2. Use the diagram below to name the following.

Answer:

Georgette did not complete the factorization; 9 is a composite number.

Step-by-step explanation:

9 can be broken down to 3x3

So it the prime factorization of 72 should be 2x2x2x3x3

Georgette’s error is Georgette should have expressed 8 as 4 × 4, not 2 × 4.

The correct option is D.

The correct prime factorization of 72 is 2³ × 3², which means it can be expressed as the product of prime numbers raised to their respective exponents.

Analyzing the factor tree provided by Georgette, we can see that she made an error when branching from 72 to 8 and 9.

The prime factorization of 8 should be 2³, not 2 × 4, and the prime factorization of 9 should be 3², not 2 × 2.

Therefore, Georgette's error is that she have expressed 8 as 2³ × 1 or 4 × 2, not as 2 × 4.

The correct factor tree for 72 would be:

    72

  /  \

2   36

    / \

   2   18

       / \

      2   9

          / \

         3   3

So, the prime factorization of 72 is 2³ × 3².

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Hey there! I think Nicole would be 28.

Details are missing;

A board of 15 balloons. 4 are purple, 3 red, 4 blue, 2 yellow and 2 green

Answer:

the probability that both the balloons you break are purple = 2/35

Step-by-step explanation:

Since there are 15 balloons and 4 are purple. It means that probability of the first balloon being purple is;

4/15

Now, if the first balloon is purple, it means we have 3 purple left out of the remaining 14. Thus probability of the second being purple = 3/14

Thus;

the probability that both the balloons you break are purple = 4/15 × 3/14 = 2/35

8000647 dollars

Step-by-step explanation:

broggxtxycycuvuh8y7rtwh4w5iwutettixgdbf

Answer:

y= -2x -2

Step-by-step explanation:

slope-intercept form:

y= mx +c, where m is the gradient and c is the y-intercept.

Given that the slope is -2, m= -2.

Susbt. m= -2 into the equation:

y= -2x +c

To find the value of c, substitute a pair of coordinates.

When x= -4, y= 6,

6= -2(-4) +c

6= 8 +c (expand)

c= 6 -8 (-8 on both sides)

c= -2 (simplify)

Thus, the equation of the line is y= -2x -2.

Answer:

   A.  Step I

Step-by-step explanation:

Appropriate application of the distributive property would give ...

  x +2x -10 = 320 . . . . . . . does not match step I

Further solution steps would be ...

  3x -10 = 320

  3x = 330

  x = 110

Answer:

x=4

Step-by-step explanation:

18 = 3(3x − 6)

Divide each side by 3

18/3 = 3( 3x-6)/3

6 = 3x-6

Add 6 to each side

6+6 = 3x-6+6

12 = 3x

Divide by 3

12/3 = 3x/3

4 =x

Answer: 4 = x

Step-by-step explanation: To solve this equation, we start by

distributing the 3 through the parenthses on the right side.

3(3x) is 9x and 3(-6) is -18.

So our equation now reads 18 = 9x - 18.

Our next step is to get the x term by itself on the right side.

So we add 18 to both sides to get 36 = 9x.

Now divide both sides by 9 to get 4 = x.

Answer:

false

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Given

[tex]\frac{1}{(t-2)^2}[/tex] = 6 + [tex]\frac{1}{(t-2)}[/tex] ( multiply through by (t - 2)²

1 = 6(t - 2)² + t - 2 ← distribute parenthesis and simplify

1 = 6(t² - 4t + 4) + t - 2

1 = 6t² - 24t + 24 + t - 2

1 = 6t² - 23t + 22 ( subtract 1 from both sides )

6t² - 23t + 21 = 0 ← in standard form

(2t - 3)(3t - 7) = 0 → in factored form

Equate each factor to zero and solve for t

2t - 3 = 0 ⇒ 2t = 3 ⇒ t = [tex]\frac{3}{2}[/tex] ← p

3t - 7 = 0 ⇒ 3t = 7 ⇒ t = [tex]\frac{7}{3}[/tex]  ← q

Thus

p × q = [tex]\frac{3}{2}[/tex] × [tex]\frac{7}{3}[/tex] = [tex]\frac{21}{6}[/tex] = [tex]\frac{7}{2}[/tex] → B

Answer:

If a = b and b = c, then a = c

Step-by-step explanation:

The transitive property of equality tells us that if we have two things that are equal to each other and the second thing is equal to a third thing, then the first thing is also equal to the third thing.

Answer:

If a = b and b = c, then a = c

Step-by-step explanation:

i got it right on a test

Answer:

25 t-shirts and 35 hats were sold

Step-by-step explanation:

Here, we want to calculate the number of hats and the number of t-shirts sold.

Let the number of hats be h and the number of t-shirts be t

The sum of both is 60;

Mathematically;

h + t = 60 •••••••••••(i)

The total revenue from selling h hats at $12 per one is 12 * h = $12h

The total revenue from selling t t-shirts at $18 per one is 18 * t = $18t

So the addition of this gives the total;

12h + 18t = 870 ••••••••(ii)

From i, h = 60-t; substitute this into ii

12(60-t) + 18t = 870

720 -12t + 18t = 870

720 + 6t = 870

6t = 870 -720

6t = 150

t = 150/6

t = 25

From the substitution;

h = 60-t

h = 60-25

h = 35

Answer:

48 hats

Step-by-step explanation:

im not sure if this is the right answer but i hope this helps

Answer:

8.66 x 10^3

Step-by-step explanation:

8.66 * 1000 (10^3) = 8660

Answer:

[tex]CD = 15[/tex]

Step-by-step explanation:

Given

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

[tex]CD = 5x[/tex]

[tex]BD = 5x + 7[/tex]

Required

Determine CD

Since Point C is on segment BD, then we have

[tex]BD = BC + CD[/tex]

Substitute x + 4 for BC; 5x for CD and 5x + 7 for BD

[tex]5x + 7 = x + 4 + 5x[/tex]

Collect Like Terms

[tex]5x - 5x - x = 4 - 7[/tex]

[tex]- x = -3[/tex]

Multiply both sides by -1

[tex]x = 3[/tex]

Substitute 3 for x in [tex]CD = 5x[/tex]

[tex]CD = 5(3)[/tex]

[tex]CD = 15[/tex]

Hence, the length of CD is 15 units

Answer:

Step-by-step explanation:

Given

Required

Determine CD

Since Point C is on segment BD, then we have

Substitute x + 4 for BC; 5x for CD and 5x + 7 for BD

Collect Like Terms

Multiply both sides by -1

Substitute 3 for x in  

Hence, the length of CD is 15 units

Step-by-step explanation:

Answer:

The equation is;

T = 87.4 ± 1.5

Maximum value of T = 88.9 °F

Minimum value of T = 85.9 °F

Step-by-step explanation:

We are given the stated temperature as 87.4 °F

Now, we are told that this stated temperature differs from the actual temperature by no more than 1.5 degrees Fahrenheit.

Thus, if the actual temperature is T, it means that T should either be 1.5 more than 87.4 or 1.5 less than 87.4.

Thus the equation is;

87.4 ± 1.5 = T

So maximum value of T = 87.4 + 1.5 = 88.9 °F

While minimum value of T = 87.4 - 1.5 = 85.9 °F

Answer:

6

Step-by-step explanation:

C=9.2v + 21.2

76.4 = 9.2v + 21.2

76.4 - 21.2 = 9.2v

55.2 = 9.2v

v= 55.2 / 9.2 = 6

Answer:

x =6

Step-by-step explanation:  Q is the midpoint of PR.

Therefore PQ = QR

3 x + 14 = 7 x -10

       -14          -14

3 x         = 7 x-24

-7x                 -7x

-4x     =      -24                             Divide both sides by -4

x = 6

The value of x for PQ = 3x + 14 and QR = 7x - 10 is 6 units.

What is midpoint of line segment?

The midpoint divides the line segment into two equal parts.

It is given that Q is the midpoint of PR which implies Q will divide PQ into two equal parts that is PQ (3x+14) equals QR (7x-10). now calculating x value  :

[tex]\begin{aligned}PQ&=QR\\3x+14&=7x-10\\7x-3x&=14+10\\4x&=24\\x&=6\end{aligned}[/tex]

Therefore, the value of x for PQ = 3x + 14 and QR = 7x - 10 is 6 units.

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Answer:

1.) 88

2.) 196

3.) 63

4.) 90

5.) 367.142857143

6.) 695. 2 repeating

7.) 109.285714286

8.) 63.5593220339

Step-by-step explanation:

Answer:

  14 cm

Step-by-step explanation:

The applicable formula is ...

  s = rθ

  s = (7 cm)(2) = 14 cm

Answer:

p= (9.1 x 10^-31)(2.18 x 10^6)   p = 1.9 x 10^-22kg*m/s

Step-by-step explanation:

for i said so

The momentum of electron is [tex]1.9\times 10^{26}[/tex] kg m per second.

Given, mass of electron is [tex]9.1\times 10^{-31}[/tex] kg.

And its velocity is [tex]2.18 \times 10^6[/tex] m per s.

We have to calculate its momentum.

We know that momentum is numerically equal to the product of mass and velocity of a particle and denoted by p.

So, [tex]p=mv[/tex]

[tex]p= 9.1\times10^{-31}\times2.18\times10^{6}[/tex]

[tex]p=19.838\times10^{25}[/tex]

[tex]p=1.9\times10^{26}[/tex]

Hence the momentum of electron is [tex]1.9\times 10^{26}[/tex] kg m per second.

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Answer:- 136.9

Step-by-step explanation:

3median=2mean+mode

3(137)=2(137.05)+mode

411=274.1+mode

411-274.1=mode

mode=136.9

Answer:

Step-by-step explanation:

The sequence above is an arithmetic sequence

So in order to find the common difference subtract the previous term from the next term

So we have

Taking 9.4 and 6

That's

9.4 - 6 = 3.4

Taking 12.8 and 9.4

12.8 - 9.4 = 3.4

Taking 16.2 and 12.8

16.2 - 12.8 = 3.4

Since the common difference is the same for any of the terms taken , the common difference is 3.4

Hope this helps you

Answer:

3.4

Step-by-step explanation:

Answer:

one half of a plus six times b divided by seven

Step-by-step explanation:

Answer:

With $30, Peter can afford 5 hours

Step-by-step explanation:

Given

Insurance Charge = $7.5

Charges = $4.5 per hour

Required

Determine the number of hours $30 can afford

First, we need to determine the equation.

Total Charges = Charges per hour + Insurance Charge

Substitute values for Charges per hour and Insurance Charge

Total Charges = 4.5 per hour + 7.5

Let the number of hours be n;

So,

Total Charges = 4.5n + 7.5

To calculate Peter's; substitute 30 for total charges

[tex]30 = 4.5n + 7.5[/tex]

Subtract 7.5 from both sides

[tex]4.5n = 30 - 7.5[/tex]

[tex]4.5n = 22.5[/tex]

Divide both sides by 4.5

[tex]n = \frac{22.5}{4.5}[/tex]

[tex]n = 5[/tex]

Hence;

With $30, Peter can afford 5 hours

Answer:

de ef     and  df

Step-by-step explanation:

Answer:

9.3

Step-by-step explanation:

Step 1: Calculate. We calculate the square root of 87 to be: √87 = 9.32737905308882.

Step 2: Reduce. 9.32.

Step 3: Round. Round 9.32 so you only have one digit after the decimal point to get the answer: 9.3.