Hank’s teacher asked him to verify that the product (y−3)(y2+3y+9) is a difference of cubes. He used the distributive property to multiply the binomial times the trinomial. Before simplifying, his product was a polynomial of the form y3+3y2+ay−3y2−ay−27. What is the value of a in the polynomial? 3 9 18 27

Answer:

Option A.

Step-by-step explanation:

The vertices of square S are (0,0), (5,0), (5,-5) and (0,-5).

The vertices of square S' are (0,1), (0,3), (2,3) and (2,1).

It is given that center of dilation is (0,0). From the point it is clear that the distance between point of S and origin is greater that S'. It means the scale factor is less than 1.

If scale factor is 2/5, then

[tex](x,y)\to (\dfrac{2}{5}x,\dfrac{2}{5}y)[/tex]

[tex](0,0)\to (\dfrac{2}{5}(0),\dfrac{2}{5}(0))=(0,0)[/tex]

[tex](5,0)\to (\dfrac{2}{5}(5),\dfrac{2}{5}(0))=(2,0)[/tex]

[tex](5,-5)\to (\dfrac{2}{5}(5),\dfrac{2}{5}(-5))=(2,-2)[/tex]

[tex](0,-5)\to (\dfrac{2}{5}(0),\dfrac{2}{5}(-5))=(0,-2)[/tex]

If the figure translated 3 units up, then

[tex](x,y)\to (x,y+3)[/tex]

[tex](0,0)\to (0,0+3)=(0,3)[/tex]

[tex](2,0)\to (2,0+3)=(2,3)[/tex]

[tex](2,-2)\to (2,-2+3)=(2,1)[/tex]

[tex](0,-2)\to (0,-2+3)=(0,1)[/tex]

These are the vertices of square S'.

A dilation by a scale factor of two-fifths and then a translation of 3 units up are used to get square S' from S.

Therefore, the correct option is A.

Answer:

the degree of that polynomial is 4

Answer:

(C)1 out of 5,005

Step-by-step explanation:

There are a total of 15 student friends.

Monica wants to invite 6 of her friends.

The number of ways this can be done is:

[tex]^{15}C_6=\dfrac{15!}{(15-6)!6!} \\=\dfrac{15!}{9!6!}\\\\=5005[/tex]

Therefore, the probability that friends Tessa, Guido, Brendan, Faith, Charlotte and Rhianna are chosen

[tex]=\dfrac{1}{5005}[/tex]

Answer:

It will take 44.3 years to reach 10,000 plants.

Step-by-step explanation:

the function describing the growth is

f(t) = 500*(1.07^t)  = 10000

Take log on both sides

t*log(1.07) = log(10000/500)

t = log(20)/log(1.07) = 44.277 years

The number years it take for the plant to become invasive are 44.3 years.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

Given that,

Use Amount= Initial value(1+r/100)ⁿ, where n is number of years

Now, 10000=500(1+7/100)ⁿ

20=(1+0.07)ⁿ

20=(1.07)ⁿ

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Exact Form:

n=ln(20)/ln(1.07)

Decimal Form:

n=44.3 years

Therefore, the number years it take for the plant to become invasive are 44.3 years.

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Answer:

The answer is 16.

Step-by-step explanation:

First, you have to make the equation into 0 by moving all the terms to one side :

[tex] - 3 = - {x}^{2} + 2x[/tex]

[tex] {x}^{2} - 2x - 3 = 0[/tex]

Next, you have to apply Discriminant Law, D = b² - 4ac :

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

[tex]let \: a = 1 \: , \: b = - 2 \: , \: c = - 3[/tex]

[tex]D = {( - 2)}^{2} - 4(1)( - 3)[/tex]

[tex]D = 4 + 12[/tex]

[tex]D = 16[/tex]

Answer:

y=|x+1|

Step-by-step explanation:

The y value appears to be 1 more than the x value, so we need to add one to the x to make them even. (x+1)

But the y value doesn’t go below zero, so we need to add the absolute value brackets |x+1|

So y=|x+1|

The graph represents the equation : g(x) = |x + 1|

We have a graph given to us.

We have to write the algebraic expression depicting this graph.

The modulus of the function y = f(x) = x is given by -  

y = |x| = [tex]\left \{ {{x\;\;for\;x > 0} \atop {-x\;\;for\;x < 0}} \right.[/tex]

Using the above property, we can find out the number of solutions of any modulus equation.

The algebraic equation for the graph can be written as -

g(x) = [tex]\left \{ {{x+1;\;for\;x \geq 0} \atop {-x-1\;for\;x < 0}} \right.[/tex]

In the form of modulus function, we can write the above equation as -

g(x) = |x + 1|

Hence, the graph represents the equation : g(x) = |x + 1|

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Answer:

AX=2 BY=5 CZ=3

Step-by-step explanation:

Lets call AX (x). Once you do so, one can tell that AZ=5-x. CZ is also 5-x. BX is also x. Therefore you can say that BY=7-x which makes CY 7-x. Now for side YZ, CZ is 5-x and CY is 7-x.

5-x+7-x=8

solving that you get x=2

AX=2

BY=7-x=5

CZ=5-x=3

Hope this explains some more than the other answer. Please ask any questions.

Answer:

a constant multiplied by y can affect the linear, because it determines a dependent variables.

Step-by-step explanation:

a linear relationship is a statistical term used to described a straight line relationship between two variables.

Answer:

Step-by-step explanation:

The total number of outcomes is 6 x 6 (because a dice has 6 sides) or 36. On the dice, there are 6 sets of matching numbers:

1,1

2,2

3,3

4,4

5,5

6,6

The probability of this is 6/36 or 1/6. The probability of not matching is 30/36 or 5/6.

The probability of rolling a pair of different numbers when two dices are rolled is 5/6.

The probability is the chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.

Total number of combinations when two dices are rolled=[tex]6^{2}[/tex]=36.

Combinations having same pair of numbers=(1,1),(2,2),(3,3),(4,4),(5,5),(6,6).

Number of combinations having same pair of numbers=6.

Number of combinations having different pairs of numbers=36-6=30.

Probability of having different pair of numbers=Number of combinations having different pair of numbers/Total combinations

Probability=30/36

=5/6

Hence the probability of rolling a pair of different numbers when two dices are rolled is 5/6.

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Answer:

126

4m + 24.25 < 34.25

Answer:

Idek I just need points

Step-by-step explanation:

Umm

Answer:

D. 2^3/2

Explanation:

3 3/2

= ²√3³

= ²√27

Hope this helped! :D

Answer:

The answer is D  

Step-by-step explanation:

hope this helps ^_^

Answer:

Mean = 30.3

Median = 30

They scored 30 or more points on 11 games.

Step-by-step explanation:

Mean = all the numbers added together divided by 21

636/21 = 30.3

Median is the middle number (the 11th) = 30

Answer:

102

Step-by-step explanation:

Since 2 + 8 = 10, then the cube root of 5x+2 = 8

Since 8×8×8=512, then 5x+2=512

5x=510, so x=102

Answer:

C) 102

Step-by-step explanation:

Hello !

2 + ∛(5x + 2) = 10

∛(5x + 2) = 10 - 2

∛(5x + 2) = 8

(∛(5x + 2))³ = 8³

5x + 2 = 512

5x = 512 - 2

5x = 510

x = 510 : 5

x = 102

Good luck !

Answer:

(x−3)(x+8)

Step-by-step explanation:

The middle number is 5 and the last number is -24.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 5

Multiply together to get -24

Can you think of the two numbers?

Try -3 and 8:

-3+8 = 5

-3*8 = -24

Fill in the blanks in

(x+_)(x+_)

with -3 and 8 to get...

(x-3)(x+8)

Answer:

See below.

Step-by-step explanation:

The y intercept is 4 so you can mark a point on the line at (0, 4).This is a point on the y-axis 4 units up from the origin (origin is where the axis cross).

The slope is negative so the line will rise to the left.

Mark a point which is  1 unit  horizontally to the left of point (0, 4) and 5 units vertically upwards.

Then draw the line to pass through this point  and the point (0, 4)

The equation of the line is y = -5x + 4.

Answer:

[tex]PQ = x + 13[/tex]

The dimension of the garden is 52.5ft by 43.5ft

Step-by-step explanation:

Given

The shape above

Required

Determine PQ

Determine dimension of the garden

Calculating Length PQ

Represent the length of the inner rectangle as L

Represent the width of the inner rectangle as W

[tex]W = x[/tex]

[tex]L = x + 9[/tex]

The distance between the inner rectangle and the outer triangle is 4ft

This implies that;

[tex]PQ = L + 4[/tex]

Substitute [tex]x + 9[/tex] for [tex]L[/tex]

[tex]PQ = x + 9 + 4[/tex]

[tex]PQ = x + 13[/tex]

Also;

[tex]QR = W + 4[/tex]

Substitute [tex]x[/tex] for [tex]W[/tex]

[tex]QR = x + 4[/tex]

Calculating The Dimension of The Garden

First, we need to determine the Area of the inner rectangle

[tex]Area_1 = L * W[/tex]

Recall that  [tex]W = x[/tex] and [tex]L = x + 9[/tex]

So;

[tex]Area_1 = x * (x + 9)[/tex]

For the bigger rectangle

[tex]Area_2 = PQ * QR[/tex]

Recall that  [tex]PQ = x + 13[/tex] and [tex]QR = x + 4[/tex]

So;

[tex]Area_2 = (x + 13)(x + 4)[/tex]

Given that the Area of the walkway is [tex]400ft^2[/tex]

This implies that

[tex]Area_2 = Area_1 + 400[/tex]

Substitute [tex]Area_1 = x * (x + 9)[/tex] and [tex]Area_2 = (x + 13)(x + 4)[/tex]

[tex](x + 13)(x + 4) = x * (x + 9) + 400[/tex]

Open All Brackets

[tex]x^2 + 13x + 4x + 52 = x^2 + 9x + 400[/tex]

[tex]x^2 + 17x + 52 = x^2 + 9x + 400[/tex]

Collect Like Terms

[tex]x^2 - x^2 + 17x - 9x = 400- 52[/tex]

[tex]8x = 348[/tex]

Divide both sides by 8

[tex]\frac{8x}{8} = \frac{348}{8}[/tex]

[tex]x = \frac{348}{8}[/tex]

[tex]x =43.5[/tex]

Since the dimensions of the garden is [tex]W = x[/tex] and [tex]L = x + 9[/tex]

Substitute 43.5 for x in both cases

[tex]L = 43.5 + 9 = 52.5[/tex]

[tex]W = 43.5[/tex]

Hence, the dimension of the garden is 52.5ft by 43.5ft

Answer:

The correct option is;

[tex]4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )[/tex]

Step-by-step explanation:

The given expression is presented as follows;

[tex]\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )[/tex]

Which can be expanded into the following form;

[tex]\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n[/tex]

From which we have;

[tex]\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}[/tex]

[tex]\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}[/tex]

Therefore, substituting the value of n = 50 we have;

[tex]\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}[/tex]

[tex]\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}[/tex]

Which gives;

[tex]4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}[/tex]

[tex]3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}[/tex]

[tex]\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}[/tex]

Therefore, we have;

[tex]4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )[/tex].

Answer:

x =4

Step-by-step explanation:

hope this is the correct answer

Answer: B

Step-by-step explanation:  B: 5^2-3^2 = 25-9 = 16. the square root of 16 is 4, so x=4

Answer:

1,910

Step-by-step explanation:

8 x 6 = 48 x 4 = 192 x 10 = 1,920 now 1,920 minus 10 = 1,910

i guess..but good luck

Answer:

144mi^2

Step-by-step explanation:

The first step would be to find the top and bottom of the shape which are two triangles.

The way you find the area of a triangle is

[tex]A= \frac{L*W}{2}[/tex]

The length is 6 and the width is 8 so you can plug in the numbers

[tex]A=\frac{6*8}{2}[/tex]

Then multiply 6 by 8

[tex]A=\frac{48}{2}[/tex]

And divide by two

[tex]A=24[/tex]

because there are two identical triangles, multiply 24 by 2 to get 48.

The two triangles make 48mi

Now you must find the area of all the rectangles on the sides separately.

The way to find the area of a rectangle is

[tex]A=L*W[/tex]

You must do one at a time, first, I will so the side with a length of 4 and width of 10

[tex]A=4*10[/tex]

Multiply 4 by 10 to get

[tex]A=40[/tex]

One of the rectangles has the area of 40mi

Now you must find the area of the other rectangles with the same formula. I will be doing the one with a length of 4 and a width of 8 next

[tex]A=4*8[/tex]

Multiply 4 by 8 to get

[tex]A=32[/tex]

The area of the second rectangle is 32mi

Finally, you want to find the area of the last rectangle that has a length of 4 and a width of 6. We will be using the same formula again

[tex]A=4*6[/tex]

Multiply 4 by 6 to get

[tex]A=24[/tex]

The area of the last rectangle is 24mi

The last step is to add all the areas together to get the surface area of the figure.

First the two triangles, then the first rectangle, the second, and finally the third.

[tex]SA = 48+40+32+24[/tex] (SA is surface area)

Once you add them all, you get

[tex]SA=144[/tex]

So the Surface area of the whole figure is 144mi^2

Hope this helps!

Feel free to ask any other questions if you have any.

Have a good day! :)

Answer:

B) Lands on red 6 times

C) Lands on yellow 4 times

Step-by-step explanation:

The rest are way too much/too little for their predicted probability.

Answer:

B C

Step-by-step explanation:

If u spin the spinner below 20 times it will land on red around 4 times.

6 is only 2 greater than 4 so it works.

Same thing with yellow.

Answer:

a) 50,000 + 2x > 70,000

Step-by-step explanation:

Mrs. Lobo has an annual salary of $50000 per year plus 4% commission on her sales.

If she makes $y commission from sales, Mrs Lobo total income per year is:

$50000 + $y.

She makes 4% commission on her sales of share with the average price of a share = $50

Average commission from sales = 4% × $50 = 0.04 × 50 = $2

If she sales x shares in a year, her commission would be $2x for the year. Therefore her total income for that year would be:

50000 + 2x

The amount of shares Mrs Lobbo must sell to make an annual income of at

least $70,000 is given by the inequality:

50,000 + 2x > 70,000

Answer:

  all are maximum values

Step-by-step explanation:

Insurance contracts specify maximum payments, not minimum payments. The numbers mean ...

The 10 means it will pay only $10,000 maximum for injury to any one person in an accident.

The 20 means it will pay a maximum of $20,000 total to people injured in one accident.

The 5 means that it will pay a maximum of $5,000 in property damage for one accident.

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

Explanation:

Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise

A = (0,0)

B = (2,-4)

C = (-4,-4)

Dilating with a scale factor 2 means we multiply each coordinate of each point by the value 2

A = (0,0) becomes A' = (0,0). No change happens. This point is fixed

B = (2,-4) becomes B' = (4,-8). This point does move

C = (-4,-4) becomes C' = (-8,-8). This moves as well

So all you need to do from here is draw triangle A'B'C'.

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

Side note: the lengths of triangle A'B'C' are twice as long as their counterparts on triangle ABC. Consequently, this means the perimeter of A'B'C' is twice as long as the perimeter of ABC. Also, triangle A'B'C's area is four times larger than the area of triangle ABC.

Triangle with the three corner points at

Meaning of Dilation in Math. Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the objects. The result of this transformation is an image with the same shape as the original.

Given:

Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise

A = (0,0)

B = (2,-4)

C = (-4,-4)

Dilating with a scale factor 2

A = (0,0) --> A' = (0,0).

B = (2,-4) --> B' = (4,-8).

C = (-4,-4) --> C' = (-8,-8).

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Answer:

30 students (30 total voters)

Step-by-step explanation:

Let s represent the number of students in the class.  Evan earned 80% of these votes, which came to 24 votes.  Symbolically, we have:

                                                                                                  24 votes

0.80s = 24 votes.  Therefore, s = total number of voters = ---------------- = 30 voters                                                                                              0.8

The total number of students (voters) in his class was 30.

Answer:

It is 30.

Step-by-step explanation:

Answer:

-25

Step-by-step explanation:

Answer:

The base is 2

Step-by-step explanation:

Exponents or powers are on top of the base.

[tex]2^x[/tex]

x is the exponent and the base is 2.

Answer:

a) 7 : 20

b)There will be 35 people with blue eye

Step-by-step explanation:

a)

This question is asking you the ratio of the number of people with blue eyes to the total number of people.

So seven people with blue eyes to the total number of 20 people.

7 : 20

b)

you got the ratio 7 : 20, this also means that there will be 7 people with blue eyes in every 20 people.

so you use 100 divides by 20, you will get the number five, this means there are 5 groups of 20 in 100 people.

so then you use 5 times 7, then you got the number 35.

That means, there are 35 people with blue eyes in 100 people.

Answer:

The answer is given below

Step-by-step explanation:

Given that the parallelogram ABCD has m∠A = 79°

A parallelogram is a quadrilateral with two pairs of parallel lines. For a parallelogram, opposite sides of a parallelogram is equal and opposite angles are also equal. Also the diagonal of a quadrilateral bisect each other.

m∠C = m∠A = 79° (opposite angles of a parallelogram are congruent)

m∠C = 79°

m∠B +  m∠A = 180° (consecutive angles of a parallelogram are supplementary)

m∠B + 79 = 180

m∠B = 180 - 79

m∠B = 101°

m∠B = m∠D = 101° (opposite angles of a parallelogram are congruent)

m∠D = 101°