Mathematics Middle School

6x + 3y = 9
2x + 3y = 1
Solve the system of equations.
A)
x = 2, y = -1
B)
x = -1, y = 2
C)
x=1/2,y=3
D)
x=3,y=-1/2
​

Answers

Answer 1

Answer:

A

Step-by-step explanation:

Given the 2 equations

6x + 3y = 9 → (1)

2x + 3y = 1 → (2)

Subtracting the 2 equations term by term eliminates the y- term

Subtract (2) from (1) term by term, that is

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

4x = 8 ( divide both sides by 4 )

x = 2

Substitute x = 2 into either of the 2 equations and evaluate for y

Substituting into (2)

2(2) + 3y = 1

4 + 3y = 1 ( subtract 4 from both sides )

3y = - 3 ( divide both sides by 3 )

y = - 1

The solution is x = 2, y = - 1 → A

Related Questions

The area of this parallelogram is 120 mm2. Find the value of x. 9 mm 12 mm 15 mm 6 mm

Answers

Answer:

[tex]x=12\:mm[/tex]

Step-by-step explanation:

[tex]A=bh[/tex]

[tex]b \times h=120[/tex]

[tex]b \times 10=120[/tex]

[tex]b=120 \div 10[/tex]

[tex]b=12[/tex]

Check all restrictions on the domain of g circle h. x not-equals 0 x not-equals negative 2 x not-equals negative two-thirds There are no restrictions.

Answers

Answer: the answer is C

Step-by-step explanation:

Answer:

Step-by-step explanation:

x = -2/3

What is the coefficient of the 2nd term of the following expression when written in standard form:
〖(7+4x)〗^3

Answers

Answer:

336

Step-by-step explanation:

Given the expansion: [tex](7+4x)^3[/tex]

[tex](7+4x)^3\\\\=(7+4x)^2*(7+4x)\\\\=(7+4x)(16x^2+56x+49)\\\\=7(16x^2+56x+49)+4x(16x^2+56x+49)\\\\=112x^2+392x+343+64x^3+224x^2+196x\\\\=64x^3+112x^2+224x^2+392x+196x+343\\\\=64x^3+336x^2+588x+343[/tex]

Therefore, the coefficient of the second term is 336.

Why is sexual reproduction citical in the process of evolution

Answers

Answer:

sexual reproduction provides evolutionary advantages to organisms that employ this mechanism to produce offspring.

Step-by-step explanation:

Answer: it creates birth

Step-by-step explanation: can i have brainliest

951/3 i dont under stand

Answers

Answer:

317 IS THE ANSWER

Step-by-step explanation:

The right answer is 317

please see the attached picture for full solution.

hope it helps

good luck on your assignment

Please help will mark brainliest ​

Answers

Answer:

Klm=(k+1)m -(m+1)k

Klm=km+m -mk-k

Klm=m-k

Which statement justifies that ∠K ≅ ∠N? answers: A) ΔHKL ≅ ΔHMN by ASA; but the two angles aren't congruent because they aren't corresponding angles. B) The two angles aren't congruent. C) ΔHKL ≅ ΔHMN by ASA; ∠K ≅ ∠N because they're corresponding angles in congruent triangles. D) ΔHLK ≅ ΔHMN by AAS; ∠K ≅ ∠N because they're corresponding angles in congruent triangles.

Answers

Answer:

Correct answer is:

D) ΔHLK ≅ ΔHMN by AAS; ∠K ≅ ∠N because they're corresponding angles in congruent triangles.

Step-by-step explanation:

We are given the diagram, in which there are 2 triangles namely [tex]\triangle HLK, \triangle HMN[/tex].

1. Side KH = Side NH

2. [tex]\angle L \cong \angle M[/tex]

From the given figure, we can derive that:

[tex]\angle KHL \cong \angle NHM[/tex]

Property used: Vertically opposite angels made by two lines crossing each other are equal.

So, we have two angles ([tex]\angle L \cong \angle M[/tex] and [tex]\angle KHL \cong \angle NHM[/tex])of the triangle as same and one side equal from the two given triangles [tex]\triangle HLK, \triangle HMN[/tex].

So, we can say that the two triangles are congruent.

[tex]\triangle HLK \cong \triangle HMN[/tex]

The side is not between the two equal angles, so it is AAS congruence.

And Congruent triangles have their corresponding angles equal.

Therefore, option D) is true :

ΔHLK ≅ ΔHMN by AAS; ∠K ≅ ∠N, because they're corresponding angles in congruent triangles.

Answer:

ΔHLK ≅ ΔHMN by AAS; ∠K ≅ ∠N because they're corresponding angles in congruent triangles.

Step-by-step explanation: I took the test

-3x^2+6x+9=
WHY JUST WHY !!!! ?

Answers

Oh, my, goodness!!!!!! :)

You are cracking me up so much right now!!!!! :)

But, yeah, I hear ya! :)

Answer:

[tex]=-3\left(x+1\right)\left(x-3\right)[/tex]

Step-by-step explanation:

[tex]-3x^2+6x+9\\\mathrm{Factor\:out\:common\:term\:}-3:\quad -3\left(x^2-2x-3\right)\\-3x^2+6x+9\\\mathrm{Rewrite\:}9\mathrm{\:as\:}3\cdot \:3\\\mathrm{Rewrite\:}6\mathrm{\:as\:}3\cdot \:2\\=-3x^2+3\cdot \:2x+3\cdot \:3\\\mathrm{Factor\:out\:common\:term\:}-3\\=-3\left(x^2-2x-3\right)\\\mathrm{Factor}\:x^2-2x-3:\quad \left(x+1\right)\left(x-3\right)\\x^2-2x-3\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(x^2+x\right)+\left(-3x-3\right)[/tex]

[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+x\mathrm{:\quad }x\left(x+1\right)\\x^2+x\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\=xx+x\\\mathrm{Factor\:out\:common\:term\:}x\\=x\left(x+1\right)\\\mathrm{Factor\:out\:}-3\mathrm{\:from\:}-3x-3\mathrm{:\quad }-3\left(x+1\right)\\-3x-3\\\mathrm{Factor\:out\:common\:term\:}-3\\=-3\left(x+1\right)\\=x\left(x+1\right)-3\left(x+1\right)\\\mathrm{Factor\:out\:common\:term\:}x+1\\=\left(x+1\right)\left(x-3\right)[/tex]

[tex]=-3\left(x+1\right)\left(x-3\right)[/tex]

Which equation describes the locus of points 5 units from points (3, -4)?
A) (x+3)^2 + (y-4)^2=5
B) (x-3)^2 + (y+4)^2=5
C) (x-3)^2 + (y+4)^2=25
D) (x+3)^2 + (y-4)^2=25
***YOU DON'T HAVE TO EXPLAIN***

Answers

Answer:

I think the D number is correct(squaring on both side)

Explain how the Quotient of Powers Property was used to simplify this expression.

three to the fourth power all over nine equals three squared

By simplifying 9 to 32 to make both powers base three and adding the exponents
By simplifying 9 to 32 to make both powers base three and subtracting the exponents
By finding the quotient of the bases to be one third and simplifying the expression
By finding the quotient of the bases to be one third and cancelling common factors

Answers

Answer:

The answer is option 2, by simplifying 9 to 3² to make both powers base 3 and subtracting the exponents.

Step-by-step explanation:

You have to make the expressions into the same base :

[tex] \frac{ {3}^{4} }{9} = \frac{ {3}^{4} }{ {3}^{2} } [/tex]

Next, you have to apply Indices Law :

[tex] {a}^{m} \div {a}^{n} \: ⇒ \: {a}^{m - n} [/tex]

[tex] {3}^{4} \div {3}^{2} [/tex]

[tex] = {3}^{4 - 2} [/tex]

[tex] = {3}^{2} [/tex]

By simplifying 9 to 3² to make both the powers base 3 as well as subtracting the exponents. A further explanation of the given question is below.

According to the question,

The equation will be:

→ [tex]\frac{(3)^4}{9} = \frac{(3)^4}{(3)^2}[/tex]

By applying the Indices law i.e.,

→ [tex]\frac{a^m}{a^n} = a^{m-n}[/tex]

then, we get

→ [tex]\frac{3^4}{3^2}[/tex]

→ [tex]3^{4-2}[/tex]

By subtracting the powers, we get

→ [tex]3^2[/tex]

Thus the above answer i.e., option B) is the correct approach.

Learn more:

https://brainly.com/question/19660607

what is the inverse of the function y=4x+5

Answers

Answer:

the answer for this question is (y-5)/4=x

What is the value of x in the equation 8 + 4 = 2 (x minus 1)? 5 StartFraction 11 Over 2 EndFraction StartFraction 13 Over 2 EndFraction 7

Answers

Answer:

7

Step-by-step explanation:

We can simplify the equation to

12 = 2x - 2

Add 2 to both sides

14 = 2x

Divide by 2

x = 7

Answer:

7

Step-by-step explanation:

For the following fraction ,tell whether you will add ,subtract, or multiply the exponents

Answers

Answer:

Add the exponents

Step-by-step explanation:

Product Rule: am ∙ an = am + n, this says that to multiply two exponents with the same base, you keep the base and add the powers.

EX:

x multiplied by  x^5=x^6

Answer:

We add them

But for negative values we always keep the negative value as a decrease.

4 x -4 as powers still becomes -8

and not -16

Step-by-step explanation:

The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. In this example, you can see how it works. Adding the exponents is just a short cut! The "power rule" tells us that to raise a power to a power, just multiply the exponents.

2^4 x 3^-4 = 16/81 shows and proves we multiply them and just use adding as a short cut.

Is my answer correct?

Answers

Answer:

No

Step-by-step explanation:

It should be -8 degrees because 5x4=20 and 12-20=-8

What’s the vertex of y=1/3(x+2)^2-5

Answers

Answer:

vertex is (2,-5)

Step-by-step explanation:

y = a(x – h)^2 + k

the  vertex is (h,k) in the equation h =2 and k = -5

Factor 4x2 - 16 using difference of two squares.

Answers

Answer:

4(x+2)(x-2)

Step-by-step explanation:

4x^2-16

4(x^2-4)

4(x+2)(x-2)

The difference of two squares formula is (a+b)(a-b), and it happens only when a^2 is minus b^2

So, 4x^2 − 16 = (2x + 4)(2x − 4).

Explanation:

4x2^ − 16 is of the form a^2 − b^2 (where a = 2x, b = 4), and as per the identity:

a^2 − b^2 = (a + b)(a − b)

So, 4x^2 − 16 = (2x + 4)(2x − 4)

there are 50 cards in a pack and each card is either red or black
the ratio of the number of red cards to the number of black cards 1:1

10 black cards are removed from the pack

find the ratio of the number of red cards in the pack to the number of black cards in the pack
Give your answer in its simplest form


Please show your working out

Answers

Step-by-step explanation:

Ratio Red to Black is 1:1

Therefore, Red and Black has 25 cards respectively

If 10B cards are removed, then 25-10=15B cards left

Current ratio Red to Black is 25:15 and simplest form is 5:3

A ratio of 1:1 means there are the same number of red and black cards, so 25 of each. Take 10 black away and now there are still 25 red but only 15 black. The ratio is 25:15, which simplifies to 5:3 ( divide 25 and 15 by 5 because 5 is the greatest common factor of 25 and 15)

select the correct answer. witch is the correct simplified form of the expression ​

Answers

Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

-1/3 -1/2 = -5/6

1/2-1/4 = 1/4

The negative makes the reciprocal

x^1/4/y^5/6

I do t o wish she sksnheisnmakakabs nsjd

Answers

Answer:

x=-12

Step-by-step explanation:

(-22 + 3x) /( 3x+7) =2

Multiply each side of the equation by 3x+7

-22+3x = 2(3x+7)

Then distribute

-22 +3x = 6x+14

Subtract 3x from each side

-22 = 3x+14

Subtract 14 from each side

-36 = 3x

Divide by 3

-12 =x

Kevin says these number lines show 7/8 is equivalent to 4/5. Is Kevin correct?

Answers

Yes, Kevin is correct

What is 5 2/3 divided by 3 1/9?? PLEASE HELP!!! D:

Answers

Answer:1 23/28

Step-by-step explanation:

17/3/3 1/9

17/3/28/9

51/28

1 23/28

Phone’s Plus charges a connection fee of 35 cents and 3 cents per minute. Fabulous Phones charges a connection fee of 45 cents and 2 cents per minute. Which equation could be used to determine the number of minutes, x, when a phone call would cost the same at both companies?

A. 0.35+0.3x=0.45+0.2x

B. 0.35+0.03x=0.45+0.02x

C. 35+0.03x=45+0.2x

D. 35+0.03x=45+0.02x

Answers

Answer:

B. 0.35 + 0.03x = 0.45 + 0.02x

Step-by-step explanation:

I don't really know how to explain it, but it is correct.

This is complicated,no how to explain its c. Jk it’s b :p

Which of the following is(are) the solution(s) to 8|x-3|=-24
O A. All values are solutions
O B. x= 6,0
C. No Solution
O D. x = 3,0

Answers

The correct answer is c. There is no solution because there is no way to divide it and simplify.

In the given triangle ABC, find DE. answers: 20 5 10 2.5

Answers

Answer:

5

Step-by-step explanation:

Let's call the length AD y.

[tex]\dfrac{x+2}{y}=\dfrac{8x-14}{2y} \\\\\\2(x+2)=8x-14 \\\\\\2x+4=8x-14 \\\\\\4=6x-14 \\\\\\6x=18 \\\\\\x=3 \\\\\\DE=x+2=3+2=5[/tex]

Hope this helps!

Classify the following triangle based on its shape.

A. Right
B. Isosceles
C. Equilateral
D. Scalene

Please answer this

Answers

Answer:

A

Step-by-step explanation

the square in the corner

The shape of the given triangle is right angle.

The square in the corner

We have given that,

A. Right

B. Isosceles

C. Equilateral

D. Scalene

We have to determine the shape of the given triangle.

What is the right angle?

A right angle is an angle of exactly 90 degrees or \pi /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.

The shape of the given triangle is right angle.

To learn more about the right angle visit:

https://brainly.com/question/101834

#SPJ2

Mrs. opsahl drove 399 miles on 14 gallons of gas.how many miles per gallon did her car get

Answers

28.5 miles per gallon

Answer:

28.5 miles per gallon

Step-by-step explanation:

399 divided by 14 gives you the number 28.5

Use the distributive property to write the following expression without parentheses.
-6(3-m+n)

Answers

________________________________

Hey!!

Solution,

-6(3-m+n)

= -18+6m-6n

= 6m-6n-18

hope it helps....

Good luck on your assignment

______________________________

Answer:

[tex]= 6m + 6n - 18 \\ [/tex]

Step-by-step explanation:

[tex] - 6(3 - m + n) \\ = - 18 + 6m + 6n \\ = 6m + 6n - 18[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Which is a zero of the quadratic function f(x) = 9x2 - 54x – 19?
x= 1/3
x=3 1/3

Answers

Answer:

x =1/3

Step-by-step explanation:

the zero quadratic function is x=1/3

Answer plz!
Which choices are equivalent to the quotient below? Check all that apply.

Answers

Answer:

A, C, and E are correct

Step-by-step explanation:

please help me with this

Answers

Answer:

3 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

3/4 + (1/3÷ 1/6 - (-1/2)=

3/4 + 2 - (-1/2)=

2 3/4 - (-1/2)=

3 1/4

hope it helps mark me as brainliest

Other Questions
explain Hammurabis purpose for writing the Code of Hammurabi. All of the following are effects of Global Warming EXCEPTYour answer:increase in hurricaneslower sea levelsincrease in diseasemelting polar ice caps please help me with this electricity has two different rates off peak is 10pm to 6am and charged at 8p per hour. peak is 6am to 10pm and is charged at 12p per hour. alison turns uses electricity from 8pm to 11:30 pm. what is the dost of her electricity for that period Meghla has brought a smartphone with length is 4 unit and breadth is 3 unit, what is the screen size of the smartphone If you had to choose a word that's fits in this sentence what will it be?I Love _ and I sometimes eat noddles.A PizzaB RiceC Candy The table shows three unique functions.Which statements can be used to compare the functions?Select two options.1X4-3-2-1Only f(x) has an x-intercept.f(x) g(x) h(x)-19 80 -12 -6-1 -7 4-2 4 ---2-2 4 .Og(x) has liic yrealesi maximum.1All three functions have a y-intercept.All three functions have the same range values.All three functions have the same domain values. Need help finding the answer Variation means which of the following? aTraits that are passed on will ultimately become common within the population bAll species will produce more offspring than will survive to adulthood cThere are variations between members of the same species dTraits that increase suitability to a species' environment are seen. Some traits are selected for, and some are selected against based on fitness. what are two things that are infinite? Prepare the adjusting journal entries for the following transactions. (If no entry is required for a transaction/event, select "No Journal Entry Required" in the first account field.) Supplies for office use were purchased during the year for $700, of which $200 remained on hand (unused) at year-end. Interest of $350 on a note receivable was earned at year-end, although collection of the interest is not due until the following year. At year-end, salaries and wages payable of $4,600 had not been recorded or paid. At year-end, one-half of a $3,000 advertising project had been completed for a client, but nothing had been billed or collected. Redeemed a gift card for $700 of services. Which best describes the reigon around Lake Victoria? A)Arid B) High Density C) Little agricultural production D) Lacking in natural resources. The rectangle has rotational symmetry of orderThe rectangle's rotational symmetry occurs for angles ofdegrees What is produced during the photosynthesis process? A. ChloroplastsB. Carbon DioxideC. Sugar The equilibrium constant for the reaction NO2(g)+NO3(g)N2O5(g) is 2.1x10-20 , therefore: a. At equilibrium, the concentration of products and reactants is about the same. b. At equilibrium, the concentration of products is greater than the reactants. c. At equilibrium, the concentration of reactants is greater than the products In each trial, you will add an indicator to themystery food sample. But you will also add theindicator to a known substance and water. Why isthat important? Check all reasons.to practice measuring volume using thegraduated pipette correctlyto match the mystery food sample to a definitepositive result (gelatin, oil, etc.)to match the mystery food sample to a definitenegative result (water)to increase the amount of data.DONE Which affixes mean without ex im Which answer best describes Lincolns tone as he delivers the Gettysburg Address:Question 1 options:a) respectableb) religiousc) frustratedd) fanaticalQuestion 2 (2 points) What is Lincolns purpose in the Gettysburg Address?Question 2 options:a) To rally the North to destroy the Southb) To remind the people of what the Civil War was all aboutc) To express his hatred of slaveryd) To teach the people about the Declaration of IndependenceQuestion 3 (2 points) Lincoln presents the Civil War as a test to the American people. What kind of test is it?Question 3 options:a) A test to determine whether the American people have the will to fightb) A test to see if the Union can hold together when the North seems to be winning.c) A test to see if slavery will survived) The war is testing whether a nation dedicated to liberty and equality can survive.Question 4 (2 points) Who is Lincolns audience?Question 4 options:Abolitionists rallying against slaveryUnion troops ready to return to battlePeople who have come to dedicate a cemeteryPeople wanting to re-elect Lincoln for a second term as presidentQuestion 5 (2 points) Which answer best summarizes Lincolns call to action:Question 5 options:a) We all must finish the work these fallen soldiers have begun.b) We must depend on the Declaration of Independence to guide us in this war.c) We must consecrate this cemetery as hallowed ground.d) We must strengthen our troops and continue fighting. It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, minutes of activity varied according to the N(373, 61) distribution. Minutes of activity for lean people had the N(525, 104) distribution. Within what limits do the active minutes for 95% of the people in each group fall The units of the subway map below are in miles. Suppose the routes between stations are straight, find the distance you would travel between the Jackson and Symphony stations.Write your answer to the nearest tenth of a mile.