For the pair of similar solids, find the value of the variable



A 12 mm

B 48 mm

C 20 mm

D 3 mm

The slope on the line containing the points (14,-42) is 1.06, as stated in the preceding sentence (-48,24).

The % slope is calculated by multiplying the distance between two locations by the differences in elevation above them. The difference in height between two places is referred to as "rise." The distance between it sites is known as the run. Therefore, the formula for percent slope is (rise / run) x 100.

The slope's formula is as follows:

m = (y₂-y₁)/x₂-x₁)

In the formula, replace the point values as follows:

m = (24-(-42))/(-48-14)

Make the fraction simpler:

m = (24-(-42))/(-48-14)

m = 66/-62

m = 1.06

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Answer:

C

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

B (3, 8 ) → B' (3, - 8 )

Answer:

[tex]10^{\circ}[/tex]

Step-by-step explanation:

Supplementary angles have measures that add to [tex]180^{\circ}[/tex].

The length of the hypotenuse of a right triangle with legs measuring 20 inches and 28 inches is approximately 34.4 inches, found using the Pythagorean theorem.

The length of the hypotenuse of a right triangle with legs measuring 20 inches and 28 inches can be calculated using the Pythagorean theorem, which states that the square of the sum of the squares of the lengths of the legs determines the length of the hypotenuse.

So, if we call the length of the hypotenuse "h", we have [tex]h^{2}[/tex] = [tex]20^2 + 28^2[/tex]

Solving for h:

[tex]h^2 = 20^2 + 28^2[/tex]

[tex]h^2[/tex] = 400 + 784

[tex]h^2[/tex] = 1184

h = [tex]\sqrt{1184}[/tex]

h ≈ 34.4 in.

So, the length of the hypotenuse is approximately 34.4 inches, rounded to the nearest tenth.

The Pythagorean theorem is a fundamental mathematical relationship that states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal tothe squared lengths of the two legs added together. In this case, the two legs have lengths of 20 inches and 28 inches, and the length of the hypotenuse can be found by solving for the square root of the total of the leg squares.

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Answer:

Step-by-step explanation:

To determine whether a value is greater than or less than a specific result from an equation, you would need to substitute the value into the equation and solve for the result. For example, if you want to determine if the value "a" is greater than or less than the result of the equation -2x^2 + 16x - 36, you would substitute "a" for the variable x and solve for the result:

-2x^2 + 16x - 36 = -2a^2 + 16a - 36

Then you can compare the value of the result to "a" to determine whether it is greater than or less than.

If the result is greater than "a", you would write:

-2a^2 + 16a - 36 > a

If the result is less than "a", you would write:

-2a^2 + 16a - 36 < a

And if the result is equal to "a", you would write:

-2a^2 + 16a - 36 = a

It's important to note that the comparison only holds for a specific value of "a". The equation -2x^2 + 16x - 36 could have many solutions where the result is greater than, less than, or equal to "a".

As per unitary method, Reeta's salary is 21,000 rupees.

The unitary method is a technique of solving problems by assuming a unit value and then finding out the required value in terms of that unit.

In this problem, we can assume Reeta's salary to be the unit value and then find out how much she spent on car repair work and how much money she has left using this unit value.

Let's assume Reeta's salary to be x rupees. Now, according to the problem, she has spent 2/7 of her salary on car repair work. So, the amount of money she spent on car repair work can be calculated as:

2/7 * x

Using the unitary method, we can now find out how much money she has left with her. We know that she has 15,000 rupees left. So, we can set up the following proportion:

2/7 * x = x - 15,000

Simplifying this equation, we get:

2x = 7(x - 15,000)

2x = 7x - 105,000

5x = 105,000

x = 21,000

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The equations x° + 65° = 180°, x° = z° and y° = 65° are true for the values of x, y and z. The solution has been obtained by using angles and line.

What are angles and line?

Straight lines with little depth or width are present. There are many different types of lines, including perpendicular, intersecting, transversal, etc. A figure called an angle is one in which two rays originate from the same point.

We are given that 2 lines intersect to form 4 angles which are 65°, x°, y°, z°.

1. x° + 65° = 180°

We know that angles on a straight line form a linear pair i.e. their sum is 180°. So, this statement is true.

2. x° = z°

We know that vertically opposite angles are equal. So, x° will be equal to z°. Thus, this statement is true.

3. y° = 65°

We know that vertically opposite angles are equal. So, y will be equal to 65°. Thus, this statement is true.

4. x° = 65°

This statement is false because these are the angles on a straight line which must add up to 180°.

5. x° + y° + z° = 115°

We know that angles in a circle add upto 360°. We know one angle as 65°. So, the remaining angles should add upto 295°. Thus, the statement is false.

Hence, the equations x° + 65° = 180°, x° = z° and y° = 65° are true for the values of x, y and z.

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Question: Which equations are true for the values of x, y, and z? Select three options.

2 lines intersect to form 4 angles as shown in the figure. Clockwise, from top, the angles are: 65 degrees, x, y, z.

x degrees + 65 degrees = 180 degrees

x degrees = z degrees

y degrees = 65 degrees

x degrees = 65 degrees

x degrees + y degrees + z degrees = 115 degrees

Answer:

Step-by-step explanation:

So first what you got to do is add and mulytplie

A polynomial term is an expression composed of constants, variables, and exponents.

A polynomial term is an expression composed of constants, variables, and exponents. Constants are the numerical values that don't change, while variables are values that can change. Exponents are numbers that indicate how many times a number is multiplied by itself. For example, 2^3 means 2 multiplied by itself 3 times, or 8. A polynomial term is an expression that combines constants, variables, and exponents, such as 6x^2 - 3x + 5. In this expression, 6, -3, and 5 are constants, x is a variable, and 2 and 1 are exponents. A polynomial term can also contain fractions, such as (2x + 1)/3. In this case, 2, 1, and 3 are constants, and x is a variable. Polynomial terms are the building blocks of polynomials, which are equations that consist of multiple polynomial terms.

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1) The mean of the data is 4.45.

2) The mode of the data is 11.

3) The median of the data is 4.

The mean of the data is the ratio of the sum of the given data and the number of the count of the data.

The mode of the data is the number that is repeated maximum number of times. The median of the data is when the data is arranged in an increasing order then the middle most value will be the median of the data.

Given data is 6 11 5 11 4 0 2 0 1.

The mean of the data is,

Mean =  ( 6 + 11 + 5 + 11 + 4 + 0 + 2 + 0 + 1 ) / 9

Mena = 4.45

Mode = 11

Median:- 0,0,1,2,4,5,6,11,11

Median = 4

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The slope of the line that models this situation is equal to 2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (0, 8).

Points on y-axis = (4, 20).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (20 - 4)/(8 - 0)

Slope, m = 16/8

Slope, m = 2.

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Answer:

62 Feet

Step-by-step explanation:

26+36=62

6 + 6 = 12

20 + 30 = 50

12 + 50 = 62

Answer:

The scuba diver is 62 feet deep.

Step-by-step explanation:

We know the scuba diver has dived 36 feet. When he stops to look at the school of fish, he doesn't dive down any further and stays at 36 feet. He then dives down another 26 feet

All we would need to do is add 36 and 26, which would give you your answer of 62.

Answer:

Your answer is: C) 400

Step-by-step explanation:

There are 6,720 possible ways to arrange the committee in a row, with students grouped by grade.

2 seniors * 5 sophomores * 3 freshman * 2 juniors = 60

60 possible arrangements for the 4 grade levels

60 * 6 (the number of ways to arrange 6 people) = 360

360 * 6 (the number of ways to arrange 6 people) = 2160

2160 * 6 (the number of ways to arrange 6 people) = 12,960

12,960 / 2 (because the order of the two grade levels can be reversed) = 6,720

6,720 possible arrangements for the school dance committee.

The school dance committee is made up of 3 freshman, 5 sophomores, 2 juniors, and 2 seniors. To find out how many ways there are to sit the committee in a row at a meeting if the students must sit together by grade, we first need to calculate the number of possible arrangements for each grade level. Since there are 2 seniors, 5 sophomores, 3 freshman, and 2 juniors, there are 60 possible arrangements for the 4 grade levels. We then multiply this by 6, since there are 6 ways to arrange 6 people. This gives us 360 possible arrangements for the first two grade levels. We then multiply this number by 6 again, since there are 6 ways to arrange 6 people. This gives us 2160 possible arrangements for the first three grade levels. We multiply this number by 6 one more time, since there are 6 ways to arrange 6 people. This gives us 12,960 possible arrangements for all four grade levels. However, since the order of the two grade levels can be reversed, we must divide this number by 2. This gives us a total of 6,720 possible arrangements for the school dance committee.

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We can rewrite ln(27000) in terms of ln(5) and ln(6) as ln(27000) = 3ln(5) + 3ln(6) by using logarithmic property.

Due of their connection to exponential functions, logarithmic functions are crucial. Logarithms can be used to examine exponential equations and the properties of exponential functions.

We can use the logarithmic property that says:

log_a(xⁿ) = n×log_a(x)

to break down 27000 into factors that involve 5 and 6.

First, we can write:

27000 = 5³× 6³

When we take the natural logarithm of both sides, we obtain:

ln(27000) = ln(5³ × 6³)

Using the property above, we can simplify this expression as:

ln(27000) = ln(5³) + ln(6³)

Using another logarithmic property that says:

log_a(bⁿ) = c×log_a(b)

we can further simplify the expression:

ln(27000) = 3ln(5) + 3ln(6)

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The length of earthworm will be 4 cm after 4 hours. And the length is 14 cm after 49 hours.

Proportions are defined when two or more ratios are made to be equal to each other.

Two quantities are said to be directly proportional if a positive change in one quantity also lead to a positive change in the other quantity.

If a is proportional to b, we denote it as a ∝ b.

Given,

Length of an earthworm, l ∝ square root of the number of hours, n, which have elapsed since it's birth.

l ∝ √n

l = k √n, for some constant k.

If a worm is 2 cm long after 1 hour, we can write it as,

2 = k × √1

⇒ k = 2

So the proportionality constant is 2.

After 4 hours,

l = k √4

l = 2 × 2 = 4 cm

If the length is 14 cm,

14 = 2 √n

√n = 14 / 2

√n = 7

n = 7² = 49 hours

Hence the length of worm is 4 cm after 4 hours. It will take 49 hours to grow to a length of 14 cm.

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Answer:

(36/5)

Step-by-step explanation:

y=x^2+36/5

Since x is squared, the result will always be a positive number, regardless of the actual value of x.  Starting with a value of x of zero, the x^2 term will only grow as one moves away from 0.  E.g., (-1)^2 = 1, (-2)^2 = 4, etc.

So the minium for this equation will occur when x = 0.  It only gets larger from that point.  The minimum is (36/5).

See the attached graph.

Boole. K-map stands for Karnaugh Map and is used to simplify and minimize the expression of logic in a similar form to algebra.

George Boole is the mathematician we honor for discovering ways to express and minimize logic through a new but similar form of algebra. The technique used to simplify and minimize these expressions is known as a Karnaugh Map, or K-map for short. A K-map is a visual representation of a Boolean expression using squares and circles to represent true or false variables in a table. By arranging the variables in the table, the same logic can be expressed in a simpler form with fewer variables. This allows for a simpler and more efficient form of logic expression. K-maps are used in many fields, such as digital logic design, where the efficiency of expression is important.

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Answer:

400 calories

Step-by-step explanation:

Let's call the number of calories in the loaded baked potato as P. Then the coleslaw had P-50 calories and the steak had 2P calories.

So the equation for the total number of calories in the meal is:

P + (P-50) + 2P = 1550

4P = 1600

P = 400

Therefore, the loaded baked potato had 400 calories.

Answer:

Below

Step-by-step explanation:

c oleslaw =   p - 50

p = potato

s = 2 p       Summed these = 1550

p-50     + p    + 2p   =  1550      Gather 'like' terms

4p - 50 = 1550                           add 50 to both sides of the equation

4p = 1600                                  divide both sides by 4

p = 400 calories

The explicit formula for the geometric series is [tex]a_n = 3(5)^{n-1}[/tex].

A geometric series is one in which there is a constant separating the two succeeding numbers. In other words, to create a geometric progression, each succeeding term is multiplied by the constant term.

Given that the geometric sequence is,

3, 15, 75......

The common ratio of the series is calculated as the ratio of the second term to the first term,

r = 15 / 3

r = 5

The explicit formula can be written as:-

[tex]a_n = a_1(r)^{n-1}[/tex]

[tex]a_n = 3(5)^{n-1}[/tex]

Therefore, the formula is [tex]a_n = 3(5)^{n-1}[/tex].

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Answer:

y=7x-8

Step-by-step explanation:

You start off with the equation y= mx+b, where m = the slope (7/1) and b, which is (0,-8). Then you can graph. You first put a dot at (0,-8). Then you count up to 7 and then go to the right 1. You continue the pattern until the line is over the graph. The equation would be y= 7x-8

The answer option which is not a characteristic of a plane include the following: C. thickness.

In Mathematics, a plane is sometimes referred to as a two-dimensional surface and it can be defined as a flat, two-dimensional surface with zero curvature and zero thickness, that extends indefinitely (infinitely). Additionally, two (2) planes intersect at a line.

Generally speaking, there are different characteristics of a plane and these include the following:

In this context, we can reasonably infer and logically deduce that thickness is not a characteristic of a plane.

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Complete Question:

Which of the following is NOT a characteristic of a plane?

A. length

B. flat surface

C. thickness

D. width

Cases are on display OA 619,200 cubic inches.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.
To calculate the number of cubic inches needed for 360 cases of 12-ounce cans of soft drink, we need to multiply the number of cases (360) by the volume of each case. The volume of each case can be calculated by multiplying its length (16 inches), width (10.75 inches) and height (5 inches):

Volume = 16.00 inches x 10.75 inches x 5.00 inches = 828 cubic inches

Therefore, 360 cases of 12-ounce cans of soft drink require (360 x 828) = 619,200 cubic inches.

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15 liquids that can be found in a kitchen include:

15 solids in a kitchen are:

When it comes to solids in the kitchen, we can mostly find either food ingredients, such as salt, flour, and spices, or actual food that can be prepared such as meat, vegetables, and bread.

As for liquids, these can be anything from drinks such as juice, water and wine, to liquids used for cooking such as oil, soy sauce and vinegar.

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The value of the missing side of the given triangle would be = 12

To calculate the value of the missing length the Pythagorean formula can be used such as;

c² = a² + b²

where;

C =?

a = 11

b = 5

C² = 11²+5²

= 121 + 25

= 146

C =√ 146

C = 12

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Answer:

Step-by-step explanation:

Mariana's quote: 135

Vicent's quote: 34x+67

Say x=1, 34(1)+67=101

For 1 hour of Vincent's work it would be $101.

Say x=2. 34(2)+67=135

Vincent would have to work for two hours to charge the exact same as Mariana.

The correct quadratic equation that can be used to determine the thickness of the frame, x, is: 2x² + 10x - 7 = 0, Therefore Option B is the right answer

Here's how we can get this equation:

We are given that the mirror and frame together have an area of 7 square feet. The mirror itself has an area of 2 x 3 = 6 square feet. So, the area of the frame is 7 - 6 = 1 square foot.

Let's assume that the width of the frame is x feet. Then the overall width of the mirror and frame becomes 2 + 2x, and the overall length becomes 3 + 2x. The area of the mirror and frame can be expressed as:

(2 + 2x)(3 + 2x) = 6 + x(10 + 4x)

We know that this expression equals 7, so we can set it equal to 7 and obtain the quadratic equation:

2x² + 10x - 7 = 0

Therefore, the correct quadratic equation is 2x² + 10x - 7 = 0.

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Matrix A is: A = [1 2 3] and Matrix B is: B = [1]

                         [2 4 6]                                 [2]

                         [1 1 1]                                    [3]

An example of a 3x3 matrix A and a 3x1 matrix B such that the solution set of Ax = b is a line in R³ that does not contain the origin:

A = [1 2 3]

   [2 4 6]

   [1 1 1]

B = [1]

   [2]

   [3]

To check that the solution set of Ax = b is a line in R³, we can solve for x in terms of a parameter t:

Ax = b

[1 2 3] [x1] = [1]

[2 4 6] [x2]   [2]

[1 1 1] [x3]   [3]

Ax = b

x1 + 2x2 + 3x3 = 1

2x1 + 4x2 + 6x3 = 2

x1 + x2 + x3 = 3

Dividing the second equation by 2 and subtracting it from the first equation, we get:

-x1 - x2 = -1

Solving for x2 in terms of x1 and x3, we get:

x2 = -x1 + 1 - (3/2)x3

Solving for x3 in terms of a parameter t, we get:

x3 = t

Then, x1 can be expressed in terms of t as:

x1 = -t + 1

Therefore, the solution set of Ax = b is:

x = [-t + 1]

   [-t + 1 - (3/2)t]

   [t]

which is a line passing through the point (1, 1/2, 0) with a direction vector [-1, -3/2, 1].

A × [0; 0; 0] = [0; 0; 0]

Therefore, the origin is not on the line of solutions.

So, Matrix A is:

A = [1 2 3]

     [2 4 6]

      [1 1 1]

and Matrix B is:

B = [1]

     [2]

     [3]

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Answer:

27 children.

Step-by-step explanation:

Let's call the number of children who chose apples x. Then, the number of children who chose bananas is 0.25x. The number of children who chose watermelon is 60 - x - 0.25x = 60 - 1.25x.

Since 30% of the children chose apples, we know that:

0.30 * 60 = x

So, x = 18, which means 18 children chose apples.

And since 25% of the children chose bananas, we know that:

0.25 * 60 = 0.25x = 15

So, 15 children chose bananas.

Finally, the number of children who chose watermelon is:

60 - 18 - 15 = 27 children.