What is the y-value in the solution to this system of linear equations?
4x + 5y = -12
-2x + 3y = -16
-4.
-2
оооо
2
5

Answer:

x = 1.5

Step-by-step explanation:

5(4x-10)+10x=4(2x-3)+2(x-4)

Distribute(5)

20x-50+10x=4(2x-3)+2(x-4)

Distribute(4)

20x-50+10x=8x-12+2(x-4)

Distribute(2)

20x-50+10x=8x-12+2x-8

Combine like terms

30x-50=10x-20

Subtract(10x)

20x-50=-20

Add(50)

20x=30

Divide(20)

x = 1.5

Hope it helps <3

Answer:

Step-by-step explanation:

5 ( 4x - 10) + 10x = 4(2x - 3) + 2(x - 4)

Expand the terms

That's

20x - 50 + 10x = 8x - 12 + 2x - 8

Simplify

30x - 50 = 10x - 20

Group the constants at the right side of the equation

That's

30x - 10x = - 20 + 50

20x = 30

Divide both sides by 20

x = 3/2

Hope this helps you

Answer: [tex]S=0.087p[/tex] .

Step-by-step explanation:

Equation for direct proportion:

y=kx

, where x= independent variable ,

y=dependent variable.

k= proportionality constant

Here, State sales tax S  is directly proportional to retail price p.

Also, dependent variable= S,  independent variable =p

Required equation: S= kp

Put S= 12.32 and x= 142

[tex]S=12.32=k(142)\\\\\Rightarrow\ k=\dfrac{12.32}{142}\approx0.087[/tex]

Hence, the required equation is [tex]S=0.087p[/tex] .

Answer:

The answers for:

Step-by-step explanation:

In order to find the value of expression, you have to apply gradient formula :

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

So for Question 1,

[tex]let \: (3,2) \: be \: (x1,y1) \\ let \: (4,j) \: be \: (x2,y2) \\ let \: m = 1[/tex]

[tex] \frac{j - 2}{4 - 3} = 1[/tex]

[tex] \frac{j - 2}{1} = 1[/tex]

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

[tex]j = 1 + 2 = 3[/tex]

Question 2,

[tex]let \: (5,0) \: be \: (x1,y1) \\ let \: (1,k) \: be \: (x2,y2) \\ let \: m = \frac{1}{2} [/tex]

[tex] \frac{k - 0}{1 - 5} = \frac{1}{2} [/tex]

[tex] \frac{k}{ - 4} = \frac{1}{2} [/tex]

[tex]k = \frac{1}{2} \times - 4 = - 2[/tex]

Question 3,

[tex]let \: (x,2) \: be \: (x1,y1) \\ let \: (3, - 4) \: be \: (x2,y2) \\ let \: m = 2[/tex]

[tex] \frac{ - 4 - 2}{3 - x} = 2[/tex]

[tex] \frac{ - 6}{3 - x } = 2[/tex]

[tex] - 6 = 2(3 - x)[/tex]

[tex] - 6 = 6 - 2x[/tex]

[tex] - 6 - 6 = - 2x[/tex]

[tex] - 2x = - 12[/tex]

[tex]x = - 12 \div - 2 = 6[/tex]

Question 4,

[tex]let \: (12, - 4) \: be \: (x1,y1) \\ let \: (r,2) \: be \: (x2,y2) \\ let \: m = - \frac{1}{2} [/tex]

[tex] \frac{2 - ( - 4)}{r - 12} = - \frac{1}{2} [/tex]

[tex] \frac{6}{r - 12} = - \frac{1}{2} [/tex]

[tex] - 1(r - 12) = 2(6)[/tex]

[tex] - r + 12 = 12[/tex]

[tex]r = (12 - 12) \div - 1 = 0[/tex]

Answer:

A

Step-by-step explanation:

Answer:

1. k=0

2. yes, result is still a polynomial.

3. yes, f and g must have the same degree to have deg(f+g) < deg(f) or deg(g)

Step-by-step explanation:

1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x)

for k=0 any polynomial f(x) will reduce f(k) to the constant term.

2. If we multiply a polynomial by a constant, is the result a polynomial?

Yes, If we multiply a polynomial by a constant, the result is always a polynomial.

3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?

Yes.  

If

deg(f+g) < deg(f) and

deg(f+g) < deg(g)

then it means that the two leading terms cancel out, which can happen only if f and g have the same degree.

Answer:

Step-by-step explanation:

Substitute x = 1 and y = 1 to the both inequalities:

[tex]x-8y\leq9\\\\1-8(1)\leq9\\1-8\leq9\\-7\leq9\qquad\bold{TRUE}\\==================\\-7x+5y<4\\\\-7(1)+5(1)<4\\-7+5<4\\-2<4\qquad\bold{TRUE}[/tex]

Answer:

(1,1) does satisfy

x - 8y ≤ 9

- 7x + 5y < 4

Step-by-step explanation:

Well, first we need to plug in (1,1) into,

x - 8y ≤ 9

- 7x + 5y < 4

→ 1 - 8(1) ≤ 9

- 7(1) + 5(1) < 4

1 - 8 ≤ 9

-7 + 5 < 4

-7 ≤ 9

-2 < 4

Thus,

(1,1) does satisfy

x - 8y ≤ 9

- 7x + 5y < 4.

Hope this helps :)

Answer:

The probability is 1

Step-by-step explanation:

Given

Number of flips = 8

Outcomes = 8 heads

Required

Probability of getting a head in the next row

This problem can be attributed to experimental probability and it'll be solved using experimental probability formula, which goes as follows;

[tex]Probability = \frac{Number\ of\ Occurence}{Total\ Trials}[/tex]

Let [tex]P(Head)[/tex] represents the probability of getting a head in the next row;

[tex]P(Head)= \frac{Outcome\ of\ head}{Total\ Flips}[/tex]

[tex]P(Head)= \frac{8}{8}[/tex]

[tex]P(Head)= 1[/tex]

Hence, the probability of obtaining a head in the next flip is 1

Answer:

Blue paint=21 ounces

Step-by-step explanation:

3/4 cup=6 ounces

1 cup=8 ounces

3/4 cup of blue paint=6 ounces of blue paint

1 cup of white paint= 8 ounces of white paint

Ava has 28 ounces of white paint

Find the required blue paint

Let the required blue paint=x

Blue paint ratio white paint

6:8=x:28

6/8=x/28

Cross product

6(28)=x(8)

168=8x

x=168/8

x=21 ounces

Answer:

21.5%

Step-by-step explanation:

51 divided by 237 to get percentage (237*.215% = 51)

Answer:

For 0,90 of Confidence we reject H₀

For  0,95 CI we reject H₀

Step-by-step explanation:

To evaluate a difference between two proportion with big sample sizes we proceed as follows

1.-Proportion 1

n = 2160

243 had rear license  p₁ = 243/2160     p₁ = 0,1125

2.Proportion 2

n = 358

55   had rear license   p₂ = 55/ 358     p₂ = 0,1536

Test Hypothesis

Null Hypothesis                            H₀      ⇒   p₂   =  p₁

Alternative Hypothesis                Hₐ     ⇒    p₂  >  p₁

With signficance level  of  0,05  means  z(c) = 1,64

T calculate   z(s)

z(s) =  ( p₂ - p₁ ) / √ p*q ( 1/n₁  +  1/n₂ )

p = ( x₁  +  x₂ ) / n₁  +  n₂

p = 243  +  55 / 2160 + 358

p = 0,1183     and then    q = 1 -  p     q =  0,8817

z(s) =  ( 0,1536 - 0,1125 ) / √ 0,1043 ( 1/ 2160   +  1 / 358)

z(s) =  0,0411 /√ 0,1043*0,003256

z(s) = 0,0411 / 0,01843

z(s) =  2,23

Then  z(s) > z(c)      2,23  >  1,64

z(s) is in the rejection region we reject H₀

If we construct a CI for  0,95   α = 0,05   α/2  =  0,025

z (score ) is  from z- table    z = 1,96

CI = ( p ±  z(0,025*SE)

CI = ( 0,1536 ± 1,96*√ 0,1043*0,003256 )

CI = ( 0,1536 ± 1.96*0,01843)

CI = ( 0,1536 ± 0,03612 )

CI = ( 0,11748  ;  0,18972 )

In the new CI we don´t find  0 value so we have enough evidence to reject H₀

Answer:

[tex]y=\frac{4}{3}x-1.75[/tex]

Step-by-step explanation:

If the slope of a line is 4/3,

and we wanna find the equation of a line that is parallel to it and crosses through (5,5).

So we already have the slope because the slope of 2 parallel lines are the same.

y = 4/3x

Look at the image below↓

So now we just need to find the y-intercept.

After some numbers we got,

[tex]y=\frac{4}{3}x-1.75[/tex]

Look at the other image below↓

Thus,

the equation of the parallel line is [tex]y=\frac{4}{3}x-1.75[/tex].

Hope this helps :)

Answer:

3

Step-by-step explanation:

If the cube has 54 stickers across its six faces, and each face has the same number of stickers, first we can find the number of stickers in each face by dividing the number of stickers by the number of faces:

[tex]stickers\ per\ face = number\ of\ stickers / number\ of\ faces[/tex]

[tex]stickers\ per\ face = 54/6 = 9[/tex]

Each face has 9 stickers.

If each row and column has the same number of stickers, we can find the numbers of rows and columns by finding the square root of the number of stickers in the face:

[tex]\ number\ of\ rows = \sqrt{9} = 3[/tex]

If we have 3 rows, and each roll has the same number of stickers, the number of stickers per row or column is:

[tex]stickers\ per\ row = stickers\ per\ face / number\ of\ rows[/tex]

[tex]stickers\ per\ row = 9/3 = 3[/tex]

Answer:

a) 3x^2-6x-3

b) 6

Step-by-step explanation:

f(x)=2x^2−4x+3

g(x)=x^2−2x−6

a)  (f+g)(x) = (2x^2−4x+3) + (x^2−2x−6)

             collect like terms

   (f+g)(x) = 2x^2+x^2-4x-2x+3-6

   (f+g)(x) = 3x^2-6x-3

b) (f+g)(3). This implies that x=3

  recall (f+g)(3) = 3x^2-6x-3

   (f+g)(3) = 3(3)^2-6(3)-3 = 27-18-3

   (f+g)(3) = 27-21 =6

Answer:

9 and 18

Step-by-step explanation:

2x and x are the numbers

1/x-1/2x=1/18

2/2x-1/2x=1/18

1/2x=1/18

2x=18X=9,

2x=18

The two integers are 9 and 18

Answer:

21 purple marbles

Step-by-step explanation:

my explanation is i looked at it like a ratio so ¾= x/28

then i took 28 ÷ 4 which equals 7, then i took 7 and multiplied it by 3 which gave me 21, so the answer is 21 purple marbles

Answer:

The Central Limit Theorem says that if the sample size is more than 30, the data follows a normal sampling distribution. Since the sample size is 180, and that is more than 30, a Normal sampling distribution can be used.

Since a normal sampling distribution can be used, we should FAIL TO REJECT the null hypothesis because p = 0.20, which is more than the significance level of α = 0.08. There is NOT sufficient evidence to suggest that the alternative hypothesis is true.

Hope this helps!

Hello!

Answer:

Choice 1.

Step-by-step explanation:

We can go through each answer choice and examine whether it represents the question:

1) This does not represent the question because 10% of 6 is 0.6. The question is asking to find a number that 6 = 10% of, not finding 10% of 6.

2) Correct because a number multiplied by 10%, or 0.1, should be equal to 6 to answer the question.

3) Correct because 6 is equivalent to 10% of the answer, which is stated in this answer choice.

4) Correct because 6 should be 10% of the answer.

Therefore, the incorrect choice would be Choice 1.

Answer:

-1.031 m/s or  [tex]\frac{-\sqrt{17} }{4}[/tex]

Step-by-step explanation:

We take the length of the rope from the dock to the bow of the boat as y.

We take x be the horizontal  distance from the dock to the boat.

We know that the rate of change of the rope length is [tex]\frac{dy}{dt}[/tex] = -1 m/s

We need to find the rate of change of the horizontal  distance from the dock to the boat =  [tex]\frac{dx}{dt}[/tex] = ?

for x = 4

Applying Pythagorean Theorem we have

[tex]1^{2} +x^{2} =y^{2}[/tex]    .... equ 1

solving, where x = 4, we have

[tex]1^{2} +4^{2} =y^{2}[/tex]

[tex]y^{2} = 17[/tex]

[tex]y = \sqrt{17}[/tex]

Differentiating equ 1 implicitly with respect to t, we have

[tex]2x\frac{dx}{dt} = 2y\frac{dy}{dt}[/tex]

substituting values of

x = 4

y = [tex]\sqrt{17}[/tex]

[tex]\frac{dy}{dt}[/tex] = -1

into the equation, we get

[tex]2(4)\frac{dx}{dt} = 2(\sqrt{17} )(-1)[/tex]

[tex]\frac{dx}{dt} = \frac{-\sqrt{17} }{4}[/tex] = -1.031 m/s

Answer: 4.8mi

Step-by-step explanation:

From Newton, getting to Bloomington takes 10mi, and getting to Arlington takes 5.2mi.  Thus, simply do 10-5.2 to get 4.8mi.

Hope it helps <3

Answer:

A.

Step-by-step explanation:

40x is the number of lawns he can do, less the time to do his grandparents time (added to other law time) and he has 660 mins of less to complete them.

Answer:

a. 40x + 110 ≤ 660

Step-by-step explanation:

Answer:

[tex]y-4=2\,(x+1)[/tex]

which agrees with answer C in your list of possible answers.

Step-by-step explanation:

We can use the general point-slope form of a line of slope m and going through the point [tex](x_0, y_0)[/tex]:

[tex]y-y_0=m(x-x_0)[/tex]

which in our case, given the info on the slope (2) and the point (-1, 4) becomes:

[tex]y-y_0=m\,(x-x_0)\\y-4=2\,(x-(-1))\\y-4=2\,(x+1)[/tex]

Answer:

4h - 6 = 70.

Step-by-step explanation:

Jahill's height is 70 inches. That is 6 inches shorter than 4 times his sister's height, h. That is the same thing as 4 times h minus 6.

70 = 4 * h - 6

4 * h - 6 = 70

4h - 6 = 70

4h = 76

h = 19.

His sister is 19 inches tall.

Hope this helps!

Answer:

Hello! The answer will be below! :3

Step-by-step explanation:

Question: Jahlil is 6 inches shorter than 4 times his sister’s height. Jahlil’s height is 70 inches. Which equation represents h, his sister’s height in inches?

Answer:The answer is 4h - 6 =70

(His sister is 19 inches tall)

Steps:

4 * h - 6 = 70

So, 4h - 6 = 70......

And 4h will be 76 which means h will equal to 19

His sisters hight is about 19in. tall.....

Hope this helps! :)

⭐️Have a wonderful day!⭐️

Answer:

7987.1569 to the nearest thousandths is 7987.157

Step-by-step explanation:

Step-by-step explanation:

Statement: ∠O ≅ ∠O

Reason: Reflexive property

Statement: m∠OKW = 90° − m∠O

Reason: Complementary angles

Statement: m∠OJP = 90° − m∠O

Reason: Complementary angles

Statement: m∠OKW = m∠OJP

Reason: Substitution

Statement: ∠OKW ≅ ∠OJP

Reason: Definition of congruent angles

Statement: ΔOKW ~ ΔOJP

Reason: AA similarity

Answer:

D. [tex]70.34 cm^2[/tex]

Step-by-step explanation:

Area of sector of a circle is given as θ/360*πr²

Where,

r = radius = 12 cm

θ = 56°

Use 3.14 as π

Plug in the values into the formula and solve

[tex] area = \frac{56}{360}*3.14*12^2 [/tex]

[tex] area = 70.34 [/tex]

Area of the sector ABC = [tex] 70.34 cm^2 [/tex]

The answer is D

Step-by-step explanation:

The formulae to find them are:

and mode= number of greatest frequency.

(note; f is frequency, N is number of data and x is x is the raw data)

hope it helps..

Answer:

C (the third table, from the second picture).

Step-by-step explanation:

First, we need to find the slope of the graph.

Two conspicuous points are (0, -3) and (2, 1).

The slope is: (1 - -3) / (2 - 0) = (1 + 3) / 2 = 4 / 2 = 2.

A: In the table, the y-values increase by 2, while the x-values increase by 4. 2 / 4 = 1 / 2 = 0.5. The slope is not the same as the graph.

B: In the table, the y-values decrease by 2, while the x-values increase by 4. -2 / 4 = -1 / 2 = -0.5. The slope is not the same as the graph.

C: In the table, the y-values increase by 4, while the x-values increase by 2. 4 / 2 = 2 / 1 = 2. The slope is the same as the graph, so C is your answer.

D: In the table, the y-values decrease by 4, while the x-values increase by 2. -4 / 2 = -2 / 1 = -2. The slope is not the same as the graph.

Hope this helps!

Answer:

Standard form = y = mx + c

m = Δy/Δx

m = 5/2

y = 5/2 x + c

Sub in (4,2)

2 = 10 + c

c = -8

y = 5/2 x - 8  

Step-by-step explanation:

Find attached to this answer the diagram of the Quadrilateral

Question:

If ABCD is a parallelogram, AD = 14, EC = 11, m∠ABC = 64°, m∠DAC = 71°, and m∠BDC = 25, find each measure.

a) BC =

b) AC =

c) m∠DAB =

d) m∠ABD =

e) m∠ACD =

f) m∠ADB =​

Answer:

a) BC = 11

b) AC = 22

c) m∠DAB = 116°

d) m∠ABD = 39°

e) m∠ACD = 45°

f) m∠ADB =​ 25°

Step-by-step explanation:

a) BC

In the question above, EC = 11

We can see that EC and BC are equal sides of a diagonal line that has been divided into two equal parts in a Quadrilateral.

Hence, In a quadrilateral ABCD,

EC = BC

Hence BC = 11

b) AC

AC is one of the diagonal lines that divided parallelogram ABCD

AC = BC + EC

AC = 11 + 11

AC = 22

c) m∠DAB

m∠ABC = 64°

m∠ADC = 64°

For the two angles above, a diagonal bisects through those angles.

Also the sum of angles in a triangle = 180°

Hence,

180° = 1/2m∠ABC + 1/2m∠ADC +

m∠DAB

m∠DAB = 180° - ( 1/2 (64) + 1/2(64))

m∠DAB = 180 ° - 64°

m∠DAB = 116°

d) m∠ABD

Since,

m∠ABC = 64° and m∠BDC = 25

m∠ABC = m∠BDC + m∠ABD

64 = 25+ m∠ABD

m∠ABD = 64° - 25°

m∠ABD = 39°

e) m∠ACD

In the above question,

m∠ABC = 64°,

m∠ADC = m∠ABC, this is because, opposite angles in a quadrilateral are congruent and equal to each other.

Hence, m∠ADC = 64°

m∠DAC = 71°,

In a triangle , all the angles in a triangle = 180°

Hence,

180° = m∠DAC + m∠ADC + m∠ACD

180° = 71° + 64 ° + m∠ACD

m∠ACD = 180° -(71 + 64)°

m∠ACD = 180° - 135°

m∠ACD = 45°

f) m∠ADB

Since

m∠DAB = 116°

m∠ABD = 39°

The sum of angles in a triangle = 180°

180° = m∠ABD + m∠DAB + m∠ADB

180° = 39 ° + 116° + m∠ADB

m∠ADB = 180° - ( 116 + 39)°

m∠ADB = 25 °

a) BC = 11

b) AC = 22

c) m∠DAB = 116°

d) m∠ABD = 39°

e) m∠ACD = 45°

f) m∠ADB =​ 25°

Given : AD=14 , EC=11, m∠ABC= 64°, m∠DAC=71° and m∠BDC=25°

To find:  BC =?  , AC =? , m∠DAB =?, m∠ABD =?  ,m∠ACD =?  ,m∠ADB =​?

Consider the figure given below ABCD is a parallelogram

To find a) BC

Given, EC = 11

As seen in figure that EC and BC are equal sides of a diagonal line that has been divided into two equal parts in a Parallelogram.

Hence, In a Parallelogram ABCD,

EC = BC

Hence BC = 11

To find b) AC

AC is one of the diagonal lines that divided parallelogram ABCD

AC = BC + EC

AC = 11 + 11

AC = 22

To find c) m∠DAB

Given, m∠ABC = 64°

m∠ADC = 64°

(For the two angles above, a diagonal bisects through those angles)

Also From Angle sum property;

Hence,

180° = 1/2m∠ABC + 1/2m∠ADC +  m∠DAB

m∠DAB = 180° - ( 1/2 (64) + 1/2(64))

m∠DAB = 180 ° - 64°

m∠DAB = 116°

To find d) m∠ABD

Since,

m∠ABC = 64° and m∠BDC = 25  

m∠ABC = m∠BDC + m∠ABD

64 = 25+ m∠ABD

m∠ABD = 64° - 25°

m∠ABD = 39°

To find e) m∠ACD

Given,  m∠ABC = 64°;

m∠ADC = m∠ABC, this is because, opposite angles in a quadrilateral (here parallelogram) are congruent and equal to each other

Hence, m∠ADC = 64°

m∠DAC = 71°,

In a triangle , all the angles in a triangle = 180°(Angle sum property)

Hence,

180° = m∠DAC + m∠ADC + m∠ACD

180° = 71° + 64 ° + m∠ACD

m∠ACD = 180° - (71 + 64)°

m∠ACD = 180° - 135°

m∠ACD = 45°

To find f) m∠ADB

Since  ,m∠DAB = 116°  and m∠ABD = 39°

From Angle sum property;

180° = m∠ABD + m∠DAB + m∠ADB

180° = 39 ° + 116° + m∠ADB

m∠ADB = 180° - ( 116 + 39)°

m∠ADB = 25 °

Learn more:

https://brainly.com/question/23163052

Answer:

You can use your graphing calculator to find the answer.

Go to STAT, then TESTS, and hit "1: Z-Test..."

Make sure it is set to Stats, then for mu0, do 70; for standard deviation, do 9; for mean, you do 62; for sample size, you do 19. For mu, you do not equal to mu0. Then you hit "Calculate".

You then get a z-value (critical value) of -3.874576839, and a p-value of 0.00010685098.

This means that...

We reject the null hypothesis that the average height of lodgepole pines in Yellowstone is 70 feet because p = 0.0001 is less than the significance level of alpha = 0.01. There is sufficient evidence to suggest that the mean height of lodgepole pines in Yellowstone is NOT equal to 70 feet.

Hope this helps!