'(a) = 2 +H

Now For height = 6 ft

Area of triangle = \frac{1}{2} × height × base

                          = \frac{1}{2} × H × ( 4ft + H ft)

                          = \frac{1}{2} × ( 4H + H² )

                          =  \frac{1}{2} × ( 24 + 36 )

                          = \frac{1}{2} × ( 60 )

                          = 30 ft²

Hence Area of triangle with height 6ft = 30 ft²      Answer

6 0
3 years ago
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