Which of the following is a quadratic equation whose roots are 3 and -1?

Answer:

[tex]f(a) = 5a + 1[/tex]

[tex]f(a + h) = 5a + 5h +1[/tex]

[tex]\frac{f(a + h) - f(a)}{h} =5[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5x + 1[/tex]

Solving (a): f(a)

Substitute a for x in [tex]f(x) = 5x + 1[/tex]

[tex]f(a) = 5a + 1[/tex]

Solving (b): f(a + h)

Substitute a + h for x in [tex]f(x) = 5x + 1[/tex]

[tex]f(a + h) = 5(a + h) +1[/tex]

Open bracket

[tex]f(a + h) = 5a + 5h +1[/tex]

Solving (c): [tex]\frac{f(a + h) - f(a)}{h}[/tex]

In (a):

[tex]f(a) = 5a + 1[/tex]

In (b):

[tex]f(a + h) = 5a + 5h +1[/tex]

So:

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a+5h+1 - (5a+1)}{h}[/tex]

Open bracket

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a+5h+1 - 5a-1}{h}[/tex]

Collect Like Terms

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a- 5a+5h+1 -1}{h}[/tex]

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5h}{h}[/tex]

[tex]\frac{f(a + h) - f(a)}{h} =5[/tex]

Answer:

20C4=4845

Step-by-step explanation:

Answer:(-4,6)

Step-by-step explanation:

you go down four then over six and you find the letter F

Answer:

(6, -4)

Step-by-step explanation:

x axis is before the y axis

Answer:

B: $18.40

Step-by-step explanation:

100% is equal to $16 so 5% would be 16/20 or $0.80 then to get 15% you would multiply $0.80 by 3 which is $2.40. This is the tip. Then do $16 + $2.40 and the total + tip is $18.40. (Double check to make sure I'm correct)

Answer:

I dont know

Step-by-step explanation:

I don’t know

Answer:

28.26

Step-by-step explanation:

A = r^2

So the equation is. Area of circle = pi(3.14) * radius(3) to the power of 2 (^2)

A = 3.14(3)^2

A = 3.14(9)

A = 28.26

Answer:

r = 80 KM/HR

w= 30 CM/HR

Step-by-step explanation:

Answer:

[tex]h = 162.0\ cm[/tex]

Step-by-step explanation:

Given

[tex]BSA = \frac{\sqrt{w*h}}{60}[/tex]

Required

Find h, when BSA = 1.5 and w = 50

We have:

[tex]BSA = \frac{\sqrt{w*h}}{60}[/tex]

Substitute 1.5 for BSA and 50 for w

[tex]1.5 = \frac{\sqrt{50*h}}{60}[/tex]

Multiply both sides by 60

[tex]60*1.5 = \frac{\sqrt{50*h}}{60}*60[/tex]

[tex]60*1.5 = \sqrt{50*h[/tex]

[tex]90 = \sqrt{50*h[/tex]

Square both sides

[tex]90^2 = (\sqrt{50*h})^2[/tex]

[tex]90^2 = 50*h[/tex]

[tex]90^2 = 50h[/tex]

[tex]8100 = 50h[/tex]

Divide both sides by 50

[tex]\frac{8100}{50} = \frac{50h}{50}[/tex]

[tex]\frac{8100}{50} = h[/tex]

[tex]162 = h[/tex]

[tex]h = 162[/tex]

[tex]h = 162.0\ cm[/tex]

Hence, the patient's height is 162.0cm

Answer and Step-by-step explanation:

22ft = x (c)

20ft = y (b)

18ft = z (a)

Plug into equation.

[tex]22^{2} = 20^{2} + 18^{2} - 2(20)(18)cosC (X)\\\\484 = 724 - 720cosC\\\\-240 = -720cosC\\\\\frac{1}{3} = cosC\\\\cosx^{1} (\frac{1}{3} ) = C\\\\C = 70.5288\\\\[/tex]

C ≈ 70.5 is the answer.

Step-by-step explanation:

///////hope it helps:)

The trigonometric function gives the ratio of different sides of a right-angle triangle. The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse.

The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

The angle of elevation is equal to,

The angle of elevation = Sin⁻¹ (4.5/11.75)

                                      = 22.5183° ≈ 23°

Hence, the angle of elevation formed by the ramp by the ground to the nearest degree is 23°.

Learn more about Sine:

https://brainly.com/question/21286835

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Answer:

18ft

Step-by-step explanation:

:p

The height of the tree is 14 feet.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Height of Man= 6 feet

Shadow height= 5 feet

and, Height of tree shadow= 15 feet

So, using Proportion

FE/ BC = FA/ AC

6 / x = 5 / 15

5x= 90

x= 14 feet

Hence, the tree is 14 feet tall.

Learn more about Proportion here:

https://brainly.com/question/26974513

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Answer:

$9.60

Step-by-step explanation:

3.20x3=9.60

Answer:

what is the surface area of this shape? 328 yd

Step-by-step explanation:

Surface area = 2 × (11×8 + 11×4 + 8×4)

Surface area = 2 × (88 + 44 + 32)

Surface area = 2 × 164

Surface area = 328 yd

Answer:

1. x = - 1 -y over 2

2. x = -4(2+y) over 3

Step-by-step explanation:

Answer:

1. x = - 1 -y over 2

2. x = -4(2+y) over 3

:)

Answer:

Step-by-step explanation:

A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable). A purchaser is offered a choice of manufacturer for each component.

Receiver: Kenwood, Sony, Sherwood

Compact disc player: Onkyo, Pioneer, Sony, Technics

Speakers: Boston, Infinity, Polk

Turntable: Onkyo, Sony, Teac, Technics

A switchboard display in the store allows a customer to hook together any selection of components (consisting of one of each type). Use the product rules:

A. In how many ways can one component of each type beselected?

B. In how many ways can components be selected if boththe receiver and the cd player are to be sony?

C. In how many ways can components be selected if noneis to be sony?

D. In how many ways can a selection be made if at leastone sony component is to be included?

E. If someone flips the switches on the selection in acompletely random fashion, what is the probability that the systemselected contains at least one sony component?

Answer:

Step-by-step explanation:

Where are the choices?

m and f are the cups of milk and flour, respectively.

m = ¼f + 1

Answer:

x-12=18

Step-by-step explanation:

Answer: if X = 30, then the equation is 30 - 12 = 18

Answer:

..................

Step-by-step explanation:

................................

Answer:

Pickles. My friends are allergic to cheese.

9514 1404 393

Answer:

Step-by-step explanation:

Using 'y' and 'z' to represent angles with the corresponding names, we have ...

  y + z = 90

  (3b -1) +(2b +6) = 90 . . . . substitute the given expressions

  5b +5 = 90 . . . . . . . . . . . . simplify

  b +1 = 18 . . . . . . . . . divide by 5

  b = 17 . . . . . . . . subtract 1

Then the angles are ...

  y = 3b -1 = 3(17) -1 = 51 -1 = 50

  z = 2b +6 = 2(17) +6 = 34 +6 = 40 . . . . note that these are complementary, as theys should be

Angles W and Y form a linear pair, so are supplementary:

  W = 180 -Y = 180 -50 = 130

Angles X and Z form a linear pair, so are supplementary:

  X = 180 -Z = 180 -40 = 140

Then the angle measures are ...

Answer:

Step-by-step explanation:

To find the expected no of broken cabinets for each strategy.

If A transport all the furniture

Suppose X₁ = number of furniture A broken

X₁ follows a binomial with n = 3, p = 0.10

E(X₁) = np

E(X₁) = 3 × 0.1

E(X₁) = 0.3

If A transport two (2) cabinets & B transport one (1) cabinet

expected no. of the broken cabinet by A out of 2 is

= 2 × 0.1

= 0.2

Suppose X₂ denotes the no of broken furniture by B

E(X₂) = np

where n= 1 and p = 0.15

E(X₂) = np

E(X₂) = 1 × 0.15

E(X₂) = 0.15

Thus. the expected number of broken cabinets = 0.2 + 0.15 = 0.35

Answer:

the first one is 5 times 5 times 5

the second is 7 times 7

the third is 2 times 2 times 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

x - 2y =8

   -2y = -x + 8

      [tex]y = \frac{-1}{-2}x+ \frac{8}{-2}\\\\y =\frac{1}{2}x - 4[/tex]

When x = 4,

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

(4, - 2)

When x = -4,

    [tex]y =\frac{1}{2}*(-4) - 4\\\\ = -2 - 4\\\\= - 6[/tex]

(-4, -6)

Plot the points (4, -2) and (-4 , -6) in the graph and Join the points

Answer:

Part A:  y = 3

Part B:  Area = 60 sq units

Step-by-step explanation:

we can create this system of equations from the information given:

8y + 2x = 34

10y + 2x = 40

now we can subtract to get:

-2y = -6

y = 3

solve for 'x':

8(3) + 2x = 34

24 + 2x = 34

2x = 10

x = 5

Area of Rectangle is 12 x 5

Answer:

2 1/10

Step-by-step explanation:

Answer:

they form a single straight line:)

Answer:

a line

Step-by-step explanation:

Here is ray AB  

     A                         B

     +----------------------+------------------->

It starts at point A, goes through point B, and goes only in one direction, to the right. Points A and B lie on line AB.

Now I'll add an opposite ray whose endpoint is also point A.

             C                A                         B

<-----------+--------------+----------------------+------------------->

Ray AC also lies on the same line as ray AB, but starting at point A, it goes in the opposite direction of ray AB. When you add ray AC to its opposite ray AB, you get the entire line AB.

Answer: a line