What are the values that go into the green box?

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If we know that the line passes through two points, (x₁, y₁) and (x₂, y₂), then we can write the slope as:

a = (y₂ - y₁)/(x₂ - x₁).

Also, for a given line:

y = m*x + s

A perpendicular line to that one must have a slope:

a = -(1/m)

And the intersection between two perpendicular lines forms four 90° angles.

So first, we need to find the slope of the line that passes through A and B.

A = (-3, 3)

B = (-1, -1)

Then the slope of the line is:

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

a = -2

The slope of a perpendicular line should be:

slope = -(1/a) = -(1/-2) = 1/2

Then the perpendicular line will be something like:

y = (1/2)*x + b

To find the value of b, we can use the other restriction.

This line needs to pass through point C.

And we can see that point C is:

C = (1, 2)

This means that when x is equal to 1, y must be equal to 2.

Then replacing these in the above equation we get:

2 = (1/2)*1 + b

2 = 1/2 + b

2 - 1/2 = 4/2 - 1/2 = 3/2 = b

Then our equation is:

y = (1/2)*x+ 3/2

The graph of this line can be seen in the image below, the green line is the line that we found.

If you want to read more about linear relations, you can see:

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Answer:

Step-by-step explanation:

Answer:

No, more information is needed to prove that Amy will get to school first.

Step-by-step explanation:

Even though Amy is traveling at a faster rate than Jeremy, the problem does not say how far away Amy's father's or Jeremy's aunt's houses are from the school.  

Answer:

Step-by-step explanation:

No, the rate with the greater positive rate of change will not necessarily reach the output with the smallest input. The initial value will also affect the outcome. Although Amy is biking at a faster rate of change, Jeremy might get to school before her if his aunt lives closer to the school than her father does.

Explanation: Edge. said so.

Answer:

C2 because 40+40+25 equals 105 not 110

Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The cylinder would show an ellipse when cut diagonally. Please Brainliest PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS.

Answer:

15

Step-by-step explanation:

Use the distance formula

d = distance

[tex]d=\sqrt{(10-1)^2 + (-4 - (8))^2\\[/tex]

Solve the equation to get the following:

[tex]d=\sqrt{9^2 + (-12)^2}[/tex]

[tex]d = \sqrt{81+144[/tex]

[tex]d=\sqrt{225[/tex]

[tex]d = \sqrt{15[/tex]

Answer:

0.02

Step-by-step explanation:

X has 10 boxes and when divided by 100 is equal to 0.1. Y is 2 boxes so just divide it by 100 and you get 0.02.

If [tex]P(x) = p_nx^n + p_{n-1}x^{n-1}+\ldots+p_0[/tex] is divided by [tex](x-a)[/tex], then [tex]P(x) = (x-a) \cdot Q(x) + R(x)[/tex] for some polynomials [tex]Q,R[/tex]. Moreover, [tex]\deg R < 1[/tex] (because [tex]\deg (x-a) = 1[/tex]), so there exists  [tex]\alpha \in \mathbb{R}[/tex] such that [tex]R(x) = \alpha[/tex] for all [tex]x \in \mathbb{R}[/tex]. But if we calculate [tex]P(a)[/tex], it turns out that [tex]P(a) = (a-a)\cdot Q(a) + \alpha[/tex], so [tex]R(x) = \alpha = P(a)[/tex]. [tex]\blacksquare[/tex]

[tex] \frac{5}{ \sqrt{3} } \\ = \frac{5 \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } \\ = \frac{5 \sqrt{3} }{ { \sqrt{3} }^{2} } \\ = \frac{5 \sqrt{3} }{3} [/tex]

This is the answer.

Answer:

n = 220, 4, -4, -220

Step-by-step explanation:

factors of 17: 17, 1, -1, -17

13 is prime number: 13 x  1 = 13

(ax+b)(cx+d) = axcx+axd+bcx+bd

(x + 17)(13x - 1) = 13x^2 + 220x - 17, n = 220

(x - 17)(13x + 1) = 13x^2 - 220x - 17, n = -220

(x + 1)(13x - 17) = 13x^2 - 4x - 17, n = -4

(x - 1)(13x + 17) = 13x^2 + 4x - 17, n = 4

Answer:

0.5 is the answer of this question

bro!

Answer:

Linear pairs add up to 180°

1st angle = x

2nd angle = x+24 (24° more than the first)

The equation would be

1st angle + second angle = 180 Subbing in the expressions we came up with:

x+x+24 = 180

Answer:

a. GBC, FCB, DCH

b. FCD+HCD=180

Step-by-step explanation:

A

B

The angles that are congruent to ABE are BCF, DCH, and CBG

Angles FCD and HCD lie on the same straight line. This means that the sum of both angles will sum up to 180degrees since the sum of angle of a straight line is 180degrees (supplementary). Hence the required equation will be:

<FCD + <HCD = 180

An angle is a point where two lines meet or intersect.

The angles that are congruent to ABE are BCF, DCH, and CBG

ABE = BCE (corresponding angle)

Since BCE = DCH (vertically opposite angles), hence:

ABE = DCH (vertically opposite angles)

Also, we can see that DCH = CBG (corresponding angles), hence:

ABE = CBG (corresponding angle)

b) From the given diagram, we can see that angles FCD and HCD lie on the same straight line. This means that the sum of both angles will sum up to 180degrees since the sum of angle of a straight line is 180degrees (supplementary). Hence the required equation will be:

<FCD + <HCD = 180

Learn mre here: https://brainly.com/question/14941189

Answer:

GH = 8.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan J = opp side / adj side

tan J = HG / HJ

tan 40 = GH / 10

10 tan 40 = GH

8.39099=GH

Rounding to the nearest tenth

GH = 8.4

Answer:

G = 140

Step-by-step explanation:

Linear pairs add to 180

H+G = 180

40+G = 180

G = 180-40

G = 140

Answer:

Where I can't see the pattern made from sticks?

Answer:

0.6192

Step-by-step explanation:

Answer:

y=(3/4)x+2

Step-by-step explanation:

write the equation in slope-intercept form: y=(3/4)x - 3

since it is parallel the slope is the same so we have y=(3/4)x + b

then plug in the point (-1) = (3/4)(-4) + b

-1 = -3 +b, b=2

y= (3/4)x + 2

Answer:

(0, -2)

(-3, 1)

(3, -4)

Step-by-step explanation:

The constraints given as;

x + y ≥ -2

3x - y ≤ 2

x - y ≥ -4

Since we want to find vertices of the feasible region, we will ignore the less than or greater than sign and use the equal to sign to some simultaneously.

Let's add first and third constraint together to get;

2x = -6

x = -6/2

x = - 3

Put - 3 for x in equation 1 to get;

-3 + y = -2

y = 3 - 2

y = 1

Thus, vertex here is; (-3, 1)

Lets add first and third equations to get;

4x + 0 = 0

Thus, x = 0

Putting this for x in eq 1;

0 + y = -2

y = -2

vertex here is; (0, -2)

Lets subtract eq 3 from eq 2 to get;

2x = 6

x = 6/2

x = 3

Put 3 for x in eq 3;

x - y = -4

vertex here is; (3, -4)

Answer:

-15,-5,0,10,25

Step-by-step explanation:

Answer:

A (-6, 0) (-2, 0), and (0,0)

Step-by-step explanation:

just took quiz on this

Answer:

20.66 cm^2

Step-by-step explanation:

area =1/2 AxB sine C

=1/2 x11x8 x sine 152

=11x4x0.46947156279

20.65674876258 cm^2

=20.6567cm^2

rounding it to the nearest hundredth we get,

20.66 cm^2

Answer:

C

Step-by-step explanation:

First, we can see that from f(x) to g(x), the change in x for each change in y is significantly increased. This represents a stretch in the x direction. A stretch/compression in the x direction is represented by

f(cx), with c > 1 representing a compression by c and 0 < c < 1 representing a stretch by a value of 1/c. From the vertex of each, when y changes by 1, in f(x) x changes by 2 (e.g. from x=2 to x=4), whereas in g(x) x changes by 4 (e.g. from x=-4 to x=0). Therefore, g(x) stretches x by 2, so c = 1/2, giving us

f(c(x))

= f(1/2(x))

Let's say f(a) =  f(1/2(x))

Then, because the graph stretched by 2, the vertex goes from x=2 to x=4. Our vertex is at x=-4 in g(x), so to make the vertex equal to that, we can flip f(a) around the y axis. To flip this around the y axis, we can plug -a in for a, resulting in

f (-(a))

= f(-(1/2)(x))

= g(x)

Answer:

prime factors are factors of a number that are prime numbers, (meaning they can only be divided by 1 and itself), while odd numbers are numbers that are odd..

all odd numbers have prime factors but not all prime factors are odd numbers

Answer:

Total income is 60,000

Step-by-step explanation:

I. if paid rate is 30%, that's mean 42,000 is 70%

II. Perform ratio 70/100 = 42,000/x

                       70*x = 100 * 42,000

                        70x = 4,200,000

                            x = 60,000

III. If you perform 30/100 = x/60,000 will be 42,000

Sorry for late.

Answer:

x=14

Step-by-step explanation:

Form an equation; since the two sides are the same length set them equal to each other. 2x-9=x+5 the solve

2x=x+14

x=14

then you can plug it back in to check if you want

2(14)-9 = 19

14+5 = 19

Answer:

14

Step-by-step explanation:

2x-9=x+5 (being isosceles triange)

2x-x=5+9

x=14

hope u understood

Answer:

1.68

Step-by-step explanation:

log723.7=2.86

multiplication in log is addition so 2.86+

log0.0667=-1.18

so 2.86+-1.18=1.68

Answer:

Greatest number is 65432

Lowest number is 23456

Step-by-step explanation:

[tex]65432+23456=88888[/tex]

Answer:

45. -7.1, -7 1/7

46. 3.7

Step-by-step explanation:

45. y < -7

Answer: -7.1, -7 1/7

46.

z > 3 2/3

Answer: 3.7