How many pairs of parallel edges are there in a rectangular prism

Answer:

24

Step-by-step explanation:

We will use the proportional concept to solve it.

So, 6/13 = x/52

x = 6*4

x = 24

So, height of tree is 24 feet

y = f(x+2) -1 is the equation which describes the graphed function.

Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same. In mathematics, a translation is the up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered.

Given,

When F crosses the x-axis when it is negative.

-1 indicates a 1 unit down translation.

So, the equation will be y = f(x+2) -1.

y = f(x+2) -1 is the equation which describes the graphed function.

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The domain of the functions F(x)=|x|, g(x)=x+9, f o g is x ∈ R the functions exist for all real numbers.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The function f(x):

f(x) = |x|

The domain of the function is:

x ∈ R

g(x) = x + 9

The domain of the function:

x ∈ R

f o g = f(g(x)) = |x + 9|

The domain of the function f o g is x ∈ R

Thus, the domain of the functions F(x)=|x|, g(x)=x+9, f o g is x ∈ R the functions exist for all real numbers.

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the sum of the internal angles of the 4-sided polygon is 360, therefore

then

answer: a. y = 116° and z = 61°

ANSWER

EXPLANATION

Two lines are perpendicular if they have opposite reciprocal slopes. So, to find the line, first, we have to find the slope of the line tangent to the graph of y = 1/x at x = 2. To do so, we have to find the derivative of the function and evaluate it at x = 2. That is the slope of the tangent line at that point.

The derivative of the function is,

So, the slope of the tangent line at x = 2 is,

Therefore, the slope of the perpendicular line is the opposite reciprocal,

So we have that the perpendicular line we are looking for is,

We have to find the y-intercept, b. We know that this perpendicular line intersects the graph at the tangency point, so with that point, we will find b.

The x-coordinate of the tangency point is x = 2, and the y-coordinate is,

Substitute (x, y) with (2, 1/2) in the equation of the line to find b,

Subtract 8 from both sides,

Hence, the equation of the line perpendicular to the tangent of the graph at x = 2 passing through the tangency point is,

Answer:

16 batches of cookies

Step-by-step explanation:

First, I converted the fraction (1/2) to a decimal (.5). Then I divided 4 by .5 and got 8. Next, multiply 8 by 2 and we get 16, which means we can make 16 batches of cookies.

4 ÷ .5 = 8
8 × 2 = 16

Area of Sector.

The area of a sector is given by the formula below:

Substituting these values into the formula above, we get

Thus, the correct answer is 46.5 square meters.

Data:

• Distance ( ,D ,)= 144 miles

• Time ( ,t ,) = 4 hours

• Speed of Ahmed (,A,): unknown

• Speed of Blake (,B,): unknown

• Formula of speed:

Procedure:

• As Blake travels 8 mph faster than Ahmed

Since they are traveling towards each other, we can add up their speeds as follows:

Using the distance formula, we can find the speed:

To know the speed of Blake:

Answer:

• Blake = 292 mph

• Ahmed = 284 mph

Marcus have 44 CDs, Sherry have 34 CDs and Kristen have 22 CDs.

Let us assume that Kristen has x numbers of CD's.

According to the provided situation,

Marcus have twice the number of CDs as Kristen.

Number of CDs of Marcus = 2x

The number of CDs of Sherry is 12 more than the CDs of Kristen

Number of CDs of of Sherry = 12 + x

Total number of CDs combined are 100.

So, we can write,

x + 2x + (12 + x) = 100

4x + 12 = 100

Any equation with the highest degree of variable as one, just like the above equation is called Linear Equation.

Further solving the Equation,

4x + 12 = 100

4x = 88

x = 22

The number of CDs that Kristen has is 22.

The number of CDs that Marcus have is 2(22).

The number of CDs Marcus gas is 44.

The number of CDs Sherry has is (12 + x) which is equal to 34.

The number of CDs Kristen, Marcus and Sherry have is 22, 44 and 34 respectively.

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STEP-BY-STEP EXPLANATION:

What to do? Convert percentage to fraction

Given parameter

0.0032%

Population means μ as a tri-linear inequality is given as 58.852< m<61.548 with a confidence interval of 99.5%.

What is a confidence interval?

Mean, x= 60.2

sample size, n= 867

standard deviation=21.9

population mean m as a tri-linear inequality is given by,

The t value for a 99.5% Confidence interval because the sigma is unknown.

From Inverse t Distribution Calculator, the Confidence interval is 0.995 and the degree of freedom is 867-1=866

One-sided t-Score: 1.8125

We can now determine the standard error E:

E=1.8125(21.9/√867)=1.348

We can now create the confidence interval by:

x - E < m< x + E

60.2-1.348< m <60.2+1.348

58.852< m<61.548

Population means μ as a tri-linear inequality is given as 58.852< m<61.548 with a confidence interval of 99.5%.

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Yes, the probability approaches each time will result in getting a sample that is representative of the population of that group class.

If you are going on and properly conducting the specific research on a specific population, you will totally want to make sure that your taken sample of that population is absolutely representative.

If in any case your sample is a kind of representative of your total population, you will be able to confidently take up and generalize the results of your study to that of the population.

In order to be a representative sample, the sample of the group must represent the total population as a whole.

For instance, if the researcher’s population of absolute interest has 60% of people of total ages 18-25 and 40% of the total people ages from about 26-40, then the representative sample must also absolutely reflect this ratio.

The best way of ensuring a representative sample is to have a complete list (i.e., sampling frame) of all the elements in the present population and know that each and every element (e.g., people or present households) on the list that has a nonzero chance (but then it is not necessarily required to be an equal chance) of being included in the entire sample.

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There is a 0.0530 percent probability that the randomly chosen study participant will be shorter than 68 inches.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.  Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

We have been given that

μ = 68.3

σ = 4.0

Find the probability that a study participant has a height that is less than 68 inches.

We are supposed to find P(x<68)

x = 68

z = (x - μ) / σ

z = (68 - 68.3) / 4

z = -0.3 / 4

z = -0.075

Use z table :

So, P(z<-0.0725)=0.0530

So, The probability that the study participant selected at random is less than 68 inches tall is 0.0530

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Looking at the figure, we can tell that the top is a triangle and the base is a trapezium. To find the area of the figure, we would find the sum of the triangle and the trapezium.

Recall, the formula for finding the area of a triangle is expressed as

Area = 1/2 x base x height

Looking at the triangle,

base = 9 + 9 = 18

height = 3

Thus, Area = 1/2 x 18 x 3 = 27

Again, the formula for finding the area of a trapezium is expressed as

Area = 1/2(a + b)h

where

h is the height of the trapezium

a and b are the lengths of the parallel sides

Looking at the trapezium,

a = 9 + 9 = 18

b = 13.4 + 13.4 = 26.8

h = 12

Area = 1/2(18 + 26.8)12

Area = 268.8

rounding to the nearest whole number,

Area = 269 squared ft

Answer: a. (-10, 0) u(12, infinity)

b. (negative infinity, -10) u(0, 12)

All of this is assuming that the ends of both functions are continuing in the direction it's going shown in the graph.

Step-by-step explanation:

f(x) and g(x) basically means the y value. So when f(x) is greater than g(x), it's saying the y value for the f(x) line is greater than the y value for g(x). This happens when x = -10 till x = 0 and x = 12 till forever going right.

Side note: (-10, 0) is a way to write the domain, with the first number meaning the start and the second number meaning the end.

1)  A number that is divided by 5, with the result as 50 less than if the number had been divided by 6 is; -1500

2) If both turtles survive until then, the number of years from today that the older turtle's age would be 3 times that of the younger turtle is; 146 years

1) Let the number be x. We are told that it is divided by 5, and the result is 50 less than if the number had been divided by 6. Thus, we have;

(x/6) - (x/5) = 50

Multiply through by 30 to get;

5x - 6x = 1500

-x = 1500

x = -1500

2) Let the older turtle be x and the younger one be y.

Today, the older turtle's age is 11 times that of the younger turtle. Thus;

Todays age;

Older turtle = 11y years

Younger turtle = y years

In 24 years, the older turtle's age will only be 7 times that of the younger turtle. Thus;

11y + 24 = 7(y + 24)

11y + 24 = 7y + 168

11y - 7y = 168 - 24

4y = 144

y = 144/4

y = 36

Thus;

Age of older turtle today = 11 * 36 = 396 years

Age of younger turtle today = 36 years

Thus, for older turtle to be thrice the age of younger turtle, then;

3(36 + t) = 396 + t

108 + 3t = 396 + t

2t = 292

t = 292/2

t = 146 years

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A linear equation has a constant slope.

For every step increase in x, there needs to be another step increase in y.

From the table,

x decreases by 2 units

y doesn't decrease by the same unit

So, this cannot be linear relationship.

To see whether it is quadratic or exponential, we graph the (x,y) points and see the general shape of the curve by connecting the points in a smooth curve.

The graph is shown below:

From seeing the graph, it is quite evident that the tabular relationship represents a quadratic function.

Thus, the correct answer is:

Solution:

Given:

The theorem that would be used to justify that triangles ABC and CDA are congruent is: SAS.

If we can show that the two sides and one included angle in one triangle is congruent to the two corresponding sides and an included angle in another triangle, then we can state that the two triangles are congruent to each other by the SAS congruence theorem.

Triangles ABC and CDA have the following:

Side AD is congruent to side BC [one pair of congruent sides]

Side AC is congruent to side CA based on the reflexive property [one pair of congruent sides]

Angle 1 is congruent to angle 2 [one pair of included congruent angle]

Therefore, the above information satisfies the SAS congruence theorem. Therefore, they are congruent triangles based on the SAS. The theorem that justifies why they are congruent is therefore SAS.

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Answer:

180

Step-by-step explanation:

So, in the first 4 games, they score 10 points. If this continues to happen in the remaining 18 games, it would be 180.

             10 x 18 = 180.

Answer:

89%

Step-by-step explanation:

Answer:

Step-by-step explanation:

The length , width and height of a box with volume 125 cubic centimeters will be

1, 5 and 25.

The volume of a box can be calculated by multiplying its length, width, and height.

here given volume = 125

V = l x w x h

125 = l x w x h

l, w, h is the factors of 125

To find the common factors, we must first list the factors of each of the given numbers.

since 125 is  composite number, it will have more than two factors.

125 → 1, 5, 25 and 125.

The factors of 125 is 1, 5, 25,125

here 125 cannot consider as length since volume is 125 other sides cannot be 0.

so the length, width, height can be 1 , 5, 25.

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Given:

When two negetive sign comes together it becomes positive.

Thus, the final answer is 21.

1) [tex]\overline{AB} \cong \overline{CD}[/tex] (given)

2) [tex]\angle BAC \cong \angle ACD[/tex] (given)

3) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)

[tex]\triangle ABC \cong \triangle CDA[/tex] (SAS)

Recall that two figures are similar if their corresponding angles have the same measure.

Therefore, if we reduce or increment the measurement of each angle, the resulting figure will not be similar to the original figure.

Now, notice that increasing the length of the sides of a polygon does not necessarily result in a similar figure, for example:

Now, recall that translations, rotations, reflections, and dilations result in similar figures.

Answer: Third and last options.

Answer: 1/2

Step-by-step explanation:

1) Find the equation of sin of angle K

Sine is opposite/hypotenuse.

Opposite of K = 5.

the hypotenuse of K = 10

You then get 5/10

2) Simplify the fraction

5/10 = 1/2

We have the following points:

A(-11, -3) and B(-2,5)

The distance between AB is:

C(7,1) and D(x, 9)

the value of x is -2

Answer:

It would be, Yes, No, Yes, Yes.

Hope this helps!

we have the equation

A=bh

solve for h

that means -----> isolate the variable h

so

step 1

Divide both sides by b

A/b=bh/b

simplify

A/b=h

rewrite