Four students were asked to write an expression that has terms that have a greatest common factor of ab. The expressions provided by the students are shown below.


Michelle
16 a + 3 b

Naomi
18 a b c minus 13 a b c

Olivia
20 a b minus 14 a b c

Peyton
15 a b c + 14 a b

Which student wrote the correct expression?
Michelle
Naomi
Olivia
Peyton

Answer:

Megan went a total distance of 1 5/12 miles

Step-by-step explanation:

Here, we want to calculate the total distance worked around the track

We are told that she ran 9/12 and skipped 8/12

The total distance around the track will be the sum of these two

Mathematically, that will be;

9/12 + 8/12

= 17/12 = 1 5/12

Answer:32

Step-by-step explanation:

Answer:

32, Trust me mate, Its 32

Answer:

B: 2 7/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

go on mathify and ask

Answer:

y=1/2x+2

Step-by-step explanation:

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

Explanation:

Add up all the frequencies that correspond to outcomes that are more than 3

So we'll add up the last three frequencies (since they correspond to outcomes of 4, 5 and 6 all of which are greater than 3) to get 20+30+38 = 88

We have 88 occurrences of rolling either a 4, a 5 or a 6. This is out of 200 rolls total.

The empirical (or experimental) probability of getting more than 3 on the die is 88/200 = 0.44

Answer:

$465 at Back Street

$515 at Main Street

Step-by-step explanation:

980 (total) - 50 (the difference between the two) = 930

930/2 = 465 (back street)

465 + 50 (the difference) = 515 ( main street)

CHECK: 465 + 515 = 980

Answer:

x = r² + 5

Step-by-step explanation:

Given

r = [tex]\sqrt{x-5}[/tex] ( square both sides to clear the radical )

r² = x - 5 ( add 5 to both sides )

r² + 5 = x

The 4 in the symbol is the index of the radical sign √.

Whether you can write this expression on a calculator depends on the calculator... If you have one with a CAS (that is, a "computer algebraic system"), chances are there is a built-in button for things like square roots and cube roots, and possibly roots of higher indices. If not, you can always express a radical expression using a fractional exponent, such as

[tex]\sqrt x\iff x^{\frac12}[/tex]

or

[tex]\sqrt[3]{x}\iff x^{\frac13}[/tex]

or

[tex]\sqrt[4]{x}\iff x^{\frac14}[/tex]

and so on. So the given expression could be typed in as (16*x^6*y^7)^(1/4), for instance.

I'm guessing you have to simplify the given expression. You could end up with

∜(16x ⁶y ⁷) = ∜(2⁴ x ⁴ x ² y ⁴ y ³)

… = 2xy ∜(x ² y ³)

(assuming x and y are positive)

Answer: The first one :)

Step-by-step explanation:

Answer:

c= 39.95 +0.15 (s + r) (take the 63 received and plug it in for r and 53.45 in for c then solve)

53.45= 39.95 +0.15 (s +63) (use the distributive property)

53.45 = 39.95 + 0.15s + 9.45 (combine like terms on the right side)

53.45 = 49.40 +0.15s (subtract 49.40 from both sides)

4.05 = 0.15s (divide both sides by 0.15 so isolate s)

s= 27 (how many text messages were sent)

Step-by-step explanation:

I hope this helps :)

Answer:

s=27

Step-by-step explanation:

Answer:

Option C wil be most effective in gathering the information that the manager requires.

Step-by-step explanation:

Internal and external environment influnces any kind of business. we should have proper knowledge of internal and external factors which affects our business.In given case, Taste and preference affects the demand and supply of consumer and shopping center. So manager must take a stratified sample from the neighbourhoods in the area.

Answer:

3520

Step-by-step explanation:

hope it helps

Answer:

wha gh filled out of my friends house to myself I don't want you so very true but I'm going back and

Answer:

mutual fund

Step-by-step explanation:

Step one:

given data

let say the investment plan will span for 5 years

so  for mutual fund

P= $1000

r= 7.5%= 0.075

t= 5

compound interest

A= P(1+r)^t

substituting

[tex]A= 1000(1+0.075)^5\\\\A=1000(1.075)^5\\\\A=1000*1.436\\\\A=$1436\\\\[/tex]

$1436

so  for bond

P= $1000

r= 7.5%= 0.075

t= 5

simple interest

A= P(1+rt)

substituting

[tex]A= 1000(1+0.075*5)\\\\A=1000(1+0.375)\\\\A=1000(1.375)\\\\A=1375\\\\[/tex]

A=$1375

$1375

I would go for mutual fund compounded interest because it offers extra

$61 (1436-1375) for the same investment capital

Answer:

555x+15

x=days

Step-by-step explanation:

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

Explanation:

Consecutive integers are integers that follow one right after another. For example, the set {3,4,5} represents consecutive integers.

Consecutive odd integers are a similar idea but that every value is odd. Example: {7,9,11,13}

Let x be some integer. If we multiply it by 2, then it's always even. So 2x is always even. Adding 1 to it makes it odd. So 2x+1 is odd.

The next odd integer after (2x+1) is (2x+3)

Add those two integers and set that sum equal to -60. Solve for x.

(2x+1)+(2x+3) = -60

4x+4 = -60

4x = -60-4

4x = -64

x = -64/4

x = -16

If x = -16, then

2x+1 = 2*(-16)+1 = -32+1 = -31

2x+3 = 2*(-16)+3 = -32+3 = -29

Then note how -31+(-29) = -60 which confirms our answers.

Answer:

a. $583

b. $30,316

Step-by-step explanation:

a. Commission last week;

= 5,300 * 11%

= $583

b. Commission in 2011 assuming weekly earnings of $583.

= 583 * 52 weeks

= $30,316

Answer:

The longer length is 35ft

Step-by-step explanation:

Given

[tex]Area = 560[/tex]

[tex]Perimeter = 102[/tex]

Required

Determine the longer length

Represent the length with L and width with W

So, we have:

[tex]L * W = 560[/tex] --- Area

[tex]2*(L+W) = 102[/tex] --- Perimeter

Divide both sides by 2 in:

[tex]2*(L+W) = 102[/tex]

[tex]L + W = 51[/tex]

Make L the subject:

[tex]L = 51 - W[/tex]

Substitute 51 - W for L in [tex]L * W = 560[/tex]

[tex](51 - W) * W = 560[/tex]

[tex]51W - W^2 = 560[/tex]

Reorder the equation

[tex]W^2 - 51W + 560 = 0[/tex]

Expand

[tex]W^2 -35W - 16W + 560 = 0[/tex]

[tex]W(W-35)-16(W-35) = 0[/tex]

[tex](W-16)(W-35) = 0[/tex]

Split:

[tex]W - 16 = 0\ \ \ W - 35 = 0[/tex]

[tex]W = 16\ \ \ W = 35[/tex]

This implies that the longer length is 35ft

Answer:

6.5m

Step-by-step explanation:

65/10 = 6.5m

hope u can understand...

Answer:

4.6 meter

Step-by-step explanation:

you can convert decimeter to meter by dividing 10

Answer:

same is so sad its either cheating or leaving

Step-by-step explanation:

Answer:

my worst fear is losin people...

Step-by-step explanation:

but I gotchu through whatever, aii?

Answer:

y = -3/8(x + 2)^2 + 8

Step-by-step explanation:

vertex form is

y = a(x - b)^2 + c     where a is a constant and (b,c) is the vertex.

The maximum is at (-2, 8)  because x 8 = height and x =-2 is equn. of symmetry

So here we have

y = a(x - (-2))^2 + 8

y = a(x + 2)^2 + 8

Now at the point (-6, 2):

2 = a(-6+2)^2 + 8

2 = 16a + 8

16a = -6

1 = -3/8.

So our equation is y = 3/8(x + 2)^2 + 8

Answer:

5/6

Step-by-step explanation:

The complement of rolling 6 will be all the possible outcomes except rolling 6 which is 5/6

Answer:

This question is solved in detail below. Please refer to the attachment for better understanding of an Ellipse.

Step-by-step explanation:

In this question, there is a spelling mistake. This is vertices not verticles.

So, I have attached a diagram of an ellipse in which it is clearly mentioned where are the vertices of an ellipse.

Vertices of an Ellipse: There are two axes in any ellipse, one is called major axis and other is called minor axis. Where, minor is the shorter axis and major axis is the longer one. The places or points where major axis and minor axis ends are called the vertices of an ellipse. Please refer to the attachment for further clarification.

Equations of an ellipse in its standard form:

[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1[/tex]

This is the case when major axis the longer one is on the x-axis centered at an origin.

[tex]\frac{x^{2} }{b^{2} } + \frac{y^{2} }{a^{2} } = 1[/tex]

This is the case when major axis the longer one is on the y-axis centered at an origin.

where major axis length = 2a

and minor axis length = 2b

Answer:

The equation of the line segment AB is:

[tex]y = -2x+11[/tex]

The graph of the line segment AB is also attached.

Step-by-step explanation:

Given the points

Determining the slope between A(3,5) and B(5,1)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(3,\:5\right),\:\left(x_2,\:y_2\right)=\left(5,\:1\right)[/tex]

[tex]m=\frac{1-5}{5-3}[/tex]

[tex]m=-2[/tex]

Using the point-slope form of the line equation

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

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -2 and the point (3, 5) in the equation

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

[tex]y - 5 = -2(x-3)[/tex]

[tex]y-5 = -2x+6[/tex]

[tex]y = -2x+6+5[/tex]

[tex]y = -2x+11[/tex]

Therefore, the equation of the line segment AB is:

[tex]y = -2x+11[/tex]

The graph of the line segment AB is also attached.

Step-by-step explanation:

12.09 - 8.30 = 3.79

The reason why her answer was wrong is because when the '2' gets slashed into a '1' during carry over, it would have been 11 - 8 = 3 instead of a 4. (the 1st column)

The error that Juanita made is that she made a computational error when subtracting.

Answer:

Step-by-step explanation:

She subtracted instead of added.

She aligned the decimal points incorrectly.

She did not regroup correctly when subtracting.

She made a computational error when subtracting.

Step-by-step explanation:

For table 1,

x =  20     36    56     80

y =  4        6       8       10

Taking 20/4 = 5

36/6 = 6

56/8 = 7

80/10 = 8

The value of x/y is not same in any of the cases. The constant of proportionality is different. It means x and y for this table is not proportional.

For table 2,

x = 28    42    56    70

y = 20    30    40    50

Taking 28/20 = 1.4

42/30 = 1.4

56/40 = 1.4

70/50 = 1.4

The value of x/y is same in each case. The constant of proportionality is same i.e. 1.4 in each case.

[tex]\dfrac{x}{y}=1.4\\\\\dfrac{y}{x}=\dfrac{1}{1.4}\\\\\dfrac{y}{x}=\dfrac{5}{7}\\\\y=\dfrac{5}{7}\times x[/tex]

So, y is 5/7 times of the x.

Answer:

[tex]2x^{2}[/tex] - x + 5

Step-by-step explanation:

g(x)=x+1

f(x)=[tex]2x^{2}[/tex]-5x+8

f∅g(x)=2[tex](x+1)^{2}[/tex]-5(x+1) + 8

= 2([tex]x^{2}[/tex]+2x+1) - 5x - 5 + 8

= [tex]2x^{2}[/tex] +4x +2 - 5x +3

=[tex]2x^{2}[/tex] -x +5

:)

Answer:

Each side of the Rhombus is 5 units

Step-by-step explanation:

Since the sides of a rhombus area all equal in length;

Then, the length of a side is enough to get the lengths of the other sides

Mathematically, finding the distance between two points out of what we are given will be enough to get the measure of one of the side of the rhombus

We apply the distance formula appropriately to get the distance between the side of the Rhombus

D = √(x2-x1)^2 + (y2-y1)^2

let us use the points (-1,0) and (4,0)

D = √(4 + 1)^2 + (0-0)^2

D = √25

D = 5