How do the graphs of the function differ from the graph of f(x)=1.5x^3

Answer:

$6340

Step-by-step explanation:

First figure out what 6.5% of 4000 is by multiplying not dividing because dividing will give you a way bigger number.

4000 x 6.5%=260

260 x 9=2340

2340+4000=6340

Answer:

The sale price of the bicycle is $120.

Step-by-step explanation:

To find the amount, simply multiply the cost by the fraction of the cost that you are paying.

$270 * 4/9 = $120

This would be the cost of the bike.

To prove a rhombus you need to show that the sides are congruent and the diagonals are perpendicular.

Sides:

[tex]d_{RM}=\sqrt{(-4-1)^2+(5-4)^2}[/tex]

    [tex]=\sqrt{(-5)^2+(1)^2}[/tex]

    [tex]=\sqrt{25+1}[/tex]

    [tex]=\sqrt{26}[/tex]

[tex]d_{MB}=\sqrt{(1-2)^2+(4+1)^2}[/tex]

    [tex]=\sqrt{(-1)^2+(15)^2}[/tex]

    [tex]=\sqrt{1+25}[/tex]

    [tex]=\sqrt{26}[/tex]

[tex]d_{BS}=\sqrt{(2+3)^2+(-1-0)^2}[/tex]

    [tex]=\sqrt{(5)^2+(-1)^2}[/tex]

    [tex]=\sqrt{25+1}[/tex]

    [tex]=\sqrt{26}[/tex]

[tex]d_{SR}=\sqrt{(-3+4)^2+(0-5)^2}[/tex]

    [tex]=\sqrt{(1)^2+(-5)^2}[/tex]

    [tex]=\sqrt{1+25}[/tex]

    [tex]=\sqrt{26}[/tex]

[tex]\overline{RM}[/tex] ≅ [tex]\overline{MB}[/tex] ≅ [tex]\overline{BS}[/tex] ≅ [tex]\overline{SR}[/tex]

Diagonals:

Use the slope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m_{RB}=\dfrac{5+1}{-4-2}[/tex]

       [tex]=\dfrac{6}{-6}[/tex]

       = -1

[tex]m_{MS}=\dfrac{4-0}{1+3}[/tex]

       [tex]=\dfrac{4}{4}[/tex]

       = 1

Slopes are opposite reciprocals so they are perpendicular.

***************************************************************************

All of the sides are congruent and the diagonals are perpendicular so RMBS is a rhombus.

Answer:

a = 629

Step-by-step explanation:

a = w * L

w = 17

L = 2w + 3

a = (17) * (2w + 3)

a = (17) * (2(17) + 3)

a = 17 * (34 + 3)

a = 17 * (37)

a = 629

Answer:

C) Symmetric

Step-by-step explanation:

The symmetric property is the idea that if A = B, then B = A. Flipping the equation around doesn't matter.

It's like saying 2+3 = 5 is the same as 5 = 2+3. We can extend the symmetric property to not only deal with equations, but include congruence statements as well.

Answer:symmetric

Step-by-step explanation: a p e x

Answer:

(i) and (iii)

Step-by-step explanation:

for i)

f(x) = [tex]\frac{x^{2}-4}{x+2}[/tex]

     =[tex]\frac{(x+2)(x-2)}{x+2}[/tex]

     =(x-2)

As x =-2

f(x)=-2-2

f(x)=-4

so it is a continuous function

for ii)

from the result of (i) we can deduce the result of second and we see that it is not equal to zero so it is not a continuous function

iii)

f(x)=[tex]\frac{x^{2}+4x+4}{x+2}[/tex]

f(x)=[tex]\frac{(x+2)^{2}}{x+2}[/tex]

f(x)=[tex]\frac{(x+2)(x+2)}{x+2}[/tex]

f(x)=x+2

as x= -2

f(x)=-2+2

f(x)=0

so it is a continuous function

iv) From the result of iii we can deduct that

f(x)=0 because it have the same equation so it is not a continuous function

Answer:

The first and third functions are continuous at x=-2

Step-by-step explanation:

Please, see the attached files.

Thanks.

Answer:

The slope is -1

Step-by-step explanation:

To find the slope when we have 2 points, we can use the formula

m = (y2-y1)/(x2-x1)

 = (-16--10)/(10-4)

 = (-16+10)/(10-4)

  = -6/6

= -1

The slope is -1

If a, b and c are the lengths of a right triangle and c is the longest side, then:

[tex]a^2+b^2=c^2[/tex]

We have a = 18cm, b = 24cm and c = 30cm. Substitute and check:

[tex]L_s=18^2+24^2=324+576=900\\\\R_s=30^2=900\\\\L_s=R_s[/tex]

The triangle with side lengths of 18cm, 24cm, and 30cm is a right triangle and this can be determined by using the Pythagorean theorem.

Given :

The triangle with side lengths of 18cm, 24cm, and 30 cm.

The following steps can be used to determine the given triangle is a right triangle or not:

Step 1 - The Pythagorean theorem can be used to determine whether the given triangle is a right triangle or not.

Step 2 - According to the Pythagorean theorem, the sum of the square of the two shorter sides of the triangle is equal to the square of the larger side of the triangle that is:

[tex]\rm H^2 = P^2+B^2[/tex]

where H is the hypotenuse, P is the perpendicular, and B is the base of the right angle triangle.

Step 3 - To determine the given triangle is a right angle triangle, the Pythagorean theorem must be satisfied.

[tex]24^2 + 18^2 = 30^2[/tex]

LHS = [tex]24^2+18^2[/tex]

       = 576 + 324

       = 900

RHS = [tex]30^2[/tex]

       = 900

So, LHS is equal to RHS. Therefore, the given triangle is a right angle triangle.

For more information, refer to the link given below:

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Lily swam a 100-meter race, completing the first half in 27.8 seconds and the second half in 30.12 seconds. The difference between these times reveals that it took Lily about 2.32 seconds longer to swim the second half of the race compared to the first half.

The student, Lily, swam a 100-meter race with the first and second halves timed separately. She completed the first half in 27.8 seconds and the second half in 30.12 seconds. To find out how much longer it took her to swim the second half than the first, we need to subtract the first time from the second.

So, the calculation would be: 30.12 seconds (second half) - 27.8 seconds (first half) = 2.32 seconds. Therefore, it took Lily about 2.32 seconds longer to swim the second half of the race compared to the first half.

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Answer:

The least common multiple is 4.

Step-by-step explanation:

Answer:

x - 1 and x + 2

Step-by-step explanation:

By the factor theorem if (x - a) is a factor then f(a) = 0.

Try x - 1:_

f(1) =  5(1)^3 + 8(1)^2 - 7 - 6

= 5 + 8 - 7 - 7

= 0  so x - 1 is a factor

We can find the other factors by long division:-

            5x^2  + 13x + 6

           -----------------------------------

x - 1 )    5x^3  + 8x^2  -  7x  -  6

           5x^3  -   5x^2

          --------------------

                        13x^2  -   7x

                         13x^2  -  13x

                         ------------------

                                       6x - 6

                                        6x - 6

                          -----------------

    5x^2  + 13x + 6   = (5x + 3)(x + 2)                          

The given radius is = 60 feet

The volume of the sphere is given by = [tex]\frac{4}{3} \pi r^{3}[/tex]

So we will find the volume of the sphere using radius as 60 and pi as 3.14

Volume = [tex]\frac{4}{3}*3.14*60*60*60[/tex] = 902059.20 cubic feet

As quarter of anything is defined as its one-fourth part, so here the volume of the quarter of sphere can be calculated by finding one fourth of the calculated volume.

So volume of quarter sphere = [tex]\frac{902059.20}{4}[/tex]

= 225514.80 cubic feet

And rounding this to nearest whole number we get 225515 cubic feet as the answer.

Answer: [tex]1.3 \times 10^{13}[/tex]

Explanation:

We are given, that in 2010, the United States national debt was estimated to be nearly 13,000,000,000,000 dollars.

We are required to find the national debt in scientific notation. The scientific notation is used to represent either very small number or very large number.

The scientific form of the given number is:

[tex]1.3 \times 10^{13}[/tex]

Answer:

See the graph of the given inequality in the attachment as shown below:

Step-by-step explanation:

Given the inequality: [tex]m > 2.8[/tex]

To graph this inequality on the number line.

Remember:

Since, in the given inequality the symbol is '>'

Now, sketch a number line and draw an open circle around the number 2.8.

You can see the number line as shown below in the attachment.

Answer: 25 people

Step-by-step explanation: 6 x 5 = 30 30-5 = 25

Answer:

7 pie is the world record. That is 1/4 under the record and your Answer.

Step-by-step explanation:

Who come up with these dump questions??

Answer:

It would be 2/13 because imagine being given 4 decks of 13 cards and you have. Higher chance of having one to two of an ace or king in the deck compared to pulling none to all four. So 2/13 due to the ratio of 13

Answer:

40

Step-by-step explanation:

x + 2x + x + 20 = 180

4x + 20 = 180

4x = 160

x = 40

Answer:

Step-by-step explanation:

x=40

Answer:

341..

Step-by-step explanation:

i would personally say 341 because 620 multiplied by 55% or .55, as written on a calculator, would be 341.

Answer: if you are looking to put it in a proportional relationship you get the same answer but I can show you how to do it.

Step-by-step explanation:

55/ 100 ✖️ n/620=

34100/100 equals 100n ➗ 100 equals 341= n

Answer:

53+3=56

56 times -35

-1960-7

-1967

i think this is how you do it.

Step-by-step explanation:

Answer:

A' (0, -1)

B' (0, 1)

C' (4, 1)

D' (4, -1)

Step-by-step explanation:

We have the following points of a quadrilateral ABCD:

A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2)

and the rule of the translation is given by:

(x, y) ---> (x + 2, y − 3)

which means that each point will move means  3 units to the left and 4 units upwards.

So the points after transformation will be:

A(−2, 2) ---> (-2+2, 2-3) ---> A' (0, -1)

B(−2, 4) ---> (-2+2, 4-3) ---> B' (0, 1)

C(2, 4) ---> (2+2, 4-3) ---> C' (4, 1)

D(2, 2) ---> (2+2, 2-3) ---> D' (4, -1)

If we plot these points on a graph and join the corresponding vertices with line segments, then we will see that all the the lines will be parallel to each other since they followed the same rule of transformation.

The new coordinates of the transformed vertices A', B', C', and D' are:

A' (0, -1)

B' (0, 1)

C' (4, 1)

D' (4, -1)

To find the new coordinates of the transformed vertices A', B', C', and D', you need to apply the transformation rule (x + 2, y - 3) to the original coordinates of A, B, C, and D.

A' = (x + 2, y - 3)

A' = (-2 + 2, 2 - 3)

A' = (0, -1)

B' = (x + 2, y - 3)

B' = (-2 + 2, 4 - 3)

B' = (0, 1)

C' = (x + 2, y - 3)

C' = (2 + 2, 4 - 3)

C' = (4, 1)

D' = (x + 2, y - 3)

D' = (2 + 2, 2 - 3)

D' = (4, -1)

So, the new coordinates of the transformed vertices A', B', C', and D' are:

A' (0, -1)

B' (0, 1)

C' (4, 1)

D' (4, -1)

Now, let's describe the characteristics of the quadrilateral ABCD and its image A'B'C'D' when the corresponding vertices are connected with line segments:

Quadrilateral ABCD:

A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2)

ABCD is a trapezoid with two parallel sides (AB and CD) and two non-parallel sides (BC and AD).

The trapezoid is located in the first quadrant.

Image A'B'C'D':

A'(0, -1), B'(0, 1), C'(4, 1), and D'(4, -1)

A'B'C'D' is also a trapezoid with two parallel sides (A'B' and C'D') and two non-parallel sides (B'C' and A'D').

A'B'C'D' is located in a different position due to the transformation. It has been shifted 2 units to the right and 3 units down.

The transformation (x + 2, y - 3) has effectively shifted the entire quadrilateral 2 units to the right and 3 units down in the coordinate plane. The basic shape and characteristics of the trapezoid are preserved, but its position in the plane has changed.

for such more question on coordinates

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Answer:

90 degrees

Step-by-step explanation:

Answer:

Option no C 600 minutes

Step-by-step explanation:

Given:

gallons of pool = 24000 gallon

Rate at which it is filled = 40 gallons per minute

To find :

Time taken to fill the pool=?

Solution:

We know that rate is the time in which a thing is being done at per minute or per hour or per second. In our question it is given that the rate is 40 gallons per minute which means that 40 gallons are filled in one minute

Now

In one minute = 40 gallons filled

Total pool size = 24000 gallons

Total time taken = [tex]\frac{Total pool size}{gallon filled in one minute}[/tex]

Putting in the values

Total time taken = [tex]\frac{24000}{40}[/tex]

Total time taken = 600 minutes

So the answer is option c which is 600 minutes

Answer:

vw = r      This is not correct

abs ( c - 450) <= 45

Step-by-step explanation:

1.  v = wr

Divide by w             Divide by wr            Divide by r

v/w = wr/w =r            v/wr = wr/wr =1         v/r = wr/r =w

vw = r      This is not correct

v/w = r    This one is good

v/wr = 1       This one is good

v/r= w    This one is good

2.  When working with absolute values, the amount that can vary is on the other side from the absolute value.  

abs( value - target)  inequality  amount that it varies by

the target is 450

no more than is less than or equal to

the amount we can vary by is 45

abs ( c - 450) <= 45

1. The first offered choice is equivalent to ...

... v = r/w . . . . . divide both sides by w

which is not the same as v = wr.

___

2. The wording "no more than 45" means ≤ 45. There's only one formula with such a relationship—the first one.

Comment on "this scenario"

The problem statement describes several relationships, and never tells us whether Lucy's goal is met. The precise "scenario" that is intended to be modeled is not clear. The first inequality has a solution that is the range of calories Lucy might have burned had she reached her goal.

The other inequalities describe other "scenarios," some of which are harder to describe.

Answer:

36.5cm²

Step-by-step explanation:

Area of quarter circle=8²[tex]\pi[/tex]/4=64[tex]\pi[/tex]/4=16[tex]\pi[/tex]cm²

Area of square+Area of shaded region =2(16[tex]\pi[/tex])=32[tex]\pi[/tex]=100.5cm²

Area of square=8²=64cm²

Area of shaded region=100.5cm²-64cm²=36.5cm²

Therefore, the area of the shaded region is 36.5cm².

Answer:

Area shaded area = 36.48

Step-by-step explanation:

Preliminary

Given

Solution

Quarter Circle Area

Formula

Area = 1/4 * pi * r^2

Solution

Triangle Area

Formula

Area = 1/2 r^2

Given

r = 8

Solution

Area of 1/2 the Shaded area

Formula

Area of 1/2 shaded area = Area of 1/4 circle - Area of Triangle

Givens

Solution

Area Shaded area = 36.48

Kevin:

[tex]\frac{2}{2+1}\cdot12=\frac{2}{3}\cdot12=8[/tex]

Answer:

HL = LM

Step-by-step explanation:

We have been given a diagram in which sides AH= EM and AL=EL.

Now we need to find which statement is missing to prove that triangles AHL and EML are congruent using SSS.

SSS means (side - side - side)

Two pair of equal sides are already given so we have completed SS of SSS.

Last "S" means we need one more pair of equal sides so that must be using remaining sides HL and LM

Hence final answer is HL = LM.