Solve the following system of equations using the substitution method.
y = -5x - 17
-3x - 3y = 3
O A) (-4,-3)
B) (-4,3)
C) (4,3)
D) (4,-3)

Answers

Answer 1

Answer:

[tex]\boxed {\boxed {\sf (B. \ -4, 3)}}[/tex]

Step-by-step explanation:

We are given 2 equations and asked to solve the system of equations using the substitution method.

The 2 equations are:

[tex]y= -5x-17 \\-3x-3y= 3[/tex]

The first equation is already solved for y, so we can substitute -5x-17 (the expression that y is equal to) into the second equation.

[tex]-3x-3(-5x-17)=3[/tex]

Solve for x by isolating the variable. First, distribute the -3. Multiply each term in parentheses by -3.

[tex]-3x + [ (-3*-5x ) \ + \ (-3* -17)][/tex]

[tex]-3x + [15x + 51]= 3[/tex]

[tex]-3x+15x+51=3[/tex]

Combine like terms. -3x and 15x can be added because both terms contain the variable x.

[tex]12x+51=3[/tex]

51 is being added to 12x. The inverse operation of addition is subtraction. Subtract 51 from both sides of the equation.

[tex]12x+51-51=3-51[/tex]

[tex]12x= -48[/tex]

x is being multiplied by 12. The inverse operation of multiplication is division. Divide both sides by 12.

[tex]\frac {12x}{12}= \frac{-48}{12}[/tex]

[tex]x= -4[/tex]

Now that we have solved for x, we must find y. We know that x is equal to -4, so we can substitute -4 in for x in the first equation.

[tex]y= -5x-17[/tex]

[tex]y= -5(-4)-17[/tex]

Multiply.

[tex]y=20-17[/tex]

Subtract.

[tex]y=3[/tex]

Coordinate points are written as (x, y), so the solution to this system of equations is (-4, 3)


Related Questions

[18].Simplify (TTE): x(2x+y+5) - 2(x²+xy+5) + y(x + y)

Answers

Answer:

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]

Step-by-step explanation:

Given

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]

Required

Simplify

We have:

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]

Open brackets

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²+xy+5x - 2x\²-2xy-10 + xy + y\²[/tex]

Collect like terms

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²- 2x\²+xy-2xy+ xy+5x -10 + y\²[/tex]

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]

URGENT PLZ SAVE ME

If c varies directly as b and c = 6 when b = 2.
Find
a) the formula for c in terms of b

b) the value of c given b = 14

c) the value of b given c = 39

Answers

Answer:

Hello,

Are you still alive ?

Step-by-step explanation:

a)

c=k*b (c varies directly as b)

6=k*2 ==> k=3 ( c = 6 when b = 2.)

[tex]\boxed{c=3*b }\\[/tex]

b)

b=14 ==> c=3*14=42

c)

c=39

[tex]b=\dfrac{c}{3} =\dfrac{39}{3} =13\\[/tex]

Consider the graph of the quadratic function. Which
interval on the x-axis has a negative rate of change?
3
0-2 to-1
2
O -1.5 to 0
O 0 to 1
-3
-2
21
2
3
x
О 1 to 2.5

Answers

Answer:

1 to 2.5

Step-by-step explanation:

A negative rate of change requires the instantaneous slope to be negative, and the interval from 1 to 2.5 is the only place segment where that can happen.

X ^2 + 2x + y’ + 6y = 15

Answers

Step-by-step explanation:

x^2+2x+7y=15

7y=15-x^2-2x

y=15/7-1/7x^2-2/7x , x ∈ all real numbers

Terms of geometric sequence are found by the formula T n = ar n - 1. If a = 3 and r = 2, find the first 4 terms of the sequence.

Answers

9514 1404 393

Answer:

 3, 6, 12, 24

Step-by-step explanation:

It helps if the formula is properly written.

 Tn = a·r^(n-1)

Fill in the given values for a, r, and use n = 1 to 4.

 T1 = 3·2^(1-1) = 3

 T2 = 3·2^(2-1) = 6

 T3 = 3·2^(3 -1) = 12

 T4 = 3·2^(4 -1) = 24

__

Additional comment

The value a=3 tells you the first term is 3. The value r=2 tells you each term is 2 times the previous one. Knowing this, you can write down the sequence based on your knowledge of multiplication tables (×2). You can use the formula as we did above, but it isn't necessary.

 3, 6, 12, 24, ...

Use the listing method to represent the following set. Hurry plz!!!

Answers

[tex]\\ \sf\longmapsto \left\{x|x \epsilon I,x\leqslant 3\right\}[/tex]

Here x belongs to set of Integersx is less than or equal to 3

In listing

[tex]\\ \sf\longmapsto \left\{\dots,0,1,2,3\right\}[/tex]

For the function y=f(x), find f’(a)

Answers

Answer:

-1

Step-by-step explanation:

f(x) = x²+3x+1

f(a) = a²+3a+1

f'(a) = 2a+3

putting a = -2

2×(-2)+3

= -4+3

= -1

x^{2} +y^{2} =?
cho mình hỏi với

Answers

Answer:

[tex]{ \sf{ {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy }}[/tex]

Step-by-step explanation:

[tex]{ \tt{ {(x + y)}^{2} = (x + y)(x + y) }} \\ { \tt{ {(x + y)}^{2} = ( {x}^{2} + 2xy + {y}^{2}) }} \\ { \tt{( {x}^{2} + {y}^{2} ) = {(x + y)}^{2} - 2xy}}[/tex]

The sum of twice a number and 3 times the same number as 40. What is the number?

Answers

Answer:

Let the number be x

According to Question ,

2x + 3x = 40

5x = 40

x = 8

therefore , the number is 8

hope that helps uh...

Let the number be x

find the answer for 10 points

Answers

Answer:

52.8

Step-by-step explanation:

(3×2.6×2/2)+(3×5×3)

= 7.8+45

= 52.8

Answered by GAUTHMATH

What does labeling a problem mean?

Answers

Answer:

im sure it means labelling or using a label is describing someone or something in a word or short phrase........

:>

For the following function, one zero is given. Find all other zeros.

f(x)=x3-7x2+17x-15; 2-i

Answers

Answer:

1,-3,-5

Step-by-step explanation:

Given:

f(x)=x^3+7x^2+7x-15

Finding all the possible rational zeros of f(x)

p= ±1,±3,±5,±15 (factors of coefficient of last term)

q=±1(factors of coefficient of leading term)

p/q=±1,±3,±5,±15

Now finding the rational zeros using rational root theorem

f(p/q)

f(1)=1+7+7-15

  =0

f(-1)= -1 +7-7-15

    = -16

f(3)=27+7(9)+21-15

   =96

f(-3)= (-3)^3+7(-3)^2+7(-3)-15

    = 0

f(5)=5^3+7(5)^2+7(5)-15

   =320

f(-5)=(-5)^3+7(-5)^2+7(-5)-15

     =0    

f(15)=(15)^3+7(15)^2+7(15)-15

    =5040

f(-15)=(-15)^3+7(-15)^2+7(-15)-15

     =-1920

Hence the rational roots are 1,-3,-5 !

A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course: 16, 21, 22, 12, 22
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

Answer:

The critical value used is [tex]T_c = 2.132[/tex]

The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation.

Sample mean:

[tex]\overline{x} = \frac{16+21+22+12+22}{5} = 18.6[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(16-18.6)^2+(21-18.6)^2+(22-18.6)^2+(12-18.6)^2+(22-18.6)^2}{4}} = 4.45[/tex]

Confidence interval:

We have the standard deviation for the sample, so the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 5 - 1 = 4

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.132. The critical value used is [tex]T_c = 2.132[/tex]

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.132\frac{4.45}{\sqrt{5}} = 4.243[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 18.6 - 4.243 = 14.357

The upper end of the interval is the sample mean added to M. So it is 18.6 + 4.243 = 22.843.

The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).

What is the equation of the parabola shown in the graph?

Answers

Answer:

[tex]-\frac{x^{2} }{4}[/tex]  -2x - 7

Step-by-step explanation:

Never seen a phone with 3 cameras before or something but ok.

Took a while to use brainly's insert character thingie since fractions and the exponent kinda threw me off.

You and your friends have tickets to attend a music concert. While standing in line, the promoter states he will give a gift card for a free album download to each person that is a multiple of 2. He will also give a backstage pass to each fourth person and floor seats to each fifth person. Which person will receive the free album download, backstage pass, and floor seats? Explain the process you used to determine your answer.​

Answers

9514 1404 393

Answer:

  20th

Step-by-step explanation:

The person will receive all gifts if the are all of a multiple of 2, a multiple of 4, and a multiple of 5. Since 4 is already a multiple of 2, the person who will receive all is the one who is a multiple of 4 and 5.

20 is 4×5, so is a multiple of both numbers. There is no smaller number that is a multiple of both 4 and 5.

The 20th person will receive all gifts.

_____

The value we have determined here is called the "least common multiple" (LCM). It is the product of the unique prime factors of the numbers of interest, raised to the highest power that appears in any of the numbers.

  2 = 2¹

  4 = 2²

  5 = 5¹

LCM(2, 4 5) = 2² × 5¹ = 20

The correct answer is the 20th person

find the squre of 17
[tex] \sqrt{17} [/tex]

Answers

The answer is 4.12310562562
The square root of 17 is 4.1231

A runner sprinted for 414 feet. How many yards is this?

Answers

Answer:

138 yards

Step-by-step explanation:

1 feet is (1/3) yard

414 feet is (1/3)*414=138 yards

5(2x-5) = 1/2(18x+40)​

Answers

Answer:

x = 45

Step-by-step explanation:

5 (2x - 5) = 1/2 (18x + 40)​

10x - 25 = 9x + 20

10x = 9x + 45

x = 45

5(2x-5)=1/2(18x+40)10x-25=18x+2010x-18x=20+25-8x=45x=45÷8x=5.62 orx=6

please mark this answer as brainlist

ALL I NEED HELP WITH IS WITH PART D, HOW DO I GET THAT

Use the function f(x) = −16x^2 + 22x + 3 to answer the questions.
Part A: Completely factor f(x). (2 points)

Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)

Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)

Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)

Answers

Step-by-step explanation:

Step 1:  Factor the equation

[tex]f(x) = -16x^{2} + 22x + 3\\f(x) = -(8x + 1)(2x - 3)[/tex]

Step 2:  Find the x-intercepts of the graph of f(x)

[tex]-8x - 1 + 1 = 0 + 1\\-8x / -8 = 1 / -8\\x = -1/8[/tex]

[tex]2x - 3 + 3 = 0 + 3\\2x / 2 = 3 / 2\\x = 3/2[/tex]

Step 3:  Describe the end behavior of the graph of f(x)

Since the function is to the power of 2, that means that it is a parabola.  And since the leading coefficient is negative, means that the arrows will be pointing down therefore, the end behavior of this graph is as x goes to infinity, f(x) goes to negative infinity and as x goes to negative infinity, f(x) goes to negative infinity.

Step 4:  What are the steps you would use to graph f(x)

The first step that I would do is factor the equation.  Then I would find the x-intercepts of the graph and plot them on the graph.  I would then plug in 0 for all of the x values to get the y intercept.  After doing that I would get the vertex using the vertex formula plotting it on the graph.  Finally, I would connect all of the dots together to form the graph of the equation.

Answer:

The person above me is correct!

18 Geometry question: Use an algebraic equation to find the measure of each angle that is representative in terms of X

Answers

Answer:

12x - 28° = 116°

7x + 32° = 116°

Step-by-step explanation:

12x - 28° and 7x + 32° are vertical angles. Vertical angles are congruent.

Therefore, to find the measure of each angle, we have to set each equation equal to each other as follows:

12x - 28° = 7x + 32°

Collect like terms

12x - 7x = 28 + 32

5x = 60

Divide both sides by 5

5x/5 = 60/5

x = 12

✔️12x - 28°

Plug in the value of x

12(12) - 28

= 144 - 28

= 116°

✔️7x + 32°

7(12) + 32

= 84 + 32

= 116°

A woman is 42years old. Her daughter is 1/3 of her age. Three years ago the sum of her age was

Answers

Answer:

50

Step-by-step explanation:

So we know that 42/3=14.

3 years before was:

14-3=11

42-3=39

The sum of 11+39 is 50

You need 675 mL of a 90% alcohol solution. On hand, you have a 25% alcohol mixture. How much of the 25% alcohol mixture and pure alcohol will you need to obtain the desired solution?

Answers

Answer:

90 ml of the 25 percent mixture and 585 of pure alcohol

Step-by-step explanation:

Firstly, you should find the quantity of alcohol in the desired mixture.

675:100*90= 675*0.9= 607.5

Firstly,  define all the 25 percents mixure as x, the pure alcohol weight is y.

1. x+y= 675 (because the first and the second liquid form a desired liquid).

Then find the equation for spirit

The first mixture contains 25 percents. It is x/100*25= 0.25x

When the second one consists of pure alcohol, it contains 100 percents of spirit,  so it is x.

2. 0.25x+y=607.5

Then you have a system of equations ( 1.x+y= 675 and 2. 0.25x+y= 607.5)

try 2-1 to get rid of y

x+y- (0.25x+y)= 675-607.5

0.75x= 67.5

x= 90

y= 675-x= 675-90= 585

It means that you need90 ml of the 25percents mixture and 585 0f pure alcohol

base:10 height:2.5 what is the slope of the ramp​

Answers

Answer:

Slope is B. ¼

Step-by-step explanation:

Slope: is hypotenuse

[tex] = { \sf{ \frac{ \delta \: height}{ \delta \: base} }} \\ \\ { \sf{ = \frac{2.5}{10} }} \\ \\ = { \sf{ \frac{1}{4} }}[/tex]

slope = b/h = 2.5/10 =0.25= 25/100
which means slope = 1/4

What is the distance between the following points?

Will give brainliest

Answers

Answer:

√65

Step-by-step explanation:

(-6,4) (-5,-4)

√(x2 - x1)² + (y2 - y1)²

√[-5 - (-6)]² + (-4 - 4)²

√(1)² + (-8)²

√1 + 64

√65

if x-y =2 and xy=15, find the value of x cube - y cube.​

Answers

Answer:

5³ = 125 : -3³ = -27

Step-by-step explanation:

let x= 5 and y= 3x - y = 25 - 3 = 2xy = 155 × 3 = 15x³ = ? : -y³ = ?5³ = 125 : -3³ = -27

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

for any Integer 'a',a ÷ 0 is _______
give me answer​

Answers

Answer:

undefined, invalid

and for a limit expression like a/x, x->0 we also say this is infinite.


Help please 6x + 3 > a if the inequality above is true for the constant a which of the following. coupd be a vakue of z

Answers

Answer:

[tex]\frac{a+3}{6}[/tex]

Step-by-step explanation:

Treat it like any other math problem with a equals sign:

6x + 3 = a

subtract 3 from both sides: 6x = a + 3

divide both sides by 6: [tex]x = \frac{a+3}{6}[/tex]

swap the ≥ back in: [tex]x \geq \frac{a+3}{6}[/tex]

the only time the sign flips is if you divide by a negative

4) If the area of a square is 48cm²,
What is the length of each side?
Simplify your answer.

Answers

Answer:

4 sqrt(3) cm

Step-by-step explanation:

The area of a square is

A = s^2  where s is the side length

48 = s^2

Take the square root of each side

sqrt(48) = sqrt(s)

sqrt(16*3) = s

4 sqrt(3) =s

Answer:

4√3 cm

Step-by-step explanation:

The area of square = s²

s meaning side. Remember, by definition of a square, all the sides have equal measurements.

Set the equation:

Area of square = 48cm²

48cm² = s²

Isolate the variable, s. Note the equal sign, what you do to one side, you do to the other. Root both sides of the equation:

√48cm² = √s²

s = √48 = √(8 x 6) = √(2 x 2 x 2 x 3 x 2) = (2 x 2)√3 = 4√3

4√3 cm is your length for a side.

~


A square piece of cardboard of sides 15 cm is folded to make a cube of sides 5 cm.
Is there enough cardboard?

Answers

Answer:

Step-by-step explanation:

The 15 cm by 15 cm piece of cardboard area = 225 cm².

A cube has six congruent faces. If each edge is 5 cm, the surface area is 6×5² = 150 cm². So there is enough cardboard to make a cube, but not by folding. You'd have to do some cutting and taping.

1. Samuel paid #34.20 for a blanket. If the marked price of the blanket is #41.78. What is the discount?

2. A mother buys a dress for her daughter at a discount of 18%. If the price of the dress is #35.00. How does she actually pay for the dress?

Answers

Answer:

1. The discount is 10%

2. 250

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