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Answer:

Hi ,

Cube of a number :

_______________

For a given number x we define cube

of x = x × x × x , denoted by x^3.

A given Natural number is a perfect

Cube if it can be expressed as the

product of triplets of equal factors.

Now ,

Write given number as product of

prime .

8788 = 2 × 4394

= 2 × 2 × 2197

= 2 × 2 × 13 × 169

= 2 × 2 × 13 × 13 × 13

= 2 × 2 × ( 13 × 13 × 13 )

Here we have only triplet of equal

factors i.e 13

To make 8788 into perfect Cube we

have multiply with 2.

Now ,

2 × 8788 = ( 2 × 2 × 2 ) × ( 13 × 13 × 13 )

17576 = ( 2 × 13 )^3 = ( 26 )^3 perfect

Cube

I hope this will useful to you.

Answer:

V = 251.3 cm³

Step-by-step explanation:

Diameter  8 cm

Radius = 4 cm

Height = 5 cm

Volume of Cat Food contained by the tin can = [tex]\pi r^2 h[/tex]

Where r = 4 cm, h = 5 cm

V = (3.14)(4)²(5)

V = (3.14)(16)(5)

V = 251.3 cm³

Answer:

251.3 cm³

Step-by-step explanation:

The diameter is 8 cm

So the radius is 8/2 = 4 cm

The height is 5 cm

Volume of tin can:

[tex]\pi r^2 h[/tex]

r = 4 & h = 5

[tex]V =\pi (4)^2 (5)\\V = \pi (16)(5)\\V = 251.3[/tex]

Answer:

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = \sqrt[3]{x^2}[/tex]

Step-by-step explanation:

Given

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}}[/tex]

Required

Rewrite in simplest radical form

Using laws of indices:

[tex]a^m/a^n = a^{m-n}[/tex]

This implies that

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{5}{6} - \frac{1}{6}}[/tex]

Solve Exponents

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{5 - 1}{6} }[/tex]

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{4}{6} }[/tex]

Simplify exponent to lowest fraction

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = x^{\frac{2}{3} }[/tex]

Using laws of indices:

[tex]a^{\frac{m}{n}} = \sqrt[n]{a^m}[/tex]

This implies that

[tex]x^{\frac{5}{6}}/x^{\frac{1}{6}} = \sqrt[3]{x^2}[/tex]

This is as far as the expression can be simplified

Answer:

5

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Answer:

5

Step-by-step explanation:

If you have 2 of something and then you get 3 more of the same thing, you can use your fingers to count how much you have in total now, which is 5.

Answer:

D. 6\sqrt{5}-4\sqrt{7}

Step-by-step explanation:

[tex]3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28} \\3\sqrt{5}-2\sqrt{7}+\sqrt{9*5}-\sqrt{4*7}\\3\sqrt{5}-2\sqrt{7} +3\sqrt{5}-2\sqrt{7}\\ 6\sqrt{5}-4\sqrt{7}[/tex]

Answer:

[tex]Probability = \frac{6}{29}[/tex]

Step-by-step explanation:

Given

------------------------------Has a brother | Does not have a brother

Has a sister --------------------------- 6 ----------------- 8

Does not have a sister  -----------2 ------------------ 13

Required

Probability of having a sister and a brother

First, the total number of students has to be calculated;

Total = 6 + 2+ 8 + 13

Total = 29

Number of students that have a sister and a brother is represented with data in row 1 and column 1 i.e. 6

At this point, the probability can then be calculated;

Probability = Number of students that have a sister and a brother divided by Total number of students

[tex]Probability = \frac{6}{29}[/tex]

Answer:

No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.

Step-by-step explanation:

Data provided in the question

m∠ABC = 45°

m∠ECD = 45°

Based on the above information, the ΔBAC ~ ΔEDC could be determined by seeing the given options

As we can see that from the last option the AA could not be postulated as it creates a reflection over the line plus the ∠ABC and ∠DEC is not congruent

Therefore the last option is correct

No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent. Therefore the option D is correct.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Data given in the question

m∠ABC = 45°

m∠ECD = 45°

Based on the above information, the ΔBAC ~ ΔEDC could be determined by seeing the given options one by one.

As we can conclude that from the last option the AA could not be postulated as it creates a reflection over the line plus the ∠ABC and ∠DEC is not congruent.

No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.

Therefore the option D is correct.

Read more about similar triangles at:

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Answer:

19 units

Step-by-step explanation:

In a parallelogram, opposite sides are congruent. So, we can set up a formula that looks like this: 3x - 8 = x + 10. When you solve for x, you'll get 9. 9 + 10 = 19 units

The length of the side TU of the parallelogram is 19 units long.

A parallelogram is a quadrilateral with opposite pair of sides parallel and equal.

In the question, we are given a parallelogram STUV.

The length of the side TU is given as x + 10.

The length of the side VS is given as 3x - 8.

As the sides, TU and VS are opposite to each other, and the quadrilateral STUV is a parallelogram, so they are equal.

∴ TU = SV

or, x + 10 = 3x - 8

or, x + 10 - 3x = 3x - 8 - 3x (Subtracting 3x from both the sides)

or, -2x + 10 = -8 (Simplifying)

or, -2x + 10 - 10 = -8 - 10 (Subtracting 10 from both sides)

or, -2x = -18 (Simplifying)

or, -2x/(-2) = -18/(-2) (Dividing both sides by -2)

or, x = 9 (Simplifying).

Now, TU = x + 10 = 9 + 10 = 19.

∴ The length of the side TU of the parallelogram is 19 units long.

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Answer: 2 <= X <= 5

Step-by-step explanation:

Answer: 2 <= X <= 5

Step-by-step explanation:

Given that a factory can work its employees no more than 5 days a week, that is, less than or equal to 5 days.

And no less than 2 days per week. That is, greater than or equal to 2 days.

Let X be the number of days employee can work. Then, according to the first statement, X <= 5 and according to the second statement, X >= 2

An inequality to represent the range of days an employee can work will be

2 <= X <= 5

Therefore, an employee can work for 2 days, 3 days, 4 days and 5 days

Answer:

10

Step-by-step explanation:

3/5 is 0.6 and 10 time 0.6 is 6.

hope this helps

Answer:

the answer is 1

Step-by-step explanation:

you convert 1/2 to a decimal, 0.5, then subtract. 0.75 and 0.25 to get 0.5, and when you add those two it equals one.

Answer:

It would equal 1

Step-by-step explanation:

Convert 1/2 to 0.5 then it would be easier to solve.

0.75-0.25=0.5

0.5+0.5=1

Hope this helps!

Answer:

q = 18 ?

Step-by-step explanation:

This is not a complete question but ill give it a shot!

If we are following a pattern then we see q is 11 more than r.

So we do 11 + r (7) to get 18!

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Answer:

20 chickens

Step-by-step explanation:

2/8= 5/x

2 times 2.5 is 5, 8 times 2.5 is 20 the ratio is true if we write this:

2/8=5/20

Therefore, with 5 roosters, there are 20 chickens.

Answer:No, every whole number is not a solution of x > 0 because the whole numbers include 0. The solution set of x > 0 does not include 0. So, 0, which is a whole number, is not a solution of x > 0.

Step-by-step explanation:

No, Is it not true that every whole number is a solution of x > 0.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

To check, Is it true that every whole number is a solution of x > 0.

Now, We know that;

Every whole number is a solution of x ≥ 0.

That is, Zero is include in the whole numbers.

Therefore, Is it not true that every whole number is a solution of x > 0.

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Answer:

Option D

Step-by-step explanation:

A third of a shipment of books is 28 pounds. Assuming that 'f' will be the total weight of the entire shipment, we would divide 'f' by 3 to get 28.

The answer should be D.

Answer:

sales tax rate = 4%

Step-by-step explanation:

In this problem formula to express one term in percentage is used

To express x as percentage of y is given by (x/y*100) %

______________________________________________

Cost of item = $480

sales tax = $19.20

we have to find sales tax rate.

sales tax rate is percentage of cost price which will levied as tax .

thus, we have to find sales tax as percentage of cost price.

using the percentage cost as given above

sales tax as percentage = sales tax/ cost of item *100

sales tax as percentage = 19.20/480 *100 = 4%

Thus, sales tax rate is 4%.

It means that if cost price of item is $100 then $4 will be the sales tax for the item.

Answer:

d. (x+2)/(-x²-5)

Step-by-step explanation

 ƒ(x) = x + 2/(2x²)

The function is undefined when x =  0.

b. ƒ(x) = (2x + 4)/(3x + 3)

The function is undefined when 3x + 3 = 0, i.e., when x = -1.

c. ƒ(x) = (6x - 5)/(x² - 7)

The function is undefined when x² - 7 = 0, i.e., when x = √7.

d. ƒ(x) = (x+2)/(-x²-5) = -(x+2)/(x² + 5)

The function would be undefined if x² + 5 = 0, i.e., if x² = -5. However, the square of a real number cannot be negative.

This function has no excluded values.

Answer:

B 267.9

Step-by-step explanation:

the formula is again the same, so you plug 4 in (because the radius is half the diameter) and solve to get around 267.9

Answer:

D.

Step-by-step explanation:

" Sum" means "+".

The sum of the number of dogs and the 6 cats.

d + 6

Answer:

Option D

Step-by-step explanation:

Sum is Adding (+)

So,

The expression becomes

=> d+6

Answer:

x = ± 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Given

x² = 24 ( take the square root of both sides )

x = ± [tex]\sqrt{24}[/tex] = ± [tex]\sqrt{4(6)}[/tex] = ± [tex]\sqrt{4}[/tex] × [tex]\sqrt{6}[/tex] = ± 2[tex]\sqrt{6}[/tex]

Answer:

centre = (-5, -4)

radius = 7.42

Step-by-step explanation:

The general form for center-radius is

(x - h)² + (y - k)²= r²

Center = (h, k)

Radius = r

Rearrange the equation.

(x² + 10x) + (y² + 8y) - 14 = 0

Add 14 on both sides.

(x² + 10x) + (y² + 8y) = 14

(10/2)² = 25

(8/2)² = 16

Add 25 and 16 to both sides.

(x² + 10x + 25) + (y² + 8y + 16) = 14 + 25 + 16

Factor left side of the equation.

(x+5)² + (x+4)² = 55

(55) = (7.416198)²

(x+5)² + (x+4)² = 7.42²

The radius is 7.42.

The centre is at (-5, -4).

Answer:

y-5=5/4(x-1)

Step-by-step explanation:

the slope is 1.25

m=y2-y1/x2-x1=10-5/5-1=5/4=1.25

y-5=(5)/(4)(x-1)=

y=(5)/(4)x+(15)/(4) this one is linear

it is a linear function and the

Answer:

C

Step-by-step explanation:

Standard form is f(x) = ax² + bx + c.

f(x) = -(x - 4)² + 2

= -(x² - 8x + 16) + 2

= -x² + 8x - 16 + 2

= -x² + 8x - 14

Hi,

the correct answer is C

This is the correct equation: f(x) = -x^2 + 8x - 14

XD

P.S. (on the image I sent the answer was B but on your test the correct one is C. The equation is still the same.)

Answer:

$105

Step-by-step explanation:

150 times 0.7 is equal to 70% of 150

70% of 150 is 105

105 is the reduced price

Answer:

(4,8)

Step-by-step explanation:

6x-4y=-8

11x+4y=76  eliminate y

6x+11y=-8+76

17 x=68

x=68/17=4

substitute x :

6x-4y=-8

6(4)-4y=-8

-4y=-8-24

y=-32/-4

y=8

Answer:

15/3 = v/7 can be a true proportion.

Step-by-step explanation:

v is a variable, which means that technically any number can be put inside.

In this case, however, when you are solving for v, the numerator must be proportional to the denominator.

In the case of the question, the questioner multiplied ~2.33 to the denominator. Do the same to the numerator:

15 x 2.33 = ~34.95

If the variable v is ~34.95, then it is a true proportion.

Answer:

5.83 units

Step-by-step explanation:

Given is a right angled triangle.

Length of base = 2 - (-3) = 2+ 3 = 5 units

Height = 4 - 1 = 3 units

By Pythagorean theorem:

[tex]RS = \sqrt{ {5}^{2} + {3}^{2} } \\ = \sqrt{25 + 9} \\ = \sqrt{34} \\ = 5.83095189 \\ = 5.83\: units[/tex]

Answer:

Step-by-step explanation:

You graph it