The system of equations shown below is graphed on a coordinate grid:

3y + x = 6
2y − x = 9

Which statement is true about the coordinates of the point that is the solution to the system of equations? (5 points)



Hint: Add the two equations and use inverse operations. When you have your y-value, plug it into any of the original equations to find your x-value.

a
It is (−6, 4) and lies on both lines.

b
It is (−3, 3) and lies on both lines.

Answers

Answer 1
b) It is (-3, 3) and lies on both lines.

Step-by-Step Explanation;

Lets solve using Elimination Method;

=> 3y + x = 6 (Eq. 1)
=> 2y - x = 9 (Eq. 2)

Adding Eq. 1 and 2, we get :-

5y = 15 (‘x’ gets Eliminated)
=> y = 15/5 = 3

Therefore, y = 3

Substitute value of ‘y’ in Eq. 1 :-

3y + x = 6
3(3) + x = 6
9 + x = 6
x = 6 - 9
=> x = -3

Therefore, x = -3

This can be written as an ordered pair as (-3, 3) where the ‘x’ coordinate is the value if x and the y coordinate is the value of ‘y’.



Related Questions

please help! this is due soon and im a bit confused

Answers

Just take the x and do what the word problem says. Number one would be 15+X
Two would be 70-y and so on

in order to make a specific shade of green paint a panter mixes 1 1/2 quarts of blue paint 2 cups of green paint and 1/2 gallion of white paint how much of each collor is needed to make 100 cups of this shade of green paint

Answers

Answer:

37.5 cups of blue

12.5 cups of green

50 cups of white

help will give brainliest

Answers

Answer:

0.7°

Step-by-step explanation:

From the figure:

CF = 4000.2 miles, CE = 4000.01 miles

so FT = √CF² - CT², TE = √CE² - CT²

so FT = 40 miles, TE = 8.94 miles

so ½ × 4000.2 × 4000.01

xsin angle FCE = ½ × 4000 × 140 + 8.94

so sin angle FCE = 0.0122

so angle FCE = 0.7°

so m SB = 0.7°

HOPE THIS HELPS AND HAVE A NICE DAY <3

3Your new mobile phone costs £360.
The probability you leave it on the bus is 0.1.
The probability someone will hand it in to lost property and you will recover it
is 0.4.
The cost of insurance to cover the loss of the phone is £30.
Should you pay for this control measure?
List any assumptions that you make

Answers

Assuming you have to pay 30 pounds for somebody handing it in to lost property, you'll have a 0.5 probability that you'll have to pay the 30 pounds if you lose the phone.
Also assuming there are no other ways to lose your phone, you have a 0.5 probability (50% chance?) to lose your phone.
Also assuming the "control measure" is the insurance and you won't have to pay a larger amount, you'll probably be better off paying the 30 pounds instead of the larger amount because you have such a high chance of losing your phone.
I apologize if I misunderstood the question.

Billy has 10 bouncy balls. His brother has 30 bouncy balls. He washed 10 of his and 10 of his brother. How many bouncy balls do they have left?

Answers

Answer:

20

Step-by-step explanation:

10 + 30 = 40

40 - 10 = 30

30 - 10 = 20

answer is 20

Answer:

20 bouncy Balls!

Step-by-step explanation:

10+30 - 20 = 20

Roberta grows pea plants, some in shade and some in sun. she picks 8 plants of each type at random and
records the heights.
shade plant heights (in.) 7 12 7 10 8 12 8 8
sun plant heights (in.) 19 24 21 22 23 19 20 20
express the difference in the means as a multiple of their ranges.
the difference in the means is times the ranges.

Answers

Difference is 12 I took the test and got it right

Of the last 15 people at a carnival booth, 6 won a prize. what is the experimental probability that the next person at the booth will win a prize?

Answers

Answer:

40% or 2/5

Step-by-step explanation:

won = 6

total no. of people = 15

probability of winning = 6/15 = 2/5

2/5*100

=40%

Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1? f(x) = 3(x 4)(x – i)(x – 2) f(x) = (x – 3)(x 4)(x – i)(x – 2) f(x) = (x – 3)(x 4)(x – i)(x i)(x – 2) f(x) = 3(x 4)(x – i)(x i)(x – 2)

Answers

The polynomial function with leading coefficient of 3 and root -4, i, and 2 all with multiplicity of 1 is f(x) = 3(x+4)(x-i)(x+2)

Polynomial function

The Leading coefficients are the numbers written in front of the variable with the largest exponent.

Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero.

The multiplicity is the number of times a given factor appears in the factored form of the equation of a polynomial.

Therefore, the polynomial f(x) = 3(x+4)(x-i)(x+2) has a root -4 , 1 and -2.

The leading coefficient is 3. The multiplicity is all one.

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Answer:

d

Step-by-step explanation:

What is the value of x innthe equation 1.5(x+4)-3=4.5(x-2)

Answers

[tex]~~~~~~1.5(x+4)-3 = 4.5(x-2)\\\\\implies 15(x+4) -30 =45(x-2)~~~~~~~~;[\text{Multiply both sides by 10]}\\\\\implies 3(x+4)-6=9(x-2)~~~~~~~~~~;[\text{Divide both sides by 5]}\\\\\implies 3x+12-6=9x-18\\\\\implies 3x+6=9x-18\\\\\implies 9x-3x = 18+6\\\\\implies 6x = 24\\\\\implies x = \dfrac{24}6\\\\\implies x =4[/tex]

Write the product using exponents.

Answers

Answer:

3^4

Step-by-step explanation:

because I took the test

The product of two consecutive integers is 72. the equation x(x 1) = 72 represents the situation, where x represents the smaller integer. which equation can be factored and solved for the smaller integer? x2 x – 72 = 0 x2 x 72 = 0 x2 2x – 72 = 0 x2 2x 72 = 0

Answers

The equation that can be factored and solved for the samller integer is x² + x - 72 = 0

How to form an equation?

The product of two consecutive integers is 72. The equation that represents the situation is as follows:

x(x + 1) = 72

where

x = smaller number

Therefore,

x(x + 1) = 72

x² + x = 72

x² + x - 72 = 0

Therefore, the equation that can be factored and solved for the samller integer is x² + x - 72 = 0

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• A bag contains 5 orange, 3 yellow, and 5 black marbles. What are the odds of picking an orange marble?​

Answers

Answer:

The odds will be 5/13.

Step-by-step explanation:

There are 13 marbles total in this situation. 5 orange, 3 yellow and 5 black (5+3+5) will give us 13 as our overall total. Now, because we have 5 orange marbles available, we'll write this as a 5/13 odds/ chance of picking an orange marbles because it is how many orange marbles are present over how many marbles there are total.

Also! You can't simplify this any further, thus you'd have 5/13 odds.

what is the initial value of the linear relationship of -2, 3

Answers

Answer: Based on the graph, what is the initial value of the linear relationship?
A coordinate plane is shown. A line passes through the x axis at negative 3 and the y axis at 5.
−4
−3
five over three
5

If point a is at (-1,2) and point b is at (11,-7), what is length of line ab?

Answers

Answer:

15

Step-by-step explanation:

Distance formula: [tex]d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]

Plug in (-1,2) and (11, -7):

[tex]d=\sqrt{(11-(-1)^{2}+(-7-2)^{2} } = d=\sqrt{(12)^{2}+(-9)^{2} }=\sqrt{144+81} = \sqrt{225} = 15[/tex]

Will mark branlyest (Polynomial Functions)
1. Find the zeros: 2x^2 + 12x + 18 = 0
A . {-3}
B .{3}
C .{-9}
D.{-3,3}
2. Find the x-intercepts: 2r^2 = 5r + 3
A. {-1/2,3}
B.{-1/2,-3
C.{1/2,3}
D.{1/2,-3}

Answers

Answer:

1. A

2. A

Step-by-step explanation:

Question 1

1 Factor out the common term 2.

2(x^2+6x+9)=0

2 Rewrite x^2+6x+9 in the form a^2+2ab+b^2a, where a=x and b=3.

2(x^2+2(x)(3)+3^2)=0

3 Use Square of Sum: (a+b)^2=a^2+2ab+b^2(a+b).

2(x+3)^2=0

4 Divide both sides by 2.

(x+3)^2=0

5 Take the square root of both sides.

x+3=0

6 Subtract 3 from both sides.

x=-3

Question 2

1 Move all terms to one side.

2r^2-5r-3=0

2 Split the second term in 2r^2-5r-3 into two terms.

2r^2+r-6r-3=0

3 Factor out common terms in the first two terms, then in the last two terms.

r(2r+1)-3(2r+1)=0

4 Factor out the common term 2r+1.

(2r+1)(r-3)=0

5 Solve for r.

r=-1/2,3

PLEASE HELP ME I NEED ANSWERS

Answers

70 is the area of the polygon

8 3/4 - 5 2/3 what is the answer

Answers

Answer:

3 1/12

Step-by-step explanation:

math help questions

Answers

After 1 year, the initial investment increases by 7%, i.e. multiplied by 1.07. So after 1 year the investment has a value of $800 × 1.07 = $856.

After another year, that amount increases again by 7% to $856 × 1.07 = $915.92.

And so on. After t years, the investment would have a value of [tex]\$800 \times 1.07^t[/tex].

We want the find the number of years n such that

[tex]\$856 \times 1.07^n = \$1400[/tex]

Solve for n :

[tex]856 \times 1.07 ^n = 1400[/tex]

[tex]1.07^n = \dfrac74[/tex]

[tex]\log_{1.07}\left(1.07^n\right) = \log_{1.07}\left(\dfrac74\right)[/tex]

[tex]n \log_{1.07}(1.07) = \log_{1.07} \left(\dfrac74\right)[/tex]

[tex]n = \log_{1.07} \left(\dfrac74\right) = \dfrac{\ln\left(\frac74\right)}{\ln(1.04)} \approx \boxed{8.3}[/tex]

Answer:

25 years

Step-by-step explanation:

total = before × percent ( in decimal ) × time

1400 = 800 × 0.07 × t

1400 = 56 × t

1400 ÷ 56 = 25

t = 25

Hope this was helpful!

If h(x) = 5 x and k (x) = startfraction 1 over x endfraction, which expression is equivalent to (k circle h) (x)? startfraction (5 x) over x endfraction startfraction 1 over (5 x) endfraction 5 (startfraction 1 over x endfraction) 5 (5 x)

Answers

The composition of the two given functions is:

(k°h)(x) = 1/5x

How to get the composition of the functions?

Here we have the functions h(x) = 5x and k(x) = 1/x.

We want to get (k°h)(x), which is equal to:

k(h(x))

Then we have:

k(h(x)) = 1/h(x)

Replacing h(x) we get:

k(h(x)) = 1/h(x) = 1/(5x)

So the composition is just one over 5x.

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The spinner is divided into 8 equal-sized sections. enter the probability of the arrow landing on a section labeled 4 on the first spin

Answers

Answer: 1/8

Step-by-step explanation:

Tanisha owns a small business selling bagels. She knows that in the last week 61 customers paid cash, 5 customers used a debit card, and 45 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash as a decimal to the nearest hundredth.

Answers

Answer:

The probability as a decimal to the nearest hundredth is 0.550.55.

Step-by-step explanation:

61 cash, 5 debit card, and 45 credit card.

\color{steelblue}{61}+5+45=

61+5+45=

\,\,\color{indianred}{111}

111

There were a toal of 111 customers. 61 paid with cash.

Probability the next customer will pay with cash:

\frac{\color{steelblue}{61}}{\color{indianred}{111}}=

111

61

=

\,\,0.549549...

0.549549...

\approx

\,\,0.55

0.55

Round to the nearest hundreth

The probability that the next customer will pay with cash is 0.55.

What is the formula for probability?

Probability is the ratio of the number of favorable events divided by the total outcome.

We have, given that, Tanisha owns a small business selling bagels. She knows that in the last week 61 customers paid cash, 5 customers used a debit card, and 45 customers used a credit card.

The total number of payments is,

61+45+5=111.

We have to find the probability that the next customer will pay with cash as a decimal to the nearest hundredth.

The number of the favorable outcome for the customer will pay with cash is 61, and the total number of outcomes is 111.

Therefore, the probability is,

P(A)=61/111

P(A)=0.5495.

Therefore, the probability of the nearest hundredth is 0.55.

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Evaluate each expression.
6! =
3! - 2!=
61/
3!
=

Answers

Answer:

6! = 720

3! - 2! = 4

6! ÷ 3! = 120

Step-by-step explanation:

I used a calculator.  ^v^

Evaluate for f(-2)
f(x) = 3/2x - 4

Answers

Answer:

f(-2) = -7

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Functions

Function Notation

Step-by-step explanation:

Step 1: Define

Identify given function.

[tex]\displaystyle f(x) = \frac{3}{2}x - 4[/tex]

Step 2: Find f(-2)

[Function] Substitute in x:
[tex]\displaystyle f(-2) = \frac{3}{2}(-2) - 4[/tex]Multiply:
[tex]\displaystyle f(-2) = -3 - 4[/tex]Subtract:
[tex]\displaystyle f(-2) = \boxed{ -7 }[/tex]

∴ the function when x = -2 is equal to -7.

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Topic: Algebra I

The image is the question

Answers

Answer:

6h^2 - 19h + 15

Find two numbers that their sum is -19 and their product is 90.

Hence, the numbers will be -9 and -10

6h^2 - 9h - 10h + 15

3h(2h - 3) -5(2h - 3)

(2h - 3)(3h - 5)

The half-life of a certain radioactive material is 36 days. An initial amount of the material has a mass of 487kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.

Answers

Answer:

442.302 kg

Step-by-step explanation:

amount = 487 (1/2)^(t/36) where t is the number of days.

if t = 5

amount = 487(.5)^(5/36)

= 442.302 kg

Gerda discovers that the lifetime of light bulbs is normally distributed with mean 1000 hours and standard deviation 100 hours. if gerda buys 50 bulbs, how many of them are expected to last less than 800 hours? give your answer correct to the nearest integer.

Answers

At least 50 of them are bound to last that much and she is on the right track and keep going you should get it soon

In a right-angled triangle, the sum of the squares of the three sides is 72. What is the length of the hypotenuse?

Answers

Answer:

The hypotenuse has a length of 6

Step-by-step explanation:

Remark

The first step is to create the 2 equations needed to solve this problem.

Then substitute one into the other.

Equations

c^2 + a^2 + b^2 = 72  

c^2 = a^2 + b^2

Solution

c^2 + a^2 + b^2 = 72             The sum of the sides each squared of a right triangle = 72

c^2 = a^2 + b^2                      The pythagorean theorem says the hypotenuse of the right triangle = the sum of the squares of two smaller sides. You can substitute the hypotenuse squared into the top equation for a^2 + b^2

c^2 + c^2 = 72

2c^2 = 72

c^2 = 36

c = 6.                      minus 6 is meaningless

Rectangular prism B is the image of rectangular prism A after dilation by a scale factor of 5. If the volume of rectangular prism B is 5125 km°, find the volume of rectangular prism A, the preimage

Answers

The volume of the rectangular prism A, the preimage is 41km^3

How to determine the volume?

The given parameters are:

Volume B = 5125km^3

Scale factor, k = 5

The volume of B is calculated using:

B = A * k^3

So, we have:

5125 =  A * 5^3

Divide both sides by 5^3

A = 41

Hence, the volume of rectangular prism A, the preimage is 41km^3

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Carl makes $10.25 per hour, h, plus a daily bonus of $25. Which equation represents his total earnings, t, each day?​

Answers

Answer:

10.25 × h + 25= t

Step-by-step explanation:

he gets 10.25 for every hour, so you do 10.25 × h, than for his extra bonus of 25 dollars a day, you add 25. than t shows the final earnings

What’s the area formula, of 48m

Answers

Answer:

The area formula of a circle is [tex]A=\pi* r^2[/tex] where r is the radius and in this case our r is 48 m.  So we would just plug in 48 m into r which would get squared and then multiplied by pi to give us [tex]7,238.23\ m[/tex].

Hope this helps!  Let me know if you have any questions

Answer:

[tex]\pi[/tex]r²

Step-by-step explanation: Youre welcome :)

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