Verify the identity cosx cos(-x) - sinx sin(-x) =1

Answer:

1. 18.84cm

2. 10 Pennies

Step-by-step explanation:

Question 1:

Circumference Formula = 2 x π x radius

We will substitute π for 3.14 so the circumference = 2 x 3.14 x radius

The radius is 3 so the circumference = 2 x 3.14 x 3

2 x 3.14 x 3 = 18.84cm

Question 2:

20% as a decimal is 0.2

To find the answer just find 20% of 50

50 x 0.2 = 10

Therefore 10 pennies were minted before 2000

The right answer is 2.8

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

144 degrees.

Step-by-step explanation:

Draw yourself a diagram with 2 horizontal lines and a transversal cutting across it.

After labeling, you will see that angle 4 is the same as angle 1. You can also see that angle 1 and 2 add up to 180, as they are sitting on a straight line.

First, before we get to the angle of 4, we have to find the value of x:

1) angle 1 + angle 2 = 180

3x + 12x = 180

2) solve the above equation for x

15x = 180

3) divide both sides by 15 for x

x= 12 degrees

We know that angle 4 is the same as angle 2, which is 12x degrees.

So, now that we know what x is, 12 x 12 degrees =  144 degrees.

Hope this helped : )

The measure of angle ∠4 is 144°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

The measure of angle 1 = ( 3x )°

The measure of angle 2 = ( 12x )°

Angle 1 and Angle 2 are on the straight lines

So , the sum of the measures of angles = 180°

On simplifying the equation , we get

3x + 12x = 180

15x = 180

Divide by 15 on both sides of the equation , we get

x = 12

Substituting the value of x in the equation , we get

The measure of angle 2 = measure of angle 4 ( corresponding angles )

So , the measure of angle 4 = ( 12x )°

And , the measure of angle ∠4 = 144°

Hence , the angle ∠4 = 144°

To learn more about parallel lines cut by transversal click :

https://brainly.com/question/28182928

#SPJ6

Answer:

For x=1 substituting in f(x) the value of x

f(1)=-3(1)+1 = -2

For x=0 substituting in g(x) the value of x

g(0)=3^(0) =1

Finally, we have to find for what value of x the function f(x) gives -8

f(x) = -8

-8 = -3x+1

-3x=-9

x=3

Answer: 24

Step-by-step explanation:

Take the factorial of that number.

4! = 4*3*2*1=24

Answer:

$0.82

Step-by-step explanation:

The full answer is 0.8225, although I believe that I was supposed to round it to the nearest hundredth, so I did that. What I did was I divided 3.29 by 4.

Answer:

.82 per chocolate bar

Step-by-step explanation:

Take the price and divide by the number of chocolate bars

3.29/4

.8225

Rounding to two decimal places

.82 per chocolate bar

Answer:

(25*9)/52

Step-by-step explanation:

Answer:

225/9

Step-by-step explanation:

Product of 25 and 9

------------------------------ = 225/52

             52'

When you are given answer choices, please share them.  Thanks.

Answer:

W(-2, -3), X(-6, -3) , Y(-6, -4) and Z(-3, -5)

Step-by-step explanation:

In the figure attached, the quadrilateral W'X'Y'Z'  is shown. Its coordinates are W'(2, 3), X'(6, 3), Y'(6, 4) and Z'(3, 5). Transforming these points according to the rule (x,y) → (-x, -y) we can get the pre-image, quadrilateral WXYZ, as follows:

W'(2, 3) -> W(-2, -3)

X'(6, 3) -> X(-6, -3)

Y'(6, 4) -> Y(-6, -4)

Z'(3, 5) -> Z(-3, -5)

Answer:

the answer is A

Step-by-step explanation:

Mark me brainliest

Answer:

A.

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] ÷ 5 = [tex]\frac{1}{3}*\frac{1}{5} =\frac{1}{15}[/tex]

Answer:

A, C, and E are correct

Step-by-step explanation:

If Lt. Bartlett spent 2 hours doing push ups, 1 hour doing sprints, and 1.5 hours benching 400 lbs, the percentage of time he spent sprinting is 22.2%.

Percentage is simply number or ratio expressed as a fraction of 100.

It is expressed as;

Percentage = ( Part / Whole ) × 100%

Given that;

First we determine the total time.

T = tPUSHUPS + tSPRINT + t BENCHING

T = 2hrs + 1hr + 1.5hrs

T = 4.5hrs

Now, percentage of time spent sprinting P will be;

Percentage = ( Part / Whole ) × 100%

Percentage = ( tSPRINT / Total time ) × 100%

P = ( 1hr / 4.5hr ) × 100%

P = ( 0.2222 ) × 100%

P = 22.2%

Therefore, if Lt. Bartlett spent 2 hours doing push ups, 1 hour doing sprints, and 1.5 hours benching 400 lbs, the percentage of time he spent sprinting is 22.2%.

Learn more about Percentages here: brainly.com/question/24159063

#SPJ2

Answer:

No picture

Step-by-step explanation:

The picture isnt attached :( but the equation for the volume of a cylinder is: Hx [tex]\pi r^{2}[/tex]

H= height    R: Radius

So for example if the height was 10 and the radius was 2 you would do the following:

Hx[tex]\pi r^{2}[/tex]

= 10x 3.14x[tex]2^{2}[/tex]

= 10x 3.14x 4

= 10x 12.56

= 125.6cm^3 :)

[tex]\pi r^{2}[/tex] is the equation on finding the are of the circle (bottom circle or top circle) we then multiply is by its height because its like the circle being stacked up together until it reaches the height. :) Hope this helps

Answer:

The next fraction in the sequence is:

Step-by-step explanation:

How you can see, the fractions are decreasing as the sequence advance, to identify the proportion in which it decreases, we will divide the first and the second fractions:

Now, we just need to divide all the fractions in 3/2 to identify the next fraction, as I show below:

As you can see, all the results own to the sequence given, for this reason, the last result 4/27 is the correct fraction next to 2/9.

_______________________________

Hey!!

Solution,

Length(l)=9 inches

Volume of cube=?

Now,

Volume of cube= (L)^3

=(9)^3

=729 inches^3

Hope it helps...

Good luck on your assignment

_____________________________

Answer:

[tex]729 {in}^{3} [/tex]

Step-by-step explanation:

[tex]volume = whl \\ [/tex]

[tex]v = x \times x \times x \\ = {x}^{3} \\ = {9}^{3} \\ = 9 \times 9 \times 9 \\ = 81 \times 9 \\ =72 9[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

A

Step-by-step explanation:

The height of the triangle is always perpendicular to the base. Therefore, in this figure, the base of the triangle corresponds to segment A

Answer:

1) False, the point would get flipped diagonally, to -4, 4.

2) True, the point would get flipped diagonally, to -2, 6

3) False, the point would get flipped diagonally, to -3, 1

4) True, the point would get flipped diagonally, to 5, 2

5) True, the point would get flipped diagonally, to 7, 5

6) False, the point would get flipped diagonally, to -9, 3

7) True, the point would get flipped diagonally, to -5, 4

8) True, the point would get flipped diagonally, to 2, 1

Answer:

1. true

2. false

3. true

4. false

5. false

6. true

7. false

8. false

Step-by-step explanation:

DONT TRUST ME ON THESE ANSWERS CAUSE IM NOT 100% SURE :0

Answer:

A = ½ * base * height

A = ½ * x * (2x-3)

17.5 = ½ * (2x² - 3x)

35 = 2x² - 3x

0 = 2x² - 3x - 35

2x² - 3x - 35 = 0 .......... (the equation)

(2x + 7)(x - 5) = 0

2x + 7 = 0

2x = - 7

x = -7/2 = -3.5

x-5 = 0

x = 5

since we have two result of x, then we can choose the positive one x = 5

so the base is 5 m and the height is

h = (2x - 3) = 2*5 - 3 = 10-3 = 7 m

Answer: .4

Step-by-step explanation:

.

Answer:

The area of the region between the graph of the given function and the x-axis = 25,351 units²

Step-by-step explanation:

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15

If 'f' is a continuous on [a ,b] then the function

            [tex]F(x) = \int\limits^a_b {f(x)} \, dx[/tex]

By using integration formula

[tex]\int{x^n} \, dx = \frac{x^{n+1} }{n+1} +c[/tex]

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15 in the interval [-6,6]

 [tex]\int\limits^6_^-6} (x^{5} + 8 x^{4} + 2 x^{2} + 5 x + 15) )dx[/tex]

On integration , we get

=   [tex](\frac{x^{6} }{6} + \frac{8 x^{5} }{5} + 2 \frac{x^{3} }{3} +\frac{5 x^{2} }{2} + 15 x)^{6} _{-6}[/tex]

[tex]F(x) = \int\limits^a_b {f(x)} \, dx = F(b) -F(a)[/tex]

= [tex](\frac{6^{6} }{6} + \frac{8 6^{5} }{5} + 2 \frac{6^{3} }{3} +\frac{5 6^{2} }{2} + 15X 6) - ((\frac{(-6)^{6} }{6} + \frac{8 (-6)^{5} }{5} + 2 \frac{(-6)^{3} }{3} +\frac{5 (-6)^{2} }{2} + 15 (-6))[/tex]

After simplification and cancellation we get

 =  [tex]\frac{2 X 8 X (6)^{5} }{5} + \frac{2 X 2 X (6)^3}{3} + 2 X 15 X 6[/tex]

on calculation , we get

= [tex]\frac{124,416}{5} + \frac{864}{3} + 180[/tex]

On L.C.M  15

= [tex]\frac{124,416 X 3 + 864 X 5 + 180 X 15}{15}[/tex]

= 25 351.2 units²

Conclusion:-

The area of the region between the graph of the given function and the x-axis = 25,351 units²

Answer:

x > 2

x ∈ ( +2 ; + oo )

Step-by-step explanation:

8 - 2x < 4

8 - 4  < 2x

4 < 2x | : 2

2 < x

x > 2

x ∈ ( +2 ; + oo )

Answer:

-15 below sea level

-Hope this helps! :)

Answer:

-15 below 0 :)

Step-by-step explanation:no u

The right answer is 40

please see the attached picture for full solution

Hope it helps

Answer:

3.125

Step-by-step explanation:

We just multiply the dimensions together and when we do so we get 3.125.

Answer:

D. The data point is 2.5 standard deviations away from 0.5.

Step-by-step explanation:

Z-score is the measure of how many number of standard deviations, the data point, is away from the mean. It also measures how many standard deviations below or above the population mean, a raw score is.

Given, a set of data has a mean (μ) of 0.5 and a standard deviation (σ) of 0.01 with a data point of the set has a z-score of 2.5.

i.e the data point is 2.5 standard deviations away from the mean 0.5.

Hope this helped!

Answer:

60 cups.

Step-by-step explanation:

2 x 25 = 50

2/5 x 25 = 10

50 + 10 = 60

Answer:

y - 8 = (3/5)(x + 3)

Step-by-step explanation:

Answer:

$35.2

Step-by-step explanation:

% saved = 25%

Money saved = $8.80

Let x be the bill before the coupon discount.

25/100 × x = 8.80

x = $35.2

Answer: 20 feet

Step-by-step explanation:

Hi, since the situation forms a right triangle we have to apply the Pythagorean Theorem:  

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (in this case the diagonal distance covered by the stairs) and a (horizontal distance) and b (vertical distance) are the other sides.  

Replacing with the values given:  

25^2 = 15^2 + b^2  

625 = 225 + b^2  

625-225 = b^2

400= b^2

√400 =b

b =20 feet

Feel free to ask for more if needed or if you did not understand something.  

Answer: 20 feet

Step-by-step explanation:

From the question, the diagonal distance covered by the stairs is 25 feet, and the horizontal distance is 15 feet. To calculate the height of the stairs, we will use the Pythagoras rule

The square of the diagonal will be equal to the addition of the square of the horizontal distance and the square of the height. This will be:

25² = 15² + height²

height² = 25² - 15²

height² = 625 - 225

height² = 400

height = ✓400

height = 20 feet

The height of the stairs is 20 feet

Answer:

Step-by-step explanation:

v=u+at

38.9=13.2+21.5 t

21.5 t=38.9-13.2

21.5 t=25.7

t=25.7/21.5≈1.195 s

Answer:

To find the time taken, we use the equation:

v

=Then to find the time taken, we use the equation:

v = u + at

where:

v is the final velocity of the train

u is the initial velocity of the train

a is the train's acceleration

t is the time taken

So, we get:

t = (v-u)/a

t = (38.9 - 13.2)/21.5

t = 25.7/21.5

t = 1.19 seconds

Answer:

 y = 0

Step-by-step explanation:

-3(y-3)=9

One solution was found :

                  y = 0

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    -3*(y-3)-(9)=0

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (0 -  3 • (y - 3)) -  9  = 0

Step  2  :

Equation at the end of step  2  :

 -3y  = 0

Step  3  :

Solving a Single Variable Equation :

3.1      Solve  :    -3y = 0

Multiply both sides of the equation by (-1) :  3y = 0

Divide both sides of the equation by 3:

                    y = 0

Answer:

No solution

Step-by-step explanation:

–3|y – 3| = 9

⇌       (Divide both sides by -3)

|y – 3| = -3  impossible

because  |y – 3| is greater than 0 and -3 is less than 0.