What is the simplified form of the rational expression below 6x^2-54 / 5x^2+15x

Answer: answers 1 and 5 are correct.

Answer: By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.

Step-by-step explanation: This is the sample response on Edge.

Both parallelograms are <L ≅ < T

Because, by the parallelogram angle theorem, opposite angles of a parallelogram are congruent.

Given parallelograms, GHLJ and GSTU such the parallelogram GSTU is inscribed inside parallelogram GHLJ with angle G coinciding on the two parallelograms.

Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.

Therefore, ∠L ≅ ∠T

A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length. The Sum of adjacent angles of a parallelogram is equal to 180 degrees.

Parallelograms are shapes that have four sides with two pairs of sides that are parallel. The four shapes that meet the requirements of a parallelogram are square, rectangle, rhombus, and rhomboid.

Rectangles, rhombus, and squares are parallelograms. A trapezoid has at least one pair of parallel sides. The parallel sides are called the bases and the non-parallel sides are called the legs. There are three types of trapezoid - isosceles, right-angled, and scalene trapezoids.

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Answer:

512

Step-by-step explanation:

Solve the parenthesis first. Note that:

2^3 = 2 * 2 * 2 = (4) * 2 = 8

4^3 = 4 * 4 * 4 = (16) * 4 = 64

Multiply:

8 * 64 = 512

512 is your equivalent expression.

~

Answer:

(2³)(4³) = 2³ x [tex]2^{6}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512

Answer:

The values are a = 5 , b = 3 , h = 0 , k = 3

The equation is x²/9 + (y - 3)²/25 = 1

Step-by-step explanation:

* Lets revise the standard equation of the ellipse

- The standard form of the equation of an ellipse with  center (h , k)

 and major axis parallel to y-axis is (x - h)²/b² + (y - k)²/a² = 1 , where  

-The length of the major axis is 2a  

- The coordinates of the vertices are (h , k ± a)  

- The length of the minor axis is 2b  

- The coordinates of the co-vertices are (h ± b , k)  

- The coordinates of the foci are (h , k ± c), where c² = a² - b²  

* Now lets solve the problem

∵ The vertices of the ellipse along the major axis are (0 , 8) , (0 , -2)

∴ The major axis is the y-axis

∴ The vertices are (h , k + a) and (h , k - a)

∴ h = 0

∴ k + a = 8 ⇒ (1)

∴ k - a = -2 ⇒ (2)

∵ The foci of it located at (0 , 7) , (0 , -1)

∵ The coordinates of the foci are (h , k + c) and (h , k - c)

∴ h = 0

∴ k + c = 7 ⇒ (3)

∴ k - c = -1 ⇒ (4)

- To find k and a add equations (1) and (2)

∴ (k + k) + (a + - a) = (8 + -2)

∴ 2k = 6 ⇒ divide both sides by 2

∴ k = 3

- Substitute the value of k in equation (1) or (2) to find a

∴ 3 + a = 8 ⇒ subtract 3 from both sides

∴ a = 5

- To find the value of c substitute the value of k in equation (3) or (4)

∴ 3 + c = 7 ⇒ subtract 3 from both sides

∴ c = 4

- To find b use the equation c² = a² - b²

∵ a = 5 and c = 4

∴ (4)² = (5)² - a²

∴ 16 = 25 - b² ⇒ subtract 25 from both sides

∴ -9 = -b² ⇒ multiply both sides by -1

∴ b² = 9 ⇒ take √ for both sides

∴ b = 3

* The values are a = 5 , b = 3 , h = 0 , k = 3

* The equation is x²/9 + (y - 3)²/25 = 1

Answer:

a=5, b=3, h=0, k=3

Step-by-step explanation:

The center of the circle is (0,3) therefore h is 0 and k is 3. If you use a graphing calculator and plot the points given you should find that a=5. Then try to c and use the equation c^2=a^2-b^2 to find b.

Answer:

Vertical angles must have the same vertex and be congruent as well.

Step-by-step explanation:

Answer:

Correct answer is B and C.

Step-by-step explanation:

Vertical angles are those angles opposite each other when two lines intersect. So, they have the same vertex.

When two lines intercept form 4 angles. Those that are opposite to each other are vertical angles, these angles are always congruent.

Answer:

The answer is both a and b

Answer:

both a and b is correct

Answer:

2/3

Step-by-step explanation:

slope = run/rise

rise = vertical distance = difference in y-coordinates

run = horizontal distance = difference in x-coordinates

Find the rise = difference in the y-coordinates: 5 - 9 = -4

Find the run = difference in the x-coordinates in the same order: -2 - 4 = -6

Divide the rise by the run: slope = -4/-6

Reduce the fraction: slope = 2/3

(-2, 5) (4, 9)

Y2 - Y1

-----------

X2 - X1

9-5

------- = 4/6

4+2

4/6 simplifies to 2/3

Slope: 2/3

Answer:

[tex]x=\frac{34z-r}{n}-17[/tex]

Step-by-step explanation:

Given

[tex]n(17+x)=34z-r[/tex]

We have to isolate x on one side of the equation

Dividing both sides by n

[tex]\frac{n(17+x)}{n} =\frac{34z}{n}-\frac{r}{n}[/tex]

Taking LCM on left side

[tex]17+x = \frac{34z-r}{n}[/tex]

Subtracting 17 from both sides

[tex]17+x-17 = \frac{34z-r}{n}-17[/tex]

So, the value of x will be:

[tex]x=\frac{34z-r}{n}-17[/tex] ..

The answer is:

[tex]x=\frac{34z-r}{n}-17[/tex]

To solve for "x" , we just need to isolate it from the equation.

So, we are given the equation:

[tex]n(17+x)=34z-r[/tex]

Then, isolating we have:

[tex]n(17+x)=34z-r\\\\17+x=\frac{34z-r}{n}\\\\x=\frac{34z-r}{n}-17[/tex]

Hence, the answer is:

[tex]x=\frac{34z-r}{n}-17[/tex]

Have a nice day!

Answer:

Second choice

and the last 2 choices

Step-by-step explanation:

32m/16m=2 and our constant is 3 not 2 so not choice A

4m^2/2m=2m so possible 6m/2m=3 so choice B

4m/2m=2 and our constant is 3 not 2 so not choice C

10m/5m=2 same reason as A and C

10m^2/5m=2m possible...15m/5m=3 so choice E

32m^2/16m=2m and 48m/16m=3 so this last choice too

Answer:

[tex](g/f) (x) =\frac{x^2-6}{3x+1}[/tex]

Step-by-step explanation:

We have the following functions

[tex]f (x) = 3x+1[/tex]

[tex]g (x) = x^2-6[/tex]

To find [tex](g/f)(x)[/tex] we must divide the function g(x) with the function f(x)

Then we perform the following operation

[tex](g/f) (x) =\frac{x^2-6}{3x+1}[/tex]

Finally we have that:

[tex](g/f) (x) =\frac{x^2-6}{3x+1}[/tex]

For [tex]x \neq -\frac{1}{3}[/tex]

Answer: 2.3, 1 3/4, 1.6, 2/5

Step-by-step explanation: Convert each fraction into a decimal (or vise versa), then order.

1 3/4 = 1.75

2/5 = 0.4

Answer:

Answer is 2/5, 1 3/4, 1.6, 2.3

Step-by-step explanation:

Lets see: 1 3/4 = 7/4

2.3 = 23/10 or 2 3/10

2/5 is 2/5

and

1.6 is 8/5

so the least is 2/5, 1 3/4, 1.6, 2.3

Hope my answer has helped you in any way!

Note: The volume of a cylinder is:

radius² × π × height

First lets work out the volume of Cylinder A:

Volume = 1² × π × 4

             = 4π  m³

Now lets work out the volume of Cylinder B

Volume = 2² × π × 4

             = 16π  m³

__________________________________________

Now lets compare the volumes ( Cylinder A : Cylinder B)  :

4π : 16π

Lets simplify this by dividing both sides by 4π:

     4π : 16π            ( ÷ 4π)

----> 1 : 4        

_____________________________________________________

Answer:

Option b) 1 : 4

Answer:

1:4

Step-by-step explanation:

Answer:

x^2 +8x+16

Step-by-step explanation

Since you didn,t  include the picture of the graph, I can still solve the equation for you

f(x+4)=(x+4)^2

=x^2 +8x+16

Find the corresponding graph in your exercise

Answer:

Im not sure what the option chocies are but I graphed both graphs online for you! :)

Answer:

2 quarts

Step-by-step explanation:

We know that an automobile's radiator has a capacity of fifteen quarts and currently carries twelve quarts of a thirty percent antifreeze solution.

We are to find the number of quarts of pure antifreeze that must be added to strengthen the solution to forty percent.

We can write the following equation for this and solve it:

[tex] 12 + x = y \\ 12 (.30) + 1 x = y ( . 4 0 ) [/tex]

[tex]3.6 + x = 0.4y[/tex]

[tex]0.4(12 + x) = 3.6 + x&\\4.8 + 0.4x = 3.6 + x[/tex]

[tex]x-0.4x=4.8-3.6[/tex]

[tex]0.6x=1.2[/tex]

[tex]x=2[/tex]

Therefore, 2 quarts are needed.

Answer:

Step-by-step explanation:

<, ≤ - line to the left

>, ≥ - line to the right

<, > - open circle

≤, ≥ - closed circle

==================================

We have the line to the left and open circle.

The circle is on -7.

Therefore is x < -7

Answer:

5/12

Step-by-step explanation:

First find the probability on the first roll

The possible results are 1,2,3,4,5,6

evens: 2,4,6

not 2 = 1,3,4,5,6

P(even)=  number of evens/total = 3/6 = 1/2

P (not 2) = number of results not 2/ total = 5/6

Since the rolls are independent (do not depend on each other), we can multiply the probabilities

P(even, then not 2) = 1/2 * 5/6 = 5/12

Answer:

f(- 1) = 14

Step-by-step explanation:

To evaluate f(- 1) substitute x = - 1 into f(x)

f(- 1) = (- 1)² - 8(- 1) + 5 = 1 + 8 + 5 = 14

Answer:

f(-1)=14

14-4=25

13=70

Step-by-step explanation:

Answer:

Step-by-step explanation:

Okay first if each unit length is 1 ft then you need to find out what the total cost would be. Then use 3.14 and find the total area of £

Answer:

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

Step-by-step explanation:

[tex]\sqrt[n]{a^m}=a^\frac{m}{n}\\\\6\sqrt[5]{x^2y}=(6)(\sqrt[5]{x^2})(\sqrt[5]{y})=6x^\frac{2}{5}y^\frac{1}{5}[/tex]

Answer:

(17+√553)/2

and

(17-√553)/2

Step-by-step explanation:

Subtract 8 from both sides. This leaves you with

sqrt(x-2) = x-8. Square both sides to get rid of the sqrt,

leaving x-2=(x-8)^2

expanding gives x-2=x^2-16x+64

subtract x from both sides leaves

-2=x^2-17x+64

add 2 to both sides

x^2-17x+66=0

this cannot be factored, however, there are other techniques.

Completing the square is a bit annoying, so I will use the quadratic formula, to give the answer.

This gives you:

(17+√553)/2

and

(17-√553)/2

Hope this helps!

Answer:

Step-by-step explanation:

We have quadratic functions f(x) = ax² + bx + c.

c - y-intercept

If a > 0, then a parabola opens up and has a minimum in a vertex.

If a < 0, then a parabola opens down and has a maximum in a vertex.

The function has maximum and y-intercept of 4:

a < 0 and c = 4

The graph of the function which will have a maximum and a y-intercept of 4 is C. f(x) = x² + 2x + 4.

y intercept is the y coordinate of the point on the line where it touches the Y axis. The x coordinate will be 0 there.

Given are four functions.

We have to find the function which has a y intercept of 4.

This means that substitute x = 0 and then find the value of f(x).

A. f(x) = 4x² + 6x - 1

When x = 0, f(x) = -1 ≠ 4

B. f(x) = -4x² + 8x - 5

When x = 0, f(x) = -5 ≠ 4

C. f(x) = x² + 2x + 4

When x = 0, f(x) = 4

D. f(x) = x² + 4x - 4

When x = 0, f(x) = -4

Hence the function which has a y intercept of 4 is C. f(x) = x² + 2x + 4.

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[tex]|2x-4|>-2\\x\in\mathbb{R}[/tex]

Answer:

2 ( x ^3 + 2 x^ 2 − 2 )

Step-by-step explanation:

Factor  2  out of  

2 x^ 3 + 4 x^ 2 − 4 .

Answer:

58 meters

Step-by-step explanation:

We are looking for the length of the base of a triangle, given the height and area. The formula for the area of a triangle  

A=1/2 bh

relates A= the area, b= length of the base, and h= the height of a triangle, so this is the formula we should use.

We are given that the area of the triangle is A=493 and the height h=17. Substitute this information into the formula and solve for b to find

A=493

493=1/2⋅b⋅17

493=17/2b

58=b

The length of the base is 58 meters.

The length of the base of the triangle is 58 meters.

Given,

A triangular flag has an area of 493 square meters and a height of 17 meters.

We need to find what is the length of the base.

The area is given by:

= 1/2 x base x height

Find the area of the triangle.

Area = 493 square meters

Height = 17 meters

Area = 1/2 x base x height

493 square meters = 1/2 x base x 17 meters

Multiply 2 on both sides.

2 x 493 = 2 x 1/2 x base x 17

986  = base x 17

Dividing both sides by 17.

986 / 17 = base

Base = 58 meters.

Thus the length of the base of the triangle is 58 meters.

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Answer:

[tex]\large\boxed{y-3=-\dfrac{1}{3}(x+6)-\text{point-slope form}}\\\boxed{y=-\dfrac{1}{3}x+1-\text{slope-intercept form}}\\\boxed{x+3y=3-\text{standard form}}[/tex]

Step-by-step explanation:

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

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have

[tex]m=-\dfrac{1}{3},\ (-6,\ 3)\to x_1=-6,\ y_1=3[/tex]

Substitute:

[tex]y-3=-\dfrac{1}{3}(x-(-6))\\\\y-3=-\dfrac{1}{3}(x+6)[/tex]

Convert to the slope-intercept form

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

[tex]y-3=-\dfrac{1}{3}(x+6)[/tex]           use the distributive property

[tex]y-3=-\dfrac{1}{3}x-2[/tex]           add 3 to both sides

[tex]y=-\dfrac{1}{3}x+1[/tex]

Convert to the standard form

[tex]Ax+By=C[/tex]

[tex]y=-\dfrac{1}{3}x+1[/tex]           multiply both sides by 3

[tex]3y=-x+3[/tex]             add x to both sides

[tex]x+3y=3[/tex]

Answer:

$299

Step-by-step explanation:

Rent+standard deviation 890+206= $1,096

John's rent: $1,395

Z-score: 1395 - 1096=$299

Answer: 2.4515

Step-by-step explanation:

Given : The mean monthly rent of students at Oxnard University is [tex]\mu=\$890[/tex] with a standard deviation of [tex]\sigma=\$206[/tex]

Using the formula , [tex]z=\dfrac{x-\mu}{\sigma}[/tex], we have the  standardized z-value for x= 1395 as

[tex]z=\dfrac{1395-890}{206}=2.45145631068\approx2.4515\ \text{ [To the nearest four decimal places.]}[/tex]

Hence, the standardized z-score = 2.4515

Answer:

Answer is 50 meters

Step-by-step explanation:

Solution:

Height of the building (h)= 90 meters.

Time taken by the ball to reach the ground (t) = 3 seconds

According to the statement;

h = kt²

90=k(3)²

90=k(9)

90=9k

Divide both the sides by 9

k=10

h=kt²

Put the value time (t)=2 in the equation

h=10(2)²

h=10(4)

h=40 meters

Distance from the ground = 90 - 40

=50 meters.

Thus the correct option is 50 meters....

Answer:

The answer is A) 50 meters

Step-by-step explanation:

Answer: FALSE

Step-by-step explanation:

The first step is to rewrite the equation in the form [tex]ax^2+bx+c=0[/tex], then:

[tex]3x^2 = 6x - 9\\3x^2-6x +9=0[/tex]

Now, we need to calculate the Discriminant with this formula:

[tex]D=b^2-4ac[/tex]

We can identify in the given equation that:

[tex]a=3\\b=-6\\c=9[/tex]

Then, we only need to substitute these values into the formula:

 [tex]D=(-6)^2-4(3)(9)[/tex]

 [tex]D=-72[/tex]

Since [tex]D<0[/tex] then the equation has no real solutions.

Answer:

infinite solutions

Step-by-step explanation:

y=5/2x+2

2y= 5x +4

Multiply the first equation by 2

y = 5/2 x +2

2y = 5/2 *2 x +2 *2

2y = 5x +4

Since this is identical to the second equation (they are the same), the system of equations has infinite solutions

Answer:

3 pounds

Step-by-step explanation: