The function f(x) is graphed below. what is f(2)-f(-1)?

This is equivalent to y = 3x+4 (slope intercept form)

By "standard form", I mean the form Ax+By+C = 0.

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Explanation:

Let's solve the first equation for y

x+3y-4 = 0

x+3y = 4

3y = 4-x

3y = -x+4

y = (-x+4)/3

y = (-x/3) + (4/3)

y = (-1/3)x + (4/3)

The equation is now in y = mx+b form, aka slope intercept form, with m = -1/3 as the slope and b = 4/3 as the y intercept. We'll focus on the slope.

Apply the negative reciprocal to this so that we go from -1/3 to +3/1 or simply 3. Flip the fraction and the sign. Note how -1/3 and 3 multiply to -1. Perpendicular slopes always multiply to -1, assuming neither line is vertical.

So this mystery perpendicular line we're after has a slope of 3.

It has the same y intercept as 2x+5y-20 = 0. Plug in x = 0 and solve for to determine the y intercept.

2x+5y-20 = 0

2(0)+5y-20 = 0

5y-20 = 0

5y = 20

y = 50/5

y = 4

The y intercept of 2x+5y-20 = 0 is y = 4, so it's also the y intercept of our final answer. Let b = 4.

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We found that:

So we know that,

y = mx+b

y = 3x+4

is the slope intercept form of the answer. Since your teacher gave you the equations in standard form (one version of it anyway), let's convert y = 3x+4 to that form as well

y = 3x+4

y-3x = 4

-3x+y = 4 .... one way to express standard form

-3x+y-4 = 0 .... another standard form

Some math textbooks use Ax+By = C as standard form, while others use Ax+By+C = 0. Unfortunately, it's a bit confusing because the same phrasing is used.

Answer:

Step-by-step explanation:

The surface area of a square pyramid = 1/2 * slant height * base perimeter + area of base

 The slant height is 5 cm

The base perimeter is 4 * 5 cm = 20 cm

The area of the base is 5 cm * 5 cm = 25 cm**2

Plugging into the formula the area =

1/2 * 5 cm * 20 cm + 25 cm**2 =

5 cm * 10 cm + 25 cm**2 =

50 cm**2 + 25 cm**2 = 75 cm**2

Answer: 3.9047 rounded to the nearest thousandth is 3.9050, or 3.905.

Step-by-step explanation:

You round 47 up to 50, which gets you to 3.9050, which you can then reduce it to 3.905.

Answer:

68

Step-by-step explanation:

A P E X

Answer:

(a) Attached to this response.

(b)

(i) 0 cups = 0.275

(ii) 4 cups = 0.125

(iii) 8 cups = 0.025

Step-by-step explanation:

(a) The frequency and relative frequency table has been attached to this response.

i. The first column, labelled x, is the number of cups of coffee consumed per day.

ii. The second column, labelled f, is the number of people that consumed x cups of coffee per day. It is found by counting the number of occurrences (i.e frequency) of the numbers of the first column, x, in the given data.

For example, 0 in first column appears 11 times in the given data. Also, 5 in the first column appears 4 times in the given data.

iii. The third column, labelled r, is the relative relative frequency of the number of cups of coffee. It is calculated by dividing the frequency of the cups of coffee by the total number of people that consumed it. As shown on the table, it is calculated by dividing the each of the values on the second column by the sum of the values on that same column (second column).

For example, the relative frequency of 2 cups of coffee is given by:

r = 7  ÷ 40 = 0.175

Also, the relative frequency of 4 cups of coffee is given by;

r = 5 ÷ 40 = 0.125

(b) The probability (Pₓ) that a randomly selected person consumed x cups of coffee is given by;

Pₓ = frequency of x ÷ total frequency

This is also the relative frequency of x

Therefore,

(i) The probability (P₀) that a randomly selected person consumed 0 cups of coffee is given by;

the relative frequency of 0 = 0.275

(ii) The probability (P₄) that a randomly selected person consumed 4 cups of coffee is given by;

the relative frequency of 4 = 0.125

(iii) The probability (P₈) that a randomly selected person consumed 8 cups of coffee is given by;

the relative frequency of 8 = 0.025

Answer:

Tip = $9

Step-by-step explanation:

Bill amount to nearest ten dollars = $60

[tex]tip = 15\% of 60 = \frac{15}{100} \times 60 = 9[/tex]

Answer:

hiii

zom I'd 213 088 8336

p 0

come for s

Answer:

113 degree

Step-by-step explanation:

missing angle is 113 degree because the relation between 113 degree and missing angle is alternate interior angle and alternate interior angles are always equal.

Answer:

2.77

Step-by-step explanation:

39.50x.07=2.77

Answer:

7 feet i think? i may be wrong tho

Step-by-step explanation:

Answer:

p = 4

Step-by-step explanation:

Given the expression x ^ 2-px + 3 = 0

If x = 0 is a solution

Substitute into the expression

0² - 0p + 3 = 0

-0p = -3

p = 3/0

p cannot be determined for this root

If x = 1

1² - 1p + 3 =0

1 - p + 3 = 0

-p+4 = 0

-p = -4

p = 4

Hence the va;ue of p is 4

Answer:

It would be 125 fish.

Step-by-step explanation:

This is because since there are 10 crustaceans for every 25 fish, there are 2.5 times more fish than crustaceans. Therefore, if there were 50 crustaceans, you would do 50 * 2.5 to get 125 fish.

Answer:

V = 696.91

Step-by-step explanation:

Volume of a sphere formula:

V = 4/3πr³

Given:

d = 11

r = d/2

r = 5.5

Work:

V = 4/3πr³

V = 4/3π(5.5)³

V = 4/3π(166.375)

V = 696.91

Answer:

Step-by-step explanation:

take theta as reference angle

using sin rule

sin theta=opposite/hypotenuse

sin theta=3/5

sin theta=0.60

theta=sin 37 degree

therefore the value of theta is 37 degree.

Answer:

326.73cm²

Step-by-step explanation:

=

2

π

r

h

2

π

r

2

=

2

π

4

9

2

π

4

2

≈

326.72564cm²

Answer:

[tex]D. a = 40; b=140; c = 90[/tex]

Step-by-step explanation:

[tex]a=2(20)\\\\=40[/tex]

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[tex]b=180-40\\\\=140[/tex]

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[tex]c=90[/tex]

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hope it helps...

have a great day!!

Answer:

SR=1/2*PO

5x-38=1/2*7x-49

2(5x-38)=7x-49

10x-76=7x-49

10x-7x=-49+76

3x=27

x=27/3

x=9

substitute the value of x in RS

5x-38

5*9-38

45-38

7

Step-by-step explanation:

Answer:

RS = 7

Step-by-step explanation:

Given a segment joining the midpoints of 2 sides of a triangle then it is half the length of the third side, that is

5x - 38 = [tex]\frac{1}{2}[/tex] (7x - 49) ( multiply both sides by 2 to clear the fraction )

10x - 76 = 7x - 49 ( subtract 7x from both sides )

3x - 76 = - 49 ( add 76 to both sides )

3x = 27 ( divide both sides by 3 )

x = 9

Then

RS = 5x - 38 = 5(9) - 38 = 45 - 38 = 7

Answer:

Step-by-step explanation:

convert either gram into kg or kg into gram

lets convert kg into g

1 kg=1000g

20kg=1000*24g

=20000g

450/20000*100%

450/200%

2.25%

first convert 450 g to kg = 0.45 kg

Now 0.45 kg as a. percentage of 20 kg = 0.45/20×100= 2.25%

Answer:

The third one

Step-by-step explanation:

Answer:

the third one

Step-by-step explanation:

Answer:

(2,-7)

Step-by-step explanation:

Answer:

1.0

2.undefined

Step-by-step explanation:

Answer:1) 0, 2) is undefined

Step-by-step explanation:

Answer:  a is 21 b is 45 and c is yes more people are going above because the median is above the speed limit

Step-by-step explanation:

Answer:

x = 14

m<D = 57

Step-by-step explanation:

All triangle interior angles add up to 180.

<D and <E are congruent because of the congruent legs which makes them congruent angles:

4x + 1 + 4x + 1 + 5x - 4 = 180

13x - 2 = 180

13x = 180 + 2

13x = 182

x = 14

m<D:

4x + 1

4(14) + 1

56 + 1

57

Answer:

20

Step-by-step explanation:

Answer:

Option 3

Step-by-step explanation:

y=3+x is a straight line that runs through y=3 and x=-3

So your 3rd option here is the one.

Answer:

I think it's the third option

Answer:

Step-by-step explanation:

[tex]x^{5} -x^{4}-2x^{3} +2x^{2} =0\\\\x^{4} (x-1) -2x^{2} (x-1) =0\\\\(x^{4} -2x^{2} ) (x-1)=0\\\\ x^{2} (x^{2} -2)(x-1) =0[/tex]

solutions are

x² =0 so x=0

x²-2 = 0 so x= ±√2

x-1 =0 so x= 1

Answer:

150.7

Step-by-step explanation:

Formula to the find volume of a pyramid:

V=1/3 (B)(h)

V=1/3 (19) (23.8)

Answer:

X = -2

Step-by-step explanation:

Hope this helps

Answer:

∠ADB= 360-90

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hope it helps...

have a great day!!