Part A
The graph of which quadratic function has roots of 7 and 3 and passes through (2, 10)?

Multiple choice question.

A)
f(x)=x2+10x+21


B)
f(x)=x2 – 10x+21


C)
f(x)=2x2 – 20x+42


D)
f(x)=2x2+20x – 42

Part B
Select the correct choices to complete the sentence.
The graph of the function has a , 1 of 1.
minimum
maximum

Answer:

The opportunity cost of playing an hour of video games is not reading 3 chapters of a book.

Step-by-step explanation:

Given that Anthony can either play 4 hours of video games or read 12 chapters of a book, to determine what is Anthony's opportunity cost of playing one hour of video games, the following calculation must be performed:

4 = 12

1 = X

1 x 12/4 = X

12/4 = X

3 = X

Therefore, the opportunity cost of playing an hour of video games is not reading 3 chapters of a book.

Answer:

I don’t know

Step-by-step explanation:

You didn’t attach a photo lol

Answer:

08-Oct-2009 — If a spherical balloon has a volume of 972 pi cubic centimeters, what is ... is 4.pi.r^2 (its area remember not volume) as 4/3.pi.r^3=972pi r=9 ... and it is good to know the squares of the next 10 numbers.

Answer:

I have this same question on my math test.

Since the radius is 9, the diameter is 18.

The shape is being dilated by 2/3, so the new radius is 6.

Volume formula: V = 4/3πr^3

So now we plug in the values.

V = 4/3 x π x (6)^3

V = 4/3 x π x 216

V = 288π

If the answers do not have the pi symbol present, then it has been multiplied into the answer.

288 x 3.14 = 904.32

The new volume of the sphere is 904.32 in^3

Step-by-step explanation:

each week kyle saves $5.00

Answer:

Score with 6 questions wrong :

= 40 - (6×2)

= 40 - 12

= 28

Score with x questions wrong :

= 40 - (x×2)

= 40 - 2x

Answer:

Step-by-step explanation:

Add all 4 sides to get perimeter so the first one is 9+9+2+2=22cm

the area is length x width so the first one is 9 x 2 =18cm ^2

Answer:

I think B

Step-by-step explanation:

Not sure but seems like so. Hope I helped U :)

Answer:

1. Not equivalent

2. Not equivalent

3. Equivalent

4. Equivalent

5. Equivalent

Step-by-step explanation:

I will prove the ones that are equivalent, since the ones that aren't are pretty straightforward.

2(3h + 7) = 6h + 14

3. 6h + 7 + 7 = 6h + 14

4. 3h + 3h + 14 = 6h + 14

5. (3h + 7) + (3h + 7) = 6h + 14

Answer:

c

Step-by-step explanation:

right on plato

Answer:

(6, 7)

Step-by-step explanation:

A rectangle means that opposite sides are parallel to each other and that opposite sides are equal in measurements.

If we look at the opposite side starting at (2, 1), we can count how long the other side should be. Counting the next point of the rectangle is (6, 1) which is a difference of 4. This means if we count from (2, 7) 4 spaces to the right, we will find our missing vertex.

(2 + 4, 7) = (6, 7)

Answer:

Step-by-step explanation:

Hope it helps u!!

Answer:

[tex]b_i = -0.020125[/tex]

Step-by-step explanation:

Given

[tex]\sum x_i= 2000[/tex]

[tex]\sum y_i= 86.6[/tex]

[tex]\sum x_i^2= 216000[/tex]

[tex]\sum x_iy_i = 8338[/tex]

[tex]n = 20[/tex]

Required

Determine the slope (b) of the regression line

This is calculated as:

[tex]b_i = \frac{\sum xy - \frac{\sum x\sum y}{n}}{\sum x^2 - \frac{(\sum x)^2}{n}}[/tex]

Substitute values for each term, we have:

[tex]b_i = \frac{8338 - \frac{2000 * 86.6}{20}}{216000 - \frac{(2000)^2}{20}}[/tex]

Simplify the numerator

[tex]b_i = \frac{8338 - 8660}{216000 - \frac{(2000)^2}{20}}[/tex]

Simplify the denominator

[tex]b_i = \frac{8338 - 8660}{216000 - 200000}[/tex]

[tex]b_i = \frac{-322}{16000}[/tex]

[tex]b_i = -0.020125[/tex]

Answer:

19/25.

Step-by-step explanation:

The total possible number of combinations of 2 cards from the 2 piles = 5*5 = 25.

Possible ways to get sum of 12 or more =

4,8   5,7   5,8   6,6   6,7  6,8  =  6 ways.

So the number of ways to get sum of < 12 = 25 - 6 = 19.

So the required probability = 19/25.

Answer:

I think the probability  is 19 out of 25    = 19/25, but I am not sure so please check by step by step solution.

Step-by-step explanation:   5  29  12  38

Hearts 2, 3, 4, 5, 6

Spades 4, 5, 6, 7, 8

Find the probability that the sum of any two randomly cards is less than 12.

I count 5²  = 25  possibilites

I found 5 + 5 + 4 + 3 + 2 combinaitons of cards whose sum is less than 12

             sum of 19 combinations less than 12

               19 /25 is the probability of the sum being less than 12

     hearts....   + spade < 12

       the 2 + any shade      5

       the 3 + any spade      5

       the 4 + the four lowest spades   4

       the 5 + the three lowest spades   3

       the 6 + the four lowest spades   2

Answer:

Train A weighs 156 tons, and Train B weighs 78 tons.

Step-by-step explanation:

Given that two trains, Train A and Train B, weigh a total of 243 tons, and Train A is heavier than Train B, with a difference of their weights of 87 tons, to determine what is the weight of each train, the following calculation has to be done:

(243 - 87) / 2 = B

156/2 = B

78 = B

243 - 87 = A

156 = A

Therefore, Train A weighs 156 tons, and Train B weighs 78 tons.

Answer:

Step-by-step explanation:

1) (x) is economy class and (y) is first class

2) The objective function is to avoid making a loss in prophet making the train have the avalibility  for 10 economy class passengers and at least 20 first class passengers.

3) The constraints are that there are only 10 spots for economy class and at least 20 for first-class passengers.

Answer: Direction opens downward

Step-by-step explanation:

X-Intercept: (1/14,0),(-1/4,0)

Y-Intercept: (0,1)

Find the vertex using x= -b/2a

Plug it into the vertex form = y=a(x-h)^2 +k

H,K will identify the direction.

sin

(

2

θ

)

=

2

(

3

5

)

(

−

4

5

)

=

−

24

25

Write the double-angle formula for cosine.

\displaystyle \cos \left(2\theta \right)={\cos }^{2}\theta -{\sin }^{2}\thetacos(2θ)=cos

​2

​​ θ−sin

​2

​​ θ

Again, substitute the values of the sine and cosine into the equation, and simplify.

)Answer:

In the previous section, we used addition and subtraction formulas for trigonometric functions. Now, we take another look at those same formulas. The double-angle formulas are a special case of the sum formulas, where \displaystyle \alpha =\betaα=β. Deriving the double-angle formula for sine begins with the sum formula,

\displaystyle \sin \left(\alpha +\beta \right)=\sin \alpha \cos \beta +\cos \alpha \sin \betasin(α+β)=sinαcosβ+cosαsinβ

If we let \displaystyle \alpha =\beta =\thetaα=β=θ, then we have

Deriving the double-angle for cosine gives us three options. First, starting from the sum formula, \displaystyle \cos \left(\alpha +\beta \right)=\cos \alpha \cos \beta -\sin \alpha \sin \betacos(α+β)=cosαcosβ−sinαsinβ, and letting \displaystyle \alpha =\beta =\thetaα=β=θ, we have

Using the Pythagorean properties, we can expand this double-angle formula for cosine and get two more interpretations. The first one is:

Similarly, to derive the double-angle formula for tangent, replacing \displaystyle \alpha =\beta =\thetaα=β=θ in the sum formula gives

\displaystyle \begin{array}{c}\tan \left(\alpha +\beta \right)=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }\\ \tan \left(\theta +\theta \right)=\frac{\tan \theta +\tan \theta }{1-\tan \theta \tan \theta }\\ \tan \left(2\theta \right)=\frac{2\tan \theta }{1-{\tan }^{2}\theta }\end{array}

​tan(α+β)=

​1−tanαtanβ

​

​tanα+tanβ

​​

​tan(θ+θ)=

​1−tanθtanθ

​

​tanθ+tanθ

​​

​tan(2θ)=

​1−tan

​2

​​ θ

​

​2tanθ

​​

​​

A GENERAL NOTE: DOUBLE-ANGLE FORMULAS

The double-angle formulas are summarized as follows:

\displaystyle \sin \left(2\theta \right)=2\sin \theta \cos \thetasin(2θ)=2sinθcosθ

\displaystyle \tan \left(2\theta \right)=\frac{2\tan \theta }{1-{\tan }^{2}\theta }tan(2θ)=

​1−tan

​2

​​ θ

​

​2tanθ

​​

HOW TO: GIVEN THE TANGENT OF AN ANGLE AND THE QUADRANT IN WHICH IT IS LOCATED, USE THE DOUBLE-ANGLE FORMULAS TO FIND THE EXACT VALUE.

Draw a triangle to reflect the given information.

Determine the correct double-angle formula.

Substitute values into the formula based on the triangle.

Simplify.

EXAMPLE 1: USING A DOUBLE-ANGLE FORMULA TO FIND THE EXACT VALUE INVOLVING TANGENT

Given that

and \displaystyle \thetaθ is in quadrant II, find the following:

\displaystyle \sin \left(2\theta \right)sin(2θ)

\displaystyle \cos \left(2\theta \right)cos(2θ)

\displaystyle \tan \left(2\theta \right)tan(2θ)

SOLUTION

If we draw a triangle to reflect the information given, we can find the values needed to solve the problems on the image. We are given \displaystyle \tan \theta =-\frac{3}{4}tanθ=−

​4

​

​3

​​ , such that \displaystyle \thetaθ is in quadrant II. The tangent of an angle is equal to the opposite side over the adjacent side, and because \displaystyle \thetaθ is in the second quadrant, the adjacent side is on the x-axis and is negative. Use the Pythagorean Theorem to find the length of the hypotenuse:

Now we can draw a triangle similar to the one shown in Figure 2.

Diagram of a triangle in the x,y-plane. The vertices are at the origin, (-4,0), and (-4,3). The angle at the origin is theta. The angle formed by the side (-4,3) to (-4,0) forms a right angle with the x axis. The hypotenuse across from the right angle is length 5.

Figure 2

Let’s begin by writing the double-angle formula for sine.

\displaystyle \sin \left(2\theta \right)=2\sin \theta \cos \thetasin(2θ)=2sinθcosθ

We see that we to need to find \displaystyle \sin \thetasinθ and \displaystyle \cos \thetacosθ. Based on Figure 2, we see that the hypotenuse equals 5, so \displaystyle \sin \theta =\frac{3}{5}sinθ=

. Substitute these values into the equation, and simplify.

Thus,

​​

Solution

EXAMPLE 2: USING THE DOUBLE-ANGLE FORMULA FOR COSINE WITHOUT EXACT VALUES

Use the double-angle formula for cosine to write \displaystyle \cos \left(6x\right)cos(6x) in terms of \displaystyle \cos \left(3x\right)cos(3x).

SOLUTION

c

Analysis of the Solution

This example illustrates that we can use the double-angle formula without having exact values. It emphasizes that the pattern is what we need to remember and that identities are true for all values in the domain of the trigonometric function.

Using Double-Angle Formulas to Verify Identities

Establishing identities using the double-angle formulas is performed using the same steps we used to derive the sum and difference formulas. Choose the more complicated side of the equation and rewrite it until it matches the other side.

EXAMPLE 3: USING THE DOUBLE-ANGLE FORMULAS TO ESTABLISH AN IDENTITY

Establish the following identity using double-angle formulas:

\displaystyle 1+\sin \left(2\theta \right)={\left(\sin \theta +\cos \theta \right)}^{2}1+sin(2θ)=(sinθ+cosθ)

​2

​​

θ

)

Step-by-step explanation:

Answer:

16.73 I THINK

Step-by-step explanation:

my guess is n1 is relating to the 4.9, and if it then you would do the Pythagorean theorem. because the degrees are there to let you know it's a right angle and you are able to use the theorem..... so -

4.9^2 + 4.9^2 =C^2

48.02 =C

√48 = 6.93 (rounded to nearest hundredth)

then you add them all together

4.9+4.9+6.93=16.73

Answer

2766.5

Step-by-step explanation:

Well to solve for average all you have to do is add the values together then divide by the number of values you started with. So we add them together(2768+3001+2663+2471+2893+2803) and get 16599. Then, since there were 6 values we divide that by 6 and you get your answer.

Answer:

Cos(θ) = 8 / 17

Step-by-step explanation:

Cos = Adjacent / Hypotenuse

Side that is adjacent to θ = 8

hypotenuse of the triangle = 17

Cos(θ) = 8 / 17

Hope this helps!

Answer:

Step-by-step explanation:

s³ = 64

Take the cube root of both sides

s = 4

Answer:

arcsin(5/6) = 56.44 degrees, or 0.99 radian

Step-by-step explanation:

Write out sin x = 5/6.

Then write out the inverse function:  arcsin 5/6 = x.

Use a calculator's 'arcsin' function to determine the angle x:

arcsin(5/6) = 56.44 degrees, or 0.99 radian

9514 1404 393

Answer:

  (a)  6

Step-by-step explanation:

The median is the middle number when they are sorted into order. If one of the numbers is 10, the remaining number must be any number less than 7. Of the offered choices, the only one less than 7 is 6.

__

The three numbers are 6, 7, 10.

Trapezoid Area =

[ ( Sum of the rules ) × ( height ) ] ÷ 2

_________________________________

Area = [ ( 2 + 3 ) × 3 ] ÷ 2

Area = [ 5 × 3 ] ÷ 2

Area = 15 ÷ 2

Area = 7.5 m^2

Answer:

[tex]\text{1. }\triangle IJH\cong \triangle LKM, \\\text{2. }\triangle RST\cong \triangle YXZ, \\\text{3a. Reflexive Property}, \\\text{3b. ASA (Angle-Side-Angle)}[/tex]

Step-by-step explanation:

ASA (Angle-Side-Angle) is a proof of congruence that states if two triangles share two angles and the side between those two angles, the triangles are congruent. In problems 1 and 2, the following demonstrate this:

[tex]\text{1. }\triangle IJH\cong \triangle LKM, \\\text{2. }\triangle RST\cong \triangle YXZ[/tex]

In problem 3, [tex]\overline{IJ}\cong \overline{IJ}[/tex] is known in geometry as the Reflexive Property. Because of this, the two triangles in the diagram for problem 3 now share two angles and the side between them, thus they are congruent from ASA (Angle-Side-Angle).

Answer:

See explanation. I attached a photo to help visualize and make it easier to understand, but tell me if handwriting was fine :)

Also, C) 436 in² is correct :)

Step-by-step explanation:

the answer is C

Step-by-step explanation:

if we take the 15 from 28

13 will be left

so 13×22=286

and 15×5=75

15×5=75

150+286=436

hopefully its helpful

Answer:

X x X=x²

X x -7=-7x

4 x X=4x

4 x -7=-28

-7x + 4x=-3x

x² + -3x -28

hope that helped :)

Step-by-step explanation:

Answer:

False because 1/2 would be half the number 2/2 or 1 would be the whole number so 3/2 would be a whole and half or 1 1/2

Answer:

false

if the number is X

3/2 of X= X 1/2

[tex]x \frac{1}{2} > x[/tex]