Can you please factor the problems below and explain/show all your steps. I will be attaching a photo with the problems as well in case they are more understandable on there. Also if you can please explain how you used the key concepts from the photo in your work if you used them.
Factor: 2a^3 + 4a^2 + 8a
Factor: 6y^4 - 294y^2
Factor: 5x^2 + 50x +125

We have

(a + bx) / (a - bx) = (b + cx) / (b - cx)

==>   (a + bx) (b - cx) = (a - bx) (b + cx)

==>   ab + (b ² - ac) x - bcx ² = ab + (ac - b ²) x - bcx ²

==>   (b ² - ac) x = (ac - b ²) x

==>   b ² - ac = ac - b ²

==>   2b ² = 2ac

==>   b ² = ac … … … [1]

Similarly, you would find

(a + bx) / (a - bx) = (c + dx) / (c - dx)

==>   ad = bc … … … [2]

and

(b + cx) / (b - cx) = (c + dx) / (c - dx)

==>   c ² = bd … … … [3]

Now:

c ² = bd   ==>   b = c ² / d

b ² = ac   ==>   c = b ² / a

ad = bc   ==>   d = bc / a

and we find

d / c = (bc / a) / (b ² / a) = c / b

and

c / b = (b ² / a) / (c ² / d) = (b ² d) / (a c ²) = b / a

which is to say, the ratio between d and c is equal to the ratio between c and b, and also equal to the ratio between b and a. Therefore (a, b, c, d) are in a geometric progression.

Answer:

Step-by-step explanation:

[tex]Mean=\frac{all.ages.added.together.of.all.kids}{total.number.of.kids}[/tex] Hopefully, that makes sense! To get the numerator of that problem, we take the number of kids and multiply it by the corresponding age and add them all together. To get the denominator, we add the total number of kids together. That will look like this mathematically, setting the mean equal to 14.44, as stated:

[tex]14.44=\frac{13(15)+14(42)+15X+16(10)+17(3)}{15+42+X+10+3}[/tex] and simplify that a bit to

[tex]14.44=\frac{195+588+15X+160+51}{70+X}[/tex] and a bit more to

[tex]14.44=\frac{994+15X}{70+X}[/tex] and cross multiply

14.44(70 + X) = 994 + 15X and

1010.8 + 14.44X = 994 + 15X and

16.8 = .56X so

X = 30

30 kids are 15 years old for the mean age to be 14.44

d.30

Answer:

Solution given:

x. [tex] \:\:\:[/tex] f. [tex] \:\:\:[/tex] fx

13. [tex] \:\:\:[/tex] 15. [tex] \:\:\:[/tex] 195

14.[tex] \:\:\:[/tex] 42 [tex] \:\:\:[/tex] 588

15. [tex] \:\:\:[/tex] x. [tex] \:\:\:[/tex] 15x

16. [tex] \:\:\:[/tex] 10. [tex] \:\:\:[/tex] 160

17. [tex] \:\:\:[/tex] 3. [tex] \:\:\:[/tex] 51

. n=70+x. [tex]\sum[/tex]=994+15x

we have

mean=sum/n

14.44=[tex]\bold{\frac{\sum}{n}}[/tex]

14.44=[tex]\bold{\frac{994+15x}{70+x}}[/tex]

doing crisscrossed multiplication

(70+x)*14.44=994+15x

1010.8+14.44x=994+15x

15x-14.44x=1010.8-994

0.56x=16.8

x=16.8/0.56

x=30

Answer:

The answer is "B"

Step-by-step explanation:

The explanation is in the picture!

Answer:

[tex]6(3f-15)=90[/tex]

[tex]3f=90/6+15=30[/tex]

[tex]f=10[/tex]

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

Hope it helps...

Have a great day!!

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{6(3f - 15) = 90^\circ}\\\\\huge\text{DISTRIBUTE}\\\\\mathsf{6(3f) + 6(-15) = 90^\circ}\\\\\mathsf{18f - 90 = 90^\circ}[/tex]

[tex]\text{NEW EQUATION: }\mathsf{18f - 90 = 90}[/tex]

[tex]\huge\text{ADD 90 to BOTH SIDES}[/tex]

[tex]\mathsf{18f - 90 + 90 = 90 + 90}[/tex]

[tex]\textsf{CANCEL out: -90 + 90 because that gives the number of 0}[/tex]

[tex]\textsf{KEEP: 90 + 90 because it helps solve for the f-value}[/tex]

[tex]\mathsf{90 + 90 = \bf 180}[/tex]

[tex]\huge\text{NEW EQUATION:\textsf{ 18f = 180}}[/tex]

[tex]\huge\text{DIVIDE 18 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{18f}{18}=\dfrac{180}{18}}[/tex]

[tex]\mathsf{CANCEL \ out: \dfrac{18}{18}\ because \ that \ gives \ the \ number \ of\ 1}[/tex]

[tex]\mathsf{KEEP: \dfrac{180}{18} \ because \ that \ gives \ the\ f-value \ result}[/tex]

[tex]\mathsf{f = \dfrac{180}{18}}[/tex]

[tex]\huge\text{SOLVE ABOVE \& YOU HAVE THE RESULT}[/tex][tex]\huge\text{OF THE F-VALUE}[/tex]

[tex]\mathsf{\dfrac{180}{18}}[/tex]

[tex]\mathsf{= \bf 18}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Therefore, your ANSWER is: \bf f = 10}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

a. 129 meters

Step-by-step explanation:

The given parameters of the tree and the point B are;

The horizontal distance between the tree and point B, x = 125 meters

The angle of depression from the top of the tree to the point B, θ = 46°

Let h represent the height of the tree

The horizontal line at the top of the tree that forms the angle of depression with the line of sight from the top of the tree to the point B is parallel to the horizontal distance from the point B to the tree, therefore;

The angle of depression = The angle of elevation = 46°

By trigonometry, we have;

tan(θ) = h/x

∴ h = x × tan(θ)

Plugging in the values of the variables gives;

h = 125 × tan(46°) ≈ 129.44

The height of the tree, h ≈ 129 meters

Answer:

C: 2 × 10⁴

Step-by-step explanation:

We are told that the average net primary production in tropical rain forests each year is 8,900 kilocalories per square meter.

Thus;

P_net,average = 8900 Kcal/m²

We are also told that net primary production of a selected portion of a tropical rain forest in a given year is 1.8 × 10^(8) kilocalories.

Thus;

P_net = 1.8 × 10^(8) Kcal

To get the average, the formula is;

P_net,average = P_net/Area

Thus;

Area = P_net/P_net,average

Plugging in the relevant values;

Area = (1.8 × 10^(8))/8900

Area ≈ 2 × 10⁴ m²

The value of x for the given equation [tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2 will be 2 so option (B) must be correct.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

Given the equation

[tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2

We know that,

xlogb = log[tex]b^{x}[/tex]

So,

2[tex]log_{8}[/tex](x) = logx²

For the same base

logA + logB = log(AB)

So,

[tex]log_{8}[/tex](16) + [tex]log_{8}[/tex](x)² = 2

[tex]log_{8}[/tex](16x²) = 2

We know that

[tex]log_{a}[/tex](b) = c ⇒ b = [tex]a^{c}[/tex]

so,

[tex]log_{8}[/tex](16x²) = 2 ⇒ 8² = 16x²

x = 2 hence x = 2 will be correct answer.

For more about logarithm

https://brainly.com/question/20785664

#SPJ2

Given:

The ratio of 45-45-90 triangle is [tex]x:x:x\sqrt{2}[/tex].

The hypotenuse of the given isosceles right triangle is [tex]7\sqrt{2}[/tex].

To find:

The lengths of the other two sides of the given isosceles right triangle.

Solution:

Let [tex]l[/tex] be the lengths of the other two sides of the given isosceles right triangle.

From the given information if is clear that he ratio of equal side and hypotenuse is [tex]x:x\sqrt{2}[/tex]. So,

[tex]\dfrac{x}{x\sqrt{2}}=\dfrac{l}{7\sqrt{2}}[/tex]

[tex]\dfrac{1}{\sqrt{2}}=\dfrac{l}{7\sqrt{2}}[/tex]

[tex]\dfrac{7\sqrt{2}}{\sqrt{2}}=l[/tex]

[tex]7=l[/tex]

Therefore, the lengths of the other two sides of the given isosceles right triangle are 7 units.

Answer:

Lines parallel to this line will have a slope of -1

Step-by-step explanation:

y = -x + 7

This line is in slope intercept form

y = mx+b where m is the slope

The slope is -1

Parallel lines have the same slope

Lines parallel to this line will have a slope of -1

Answer:

-1

Step-by-step explanation:

Parallel lines have the same slope

The equation y = -x + 7 has a slope of -1 meaning that a line parallel to it would also have a slope of -1

Answer:

29

Step-by-step explanation:

all in all it is 180 so 61 + m (which is 90 because it is a right angle)=151

then 180-151=29

Answer: He bought 6 pounds of coffee.

Step-by-step explanation:

Money he have = 70

money he used to buy = 70.00 - 23.62 = 46.38

so

7.73 dollar = 1 pound

1 dollar = 1/(7.73) = 100/773 pound

46.38 dollar = (100/773) * 46.38 = 6 pound

Answer:

its not 80k/3000 someone answer

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

a^2

Let a= 1/2

(1/2)^2

(1/4)

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{a^2}\\\\\mathsf{= \ (\dfrac{1}{2})^2}\\\\\mathsf{= \ \dfrac{1}{2}\times\dfrac{1}{2}}\\\\\mathsf{= \ \dfrac{1\times1}{2\times2}}\\\\\mathsf{= \ \bf \dfrac{1}{4}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Therefore, the ANSWER is: }\boxed{\mathsf{\bf \dfrac{1}{4}}}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

chemical

Step-by-step explanation:

Answer:

- 22.5

Step-by-step explanation:

Substitute x = 3 into f(x) and x = 16 into h(x) , then

[tex]\frac{1}{2}[/tex] g(3) - h(16)

= [tex]\frac{1}{2}[/tex] × - 3(3)² - (2[tex]\sqrt{16}[/tex] + 1)

= [tex]\frac{1}{2}[/tex] × - 3(9) - (2(4) + 1)

= [tex]\frac{1}{2}[/tex] × - 27 - (8 + 1)

= - 13.5 - 9

= - 22.5

Answer:

10%

Step-by-step explanation:

Answer:

given that the only one that actually adds up to 65%

is B....

B. 25% + 10% + 10% + 10% + 10%

Step-by-step explanation:

Answer:

The top answer is correct

Step-by-step explanation:

Vertical angles are formed when two lines meet each other at a point and they are always equal to each other. Their angles are also equal. In this problem number two has angles that do not match and number three also has different angles. Finally number four also has different angles and is not equal to each other. Leaving number one (the top answer) which looks to have the same angle, and is equal to each other.

Answer:

a =2 5

b =50

Step-by-step explanation:

Answer:

(A, B, D)

Step-by-step explanation:

Let's evaluate each answer choice:

"The independent variable is the number of people"

Correct. The number of people is independent and DOESN'T depend on the total cost to change.

"The initial value (initial fee) for the pinic is $40"

Correct. In this table, every 3 people increases the cost by $6. So that means 6 people would increase the cost by $12. From the first row of 6 people and $52, if we "subtracted" 6 people and "subtracted" $12, we would get a value of 0 people with a total cost of $40.

"The rate of change is $8.67 per person"

Wrong. To find the rate of change (also called slope), use this method below:

(y_2 - y_1)/(x_2 - x_1)

(6, 52) (9, 58)

x_1 = 6

x_2 = 9

y_1 = 52

y_2 = 58

(58 - 52)/(9-6)

6/3 = 2

The rate of change is 2, not 8.67.

"As the number of people increases, the total cost of the picnic increases."

Correct. As you can see in the table, as the number of people increase (6, 9, 12, 15), the total cost increases as well (52, 58, 64, 70).

"If 4 people attended the picnic, the total cost would be $46."

Wrong. In one of the previous answer choices, we found out that the rate of change, or the cost per person at picnic, is $2, and the intial fee is $40. From this info, we can form this equation:

y = 2x + 40

And if we plug in 4 people into this equation, we DON'T end up with total cost of $46:

2(4) + 40

8 + 40 = 48

The total cost for 4 people is $48, NOT $46

Hope this helps (●'◡'●)

For sinø = cosø, ø = 45°. Because it is right, it is also a right, isosceles  triangle

Answer:

78

Step-by-step explanation:

For every 1 bout Lina makes, Harry makes two boats.

1 + 2 is 3.

117 divided by 3 = 39, which is how many boats Lina made.

39 x 2 = 78, which is how many boats Harry made.

To check our answer, 39 + 78 = 117, which is how many boats they made altogether, so the answer is correct.

Answer:

78

Step-by-step explanation:

My knowledge!!

Hope it helps!

Answer:

Step-by-step explanation:

x1 y1 x2 y2

-2 -2 0 3

ΔY 5

ΔX 2

slope= 2 1/2

B= 3

Y =2.5X +3

Answer:

tan x = c/b

cos x = b/a

sin x = c/a

Step-by-step explanation:

an easy way to memorize it would be SOH CAH TOA

SOH = sin, opposite, hypotunese

-- you find the angle and you divide it's opposite and hypotunese when it asks for sin

CAH = cos, adjacent, hypotunese

-- you find the angle's adjacent side and hypotunese, then divide

TOA = tan, opposite, adjacent

-- you find the angle's opposite side and divide it by the adjacent side

Answer:

what is that? I can't understand it.

Answer:

https://www.dasd.org › 4444PDF

Web results

Entering Algebra 2: Answer Key

Answer:

[tex]{ \tt{ \sqrt[3]{8} {}^{ \frac{1}{4} x} }} \\ = { \tt{ {8}^{( \frac{1}{4}x) \frac{1}{3} } }} \\ = { \tt{ {8}^{ \frac{1}{12} x} }} \\ = { \tt{ \sqrt[12]{8} {}^{x} }}[/tex]

Answer:

[tex]\sqrt[12]{8^{x} }[/tex]

Step-by-step explanation:

[tex]\sqrt[12]{8^{x} }[/tex]

Answer:

A) 14

B) 48

Step-by-step explanation:

[tex]x^{a}[/tex] · [tex]x^{b}[/tex] = [tex]x^{a+b}[/tex]

[tex](x^{a}) ^{b}[/tex] = [tex]x^{ab}[/tex]

Answer:

DF

Step-by-step explanation:

The side opposite the largest angle has the longest measurement

<E has  the largest measurement so DF is the longest side