Answer with explaination every steps​

Answer:

[tex](x -12)(x + 12)[/tex]

Step-by-step explanation:

Given

See attachment for chart

Required

The factors of [tex]x^2 - 144[/tex]

First, express [tex]x^2 - 144[/tex] as [tex]ax^2 + bx + c[/tex]

So, we have:

[tex]x^2 - 144 = x^2 + 0x - 144[/tex]

Compare the above expression to: [tex]ax^2 + bx + c[/tex]

We have:

[tex]ax^2 + bx + c = x^2 + 0x - 144[/tex]

So:

[tex]a =1[/tex]

[tex]b =0[/tex]

[tex]c = -144[/tex]

and

[tex]a * c = d * e[/tex]

Calculate ac

[tex]a* c = 1 * -144[/tex]

[tex]a* c = -144[/tex]

Rewrite as:

[tex]a* c = -12 * 12[/tex]

Recall that:

[tex]a * c = d * e[/tex]

Hence:

[tex]d = -12; e = 12[/tex]

So, on the x chart, we have:

        ac

d                  e

        b

This gives:

        -144

-12                  12

        0

The factors are

[tex](x + d)(x + e)[/tex]

[tex](x -12)(x + 12)[/tex]

Answer:

✔ (x – 12)

 and  

✔ (x + 12)

Step-by-step explanation:

Answer:

67.5

Step-by-step explanation:

I've learned this multiple ways but in my opinion this is the easiest. Just times everything together so, 40 x 2.5 x 1.2 which equals 135 and then divide 135 by 2 which equals your answer of 67.5 which is rounded to the nearestt tenth already.

Answer:

1) 1 ≥ 2·x

2) 6·x ≥ 3 + 8·x - 4

3) 1/2 ≥ x The third option and the first number line inequality diagram, please see attached drawing of the number line created with MS Visio

Step-by-step explanation:

The given inequality is presented as follows;

6·x ≥ 3 + 4·(2·x - 1)

By expanding the right hand side of the inequality, we get;

6·x ≥ 3 + 8·x - 4

4 - 3 = 1 ≥ 8·x - 6·x = 2·x

∴ 1 ≥ 2·x

1/2 ≥ x

Therefore, the correct options are;

1) 1 ≥ 2·x

2) 6·x ≥ 3 + 8·x - 4

3) 1/2 ≥ x The third option and the first number line inequality diagram

Answer:

5.0956537e-46

Step-by-step explanation:

^ means root

* means multiply

f(x) = ab^x

f(-1.5)=26 = ab^-1.5

f(5.5)=7 = ab^5.5

f(5.5)/f(-1.5) = 26/7 = ab^5.5/ab^-1.5

3.714 = b^7

b = 3.714^-7

f(-1.5)=26 = ab^-1.5

26 = ab^-1.5

26 = a * 3.714^-7

a = 3.714^-7 / 26

a = 0.00000394578

f(10) = ab^10

f(10) = 0.00000394578 * (3.714^-7)^10

f(10) = 5.0956537e-46

The red line is perpendicular to the y-axis.

Given:

The expression is:

[tex]\left(x^{\frac{2}{5}\right)^n[/tex]

To find:

The decimal value of n so that the value of the given expression is equal to x.

Solution:

We have,

[tex]\left(x^{\frac{2}{5}\right)^n[/tex]

This expression is equal to x.

[tex]\left(x^{\frac{2}{5}\right)^n=x[/tex]

[tex]x^{\frac{2}{5}n}=x^1[/tex]                     [tex][\because (a^m)^n=a^{mn}][/tex]

On comparing the exponents, we get

[tex]\dfrac{2}{5}n=1[/tex]

[tex]2n=5[/tex]

[tex]n=\dfrac{5}{2}[/tex]

[tex]n=2.5[/tex]

Therefore, the required value of n is 2.5.

Answer:

[tex]{ \tt{ = 3 \div \frac{2}{5} }} \\ = { \tt{3 \times \frac{5}{2} }} \\ = \frac{15}{2} [/tex]

Answer:

113

Step-by-step explanation:

Answer:

0. 116

Step-by-step explanation:

The function is given as :-

[tex]\boxed{f(d) = 5(1.02)^d }[/tex]

and we have to find the rate of change from d = 4 to d = 11

[tex]\boxed{\blue{\mathfrak{Rate\: of\: change = \frac{final\:output-intital\:output}{final\:input-initial\:input} } }}[/tex]

The final input value is 11 whereas the initial input value is 4.

The final and initial outputs can be calculated by placing the respective values of initial and final inputs (that are 4 and 11).

f(4) = [tex]5(1.02)^4[/tex]

f(4) = 5 × 1. 08

f(4) = 5. 41

f(11) = [tex]5(1.02)^11[/tex]

f(11) = 5 × 1. 24

f(11) = 6. 22

[tex]\underline{Avg\:Rate \: of \: change} = \frac{6. 22-5.41}{11-4} \\ = \frac{0.81}{7} \\ = 0.116 [/tex]

[tex]\bigstar[/tex] Hence, the average rate of change is [tex]\red{\underline{\pmb{0. 116}}}[/tex]

Answer:

5/14

Step-by-step explanation:

There are 15 tiles in total

5 white| 6 black | 4 blue

event A results in the subject pulling a white tile and not replacing it

5-1= 4

so the first answer should be 4/15

event B results in the subject pulling another tile, a black one and not replacing it.

6-1= 5

given this answer, there is one less tile in the total, since we removed another tile.

So our answer would be-

5/14 or D

Answer:

B

Step-by-step explanation:

To find which ordered pairs are solutions to the inequalities we can simply plug in the x and y values of the ordered pairs into the inequalities and if the equation is true for both inequalities then the ordered pair is a solution to the inequalities.

For (0,0)

x = 0

y = 0

y > x + 5

Substitute 0 for y and x

0 > 0 + 5

Simplify right side

0 > 5

The inequality is not true as 5 is greater than 0, not less than. So immediately we can eliminate answer choice A.

For (5,1).

x = 5

y = 1

y > x + 5

Substitute 5 for x and 1 for y

1 > 5 + 5

Simplify right side

1 > 10

Again, the equation is not true as 1 is not greater than 10. This means that c cannot be the answer

For (3,7)

x = 3

y = 7

y > x + 5

Substitute 3 for x and y for 7

7 > 3 + 5

Simplify right side

7 > 8

7 is not greater than 8 meaning that (3,7) cannot be a solution to the inequalities

None of the ordered pairs created true equations hence the answer is B

Answer:

Step-by-step explanation:

To solve this, we can use polynomial long division.

Seeing the picture, we first divide x (the variable to the largest degree in x+1) from 2x³. We divide from 2x³ because that is the variable with the largest degree in the polynomial. That is equal to 2x², so we put that on top and subtract (x+1) * (2x²) from the polynomial. Then, we repeat the process, but with x² instead of 2x³, and again with -6x as the variable with the largest degree.

[tex]\displaystyle\bf 1\frac{1}{3} -3\frac{5}{6} +5\frac{1}{9} =5+1-3+\frac{1^{/6}}{3} +\frac{1^{/2}}{9} -\frac{5^{/3}}{6}\\\\\\\ =3+\frac{6+2-15}{18} =3-\frac{7}{18}=\boxed{2\frac{11}{18} }[/tex]

Answer:

option 1

Step-by-step explanation:

I am not sure, what your are asking about.

in your text you define the length of DF (20), but the answer options (only 2 visible) also specify DF but differently.

so ... ?

when you said DF=20, did you actually mean DE ?

under that assumption

DE = 20 = Hypotenuse of the right-angled triangle (the opposite side of the 90 degree angle).

EF = 17

based on Pythagoras

c² = a² + b²

we have here now

20² = 17² + DF²

400 = 289 + DF²

DF² = 400 - 289 = 111

DF = sqrt(111)

Answer:

120 miles

Step-by-step explanation:

30 miles per hour * 4 hours

120 miles

Answer:

She travels 120 miles in 4 hours.

Step-by-step explanation:

She travels 120 miles in 4 hours

The question seems incomplete ; as the total number of tickets to be sold isn't given.

Answer:

61 / X

Step-by-step explanation:

Let's take the total Number of tickets to be sold as : X

Number of tickets sold on Thursday = 47

Number sold on Friday = 14

Fraction of tickets available for sale on Saturday :

(Total number of tickets already sold) / Total number of tickets to be sold

(Thursday + Friday sales) / total number of tickets to be sold

Fraction available for sale on Saturday = (47+14) / X

Fraction available for sale on Saturday = 61 / X

Kindly put value of x = total number of tickets available for sale to get the exact fraction.

Answer:

[tex]\frac{-1+1}{0-(-2)}=0[/tex]

[tex]ANSWER: A)~0[/tex]

------------------------------

HOPE IT HELPS

HAVE A GREAT DAY!!

Answer:

2a(b+c)

Step-by-step explanation:

Find HCF (2a)

Then factorise

Answer:

2a(b+c)

.............

Answer:

A.

Step-by-step explanation:

To find the inverse of a function, first make f(x) a y

So,

y = [tex]\frac{12}{x}[/tex] -18

Then switch the x and the y

x = [tex]\frac{12}{y}[/tex] - 18

Solve, for y

Answer:

B=-5

Step-by-step explanation:

Slope=rise/run

The line passes in

P1(-1,3)

and

P2(0,-2)

So slope=(3-(-2))/(-1-0)=5/-1=-5

Answer:

40/30

Step-by-step explanation:

Since tan∅= o/a, 40 is opposite, and 30 is adjacent to angle A, 40/30 is the ratio for tanA.

Answer:40/30

Step-by-step explanation:

....

Answer:

13

Step-by-step explanation:

Distance between points (1, 3) and (6, 15) is 13

Step-by-step explanation:

70

*4

___

280.......ans

The area of the triangle bounded by the lines y=x y=-x and y=6 is 36 units.

The formula for finding area could be represented in the form of determinants as given below.

[tex]A = \frac{1}{2} \left[\begin{array}{ccc}x1&y1&1\\x2&y2&1\\x3&y3&1\end{array}\right][/tex]

First, we need to find the coordinates of the point of intersection of these lines.

y = x

y = -x

Adding the two equations,

2y = 0

y = 0

x = 0

coordinate: (0, 0)

y = x

y = 6

Subtracting the two equations,

0 = x - 6

x = 6

coordinate: (6, 6)

y = -x

y = 6

Subtracting the two equations,

- x - 6 = 0

x = -6

coordinate: (-6, 6)

Calculating area of triangle bounded by the given line:

Area of triangle =

[tex]\frac{1}{2}\left[\begin{array}{ccc}0&0&1\\6&6&1\\-6&6&1\end{array}\right][/tex]  =  [tex]\frac{1}{2} (36 + 36) = \frac{72}{2} = 36[/tex]

Learn more about area of triangle here

https://brainly.com/question/19305981

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Answer:

true

Step-by-step explanation:

Because a logically equivalent is the same as biconditional statement

Step-by-step explanation:

hello the answer is true, you can check but it's obviously true

Answer:

Is it the answer is C?

2+4+3+5+1=15

Answer:

Step-by-step explanation:

Given function is,

f(x) = -x² - 2x - 1

     = -(x² + 2x + 1)

     = -(x + 2)²

Comparing this equation with the vertex form of a quadratic function,

f(x) = a(x - h)² + k

Here, (h, k) is the vertex.

Vertex of the function is (-2, 0)

Leading coefficient of the function = -1

Therefore, parabola will open downwards.

Function will be increasing in the interval (-∞, -2).

Function will be decreasing in the interval (-2, -∞).

Domain of the function → (-∞, ∞)

Range of the function → (-∞, 0]

Answer:

Step-by-step explanation:

edge