5.5 - Solving Quadratic Equations - Perfect Square Trinomials and Difference of Squares
Factor the following if they are a perfect square trinomial or a difference of squares.
a) x^2 + 24x + 144 = 0
b) 9x^2 - 36x + 36 = 0
c) x^2 - 64 = 0
d) 4x^2 - 81 = 0

1

Step-by-step explanation:

Seeing its an arithmetic sequence

T1=1......T2=2.....T3=3

To get your constant difference

T2=T1 is also equals to T3=T2

so 3-2=1 and 2-1=1

therefore the constant difference is 1

Answer:

x = -1

x = 3

Step-by-step explanation:

[tex]\sf x^2 - 2x = 3[/tex]

Add 1 to both sides:

[tex]\sf \implies x^2 - 2x+1 = 3+1[/tex]

Factor the left side:

[tex]\sf \implies (x-1)^2 = 4[/tex]

Square root both sides:

[tex]\sf \implies x-1 = \pm2[/tex]

Therefore:

[tex]\sf \implies x-1=-2 \implies x=-1[/tex]

[tex]\sf \implies x-1=2 \implies x=3[/tex]

Answer:

D, I think…

Step-by-step explanation:

I used PEMDAS to go through and simplify and see which values match.

Answer: 12:14 21:18 42:36

Answer:

no 2. cube a' will be smaller because it was multiplied by a fraction

no 3. c

Answer:

205,000

Step-by-step explanation:

(100,000*0.05) *21 +100,000

Answer:

D

Step-by-step explanation:

the answer Is obviously D

Answer:

so on the graph you can

Step-by-step explanation:

first the y axis number comes first so you look at that the you do the x axis it should look like 2,3 or 2,-3 hope this works

Answer: 2x3=y. 2x3=6

Step-by-step explanation:

one: figure out what the question is asking you. Two: do 2x3 and then get the answer. Last: switch it around to find your answer.

Answer:

160 fluid ounces

Step-by-step explanation:

There are 16 ounces in one pint, therefore multiply the number of pints by 16 to get your answer.

16 * 10 = 160

Hope this helped ! <3 Brainliest please :)

Zach  runs with 14.31 feet per second speed  and faster than other runners.

Speed is measured as the ratio of distance to the time in which the distance was covered

Given that Frank runs 9 feet per second.

Speed=Distance /time

=9 feet/ 1 second

=9 feet per second.

Tony runs 299 feet in 34 seconds

Speed=299/34

=8.794 feet per second.

Zach runs 1 mile in 396 seconds.

We know that 1 mile =5280 feet

Speed=5280/369

=14.31 feet per second.

Will runs 675 feet in 1 minute

1 minute is 60 seconds

Speed=675/60

=11.25 feet per second.

Hence, Zach  runs with 14.31 feet per second speed  and faster than other runners.

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Using arithmetic sequence concepts, it is found that the common difference is of 0.25.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, we have that:

[tex]a_3 = 8, a_7 = 9[/tex]

Hence:

[tex]a_7 = a_3 + (7 - 3)d[/tex]

9 = 8 + 4d

4d = 1.

d = 0.25.

The common difference is of 0.25.

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Answer:

[tex]\bold{ \sf \theta = \dfrac{\pi }{9} , \ \ \dfrac{2}{9} \pi , \ \dfrac{7 \pi }{9}, \ \ \dfrac{8\pi }{9}, \ \dfrac{13\pi }{9}, \ \dfrac{14\pi }{9}}[/tex]

Explanation:

[tex]\dashrightarrow \ \ \sf 2sin(3\theta) = \sqrt{3}[/tex]

[tex]\dashrightarrow \ \ \sf sin(3\theta) = \dfrac{ \sqrt{3}}{2}[/tex]

[tex]\dashrightarrow \ \ \sf 3\theta = sin^{-1}(\dfrac{ \sqrt{3}}{2})[/tex]

[ your calc should be in radian mode [R] ]

[tex]\dashrightarrow \ \ \sf 3\theta = \dfrac{\pi }{3} , \ \ \dfrac{2}{3} \pi , \ \ \dfrac{7 \pi }{3}, \ \ \dfrac{8\pi }{3}, \ \dfrac{13\pi }{3}, \ \dfrac{14\pi }{3}[/tex]

[tex]\dashrightarrow \ \ \sf \theta = \dfrac{\pi }{9} , \ \ \dfrac{2}{9} \pi , \ \ \dfrac{7 \pi }{9}, \ \ \dfrac{8\pi }{9}, \ \dfrac{13\pi }{9}, \ \dfrac{14\pi }{9}[/tex]

Answer:

g + a = 24. 2 g + a = 42.

Step-by-step explanation:

Each goal gets 2 points and each assist gets 1 point

If # of goals = g , and you get 2 points for each goal, then points acquired by goals can be represented by 2g

If # of assists = a, and you get 1 point for each assist, then points acquired by assists can be represented by a

The total # of points the player had was 42. This means that 2g + a = 42 (this is the first equation)

We are also told the player scored a total of 24 goals and assists. If g = # of goals and a = of assists, then g + a = 24 (this is the second equations)

So the two equations are g + a = 24. 2 g + a = 42.

Answer:

g + a = 24. 2 g + a = 42.

Step-by-step explanation

trust

Answer:

480 in³

Explanation:

Volume of Rectangular Prism = Length * Height * Width

Front Volume:

Behind Volume:

Total volume:

Both are cuboids

#1

Volume:-

#2

Volume:-

Total:-

400+80=480in³

Answer:

22 in.

Step-by-step explanation:

total volume= big thingy + long thingy

=>x=2.2.3+5.2=12+10=22

Answer:

3.

Step-by-step explanation:

Hey there!

This scenario shows that Victoria ate 6/7 of a pizza and ate 1/4 of that pizza the same day for dinner showing that she at one fourth of the six-sevenths pieces

Answer:

It is the third one.

Step-by-step explanation:

Let's take a look at each story. We need to find out which story is [tex]\frac{6}{7}[/tex]×[tex]\frac{1}{4}[/tex].

1. Victoria drinks six-sevenths of a cup of milk. She drinks one-fourth of a cup more of milk. How much milk did she drink in all?

This story is adding the fractions together since it wants to know how much did she drink in ALL. So this is not it.

(Here are some keywords to tell you if you need to add, altogether, all, in all, together, total, total number, add, increase, increased by, more than.)

2. Mike walked one-fourth mile and then he took the bus for six-sevenths mile to school. How many miles did he travel in total?

Once again this story is adding. It uses the word total. So this is not it.

3.Victoria has six-sevenths of a pizza. She ate one-fourth of it for dinner. How much pizza did Victoria eat for dinner?

This is correct since it wants to know how much she ate for dinner. She ate [tex]\frac{1}{4}[/tex] of [tex]\frac{6}{7}[/tex] of the pizza.

4.Mike has six-sevenths of a pie. He gives one-fourth to his brother. How much pie does he have left

This story is subtracting. So it is not it. (Subtracting words, minus, greater than, take away, fewer than, less than, subtract, decreased by.)

June's earning in dividends per year will be  $4676.66

Earnings are the profit that a company produces in a specific period, usually defined as a quarter or a year. After the end of each quarter

It is given in the question that:

No. of shares of Parchar Special Effects = 177

If Parchar Special Effects pays a yearly dividend of $8.21 per share

So, It pays a yearly dividend for 177 shares

= [tex]177\times 8.21=1453.17[/tex]

No. of shares of Giaco Household Goods = 213

Giaco Household Goods pays $6.97 per share

So, It pays a yearly dividend for 213 shares

= [tex]213\times6.97=1484.61[/tex]

No. of shares of of Raxin Accounting= 152

Raxin Accounting pays $11.44 per share

So, It pays a yearly dividend for 152shares

= [tex]152\times 1.44=1738.88[/tex]

So,June earn in dividends per year

=[tex]1453.17+1453.17+1738.88=4676.66[/tex]                

Hence June earn $4676.66 dividends per year

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Answer:

B

Step-by-step explanation:

$4,676.66

Answer:

Option D

Step-by-step explanation:

I am taking a guess here, but since the volume of the rectangle part is 594, and it is sort of a similar size as the top part, then I assume it is D.

Let me know how it goes.

Answer:

I think it's B.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

2 + root 9 can be written as 2 + 3 which is answer as 5

Answer:

HOPE IT HELPS!

MARK AS BRAINLIAST.

Answer:

Step-by-step explanation:

an = (an-1)2 + 5. a1 = 4. Then: a1 = 4. a2 = (4)2 + 5 = 16 + 5 = 21. a3 = (21)2 + 5 = 441 + 5 = 446. a4 = (446)2 + 5 = 198916

Answer:

find the ratio of 15 min and 1hiyr

Answer:

Slope: -1/2
y-intercept: 7

Step-by-step explanation:

The slope is the interger/number in front of x in a linear equation.

y-intercept is the constant after the slope, 7, which is the value of y when x is 0.

Answer:

equation: y=mx+b

b=y intercept

the y intercept is 7

the slope is -1/2

Answer: Solve this problem using the angle bisector theorem. This theorem states that when given a triangle with an angle bisector (line that cuts one of the angles in half, into two of the same angles), that angle bisector divides the opposite side into two segment proportional to the sides of the triangle

Answer:324pie cm^2

Step-by-step explanation:

Answer:

The formula for the area of a circle:

[tex]A = \pi r^{2}[/tex]

You have said:

[tex]r = 14m[/tex]

So substitute the values of pi and r into the formula:

[tex]A = \pi r^{2} \\A = (3.14)(14m)^{2} \\A = (3.14)(196m^{2} )\\A = 615.44m^{2}[/tex]

Answer:

6.3 :)

Step-by-step explanation:

Pythagorean theorem: a^2 + b^2 = c^2

Now lets solve!!!

3^2 + b^2 = 7^2

9 + b^2 = 49

Now we subtract!!

49 - 9 = b^2

40 = b^2

Now we need to find the square root!!

[tex]\sqrt{40}[/tex] = 6.3

Have an amazing day!!

Please rate and mark brainliest!!!

Answer:

A

Step-by-step explanation:

A) r = 8

B) r = 4

C) r = [tex]\sqrt{\frac{30}{\pi } }[/tex] ~ 3.09

D) r = [tex]\frac{30}{2\pi} = \frac{15}{\pi } ~ 4.77[/tex]

Circle A has the largest radius, and thus is the largest circle