Select the expressions that are equivalent to 4(5q+6)+7q

Answer:

Please check the explanation.

Step-by-step explanation:

Given

ABC ↔ RQP

It means

Please check the attached diagram.

Here,

Parts of ΔABC that correspond to

(i) PQ

From the diagram, it is clear that:

PQ corresponds to CB

(ii) ∠Q

∠Q corresponds to ∠B

(iii) RP

RP corresponds to AC

According to the table, there are no entries for how many students in the seventh grade bike to school. The only data given is that 79 seventh-grade students take the bus and 128 seventh-grade students get to school by some means other than biking or taking the bus.

Therefore, we cannot determine from this table how many students in the seventh grade bike to school.

Step-by-step explanation:

To check if the given function is continuous or not at a particular point, we have to follow the given continuity checklist:

The function should be defined at that point.

Check the limit of the function at the given point, if it exists.

Check if the function value is equal to the limit value at the given point.

If the above conditions are satisfied, then the function is continuous at that point.

\(f(x) = 1 / (x-20); a = 20\)

To check whether the given function

\(f(x) = 1 / (x-20); a = 20\)  is continuous or not at a = 20, we have to use the given continuity checklist.

1) Check if the function is defined at x = 20.

The given function is defined at x = 20.2) Check the limit of the function at x = 20.

Limit of the function, as\(x → 20:f(x) = 1 / (x - 20)lim_{x \to 20} f(x) = lim_{x \to 20} 1 / (x - 20)\)

Here, we can directly substitute x = 20. Hence, we get:\(lim_{x \to 20} f(x) = 1 / (20 - 20)lim_{x \to 20} f(x) = 1 / 0\)

The limit value does not exist, and hence the function is not continuous at x = 20.

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answer is 2.

x is divided by 28 and 7 is divided by x

after that cut 28 by 7

and the anwer will be x square = 4

and the square will go to 4

and four will be root 4

and the answer will be x = 2

Answer: 75

Step-by-step explanation:

Answer:

Step-by-step explanation:

The percentage increase from x to 5x is given by the equation P = 400 %

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the percentage increase be P

Now , the equation will be

Let the original value be = A

The value of A = x

Now , the increased value = B

The value of B = 5x

And , the percentage increase is given by the equation ,

P = ( ( Increased value - Original value ) / Original value ) x 100 %

Substituting the values in the equation , we get

The percentage increase P = ( ( 5x - x ) / x ) × 100 %

The percentage increase P = ( 4x/x ) × 100 %

The percentage increase P = 4 x 100 %

The percentage increase P = 400 %

Therefore , the value of P is 400 %

Hence , The percentage increase from x to 5x is 400 %

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Vocabulary:

Graph: A visual representation of data.

Data: Gathered information.

Situated Problem:

Graph: \(y=\sqrt[3]{x} -2\)

The correct labels are matched to their appropriate locations on the graph as shown in the image attached below.

A graph refers to a type of chart that's used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

In this exercise, you're required to drag the correct labels to their appropriate locations on the graph as shown in the image attached below.

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Part A:

According to a life cycle analysis of the U.S. food system conducted by the University of Michigan, the U.S. consumes 13.9 quads of mostly fossil fuel energy to produce 1.75 quads of food energy annually. A quad is a unit of energy equal to 1 quadrillion (10¹⁵) British thermal units (BTUs). One quad is equal to the energy of 183 million barrels of petroleum.

The margin of error can be calculated using the formula:
Margin of error = (upper limit of the confidence interval - lower limit of the confidence interval) / 2

In this case, a margin of error of 9.55 suggests that the sample mean is quite precise, since it's relatively close to the true population mean (which we know to be 52.90).

In this case, the lower limit of the confidence interval is 43.85 and the upper limit is 61.95.
Margin of error = (61.95 - 43.85) / 2
Margin of error = 9.55
Therefore, the margin of error is 9.55. This means that if the sample size were to be repeated, we would expect the sample mean to be within 9.55 units of the true population mean 95% of the time.
It's worth noting that the confidence interval provides a range of values within which we can be reasonably certain that the true population mean lies. The margin of error, on the other hand, gives us an indication of the precision of our estimate. However, if the margin of error were larger, this would indicate that our estimate is less precise and that we need a larger sample size to obtain a more accurate estimate of the population mean.

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Answer:

5

Step-by-step explanation:

the image shows VW and SR to be congruent therefore the difference is 10 between the sizes. to find SP you subtract 10 from TW

15 - 10 = 5

Step-by-step explanation:

To figure out how much smaller Max's sandbox is, we will divide 25 by 10, 25/10 = 2.5. Max's sandbox is 2.5 times smaller than the one in the park.

To find x we will divide 15 by 2.5 to keep the proportions the same, 15/2.5 = 6, so x = 6 feet.

To find y, we will do the same but with 12.5, 12.5/2.5 = 5, so y = 5 feet.

To find the perimeter, we will add all the sides together, 10 + 6 + 5 = 21, so the perimeter of Max's sandbox is 21 feet.

Hope this helps!

Yes, the function f(x) = x / (x + 2) satisfies the hypotheses of the mean value theorem on the given interval [1, 4]. This is because f is continuous on [1, 4] and differentiable on (1, 4).

Given f(x) = x/ x + 2

We are asked to check whether the function satisfies the hypotheses of the mean value theorem on the given interval [1, 4].

Mean Value Theorem: If f(x) is continuous on the closed interval [a, b] and is differentiable on the open interval (a, b), then there exists a number c in (a, b) such that: f(b) − f(a) / b − a = f'(c)

For the given function, we have the interval [1, 4]. The function is continuous on [1,4].

Also, the function is differentiable on (1,4).

Therefore, the given function satisfies the hypotheses of the mean value theorem on the given interval [1, 4]. Hence, the correct option is Yes, f is continuous on [1,4] and differentiable on (1,4).

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The justification for each step in the flowchart proof is given as:

A. given

B. definition of congruent

C. definition of bisect

A segment that divides an angle into two equal halves is known as an angle bisector.

In the image attached below, we want to prove that BC is an angle bisector of angle ABD.

The following justofy each step in the flowchart proof:

m∠ABC ≅ ∠CBD (given)

m∠ABC ≅ ∠CBD (definition of congruent)

BC bisects ABD (definition of bisect)

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Answer:

Step-by-step explanation:

Answer:

96 tiles

Step-by-step explanation:

The kitchen floor is rectangular on shape.

The dimensions of the kitchen floor were 8 feet by 12 feet.

Hence, Area of a rectangle = Length × Width

Length = 8ft

Width = 12ft

Hence:

Area = 8ft × 12ft

= 96 ft²

If each tile was 1 square foot, the number of tiles he would need is

1 ft² = 1 tile

96 ft² = x

Cross Multiply

1ft² × x = 96 ft² × 1 tile

x = 96 ft² × 1 tile/1 ft²

x = 96 tiles

Therefore, Mark's father would need 96 tiles

Answer:

r=3.10in

SA= 138.22 in square

Step-by-step explanation:

Given data

Volume = 121 in^3

Height= 4 in

a) What is the radius of the cylinder?

 We know that volume

 V=πr^2h

121= 3.14*r^2*4

121= 12.56r^2

121/12.56= r^2

9.63=r^2

r= √9.63

r=3.10in

b) What is the surface area of the cylinder? Give your answer in terms of īt.

The surface area of cylinder is expressed as

SA=2πrh+2πr^2

SA= 2*3.14*3.1*4+ 2*3.14*3.1^2

SA= 77.872+60.3508

SA= 138.22 in square

Answer:

X = savings, p= pay per hour

X+4p = 86 - - - - (1)

X+6p=104 - - - - - (2)

Re arrange equation (1)

X=86-4p-----(3)

Substitute (3) in (2)

86-4p +6p=104

86+2p=104. (subtract 86 from both side)

2p = 18. (divide by 2 from both side)

Then p =$9

By substitute in equation (1)

X = $50

Answer:

To solve for x in the equation 45x+225=1060, we can use algebraic manipulation.

First, we can subtract 225 from both sides of the equation to isolate the variable term on the left side:

45x + 225 - 225 = 1060 - 225

Simplifying both sides:

45x = 835

Finally, we can solve for x by dividing both sides of the equation by 45:

45x/45 = 835/45

Simplifying:

x = 18.56

Therefore, the value of x is approximately 18.56 when rounded to two decimal places.

Step-by-step explanation:

Answer:

The answer is 13/4

Step-by-step explanation:

I divides and cross miltiplied.

The slope of an angle 30 which in the positive x direction is tanФ = tan30= 1/√3

Slope:

Slope describes the steepness of a line and it also remains constant with the line it also gives us information about the direction. If the slop is negative then the line will be in the negative x-axis if the slop is positive the line will be in the positive x-direction.

A slope of a line is the change in the y coordinate w.r.t the change in the x coordinate.

m = Δy/Δx

m=tan θ = Δy/Δx

m=tan 30 = 1/\(\sqrt{3}\)

Therefore the slope of a line that makes an angle of 30 with the positive x direction will be 1/√3

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Answer:

7. divide both sides by 18.

8. subtract 4 from both sides.

9. add 3 on both sides.

10. multiply by 6 on both sides

Hope that helps! :3

Step-by-step explanation:

A total of 24 boxes of paper were shipped weighing 1410 pounds altogether, the system of equations are  X + Y =  24, and 45X + 75Y  = 1410 and the variables that you use to write the system X = 13 and Y = 11.

The primary unit of sterling is the pound (sign: £), while the term "pound" is also frequently used to refer to the British pound or pound sterling in foreign settings.

The oldest currency that is still in the circulation and has been used continuously since its origin is sterling. After US dollar, euro, and Japanese yen, it is currently fourth most traded currency on the foreign exchange market. It makes up basket of currencies used to determine the value of IMF special drawing rights along with the other three currencies and the renminbi. Sterling is also fourth-most-held reserve currency in the world's reserves as of mid-2021.

Let X equal  number of small boxes

Let Y equal number of big boxes

The first equation is:  X + Y =  24     ( this shows that total number of boxes = 24)

The second equation is:    45X + 75Y  = 1410    ( this is because small box weighs 24 pounds and big box weighs 75 pounds.  The total weight of small boxes is 45 times weight of each individual box. And the total weight of second boxes is equal to 75Y.  

When you solve system,  X = 13 and Y = 11

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Answer:

i think 31

Step-by-step explanation:

y^2 - 3y + 12 is a trinomial with a degree of 2, also known as a quadratic trinomial.

The given polynomial y^2 - 3y + 12 is a trinomial with a degree of 2. A polynomial is a mathematical expression that contains one or more terms involving variables and coefficients. In this case, there are three terms: y^2, -3y, and 12. A binomial is a polynomial consisting of two terms, while a trinomial has three terms. Therefore, y^2 - 3y + 12 is a trinomial.

The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the highest exponent of y is 2, so the degree of the polynomial is 2. This degree is also known as the quadratic degree.

It is important to identify the number of terms and degree of a polynomial when solving equations or simplifying expressions involving polynomials. Additionally, the properties of polynomials, such as factoring and graphing, are also influenced by these characteristics.

In summary, y^2 - 3y + 12 is a trinomial with a degree of 2, also known as a quadratic trinomial.

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Answer:

C.) the quantitnes are equal

Step-by-step explanation:

The largest area is 8.978 unit²

Given:

A rectangle is to be inscribed under the arc of the curve y = 4cos(0.5x)

from x = -π to x = π.

it is clear that the coordinates of the rectangle are

(−x,0),(x,0),(−x,4cos(0.5x)) and (x,4cos(0.5x)) where x∈(−π,π)

Thus, the area of the rectangle is

A =2x(4cos(0.5x))=8xcos(0.5x)

Now, find the value of x for which the area is largest by using derivative tests.

Differentiate A with respect to x,

A′=8(1(cos(0.5x))+x(−(0.5)sin(0.5x)))=8cos(0.5x)-4xsin(0.5x)

Now, find critical values by putting A′=0,

A′=0

8cos(0.5x)−4xsin(0.5x)=0

8cos(0.5x)=4xsin(0.5x)

2=xtan(0.5x)

Use the graph utility to get,

x≈1.721

At x=1.721, A'′<0. So, the area is largest at x=1.721.

Therefore, the dimensions of the rectangles will be:

Length will be:

2x=2(1.721)=3.442unit.

Width will be:

4cos(0.5x)=4cos(0.5(1.721))=2.608unit.

And the area will be:

A=8xcos(0.5x)

=8(1.721)cos(0.5(1.721))

=8.978 unit²

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Answer:

For the top half add all of the numbers of a given set together, then divide by how many numbers there are.

1.) 9

2.) 7

3.) 4

4.) 3

5.) 47.5

6.) 67 1/3

For the bottom half questions, literally the same thing.

7.) 9

8.) 34

9.) 66

10.) -28

11.) -21

12.) 3

Step-by-step explanation:

your welcome for doing you 2 minute homework

Answer:

86

Step-by-step explanation:

Answer:

The answer is 11.401754

Answer: Approximately 11.4 units

================================================

Work Shown:

(x1,y1) is the first point (-6,-2)

(x2,y2) is the second point (5,1)

Apply the distance formula

\(d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(-6-5)^2+(-2-1)^2}\\\\d = \sqrt{(-11)^2+(-3)^2}\\\\d = \sqrt{121+9}\\\\d = \sqrt{130}\\\\d \approx 11.4017542509913\\\\d \approx 11.4\\\\\)

The distance between the two points is roughly 11.4 units.