Your best friend made 60% of the 40 shots he took. how many shots did your friend make?​

The domain is the set of x values that has a corresponding y-values in a function or a graph.

The domain of the graph is: [tex]-10 \le x \le 10[/tex]

From the graph (see attachment), we have the following observation

These values can be represented as:

[tex]x_1= -10[/tex]

[tex]x_2 = 10[/tex]

So, the domain of x is: [tex]-10 \le x \le 10[/tex]

Read more about domain at:

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Answer:

Step-by-step explanation:

The given trigonometric expression is :

11 cos^2 x +3 sin^2 x+6sinx cosx +5

or, we can write it as,

(9 cos^2 x + 2 cos^2 x) + (2 sin^2 x + sin^2 x) + 6sinx cosx +5

Again, after rearranging the terms, we can write the whole expression as,

(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5

Then if you factor the following underlined section as you would with a polynomial:

(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5

You get:

(3 cos x + sin x)^2 + 2 (cos^2 x + sin ^2 x) + 5

Now, the term inside the second bracket (cos^2 x + sin ^2 x) is a very popular trigonometric identity and it's value is equal to one.

So, now the whole expression becomes,

(3 cos x + sin x)^2 +7

Now, the maximum and the minimum value of the whole expression depends upon the maximum and the minimum value of the term (3 cos x + sin x), which is of the form (a cosx + b sinx),

The maximum and minimum value of (a cosx + b sinx) is relatively easy to find.

So, I've attached a screenshot from a relevant document below:

Here, a=3 and b=1,

So, R= √10

As the value of cosine of any angle lies between -1 to 1, so the value of the value of expression cos(x − α) will lie between -1 to 1.

Hence, the maximum and the minimum value of (a cosx + b sinx) will be -R and R and all the values of the expression will lie between them.

i.e., in our case between (-√10) to √10.

Again, coming back to our original expression,

(3 cos x + sin x)^2 +7

The value of the term in bracket will lie between (-√10) and √10.

But, there is a catch here, as the squares of negative terms come out be positive, hence we can't take the negative term to find the minimum value of our expression. the minimum value of the expression will be at the minimum non-negative value in the range, which is zero.

So, the minimum value will be,

(0)^2 + 7=7

and the maximum value will be,

(√10)^2 +7 = 17

Answer:

1 f(n) = 3(5)^x-1

2 f(n) = 40(3/2)^x-1

Step-by-step explanation:

The first number in the sequence, times the (multiplicative factor)^ x-1 is the rule for geometric sequences.

Answer:

graph A on edge 2020

Step-by-step explanation:

I took the test

Answer: D) w = 9 feet

Work Shown:

[tex]L = \sqrt{w^2+h^2}\\\\L^2 = w^2+h^2\\\\L^2-h^2 = w^2\\\\w^2 = L^2-h^2\\\\w = \sqrt{L^2-h^2}\\\\w = \sqrt{15^2-12^2}\\\\w = \sqrt{225-144}\\\\w = \sqrt{81}\\\\w = 9\\\\[/tex]

That points us to the final answer choice D.

Answer:

Step-by-step explanation: 10 meters/3 meters =x/4.5 meters

Where x = the maximum distance the projector can be placed that can produce an image 4.5 meters high

3x = 10 (4.5)

3x = 45

X= 45/3

X= 15 meters

So, the maximum distance that the projector can be placed from the screen which produces an image 4.5 meters high is 15 meters.

Answer:

Option (3)

Step-by-step explanation:

This question is not complete; here is the complete question.

Triangle A″B″C″ is formed by a reflection over y = −3 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C″?

Coordinates of the vertices of the triangle ABC are,

A(-3, 3), B(1, -3) and C(-3, -3)

When triangle ABC is reflected over y = -3

Coordinates of the image triangle A'B'C' will be.

A(-3, 3) → A'(-3, -9)

B(1, -3) → B'(1, -3)

C(-3, -3) → C'(-3, -3)

Further ΔA'B'C' is dilated by a scale factor of 2 about the origin then the new vertices of image triangle A"B"C" will be,

Rule for the dilation will be,

(x, y) → (kx, ky) [where 'k' is the scale factor]

A'(-3, -9) → A"(-6, -18)

B'(1, -3) → B"(2, -6)

C'(-3, -3) → C"(-6, -6)

Length of AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                      = [tex]\sqrt{(-3-1)^2+(3+3)^2}[/tex]

                      = [tex]\sqrt{52}[/tex]

                      = [tex]2\sqrt{13}[/tex]

Length of A"B" = [tex]\sqrt{(-6-2)^2+(-18+6)^2}[/tex]

                         = [tex]\sqrt{64+144}[/tex]

                         = [tex]\sqrt{208}[/tex]

                         = [tex]4\sqrt{13}[/tex]

Therefore, [tex]\frac{\text{AB}}{\text{A"B"}}=\frac{2\sqrt{13}}{4\sqrt{13}}[/tex]

[tex]\frac{\text{AB}}{\text{A"B"}}=\frac{\sqrt{13}}{2\sqrt{13}}[/tex]

[tex]AB(2\sqrt{13})=A"B"(\sqrt{13})[/tex]

Option (3) is the answer.

Answer:

Option A) A = 100(1.005)^12t

Step-by-step explanation:

The formula for Total Amount obtained using compound interest is given as:

A = P( 1 + r/n) ^nt

Where

A = Total amount received or obtained after investing

P = Principal or Initial Amount invested

r = interest rate

n = rate or number of times the interest is compounded

t = time in years.

In the question we obtained this values

P = $100

r = 6% = 0.06

n = compounded monthly, we have 12 months in a year, hence, n = 12

t = t

Using the compound interest formula for Amount A,

A = P( 1 + r/n) ^nt

A = 100(1 + 0.06/12)^12 × t

A = 100(1 + 0.005)^12t

A = 100(1.005)^12t

Therefore, the value of Mari's Investment if the interest is compounded monthly is

A = 100(1.005)^12t

Hence, Option A is correct.

Answer:

11

Step-by-step explanation:

Find the range by calculating the difference between the smallest and largest numbers in a set.

The smallest number is 1, and the largest number is 12.

Find the difference:

12 - 1

= 11

So, the range is 11.

Answer:

11

Step-by-step explanation:

1,2,,3,4,5,10,12

Range is lowest value subtracted from highest value so: 12 -1 = 11

answered by g a u t h m a t h

Answer:

She must jog 7 laps in order to meet her goal.

Step-by-step explanation:

A more accurate answer would be that she needs to run 6 1/4 laps to meet her goal. However, because the problem states that she will not be running partial laps, then the number of laps she runs must be a whole number, which in this case works out to be 7 laps.

Answer:

12

Step-by-step explanation:

Substitute the given numbers for the variables.

-(-2)(6-3)2

2(3)2

12

Answer:

x = 60

Step-by-step explanation:

Given

[tex]\sqrt{x+4}[/tex] - 7 = 1 ( add 7 to both sides )

[tex]\sqrt{x+4}[/tex] = 8 ( square both sides )

([tex]\sqrt{x+4}[/tex] )² = 8² , that is

x + 4 = 64 ( subtract 4 from both sides )

x = 60

Answer:

7 and 42

Step-by-step explanation:

The difference 35 is actually equivalent to 5 units if you draw it out into a model, thus 35 divide 5 is 7 and the other number is 7x6 which is 42

Answer:

Step-by-step explanation:

let the cost based on number of book bought be x and the constant be c:

4800 = 20x + c

8000 = 40x + c

c is common in both equations:

c =4800-20x

c = 8000-40x

equate the two:

4800-20x = 8000 - 40x

20x = 3200

x = 160

and c = 4800-20*160

c = 1600

Cost of 1000 books:

160*1000 + 1600

= 161600

Answer:

[tex]SU=18[/tex]

Step-by-step explanation:

The segments ST and TU make up the line segment SU. Add the values to find SU:

[tex]ST+TU=SU\\\\13+5=18[/tex]

The length of SU is 18.

The length of SU is 18 units.

We have a point T is between S and U.

We have to determine the length SU.

According to the question -

ST = 13 units

TU = 5 units

Now -

SU = ST + TU = 13 + 5 = 18 units

Hence, the length of SU is 18 units.

To solve more questions on Line Segments, visit the link below-

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Answer:

[tex]x = 15[/tex]

Step-by-step explanation:

Since lines f and g are parallel, that means that the top angles will be the same, while the bottom angles will also be the same.

The angles of any quadrilaterals all add up to 360°, so we can create the equation like this:

[tex]3x + 3x + (6x + 45) + (6x+45) = 360[/tex]

Combine like terms so we can get a simpler equation:

[tex]6x + 12x + 90 = 360\\18x + 90 = 360[/tex]

Now let's solve for x!

[tex]18x + 90 - 90 = 360 - 90\\18x = 270\\18x\div18 = 270\div18\\x = 15[/tex]

So [tex]x = 15[/tex].

Hope this helped!

Answer:

15

Step-by-step explanation:

3x + 6x + 45 = 180

9x = 135

x = 15

Answer:

1. Apples, Cauliflower, Green beans

2. Apples, Cauliflower, Salmon

...

27. Grapes, Corn, Almonds

Step-by-step explanation:

There are 3x3x3 = 27 combinations possible. You can enumerate them systematically.

Answer:

There are 27 combinations possible.

Hope this helps!

Answer:

Option C. 2296 units² is the answer

Answer:

Option C, 2296 units²

Step-by-step explanation:

surfaceaArea of a rectangular prism,

2(wl+hl+hw)

= 2×(10×16+38×16+38×10)

= 2296 units²

Answer:

Area: x^2+x-6

Perimeter: 4x+2

Step-by-step explanation:

Area: multiply x+3 and x-2 and combine the like terms

Perimeter: multiply the length and width by two, then combine the like terms.

Answer:

x = -1

Step-by-step explanation:

14x + 2 = 9x -3

Transpose

14x -9x = -3 -2

5x = -5

x= -5/5

x = -1

Answer:

x = -1

Step-by-step explanation:

[tex]14x+2=9x-3\\\\5x+2=-3\\\\5x=-5\\\\x=-1[/tex]

Answer:

17.50

Step-by-step explanation:

First find the discount

25 * .3

7.5

Subtract this from the original price

25-7.5

17.50

Answer:

The rule of the transformation is 6 units up and 3 units to the right [tex]T_{(3, \ 6)}[/tex] and an horizontal dilation of 2 as well as a vertical dilation of 4.

Step-by-step explanation:

The given coordinates of EFG and E'F'G' from the chart are;

E(3, 2)

F(9, 5)

G(9, 2)

E'(6, 8)

F'(18, 20)

G'(18, 8)

Therefore, we have, given that the y-coordinates of E and G are the same, the length of segment EG = 9 - 3 = 6 units

Similarly, given that the x-coordinates of F and G are the same, the length of segment FG = 5 - 2 = 3 units

The length of segment FE =  [tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex] which gives;

Length from E(3, 2) to F(9, 5) = [tex]l = \sqrt{\left (5-2 \right )^{2}+\left (9-3 \right )^{2}} = 3 \cdot \sqrt{5}[/tex]

For similarly oriented E'F'G', we have;

E'G' = 18 - 6 = 12

F'G' = 20 - 8 = 12

E'F' = 12·√2

Therefore, the transformation is 6 units up and 3 units to the right and an horizontal dilation of 2 as well as a vertical dilation of 4.

Answer:

● 23.55 units

Step-by-step explanation:

Arc length = 5( 270 π/ 180)

= 7.5 π units

= 7.5 (3.14)

= 23.55 units

OAmalOHopeO.

============================================================

Explanation:

For now, we'll just find the perimeter of the full circle. The term "circumference" is the same as the perimeter of the circle.

Use the circumference formula to get

C = 2*pi*r

C = 2*3.14*5

C = 31.4

The distance around the full circle is approximately 31.4 units. It's approximate because pi = 3.14 is approximate.

We don't want the full distance around the circle. Instead, we want just the length of the green arc shown in the drawing. This is exactly 3/4 of the full circle, aka 3/4 = 0.75 = 75% of the full perimeter.

The length of the green arc is about 0.75*C = 0.75*31.4 = 23.55 units long. Imagine using a cloth ruler (used in tailoring clothes) as one way to confirm that this arc length is roughly 23.55 units long. Or you could imagine unwrapping this curved portion to lay it completely straight and flat against a ruler.

Answer:

The integer represented by H is -2

Its opposite is 2 and the absolute value is also 2

Answer:The integer represented by H is -2

Step-by-step explanation:

One shaded triangle has a base of 4.5 ft and a height of 9 ft, so its area is 0.5 * 4.5 * 9 = 20.25.

There are two such triangles, so the area of the shaded region is 40.5.

Answer:

cos theta = √8/3

tan theta = √8/8

Step-by-step explanation:

sin theta = 1/3

1² + x² = 3²

x = √8

cos theta = √8/3

tan theta = 1/√8 = √8/8

Answer:

An obtuse angle is an angle that is bigger than 90° degrees, but doesn’t reach a straight line at 180°.

Step-by-step explanation:

i didnt see a figure above but this is the answer to "what is the measure if obtuse angle in degrees?"

Answer:

Step-by-step explanation:

To evaluate the expression substitute the values of a , b , c and d into the above expression

a = - 9

b = - 7

c = 9

d = 3

So we have

2cd + 3ab = 2(9)(3) + 3(-9)(-7)

= 2(27) + 3( 63)

= 54 + 189

We have the final answer as

Hope this helps you

Answer:

x = 1

Step-by-step explanation:

x² = x

x² / x = 1

x = 1

Check:

1² = 1

Answer:

40 degrees.

Step-by-step explanation:

Rotations are a rigid transformation and therefore preserve size and angles.

Answer:

80 grades is the answer.

Step-by-step explanation:

72° into grades

1° = 10/9 grades

72° = 10/9 × 72grades

= 720/9 grades

= 80 grades

Answer:

80 grades

Step-by-step explanation:

72° into grades  

=>1° = 10/9 grades

=>72° = 10/9 × 72 grades  

=>72° = 720/9 grades

=>72° = 80 grades