What is the solution to the system of equations? 3 x - 4 y = 16. 2 x + 3 y = 5.

a. The inequality that models the possible change in the number of feet, r, of the whale's elevation is: 35 - r ≤ 17.

This inequality represents the starting depth of 35 feet below the surface (35), minus the possible change in elevation (r), which should be less than or equal to the maximum height the whale jumps, which is nearly 17 feet above the surface (17).

b. By solving the inequality 35 - r ≤ 17, we can find the range of possible values for r.

First, subtract 35 from both sides of the inequality: -r ≤ 17 - 35. Simplifying further, we have -r ≤ -18. Then, multiply both sides by -1, remembering to reverse the inequality direction: r ≥ 18.

The solution to the inequality is r ≥ 18, meaning that the possible change in the number of feet of the whale's elevation must be equal to or greater than 18. This implies that the whale's jump cannot be less than 18 feet above the surface.

Therefore, the whale's elevation can change by any value equal to or greater than 18 feet, allowing it to jump to a height of nearly 17 feet above the surface.

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a) The inequality can be written as 35 - r ≤ 17. b) The solution to the inequality is r ≥ 18, which means that the change in the number of feet, r, of the whale's elevation must be greater than or equal to 18.

a.

Since the whale swims upward and jumps to a height of nearly 17 feet above the surface, we can represent the change in elevation as r.

The inequality can be written as:

35 - r ≤ 17

Here, 35 represents the starting depth below the surface, and 17 represents the height above the surface that the whale reaches.

By subtracting r from the starting depth, we account for the possible decrease in elevation as the whale swims upward.

b. To solve the inequality, we can isolate r on one side of the equation:

35 - r ≤ 17

Adding r to both sides of the inequality:

35 - r + r ≤ 17 + r

35 ≤ 17 + r

Subtracting 17 from both sides:

35 - 17 ≤ 17 + r - 17

Simplifying further:

18 ≤ r

Therefore, the solution to the inequality is r ≥ 18.

In terms of the situation, the inequality r ≥ 18 means that the change in the number of feet, r, of the whale's elevation must be greater than or equal to 18.

This indicates that as the whale swims upward and jumps to a height of nearly 17 feet above the surface, the whale's elevation can increase by at least 18 feet from its starting depth of 35 feet below the surface.

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A/b= h

h=12 ft

Step-by-step explanation:

The formula for area is given as ;

A=b*h

A/b= h .................equation for h

If Area=96 ft²  and b =8 then h=96/8 =12 ft

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Answer:b/9

Step-by-step explanation: the expression b divided by 9 is b/9

Answer: b ÷ 9

Step-by-step explanation:

Well, since the question is to write an expression for b divided by 9, you just write b divided into 9 parts.

NOTE: Remeber, an expression is an equation but WITHOUT an answer.

Hope this helps! Please feel free to correct me if I'm wrong!

Answer:

Camacho pays in total for the monster truck = $x + $0.13x = $1.13x

Step-by-step explanation:

i.) The price of truck is $x

ii.) Monstor truck tax  = 13% of price of truck = [tex]\frac{13}{100}\times $x[/tex] = $0.13x

iii) Camacho pays in total for the monster truck = $x + $0.13x = $1.13x

Options A and D correctly represent how much Camacho pays in total for the truck:

A. (1 + 0.13)x

D. 1.13x

The total amount Camacho pays for the monster truck includes the price of the truck plus the tax, which is 13% of the price of the truck. Therefore, the total amount can be represented by the expression:

[tex]\[ \text{Total amount} = \text{Price of the truck} + \text{Tax amount} \][/tex]

Given that the price of the truck is x dollars and the tax is 13\% of the price, we can represent the tax amount as 0.13x .

So, the total amount Camacho pays is:

[tex]\[ \text{Total amount} = x + 0.13x \][/tex]

[tex]\[ \text{Total amount} = 1.13x \][/tex]

Therefore, options A and D correctly represent how much Camacho pays in total for the truck:

A. (1 + 0.13)x

D. 1.13x

The complete Question is given below:

Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13% monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck? Choose 2 answers:

A. (1+0.13)x

B. 13x/100

C. 13x

D. 1.13x

E .13x+x

Answer:

[tex]-27x[/tex]

Step-by-step explanation:

Given Equation:

                    [tex]-3 x [75/(9 - 4)^2]^2[/tex]

On simplifying the equation:

               [tex]=-3 x [75/(9 - 4)^2]^2\\=-3 x [75/(5)^2]^2\\=-3 x [75/25]^2\\=-3 x [3]^2\\=-3x*9\\=-27x[/tex]

The value of 'x' can be find by equating the simplified value to some certain value according to the equation.

Answer:

Volume of box = 12x³ + 10x² - 14x - 8

Step-by-step explanation:

Volume of box = Length × Width × Height

Volume of box = (x + 1) (4x - 2) (3x + 4)

Volume of box = (4x² - 2x + 4x - 2) (3x + 4)

Volume of box = (4x² - 2x - 2) (3x + 4)

Volume of box = 12x³ + 10x² - 14x - 8

Answer:

12x^3+22x^2-2x-8

Step-by-step explanation:

i took the test ^^

Answer:

Step-by-step explanation:

Populations is who is surveyed or what the questions is targeting. More specifically who. That would be households with a car.

Use what I put as the definition for population to answer the other questions!

Answer:

Answer is B. (4,0)

Step-by-step explanation:

2x - y = 8

x + y = 4

solve the equation

2x - y = 8

y = 4 - x

substitute the value of y into the equation

2x - (4 - x) = 8

solve the equation

x = 4

substitute the value of x into an equation

y = 4 - 4

solve the equation

y = 0

answer is (4,0)

Answer:

x = -20

Step-by-step explanation:

First we can rearrange the equation:

[tex]\frac{x}{2}[/tex] -18 = -28

2 * [tex]\frac{x}{2}[/tex] - 18 = -28 * 2

The 2s canel out

x - 36 = - 56

x = -20

[tex]\bf \cfrac{cot(A)}{tan(A)}\implies \cfrac{~~\frac{1}{tan(A)}~~}{tan(A)}\implies \cfrac{~~\frac{1}{tan(A)}~~}{\frac{tan(A)}{1}}\implies \cfrac{1}{tan(A)}\cdot \cfrac{1}{tan(A)} \\\\\\ \cfrac{1}{[tan(A)]^2}\implies \cfrac{1}{tan^2(A)}\implies \cfrac{1^2}{tan^2(A)}\implies \left( \cfrac{1}{tan(A)} \right)^2\implies cot^2(A)[/tex]

Final answer:

To simplify cotA/tanA, we recognize that cotA is the reciprocal of tanA. The expression simplifies to cosA^2/sinA^2, which can also be written as cotA^2.

Explanation:

To simplify the expression cotA/tanA, we can use the fundamental trigonometric identities that relate the cotangent and tangent functions. The cotangent function, cotA, is the reciprocal of the tangent function, tanA, which means cotA = 1/tanA. Therefore, when we simplify cotA/tanA, we are effectively dividing the reciprocal of the tangent function by the tangent function itself.

The simplification would thus be:

Answer:

She makes $60 per hour

Step-by-step explanation:

There are 5 days in a week and 40 divided by 5 is 8 and 8x10=80 and 80 subtracted by 20 gives you 60.

Final answer:

After deducting childcare expenses, Sally's actual hourly wage is $7.50 per hour.

Explanation:

The original question is about calculating Sally's actual hourly wage after accounting for childcare expenses. Sally works 40 hours a week and earns $10 per hour. However, she incurs a cost of $20 per day for childcare. Assuming she works 5 days a week, her weekly childcare expenses are $20 x 5 = $100. Therefore, her weekly take-home pay after childcare is (40 hours x $10/hour) - $100 = $400 - $100 = $300. Now, to find Sally's actual hourly wage after childcare expenses, divide her take-home pay by the number of hours worked: $300 / 40 hours = $7.50 per hour.

Answer:

She can buy 62 smoothies

Step-by-step explanation:

Answer:

Pam had 4 times as many pencils as erasers

Step-by-step explanation:

24 pencils

6 erasers

24 pencils = x * 6 erasers

Divide by 6 on both sides to isolate x

x = 4

Pam had 4 times as many pencils as erasers

Hope this helps :)

Step-by-step explanation:

Equation of given line is:

[tex]y = \frac{2}{5} x + 1 \\ equating\: it \: with \: y = m_1x + c, \:we\:find \\ slope \: of \: given \: line \: (m_1 )= \frac{2}{5} \\ y - intercept \: (c) = 1 \\ let \: the \: slope \: of \: required \: line \: be \: m_2. \\ \therefore \: m_1 \times m_2 = - 1..( \because \: lines \: are \: \perp) \\ \therefore \: \frac{2}{5} \times m_2 = - 1 \\ \therefore \:m_2 = - \frac{5}{2} \\ \\ equation \: of \: required \: line \: in \: slope \: \\intercept \: form \: is \: given \: as: \\ y = m_2x + c \\ \huge \orange{ \boxed{\therefore \: y =- \frac{5}{2}x + 1}} \\ [/tex]

Answer:

no answer

Step-by-step explanation:

x^2+4x+5=0

(x+2)^2+1=0

(x+2)^2=-1

this is impossible,

so this equation has no answer

Answer:

Step-by-step explanation:

Answer:

y-6=-4(x-1)

Step-by-step explanation:

y-y1=m(x-x1)

y-6=-4(x-1)

Answer:

27200 rounded will be 30000

Step-by-step explanation:

firstly you find 1% which is 200

then you multiply by 6 to get 6%

then you multiply by 6 again to get the total

Difference in elevation is 6 meters.

Answer: -4

Step-by-step explanation: -5 + 1= -4

Answer: $22.50

Step-by-step explanation:

Since the price is 50% off, you need to find half of 45. 45/2 is 22.5, so she saves $22.50

Step-by-step explanation:

To complete the square, take half of the second coefficient, square it, then add the result to both sides.

(-8/2)² = (-4)² = 16

x² − 8x + 16 = 9 + 16

Solving:

(x − 4)² = 25

x − 4 = ±5

x = 4 ± 5

x = -1 or 9

Answer:

part 1: x^2 + -8 x=9

part 2: Add 16 to each side

part 3: (x-4)^2 =25

part 4: -1 and 9

Answer:

The z-score represents the number of standard deviations an observation is from the mean.

Step-by-step explanation:

We want to complete the statement:

The _______ represents the number of standard deviations an observation is from the mean.

Whenever we calculate z- scores, we are finding how many standard deviations an observation is from the mean.

A z-score of 3, means an observation is 3 standard deviation above the mean.

Therefore the best complete is:

z-score.

The Z-score represents the number of standard deviations an observation is from the mean. It provides a comparative measure that standardizes data, making it easier to compare data from different sets.

The Z-score represents the number of standard deviations an observation is from the mean. In statistics, it is a way to compare the position of any observation relative to the overall distribution.

Here's an example: if a Z-score of a data point is 2, it means that the data point is 2 standard deviations above the mean. Conversely, if a Z-score of a data point is -1, it means that the data point is 1 standard deviation below the mean.

Z-scores provide a standardized way to interpret data, which makes the comparison of different data sets more straightforward and undistorted by differences in units or scales.

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Answer:

???

Step-by-step explanation:

you don't have a question to answer

Answer:

Translate each point of g(x) 5 units up.

Step-by-step explanation:

The given the graph of the parent function

[tex]g(x) = log_{2}(x) [/tex]

We want to use this graph to draw the graph of

[tex]f(x) = log_{2}(x) + 5[/tex]

We can observe that:

[tex]f(x) = g(x) + 5[/tex]

This means the graph of the parent function, g(x) must be shifted up 5 units.

Therefore the correct answer is A.

Answer:

The actual answer is A or 1 as you have it.

Step-by-step explanation:

All you have to do is just map out the coordinates yourself. You're looking for a reflection that goes across the Y axis, but NOT across the X axis.

Hope this helps you and anyone looking for an answer to their headache.

Final answer:

The reflected coordinates of the rectangle over the y-axis are L'(-1, -1), M'(-1, -9), N'(-8, -9), and O'(-8, -1), matching option 1.

Explanation:

The student is asking about finding the coordinates of a rectangle's vertices after it has been reflected over the y-axis. Reflecting a shape over the y-axis changes the sign of the x-coordinate of each vertex, while the y-coordinate remains the same. So, if we have a point (x, y), the reflected point over the y-axis would be (-x, y). Applying this to the rectangle's vertices we have:

For L(1, -1), the reflection L' would be (-1, -1).

For M(1, -9), the reflection M' would be (-1, -9).

For N(8, -9), the reflection N' would be (-8, -9).

For O(8, -1), the reflection O' would be (-8, -1).

Therefore, the correct reflected coordinates are L'(-1, -1), M'(-1, -9), N'(-8, -9), and O'(-8, -1), which corresponds to option 1.

The salesman's commission for selling a car at Sal's car shop is $901.50.

To calculate the salesman's commission for selling a car at Sal's car shop, we must first determine the sale price's profit margin over the dealership's purchase price. The profit is found by subtracting the purchase price ($16,235) from the selling price ($22,245).

Profit = Selling Price - Purchase Price
Profit = $22,245 - $16,235
Profit = $6,010

Next, we calculate the commission by taking 15% of the profit:

Commission = Profit * Commission Rate
Commission = $6,010 * 0.15
Commission = $901.50

Therefore, the salesman's commission for selling the car is $901.50.

Answer:

well i dont really get ehat yours saying but the qustions are

3x+y=5

3^1+1=5

and then

4z+2y=20

i think

4^6+2^6=20

Step-by-step explanation:

Answer: they will have to pay 50 dollars

Step-by-step explanation: you have to multiply 2,500 by 0.02 as it is the same as a percent then you should get 50

Answer:

0.7 km

Step-by-step explanation:

Actual distance in cm = 7(10000)

= 70 000 cm

Actual distance in km = 0.7 km

Answer:

0.7

Step-by-step explanation:

Answer:

w = 5/8

Step-by-step explanation:

divide by 8 to both sides to get 8/8w = 5/8

8/8 = 1, w = 5/8.

Answer:

W= 5/8

Step-by-step explanation:

divide both sides by 8