Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality
7.2b + 6.5 > 4.8b – 8.1.

Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1.
Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.
Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6.
Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b.
Which student’s first step was incorrect, and why?

Amelia’s, because the variable term must be isolated on the left side
Luis’s, because he flipped the inequality sign when he subtracted
Shauna’s, because she did not apply the subtraction property of equality properly
Clarence’s, because the terms he added together were not like terms

Answer: 81, 243, 729

Step-by-step explanation:

STEP ONE: Find a pattern in the sequence

3 ÷ 1 = 3

9 ÷ 3 = 3

27 ÷ 9 = 3

As we can see from the given sequence, each number multiplies 3 to get the next term.

STEP TWO: Find the next three terms

27 × 3 = 81

81 × 3 = 243

243 × 3 = 729

Hope this helps!! :)

Please let me know if you have any questions

Final Answer:

x = 20

Step-by-step explanation:

we'll be using the pythagorean theorem method, in this triangle the missing letter is a.

formula: [tex]a=\sqrt{c^2-b^2}[/tex]

a = x

b = 21

c = 29

a = [tex]\sqrt{29^2-21^2}[/tex]

a = [tex]\sqrt{841-441}[/tex]     (note: 29² = 29 × 29 = 841 and 21² = 21 × 21 = 441)

a = [tex]\sqrt{400}[/tex]

a = 20

x = 20

Answer:

mean = 10

Step-by-step explanation:

The mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

         = [tex]\frac{6+7+10+12+12+13}{6}[/tex]

        = [tex]\frac{60}{6}[/tex]

       = 10

Answer:

Rajan = 436.36 rupees and Kamal = 363.63 rupees

Step-by-step explanation:

Total ratio = 11/30

Amount to be shared = 800

Rajan = Individual ratio / Total ratio x the total amount to be shared

1/5 ÷11/30 × 800 = 436.36

Kamal = 1/6 ÷ 11/30 × 800 = 363.63

Answer:

D. 17

Step-by-step explanation:

No-

Answer:

4th option, x = -1 and x = 9

Step-by-step explanation:

3(x-4)²=75

or, (x-4)²=25

or, x²-8x+16-25=0

or, x²-8x-9=0

or, x²-9x+x-9=0

or, x(x-9)+1(x-9)=0

or, (x-9)(x+1)=0

so, x-9=0 or, x=9

and x+1=0 or, x=-1

The two solutions of the quadratic equation are:

x = -1 and x = 9

The quadratic equation is:

3*(x - 4)^2 = 75

We can expand it as:

3*x^2 - 3*2*4*x + 3*16 = 75

3x^2 - 24x  -27 = 0

Now, using Bhaskara's formula we get:

[tex]x = \frac{-(-24) \pm \sqrt{(-24)^2 - 4*3*(-27)} }{2*3} \\\\x = \frac{24 \pm 30 }{6}[/tex]

So the two solutions are:

x = (24 + 30)/6 = 9

x = (24 - 30)/6 = -1

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Answer:

1. La ecuación vectorial de la línea es [tex]\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}[/tex]

2. La ecuación de la recta es, y = -5·x - 6

Step-by-step explanation:

 1. El punto dado en la línea es A (4, -2), el vector paralelo a la línea es (2, 5)

Por tanto, la ecuación vectorial de la línea es;

[tex]\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}[/tex]

Donde;

t = Cualquier número

2. El punto por el que pasa la recta es P (-2; 4)

La pendiente de la recta, m = -5

Por lo tanto, la ecuación de la línea en forma de punto y pendiente se presenta de la siguiente manera;

y - 4 = (-5) · (x - (-2)) = -5 · x - 10

∴ y - 4 = -5 · x - 10 + 4 = -5 · x - 6

La ecuación de la recta es, y = -5·x - 6

9514 1404 393

Answer:

  (c)  CPCTC

Step-by-step explanation:

Even if you don't know the meaning of CPCTC, you can eliminate the other choices because they refer to the whole triangle, not two corresponding angles.

Angles B and D are corresponding angles in the congruent triangles. The reason they are congruent is ...

  Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Answer:

B. on edge 2021

Step-by-step explanation:

y 1 = StartFraction log x Over log 2 EndFraction + StartFraction log (x minus 2) Over log 2 EndFraction, y 2 = 4; x = 4

Answer:

It's B :))

Step-by-step explanation:

Answer:

- [tex]\frac{7}{4}[/tex]

Step-by-step explanation:

Given

- [tex]\frac{7}{10}[/tex] ÷ [tex]\frac{2}{5}[/tex]

Leave the first fraction

Change division to multiplication

Turn the second fraction upside down

= - [tex]\frac{7}{10}[/tex] × [tex]\frac{5}{2}[/tex] ← cancel 5 and 10 by 5

= - [tex]\frac{7}{2}[/tex] × [tex]\frac{1}{2}[/tex]

= - [tex]\frac{7(1)}{2(2)}[/tex]

= - [tex]\frac{7}{4}[/tex]

The area of one side of the coin is 41.605 mm².

Given that, the diameter of a $1 coin is 26.5 mm.

We need to find the area of one side of the coin.

The area of a circle formula is A=πr².

Now, radius=26.5/2=13.25 mm.

Area of a coin=3.14×13.25=41.605 mm².

Therefore, the area of one side of the coin is 41.605 mm².

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Answer:

pi × 18cm^2

Or approximately,

56.52cm^2 (using 3.14 for pi)

or

56.5487cm^2 (using pi button on calculator)

Step-by-step explanation:

Area of a circle is pi times [radius squared].

All circles are 360°.

Problem can be solved by finding area of whole circle, and then using ratios.

Whole Circle: area = pi × (9cm)^2 = pi × 81cm^2

80° / 360° = Area[shaded] / (pi × 81cm^2)

pi × 18cm^2 = Area[shaded]

((If you read my answer before the edit, I am sorry. I made a calculator error.))

Answer:

2020³-1/4041

Step-by-step explanation:

Step-by-step explanation:

here's the answer to your question

Answer:

[tex]g(x) \times f(x) = 3{x}^{3} -3x[/tex]

X exists for all real numbers.

Y exists for all real numbers.

Answer:

1093 tickets

Step-by-step explanation:

Take the total amount and divide by the amount per ticket to determine the number of tickets

6558/6

1093 tickets

Answer:

The band have to sell 1093 Ticket to meet its goal

Step-by-step explanation:

Total cost = $6,558

Per Ticket cost =$6

formula:

No of Tickets = Total cost of Ticket ÷  Per Ticket Cost

                       = 6558 ÷ 6

No of Tickets = 1093

Check:

Total Cost = No of Ticket × Per ticket cost

                 = 1093 × 6

Total Cost =$6558

Answer:

Step-by-step explanation:

OK

Answer:

rshjgdlf

FGshjfgsfds

Step-by-step explanation:

GIMME'

Answer:

-80

Step-by-step explanation:

We can write the quadratic as

ax^2 + bx+c

4x^2 +8x+9

a=4  b = 8  c=9

The discriminant is

b^2 -4ac

8^2 - 4(4)(9)

64 - 144

-80

Answer:

-80

Step-by-step explanation:

The discriminant is the value under the radical in the quadratic formula. The part of the quadratic formula that is under the radical is [tex]\sqrt{b^2-4ac}[/tex]. So, plug in the needed values and solve for what is under the radical. The b-value is 8; this squared is 64. Then, plug in a and c, 4 and 9. Then multiply these by 4, 4*4*9=144. Finally subtract, 64-144=-80.

Cost of 12 notebooks = $9

Ratio of number of notebooks to its price

= 12:9

= 4:3 (because we reduced it to the simplest form by dividing both numerator and denominator by 3)

Let the cost of 8 notebooks be x.

Then, 8:x = 4:3

=> 8/x = 4/3

=> (8×3)/4 = x

=> 24/4 = x

=> 6 = x

So, the cost of 8 notebooks is $6.

9514 1404 393

Answer:

  (a)  1/12

Step-by-step explanation:

The difference of adjacent terms is ...

  1/4 -1/6 = 3/12 -2/12 = 1/12

Answer: Her earnings after taxes will be $415.80 (choice C)

How?

PER 1 HOUR: 0.77 x (13.50 x 1) = 0.77 x $13.50 = $10.395

PER 40 HOURS: 0.77 x (13.50 x 40h) = 0.77 x 13.50 x 40 = $415.80

Answer:

Length of x+3= 6.75

Length of 4x=15

Length of 3x-1=10,25

Step-by-step explanation:

Answer:

293

Step-by-step explanation:

✓85849=. 85849^1/2

= 293

Answer:

the answer is 205 millimeters

Answer:

205 millimeters.

Step-by-step explanation:

just is

Answer:

1

Step-by-step explanation:

add 1/2 + 1/2 = 2/2 = 1

Answer:

0.07245

Step-by-step explanation:

Just work out 345*21 and then divide by 10,000 because 0.345 is 3 digits from zero and 2.1 has 1 digit from zero, so total of 4 zeroes (10,000 since 10,000 has 4 zeroes).

Answer:

D. linear; y = –x – 1

Step-by-step explanation:

Linear; y=-x - 1

The slope is negative since it’s decreasing. So it’s not the first equation. It’s not a quadratic equation because there is no forming U shape for this data. It’s not a exponential function because the slope is not 3 and a exponential function is in the form y=a(b)^x

...............................................................................................................................................

Answer:

The correct answer is D) linear; y = –x – 1

Step-by-step explanation:

To find this, use any values in the table and it will produce a true statement. This is how we check to see if a model is correct. See the two examples below for proof.

(4, 5)

y = -x - 1

-5 = -4 - 1

- 5 = -5 (TRUE)

(0, -1)

y = -x - 1

-1 = 0 - 1

-1 = -1 (TRUE)

Answer:

17

Step-by-step explanation:

these positive integers are :

4, 64, 124, 184 ... , 964

964 = 4 + (n-1) (60)

964 = 4 + 60n -60

964 = 60n -56

60n = 1020

n = 1020/60

n = 17

so, the number of special integers smaller than 1000 are = 17

The digits n, n+1 and n+2 implies that the special numbers are consecutive i.e. they follow one another. The count of special numbers less than 1000 is 17.

Given that:

[tex]\{n,n+1,n+2\} = \{4,5,6\}[/tex]

[tex]Range = 1000[/tex]

First, calculate the LCM of 4, 5 and 6.

[tex]4 = 2 \times 2[/tex]

[tex]5 = 5[/tex]

[tex]6 = 2 \times 3[/tex]

So, the LCM is:

[tex]LCM = 2 \times 2 \times 5 \times 3[/tex]

[tex]LCM = 60[/tex]

This means that the special digit occurs after every other 60 digits (i.e. the difference between a special digit and another is 60)

To calculate the count of special digits, we make use of arithmetic progression formula

[tex]L = a + (n - 1) \times d[/tex]

Where

[tex]L = 1000[/tex] --- the last term

[tex]a = 4[/tex] --- the first special digit

[tex]d = 60[/tex] --- the common difference as explained above

So, we have:

[tex]L = a + (n - 1) \times d[/tex]

[tex]1000 = 4 + (n - 1) \times 60[/tex]

Collect like terms

[tex]1000 - 4 =(n - 1) \times 60[/tex]

[tex]996 =(n - 1) \times 60[/tex]

Divide both sides by 60

[tex]16.6 =n - 1[/tex]

Add 1 to both sides

[tex]1 + 16.6 =n[/tex]

[tex]17.6 =n[/tex]

Rewrite as:

[tex]n =17.6[/tex]

Remove the decimal part (do not approximate)

[tex]n =17[/tex]

Hence, the special numbers are 17 in total (that are less than 1000).

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