What is the solution to the system of linear equations?

6x+7y=59

4x+5y=41 how do you do it

Answers

Answer 1

Answer:

The correct answer is 4, 5 :)

Step-by-step explanation:

Answer 2

A system of linear equations can be solved by elimination, substitution or using graphs.

The values of x and y for [tex]6x + 7y= 59[/tex] and [tex]4x + 5y =41[/tex] are 4 and 5, respectively.

Given

[tex]6x + 7y= 59[/tex]

[tex]4x + 5y =41[/tex]

Make x the subject in [tex]4x + 5y =41[/tex]

[tex]4x = 41 - 5y[/tex]

Divide by 4

[tex]x = \frac 14(41 - 5y)[/tex]

Substitute [tex]x = \frac 14(41 - 5y)[/tex] in [tex]6x + 7y= 59[/tex]

[tex]6 \times \frac 14(41 - 5y)+ 7y = 59[/tex]

[tex]\frac 32(41 - 5y)+ 7y = 59[/tex]

Multiply through by 2

[tex]2 \times \frac 32(41 - 5y)+ 2 \times 7y = 2 \times 59[/tex]

[tex]3(41 - 5y)+ 14y = 118[/tex]

Open brackets

[tex]123 - 15y+ 14y = 118[/tex]

Collect like terms

[tex]- 15y+ 14y = 118 - 123[/tex]

[tex]-y = -5[/tex]

[tex]y = 5[/tex]

Substitute [tex]y = 5[/tex] in [tex]x = \frac 14(41 - 5y)[/tex]

[tex]x = \frac 14(41 - 5 \times 5)[/tex]

[tex]x = \frac 14(41 - 25)[/tex]

[tex]x = \frac 14(16)[/tex]

[tex]x = 4[/tex]

Hence, the solution to the system of linear equations is:

[tex]x = 4[/tex]

[tex]y = 5[/tex]

Read more about system of linear equations at:

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Related Questions

A line passes through the point (–2, 7) and has a slope of –5. What is the value of a if the point (a, 2) is also on the line?
A.–7
B.–1
C.1
D.7

Answers

Answer:

The correct option is B.

Step-by-step explanation:

The slope of a line is constant.

If a line passes through two points then the slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

It is given that the line passes through (-2,7) and (a,2).

Using the above formula the slope of the line is

[tex]m=\frac{2-7}{a-(-2)}[/tex]

[tex]m=\frac{-5}{a+2}[/tex]

It is given that the slope of the line is -5. Substitute m=-5 in the above equation.

[tex]-5=\frac{-5}{a+2}[/tex]

On cross multiplication we get

[tex]-5(a+2)=-5[/tex]

Divide both sides by -5.

[tex]a+2=1[/tex]

Subtract 2 from both the sides.

[tex]a=1-2[/tex]

[tex]a=-1[/tex]

The value of a is -1. Therefore the correct option is B.

Answer:

The answer is B.

Step-by-step explanation:

what hourly rate does the repair shop charge for labor?

Answers

its two hundred bucks

The mechanic's hourly rate is $55.

Understanding Labor Costs in a Repair Shop

To determine the hourly rate a repair shop charges for labor, we must analyze the information given and apply simple arithmetic operations. According to the examples provided, an auto mechanic charges a flat fee and an hourly rate for labor. For instance, a mechanic charging a flat fee of $75 per car, plus an hourly rate of $55 can be represented by the linear equation y = 75 + 55x, where 'y' is the total labor charge, and 'x' is the number of hours worked.

Example Calculation

Using the equation above, if the job takes 3.5 hours, the labor charge (y) would be calculated as $75 + ($55  imes 3.5) = $75 + $192.50 = $267.50. Hence, we can infer that the mechanic's hourly rate is $55.

Could -2 be used as a base to rewrite 32? 64? Why or why not?

Answers

Since a base means that a value can be to the power of something to equal another number, we can try with -2. (-2)^1=-2, (-2)^2=4, (-2)^3=-8, (-2)^4=16, (-2)^5=-32, and  (-2)^6=64. If a value (x) to the power of something (y) is equal to something (z), then x cannot be to the power of any number to equal -z unless x is -1. Therefore, since x=/ -1 in this case, -2 cannot be a base of 32 but it can be for 64

The equation 14m = 400.40 can be used to find the cost per yard m, in dollars, of mulch. what is the value of m? m = $

Answers

14m = 400.40
14m ÷14 = 400.40 ÷ 14
m = 28.60

If f(x)=3/x+2-root x-3 complete the following statement (round answer to the nearest hundredth) f(7)=

Answers

hello : 
 f(x) = 3 /(x+2)  -  √(x-3)
f(7 ) = 3/(7+2) - √(7-3)
f(7) = 1/3 - √2  = 0.33 - 1.41 = - 1.1

90 points correct answer

If the parent function f(x) = x2 is modified to g(x) = 2x2 + 1, which statement is true about g(x)?


It is an even function.



It is an odd function.



It is both an even and an odd function.



It is neither an even nor an odd function.

Answers

A is the answer
hope it helps
The answer is A because the function is even itself.

The population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 7 years, how long will it take to triple? (round your answer to one decimal place.)

Answers

Final answer:

To determine how long it will take for the population to triple, we need to solve the equation 3P0 = P0e^(rt) for t. Rounding the answer to one decimal place, it will take approximately 10.1 years for the population to triple.

Explanation:

To solve this problem, we can use the equation P = P0e^(rt), where P is the population at a given time, P0 is the initial population, e is the base of the natural logarithm (approximately 2.71828), r is the growth rate, and t is the time in years.

In this case, the population has doubled in 7 years, so we can write the equation as 2P0 = P0e^(r*7). We need to solve for r.

Dividing both sides of the equation by P0 gives us 2 = e^(7r). Taking the natural logarithm of both sides gives us ln(2) = 7r. Solving for r, we find that r ≈ ln(2)/7.

Now, to determine how long it will take for the population to triple, we need to solve the equation 3P0 = P0e^(r*t) for t. Substituting the value of r we found, we get 3 = e^((ln(2)/7)*t). Taking the natural logarithm of both sides to solve for t, we have ln(3) = (ln(2)/7)*t. Solving for t, we find that t ≈ 7 * ln(3)/ln(2). Rounding the answer to one decimal place, it will take approximately 10.1 years for the population to triple.

It takes approximately 11.1 years for the population to triple.

The population growth can be modeled by the exponential function [tex]P(t)=P_0 \times e^{k t}[/tex], where [tex]P_0[/tex] is the initial population, k is the growth rate, and t is time.

In this case, since the population doubles in 7 years, we have the relationship P(7) = 2 x [tex]P_0[/tex].

[tex]P(7)=P_0 \times e^{7 k}[/tex]

[tex]2 \times P_0=P_0 \times e^{7 k}[/tex]

Divide both sides by [tex]P_0[/tex].

[tex]2=e^{7 k}[/tex]

Take the natural logarithm (ln) of both sides to solve for k:

ln(2) = 7k

[tex]k=\frac{\ln (2)}{7}[/tex]

Now that we have the growth rate k, we can use it to find the time it takes for the population to triple.

[tex]P(t)=P_0 \times e^{k t}[/tex]

For tripling, [tex]P(t)=3 \times P_0[/tex].

[tex]3 \times P_0=P_0 \times e^{k t}[/tex]

[tex]3=e^{k t}[/tex]

Take the natural logarithm again:

ln(3) = kt

[tex]t=\frac{\ln (3)}{k}[/tex]

Substitute the value of k we found earlier:

[tex]t=\frac{\ln (3)}{\frac{\ln (2)}{7}}[/tex]

Using natural logarithm values:

[tex]t \approx \frac{1.0986}{\frac{0.6931}{7}}[/tex]

[tex]t \approx \frac{1.0986}{0.0990}[/tex]

t ≈ 11.09

Which graph represents the system of inequalities?

Answers

I think it's C.
sorry if i'm wrong
an easy way is to test points
try (0,0), if it's true then the answer is C
it's false, not C

try (-4,5), if it's true, it's D
it's false, it's not D

try (1,4), if it's true, it's A
it's true

answer is A

If a(x)=3x+1 and b(x)=

Answers

b°a means that we plug a into the x value of b and go from there. In this case, we get [tex] \sqrt{(3x+1)-4} = \sqrt{3x-3} = \sqrt{3(x-1)} [/tex] (using the distributive property) and we have to figure out what the domain is. The domain is what x can equal, and since you can't have a square root of a negative number, 3(x-1) has to be greater than or equal to 0. Solving for that, we get 3(x-1)≥0. Dividing both sides by 3, we get x-1≥0. Next, we can add 1 to both sides to get x≥1. In interval notation, [1 encompasses 1 while (1 is everything above 1. In addition, it doesn't have to be less than anything, so we have ∞) at the end, making it [1, ∞). We have the parenthesis at the end because it doesn't include infinity, but everything less than it

The answer is C. [1, ∞] on edge

let f(x)=4x-7 and g(x)-5+9x. what are f+g and f-g? what are their domains?

Answers

the answer is 13x-12 f-g is -5x-2 and the domains are all real numbers i believe the multiply is [tex] 36x^{2} -83x-35[/tex] and divide i'm not sure sorry hope the rest helps though':p

Which equation is equivalent to
X/ +11 = 15

Answers

√x + 11=15 x=16
√x= 15-11 x=16

24% of 1321 is how much? round the answer to the nearest hundredth

Answers

1,321/31% is equal to 317.04
24% of 1,321 would be 317.04.

A quota is when one country

Answers

A quota is when one country limits the amount of a good that can be imported from another country.
This is done in order to give prominence to domestic suppliers and producers. If you limit the amount of foreign goods, then its price will rise, which will make consumers buy more domestic goods and thus help develop domestic trade.

Find the value of x in the equation 2√ x
a. –5
b. 1
c. 16
d. 25 11. simplify the expression .
a.
b.
c.
d. + 20 = 15 + 3√ x

Answers

the answer to that question would be a c d

Is g(x)= 5 + 6/x a linear function

Answers

No. A linear function must be in the form f(x)= mx+b. Anytime you divide by x, the result when graphed is no longer linear. In fact, this is a reciprocal function.

The sum of -4 and 8 times a number is multiplied by 3. The result is 15 less that 25 times the number. What is the number?

A) -12
B) 6/7
C) 0
D) 3
E) none of the above

Answers

3(-4 + 8x) = 25x - 15
-12 + 24x = 25x - 15
25x - 24x = -12 + 15
 x = 3

answer is
D) 3

Tom and Rob are brothers who like to make bets about the outcomes of different contests between them. Before the last bet, the ratio of the amount of toms money to the amount of robs money was 4:7. Rob lost the latest competition, and now the ratio of the amount of robs money is 8:3. If rob had $280 before the last competition, how much rob have now that he lost the bet?

Answers

After Rob has lost, he will have 120 dollars.

before the bet Rob had 7 out of 11 ( 4+7)

280/7 = 40

after bet Rob had 3

3*40 = 120

 he has $120

6=x+2/3

Please help ASAP!!! 10 Points!!! :)

Answers

x=18 you multiply 2/3 by its reciprocal 3/2 which cancels it and then multiply 6 by 3 which gives you 18
The answer is x= 16/3. I hope this helps love! :)

Kwamee bought kona beans that cost 11.00 and bought fuji beans that cost 7.50.he bought a total of 23 pounds of coffee and it cost 197.00 write a system of equations to solve how many pounds of kona and fuji beans kwamee bought

Answers

k= kona beans. f= fugi beans

k + f= 23. ==> -75k - 75f= -1725
11k + 7.5f= 197 ==> 110k + 75f= 1970

35k = 245
k= 7 lb of kona beans

7 + f = 23
f= 16 lb of fugi beans

Find the quotient.

110/10=

Answers

110/10 
the / means divide 
110 divided by 10 is 11.

The quotient is 11.

Hope this helps.

The product of (a − b)(a − b) is a2 − b2.

Sometimes

Always

Never

Answers

Final answer:

The statement that the product of (a − b)(a − b) equals [tex]a^2 - b^2[/tex] is never true; the correct product is always [tex]a^2 - 2ab + b^2[/tex], representing the square of a difference formula.

Explanation:

The statement "The product of (a − b)(a − b) is  [tex]a^2 - b^2[/tex]." is never true. Instead, using the distributive property to expand the expression (a − b)(a − b) yields a different result, as each term in the first binomial must be multiplied by each term in the second binomial.

The correct expansion is:

(a − b)(a − b) = a(a − b) - b(a − b)= aa - ab - ba + bb=  [tex]a^2 - 2ab + b^2[/tex](since ab and ba are equivalent)

Thus, the product of (a − b)(a − b) is always  [tex]a^2 - 2ab + b^2[/tex], which is the square of a difference formula, not  [tex]a^2 - b^2[/tex] which is the difference of squares formula. The latter is applicable to the product (a + b)(a - b).

What's the parabola in vertex for for (-5,0) and has a vertex (-2,1)

Answers


hello :
the parabola's equation is : f(x) = a(x+2)²+1

but ; f(-5) = 0
0 = a(- 5+2)²+1
9a+1=0.....a= -1/9
f(x) = (-1/9)(x+2)²+1

Including a 8 %8% sales​ tax, an inn charges $ 135$135 per night. Find the​ inn's nightly cost before the tax is added.

Answers

that would be $135 / 1.08  =   $125

How to find mass when given density and volume?

Answers

mass equals density times volume

The perimeter of a square garden is to be at least 20 ft but no more than 32 ft. find all possible values for the lengths of its sides using a compound inequality

Answers

20 < = 4a < = 32
20/4 < = (4/4)a < = 32/4
5 < = a < = 8

so the squares perimeter can be at least 5 ft but no more then 8 ft

Answer:

Answer in pic

Step-by-step explanation:

Summer paints a room that has 400 square feet of wall space in 2.5 hours. at this rate, how long will it take her to paint a room with 720 square feet of wall space?

Answers

400/2.5 = 160 sq feet every hour

720 sq ft/160 sq ft = 4.5 hours

How to solve equations

Answers

Here are some things you should know when solving algebraic equations.

If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.

You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.

To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.

The distributive property is another important rule you will need to understand.

The distributive property is used mostly for simplifying parentheses in expressions/equations. 

For example, how would you get rid of the parentheses here?

6(x + 1)

If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves.
The distributive property states that a(b + c) = ab + ac
So, now we can simplify our expression.

6(x + 1) = 6x + 6

If the federal reserve decreases the reserve rate from 7% to 5%, how does this affect the amount of money that would result because of fraction-reserve rbanking from an initial deposit into a bank of $30,000

Answers

If the federal reserve rate was 7%, the money supply would be
30,000÷0.07=428,571

If the federal reserve rate was 5%, the money supply would be
30,000÷0.05=600,000

If the federal reserve decreases the reserve rate from 7% to 5%
600,000−428,571=171,429
The money supply increases by 171429

Hope it helps!
Final answer:

When the Federal Reserve decreases the reserve rate from 7% to 5%, the amount of money resulting from fraction-reserve banking increases. In this case, an initial deposit of $30,000 would result in $28,500 due to the change in reserve rate.

Explanation:

When the Federal Reserve decreases the reserve rate from 7% to 5%, it means that banks are required to hold a smaller percentage of deposits as reserves. This change allows banks to lend out a larger portion of the initial deposit. In this case, if the initial deposit into a bank is $30,000, the amount that would result from fraction-reserve banking would increase because the bank can now lend out a greater percentage of the deposit.



To calculate the new amount that would result from fraction-reserve banking, we need to calculate the reserve amount and the loan amount.



Calculate the reserve amount by multiplying the initial deposit ($30,000) by the new reserve rate (5%):

Reserve amount = $30,000 * 0.05 = $1,500

Calculate the loan amount by subtracting the reserve amount from the initial deposit:

Loan amount = $30,000 - $1,500 = $28,500



Therefore, the amount that would result from fraction-reserve banking from an initial deposit of $30,000 would be $28,500.

Learn more about Federal Reserve reserve rate and fraction-reserve banking here:

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Jen bought 5 cds for 57.50. What was the unit price

Answers

57.5/5 = 11.5

$11.50

Hope this helps!

Find the value of x for which l is parallel to m. The diagram is not to scale.
a. 31
b. 62
c. 93
d. 149

Answers

If we continue the  line which comes from line segment  I till we reach line n  then the angle formed will be 31 degrees ( interior alternate to 31 degrees)

x + 31 = 62 ( external angle of a triangle theorem).

Therfore x = 31 degrees answer
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