(20pts) Please help! Sometimes, always, or never true. Prove why​

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:

8 dollars

Step-by-step explanation:

f(10)=6

g(6)=8

8 dollars

Answer:

65

Step-by-step explanation:

You multiply the factors by each other.

Answer:

65

Step-by-step explanation:

13 x 5 = 65

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

Answer:

43 if yousubtract it

STEP-BY-STEP EXPLANATION

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:

64

Step-by-step explanation:

let the number be x, then

[tex]\frac{1}{8}[/tex] x + 5 = 13 ( subtract 5 from both sides )

[tex]\frac{1}{8}[/tex] x = 8 ( multiply both sides by 8 )

x = 64

The number is 64

Answer:

The number is 64

Step-by-step explanation:

Let x be the number

1/8 x +5 = 13

Subtract 5 from each side

1/8x +5-5 = 13-5

1/8 x = 8

Multiply each side by 8

8*1/8x = 8*8

x = 64

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:

-2

Step-by-step explanation:

-12 -14

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: 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.

The height of house is 26.53 m

The angle of elevation and angle of depression are opposites of each other. In an angle of elevation, the object is placed above the observer, while in the case of the angle of depression, it is placed below the observer.

If you are standing at your terrace and looking at the sun, then the angle of elevation will be formed. On the other hand, if you will look at the dog standing on the road from your terrace, then the angle of depression will be formed. In both cases, we use trigonometry angles to find the heights and distances.

Given:

Window height = 20 m

angle of elevation =5

angle of depression= 15

Using trigonometry

tan 15 = P/B

0.2679= 20/B

B= 74.654 m

Again

tan 5 =P/B

0.0874 = P/ 74.645

P= 6.5305 m

Hence, height of the tree is 6.53 + 20= 26.53 m

Learn more about angle of elevation here:

https://brainly.com/question/21137209

#SPJ2

Answer:

4

Step-by-step explanation:

5ˣ⁺¹ = 5²ˣ⁻³

x+1 = 2x -3

x = 4

Answer:

[tex] w = \frac{11}{35} [/tex]

Step-by-step explanation:

To solve, [tex] \frac{3}{5w} - \frac{2}{7w} = 1 [/tex], make both fractions on your left as one fraction by finding a common denominator.

Common denominator of 5w and 7w is 35w

Thus,

[tex] \frac{7(3) -5(2)}{35w} = 1 [/tex]

[tex] \frac{21 - 10}{35w} = 1 [/tex]

[tex] \frac{11}{35w} = 1 [/tex]

Multiply both sides by 35w

[tex] \frac{11}{35w}*35w = 1*35w [/tex]

[tex] 11 = 35w [/tex]

Divide both sides by 35

[tex] \frac{11}{35} = \frac{35w}{35} [/tex]

[tex] \frac{11}{35} = w [/tex]

[tex] w = \frac{11}{35} [/tex]

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

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:

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:

$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:

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

Answer:

The answer is 51

Step-by-step explanation:

Because 18 + 23 = 51

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:

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: Complementary

x=58

Step-by-step explanation:

Answer:

2,irrational,2,irrational :)

Step-by-step explanation:

Answer: I think its a tell me if im wrong

Step-by-step explanation:

Answer:

0.074 or 37/500

Step-by-step explanation:

also 7.4%

Answer:

2 3/6 or 2 1/2

Step-by-step explanation:

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