What is the simplest form of [tex]\sqrt[3]{7} -\sqrt[5]{7}[/tex]

The completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]

Then writing b in terms of alpha and beta would help us getting common factors out.

Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any  trial and error.

For this case, the given quadratic expression is:

[tex]4x^2 + 28x + 49[/tex]

So we've to find two numbers such that:

Their sum = b =  28

Their product = [tex]ac = 4\times 49 = 196[/tex]

We can see that 196 is square of 14, and that 14 added twice forms 28, thus:

14 + 14 = 28

14×14 = 196

Writing b = 28 as sum of 14 twice, we get:

[tex]4x^2 + 28x + 49 = 4x^2 + 14x + 14x +49 \\4x^2 + 28x + 49 = 2x(2x+7) + 7(2x + 7)\\4x^2 + 28x + 49 = (2x+7)(2x+7)[/tex]

Thus, the completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

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Answer:

x = - 3

Step-by-step explanation:

5x - 5 = 7x + 1 ( subtract 7x from both sides )

- 2x - 5 = 1 ( add 5 to both sides )

- 2x = 6 ( divide both sides by - 2 )

x = - 3

Answer: x = -3

Step-by-step explanation: Here is my explanation...

Step 1: Take away 5x from both sides 5x - 5x - 5 = 7x - 5x + 1.

Step 2: You should then get -5 = 2x + 1, then take away 1 from both sides -5 - 1 = 2x + 1 - 1

Step 3: -6 = 2x, divide 2x on both sides -6/2 = 2x/2

x = -3

Work Check:

5 (-3) - 5 = 7 (-3) + 1

-15 - 5 = -21 + 1

-20 = -20

If the -20 = -20 then this proves that x = -3. I hope this helped!

Answer:

108 square yards

Step-by-step explanation:

l = 6 yd

w = 4 yd

h = 3 yd

Surface  area of rectangular prism = 2*(lw +wh + hl)

                                                            = 2*(6*4 + 4*3 + 3*6)

                                                            = 2* ( 24 + 12 + 18)

                                                            = 2 *54

                                                            = 108 square yards

The statements that must be true according to the data presented by the considered histogram are:

A skewed distribution is a distribution having bias on one of the two sides (either left or right).

It is like leaning mountain on one side (left or right).

The missing image of the considered histogram is attached below.

Checking all the options:

It is wrong. The data is numeric, and therefore, not describing qualities, so its not a qualitative data.

The histogram has long tail on the right side, so its right skewed. Thus, this option is correct.

Age group     Frequency (number of people of that age group in party)

0-20                   5

21-40                 13

41-60                  8

61-80                  3

81-100                2

total              5+13+8+3+2 =31

So yes, there were total 31 people at the party as a person can be at max in one age group, so no repeated counting.

From 0 to 20 age group, there were 5 people. But it isn't known if they were < 18 or ≥ 18 (this is the side effect of grouped data, the loss of some information). So this option is not necessarily correct.

It is false. The most common age was from the group 21-40 years old. And 13 is < 20, so it doesn't lie in this group.

Option 6: the majority of the people at the party were less than 61 years old.

Total number of people < 61 = 5+13+8 = 26

26 is more than half of 31 people. So yes, this option is correct.

Thus, the statements that must be true according to the data presented by the considered histogram are:

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Check the picture below.

Answer:

40 cm

Step-by-step explanation:

10cm*4cm=40cm

Answer:

To find the last term, divide the coefficient of the middle term by 2 then raise to the power of 2,that will be :

[tex]( \frac{ - 12}{2} )^{2} = { - 6}^{2} = 36 [/tex]

Answer:

add 36

Step-by-step explanation:

Answer:

A total of 142 units of water bottles must be sold to recover the costs of renting costumes.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer: $6.75

Step-by-step explanation:

Popcorn95 × 0.75 = 71.25

Candy35 × 1.20 =42

Totally 113.25

Deduct from 120

Drinks6.75

Answer:

Step-by-step explanation:

a c d are the answer

Answer:

A.

Step-by-step explanation:

4/5 = 0.8

3/4 = 0.75

0.75 < 0.8

Answer: 4.4

To find the mad you have to first find the mean of the data set then you have to find the sum of the data values and divide the sum by the number of data values.

Answer:

114

Step-by-step explanation:

25% = 25/100 = 0.25

152 × 0.25 = 38

152 - 38 = 114

Answer:

$114

Step-by-step explanation:

152x0.75 = 114

answer

7

Step-by-step explanation:

cause I said so

Answer:

m=3/4

Step-by-step explanation:

Explanation:

The slope of a line parallel to a line L has the same slope as line L.

6x−8y=−2

6x+2=8y

y=6/8x+2/8

Simplfied= y=3/4x+1/4

Therefore the answer is 3/4.

Answer:

n > 10 meaning, n is greater than 10

Step-by-step explanation:

Two times a number  :  2n

Less 4  :  -4

2n-4

Greater than the same number :  >n

Plus 6  :  +6

> n+6

2n-4 > n+6

To find n, we have to get n alone and equal to a single number. To do this, we first subtract 6 from both sides.

2n-10 > n

Then, subtract 2n from both sides

-10 > -n

Now, divide by -1

10 < n

So, n is greater than 10

Answer:

430 in^2

Step-by-step explanation:

Area of parallelogram =    base * height = 20 * 21.5 = 430 in^2

Answer:

$16.11

Step-by-step explanation:

10.74÷6

times the number you get by 3

add that number to 10.74

Answer:

7x+21

Step-by-step explanation:

Answer:

7x + 21

Step-by-step explanation:

Given

Solving

Answer:

490.1 (If the radius is 6ft and height is 7ft)

571.8 (If the radius is 7ft and height is 6ft)

Step-by-step explanation:

A=2πrh+2πr2

Plug in the value for the radius and height. Then solve.

The correct option is D. The cost of natural gas is $0.83 per unit.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation

Consider the provided equation.

116y=96.28

We need to solve the above equation for y.

Divide both sides by 116.

[tex]\dfrac{116y}{116}=\dfrac{96.28}{116}[/tex]

[tex]y=0.83[/tex]

Now consider the provided options.

Hence, the correct option is D. The cost of natural gas is $0.83 per unit.

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Answer:

73 m

Step-by-step explanation:

The formula for the area of a rectangle is a = w(l). Using this, we can plug in the given values and solve for l, the length.

4526 = 62(l)

[tex]\frac{4526}{62} =\frac{62l}{62}[/tex]

l = 73

hope this helps!

Answer: 73 meters

Step-by-step explanation:

The simple formula to calculate the area of a regular rectangle is (Length x Width)

Given the area is 4526, and the width 62, we can use "y" to represent the unknown length.

So, '

62(y)=4526

Divide both sides by 62

1/2[62(y)]=4526/62

Y= 73 meters.

To check, 73x62= 4526, which follows the formula

Answer:

[tex]\longmapsto \sf \: \: - 14x \cdot\sqrt{14x}[/tex]

Step-by-step explanation:

[tex] \sf \: if \: x > 0 [/tex]

[tex] \sf 6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } [/tex]

[tex] \sf Let's \: solve \: for \sqrt{56 {x}^{3} } \: first, \\\longmapsto \sf \sqrt{56 {x}^{3} } = \sqrt{14 \times 4 {x}^{2} \times x } \\ \sf \longmapsto \sqrt{56 {x}^{3} } = 4x \sqrt{14x} [/tex]

Substituting above value in given equation,

[tex]\longmapsto \sf 6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } \\ \longmapsto\sf 6x \sqrt{14x} - 5 \times 4x \sqrt{14x} \\ \longmapsto \sf \: 6x \sqrt{14x} - 20x \sqrt{14x} \\\longmapsto \sf \: \sqrt{14x}(6x - 20x) \\ \longmapsto \sf \: \: - 14x \cdot\sqrt{14x}[/tex]

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Answer:

Step-by-step explanation:

open the page below

Answer:

please read through the ten symbols of logic mathematics

Answer:

[tex]x^{9}[/tex] = ± 5

Step-by-step explanation:

([tex]x^{9}[/tex] )² = 25 ( take square root of both sides )

[tex]\sqrt{(x^{9})^2 }[/tex] = ± [tex]\sqrt{25}[/tex]

[tex]x^{9}[/tex] = ± 5

Step-by-step explanation:

make the figure into 1 rectangle with dimensions 25 and w,and rite triangle with hypotenuse = 18 and h = 8

applying Pythagoras theorem

18^2 = 8^2 + b^2

b^2 = 260

b = 2√65ft

area of rectangle = 2√65 * 25= 50√65

area of triangle = 1/2 * 2√65*8 = 8√65

total area = 58√65 ft^2

Let the number of cats in a farm be [tex]x[/tex] and the number of rabbits be [tex]y[/tex]. The total number of cats and rabbits would be be [tex]x + y[/tex]. As the number of dogs in the farm are [tex]\frac{3}{5}^{th}[/tex] the total number of cats and rabbits, so:

Number of dogs in the farm = [tex]\frac{3}{5} (x + y)[/tex]

Answer:

A. ZA+ZB =180

B. ZA is 135 and ZB is 45

Step-by-step explanation:

Step-by-step explanation:since ZA and ZB are supplementary

ZA+Zb =180°

But ZA=3ZB

∴ 3ZB+ZB=180° ⇒4ZB=180°

∴ZB =45

Answer:

23

Step-by-step explanation:

the 1st number is x

because they are consecutive:

2nd number is (x+1)

now,

x+(x+1)= 23

2x=23–1

2x=22

x=22/2= 11

so two consecutive numbers are 11 & (11+1)=12

now 11+12=23

Answer:

11 and 12

Step-by-step explanation:

Let the integers be x and x + 1.

Sum of two consecutive integers is 23.

x + x + 1 = 23

2x + 1 = 23

2x = 23 - 1

2x = 22

x = 22 / 2

x = 11

x + 1

= 11 + 1

= 12

The numbers are 11 and 12.

Answer:

Square root of 20 :)

Step-by-step explanation:

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

Now lets solve!!

2^2 + 4^2 = c^2

4 + 16 = c^2

20 = c^2

Now lets find the square root if any :)

[tex]\sqrt{20}[/tex] = no square root

Have an amazing day!!

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Answer:

im answering so you can give other guy brainliest :)

The Area is a two-dimensional scalar quantity. The area of the composite figure is 264 cm².

The area of a two-dimensional region, form, or planar lamina in the plane is the quantity that represents its extent. On the two-dimensional surface of a three-dimensional object, the surface area is its counterpart.

The composite figure can be broken down into four parts a square(A), a triangle(B) and two rectangles(C and D).

Now, if the area of the composite figure is taken out it will be,

[tex]\text{Area of composite}=\text{Area of Square A} + \text{Area of triangle B} + \text{Area of Rectangle C} + \text{Area of Rectangle D}\\[/tex]

[tex]\text{Area of Composte}=(10^2)+(\dfrac12 \times 6 \times 4)+(8 \times 4)+(20 \times 6)\\\\\text{Area of Composte}= 100+ 12 + 32 + 120 =264\rm\ cm^2[/tex]

Thus, the area of the composite figure is 264 cm².

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