Find an equivalent ratio in simplest terms: 25:75

Answer:

Slope = 2/3

Y-intercept = -5

Step-by-step explanation:

Since the equation is written in y = mx + b format. The m is the slope and b is the y-intercept. In place of m is 2/3 and in place of b is -5. Therefore, the slope is 2/3 and the y-intercept is -5.

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The equation of line is y = ( -2/3 )x - 5 , where the slope is m = -2/3 and the y intercept is b = -5

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = ( -2/3 )x - 5

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

Substituting the values in the equation , we get

Slope m = ( -2/3 )

The y-intercept b = -5

Hence , the equation of line is y = ( -2/3 )x - 5

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If the area of the triangle is 120 cm^2, the value of x is equal to 6.

Mathematically, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle (A) = 1/2 × b × h

Where:

According to Hero's Formula area of triangle by Heron of Alexandria, if a, b, c are the side lengths of a triangle, then, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle (A) = √[s(s − a)(s − b)(s − c)]

Where:

s = (a + b + c)/2

s = (x + x + 1 + 2x - 1)/2

s = 4x/2

s = 2x

Substituting the parameters into Hero's Formula formula, we have the following;

x√10 = √[2x(2x − x)(2x − x - 1)(2x − 2x + 1)]

x√10 = x√2(x − 1)

√10 = √2(x − 1)

Taking the square of both sides, we have:

10 = 2(x - 1)

10 = 2x - 2

2x = 12

x = 12/2

x = 6.

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Answer:

90

Step-by-step explanation:

Positive 72 - (-18), is the same as 72 + 18, because two negatives cancel out and is the same as if you were adding. In other words, if you subtract a negative number, you are contradicting the negative, so you have one positive.

Hopefully that will help. :)

The equation used in writing a partial fraction decomposition is given as:

Negative 15 x + 10 / (5 x - 2) = a / (5 x - 2) + b / (5 x - 2).

To determine the values of a and b, we can use a system of equations. This system of equations consists of two equations, one for a and one for b. The equation for a is: Negative 15 x + 10 = a * (5 x - 2). The equation for b is: 0 = b * (5 x - 2). We can solve these equations simultaneously to get the values of a and b.

For example, if x = 1, then the equation for a becomes: Negative 15 + 10 = a * (5 - 2), which simplifies to -5 = a * 9. Therefore, a = -5/9. The equation for b becomes: 0 = b * (5 - 2), which simplifies to 0 = b * 3. Therefore, b = 0.

In summary, the system of equations used to determine the values of a and b is:

Negative 15 x + 10 = a * (5 x - 2) and 0 = b * (5 x - 2). By solving these equations simultaneously, we can get the values of a and b.

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Answer:

B!!!

Right on Edge

Step-by-step explanation:

The result of 32 modulo 5 is 2, and when 1.6 is subtracted from 2, the final answer is 0.4.

Let's break down the calculation step by step:

32 modulo 5:  

The modulo operator (%) returns the remainder when one number is divided by another. In this case, 32 modulo 5 means dividing 32 by 5 and finding the remainder. When 32 is divided by 5, it results in 6, with a remainder of 2. Therefore, 32 modulo 5 is equal to 2.

Subtracting 1.6 from 2:

Subtracting 1.6 from 2 involves finding the difference between the two numbers. By subtracting 1.6 from 2, we get:

2 - 1.6 = 0.4

Thus, when 1.6 is subtracted from 2, the final result is 0.4. This means that there is a difference of 0.4 units between the values of 2 and 1.6 when subtracted from each other. It is important to note that the final answer, 0.4, represents the remaining value after the subtraction operation.

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Answer: 87% is equivalent to 0.87, so 8.87 can be expressed as 87/100 or 87 percent. Any remainders (less than 0.87) are expressed in fraction form, such as 8.87/10 or 87/100 of a percent.

Answer:

3. x= 20.1

4. x = 22.0

Step-by-step explanation:

SohCahToa. S= sin, C= cos, T=tan.

o = Opposite (the side on the other side of the given angle, also referred to as theta.)

h = Hypotenuse (the side on the other side of the right angle, represented as the square thing.)

a = Adjacent (side next to the given angle.)

3. We have opposite = x, adjacent = 24. We can use tan (Toa.)

  tan(40º) = x/24         Multiply both sides times 24.

  x = 24*tan(40º)         Put into calculator

  x = 20.1

4. We have adjacent = 12, hypotenuse = x. We can use cos (Cah.)

  cos(57º) = 12/x         Multiply both sides by x

  x*cos(57º) = 12         Divide by cos(57º)

  x = 12/cos(57º)         Put into calculator

  x = 22.0

Answer:

(i) 2197

Step-by-step explanation:

(i) 13^3

=  (10+3)^3

=  10^3 + 3^3 + 3(10)(3) (10+3)

=  1000 + 27 + 90(13)

=  1027 + 1170

= 2197

In order for f(x) to be a linear function, determine the value of k in the data set.

x = {-7, -2, 2, 5}

f(x) = {-15, k, 3, 9}

The value of k is {-5}.

Given that to find the value of k in the data set such that the data set represents a linear function.

Linear Function is a straight line on the coordinate plane is represented by a linear function. The formula for a linear function is f(x) = mx + b, where m and b are real values.

Here, f(x) or y is the dependent variable, m is a slope of the line, x is the independent variable and b is the y-intercept.

Here,(x,f(x)) are {(-7,-15),(-2,k),(2,3),(5,9)}

The slope of the function,

(x, f(x)) = (2,3) and (5,9)

Slope formula is m=\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\).

Slope m= \(\frac{9-3 }{5-2}\)

Slope m=\(\frac{6}{3}\)

Slope m=2.

Using the point slope form, determine the linear function's equation.

\(y-y_{1} =m(x-x_{1})\)

Here, \((x_{1},y_{1})=(-7,-15)\) and m=2

We get

y + 15 = 2 (x + 7)

y = 2x - 1

Now at x = -2 and f(x) = k

k = 2(-2) - 1

k = -4-1

k=-5

Therefore, the value of k is -5.

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Answer:

4 times

Step-by-step explanation:

there is 16 cups of water in a gallon

16/4=4

Answer: 0

Step-by-step explanation:

So the slope of a line is equal to rise over run, or the change in x over the change in y. We can solve for the change in x and the change in y by finding their differences. For the math, we use the formulas y2 - y1/x2 - x1. Filling in this formula we get, (5-5)/(3-13), which is equal to 0/10. Because 0 divided by anything is 0, the answer here is 0.

Answer:

Then find the product of the common prime factors. 42 = 2 ⋅3 ⋅7. 70 = 2 ⋅5 ⋅7 ... 6d2 − 21d. 27. 3y3 − 9y2. 28. 20x3 + 30x2. 29.

Answer:

She should use 1.875 cups of sugar

Step-by-step explanation:

Find the ratio by cross multiplying

Answer:

I think it is 0.3

Step-by-step explanation:

Because, 3/4 divided by 2.5= 0.3

Answer:

x≥-16

Step-by-step explanation:

-3/4x≤12

Multiply each side by -4/3, remembering to flip the inequality

-4/3 *-3/4x≥ -4/3 *12

x≥-16

Answer: x ≥ -16

Step-by-step explanation:

Divide both sides by -3/4 to get x alone.

When you divide or multiply both sides by a NEGATIVE, the inequality FLIPS.

-3/4x ≤ 12

Divide both sides by -3/4:

x ≥ -16

Hope this helps!

Answer:

The airspeed is 201.17 mph and bearing is  and this can be determined by using the vector form of velocity

Plane to fly 700 miles due north in 3.5 hours if the wind is blowing from a direction of 338 degrees at 10 ​mph

The number of months at which each swim team has a balance equal to $1200 is; 2 months

We are told that the graph attached shows the amount remaining, y, in dollars, in the accounts for each swim team after x months since the accounts were opened.

Thus;

The x-axis shows the number of months since the accounts were opened for each swim team

The y-axis shows the amount remaining for each swim team after a specific number of months.

Now, we are told to find the number of months at which each swim team has a balance equal to $1200. This point would definitely be the point at which both graphs intersect and as such from the graph it is at x = 2 months.

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Type I error is We conclude that the mean is not 34 years when it really is 34 years. The correct option to this question is C.

Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes.

The significance level you select (alpha or ) determines the likelihood that you will make this mistake. You determined that figure at the start of your research to determine the statistical likelihood of getting your results (p-value).

The typical significance level is 0.05 or 5%. If the null hypothesis is accurate, your results only have a 5% chance or less of occurring.

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The proportion of the variation in the values of a response y that is explained by the least-squares regression of y on x is: square of correlation coefficient.

What is square of correlation coefficient?

A helpful number in linear regression is the square of the correlation coefficient, or r2.

The percentage of the variance in one variable that can be partially explained by another variable is represented by this value.

The summary table in the Regression output contains the "R" value, which is the coefficient of correlation.

Coefficient of determination is another name for R square. To calculate R squared, multiply R by R.

The square of the correlation coefficient is what is meant by the term "coefficient of determination."

Hence, the proportion of the variation in the values of a response y that is explained by the least-squares regression of y on x is: square of correlation coefficient.

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Answer: A. 1120 in³

Step-by-step explanation:

the formula for the volume of the pyramid: \(V=\frac{1}{3} lwh\)

l (length)=16

w (width)=14

h (height)=15

     \(V=\frac{1}{3} lwh\)

     \(V=\frac{1}{3} (16)(14)(15)\)

     \(V=\frac{1}{3} 3360\)

     \(V=1120\)

Answer:

The answer is option A.

Step-by-step explanation:

Hey there!!

Given,

Length (l)= 16 in.

breadth (b)= 14 in.

height (h)= 15 in.

we have,

\(v. of \: pramid = \frac{1}{3} \times a \: of \: base \times height\)

or, volume = {1/3 × (16×14)×15} cubic inch.

by simplifying it we get,

The volume is 1120 cubic inch.

Hope it helps..

Answer:

-5/10 equals to 5/-10 because even though the numerator/denominator is negative, when you simplify -5/10 or 5/-10, it give you -1/2 and 1/-2.

Step-by-step explanation:

The price that maximizes revenue is p = 120.

The price that maximizes revenue, we need to find the value of price (p) that corresponds to the maximum value of revenue (R). Revenue is calculated by multiplying the quantity (q) sold by the price (p), so we can express revenue as R = p × q.

Given the demand function q = -5p + 1200, we can substitute this expression for q into the revenue equation:

R = p × q

R = p × (-5p + 1200)

To find the price that maximizes revenue, we can take the derivative of the revenue function with respect to price (p), set it equal to zero, and solve for p.

dR/dp = -10p + 1200 = 0

Solving this equation for p:

-10p + 1200 = 0

-10p = -1200

p = -1200 / -10

p = 120

Therefore, the price that maximizes revenue is p = 120.

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Answer:

there are 6 trucks

Step-by-step explanation:

hope it will help

The dy/dx of y cos(x) = 4x² + 3y² by implicit differentiation is dy/dx = (8x - y cos(x))/(3y + 2y*cos(x)).


1. Differentiate both sides of the equation with respect to x using the product rule and chain rule.

2. For y cos(x), the derivative is -y sin(x) + cos(x) dy/dx.

3. For 4x² + 3y², the derivative is 8x + 6y dy/dx.

4. Set the derivatives equal: -y sin(x) + cos(x) dy/dx = 8x + 6y dy/dx.

5. Solve for dy/dx by moving all terms with dy/dx to one side: dy/dx (cos(x) - 6y) = 8x + y sin(x).

6. Divide by (cos(x) - 6y) to get dy/dx = (8x - y cos(x))/(3y + 2y*cos(x)).

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The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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Answer: 39 is the answer maybe

Step-by-step explanation:

3 x 2 = 6 + 5 = 11 x -1 = -11 - 24 = -13 x 3 = 39

Answer:

3

Step-by-step explanation:

3x - ( x - 4 ) = 3x + 1

3x - x + 4 = 3x + 1

2x + 4 = 3x + 1

3x - 2x = 4 - 1

x = 3

Hope it will help :)

Answer: 3

Step-by-step explanation:

3x - x + 4=3x+ 1

x = 4 - 1 = 3.