1. find the exact value of cos2θ if sin 2θ=3/4 and θ is between 0° and 90°

2. verify that sinθ(cos²θ-cos2θ)=sin³θ

Answer:

-58

Step-by-step explanation:

We are to find tfhe dot product of u=<-8,9> and v=<5,-2>

u*v = <-8,9>*<5,-2>

u*v = -8(5)+9(-2)

u*v = -40 - 18

u*v = -58

Hence the product of the vectors is -58

Answer:

Step-by-step explanation:

Question 3 Reflects over x acis

Question 5 reflects over y axis

Answer:

i think 3 is reflected across the x and 5 is reflected across the y axis

Answer:

-3.3125[tex]\frac{-10.125-(-3.5)}{4-2} =\frac{-6.625}{2} = -3.3125[/tex]

Step-by-step explanation:

Average rate of change is the slope between two points.

Slope getween points  [tex]\left(x_1,\,y_1\right)[/tex]  and  [tex]\left(x_2,\,y_2\right)[/tex]  is  [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

Using the points (2, -3.5) and (4, -10.125), the slope is

Answer:

C. 103/1/8

Step-by-step explanation:

Answer:

3 : 1

Step-by-step explanation:

A jewellery shop sells 240 necklaces in a month 180 of the necklaces were sold via the shop website work out the simplest form. The rest were sold in a High Street shop.

Work out the ratio of online sales to shop sales.

Give your answer in its simplest form.

Necklace sold in the shop = 240 - 180 = 60

180 : 60

to convert to simplest form, divide both numbers by 60

3 : 1

Answer:

Divide one of the sides in the bigger triangle by its corresponding side in the smaller triangle to determine the scale factor for the smaller triangle to the bigger triangle.

El porcentaje es la forma de expresar un número como una fracción que tiene como denominador el número 100, conocido también, como tanto por ciento. También es un símbolo que significa una fracción de cien, que su símbolo es % que se lee tanto por ciento.

Answer:

[tex](a)\ t = -2.146[/tex]

The null hypothesis is rejected

[tex](b)\ t = 2.014[/tex]

The null hypothesis is accepted

[tex](c)\ t = 2.128[/tex]

The null hypothesis is accepted

[tex](d)\ t = -2.146[/tex]

The null hypothesis is rejected

Step-by-step explanation:

Given

[Missing from the question]

[tex]\alpha = -1.001[/tex] --- critical value

Left tailed test

Required

State what the standardized test statistics indicates

Since it is a left-tailed test, the null hypothesis will be rejected if the standardized test statistics less than or equal to the critical value

Using the above rule, we have:

[tex](a)\ t = -2.146[/tex]

Compare t and [tex]\alpha[/tex]

[tex]-2.146 < -1.001[/tex]

The null hypothesis is rejected

[tex](b)\ t = 2.014[/tex]

Compare t and [tex]\alpha[/tex]

[tex]2.014> -1.001[/tex]

The null hypothesis is accepted

[tex](c)\ t = 2.128[/tex]

Compare t and [tex]\alpha[/tex]

[tex]2.128> -1.001[/tex]

The null hypothesis is accepted

[tex](d)\ t = -2.146[/tex]

Compare t and [tex]\alpha[/tex]

[tex]-2.146 < -1.001[/tex]

The null hypothesis is rejected

Answer: Warsaw

Step-by-step explanation:

Warsaw is the capital and largest city of Poland. It is located on the Vistula River, in east-central Poland, roughly 260 kilometres from the Baltic Sea and 300 kilometres from the Carpathian Mountains.

Answer:

100÷(20÷5)

Step-by-step explanation:

first find out how many chairs each worker made

20÷5=4

then divide 100 by 4 and that will give you 25

they would need 25 workers the equation that they should use is

100÷(20÷5)

Answer:

Part A

aₙ = 5 + (n - 1)·4

Part B

y = 4·x + 1

Step-by-step explanation:

Part A

The number of orange blocks in Figure 1 = 5

The number of orange blocks in Figure 2 = 9

The number of orange blocks in Figure 3 = 13

Therefore, we get;

5, 9, 13, ... with increments of 4

The first term, a = 5

The common difference, d = 4

The sequence is in the form of an Arithmetic Progression, therefore, we have;

aₙ = 5 + (n - 1)·4

Where;

n = The Figure number

When n = 3, we have;

a₃ = 5 + (3 - 1) × 4 = 12 orange blocks as in the diagram in the question

Part B

To express the number of blocks using the linear function, y = m·x + b, we have;

Let 'x', represent the number of each figure, let 'y' represent the total number of blocks in each figure, let 'd' represent the initial amount of blocks present when x = 0, and let 'm' represent the rate of  change of 'y' with each change in 'x'

We note that the rate of change the total number of blocks for each increase in figure number is 4, therefore, we have;

The rate of change, m = 4

∴ y = 4·x + d

When x = 1, y = 5, we get;

5 = 4 × 1 + d

∴ d = 5 - 4 = 1

d = 1

The linear equation that gives the number of blocks is therefore;

y = 4·x + 1.

Answer:

3.

Step-by-step explanation:

X+2=-1/4(4x-8)

x+2=-x+2

0=0

Answer:

see explanation

Step-by-step explanation:

The length of the arc is calculated as

AB = circumference of circle × fraction of circle

(11)

AB = 2πr × [tex]\frac{90}{360}[/tex]

     = 2π × 7 × [tex]\frac{9}{36}[/tex]

     = 14π × [tex]\frac{1}{4}[/tex]

     = [tex]\frac{7}{2}[/tex] π in

(12)

AB = 2πr × [tex]\frac{135}{360}[/tex] ( r = 20 ÷ 2 = 10 )

      = 2π × 10 × [tex]\frac{3}{8}[/tex]

      = 20π × [tex]\frac{3}{8}[/tex]

      = [tex]\frac{60}{8}[/tex] π

      = [tex]\frac{15}{2}[/tex] π cm

Answer:

$405

Step-by-step explanation:

This is a proportion problem!

Build fractions that have euros on top and dollars on the bottom (or the other way around, you decide, but make it the same in both fractions).

Let's do euros over dollars.

Setup:

[tex]\frac{200}{270}=\frac{300}{d}[/tex]

"Cross multiply."

[tex]200d=300\times 270\\\\200d=81000\\\\d=\frac{81000}{200}=405[/tex]

Answer:

$45

y = 45x + 15

Step-by-step explanation:

Given :

Days Total Cost

(d) (C)

2. $105

4 $195

6 $285

10 $465

The daily rate is the slope :

Slope = Rise / Run

Slope = (y2 - y1) / (x2 - x1)

Slope = (465 - 105) / (10 - 2)

Slope = 360 / 8

Slope = 45

Daily rate = $45

Using the slope intercept relation :

y = mx + c

m = slope, c = intercept

105 = 45x + c

105 = 45(2) + c

105 = 90 + c

105 - 90 = c

15 = c

Pricing plan :

y = 45x + 15

Answer is 45 because if you divide 90/2 it equal 45

C=45d+15

Answer:

like is the proper way and unlike is the improper way

hope it helps u

Answer:

like terms are terms that have the same variable or powers. They don't need the same coefficient (the number in front of it). Unlike terms is basically the opposite, so different variables and powers.

In the image provided by you, it is asked that, what percentage of the individuals rode the Ferris Wheel and not the roller coaster?

Percentage of Individuals who rode the Ferris Wheel but not the roller coaster =[tex] \sf \frac{individuals \: who \: rode \:the \: ferris \: wheel \: but \: not \: roller \: coaster }{total \: number \: of \: individuals \: who \: went \: to \: amusement \: park} [/tex]

Substituting the values given in the formula, We get,

⇒ Percentage of Individuals who rode the Ferris Wheel but not the roller coaster = [tex] \sf \frac{individuals \: who \: rode \:the \: ferris \: wheel \: but \: not \: roller \: coaster }{total \: number \: of \: individuals \: who \: went \: to \: amusement \: park} [/tex]

⇒ Percentage of Individuals who rode the Ferris Wheel but not the roller coaster = [tex] \sf \frac{28 }{112} [/tex]

Calculating further, We get,

⇒ Percentage of Individuals who rode the Ferris Wheel but not the roller coaster = [tex] \sf \frac{1 }{4} [/tex]

Now, to convert any fraction into percentage, We multiply it by 100, We get,

⇒ Percentage of Individuals who rode the Ferris Wheel but not the roller coaster = [tex] \sf \frac{1 }{4} \times 100 [/tex]

Calculating further, We get,

⇒ Percentage of Individuals who rode the Ferris Wheel but not the roller coaster = [tex] \bf 25\% [/tex]

Answer:

953.78 in³

Step-by-step explanation:

Area of circle = πr²

The area of the base

= 3.14×(9÷2)²

= 63.585 in²

The capacity of the container

= 63.585×15

= 953.775 in³

Answer:

A. shifted 4 units left and 3 units up.

Step-by-step explanation:

Answer:

I think B .......................................

Answer:

1 and 0

Step-by-step explanation:

Let's call the smaller number x and the larger number y.

This means 5y+2x=5.

Also, 4y-x=4.

This is a system of equations. There are two main ways two solve this.

Method 1: Substitution

5y+2x=5

4y-x=4

Solve for one of the variables, then substitute it back into one of the equations to solve for the other variable.

I will take 4y-x=4 and solve for x.

4y=4+x

x=4y-4

Then substitute for x in the other equation and solve for y.

5y+2x=5

5y+2(4y-4)=5

5y+8y-8=5

13y=13

y=1

Now we can go back to our equation for x and substitute for y.

x=4y-4

x=4(1)-4=0

y, the larger number, is 1 and

x, the smaller number, is 0

Method 2: Elimination

5y+2x=5

4y-x=4

Change the equations so that the coefficient of one of the variables in an equation is opposite the one in the other equation. Then add the equations and solve for each variable.

If I multiply both sides of the second equation, 4y-x=4, by 2, the coefficient of x will become -2. In the first equation, the coefficient is 2, so they will become opposites.

4y-x=4

becomes

8y-2x=8

Now we have 5y+2x=5 and 8y-2x=8.

Add the sides of both equations to cancel the x values.

5y+2x+8y-2x=5+8

13y=13

y=1

like last time, we can substitute for y in any of the original equations to get x.

5y+2x=5

5(1)+2x=5

5+2x=5

2x=0

x=0

y, the larger number, is 1 and

x, the smaller number, is 0

oof oof oof oof oof oof

Answer:

13%

Step-by-step explanation:

Answer:

Hello There!!

Step-by-step explanation:

The answer is 13% as you convert 2 3/5 to an improper fraction which is 13/5. Convert this into a decimal which is 2.6 . 2.6 ÷20=0.13 ×100 (to get it as a fraction) which equals 13%.

hope this helps,have a great day!!

~Pinky~

Answer:

14

Step-by-step explanation:

42=3p

42/3=3p/3

14=p

Answer:

Step-by-step explanation:

F(x) = x² - 2x + 1

      = (x - 1)²

By comparing this equation with the vertex form of the quadratic equation,

y = (x - h)² + k

Here, (h, k) is the vertex

Vertex of the parabola → (1, 0)

x-intercepts → (x - 1)² = 0

                       x = 1

y-intercepts → y = (0 - 1)²

                       y = 1

Now we can draw the graph of the given function,

From this graph,

As x → 0,

[tex]\lim_{x \to 0^{-}} (x-1)^2=1[/tex]

[tex]\lim_{x \to 0^{+}} (x-1)^2=1[/tex]

f(0) = (0 - 1)²

     = 1

Since, [tex]\lim_{x \to 0^{-}} (x-1)^2=\lim_{x \to 0^{+}} (x-1)^2=1[/tex]

Therefore, given function is continuous at x = 0.