Simplify the following...

The question is asking us to make the denominator a rational function by finding a way to remove the square root without changing the value of the overall function.

We can do this by multiplying the denominator and numerator by the √(4x + 7), since multiplying a root term by that root term = the number being rooted  (√x × √x = x).

   - 5x⁴         ×      √(4x + 7)    =    (-5x⁴)(√(4x + 7))  

√(4x + 7)              √(4x + 7)                 4x + 7

[tex]\\ \sf\longmapsto C=10\pi mm[/tex]

[tex]\\ \sf\longmapsto 2\pi r=10\pi mm[/tex]

[tex]\\ \sf\longmapsto 2r=10[/tex]

[tex]\\ \sf\longmapsto r=5mm[/tex]

[tex]\\ \sf\longmapsto Volume=V=\pi r^2h[/tex]

[tex]\\ \sf\longmapsto V=\pi (5)^2(4)[/tex]

[tex]\\ \sf\longmapsto V=\pi 25(4)[/tex]

[tex]\\ \sf\longmapsto V=100\pi mm^3[/tex]

volume is 100pi mm³.

In mathematics, volume is the space taken by an object.

Here, given that,

The height of a cylinder is 4 millimeters.=h

The circumference of its base is 10 pi mm​=2r*pi

So, we get,

r=5

Volume =pi*r²*h

             =100pi mm³

Hence volume is 100pi mm³.

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Answer:

B

Step-by-step explanation:

Answer:

Straight line is 180 degrees

Subtract what you know 180-55-90 = 35

(6r-7)=35

35-7=28

28/6=4.66666

r=4.6666

Answer:

7

Step-by-step explanation:

90(right angle) + 55(Acute angle) = 145.

We know the whole angle equals 180 because it is 2 right angles. 90 + 90.

So, we will do 180 - 145 = 35.

Now we know our mystery angle equals 35.

To figure out r, we will do 35 + 7 = 42.

Then, 42 is divided by 6 and gets 7.

Therefore, 7 would be your answer.

-kiniwih426

(a) The amount that is deducted from each of Page's paychecks semimonthly is $717.

(b) The amount deducted per week is option A, $29.23.

(a) Given that:

The amount earned by Page semimonthly = $1320

Total cost for the insurance plan = $2868

The school pays 75 per cent of the cost.

The percentage of the insurance cost that Page has to pay = 100% - 75% = 25%.

The amount deducted from the paycheck of Page is:

A = 25% × $2868

  = $717

(b) Given that:

The annual cost of medical insurance = $3500

The percentage of this insurance he has to pay = 100% - 60% = 40%.

Annual deduction from his paycheck = 40% × 3500

                                                              = $1400

The annual cost of travel insurance = $1200

The percentage of this insurance he has to pay = 100% - 90% = 10%.

Annual deduction from his paycheck = 10% × 1200

                                                              = $120

Total amount deducted per year = $1400 + $120

                                                       = $1520

Number of weeks in a year = 52 weeks

The amount deducted per week = [tex]\frac{1520}{52}[/tex]

                                                       = [tex]$29.23[/tex]

Hence, the correct option is A. $29.23.

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Answer:

x=[tex]\sqrt{220}[/tex]

Step-by-step explanation:

Since this is a right angle triangle, and we have two lengths already found, we can use pythagoras to find x.

We know that  

a²+b²=c²

Where a, and b are the smaller lengths (the adjacent and opposite), and C is always the longest one (the hypotenuse).

In this case,

x=a

b=6

c=16

So to plug these into the equation, we get:

x²+6²=16²

To isolate x,

we get:

x²=16²-6²

x=[tex]\sqrt{16^2-6^2}[/tex]

[tex]x=\sqrt[]{220}[/tex]

_________

[tex] \: [/tex]

x² = 16² - 6²

x² = 256 - 36

x² = 220

x = √220

x ≈ 14.9cm

Answer:

$9

Step-by-step explanation:

A video store is selling previously owned DVDs for 40% off the regular price of $15. What is the sale price of the DVDs?

40% = 0.4

15 * 0.4 = $6 (Discount)

15 - 6 = $9 (Sale Price)

Therefore the Answer is: $9

Answer:

−x^6−2x^5+x^2+2x

Step-by-step explanation:

Answer:

line L1 and line L2 passes L2.

The x-coordinate of the point where L2 meets the x-axis is (1, 4).

The equation of the straight line has its slope and given point.

The equation of the line L2, we will use the point-slope equation of a line expressed as y-y₀ = m(x-x₀)

m is the slope of the unknown line (x₀, y₀) is the given point.

First is to get the slope of the known line:

The standard equation of the line

y = mx+c, it can be seen that m = 2

Then we will calculate the slope of the required line.

Since L1 is perpendicular to L2, the product of their slope will be -1 so,

mm₁ = -1 where m₁ is the slope of the required line L2.

Given m =2

m₁ = -1/m

m₁ = -1/2

Now we will calculate the equation of line L2 by substituting the slope of line L2 and the point in the point slope equation above;

y-y₀ = m(x-x₀)

Given (x₀, y₀) = (2, 1) and m₁ = -1/2

y-2 = -1/2(x-1)

open the parenthesis;

y-2 = -x/2+1/2

multiply through by 2:

2y-4 = -x+1

2y+x = 1+4

2y+x = 5

Hence, the equation of the line L2 is 2y+x = 5

Therefore, the x-coordinate of the point where L2 meets the x-axis is (1, 4).

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Using the distributive property with FOIL:

(3n + 2) ( n + 3)

3n² + 9n + 2n + 6

3n² + 11n + 6

Answer:

i think it is 110

Step-by-step explanation:

sorrt if i am wrong

Answer:

The graph below

Step-by-step explanation:

Start at -2 on the y-axis and go up 1/2 every space you go on the x-axis

Hope this Helps

Answer:

Step-by-step explanation:

The explanatory variable (or the independent variable) always belongs on the x-axis (represented as the first column of the table).

The response variable (or the dependent variable) always belongs on the y-axis (represented as the second column of the table).

According to the explanation above the correct choice is A

Answer:

C: In the trigonometric regression model, the explanatory variable is time and the response variable is the height.

Step-by-step explanation:

A quadratic regression model is a parabola. If time is x and height is y, it doesn't make sense if the height is 3,600 feet after a minute. (Not to scale) A trigonometric regression model is a sine wave like a sound wave. This makes sense because the Ferris wheel can only go so high. So after a minute, the height might be 8 feet. (Not to scale)

An explanatory variable is what what you manipulate or observe changes in.

A response variable is what changes with the explanatory variable.

For example, age would be an explanatory variable while height would be the response variable. Or, a caffeine dose would be explanatory, while say reaction time would be the response.

Answer:

it would be 15 or 14 that only came up when I did it

Step-by-step explanation:

Answer:

70 i think i dont know for sure

Step-by-step explanation:

40 x 70

__________

100

= 28

Answer:

Step-by-step explanation:

The roots are:

The roots are:

The roots are:

Using the principle of parallel lines, the value of x in the given triangle is calculated to be 8

The smaller triangle can be expressed as :

The larger triangle can be expressed as :

Equating (1) and (2) :

6/x = 15 / 20

15x = 20 × 6

15x = 120

x = 120 / 15

x = 8

Therefore, the value of x in the triangle is 8.

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Answer:

$21,240

Step-by-step explanation:

8 percent *9000 =

(8:100)*9000 =

(8*9000):100 =

72000:100 = $720 per years of interest

720* 17

= 12,240

12,240+9,000

= 21,240

Answer: 67.8°

Step-by-step explanation:

A quadrilateral's interior angles always add up to 360°.

An equality statement can be set up to satisfy this rule:

103.8+77+111.4+p=360

Collect known values

292.2+p=360

Isolate and solve for p

292.2 (-292.2) +p=360 (-292.2)

p=67.8

Answer:

68.6

Step-by-step explanation:

hello sir / mam!

as the opposite sides of quadrilateral should be 180°

111.4+p=180°

p=180-111.4

p=68.6°

therefore the value of p = 68.6°

hope it helps!

Answer:

ME TOO

Step-by-step explanation:

Function transformation involves changing the position of a function.

The relationship between f(x) and g(x) is (d) The graph of g(x) is translated 2 units up and is steeper than the graph of f(x).

The functions are given as:

[tex]\mathbf{f(x) = x}[/tex]

[tex]\mathbf{g(x) = -5f(x) + 2}[/tex]

Substitute x for f(x) in g(x)

[tex]\mathbf{g(x) = -5x + 2}[/tex]

The +2 in [tex]\mathbf{g(x) = -5x + 2}[/tex] means that, g(x) is gotten by translating f(x) up by 2 units.

The -5 in [tex]\mathbf{g(x) = -5x + 2}[/tex] means that, g(x) has a steeper slope.

Hence, the correct option is (d)

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X - 2 = 10

To solve for x add 2 to both sides of the equal sign:

X = 12

Answer:

x = 12

Step-by-step explanation:

Add 2 to both sides of the equation

x−2=10

−2+2=10+2

Simplify

Solution:

x = 12

⇒ 3x² - 5x = 0

⇒ (3x - 5) · x = 0

3x - 5 = 0

x = 0

x = 0, 5/3

Answer:

1.3235

Step-by-step explanation:

If you take 2.2 and subtract .8765 from it you get 1.3235. If you take that and subtract it from 2.2 you get .8765.

Answer:

4x+31

Step-by-step explanation:

2(x + 4) – 3(x – 6) + 5(x + 1)

Distribute

2x+8 -3x+18 +5x +5

Combine like terms

2x-3x+5x  +8+18+5

4x+31

Answer:

$5.00

Step-by-step explanation:

Answer:

5.00

Step-by-step explanation: this question was already answered but i need the points :p

Answer:

-20xi -4x

Step-by-step explanation:

Step-by-step explanation:

x1+x2 = (-1-√2)/3 + (-1+√2)/3

= -2/3

(x1) (x2) = (-1-√2)/3 × (-1+√2)/3

= -1/9

the equation :

x² -(-2/3)x + (-1/9) = 0

x² + ⅔ x - 1/9 = 0

Step-by-step explanation:

4a)

the principle of similar triangles : they have the same angles.

and we do not forget : the sum of all angles in a triangle is always 180 degrees.

a = 180 - 65 - 45 = 70 degrees

b = 65 degrees

c = 70 degrees

b)

same principles.

x = 58 degrees

y = 52 degrees

z = 180 - 58 - 52 = 70 degrees

c)

same principles.

plus the fact that complementary angles around a point on one side of a line are also together 180 degrees.

x = 85 degrees

y = 180 - 40 - 85 = 55 degrees

z = 180 - 85 = 95 degrees

d)

again same principles.

y = 2x (as these 2 angles correspond to each other among the 2 similar triangles).

the angle POQ is again complementary with 87 degrees,

POQ = 180 - 87 = 93 degrees

x + y + 93 = x + 2x + 93 = 180

3x = 87

x = 29 degrees

y = 2x = 2×29 = 58 degrees

Answer:

the place value changes by dividing by 10 or multiplying by 10. take one and go right on the number line you get 10. go left from 1 and you get 0.1