If you horizontally stretch the quadratic parent function, f(x) = x^2, by a factor
of 5, what is the equation of the new function?

Answer:

Assuming that x is in degrees (you could generalize this to any unit)

For an equation like:

sin(a*x) = K

The principle solutions are the values of x in the range:

0° ≤ x < 360°

And the symmetric ones are the solutions:

xₙ = x + n*360°

where n is an integer.

Ok, first let's solve:

2*cos(x) = -1

isolating the cosine part, we get:

cos(x) = -1/2

Now we can use the inverse cosine function, Acos(x)

If we apply this function to both sides, we get:

Acos (cos(x)) = Acos(-1/2)

x = Acos(-1/2) = 120°

x = 120° is the princpiple solution.

And the symmetric solutions are:

xₙ = 120° + n*360°

So for example:

x₁ = 120° + 1*360° = 480°

x₃ = 120° + 3*360° = 1200°

etc...

Answer:

A ∩ C   [ -6, -4 )

Step-by-step explanation:

A ∩ C

-6 ≤ x < -4

[ -6, -4 )

Answer:

Alternate exterior

Step-by-step explanation:

Angles 2 and 7 are on exterior sides of the transversal and also are opposite to one another. They are classified as alternate exterior.

Answer:

alternate exterior angles

Step-by-step explanation:

2 and 7 are on opposite sides of the transversal so they are called alternate

They are on the outside of the parallel lines so the are called exterior

Step-by-step explanation:

n(AUB)=n(A)+n(B)-n(AnB)

hope it helps

Answer:

ok 200 we have to find 5% of 200 so since 200 is doable 100 we just multiply 5 by 2 to get 10

so out of the 200 people 10 of them have the mutation

Hope This Helps!!!

Answer:

B

Step-by-step explanation:

You always have to use the Big Three trig functions (those that are on your calculator when answering this kind of question involving right angle triangles).

y is the adjacent side of the triangle. It is the side (other than the hypotenuse -- which is the longest side of the right triangle) that makes up the cosine.

Cos(45) = y / 4 sqrt(2)

Cos(45) = sqrt(2)/2

Multiply both sides by 4 sqrt(2)

4*sqrt(2) * cos(45) = y

4*sqrt(2) * sqrt(2)/2 = y

2*2 = y

y = 4

I can't tell you where all the other choices are coming from.

Answer:

4, or B

Step-by-step explanation:

Answer:

The graph is in the second attached image.

Step-by-step explanation:

In the first attached image, you have three equation graphed, the first is in red color, it's the original equation:

I graphed this to obtain a clear relation between the equation and its derivatives, the second graphed equation is in blue color and it's the first derivative:

And at last, we have in green color the second derivative:

As you can see, you only need the first and the second derivatives in the exercise, by this reason, in the second attached image you have the graph as you need to show in this exercise.

Answer:

the area is 27

Step-by-step explanation:

Answer:

the base of this shape is 6

lets break it up into a rectangle and a triangle

the rectangle is 6(base) time 3(height)=18

the triangle is 6(base) times 3(height) divided by two = 9

18 plus 9 = 27

Step-by-step explanation:

Objective: Recall the properties.

a) 3+1=4

b) 3+7=7+3

c) 3+(7+4)=7+(3+4)

d). 3(7+4)=(3×7)+(3×4)

Answer:

(1)

compound amount = 802.5 $

invest earned = 52.5 $

Step-by-step explanation:

total amount = 10000 $

let amount x invested in ventures A and remaining (1000-x) on ventures B

now,

6x/100 +23/400(1000-x ) = 588.75

{24x+23(1000-x)}/400 =588.75

x=235500-230000

x=5500

Amount invested on A = 5500$

Amount invested on B = 4500$

(2)

principle=750$

time= 1 year

effective invest rate = 7%

a) compound amount = p(1+(r/w)^t

=750{1+(7/100)}^1

=802.5$

b) invest earned = 802.5-700 = 52.5$

Answer:

whats the question?

comment so i can help:)

Answer:

NUMBERS end in 12581... YEP.

Answer:

End 12581 yes

Answer:

V=πr2h /3

so we just substate and we get

V≈130.9

Answer: 130.83 units cubed

Step-by-step explanation:

The formula for finding the volume of a cone is [tex]\pi r^2\frac{h}{3}[/tex]

We will use 3.14 for pi.

[tex]3.14r^2\frac{h}{3}[/tex]

Now let's sub in our variables and solve

[tex]3.14(5^2)(\frac{5}{3})\\3.14(25)(\frac{5}{3})\\78.5(\frac{5}{3})\\130 \frac{5}{6}[/tex]

5/6 is about .83

130.83

Answer:

81

Step-by-step explanation:

4 quarts = 1 gallon

there are 22 gallons so multiply 4 by 22

that equals 88 quarts then subtract 7

leaving you with 81 quarts

Answer:

3,770,461,100,000 different playlists are possible.

Step-by-step explanation:

To solve this question, the arrangements formula and the combinations formula are used. The arrangements formula is used considering the order of the musics being played, and the combinations formula is used to find the number of possible combinations of musics.

Arrangements of n elements:

The number of possible arrangements of n elements is given by:

[tex]A_{n} = n![/tex]

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

0 pop songs

10 non-pop from a set of 8 + 4 + 4 = 16.

Arrangements of 10(order in which the musics are played). So

[tex]P(0) = 10!C_{16,10} = 10!\frac{16!}{6!10!} = \frac{16!}{6!} = 29059430400[/tex]

1 pop song:

9 non-pop from a set of 16, 1 pop from a set of 7. So

[tex]P(1) = 10!C_{16,9}C_{7,1} = 10!\frac{16!}{7!9!}\frac{7!}{1!6!} = 290594304000[/tex]

2 pop songs:

8 non-pop from a set of 16, 2 pop from a set of 7. So

[tex]P(2) = 10!C_{16,8}C_{7,2} = 10!\frac{16!}{8!8!}\frac{7!}{2!5!} = 980755776000[/tex]

3 pop songs:

7 non-pop from a set of 16, 3 pop from a set of 7. So

[tex]P(3) = 10!C_{16,7}C_{7,3} = 10!\frac{16!}{7!9!}\frac{7!}{3!4!} = 1452971500000[/tex]

4 pop songs:

6 non-pop from a set of 16, 4 pop from a set of 7. So

[tex]P(4) = 10!C_{16,6}C_{7,4} = 10!\frac{16!}{6!10!}\frac{7!}{3!4!} = 1017080100000[/tex]

How many different playlists are possible?

[tex]T = P(0) + P(1) + P(2) + P(3) + P(4) = 29059430400 + 290594304000 + 980755776000 + 1452971500000 + 1017080100000 = 3770461100000[/tex]

3,770,461,100,000 different playlists are possible.

Answer:

34

Step-by-step explanation:

The angles of a triangle add to 180

56+ F + 90 = 180   ( the box means 90 degrees)

Combine like terms

146+F = 180

Subtract 146 from each side

F = 180-146

F = 34

Answer:

1

Step-by-step explanation:

Given the pulse rate for 12 students :

76 60 59 60 81 72 91 80 80 68 73 77

Creating class intervals ::

Width = 10

59, 60, 60, 68, 72, 73, 76, 77, 80, 80, 81, 91

Interval ____ Frequency

50 - 59 ______ 1

60 - 69 ______ 3

70 - 79 ______ 4

80 - 89 ______ 3

90 - 99 ______ 1

Frequebcy if the 50 - 59 class interval is 1

Answer:

Scale factor = 3

Step-by-step explanation:

Scale factor used for the dilation = the ratio of the corresponding side length of the new figure to the side length of the original figure

Scale factor = B'C'/BC

B'C' = 9 units

BC = 3 units

Scale factor = 9/3 = 3

Answer:

I say number 2 idrk so I hope I helped >-<

Answer:

The number is four (4)

Step-by-step explanation:

look at the picture above, it explains everything

Answer:

It's C

Step-by-step explanation:

because there is a 90 degrees sigh behind it and those two angles need to add up to 90

Answer:

31

Step-by-step explanation:

b+59=90

b=90-59

b=31

hope it helps

Answer:

I think it's simple sentence

Answer:

A

Step-by-step explanation:

Answer:

Answer is A

Step-by-step explanation:

Answer:

3,964 ft

Step-by-step explanation:

555 / tan 8° = 555/0.14 = 3,964 ft

Answer:

[tex]36 - 3m[/tex]

Step-by-step explanation:

[tex]3(12−m)[/tex]

[tex]3 \times 12+3(−m)[/tex]

[tex]36+3(−m)[/tex]

[tex]36−3m[/tex]

9514 1404 393

Answer:

  (d)  reflection about the x-axis, up 6 units

Step-by-step explanation:

The parent function y=1/x is multiplied by -1, which reflects it over the x-axis. Then 6 is added, which shifts it up 6 units.

The transformations are ...

  reflection about the x-axis, up 6 units

Answer:

m<1 = 60

m<2 = 30

m<3 = 80

Step-by-step explanation:

1. Solve for angle (1)

The sum of angles in any triangle is (180) degrees. As one can see, there is a (30) degree angle in this triangle, and a (90) degree angle. Bear in mind that the box around an angle indicates that it is a (90) degree angle. One can form an equation and solve for the unknown angle using this given information;

(30) + (m<1) + (90) = 180

Simplify,

120 + m<1 = 180

Inverse operations,

m<1 = 60

2. Solve for angle (2)

The vertical angles theorem states that when two lines intersect, the angles opposite each other are congruent. One can apply this theorem here by stating the following,

m<2 = 30

Thus one gets their answer, the measure of angle (2) must be (30) degrees by the vertical angles theorem.

3. Solve for angle (3)

As states above, the sum of angles in a triangle is (180) degrees. Since one has found the measure of angle (2), one can form an equation and solve for the measure of angle (3) using the given information, combined with the information found.

(m<2) + (70) + (m<3) = 180

Susbtitute,

30 + 70 + (m<3) = 180

Simplify,

100 + m<3 = 180

Invers eoperations,

m<3 = 80

Step-by-step explanation:

Everything has been written ..

Answer:

a. m<Q = 75°

b. m<M = 60°

Step-by-step explanation:

a. The triangle has two equal sides, therefore it is an isosceles triangle. Thus, its base angles would be equal also. m<Q = m<S

Therefore:

m<Q = ½(180 - 30)

m<Q = 75°

b. All sides of the triangle are equal. Therefore, it is an equilateral triangle with equal angles measuring 60° each.

m<M = 60°