Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?

9x + 4y = 36

6x + 2.5y = 24

Infinite solutions: 0x – 0y = 0
No solutions: 0x + 15.5y = 144
One solution: 0x + 0.5y = 0
Two solutions: 0x – 0.5y = 60

Answers

Answer 1

Answer:

One solution: 0x + 0.5y = 0

Step-by-step explanation:

9x + 4y = 36

6x + 2.5y = 24

2 * Eq. 1

18x + 8y = 72

-3 * Eq. 2

-18x - 7.5y = -72

Add the multiples of the equations.

0x + 0.5y = 0

Answer: One solution: 0x + 0.5y = 0

Answer 2

The linear combination that reveals the number of solutions to the system is as follows:

One solution: 0x + 0.5y = 0

The system of linear equation is as follows:

9x + 4y = 36

6x + 2.5y = 24

He multiplied the first equation by 2 and the second equation by –3. Therefore,

Combined equation:

18x + 8y = 72

-18x - 7.5y = -72

Therefore, let's add the equation

0x + 0.5y = 0

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Related Questions

F(x) = 6x+2, find f (x+3)

Answers

Answer:

6x+20

Step-by-step explanation:

F(x) = 6x+2

f(x+3) means replace x with x+3

F(x+3) = 6(x+3)+2

         = 6x+18+2

         = 6x+20

Answer:

A; F(x+3) = 6x^2 + 20x + 6

Step-by-step explanation:

To find it you just would multiply F(x) onto the other side. So it would look like this:

           F(x+3) = 6x + 2 (x+3)            

          F(x+3) = 6x^2 + 2x + 18x + 6            *combine like terms getting you

           F(x+3) = 6x^2 + 20x + 6    

Hope this helped!!

Estimate the sum of 7.2 + 7.3 + 6.9 + 6.8.

Answers

Answer:

28

Step-by-step explanation:

7.2 is rounded down to 7, 7.3 is rounded down to 7, 6.9 is rounded up to 7, and 6.8 is rounded up to 7. Then you can add 7+7+7+7 to get an estimation of 28.

Factor of 3x^3-x^2-20x-12

Answers

Answer:

(−3)(+2)(3+2)

Step-by-step explanation:

Factor by grouping

Factor by grouping

Factor by grouping

Factor by grouping

(−3)(32+8+4)

Factor by grouping

Factor by grouping

Factor by grouping

Factor by grouping

(−3)(+2)(3+2)

What is the measure of m

Answers

The answer is 9 bc it must be longer than the base of the trianngle

What is the probability of rolling 2 standard dice which sum to 9?

Answers

Answer: 1/9

Explanation: Tbh I can’t explain how my brain just clicks sometimes

A landscape-supply company sells mulch at a rate of $30 per cubic yard. What price does the company charge for 54 cubic feet of mulch? (1 yard = 3 feet.

$54
$60
$810
$1,620​

Answers

Answer:

$60

Step-by-step explanation:

The details given the in the question are;

The rate at which the landscape-supply company sells each cubic yard of mulch = $30 per cubic yard

The price the company charges for 54 cubic feet of mulch = Required

The factor for converting yard to feet is 1 yard = 3 feet

Therefore;

1 cubic yard = 1 yard × 1 yard × 1 yard = 3 feet × 3 feet × 3 feet = 27 cubic feet

∴ 2 cubic yard = 2 × 1 cubic yard = 2 × 27 cubic feet = 54 cubic feet

1 cubic yard = $30

∴ 2 cubic yard = 54 cubic feet = 2 × $30 = $60

Someone, please help me on this one

Answers

Answer:

D

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 4x² + 7x - 3 + 6x³ - 7x² - 5 ← collect like terms

= 6x³ - 3x² + 7x - 8

Answer:

D. (f + g )( x ) = 6x³ - 3x² + 7x - 8

Step-by-step explanation:

Given :-

f ( x ) = 4x² + 7x - 3.g ( x ) = 6x³ - 7x² - 5.

To Find :-

( f + g ) ( x ).

Solution :-

(f + g )( x ) = 4x² + 7x - 3 + 6x³ - 7x² - 5.

Arranging like terms.

(f + g )( x ) = 6x³ - 7x² + 4x² + 7x -5 - 3

Combine like terms.

(f + g )( x ) = 6x³ - 3x² + 7x - 8

Determine what type of model best fits the given situation:
The temperature of a cup of coffee decreases by 5 F every 20 minutes.
A. none of these
B. quadratic
C. exponential
D. linear

Answers

Answer:

T = -t / 4 + T0   where t is the temperature in minutes elapsed, T is the final temperature, and T0 is the initial temperature

This is a linear equation in T and t

(-1 / 4 represents -5 deg / 20 min  = - 1 deg / 4min

The given situation is linear equation in T and t. so option D is correct option.

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given situation:

The temperature of a cup of coffee decreases by 5 F every 20 minutes.

T = -t / 4 + T0  

where t is the temperature in minutes elapsed.

T is the final temperature.

T0 is the initial temperature.

We need to find the type of model best fits the given situation.

(-1 / 4 represents -5 deg / 20 min  = - 1 deg / 4min

Therefore, The given situation is linear equation in T and t. so option D is correct option.

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The equation of the line with slope −4 that goes through the point (8,−3)
can be written in the form y=mx+b
where m is:
and where b is:

Answers

Answer:

y = -4x + 29

Step-by-step explanation:

-3 = -4(8) + b

-3 = -32+b

29=b

The equation whose slope is -4 and passes through (8,-3) is y=-4x+29 where slope is -4.

What is equation?

Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.

How to form equation?

We have been given slope of line being -4 and point through which it passes (8,-3) and we have to find the equation of line.

The equation from two points can be calculated through the following formula:

y-[tex]y_{1}[/tex]=m(x-[tex]x_{1}[/tex]) and slope is m.

Putting the values of points and slope in the formula given above.

y-(-3)=-4(x-8)

y+3=-4(x-8)

y+3=-4x+32

y=-4x+32-3

y=-4x+29

Hence the equation is y=-4x+29 where slope is -4.

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Wendy brought 4 cakes and 2 pies for $20. The cost of a cake is twice the cost of 1 pie. A) What was the cost of one cake b)What was the cost of 1 pie?

Answers

Answer:

a. The cost of one cake is $4.

b. The cost of one pie is $2.

Step-by-step explanation:

Let the cost of cake be C.Let the cost of pie be P

C = 2P  .....equation 1

4C + 2P = 20  .....equation 2

Substituting eqn 1 into eqn 2, we have;

4(2P) + 2P = 20

8P + 2P = 20

10P = 20

P = 20/10

Pie, P = $2

Next, we would determine the cost of a cake;

From equation 1;

C = 2P

Substituting the value of "P" we have;

C = 2 * 2

Cake, C = $4

Therefore, we would have the following answers;

a. The cost of one cake is $4.

b. The cost of one pie is $2.

Check:

From equation 2;

4C + 2P = 20

4(4) + 2(2) = 20

16 + 4 = 20

20 = 20

what is the equation of the following line (1,5) and (-1,-5) written in slope-intercept form

Answers

Answer: y = 5x

Step by step process: Use the slope form and then substitute in the equation y = mx + b.

what is constant in graphing ?

Answers

Answer:

the constant is the number without an x attaches to it.

Ex:

y = 2x + 9

9 is a constant because it is not attached to any x

y = x^3 + 2x^2 + 10x + 19

19 is a constant because it is not attached to any x

Choose the correct sum of the polynomials (6x3 − 8x − 5) + (3x3 + 6x + 2).

Answers

Answer:

9x³ - 2x - 3

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

(6x³ - 8x - 5) + (3x³ + 6x + 2)

Step 2: Simplify

Combine like terms (x³):                                                                                   9x³ - 8x - 5 + 6x + 2Combine like terms (x):                                                                                    9x³ - 2x - 5 + 2Combine like terms:                                                                                         9x³ - 2x - 3

Suppose △ABC≅△LMN.

Which other congruency statements are correct?



Select each correct answer.


△BAC≅△MLN

△BCA≅△NML

△ACB≅△LNM

△CBA≅△M

Answers

if so then let's say just want to try am new MNL

your answer is triangle MLN.

The relationship between degrees Fahrenheit (F) and degrees Celcius (C) is given by the formula straight F space equals space 9 over 5 space C space plus space 32. What is the Celcius temperature when the Fahrenheit temperature is 41? Round answer to the nearest whole number. 55 5 -9 41 16

Answers

Answer:

[tex]C = 5[/tex]

Step-by-step explanation:

Given

[tex]F = \frac{9}{5}C + 32[/tex]

Required

Find C when [tex]F = 41[/tex]

We have:

[tex]F = \frac{9}{5}C + 32[/tex]

Substitute 41 for F

[tex]41 = \frac{9}{5}C + 32[/tex]

Collect like terms

[tex]\frac{9}{5}C = 41- 32[/tex]

[tex]\frac{9}{5}C = 9[/tex]

Multiply both sides by 5/9

[tex]C = 9 * \frac{5}{9}[/tex]

[tex]C = 5[/tex]

Find side b, in triangle ABC. if angle B =42 degrees, a=6, c=4

Answers

Answer:

There is no valid value for b

Step-by-step explanation:

We solve the above question using the law of cosines

b² = a² + c² - 2ac × Cos B

B = 42°, a = 6, c = 4

b² = 6² + 4² - 2 × 6 × 4 × Cos 42

b =√6² + 4² - 2 × 6 × 4 × Cos 42

b = √36 + 16 - 48 × Cos 42

Solving the above question, there is no valid value for b

FOR EASY BRAINLIEST ANSWER AND EXPLAIN!! ASAP

QUESTION: A 30minute radio program, the entertainment portion lasts 2 minutes longer than 3 times the duration of the commercial portion. How much is devoted to commercials during the 30 minutes

Answers

Answer: 9 1/3 minutes
First create an equation with the given information; with x being the commercial time, 30=3x+2, now solve for x. First subtract 2 from each side and get 28=3x and then divide each side by 3 to get 9 and 1/3 minutes.

Make x the subject of the formula y=4x²-2​

Answers

Step-by-step explanation:

y=4x²-2y+2=4x²√(y+2)/4=xx=√(y+2)/4

hope it helps.stay safe healthy and happy....

Which of the following is not a real number?

Answers

Answer:

D

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

PLEASE HELPPPPPP!! I need to find x!!!!

Answers

Here

[tex]\\ \sf\longmapsto \frac{7}{x} = \frac{15}{10} \\ \\ \sf\longmapsto 7 \times 10 = 15x \\ \\ \sf\longmapsto 15x = 70 \\ \\ \sf\longmapsto x = \frac{70}{15} \\ \\ \sf\longmapsto \boxed{ \sf x = 4.6cm}[/tex]

Answer:

i can help you i know this answer

HELP ME PLEASE
23. Two swimmers are training over a two-week period to increase the number of laps each can do consecutively. Swimmer A can do 14 laps to start, and increase her total by 3 laps each day. Swimmer B is charting her progress in the table below. Compare the initial values for each. ​

Answers

Answer:

Answer is A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer is C because if swimmer A does 14 laps to start an 3 laps every day after that and on the chart swimmer B does 11 laps to start and 2 laps every day after that you would compare.

on day 3 swimmer B has 17 (shown on chart)

on day 3 swimmer A has 23 (14, 17, 20, 23)

if you would want it to complicate it 14:3 and 11:2

14 ÷ 14 is 1

3 ÷ 14 is .214

11 ÷ 11 is 1

2 ÷ 11 is .181

what is 3 over 4 divided by 1 over 6

Answers

The answer is eighteen
3 over 4 of 6 over 1
18 divided by 4
4.5

Sarah earned 45 1/2 dollars in 5 3/4 minutes. What is the unit rate in dollars per
minute?

Answers

Answer:

7 21/23 dollars per minute

Step-by-step explanation:

Total amount Sarah earns = 45 1/2 dollars

Time taken to earn = 5 3/4 minutes

What is the unit rate in dollars per

minute?

unit rate in dollars per

minute = Total amount Sarah earns / Time taken to earn

= 45 1/2 ÷ 5 3/4

= 91/2 ÷ 23/4

= 91/2 × 4/23

= (91 * 4) / (2 * 23)

= 364/46

= 7 42/46

= 7 21/23 dollars per minute

unit rate in dollars per

minute = 7 21/23 dollars per minute

if sectheta=13/12 and 270°<theta<360°, then tantheta=​

Answers

Answer:

this should be 450° hahah sorry if I am wrong I don't know!

Which values for h and k are used to write the function f(x) = x2 + 12x + 6 in vertex form?
h=6, k=36
h=-6, k=-36
h=6, k=30
hs-6, k=-30

Someone please help me with this I can’t fail this test !

Answers

i gotchu bro you ain’t getting this wrong

ITS D!!! h = -6 k = -30

The equation of a vertical parabola in vertex form is equal to

f(x)= a(xh)² + k

where

a is a coefficient

(h,k) is the vertex

we have

f)x) = x² + 12x + 6

Convert to vertex form

Complete the square

f)x) 6= x² + 12x

f)x) - 6+36= (x² + 12x +36)

f)x)+ 30 = (x² + 12x +36) -

f)x)+30= (x+6)²

f)x) = (x+6)² – 30. -----> equation in vertex form

therefore

The vertex is the point (-6,-30)

h=-6, k=-30

please help me! asap!!

Answers

Answer:

C

Step-by-step explanation:

What is the equation of the graph ? ILL pay

Answers

Answer:

Step-by-step explanation:

You have it right it is 6^x -3

You have the right idea, but you don't need to type in the "y=" portion since that is already taken care of. So you just need to type in -3 + 6^x

ASAP please help meeeeeeeeeee

Answers

Answer:

Step-by-step explanation:

1/16 + 1/2 = 1/16 + 8/16 = 9/16

What is the value of expression below when z=5? 5z−4

Answers

Answer:

21

Step-by-step explanation:

5×5-4 you replace the z with the 5 then multiply by 5 and subtract by 4

Answer:

21

Step-by-step explanation:

5×5-4 you replace the z with the 5 then multiply by 5 and subtract by 4

Help me with this please I don’t understand

Answers

Answer: IT IS CONGRUENT BY ASA POSTULATE.

Step-by-step explanation:

ACCORDING TO THE GIVEN IMAGE

CONSIDER TRIANGLE 1 AS TRIANGLE ABC AND TRIANGLE 2 AS TRIANGLE PQR

IN TRIANGLE ABC AND PQR

ANGLE B = ANGLE C ( 90 DEGREES )

AC = PR ( GIVEN IN FIGURE )

A TRIANGLE HAS SUM OF INTERIOR ANGLES AS 180 DEGREES

IF ANGLE B AND ANGLE Q ARE 90 DEGREES, ANGLE A + ANGLE C = ANGLE P + ANGLE R

WE HAVE ALREADY PROVED THAT AC = PR

If two triangles have one angle equal to one angle, two sides adjoining the equal angles equal, namely, one side adjoining the equal angles, and one opposite the equal angles, and the remaining angles either both less or both not less than a right angle, then the remaining side equals the remaining side and the remaining angles equal the remaining angles.

SO ANGLE A = ANGLE P

THEREFORE BY ASA CONGRUENCY TRIANGLE ABC IS CONGRUENT TO TRIANGLE PQR

HOPE IT HELPS YOU......

(IF I HAVE MADE ANY MISTAKES PLS COMMENT BELOW)

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