The polynomial is a difference of perfect squares. Use the formula a2 – b2 = (a + b)(a – b) to factor completely.

81x2 – 49

The value of a is .



The value of b is .



The product of the prime factors is

Answer:

[tex](x-a)^{2} (x-b)^{3}[/tex]

Step-by-step explanation:

This is an openended question, but the anwer would be the following (where a and b are different real numbers)

[tex](x-a)^{2} (x-b)^{3}[/tex]

This would make the roots a (multiplicity of 2) and b (multipicity of 3).

Answer:

k=13.5

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well we know there is a scale factor of 3 for the first triangle to the second.

4.5 to k

3 to 9

4 to 12

Hence, all we need to do it 4.5*3=k

4.5*3=13.5

k=13.5

(っ◔◡◔)っ ♥ Hope this helped, have a great day! ♥

˜”*°•.˜”*°• ~Star •°*”˜.•°*”˜

Answer:

13.5

Step-by-step explanation:

Because they are similar you can create a ratio problem

4.5/k = 3/9

3k = 40.5

k = 13.5

Answer:

Median :)

Step-by-step explanation:

The term that describes the measure indicated by the black arrow below is option (C) median is the correct answer.

The median is the middle value when a data set is ordered from least to greatest. Median is a measure of central tendency which gives the value of the middle-most observation in the data.

For the given situation,

The diagram shows the graph of data plotted in the plane.

In the graph, the black arrow is drawn in the middle of the data set.

The right side of the data is symmetric to the left side of the data.

Thus the arrow gives the value of the middle-most observation in the data.

Hence we can conclude that the term that describes the measure indicated by the black arrow below is option (C) median is the correct answer.

Learn more about median here

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Answer:

30x^4−12x^3=6x^3(5x−2) = True

4x^2+10x=2x(2x+5) = True

100x^3+5=5x^3(20x+1) = False

8x^3−6x=2x^3(4−3x3) = False

Step-by-step explanation:

The statements which are true are 30x4−12x3=6x3(5x−2) ,  4x2+10x=2x(2x+5)  and  100x3+5=5x3(20x+1)

To determine which of the statements are true, we can simplify each equation and compare.

Option a :

30x4−12x3=6x3(5x−2): Factoring out the common term we can see this equation is true.
Option b:

4x2+10x=2x(2x+5): After simplifying both sides we find that 2x(2x + 5) = 4x2 + 10x, so statement (b) is true.

Option c:

100x3+5=5x3(20x+1): Attempt to simplify this equation as 5x3(20x + 1). Since this simplification holds, statement (c) is also true.

Option d:

8x3−6x=2x3(4−3x3): Simplifying the right side does not give us the left side; thus, statement (d) is false. The correct form would be 2x(4x2 - 3), assuming a typo in exponent notation.

Answer:

60%

Step-by-step explanation:

P(A or B) = P(A) + P(B)

175/500 are wool and 125/500 are nylon

Add them to get 300/500 or 3/5 or 60%

There are 300 coats that are either wool or nylon.

A store has 500 winter coats. 35% are wool, and 1/4 are nylon.

To find the number of coats that are either wool or nylon, we add the number of wool coats and nylon coats.

First, calculate the number of wool coats: 500 coats * 35% = 0.35 * 500 = 175 wool coats.

Then, calculate the number of nylon coats: 500 coats * 1/4 = 500 * 1/4 = 125 nylon coats.

Finally, add the number of wool and nylon coats to find the total number of coats that are either wool or nylon: 175 wool coats + 125 nylon coats = 300 coats.

Answer:

27x^6

Step-by-step explanation:

(3x^2)^3=

3^3(x^2)^3=

27x^6

Final answer:

The expression equivalent to (3x²)³ simplifies to 27x⁶, by cubing the coefficient and multiplying the exponent by 3.

Explanation:

The expression equivalent to (3x²)³ is found by cubing the digit term and multiplying the exponent by 3. When we cube 3, we get 3 x 3 x 3 which equals 27. Then, we apply the cubing to the variable term x², by multiplying the exponent 2 by 3, giving us x²ˣ³ or x⁶. Thus, the expression simplifies to 27x⁶.

Step-by-step explanation:

4.5x-2.3=6.7 (add 2.3 so no number in the equation)

6.7+2.3 is 9

4.5x=9 (divide by 4.5 as it's 9 is divisible by 4.5

9/4.5 is 2

X=2

put it back into the equation

4.5*2 is 9

9-2.3 is 6.7

Therefore X=2

Answer:

x = 2

Step-by-step explanation:

Add 2.3 to both sides.  We get:

4.5x = 6.7 + 2.3 = 9

If 4.5x = 9, then x = 2

Answer:

174.68

Step-by-step explanation:

Use PEMDAS. First, multiply 1/-25 by 8. (-8/25 or-.32)

Then, add 175 and y should= 174.68.

Answer: £460

Step-by-step explanation:

Use this formula to find the total interest [tex]I=\frac{P*R*T}{100}[/tex]

I stands for interest, P is principal, R is rate, and T is time.

Principle = £2300

Rate = 5%

Time = 4 years

[tex]\frac{2,300*5*4}{100} =\frac{46,000}{100} =460[/tex]

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! :-)  

- Cutiepatutie ☺❀❤

Answer:

£460

Step-by-step explanation:

Simple interest =PRT/100

Where P = principal

R= rate

T = Time

Given

P= £2300

T= 4yrs

R = 5%

Interest = 2300 x 5 x 4/100

Multiply through

Interest = 46000/100

Interest = £460

Answer:

The answer for addition one is 11 1/2. The answer for subtraction would be -5/6.

Hope this helps. Can I please get brainliest if possible?

The answer you are looking for is 11 and 1/2.

To find this answer, you must first add the fractions together. Before you do so, you must make sure they have a common denominator. So, multiply 1/3 by 2/2 to get 2/6. Now, add 2/6 and 1/6 to get 3/6. 3/6 simplified (divided by 3/3) is 1/2.

Next, add the whole numbers. 5 + 6 is 11. Thus making your final answer 11 and 1/2.

I hope this helps!

Answer: -11

Step-by-step explanation:

f(-2)=5(-2)-1

f(-2)= -10-1

f(-2)= -11

Answer:

f(-2) = -11

Step-by-step explanation:

x = -2

plug in -2 for x in the given equation:

f(x) = 5x - 1

f(-2) = 5(-2) - 1

Simplify. Remember to follow PEMDAS. First, multiply, then subtract:

5(-2) = 5 * -2 = -10

-10 - 1 = -11

f(-2) = -11.

~

Answer: [tex]n=8[/tex]

Cross-multiply

[tex]2/3=n/12[/tex]

[tex](2)*(12)=n*(3)[/tex]

[tex]24=3n[/tex]

Flip the equation

[tex]24=3n---->3n=24[/tex]

Divide both sides by 3

[tex]3n/3=24/3[/tex]

[tex]24/3=8----> n=8[/tex]

Final answer:

To solve the proportion 2/3 = n/12, cross multiply to get 2×12 = 3×n. Simplify the equation to 24 = 3×n, and divide both sides by 3 to get n = 8.

Explanation:

To solve the proportion 2/3 = n/12, you begin by cross multiplying to find the value of n. This means you multiply 2 by 12 and 3 by n. The equation now looks like this: 2×12 = 3×n.

Next, simplify the left side of the equation, which results in 24 = 3×n.

Finally, solve for n by dividing both sides of the equation by 3, leading to n = 8.

This method of cross multiplication and division is a common technique used to solve proportions and find missing values in ratios.

Answer:

1,2,3,4,5,7

Step-by-step explanation:

1+2+3+4+5+7 = 22

Final answer:

Six different natural numbers that add up to 22 are 1, 2, 3, 4, 5, and 7. The process involved starting with the smallest natural numbers and then incrementally adjusting the sequence to arrive at the sum of 22.

Explanation:

The question asks to find six different natural numbers whose sum equals to 22. We can begin with the smallest natural numbers, knowing that 1 cannot be included because the sum of the next five natural numbers (2, 3, 4, 5, and 6) already exceeds 22. If we start with 2 and follow with the next smallest numbers (3, 4, 5, and 6), the sum would be 20, which is close but not quite the target sum. To reach the sum of 22, we need to replace one of these numbers with a slightly larger number while still maintaining the rule that every number must be different.

Let's replace the 6 with a 7, so our numbers are now 2, 3, 4, 5, and 7. If we sum these up (2 + 3 + 4 + 5 + 7), we get 21. We need to add one more number to reach 22. The smallest number we haven't used yet is 1, but adding 1 to our sequence would require us to adjust another number as follows: 1, 2, 3, 4, 5, and 7 add up to 22. Therefore, the six different natural numbers whose sum is 22 are 1, 2, 3, 4, 5, and 7.

Step-by-step explanation:

[tex] \frac{2 + 3i}{4 - 5i} [/tex]

[tex] \frac{(2 + 3i)(4 + 5i)}{(4 - 5i)(4 + 5i)} [/tex]

[tex] \frac{8 + 10i + 12i + 15 {i}^{2} }{16 - 25 {i}^{2} } [/tex]

[tex] \frac{8 + 22i + 15( -1 )}{16 - 25 ( - 1)} [/tex]

[tex] \frac{8 - 15 + 22i}{16 + 25} [/tex]

[tex] \frac{ - 7 + 22i}{41} [/tex]

So, a= -7

b= 22

c= 41

Answer:

No

Step-by-step explanation:

Apply the distributive property to 5(2x - 3y):

Multiply 5 by each term inside the parentheses.

5(2x - 3y) = 10x - 15y

The other expression is 10x - 10y.

The terms 10x in both expressions are equal.

Since the term -15y is not equal to the term -10y, the expressions are not equivalent.

Answer:

$112

Step-by-step explanation:

Answer:

[tex](fg)(7) = - 35[/tex]

Step-by-step explanation:

The given functions are:

[tex]f(x) = {x}^{2} - 14[/tex]

and

[tex]g(x) = 6 - x[/tex]

We want to to find

[tex](fg)(7)[/tex]

Note that:

[tex](fg)(x) = f(x) \times g(x)[/tex]

We substitute the functions to obtain:

[tex](fg)(x) = ( {x}^{2} -1 4 ) \times (6 - x)[/tex]

We now substitute x=7, to get:

[tex](fg)(7) = ( {7}^{2} -1 4 ) \times (6 - 7)[/tex]

This implies that

[tex](fg)(7) =( 49-1 4 ) \times (6 - 7)[/tex]

[tex](fg)(7) = 35 \times - 1 = - 35[/tex]

Let [tex]v[/tex] be the usual speed, and [tex]t[/tex] be the usual time.

Following the equation [tex]s=vt[/tex], where s is the space, v is the velocity and t is time, we know that usually we have

[tex]200=vt[/tex]

But this time we were 10mph faster and it took one hour less, so we have

[tex]200=(v+10)(t-1)[/tex]

Since both right hand sides equal 200, they must equal each other:

[tex]vt=(v+10)(t-1)=vt+10t-v-10 \iff 10t-v-10=0 \iff v=10t-10[/tex]

Plug this value in the first equation and we have

[tex]200=vt=(10t-10)t \iff 10t^2-10t-200=0[/tex]

This equation has solutions [tex]t=-4,\quad t=5[/tex]. We can only accept positive solutions, so we have t=5. We finally deduce, again from the first equation,

[tex]200=5v \iff v=\dfrac{200}{5}=40[/tex]

Answer:-6x+12

Step-by-step explanation:-3 • 2x = -6x

-3 • -4 = 12. Distribute the -3 to both numbers in the parentheses

The solution to the compound inequality is x > -2 and x < -5, or (-∞, -5) ∪ (-2, ∞).

To find the solution to the compound inequality, we need to solve the individual inequalities separately and then find the intersection of their solution sets.

The solution to the compound inequality is the intersection of the solution sets of the individual inequalities, so the solution is x > -2 and x < -5. To express this in interval notation, we write (-∞, -5) ∪ (-2, ∞).

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Answer:

y=2/4x+9

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

[tex]4x + 6 = 2x + 10 \\ \\ 4x - 2x = 10 - 6 \\ \\ 2x = 4 \\ \\ x = \frac{4}{2} \\ \\ x = 2[/tex]

Answer:

The cubed-root of v (/v)

Step-by-step explanation:

Like your work on the second question illustrated, the cubed root of v (which is 216) is your expression for the edge length of the box in inches.

Hope this helps!

Step-by-step explanation:

Part A

Since volume of jewelry box is v cubic inches

Therefore,

Answer: Length of edge = v inches

Part B

Answer: 6 inches

Answer:

a) 28 quarters

b) 14 quarters  

Step-by-step explanation:

We are given the following in the question:

Number of quarters = 20 quarters

Number of quarters in room = 40%

Total number of quarter in room =

[tex]=40\%\times (20)\\\\=\dfrac{40}{100}\times 20\\\\=8[/tex]

Thus, the total quarters taken to shopping =

[tex]=20 +40\%\times (20)\\\\=20+8\\=28[/tex]

Thus, 28 quarters were taken to shopping.

Quarter spent on shopping = 50%

Total number of quarter spent in shopping =

[tex]=50\%\times (28)\\\\=\dfrac{50}{100}\times 28\\\\=14[/tex]

Money left =

Money taken for shopping - Money spent

[tex]= 28-14\\=14[/tex]

Thus, we are left with 14 quarters after shopping.

Answer:

27

Step-by-step explanation:

jacob copies 30% of a document which is 8 pages

we can solve this using cross multiplication

30 %       :        8

100%      :         x

30%x = 100%*8

30% x = 8

x = 8/ 30%

x = 26.667

to 2sf

Final answer:

John will need 4.5 bottles of paint to cover the entire cube, with one-eighth of a bottle covering one-sixth of one face and a cube having 6 faces.

Explanation:

The question asks how many bottles of paint John will need to paint the entire cube. If one-eighth of a bottle covers one-sixth of one face, then to cover the whole face, John would need 6 times the amount of paint for one-sixth of the face, which is 6 x 1/8 = 3/4 of a bottle. Since a cube has 6 faces, he will need 6 times 3/4 bottles to paint the entire cube. Therefore, John will need 4.5 bottles to paint the entire cube, as each face requires 3/4 of a bottle and there are 6 faces.

Answer:

231 miles.

Step-by-step explanation:

Tom rented a truck with a base fee of 19.95. You will subtract this from the total since you just want to get the mileage.

Tom is getting charged .85 cents per mile driven.

Tom payed 216.30 subtotal minus the 19.95 base fee since we are trying to only see how many miles he drove.

(216.30-19.95=196.35) This will be total for each mile. All we need to do is divide to get the total of miles

(196.35÷.85= 231)

231 is the number of miles Tom drove.

Answer:

DAB is 117.

Step-by-step explanation:

You can solve 2 ways, either by adding the opposite angles together or by finding the 3rd angle of the triangle and using linear pair.

First Method: 63 + 54 = 117

Second Method:

180 - 63 - 54 = 63 (All triangles = 180)

180 - 63 = 117 (All linear pairs = 180)

Answer:

  D. 2/7

Step-by-step explanation:

We assume that the intention is that one of the places is chosen at random from the list of 7 places.

2 of those are cities in North America, so the probability that a place randomly chosen from this list is a city in North America is ...

  P(A & B) = 2/7

Answer: 4/7

Step-by-step explanation: