A motorboat traveling with the current went 80 miles in 4 hours. Against the current, it took 5 hours to travel the same distance. Find the rate of the motorboat in calm water.

I'm pretty sure the answer is 5 because 5 is the greatest common factor. :)

Answer: I'm pretty sure the answer is 5 because 5 is the greatest common factor.

Step-by-step explanation:

y = 2x + 7

the equation of a line in ' slope-intercept form ' is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the ' gradient formula '

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (0, 7 ) and (x₂, y₂ ) = (1, 9)

m = [tex]\frac{9-7}{1-0}[/tex] = 2

given the point (0, 7 ) then c = 7

y = 2x + 7  ← in slope-intercept form

Answer: A= -3

Step 1: Simplify both sides of the equation.

a−2=

3+6a

3

a+−2=2a+1(Distribute)

a−2=2a+1

Step 2: Subtract 2a from both sides.

a−2−2a=2a+1−2a

−a−2=1

Step 3: Add 2 to both sides.

−a−2+2=1+2

−a=3

Step 4: Divide both sides by -1.

−a

−1

=

3

−1

a=−3

Hi!

If the pattern starts off with 5 going to 10, then that would be multiplying by 2. Then, from 10 to 30 would be multiplying by 3. From 30 to 60 would be 2, and 60 to 180 would be 3. So, the pattern is multiply by 2, then multiply by 3, then by 2, then by 3, and so on. So, if we multiply 180 by 2, we get 360, the answer.

Hope this helps!

270 because you can realize it starts going up by 30 so you had to multiply 3 × 30 to get 90 then add 90 to 180 and get 270

9(3x + 8) = 180

Distributive property.

27x + 72 = 180

Subtract 72 from both sides.

27x = 108

Divide both sides by 27.

x = 4

The value of x is equal to 4.

Answer:

The required inequality is: [tex]8x+6y\geq 700[/tex]

The required graph is shown in figure 1.

Yes, he make enough money.

Step-by-step explanation:

Consider the provided information.

Part (A)

Carlos estimates that he will need to earn at least $700 to take his girlfriend to the prom.

Let the number of hours worked in Deli is x and the number of hours worked for babysitting is y.

Deli $8 per hour and babysitting $6 per hour. Carlos need to earn at least 700.

For at least use the inequity ≥

The required inequality is: [tex]8x+6y\geq 700[/tex]

Part (B)

Rewrite the inequity as an equation to find the the x and y intercept.

[tex]8x+6y=700[/tex]

Substitute x=0 in the above

[tex]8(0)+6y=700[/tex]

[tex]y=\frac{700}{6}[/tex]

[tex]y= 116.67[/tex]

Substitute y=0 in the above

[tex]8x+6(0)=700[/tex]

[tex]x =\frac{700}{8}[/tex]

[tex]x= 87.5[/tex]

Use the point (0,116.67) and (87.5,0) to draw the graph.

Since the sign of inequality is greater than equal to, so shade the graph above the line. Use solid line as the sign of inequality is ≥.

Thus, the required graph is shown in figure 1.

Part (C)

We need to find he make enough money if he works 50 hours at each job.

Substitute x=50 and y=50 in the inequality.

[tex]8(50)+6(50)\geq 700[/tex]

[tex]400+300\geq 700[/tex]

[tex]700\geq 700[/tex]

Which is true.

Hence, he make enough money.

Answer:

A. [tex]t=25\ln(5)[/tex]

Step-by-step explanation:

We want to solve for t in [tex]500=100e^{0.04t}[/tex]

Divide through by 100

[tex]5=e^{0.04t}[/tex]

Take natural logarithm of both sides

[tex]\ln(5)=\ln(e^{0.04t})[/tex]

This simplifies to: [tex]\ln(5)=0.04t[/tex]

Divide both sides by 0.04

[tex]\frac{\ln(5)}{0.04}=t[/tex]

[tex]t=25\ln(5)[/tex]

The equivalent number to the given equation is 54.861, calculated by using the order of operations and understanding of place value.

To solve this problem, you need to understand the concept of place value and order of operations in mathematics. Given the equation 5*10 + 4*1 + 8*1/10 + 6*1/100 + 1*1/1,000, we can begin solving using the order of operations, which is often remembered as PEMDAS - Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Here, we multiply before adding. The solution would look like this:

Adding these results together, you get 50 + 4 + 0.8 + 0.06 + 0.001 = 54.861

So the equivalent number is 54.861, which corresponds to answer choice A.

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Answer: 11 sqrt3

Well, since this is an equilateral triangle, you know that all of the sides have the same length: 22 inches. If you want to find the altitude (height), you would have to use the Pythagorean theorem: a^2 + b^2 = c^2

This means that the sum of the two legs squared is equal to the hypotenuse of the triangle squared.

We already know that the hypotenuse is 22 inches, so we can plug that in as c.

We also know that to make the triangle a right triangle, we will need to halve the bottom side, getting 11 inches, which we can plug in as b.

Lastly, we need to know a, so that is our variable to solve (the height). Here is the equation:

a^2 + (11^2) = (22^2)

This is equal to:

a^2 + 121 = 484

Now subtract 121 from both sides to get a^2 on its own:

a^2 = 363

Lastly, take the square root of both sides to solve for a:

a = 11 sqrt3

The altitude of an equilateral triangle with a side length of 22 inches is 11√3 inches.

The altitude of an equilateral triangle can be found using the formula  altitude = (side length * √3) / 2.

In this case, the side length of the street sign is 22 inches. Plugging this value into the formula, we get:

altitude = (22 * √3) / 2.

Simplifying, we have:

altitude = 11√3 inches.

Therefore, the exact altitude length is 11√3 inches.

The percent increase in Anil's hourly wage from $4 to $4.50, find the difference ($0.50), divide it by the original wage ($4), and multiply by 100, resulting in a 12.5% increase.

The student is asking how to calculate the percent increase in Anil's hourly wage from one week to the next. He was earning $4 per hour and then began to earn $4.50 per hour. The percentage increase is found by dividing the change in the quantity (the increase in pay) by the original quantity (the original pay) and then multiplying by 100 to get a percent.

To calculate the percentage increase:

Find the difference in pay: $4.50 - $4 = $0.50.

Divide this difference by the original pay: $0.50 / $4 = 0.125.

Multiply by 100 to get the percentage: 0.125 × 100 = 12.5%.

Therefore, the percent increase in Anil's hourly rate is 12.5%.

easy 214.7 because if it was rounded it would be 214.700 an this is way bigger than 214.275

Answer:

Answer is A. 12

Step-by-step explanation:

Volume of a rectangular prism     = Length * Width * Height

Volume of the rectangular prism  = [tex]2376cm^{3}[/tex]

Length of the prism                       = 18cm

Width of the prism                         = 11cm

We need to find the Height of the Prism,

For that first make the Height as subject of the equation,

Height = [Volume of the rectangular prism/(Length * Width)]

            =[tex]2376cm^{3}[/tex]/(18cm*11cm)

            =[tex]2376cm^{3}[/tex]/[tex]198cm^{2}[/tex]

            =[tex]12cm[/tex]

Therefore,

Answer is A. 12

It's writen as 7,030

split ∠ P into a ∠45° and a ∠60° with altitude PO. ΔPOK is isosceles and ΔPOS is 30-60-90. PO=6=KO Pk=6√2

Answer:

6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Look at the pic below

Let me know if you have any questions

Also, if it's wrong will do my best to fix it

If right please give me brainiest

Thanks

I think it will be 6. So, absolute value is making everything positive, so even if your answer in the absolute value is negative it will be positive.

The new expression will be 1+2+3. Your answer will be 6!

Here is your equation:

[tex](-8+35) + |-16+4|[/tex]

Let's start with the equation in | |. ←These signs are used for absolute value. Absolute value is the distance between a number and 0. Absolute value is ALWAYS positive.

Here is the equation in the | |:

[tex]-16 + 4[/tex]

The negative number is greater than the positive number. That means your answer will be negative. When adding a greater negative number and a positive number, you can just subtract the positive number from the negative number and add the negative(-) sign.

[tex]16-4 = 12[/tex]

Add the (-) sign and it becomes:

[tex]12 \rightarrow -12[/tex]

Remember you have to find the absolute value of it, and absolute value is ALWAYS positive.

[tex]|-12| \rightarrow 12[/tex]

Here is your new equation:

[tex](-8+35)+12[/tex]

In the parentheses, the positive number is greater than the negative number. An easier way to do it is to subtract the negative number from the positive number.

[tex]35-8 = 27[/tex]

Here is your new(and last) equation:

[tex]27+12[/tex]

Add:

[tex]27+12=39[/tex]

The answer choice that matches is C, so that means your answer is C. 39

If you have any questions, feel free to ask in the comments! :)

The inequality is [tex]\( S > 2 \),[/tex] indicating the special sundae weighs more than 2 kilograms of ice cream.

Sure, here's a detailed stepwise solution with explanation:

1. **Understand the problem**: We're tasked with writing an inequality that describes the weight  [tex]\( S \)[/tex] of the special sundae in kilograms. The sundae contains over 2 kilograms of ice cream plus any number of toppings.

2. **Define the variables**: Let [tex]\( S \)[/tex] represent the total weight of the special sundae in kilograms.

3. **Write the inequality**: The problem states that the sundae contains over 2 kilograms of ice cream. Therefore, the weight of the sundae [tex](\( S \))[/tex] must be greater than 2 kilograms. This can be expressed as the inequality:

[tex]\[ S > 2 \][/tex]

4. **Explanation of the inequality**:

  - The inequality [tex]\( S > 2 \) indicates that the weight of the special sundae (\( S \))[/tex]  is greater than 2 kilograms.

  - This inequality ensures that the sundae contains more than 2 kilograms of ice cream, as specified in the problem statement.

5. **Conclusion**: The inequality [tex]\( S > 2 \)[/tex] accurately describes the weight of the special sundae, confirming that it contains over 2 kilograms of ice cream plus any number of toppings.

Find -4 on the number line.

Go to the right 6 place values (+6)

You will find your answer

-4 (+6) = 2

2 is your answer

hope this helps

As triangles are similar therefore the ratio of their corresponding sides are equal . In this case

9/c = 7.5/d

Cross multiply

9d =7.5 c

Now arrange

d/c = 7.5/9

d/c = 75/90

d/c = 5/6

The value of d/c is 5/6

In order to find this, we need to simply replace the values of the triangles that match up. The d portion would match up with 7.5 and the c portion would match up with the 9. So, we can put them into the equation and simplify.

d/c = 7.5/9

d/c = 5/6

the beginnings of the sentence are dependent and after is independent. (The dependent variable is what is being studied and measured)

f(t)=7x

1. The wording tells you the independent variable: it is the phrase following "based on" or "depends on." The other variable is the dependent variable. Your variables are (independent, dependent) ...

A) (expenses, cost of running the business)

B) (area, house price)

C) (distance, time to run it)

D) (size of the carton, number of items in it)

2. f(h) = 7h . . . . . . . where h is the number of hours of babysitting and f(h) is the cost of babysitting. 0 ≤ h ≤ 4 is the domain for which this function is defined.

[tex]f(x)=2x\to y=2x\\\\\text{change x and y}\\\\x=2y\\\\\text{solve for y}\\\\2y=x\qquad|:2\\\\y=\dfrac{x}{2}\\\\Answer:\ f^{-1}(x)=\dfrac{x}{2}[/tex]

To get d . you would do the opposite to move it to the other side..so you would multiply.. v×d=t

Since it is perp. to y = 5x +4, the slope would be the negative reciprocal of 5, which is -1/5. In order to find the y-in. you have to plug in the values you already know into y=mx+b.

-2 = -1/5(3) + b

b=-7/5

y = -1/5x -7/5

The equation of the line perpendicular to y = 5x + 4 and passes through the point (3, -2) is y = -1/5x - 7/5.

The standard form equation of a line is y = mx + b, where m is the slope and b is the y-intercept. The question provides a line equation y = 5x + 4 and informs that the desired line is perpendicular to it. Two lines are perpendicular if the product of their slopes is -1. Hence, the slope of the perpendicular line will be the negative reciprocal of 5 which is -1/5.

Then to find the y-intercept, we use the point that the line passes through which is (3, -2). Insert these values into the equation:y = mx + b, so -2 = -1/5(3) + b, solve to find b = -7/5.

Therefore, the equation of the line in standard form is y = -1/5x - 7/5.

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Answer:

19.625 cm² is your answer

Step-by-step explanation:

Area of the circle can be solved using the equation: Area = [tex]\pi r^2\\[/tex]

Solve for r (radius). To find radius, use Radius = [tex]\frac{diameter}{2}[/tex]

Solve for radius

[tex]\frac{5}{2} = 2.5\\[/tex]

Plug in 2.5 for radius. Remember that Area = [tex]\pi r^2\\[/tex]

Area = [tex]\pi 2.5^2\\[/tex]

Simplify

Area = [tex]\pi 6.25\\[/tex]

Area = [tex]\((3.14)(6.25)\\[/tex]

Multiply

Area = [tex]\ 19.625\\[/tex]

19.625 cm² is your answer

~Rise Above the Ordinary, Senpai

1.  Straight lines are 180 degrees.  That means 180-126=x.  So, x=54.  

You can then use x to find y.  180-54=y.  y=126.  OR  You can use vertical angles to find y.  Vertical angles are the same degree.  So if y is vertical to the angle with 126 degrees, then y=126.

Either way, you will get x=54 and y=126.

2.  You would solve problem 2 the same way as problem 1.  I encourage you to try to do it yourself, but here's how you would do it.

180-103=y, so y=77.  You can either use vertical angles or x=180-77 to find x.  You will end up with x=103.

So y=77 and x=103.

3.  Here you would use vertical angles.  Remember, vertical angles have the same degree!  So 2x+29=5x+20.  Then all you have to do is solve it.

You would end up with x=3.

I hope that helps!

One answer is 2 cars and 20 buses

The toll collector collected $188 in a 2-hour period. There are three possible solutions: 44 cars and 12 buses, 35 cars and 18 buses, or 26 cars and 24 buses.

Let's assume the number of cars passing through the toll booth is 'x' and the number of buses is 'y'.

We can form the following equations based on the given information:

4x + 9y = 188  (total amount collected)

2x + 2y = 2  (total number of hours)

Now we can solve these equations simultaneously to find the values of 'x' and 'y'.

Using substitution or elimination method, we can find that 'x = 44' and 'y = 12', or 'x = 35' and 'y = 18', or 'x = 26' and 'y = 24'.

Therefore, there are three possible solutions:

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