Help plz I really need this

Answer:   see proof below

Step-by-step explanation:

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

Use the Difference Identity: cos(A - B) = cosA · cosB + sinA · sinB

Use the Double Angle Identity: cos 2Ф = 1 - 2sin²Ф

Proof LHS → RHS

LHS:                                          (cosA - cosB)² + (sinA - sinB)²

Expand:          cos²A - 2cosA · cosB + cos²B + sin²A - 2sinA · sinB + sin²B

Pythagorean Identity:   2 - 2cosA · cosB  - 2sinA · sinB

Factor:                           2(1 - (cosA · cosB  + sinA · sinB))

Difference Identity:       2(1 - (cos(A - B))

Let Ф = (A-B)/2:             2(1 - cos2Ф)

Double Angle Identity:  2(1 - (1 - 2sin²Ф))

Simplify:                         2(1 - 1 + 2sin²Ф)

                                   = 4sin²Ф

Substitute (A-B)/2=Ф:    4sin²(A-B)/2

LHS = RHS: 4sin²(A-B)/2 = 4sin²(A-B)/2   [tex]\checkmark[/tex]

Answer:

0.074 or 37/500

Step-by-step explanation:

also 7.4%

Answer:

AX = 14

Step-by-step explanation:

The medians of a triangle intersect at its centroid.

The position of the centroid X from the vertex A is

AX = [tex]\frac{2}{3}[/tex] AL = [tex]\frac{2}{3}[/tex] × 21 = 14

Expanding parentheses,

➝ (x - 3)(x + 7)

➝ x(x + 7) - 3(x + 7)

➝ x² + 7x - 3x - 21

➝ x² + 4x - 21

Option B

Expanding brackets involves removing the brackets by multiplying each term in the brackets by every term outside of the brackets. The process of expansion is also known as the distributive law. When expanding brackets be very careful of negative numbers. 

Once a set of brackets has been expanded, it is possible for several like terms to appear. 

When this is the case you can use the box method or FOIL to ensure you expand the set of brackets properly. In general:

[tex] \large{ \boxed{ \rm{(a + b)(c + d) = ac + ad + bc + bd}}}[/tex]

━━━━━━━━━━━━━━━━━━━━

Answer:

Step-by-step explanation:

[tex] \sf{(x - 3)(x + 7)}[/tex]

Use the distributive property to multiply each term of the first binomial by each term of the second binomial.

⇒[tex] \sf{x(x + 7) - 3(x + 7)}[/tex]

⇒[tex] \sf{ {x}^{2} + 7x - 3x - 21}[/tex]

Collect like terms

⇒[tex] \sf{ {x}^{2} + 4x - 21}[/tex]

Hope I helped!

Best regards!!

Answer:

[tex] \boxed{\boxed{\boxed{\red{{x}^{2} + 4x - 21}}}}[/tex]

Step-by-step explanation:

[tex](x - 3)(x + 7) \\ x(x + 7) - 3(x + 7) \\ {x}^{2} + 7x - 3x - 21 \\ {x}^{2} + 4x - 21[/tex]

Answer: The correlation between variables must be significant

Step-by-step explanation: In order to make reliable predictions using the equation of a regression model, the correlation Coefficient between the dependent and independent variables must be significant (that is a correlation Coefficient value close to either 1 or - 1). This is because the range of value of the correlation Coefficient is between - 1 to +1 and the closer the correlation Coefficient value is to either of these numbers, depicts the strength of the relationship which exists between them hence, enabling us to make good and accurate predictions which are close to the actual value.

Regression Analysis is a statistical and reliable process for making predictions using the regression model.

The correct option is:

Option B. The correlation between variables must be significant

The regression line can be explained as:

1. The correlation coefficient between the dependent and independent variables must be significant.

2. The correlation coefficient value should be near 1 or -1.

3. Thus, the values closer to - 1 and +1 will depict the strength of the relationship between the coefficient values.

Thus, regression lines help to predict accurate and reliable results that are close to the actual value.

To know more about regression lines, refer to the following link:

https://brainly.com/question/4341286

Answer:

4

Step-by-step explanation:

5ˣ⁺¹ = 5²ˣ⁻³

x+1 = 2x -3

x = 4

Answer:

The answer is 51

Step-by-step explanation:

Because 18 + 23 = 51

Answer:

2 3/6 or 2 1/2

Step-by-step explanation:

8 4/6 - 6 1/6 = 2 3/6

Answer:

8 dollars

Step-by-step explanation:

f(10)=6

g(6)=8

8 dollars

Answer:

$24.50

Step-by-step explanation:

Money saved for each shirt:

=$9. 10/2

=$4.55

Original price of the shirt:

=$19. 95 + $4.55

=$24.50

Answer:

-14°C

Step-by-step explanation:

6 + 8 = 14

So in 24 hour time that would be 2pm

From 6am to 2pm is 8 hours

If the degrees is going down by 2 you would times the 8 by 2 because it is doubled

That = 16

Then you'll minus 16°C from the 2°C

2°C - 16°C

= -14°C

Answer: Complementary

x=58

Step-by-step explanation:

Answer:

43 if yousubtract it

STEP-BY-STEP EXPLANATION

Answer: 128

Step-by-step explanation:

Given : Total ingredients =7

When we select any one of ingredient for salad, then total choices for each ingredient = 2 (Yes or No)

So for all 7 ingredients there will be [tex]2\times2\times2\times2\times2\times2\times2=2^7=128[/tex] choices [By fundamental principle of counting]

Hence, there are 128 different salads are possible where two salads are different if they don't include identical ingredients

Answer:

27

Step-by-step explanation:

Given

- 3w - 5p ← substitute w = - 4 and p = - 3 into the expression

= - 3(- 4) - 5(- 3 )

= 12 + 15

= 27

Answer:

127x

Step-by-step explanation:

The expression 127x will represent this situation.

Since x represents the number of textbooks, we can put the coefficient 127 in front of it to include the cost.

For example, 2 textbooks will be $254 if we plug in 2 as x into the expression, since 127(2) = 254.

Answer:

[tex]24x+6[/tex]

Step-by-step explanation:

We know that the perimeter of a rectangle's formula is [tex]2l + 2w = p[/tex], where l is the length and w is the width - p is the perimeter. We know the length and width, so we can substitute into the equation.

[tex](2\cdot(10x-3)) + (2\cdot(2x+6))\\\\(20x-6) + (4x+12)[/tex]

We can now combine like terms to get [tex]24x + 6[/tex].

Hope this helped!

Answer:

The rational numbers include all the integers, plus all fractions, or terminating decimals and repeating decimals. Every rational number can be written as a fraction a/b, where a and b are integers. If a number is a whole number, for instance, it must also be an integer and a rational.

Step-by-step explanation:

Answer: X= -1 OR X= 11

Step-by-step explanation:

Step 1 : Equate ( x-5)² since it occurred twice, hence the reason 2 is added in front of (x-5)²

= (x-5)²

= (x-5)(x-5)

= (x²-5x-5x+25)

= (x²-10x+25)

Step 2: multiply the result by two since it occurs twice and also bring the equation

= 2 (x²-10x+25) +7 = 79

= 2x²- 20x+50+7 = 79

= 2x²- 20x+57 =79

Step 3: most quadratic equation are always equal to zero, let's make this one equal to Zero by subtracting 79 from both sides

= 2x²-20x+57-79 = 79-79

= 2x²-20x-22=0

Step 4: divide the equation by a common number to get the least coefficient of the three coefficients

Dividing the three by 2

(2x²-20x-22)/2 = x²- 10x- 11

Step 5: Factorise completely

Sub step 1 : the first term in the equation is X² which makes the first term coefficient 1; the second term in the equation is -10x which makes the second term coefficient -10, the constant has a coefficient of -11

Sub step 2: multiply the coefficient of the first term (1) and the constant (-11) which gives us (-11)

1*-11 = -11

Sub step 3: Get two numbers in such a way that the addition of the first number and the second number gives the second coefficient in the quadratic equation and the multiplication of the two numbers will give us the product of the first coefficient and the constant.

And the two numbers is +1 and -11, the sum of the two numbers will give us -10 and the product will give us -11.

Step 6: slot the two numbers (+1, -11) into the equation by making themr replace the second coefficient

x²-10x-11=0

= x²+x-11x-11 =0

Step 7: split the equation into two and Factorise further

= (x²+x)(-11x-11) =0

= x(x+1)-11(x+1) = 0

= x+1= 0 or x-11 =0

Step 8 split them into individual equation

= x+1= 0.

Subtract 1 from both sides

= X+1-1=0-1

= x= -1

Or X should be

= x-11=0

Add 11 to both sides

= X-11+11 = 0+11

= x= 11

Answer for the first box = 6000

Answer for the second box = 1.004

Answer for the third box = 720

So the full equation is [tex]C(t) = 6000(1.004)^{12t} + 720t[/tex]

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

Explanation:

The compound interest formula is

A = P( 1+r/n )^(n*t)

where

In this case,

So we go from this

A = P( 1+r/n )^(n*t)

to this

A = 6000( 1+0.042/12 )^(12t)

A = 6000(1.0035)^(12t)

A = 6000(1.004)^(12t)

The 1.0035 rounded to 1.004 when rounding to three decimal places, as the instructions mention.

So far we only considered the amount placed into the bank. But there's also the amount placed in the safe at home. We have $60 placed in here per month. This is 60*12 = 720 dollars per year. If t years go by, then a total of 720t dollars is put in the safe.

----------

So in summary we found

[tex]b(t) = 6000(1.004)^{12t}[/tex] = amount in savings account after t years go by

[tex]h(t) = 720t[/tex] = amount in safe after t years

leading to

[tex]C(t) = b(t) + h(t) = 6000(1.004)^{12t} + 720t[/tex]

Answer:

12,662 books

Step-by-step explanation:

Total number of books = 75,972

No. of science books = ⅓ of 75,972 = ⅓*75,972 = 25,324 books.

No. of business books = 75% of the remaining books = 75% of (75,972 - 25,324)

= [tex] \frac{75}{100}*50,648 = 37,986 [/tex]

No. of business books = 37,986

No. of maths books in the math section = 75,972 - (25,324 + 37,986)

= 75,972 - 63,310

= 12,662 books

Answer:

y > -255, or (-255, infinity)

Step-by-step explanation:

y + 51 > - 204

Solve for y:  subtract 51 from both sides, obtaining:

y > -255, or (-255, infinity)

The solution of the inequality is y > -255.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that translate and solve: 51 more than y is greater than −204. The inequality expression can be written as:-

y + 51 > - 204

Solve for y:  subtract 51 from both sides, and solve the inequality:-

y > -255,

Hence, the solution to the inequality is y > -255.

To know more about inequality follow

https://brainly.com/question/24372553

#SPJ2

Answer:

-2

Step-by-step explanation:

-12 -14

Answer:

9.25b=46.25

Step-by-step explanation:

9.25b=46.25/:9.25

b=5

Richard purchased 5 books for $9.25 each

Answer:

y=72

Step-by-step explanation:

y varies jointly as x and z

y=k*x*z

Where,

k= constant of proportionality

y=144, x=6, z=10

y=k*x*z

144=k*6*10

144=60k

Divide both sides by 60

144/60=k

2 24/60=k

2 6/15=k

2 2/5=k

k=12/5

Find y when x=5 and z=6

y=k*x*z

y=12/5*5*6

=360/5

=72

y=72

Answer:

w=sa

Step-by-step explanation:

move the a into multiplication on the other side so

w=sa

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                          PEACE!

Answer:

W = SA

Step-by-step explanation:

S = W/A

Multiply both sides by 'A'

S* A = [tex]\frac{W}{A }*A[/tex]

SA = W

W = SA

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

Explanation:

Assume the ground is completely flat and level. We have a right triangle with hypotenuse 30, and the horizontal base leg is 18. The vertical leg is unknown, so we'll call it x.

Use the pythagorean theorem to solve for x

a^2+b^2 = c^2

x^2+18^2 = 30^2

x^2 + 324 = 900

x^2 = 900 - 324

x^2 = 576

x = sqrt(576)

x = 24

The height of the tower's floor is 24 feet.