Colton solved an equation incorrectly, as shown below:
Step 1: x − 13 = 26
Step 2: x = 26 − 13
Step 3: x = 39
Which statement best explains why Step 2 is incorrect in Colton’s solution?
He did not subtract 13 from 26.
He did not multiply 26 by 13.
He did not add 13 to 26.
He did not divide 26 by 13.

Answer:

- 28 - 40i

note that i² = (√-1)² = - 1

expand product of factors using FOIL

= - 6 - 6i - 14i - 14i² - 20i + 36i²

= - 6 - 6i - 14i + 14 - 20i - 36

= - 28 - 40i

Step-by-step explanation:

Got right on PLATO

The solution to the complex expression (3+7i) (-2-2i) -4i(5-9i) is -28 - 40i

A complex number is a number of the form a + bi, where a and b are real numbers, and i = √-1

i² = (√-1)² = -1

Given the expression:

(3+7i) (-2-2i) -4i(5-9i)

= -6 - 14i -6i + 14 - 4i(5 - 9i)

= 8 - 20i - 20i - 36

= -28 - 40i

The solution to the complex expression (3+7i) (-2-2i) -4i(5-9i) is -28 - 40i

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7. Loan amount = $12000

Monthly payment = $380

Duration of the repayment = 3 years = 3(12) = 36 months.

Total amount Jason repaid = 36 × 380 = 13680

Interest on loan amount = amount repaid - loan amount

= 13680 - 12000

= 1680

Hence, total amount Jason paid in interest on loan = $1680 and the correct option is (D).

8. Loan amount = $35000

Monthly payment = $315

Duration of the repayment = 10 years = 10(12) = 120 months.

Total amount Gerald repaid = 120 × 315 = 37800

Interest on loan amount = amount repaid - loan amount

= 37800 - 35000

= 2800

Hence, total amount Gerald paid in interest on loan = $2800 and the correct option is (B).

Final answer:

Given that the average of m, n, and -1 is 0, the sum of m+n is calculated to be 1.

Explanation:

The question asks for the sum m+n given that the average of m, n, and -1 is 0. To find the sum, we can set up an equation using the definition of the average:

(m + n + (-1)) / 3 = 0

Solving this equation, we get:

m + n - 1 = 0

And once we add 1 to both sides:

m + n = 1

Therefore, the value of m+n is 1.

7+3 =10 or 3(10) 30                                                

Dolphin: 5/15=1/3= .3333- miles per minute

Stingray: 11/30= .3666- miles per minute

Great White Shark: 92/(4 x 60)= .38333- miles per minute

The great white shark is the fastest.

Answer:

The great white shark is the fastest.

Step-by-step explanation:

22a. False

22b. True

22c. True

22d. False

For each scenario, we multiply Rachel's daily earnings ($21) by the number of days worked to find her total earnings.

In 22a, Rachel earns 21 × 20 = $420, not $421 as stated.

In 22b, Rachel indeed earns 21 × 15 = $315, making the statement true.

Similarly, in 22c, Rachel earns 21 × 13 = $273, confirming the statement as true.

However, in 22d, Rachel's earnings for 13 days amount to 21 × 13 = $273, not $250, rendering the statement false.

Therefore, the true statements are 22b and 22c, while 22a and 22d are false.

Complete Question:

[tex]c^2-4=0\qquad|+4\\\\c^2=4\to c=\pm\sqrt4\\\\c=-2\ \vee\ c=2[/tex]

9.20 divides by 4 is 2.3 per quarter pound

There are 9 quarters in 2 1/4

So 9 times 2.3 is 20.7

2x5x10^5=1000000. You do the exponent first,10^5 = 100000. Then you multiply that by 5, 5x100000=500000. Then by 2, 500,000x2= 1000000.

Answer: 5 1/10

Solution:

2/5-[-4 7/10]

2/5-[-(4*10+7)/10]

2/5-[-(40+7)/10]

2/5-[-47/10]

2/5+47/10

2*2/(5*2)+47/10

4/10+47/10

(4+47)/10

51/10

(50+1)/10

50/10+1/10

5 1/10

The area of the outer ring of the circle can be found by subtracting the area of the inner circle from the area of the whole circle.

The area of the whole circle is represented by the expression 25x2 - 12x - 9. To find the area of the outer ring of the circle, we need to subtract the area of the inner circle from the area of the whole circle.

The area of the inner circle can be represented as a difference of squares: (5x - 3)(5x + 3).

Therefore, the area of the outer ring of the circle is given by the expression (25x2 - 12x - 9) - (5x - 3)(5x + 3).

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The equation is saying [tex]t+3\geq 21[/tex]. We can use algebra to subtract 3 from both sides to create [tex]t\geq 18[/tex].

Therefore, the value t is greater or equal to 18.

Answer:

D

Step-by-step explanation:

The longest side is twice as long as the shortest side because lets suppose I have a triangle that has vertices with angles 30 and 60, the last one has to be 90 because the total is 180 degrees. Now for a 30 60 triangle, if the hypotenuse has a length of 2, the following ratios will hold true for the other two sides. The side that shares the 90 degrees and 60 degrees corners will be of length 1 and the side that shares the 30 degrees and 90 degrees corners (vertices) will be of length sqrt(3). This is true all the time. In this case the correct answer is that the longest side is twice as long as the shortest side because the longest side is the hypotenuse with length 2 and the shortest side will be the one that shares the 90 degrees and 60 degrees corners and is of length 1.

Answer:

A

Step-by-step explanation:

Remember to follow PEMDAS, and left -> right rule.

First, solve the Parenthesis:

(4 + 2^3)

Solve the exponent.

2^3 = 2 x 2 x 2 = 4 x 2 = 8

4 + 8 = 12

_______________________________________________________________

(5^2) x (12)

5^2 = 5 x 5 = 25

25 x 12

_______________________________________________________________

Multiply

25 x 12 = 300

________________________________________________________________

300 is your answer

________________________________________________________________

~Rise Above the Ordinary

Answer: the answer is lifeguard hope that helps.

Step-by-step explanation:

On the number line, smaller numbers are located to the left of larger numbers, which are located on the right.

So, if you have two numbers x and y on the number line, the smaller of the two will be on the left, the larger one on the right.

So, -13 is located to the right of -15, because it's larger.

For the same reason, -11 is located to the right of -13.

On the number line, you would have something like

<--------(-15)-------(-13)--------(-11)---------->

On a number line, negative values decreases as we move to the left while positive values increases to the right. Hence,

Starting from 0 to the left, we have - 1, - 2, - 3,... which continues in that sequence as decreases as we move to the left of the number line.

Moving towards the left, - 13 appears before - 15 ; Hence - 13 is located relative to the right of - 15 on the number line

Similary, - 11 appears before - 13 ; Hence - 11 is located relative to the right of - 13 on the number line.

Therefore, - 13 and - 11 are located to the right of - 15 and - 13 respectively on the number line.

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12 - 5[(4 +2)² - (22 + 10)]

Remember to follow PEMDAS. First, solve both parenthesis

12 - 5[(4 +2)² - (22 + 10)]

12 - 5[(6)² - (32)]

Next, solve the exponent

(6)² = 6 x 6 = 36

12 - 5[(36) - (32)]

Then, solve the bracket.

36 - 32 = 4

12 - 5[4]

Next, multiply

-5 x 4 = -20

Finally, subtract.

12 - 20 = -8

None of the above. The answer is -8. Please check the answers and the question again

~Rise Above the Ordinary

Square yards or square feet

The quadratic function is given by the equation [tex]h(t)=-0.075t^2+0.6t+2.5.[/tex]

The maximal height will be at vertex. Find t-coordinate of the parabola vertex:

[tex]t_{vertex}=-\dfrac{b}{2a}=-\dfrac{0.6}{2\cdot (-0.075)}=4\text{ seconds.}[/tex]

At t=4,

[tex]h(4)=-0.075\cdot 4^2+0.6\cdot 4+2.5=-1.2+2.4+2.5=3.7\text { feet. }[/tex]

Answer: it will take 4 seconds for the ball to reach the maximal height of 3.7 feet.

I'm pretty sure the unit price is $0.14. :)

Answer: The total weight  is [tex](1.14)(10^{7})[/tex] pounds.

Step-by-step explanation:

1. To solve this problem you need to multiply the number of whales by the weight. Based on the given information, the weight of each whale is approximately [tex](3.8)(10^{5})[/tex] pounds, therefore:

[tex](30)[(3.8)(10^{5})]=11,400,000[/tex] pounds.

3. To express the result in scientific notation, you must move the decimal point to the right until you have a non-zero number on the left of the decimal point. Then, it is:

[tex](1.14)(10^{7})[/tex]

Answer: The group weights 1.14x10^7 pounds

Step-by-step explanation:

The group has 30 whales.

Each whale weights 3.8x10^5 pounds, then, 30 whales weight 30 times that amount:

Total weight = (30)*(3.8x10^5)

Remember that for the scientific notation we want only one digit before the decimal point.

Here, i will use that 30 = 3x10^1

(3x10^1)*(3.8x10^5) pounds = (3*3.8)x10^(5 + 1) pounds

(11.4)x10^6 pounds

and 11.4 = 1.14x10^1

(11.4)x10^6 pounds =  1.14x10^(1 + 6) pounds = 1.14x10^7 pounds

12 ÷ 75 = 0.16.

So she runs 0.16 miles per minute.

Hope it helps!

Step 1

Find the equation in function notation

Let

h-------> the number of hours

y-------> the function for the walker fee in dollars

we know that

the hourly rate is [tex]30\frac{\$}{hour}[/tex]

[tex]y=6+30h[/tex]

in this linear equation

the independent variable is the variable h

the dependent variable is the variable y

Convert to function notation

Let

[tex]f(h)=y[/tex]

[tex]f(h)=6+30h[/tex]

Step 2

Find how much does the dog walker charge for a 45 minute walk

Convert the time in hours

[tex]1\ hour=60\ minutes[/tex]

[tex]45\ minutes=45/60=0.75\ hours[/tex]

substitute in the equation

For [tex]h=0.75\ hours[/tex]

[tex]f(0.75)=6+30*(0.75)=\$28.5[/tex]

therefore

the answer is

the dog walker charge for a 45 minute walk [tex]\$28.5[/tex]

Statements

Step 3

The dependent variable is the number of hours true or false

The statement is false,

because the independent variable is the number of hours and the dependent variable is the walker fee in dollars

Step 4

The function for the walker fee is f(h)= 30h+6 true or false

The statement is True --------> see the Step 1

Step 5

The dog walker charges $22.5 for a 45 min walk true or false

The statement is False

Because the dog walker charges for a 45 minute walk [tex]\$28.5[/tex]

The dependent variable is indeed the number of hours. The proper function for the walker's fee is f(h)= 6+30h. When using the function to calculate a 45-minute walk, we find the cost to be $28.5, not $22.5.

The subject of this question is Mathematical analysis, more specifically, function notation and applied arithmetic. Here, the dependent variable is indeed the number of hours, it is true. We can express the cost of dog walking as a function of the time in hours. We denote the function with 'f' and the hours with 'h'. The flat rate plus the hourly rate can be express as f(h) = 6 + 30h. So the function given f(h)= 30h+6 is  true.

To find a 45-minute walk cost, we need to express 45 minutes in hours, because our function is defined in terms of hours. 45 minutes is 0.75 of an hour. Substituting h = 0.75 into the function, we get f(0.75) = 6 + 30* 0.75 = 6 + 22.5 = 28.5, not $22.5. So, the statement 'The dog walker charges $22.5 for a 45min walk' is false.

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either 0 or 1 plane(s)

The place value of the 8 in 2,894 would be the hundredths.

Hope helps!-Aparri

the value of the eight is 800 because i actually dont know how to explain this but basiclly the 3 rd digit from the right would always be the hundereds place.

A.)  34.68

hope this helps

A is your answer. Take the $289 and multiply that by 0.12.

Hope this helps & good luck. :)

no it would not be congruent

Hello!

No, these shapes would not be considered congruent. In geometry, figures would only be congruent if they have the same size and shape. In the above image, the two figures have the same shapes, but they do not have the same size.