If 2a+ 2/a =4, what is the value of 2a^2− 2/a^2 ?

Answer:

Step-by-step explanation:

Let the number = x

Read carefully the sentence part beginning with 4 times larger

4* something

4 times larger than the square of 1/2 the number

4 * (x/2)^2

4*(x/2)^2 = x

4*x^2/4 = x

x^2 = x  be very careful how you handle this. It looks like 0 might be an answer, but it isn't. If you divide x on both sides and you allow 0, you will get 0 / 0 and that is undefined. You must exclude that possibility with some sort of statement.

x cannot be 0.

x^2/x= x/x

x = 1

Answer:

Step-by-step explanation:

We have:

h = 40 ft

2r = 20 ft → r = 10 ft

Substitute to the formula of a Surface Area of a cylinder:

[tex]SA=2\pi r^2+2\pi rh[/tex]

[tex]SA=2\pi(10^2)+2\pi(10)(40)=2\pi(100)+2\pi(400)\\\\=200\pi+800\pi=1,000\pi\ ft^3\\\\\pi\approx3.14\to SA\approx1,000(3.14)=3,140\ ft^3[/tex]

Answer:

The answer is [tex]\frac{4y}{y+3}[/tex] ⇒ the 4th answer

Step-by-step explanation:

* Lets talk about the product of two fraction

- If we have two fraction a/b and c/d, the product of them

  will be ac/bd

- The there is any simplify can do between numerator and

  denominator we must to make it

Ex: 2a²/5b × 15b/4a, we can simplify 2a² with 4a at first and

      simplify 15b with 5b and then put the answer

∵ 2a²/4a = a/2 ⇒ 2 ÷ 4 = 1/2 and a² ÷ a = a

∵ 15b/5b = 3 ⇒ 15 ÷ 5 = 3 and b ÷ b = 1

∴ 2a²/5b × 15b/4a = a/1 × 3/2 = 3a/2

* Now lets solve the problem

∵ [tex]\frac{2y}{y-3}*\frac{4y-12}{2y+6}[/tex]

- We can simplify the second fraction at first

∵ [tex]\frac{4y-12}{2y+6}=\frac{4(y-3)}{2(y+3}=\frac{2(y-3)}{y+3}[/tex]

- At first we took 4 as a common factor from 4y - 12 ⇒ 4(y - 3)

 and then simplify 4 with 2 in the denominator

- we can cancel the term x - 3 in the numerator of the second

 fraction with the same term in the denominator of the first fraction

∴ [tex]\frac{2y}{1}*\frac{2(1)}{y+3}=\frac{4y}{y+3}[/tex]

* The answer is [tex]\frac{4y}{y+3}[/tex]

Divide total miles by miles per gallon:

1200 / 30 = 40 gallons of gas are needed.

Multiply gallons by price per gallon:

40 x 3.85 = $154 total for gas.

Now add the total for gas to the rental cost:

154 + 99 = $253 total cost

Answer:

(A) [tex]x=60^{\circ}[/tex]

Step-by-step explanation:

Given: It is given that the circle P is circumscribed about quadrilateral ABCD and ∠BCD=120°.

To find: The value of x

Solution: It is given that the circle P is circumscribed about quadrilateral ABCD and ∠BCD=120°.

Now, we know that the sum of opposite angles in a cyclic quadrilateral is 180°, therefore

[tex]{\angle}BAD+{\angle}BCD=180^{\circ}[/tex]

substituting the given values, we get

[tex]x+120^{\circ}=180^{\circ}[/tex]

[tex]x=60^{\circ}[/tex]

Thus, the value of x is 60°.

Hence, option A is correct.

Answer: 60

Step-by-step explanation:

Answer:

Not entirely positive of about the answers, but all of the values would equal 15

First Y = 5

First X = 15

Second X = -3

Answer:

x / y

0/5

15/0

-3/6

Step-by-step explanation:

Answer:

8/11

Step-by-step explanation:

you would move the decimal to the right four times giving you 782000

The area of the copy would be 36 in x16in

The area of the copy of the photograph, with doubled dimensions of 12 inches by 8 inches, is 96 square inches, which is four times the area of the original photograph.

To find the area of a copy of a photograph with dimensions that are double the original, you first find the new dimensions. Since the original photograph is 6 inches by 4 inches, doubling both the length and the width gives us dimensions of 12 inches by 8 inches for the copy.

The area of a rectangle is found by multiplying the length by the width. Therefore, the area of the copied photograph is 12 inches x 8 inches, which equals 96 square inches. This is four times the area of the original photograph since the scale factor for both the length and the width is 2, and the area scales with the square of the scale factor (22).

In conclusion, the area of the copied photograph is 96 square inches. This calculation demonstrates that when you change the linear dimensions of a figure by a scale factor, the area changes by the square of that scale factor.

Answer:

4.5 * 10^-11

Step-by-step explanation:

the reason why is there is 11 zeros in front of the 45

hope this helps :)

Answer:

between 90° and 180°

Step-by-step explanation:

Answer:

The line y = 5x - 13, looks slanted right upwards

Step-by-step explanation:

To easily solve this question, we use a graphing tool, or a calculator to plot the graph.

Please see image below.

From looking at the graph, we know that the function is slanted right upwards.

Answer:

Step-by-step explanation:

∠6 and ∠7 are Alternate Interior Angles.

The lines l and m are parallel, therefore ∠6 and ∠7 are congruent.

m∠6 = m∠7 → 4x - 15 = x + 30        add 15 to both sides

4x = x + 45          subract x from both sides

3x = 45            divide both sides by 3

x = 15

Answer:

[tex]\angle 6 =45^{\circ}[/tex]

Step-by-step explanation:

We are given that l || m

[tex]\angle 6 = 4x-15[/tex]

[tex]\angle 7 = x+30[/tex]

Since l || m

So, [tex]\angle 6 = \angle 7[/tex] (Alternate interior angles are equal )

So, [tex]4x-15 =  x+30[/tex]

[tex]3x= 45[/tex]

[tex]x= 15[/tex]

[tex]\angle 6 = 4x-15=4(15)-15 = 45^{\circ}[/tex]

So, [tex]\angle 6 =45^{\circ}[/tex]

Answer:

Answer:

4(x-3)(x+6)

Step-by-step explanation:

We factor out the 4 first since all numbers are divisible by 4. That leaves us with x^2+3x-18.

Then we factor this to get (x-3)(x+6).

So the factored form of the equation is 4(x-3)(x+6)

Step-by-step explanation:

The factors of the equation 4x²+12x -72 will be 4(x-3)(x+6).

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Factor out the 4 first since all numbers are divisible by 4. That leaves us with x² +3x -18.

4( x² +3x -18 ) = 4 ( x² + 6x - 3x -18 )

                      = 4 ( x(x+6) -3 (x + 6)

                      = 4 ( x + 6 ) ( x - 3 )

Hence, the factors are 4 ( x + 6 ) ( x - 3 ).

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Answer:

[tex]\large\boxed{\ln e^4=4}[/tex]

Step-by-step explanation:

[tex]Use\\\\\log_ab^n=n\log_ab\\\\\log_aa=1\\\\\ln a=\log_e a\to\ln e=1\\====================================\\\\\ln e^4=4\ln e=4(1)=4[/tex]

4 is the value of the given logarithmic function.

The natural logarithm (ln) and the exponential function [tex](e^x)[/tex] are inverse operations of each other. Therefore, [tex]ln(e^x)[/tex] will cancel out and leave us with just x.

In this case,[tex]ln(e^4)[/tex] simplifies to just 4:

[tex]ln(e^4) = 4[/tex]

So,  the value of [tex]ln(e^4)[/tex] is 4.

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Answer:

the answer is a b and e

Step-by-step explanation:

i jus took the assignment

Answer:

A,B,E

Step-by-step explanation:

passed the assignment

Answer:

2x + 3y = -10

Step-by-step explanation:

First convert the line into slope intercept form to find the slope of the line.

2x + 3y = 4

3y = 4 - 2x

y = -2/3x + 4/3

The slope of the line is -2/3. Parallel lines have the same slope so the slope for a line through the point (1,-4) will be -2/3. Substitute m = -2/3 and (1,-4) into the point slope of a line.

[tex]y --4 = -\frac{2}{3}(x-1)\\y + 4 = -\frac{2}{3}(x -1)[/tex]

Now convert the line into standard form by using the distributive property.

[tex]y + 4 = -\frac{2}{3}(x -1)\\y + 4 = -\frac{2}{3}x + \frac{2}{3}\\3y + 12 = -2x + 2\\2x + 3y + 12 = 2\\2x + 3y = -10[/tex]

Answer:

[tex]\large\boxed{y=-\dfrac{3}{2}x+11}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the point A(8, -1) and B(-4, 17). Substitute:

[tex]m=\dfrac{17-(-1)}{-4-8}=\dfrac{18}{-12}=-\dfrac{3}{2}[/tex]

The equation of a line:

[tex]y=-\dfrac{3}{2}x+b[/tex]

Put the coordinates of the point A(8, -1) to the equation of a line:

[tex]-1=-\dfrac{3}{2}(8)+b[/tex]

[tex]-1=-3(4)+b[/tex]

[tex]-1=-12+b[/tex]     add 12 to both sides

[tex]11=b\to b=11[/tex]

Finally we have the equation of a line in a slope-intercept form:

[tex]y=-\dfrac{3}{2}x+11[/tex]

Hello, this is a bet tough so follow the steps!

First we need to set up long division.

     __

33|35

    If we calculate 33 divided by 35 we get 1 with a remainder of 2.

Our work:

  1

   __

33|35

   -33

_____

      2

So therefore we get 1 with a remainder of 2.

Enjoy your day!

Answer:  The correct option is (B) 9.

Step-by-step explanation:  We are given to simplify the following expression :

[tex]E=3^5\div 3^3.[/tex]

We will be using the following property of exponents :

[tex]\dfrac{x^a}{x^b}=x^{a-b}.[/tex]

Therefore, the simplification of the given expression is as follows :

[tex]E\\\\=3^5\div 3^3\\\\\\=\dfrac{3^5}{3^3}\\\\\\=3^{5-3}\\\\=3^2\\\\\=9.[/tex]

Thus, the required simplified answer is 9.

Option (B) is CORRECT.

Answer:

it’s d

Step-by-step explanation:

just took the test

The graph represents the equation g(x) = -∛(x - 1).

Option  D is the correct answer.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

f(x) = ∛x

Reflection over the x-axis.

f(x) = -∛x

And,

Translated one unit to the left.

g(x) = -∛(x - 1)

The graph of g(x) = -∛(x - 1) is shown on the given graph.

Thus,

The graph represents the equation g(x) = -∛(x - 1).

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Answer:

the first one

Step-by-step explanation:

the 36 and the 5 stay in the same places

the x with the negative 4 exponent moves to the bottom and combines with x squared so that makes x to the 6th power on the bottom.

The y  and x move to the top to combine with what is there.

Answer:   [tex]\bold{a)\quad \dfrac{36y^5z^2}{5x^6}}[/tex]

Step-by-step explanation:

[tex]\dfrac{36x^{-4}y^2z^0}{5x^2y^{-3}z^{-2}}\\\\\\=\dfrac{36x^{-4+4}y^{2+3}z^{0+2}}{5x^{2+4}y^{-3+3}z^{-2+2}}\\\\\\=\dfrac{36x^{0}y^5z^2}{5x^6y^{0}z^{0}}\\\\\\=\dfrac{36y^5z^2}{5x^6}[/tex]

Answer:

Choice C.

Step-by-step explanation:

Kermit likes :

15 tea bags

every 2 liters

Peggy:

90 tea bags

12 liters

You would simplify it by dividing 90 by 15, equaling 6. And 12 divided by 2, also equaling 6. Which would mean they are equal and Peggy's tea is exactly like Kermit's favorite iced tea.

Answer:  The correct choice is

Choice (C)  It is just right.

Step-by-step explanation:  Given that Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water and Peggy made a 12 liter batch of iced tea with 90 tea bags.

We are to select the correct choice that describes the thinking of Kermit about Peggy's Iced tea.

The ratio of quantity of water and number of tea bags in Kermit's favorite iced tea is given by

[tex]R_k=2:15.[/tex]

And the ratio quantity of water and number of tea bags in Peggy's iced tea is given by

[tex]R_p=12:90=\dfrac{12}{90}=\dfrac{2}{15}=2:15.[/tex]

Since the ratio of water and number of tea bags in Peggy's iced tea is same as that in Kermit's favorite iced tea, so

Kermit will think that Peggy's iced tea is just right.

Choice (C) is CORRECT.

Answer:

x=37

Step-by-step explanation:

Since this is a right triangle, we can use Pythagorean theorem

a^2 +b^2 =c^2

12^2 +35^2 = x^2

144+1225= x^2

1369 = x^2

Take the square root

sqrt(1369) = sqrt(x^2)

37 = x

Answer:

x = 37

Step-by-step explanation:

Two leg lengths (35 and 12) are given, and the hypotenuse length is to be found.  The Pythagorean Theorem links, these three quantities and enables us to find x quickly and easily:

35² + 12² = x²  →  1225 + 144 = 1369  →  x² = 1369

Find x by taking the square root of both sides:

√(x²) = ±√1369  →  x = ± 37.

Because length is always +, omit x = -37 and keep x = +37.

Final answer:

Explanation of values of t for which the given expression can be factored into binomials.t = 0; pairs of binomials: (x) and (3x + 8)

t = 1; pairs of binomials: (x + 1) and (3x + 8)

t = 2; pairs of binomials: (x + 2) and (3x + 4)

Explanation:

Values of t for which 3(x²) + tx + 8 can be factored into binomials: To factor this expression, we need to identify values of t that allow the expression to be split into two binomials that, when multiplied, give the original expression.

t = 0; pairs of binomials: (x) and (3x + 8)

t = 1; pairs of binomials: (x + 1) and (3x + 8)

t = 2; pairs of binomials: (x + 2) and (3x + 4)

Answer:

S+T

Step-by-step explanation:

Answer:

4.29

Step-by-step explanation:

Answer:

Step-by-step explanation:

We want to round 4.732 to 2 decimal places, it will either round to 4.73 or 4.74. 4.732 rounded to 2 decimal places would be 4.73 (because it is the nearest number to 2 decimal places). 4.737 rounded to 2 decimal places would be 4.74

Answer:

A

Step-by-step explanation:

This is an even polynomial because both ends end up. This means the degree of the polynomial is even. This means b and c are not solutions since their degrees are odd.

To determine between A and D look at the x-intercepts. The x-intercepts of a polynomial graph have a special relationship with its equation. The x-intercepts are the solutions or roots of the factors. This means that when each factor is set equal to 0 and solved, its solution is an x-intercept. Here the x-intercepts are x = -1, 0,3. This means the factors are x(x+1)(x-3).

Notice at x = -1, the function touches but does not cross? This means the factor has an even exponent on it.

So the expression is likely x(x+1)^2 (x-3).

Since only one factor has an exponent, the answer is A.

Answer:

The perimeter of both figures is equal to [tex]64\ units[/tex]

Step-by-step explanation:

step 1

we know that

The perimeter of a square is equal to

[tex]P=4b[/tex]

where

b is the side length of the square

we have

[tex]b=8x\ units[/tex]

substitute

[tex]P=4(8x)=32x\ units[/tex]

step 2

we know that

The perimeter of a rectangle is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]L=(5x+8)\ units[/tex]

[tex]W=(14)\ units[/tex]

substitute

[tex]P=2(5x+8+14)=10x+44\ units[/tex]

step 3

Equate both perimeters and solve for x

[tex]10x+44=32x[/tex]

[tex]32x-10x=44[/tex]

[tex]22x=44[/tex]

[tex]x=2\ units[/tex]

step 4

Find the perimeter of both

square

[tex]P=32x=32(2)=64\ units[/tex]

rectangle

[tex]P=10x+44=10(2)+44=64\ units[/tex]

Answer:

Step-by-step explanation:

Two negatives make a positive, so -(-4) = +4. On a number line, -(-4) would be located 4 units to the right of 0.

The statement "It is 4 units to the right of 0" best describes the location of −(−4) on a number line.

When you have a double negative like −(−4), it becomes positive, so −(−4) is equal to 4, and it is 4 units to the right of 0 on the number line.

The statement "It is 4 units to the right of 0" accurately describes the location of −(−4) on a number line. When dealing with a double negative like −(−4),

it effectively becomes a positive value. In this case, −(−4) simplifies to 4. Therefore, the point −(−4) is located at the position corresponding to the number 4 units to the right of the origin, which is represented by 0 on the number line.

Moving to the right on the number line means increasing the numerical value, so, as a result, −(−4) is found 4 units to the right of 0.

This concept highlights the fundamental principle that negating a negative value results in a positive value, and the position of that positive value is to the right of the origin on the number line.

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Answer: perpendicular

Step-by-step explanation: perpendicular lines are lines that intersect at right angles.

Answer: Perpendicular lines intersect so much so that they create 4 90 degree angles around them.