A pair of linear equations is shown below:

y = −x + 1
y = 2x + 4

Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)

On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.
On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.
On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

Answer: 8 students

Step-by-step explanation:

2/5 of 40 = 16

1/5 of 40 = 8

16 - 8 = 8

Answer:

7/24

Step-by-step explanation:

in order to get the fraction, you need to add all of the books read together; you should get 120.

Then add all of the books read in even classes(2nd grade and 4th grade) and you should get 35.

Then place 35 on top of 120 to form the fraction: 35/120.

Then simplify the fraction by finding the greatest common factor, which is 5, and divide 35 and 120 by 5 to get 7 and 24.

Answer:

x^2-5x + 6

Step-by-step explanation:

Here, we want to expand the given expressions

To do this, we multiply each term in the first bracket with each term in the second

We then proceed to collect like terms

We have this as;

x(x-3) - 2(x-3)

= x^2 - 3x -2x + 6

= x^2 -5x + 6

Answer:

d

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

We need to find 12k - h² , where

Subsitute upon respective values ,

=> 12k - h² = 12*3 - 2²

=> 12k - h² = 36 - 4

=> 12k - h² = 32

The answer is A. unchanged

9514 1404 393

Answer:

  y = 2/3x -20/3

Step-by-step explanation:

The perpendicular line will have a slope that is the opposite of the reciprocal of the slope of the given line:

  -1/(-3/2) = 2/3

You can use the point-slope form to write the equation of that perpendicular line.

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y +2 = 2/3(x -7) . . . . . the equation of the perpendicular line

__

This can be put into slope-intercept form by solving for y and simplifying.

  y +2 = 2/3x -14/3

  y = 2/3x -20/3

Answer:

slope is 0

Step-by-step explanation:

The slope of any horizontal line is zero, 0.

Answer:

13.7%

Step-by-step explanation:

Percentage decrease = (3.65 - 3.15) / 3.65 * 100% = 13.7%

Answer:

4 goats

Step-by-step explanation:

Let us represent

Number of quails = x

Number of goats = y

Quails have 2 legs

Goats have 4 legs

Hence:

There are 6 animals in the pen some are quails and some are goats

x + y = 6...... Equation 1

x = 6 - y

if there are 20 legs in all how many quails

2x + 4y = 20..... Equation 2

We substitute 6 - y for x in Equation 2

2(6 - y) + 4y = 20

12 - 2y + 4y = 20

Collect like terms

- 2y + 4y = 20 - 12

2y = 8

y = 8/2

y = 4 goats

The number of goats there are 4 goats

Answer:

sorry dont know

Step-by-step explanation:

Answer:

a = 8

b = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

I've attached a picture of the 45-45-90 triangle's formula, which is the length of the hypotenuse = [tex]\sqrt{2}[/tex] times the length of a leg (one of the sides of the triangle).

So, applying this to your problem, if 4[tex]\sqrt{2}[/tex] if one of the legs of the triangle, the other leg, which is b , would be the same length.

b = 4[tex]\sqrt{2}[/tex]

To solve for a, you would have to multiply the leg by [tex]\sqrt{2}[/tex].

a = 4[tex]\sqrt{2}[/tex] x [tex]\sqrt{2}[/tex]

I would separate the 4 and the [tex]\sqrt{2}[/tex].

a = 4 x [tex]\sqrt{2}[/tex] x [tex]\sqrt{2}[/tex]

a = 4 x [tex]\sqrt{2 *2}[/tex]

a = 4 x [tex]\sqrt{4}[/tex]

a = 4 x 2

a= 8

Answer:

Radical expressions must be simplified before adding or subtracting so that you are combining “like terms”. In the same way that 2x2 and 3x cannot be combined because they are not like terms, terms involving radicals cannot be combined unless the value under the radical is the same for both terms.

Answer:

180

Step-by-step explanation:

Given:

In ΔFGH, the measure of ∠H=90°, FH = 39, GF = 89, and HG = 80.

To find:

The ratio which represents the cotangent of ∠G.

Solution:

In a right angle triangle, the ratio of the cotangent of an angle is

[tex]\cot \theta =\dfrac{Base}{Perpendicular}[/tex]

It is also written as

[tex]\cot \theta =\dfrac{Adjacent}{Opposite}[/tex]

In ΔFGH, the measure of ∠H=90°. So,

[tex]\cot G =\dfrac{HG}{FH}[/tex]

[tex]\cot G =\dfrac{80}{39}[/tex]

Therefore, the ratio for the cotangent of ∠G is [tex]\cot G=\dfrac{80}{39}[/tex].

Answer:

step 2

Step-by-step explanation:

instead of subtracting 7 to the oposite side they set it aside to then later on add it towards the end.

Answer:

Step-by-step explanation:

85°

Answer:

60

Step-by-step explanation:

All the sides are equal

Answer:

c=3

Step-by-step explanation:

Answer:

Let [tex]\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)[/tex], we proceed to prove the trigonometric expression by trigonometric identity:

1) [tex]\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)[/tex] Given

2) [tex]\left(1+\frac{\cos^{2}A}{\sin^{2}A} \right)\cdot \left(1+\frac{\sin^{2}A}{\cos^{2}A} \right)[/tex]   [tex]\tan A = \frac{1}{\cot A} = \frac{\sin A}{\cos A}[/tex]

3) [tex]\left(\frac{\sin^{2}A+\cos^{2}A}{\sin^{2}A} \right)\cdot \left(\frac{\cos^{2}A+\sin^{2}A}{\cos^{2}A} \right)[/tex]    

4) [tex]\left(\frac{1}{\sin^{2}A} \right)\cdot \left(\frac{1}{\cos^{2}A} \right)[/tex]    [tex]\sin^{2}A+\cos^{2}A = 1[/tex]

5) [tex]\frac{1}{\sin^{2}A\cdot \cos^{2}A}[/tex]

6) [tex]\frac{1}{\sin^{2}A\cdot (1-\sin^{2}A)}[/tex]    [tex]\sin^{2}A+\cos^{2}A = 1[/tex]

7) [tex]\frac{1}{\sin^{2}A-\sin^{4}A}[/tex] Result

Step-by-step explanation:

Let [tex]\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)[/tex], we proceed to prove the trigonometric expression by trigonometric identity:

1) [tex]\left(1+\frac{1}{\tan^{2}A} \right)\cdot \left(1+\frac{1}{\cot^{2}A} \right)[/tex] Given

2) [tex]\left(1+\frac{\cos^{2}A}{\sin^{2}A} \right)\cdot \left(1+\frac{\sin^{2}A}{\cos^{2}A} \right)[/tex]   [tex]\tan A = \frac{1}{\cot A} = \frac{\sin A}{\cos A}[/tex]

3) [tex]\left(\frac{\sin^{2}A+\cos^{2}A}{\sin^{2}A} \right)\cdot \left(\frac{\cos^{2}A+\sin^{2}A}{\cos^{2}A} \right)[/tex]    

4) [tex]\left(\frac{1}{\sin^{2}A} \right)\cdot \left(\frac{1}{\cos^{2}A} \right)[/tex]    [tex]\sin^{2}A+\cos^{2}A = 1[/tex]

5) [tex]\frac{1}{\sin^{2}A\cdot \cos^{2}A}[/tex]

6) [tex]\frac{1}{\sin^{2}A\cdot (1-\sin^{2}A)}[/tex]    [tex]\sin^{2}A+\cos^{2}A = 1[/tex]

7) [tex]\frac{1}{\sin^{2}A-\sin^{4}A}[/tex] Result

Answer:

30f+25 I hope it is a right answers

I hope this answers is useful for you

Answer:

Outlier

Step-by-step explanation:

Answer:

1. If x=5, 3*5=15, 15*15=225 + y (3) = 228.

2. If y=4, then 10*4 = 40, 4^2 is 16, so 40 + 16 is 56.

I might be wrong, but the first one you answered, x^2, x= 1/2, I think that is wrong. when something is squared, you don't go, "Oh, well since 1/2 equals 1, that's the answer." The way to figure out something like this is... 1/2 times 1/2, which is .25, or 1/4. Another example: 3^5 . The way to find this out is 3*3*3*3*3 = 243. But  you don't go 3*5, because that answer would be 15, which is not correct.

Answer:

30/40 and 12/16 are equivalent fractions.

Answer:

y=5

Step-by-step explanation:

It has same slope of y=3, which means it is also a horizontal line. A horizontal slope will only have one y value. So, if we use the point (1, 5), we can say that the equation is y=5.

Answer:

The time would become 13:40

Step-by-step explanation:

8 in 8:40 is hours

40 in 8:40 is minutes.

Answer:

1:40pm

Step-by-step explanation: