someone help me solve these three math year7 questions , thank you

Answer:

[tex]\displaystyle \cos(2x)=-\frac{7}{25}[/tex]

Step-by-step explanation:

We want to find:

[tex]\displaystyle \cos(2x)\text{ given that }\sin(x)=-\frac{4}{5}[/tex]

And x is in QIII.

Recall that sine is the ratio of the opposite side to the hypotenuse.

Therefore, the adjacent side is (we can ignore the negative for now).

[tex]a=\sqrt{5^2-4^2}=\sqrt{25-16}=\sqrt{9}=3[/tex]

So, the adjacent side is 3, the opposite side is 4, and the hypotenuse is 5.

Using the double angle identity, we can rewrite:

[tex]\cos(2x)=\cos^2(x)-\sin^2(x)[/tex]

Since x is in QIII, cosine is positive, sine is negative, and tangent is negative.

Using the above values, we can conclude that:

[tex]\displaystyle \cos(x)=\frac{3}{5}\text{ and } \sin(x)=-\frac{4}{5}[/tex]

Substitute:

[tex]\displaystyle \cos(2x)=\Big(\frac{3}{5}\Big)^2-\Big(-\frac{4}{5}\Big)^2[/tex]

Evaluate:

[tex]\displaystyle \cos(2x)=\frac{9}{25}-\frac{16}{25}=-\frac{7}{25}[/tex]

Answer:

25^-1.5=0.008

Step-by-step explanation:

Answer: 1420

Step-by-step explanation:

Answer: division properties

Step-by-step explanation:

Answer:

x=−4 or x=5 This is the awnser to x^2-20=0

Answer:

Step-by-step explanation:

x^9 + 3x^8 +2x^7 +4=0

Hey,I'm not sure enough...i guess if the highest power is 9 then we get 9 roots..sorryvif I'm wrong:')

Step 1: Set up a table.

Algebra Age Problems

Step 2: Fill in the table with information given in the question.

John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three times as old as Alice. How old is Peter now?

Let x be Peter’s age now. Add 5 to get the ages in 5 yrs.

Algebra Age Problems

Write the new relationship in an equation using the ages in 5 yrs.

In 5 years, John will be three times as old as Alice.

2x + 5 = 3(x – 5 + 5)

2x + 5 = 3x

Isolate variable x

x = 5

Answer: Peter is now 5 years old.

Answer:

x > 3/2

Step-by-step explanation:

2x - 3 > -4x + 6

Add 4x to each side

2x+4x - 3 > -4x+4x + 6

6x-3 > 6

Add 3 to each side

6x-3+3>6+3

6x>9

Divide each side by 6

6x/6 >9/6

x > 3/2

Answer:

Step-by-step explanation:

Answer:

1st-joanna

2nd-Mary

3rd-Betty

4th-leah

Step-by-step explanation:

joanna won the race

Answer:

Joanna won followed by Leah ,then Betty and lastly Marry

Answer:

m = 2

Step-by-step explanation:

∠ GLI = 90°

∠ GLH + ∠ HLI = ∠ GLI , that is

9m + 25m + 22 = 90

34m + 22 = 90 ( subtract 22 from both sides )

34m = 68 ( divide both sides by 34 )

m = 2

Then

∠ HLG = 9m = 9 × 2 = 18°

Answer: Quadratic Function: A function with the highest power of variable as 2.

Vertex: The lowest or highest point on the graph of a quadratic function.

Two Types of Problems: Finding quadratic function (a) given the vertex and another point; and (b) given three points.

Step-by-step explanation:

Answer:

A. 157.21. is the answer

Step-by-step explanation:

I hope this helps

Answer:

12.7075

Step-by-step explanation:

Answer:

I would go on quizlet and find the answer

Step-by-step explanation:

Answer:

Set up trig ratio using tangent.

Tan theta = opp/adj

Tan theta = 500/800

Tan^-1 (500/800) = 32 degrees

Answer:

34

Step-by-step explanation:

Because it is a mixed fraction, it tells us the whole number already. After that, we need to look at the actual fraction part and decide if it's large enough to round the whole number up. 1/8 is not, so we keep the whole number at 34

Answer:

That would be 34

Hope that helps!

Step-by-step explanation:

Answer:

3   4   1

Step-by-step explanation:

Answer:

283

Step-by-step explanation:

458-175=283

and you have your answer.

Answer:

$6

Step-by-step explanation:

1.50 * 4

6

Hope it is useful

Answer:

6 dollars

Step-by-step explanation:

$1.50 * 4

Answer:

Inverse operation

Step-by-step explanation:

Basically it is an operation that reverses the effect of another operation.

Answer:

28

Step-by-step explanation:

Answer: 15 √ 2

Step-by-step explanation:

Equilateral triangles have three equal side lengths, three equal angles of 60 degrees, and three equal altitudes.

You would think that the height of an equilateral triangle would also be equal to it's sides, but it's not. The formula for height is: side/2 x √3

10√6 / 2 * √ 3 = 15 √ 2

The decimal form: 21.2

Answer:

[tex] 687.5 \: {ft}^{2} [/tex]

Step-by-step explanation:

Area of polygon = Area of square + Area of triangle

[tex] = {25}^{2} + \frac{1}{2} \times 25 \times (30 - 25) \\ \\ = 625 +\frac{1}{2} \times 25 \times5 \\ \\ = 625 + \frac{1}{2} \times 125 \\ \\ = 625 + 62.5 \\ \\ = 687.5 \: {ft}^{2} [/tex]

Answer: 476m²

Step-by-step explanation:

Find the area of the triangle and then subtract it from the area of the rectangle.

Area of triangle = 1/2 * base * height

= 1/2 * 8 * 6

= 24m²

Area of rectangle:

= Length * Width

= 25 * 20

= 500m²

Area not covered by garden:

= 500 - 24

= 476m²

Answer:

B is the only one i know, sorry.

Step-by-step explanation:

Hope this helped

Answer:

The inverse of

y

=

2

x

is

y

=

log

2

x

Explanation:

This is how to do it.

From the given

y

=

2

x

interchange the variables so that

x

=

2

y

then solve for y:

x

=

2

y

take the logarithm of both sides with base

=

2

log

2

x

=

log

2

2

y

log

2

x

=

y

and

y

=

log

2

x

The graph of

y

=

2

x

and its inverse

y

=

log

2

x

. They are symmetric with the line

y

=

x

graph{(y-2^x)(y-log x/log 2)(y-x)=0[-20,20,-10,10]}