Using the slope formula, find the slope of the line through the given points.
(2,9) and (4,5)
What is the slope of the line? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The slope of the line is
OB. The slope of the line is undefined.
(Type an integer or a simplified fraction.)

The Average value  of the function f(x)=(12)/(x-10) from x=1 to x=7 -2 ln3.

The average value of a function f(x) over the interval [a,b] is given by the formula:

Average value = (1/(b-a)) ∫[a,b] f(x) dx

In this case, the function is f(x) = (12)/(x-10), the interval is [1,7], and we need to find the average value. Plugging in the values into the formula, we get:

Average value = (1/(7-1)) ∫[1,7] (12)/(x-10) dx

Average value = (1/6) ∫[1,7] (12)/(x-10) dx

Next, we need to find the integral of the function. We can use the formula for the integral of a rational function:

∫ (a)/(x-b) dx = a ln|x-b| + C

In this case, a = 12 and b = 10, so the integral of the function is:

∫ (12)/(x-10) dx = 12 ln|x-10| + C

Plugging this back into the formula for the average value, we get:

Average value = (1/6) (12 ln|7-10| - 12 ln|1-10|)

Average value = (1/6) (12 ln|-3| - 12 ln|-9|)

Average value = (1/6) (12 ln|3| - 12 ln|3^2|)

Average value = (1/6) (12 ln|3| - 12 (2 ln|3|))

Average value = (1/6) (12 ln|3| - 24 ln|3|)

Average value = (1/6) (-12 ln|3|)

Average value = -2 ln|3|

Therefore, the average value of the function f(x) = (12)/(x-10) from x = 1 to x = 7 is -2 ln|3|. We can express this as a constant times ln3 by factoring out the ln3:

Average value = -2 ln|3| = -2 ln3

To know more about rational function click on below link:

https://brainly.com/question/20850120#

#SPJ11

The value of the angles in the parallel line is 34 degrees.

When parallel are cut by a transversal line, angle relationships are formed such as corresponding angle, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.

Therefore, the angle 5 can be found using the angle relationship.

Hence,

m∠1 ≅ m∠5(corresponding angles)

Corresponding angles are congruent to each other.

Therefore,

m∠5 = 34 degrees

learn more on angle here: https://brainly.com/question/341040

#SPJ1

So, the final answers are:

a.) f(g(-2)) = 1/3

b.) g(f(1)) = 8

Question 1: Use the following functions to evaluate each expression f(x) = 1/(x + 2) and g(x) = 3x + 7.

a.) f(g(-2)) = f(3(-2) + 7) = f(1) = 1/(1 + 2) = 1/3

b.) g(f(1)) = g(1/(1 + 2)) = g(1/3) = 3(1/3) + 7 = 1 + 7 = 8

So, the final answers are:

a.) f(g(-2)) = 1/3

b.) g(f(1)) = 8

In summary, to evaluate the expression f(g(x)) or g(f(x)), we need to first find the value of the inner function and then substitute it into the outer function. This process is called function composition. It is important to follow the order of operations and simplify the expression as much as possible.

Learn more about Classify the expression

brainly.com/question/13947055

#SPJ11

1- This is a rotation matrix because the determinant is 1 and the transpose is equal to the inverse. 2- The line passing through the origin and the point (1, 1, 1) is the axis of rotation. 3- 120° is the angle of rotation.

1. To show that this is a rotation matrix, we need to check that the matrix satisfies the following properties:
- The determinant of the matrix is 1.
- The transpose of the matrix is equal to its inverse.
The matrix that transforms a vector (x1, x2, x3) into (x2, x3, x1) is:
| 0  1  0 |
| 0  0  1 |
| 1  0  0 |
The determinant of this matrix is:
det = 0×0×0 + 1×1×1 + 0×0×0 - 0×0×1 - 1×0×0 - 0×1×0 = 1
The transpose of this matrix is:
| 0  0  1 |
| 1  0  0 |
| 0  1  0 |
The inverse of this matrix is:
| 0  0  1 |
| 1  0  0 |
| 0  1  0 |
Since the determinant is 1 and the transpose is equal to the inverse, this is a rotation matrix.

2. To find the axis of rotation, we need to find the eigenvector of the matrix corresponding to the eigenvalue of 1. The characteristic equation of the matrix is:
| -λ  1  0 |
| 0  -λ  1 |
| 1  0  -λ | = 0
Expanding the determinant, we get:
-λ × (-λ × (-λ)) - 1 × 1 x 1 = 0
λ = 1
The eigenvector corresponding to the eigenvalue of 1 is:
| -1  1  0 | | x1 | = | 0 |
| 0  -1  1 | | x2 |   | 0 |
| 1  0  -1 | | x3 |   | 0 |
Solving this system of equations, we get:
x1 = x2 = x3
So the eigenvector is:
| 1 |
| 1 |
| 1 |
This means that the axis of rotation is the line passing through the origin and the point (1, 1, 1).

3. To find the angle of rotation, we can use the formula:
cosθ = (trA - 1)/2
Where trA is the trace of the matrix A. The trace of the matrix is:
trA = 0 + 0 + 0 = 0
So the angle of rotation is:
cosθ = (0 - 1)/2 = -1/2
θ = 120°
Therefore, the angle of rotation is 120°.

You can learn more about matrix at: brainly.com/question/28180105

#SPJ11

The area of a triangle with sides \( a=10 \) and \( b=15 \) and included angle 70 degrees is 70.47675 square units.

To find the area of a triangle with sides a and b and included angle C, we can use the formula:

\[Area = \frac{1}{2}ab\sin{C}\]

In this case, we have a = 10, b = 15, and C = 70 degrees. Plugging these values into the formula, we get:

\[Area = \frac{1}{2}(10)(15)\sin{70}\]

\[Area = 75\sin{70}\]

Using a calculator, we find that sin(70) = 0.93969. So:

\[Area = 75(0.93969)\]

\[Area = 70.47675\]

Therefore, the area of the triangle is approximately 70.47675 square units.

Learn more about Area:

https://brainly.com/question/17335144

#SPJ11

The original equations for these two transformed equations can be found by reversing the transformations that have been applied to the standard sine function y = sin(x).

For Equation 1: [tex]y = 3sin(2x-2)[/tex], the original equation is y = sin(x). The transformations that have been applied are a vertical stretch by a factor of 3, a horizontal compression by a factor of 2, and a horizontal shift to the right by 2 units. To reverse these transformations, we would divide the y-values by 3, divide the x-values by 2, and shift the graph to the left by 2 units.

For Equation 2: [tex]y = 4sin(x-1)+3[/tex], the original equation is also y = sin(x). The transformations that have been applied are a vertical stretch by a factor of 4, a horizontal shift to the right by 1 unit, and a vertical shift up by 3 units. To reverse these transformations, we would divide the y-values by 4, shift the graph to the left by 1 unit, and shift the graph down by 3 units.

Therefore, the original equations for these two transformed equations are both y = sin(x).

See more about equation at: https://brainly.com/question/94043

#SPJ11

Answer:

B

Step-by-step explanation:

that means we put -6 into every place, where n is showing in the expression, and then we simply calculate.

cubic root(4n - 3) + n

n = -6

cubic root(4×-6 - 3) - 6 = cubic root(-27) - 6 =

= -3 - 6 = -9

Option b) O x1 =0.99893, x2 -1.00254, x3 =1.00155 is the correct answer. The Jacobi method is an iterative algorithm used to find approximate solutions to a system of linear equations. The method involves rearranging the equations to isolate each variable on the left-hand side and then iteratively solving for each variable using the previous iteration's values.

To begin, we need to rearrange the given system of equations to be diagonally dominant:

3x1 + 10x2 - 4x3 = 201

2x1 + 2x2 + 3x3 = 25

2x1 + 2x2 + 5x3 = 6

Next, we isolate each variable on the left-hand side:

x1 = (201 - 10x2 + 4x3)/3

x2 = (25 - 2x1 - 3x3)/2

x3 = (6 - 2x1 - 2x2)/5

Now, we can begin iterating using the initial values x1 = 1, x2 = 1, and x3 = 1.2:

x1^(1) = (201 - 10(1) + 4(1.2))/3 = 63.8/3 = 21.26667

x2^(1) = (25 - 2(1) - 3(1.2))/2 = 20.4/2 = 10.2

x3^(1) = (6 - 2(1) - 2(1))/5 = 2/5 = 0.4

We then use these new values to calculate the next iteration:

x1^(2) = (201 - 10(10.2) + 4(0.4))/3 = 155.2/3 = 51.73333

x2^(2) = (25 - 2(21.26667) - 3(0.4))/2 = -14.33334/2 = -7.16667

x3^(2) = (6 - 2(21.26667) - 2(10.2))/5 = -53.73334/5 = -10.74667

We continue iterating until the error between iterations is less than 2%. After 12 iterations, we obtain the following approximate solutions:

x1 = 0.99893, x2 = -1.00254, x3 = 1.00155

Therefore, the correct answer using Jacobi method is b) O x1 = 0.99893, x2 = -1.00254, x3 = 1.00155.

Know more about Jacobi method here:

https://brainly.com/question/13567892

#SPJ11

Answer:

3

Step-by-step explanation:

7.2<x+4.2

3<x
x>3
the graph would be

Answer:

its i think algebraic equation

The equation of the circle whose center is (-1, -1) and passes through the point (7, -7) is (x + 1)2 + (y + 1)2 = 100. This can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is √((x2 - x1)2 + (y2 - y1)2). In this case, the distance between the center and the point on the circle is the radius of the circle. So, we can plug in the values for the center and the point on the circle to find the radius:√((7 - (-1))2 + (-7 - (-1))2) = √((7 + 1)2 + (-7 + 1)2) = √(82 + (-6)2) = √(64 + 36) = √100 = 10Therefore, the radius of the circle is 10. Now, we can use the general equation of a circle, (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is the radius, to find the equation of the circle. Plugging in the values for the center and the radius, we get:(x - (-1))2 + (y - (-1))2 = 102(x + 1)2 + (y + 1)2 = 100So, the equation of the circle is (x + 1)2 + (y + 1)2 = 100, which is option a.

Learn more about equation of the circle here: https://brainly.com/question/29288238

#SPJ11

The value of [tex](5 - x)/(2)[/tex] is [tex]2[/tex] when[tex](5x - 1)/(2)[/tex] is equivalent to [tex](3x - 6)/(3)[/tex].

The given expression is [tex](5x - 1)/(2)[/tex] and it can be written in the equivalent form [tex](3x - 6)/(3)[/tex].

To find the value of [tex](5 - x)/(2)[/tex], we can use the property of equivalent fractions, which states that if two fractions are equivalent, then the cross products are equal.

So, we can cross multiply the given equivalent fractions to get:

[tex](5x - 1)(3) = (3x - 6)(2)[/tex]

Simplifying the equation, we get:

[tex]15x - 3 = 6x - 12[/tex]

[tex]9x = 9[/tex]

[tex]x = 1[/tex]

Now, we can substitute the value of x into the expression [tex](5 - x)/(2)[/tex] to find the value of the expression:

[tex](5 - 1)/(2) = 4/2 = 2[/tex]

Therefore, the value of [tex](5 - x)/(2)[/tex] is 2 when [tex](5x - 1)/(2)[/tex] is equivalent to [tex](3x - 6)/(3)[/tex].

See more about equivalent expressions at: https://brainly.com/question/15775046

#SPJ11

Answer: You have to simplify divide by x

Step-by-step explanation:

The time can be obtained from 1/0.042 * ln (p(t)/1000)

An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive constant and x is a variable. The base a is usually a number greater than 1, although it can be any positive number.

Exponential functions have a distinctive characteristic that sets them apart from other types of functions: the value of the function increases or decreases exponentially as the value of x increases or decreases. In other words, the rate of change of the function is proportional to its current value, which results in a rapid growth or decay.

We have that;

p(t) = 1000e^0.042t

p(t)/1000 = e^0.042t

ln (p(t)/1000) = 0.042t

t = 1/0.042 * ln (p(t)/1000)

Learn more about exponential function:https://brainly.com/question/14355665

#SPJ1

Both numbers are divisible by 2, 2 and 7.

What is Greatest Common Factor?

The greatest common factor (GCF) is the largest number that divides two or more numbers evenly. It is also known as the greatest common divisor (GCD) or highest common factor (HCF).

If 28 is the greatest common factor of two numbers, it means that both numbers have 28 as a factor. Thus, both numbers are divisible by 2, 2 and 7.

Additionally, the prime factorization of each number must contain all of the prime factors that are factors of 28, which are 2 and 7. However, there may be other prime factors as well. Without additional information, it is not possible to determine the complete prime factorization of each number.

To learn more about Greatest Common Factor from the given link

https://brainly.com/question/219464

#SPJ1

Answer:

The two teachers are 26 meters apart. To calculate this, you can use the Pythagorean Theorem, which states that the distance between two points is equal to the square root of the sum of the squares of the differences between the coordinates of the two points. In this case, the coordinates of the math teacher are (10, 0) and the coordinates of the science teacher are (0, 24), so the distance between them is the square root of [(10-0)^2 + (0-24)^2] = √(100 + 576) = √676 = 26 meters.

We can use the Pythagorean theorem to solve this problem. Let's draw a diagram:

A (Amy)

/|

/ |

/ |10 meters

/ |

/____|

B C (science teacher)

We have a right triangle ABC, where AB = 10 meters and BC = 24 meters. We want to find the length of AC, which is the distance between the two teachers.

Using the Pythagorean theorem:

AC^2 = AB^2 + BC^2

AC^2 = 10^2 + 24^2

AC^2 = 676

AC = sqrt(676)

AC = 26 meters

Therefore, the two teachers are 26 meters apart.

Answer:

75mm

Step-by-step explanation:

1cm = 10mm
u multiply 7.5 by 10

Answer:75

Step-by-step explanation:

The slope is 3. After 1 second, the car's distance increases by 7 feet.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided, we have the following equation that represents the relationship between distance and time;

y = 3x + 4

At x = 1 second, the distance is given by;

y = 3(1) + 4

y = 3 + 4

y = 7 feet.

Read more on y-intercept here: brainly.com/question/6240745

#SPJ1

The width of the walkway is approximately 0.343 feet or about 4.12 inches.

Let's suppose that the pathway is x feet wide.

The total length of the garden with the walkway is 8 + 2x feet (since there is a walkway on both sides of the garden), and the total width of the garden with the walkway is 12 + 2x feet.

The area covered by the garden and the walkway is the product of the length and width, which is:

[tex](8 + 2x) \times (12 + 2x) = 192[/tex]

Expanding this equation, we get:

[tex]96 + 32x + 16x + 4x^2 = 192\\4x^2 + 48x - 96 = 0[/tex]

Dividing both sides by 4, we get:

[tex]x^2 + 12x - 24 = 0[/tex]

Using the quadratic formula, we get:

x = (-12 ± [tex]\sqrt{ (12^2 - 41(-24))) / (2\times1}[/tex])

x = (-12 ±[tex]\sqrt{(288)) / 2}[/tex])

x = (-12 ± [tex]12\sqrt{(2)) / 2}[/tex]

x = -6 ± [tex]6\sqrt{(2)}[/tex]

Since the width of the walkway cannot be negative, we take the positive value of x:

[tex]x = -6 + 6\sqrt{(2)} \\x= 0.343 feet[/tex]

Therefore, the width of the walkway is approximately 0.343 feet or about 4.12 inches.

for such more question on width

https://brainly.com/question/25855344

#SPJ4

The equation of the line containing points (3,1),(9,3), and (27,9) is y = 0.333x.

We may use the point-slope form of the equation of a line, which is: to determine the equation of a line passing through three specified points.

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is one of the provided locations.

Using any two of the given locations, determine the slope of the line:

m = (y2 - y1) / (x2 - x1) = (3 - 1) / (9 - 3) = 0.333

Choose one of the points, say (3,1), and substitute the slope and coordinates into the point-slope form:

y - 1 = 0.333(x - 3)

Simplify the equation by distributing the 0.333:

y - 1 = 0.333x - 1

Add 1 to both sides:

y = 0.333x

By entering the coordinates of the other two points, (9,3) and (27,9), into the equation and confirming that the left and right sides are equal, you can confirm that the equation also goes through those two places.

For (9,3):

3 = 0.333(9) = 3

For (27,9):

9 = 0.333(27) = 9

Checking the equation also goes through the other two points (9,3 and (27,9) by entering their coordinates into the formula and confirming that the left and right sides are y = 0.333x.

Learn more about the equation of line at

https://brainly.com/question/2564656

#SPJ4

The solutions for the given equations are:

31. x = 4 or x = -2

32. x = 2+√13 or x = 2-√13

33. x = -3+√5 or x = -3-√5

34. x = -0.5+√4.25 or x = -0.5-√4.25

35. x = 1.5+√1.25 or x = 1.5-√1.25

To solve the equations by completing the square, we will use the following steps:

Step 1: Move the constant term to the right side of the equation.

Step 2: Take half of the coefficient of the x term and square it.

Step 3: Add this value to both sides of the equation.

Step 4: Factor the left side of the equation.

Step 5: Take the square root of both sides of the equation.

Step 6: Solve for x.

Let's apply these steps to the given equations:

31. x^2-2x-8 = 0

Step 1: x^2-2x = 8

Step 2: (-2/2)^2 = 1

Step 3: x^2-2x+1 = 9

Step 4: (x-1)^2 = 9

Step 5: x-1 = ±3

Step 6: x = 4 or x = -2

32. x^2-4x-9 = 0

Step 1: x^2-4x = 9

Step 2: (-4/2)^2 = 4

Step 3: x^2-4x+4 = 13

Step 4: (x-2)^2 = 13

Step 5: x-2 = ±√13

Step 6: x = 2+√13 or x = 2-√13

33. x^2+6x+4 = 0

Step 1: x^2+6x = -4

Step 2: (6/2)^2 = 9

Step 3: x^2+6x+9 = 5

Step 4: (x+3)^2 = 5

Step 5: x+3 = ±√5

Step 6: x = -3+√5 or x = -3-√5

34. x^2+x-4 = 0

Step 1: x^2+x = 4

Step 2: (1/2)^2 = 0.25

Step 3: x^2+x+0.25 = 4.25

Step 4: (x+0.5)^2 = 4.25

Step 5: x+0.5 = ±√4.25

Step 6: x = -0.5+√4.25 or x = -0.5-√4.25

35. x^2-3x+1 = 0

Step 1: x^2-3x = -1

Step 2: (-3/2)^2 = 2.25

Step 3: x^2-3x+2.25 = 1.25

Step 4: (x-1.5)^2 = 1.25

Step 5: x-1.5 = ±√1.25

Step 6: x = 1.5+√1.25 or x = 1.5-√1.25

Therefore, the solutions for the given equations are:

31. x = 4 or x = -2

32. x = 2+√13 or x = 2-√13

33. x = -3+√5 or x = -3-√5

34. x = -0.5+√4.25 or x = -0.5-√4.25

35. x = 1.5+√1.25 or x = 1.5-√1.25

Learn more about Completing

brainly.com/question/25108907

#SPJ11

Using quadratic formula we get, Part A: The solutions for x are: x = (3 + √(57))/(3/2) and x = (3 - √(57))/(3/2). Part B: The first system solution is: ((3 + √(57))/(3/2), -(76 + 6√(57))/(9) + 5)  and second system solution is:                                                 ((3 - √(57))/(3/2), -(76 - 6√(57))/(9) + 5)

Part A: To solve for x, we need to first rearrange the equation so that all terms are on one side of the equal sign.  Adding (1/4)x^(2) to both sides of the equation:
-x^(2) + (1/4)x^(2) + 3x + 14 = 5

Next, combining like terms:
-(3/4)x^(2) + 3x + 14 = 5

Now, subtracting 5 from both sides:
-(3/4)x^(2) + 3x + 9 = 0

Finally, using quadratic formula to solve for x:
x = (-3 ± √(3^(2) - 4(-3/4)(9)))/(2(-3/4))

Simplifying:
x = (-3 ± √(57))/(2(-3/4))
x = (-3 ± √(57))/(-3/2)
x = (3 ± √(57))/(3/2)

Part B: To determine the system solutions, we need to plug in the values of x into the original equation and solve for y. For the first solution:
y = -(1/4)((3 + √(57))/(3/2))^(2) + 5
y = -(1/4)((9 + 6√(57) + 57)/(9/4)) + 5
y = -(1/4)((76 + 6√(57))/(9/4)) + 5
y = -(19 + (3/2)√(57))/(9/4) + 5
y = -(76 + 6√(57))/(9) + 5

For the second solution:
y = -(1/4)((3 - √(57))/(3/2))^(2) + 5
y = -(1/4)((9 - 6√(57) + 57)/(9/4)) + 5
y = -(1/4)((76 - 6√(57))/(9/4)) + 5
y = -(19 - (3/2)√(57))/(9/4) + 5
y = -(76 - 6√(57))/(9) + 5

Know more about quadratic formula here:

https://brainly.com/question/1214333

#SPJ11

Answer:  x < -1

Step-by-step explanation:

-4x + 6 > 10

-4x > 10 - 6

-4x > 4

x < 4/-4

x < -1

Answer:

Step-by-step explanation:

[tex]\tt -4x + 6 > 10[/tex]

Subtract 6 from both sides:-

Divide both sides by -4:-

________________________

Hope this helps! :)

To solve the system of linear inequalities, we need to graph each inequality and find the region that satisfies both inequalities.

Here are the steps:
1. Graph the first inequality: -2x-y1. We can rearrange the equation to get y>-2x-1. This means that the region above the line y=-2x-1 is the solution to the first inequality.
2. Graph the second inequality: 3x+y<6. We can rearrange the equation to get y<-3x+6. This means that the region below the line y=-3x+6 is the solution to the second inequality.
3. The solution to the system of inequalities is the region that satisfies both inequalities. This is the region above the line y=-2x-1 and below the line y=-3x+6.
4. To find the coordinates of the vertices of the solution region, we can find the intersection point of the two lines. Setting the two equations equal to each other, we get: -2x-1=-3x+6. Solving for x, we get x=7. Substituting x=7 into one of the equations, we get y=-3(7)+6=-15. So the intersection point is (7,-15).
5. The solution region is the triangular region with vertices at (7,-15), (0,-1), and (2,0).

Therefore, the solution to the system of linear inequalities is the region with vertices at (7,-15), (0,-1), and (2,0).

To know more about linear inequalities refer here:

https://brainly.com/question/11897796

#SPJ11

The series converges.

To test the series 3 + 3/5 + 3/5^2 + 3/5^3 + … =∑n=0[infinity] 3/5^n,

we can use the ratio test.

Specifically, we can look at the ratio of each successive term.

Let an+1/an = 3/5n+1/3/5n = 1/5. Since this is less than 1, the series converges.

Learn more about converges

brainly.com/question/15415793

#SPJ11

Answer:

Step-by-step explanation:

The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it is  114 cm².

The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it can be found by calculating the area of the circle and the area of the square and then subtracting the two.

First, calculate the area of the circle using the formula

A = πr²,

where A is the area and r is the radius.

A = π(10)² = 100π ≈ 314.16 square centimeters

Next, calculate the area of the square. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square. The diameter of the circle is 2r, or 20 centimeters.

Using the Pythagorean theorem, we can find the side length of the square:

s² + s² = (20)²

2s² = 400

s² = 200

s ≈ 14.14 centimeters

The area of the square is s² or (14.14)² ≈ 199.97 square centimeters.

Finally, subtract the area of the square from the area of the circle to find the difference:

314.16 - 199.97 ≈ 114.19 square centimeters

To the nearest whole, the difference in area is 114 square centimeters.

Learn more about circle here:

https://brainly.com/question/10209400

#SPJ11

Simona is left with 7 cups of milk.

What is Mixed fraction?

An example of a mixed fraction is one that consists of both a whole integer and a fractional component. A mixed fraction is, for instance, 3 1/7. It's also known as a jumbled number.

Conversion procedures for a mixed fraction to a simple fraction

Step 1: Multiplying the denominator of the mixed fraction by the whole number component is the first step.

Step 2: To the end result achieved in Step 1, add the numerator.

Step 3: Format the improper fraction in numerator/denominator form using the sum from step 2 as the denominator.

Simona has 8 3/4 cups of milk .

She uses 1 1/2 cups of milk to make the cake and 1/4 cup of the milk to make frosting for the cake.

So, cups of milk left = total cups of milk - cups of milk used for cake

                                = 8 3/4 - 1 1/2 - 1/4

                                = 35/4 - 3/2 - 1/4

                                = (35 - 6 - 1)/4

                                = 28/4

                                = 7 cups of milk.

To learn more about Fractions, visit the link:

https://brainly.com/question/78672

#SPJ1

The value of x, considering the angle addition postulate, is given as follows:

x = -5.

The angle addition postulate states that if two angles share a common vertex and a common angle, forming a combination, the larger angle will be given by the sum of the smaller angles.

The larger angle in this problem is QRS, hence the equation to obtain the value of x is given as follows:

3x + 93 + 66 + x = -x + 134

4x + 159 = -x + 134

5x = -25

x = -25/5

x = -5.

More can be learned about the angle addition postulate at https://brainly.com/question/24782727

#SPJ1

An equation in slope-intercept form is y = -7x + 12.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (2, -2), an equation of this line can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-2) = (-9 - (-2))/(3 - 2)(x - 2)

y + 2 = (-9 + 2)/(3 - 2)(x - 2)

y = -7x + 14 - 2

y = -7x + 12

Read more on slope here: brainly.com/question/3493733

#SPJ1

Answer:

Let q be the number of quarters in the jar and d be the number of dimes in the jar.

The total number of coins in the jar is given as 54, so we can write:

q + d = 54

The total value of the coins is $16.85. We can express this as the sum of the values of the quarters and the dimes in the jar:

0.25q + 0.10d = 16.85

Therefore, the system of equations that can be used to determine the number of quarters and dimes in the jar is:

q + d = 54

0.25q + 0.10d = 16.85