Area of the base, B = 42 square meters

and height = 3 meters

Answer:

The mode is 5, which occurs the most times (four).

The proof that line n is perpendicular to both a and b is proved below using definition of right angle and perpendicular transversal theorem.

We are given that;

Line a is parallel to line b

Line m is parallel to line n.

A) We want to prove that line a is perpendicular to n.

From the image, we see that there is a right angle sign on the opposite side of ∠1 facing m.

Now, we know that by definition of a right angle that ∠1 will also be a right angle.

Since angle 1 is a right angle, then we can say the line transversal a is perpendicular to line m.

B) We want to prove that line b is perpendicular to n.

The definition of the perpendicular transversal theorem, states that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Thus, b will be perpendicular to n.

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The y-coordinates of the system of equations is 3

From the question, we have the following parameters that can be used in our computation:

y = x + 4

x + y = 2

By direct substitution, we have

y - 4 + y = 2

Evaluate the like terms

2y = 6

So, we have

y = 3

Hence, the value of y is 3

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The calculated value of the mode(s) of the data is (a) 1

From the question, we have the following parameters that can be used in our computation:

1, 0, 2, 2, 3, 0, 1, 1, 4, and 5

By definition, the mode of a data is the data that has the highest frequency

Using the above as a guide, we have the following:

The data element 1 has the highest frequency of 3

Other data elements have lesser frequencies

Hence, the mode(s) of the data is (a) 1

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The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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The true similarity statement are using Right Triangle Altitude Theorem :

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.

By the Right Triangle Altitude Theorem,

If the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then the triangles formed by the division are similar to each other and both are similar to the original triangle.

Using this,

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Hence the true statements are ΔABD similar to ΔBCD, ΔABC similar to ΔADB, ΔABC similar to ΔBDC.

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The complete question is given below.

Answer:

the answer is c

Step-by-step explanation:

CAN I PLEASE GET BRAINLESS

Answer:

Answer is 5. Hope you like answer

Answer:

$22.50

Step-by-step explanation:

Multiply to find the amount of discount:

30 x 25% = 7.50

Subtract the discount amount, from the total:

30 - 7.50 = 22.50

Answer: x = 70

Step-by-step explanation:

We are looking at the supplementary angles so 180-45 = 2x -5

135 = 2x-5 add 5 to both sides

135+5 = 2x

140 = 2x Divide both sides by 2

70=x

Check: 2(70)- 5 = 135

135 + 45= 180

OK!

Answer:

D. AC ≅ DF

Step-by-step explanation:

According to the AAS Theorem, two triangles are considered congruent to each other when two angles and a mon-included side of one triangle are congruent to two corresponding angles and a corresponding non-included side of the other.

Thus, in the diagram given:

<A and <B in ∆ABC are congruent to corresponding angles <D and <E in ∆DEF.

The only condition left to be met before we can conclude that both triangles are congruent by the AAS Theorem is for a mon-included side AC to be congruent to corresponding non-included side DF.

So, AC ≅ DF is what is needed to make both triangles congruent.

Answer:

Step-by-step explanation:

Exact Form:

9

4

Decimal Form:

2.25

Mixed Number Form:

2

1

4

Answer:

-23

Step-by-step explanation:

-3✓81+✓16

-3✓81=-27

✓16=4

=-27+4

=-23

1. Choosing percents in each category.

In this case, we can choose any number within the given range as long as the total of all categories equals 100%.

• Housing: 25%

• Food/Household: 10%

• Savings: 10%

• Transportation: 15%

• Debt: 5%

• Entertainment: 10%

• Medical/Personal Care: 7%

• Giving: 10%

• Clothing: 3%

• Miscellaneous: 5%​

The percentages were chosen within the range given. Now, we have to evaluate if they add up to 100%.

As they add up to 100%, they are correct and we can use them in the following steps.

2.

As we have to make a monthly budget, we have to calculate a monthly net pay. Assuming that a month has 4 weeks, then the monthly net pay is:

With the monthly net pay, we can now calculate the maximum amount that can be spent in each category monthly using the chosen percentage.

• Housing: 25%

• Food/Household, Savings, Entertainment, and Giving: 10% per each

• Transportation: 15%

• Debt and Miscellaneous: 5%

• Medical/Personal Care: 7%

• Clothing: 3%

The total should add up $2384.9:

Answer:

• Housing: 25%, $596.23

• Food/Household: 10%, $238.49

• Savings: 10%, , $238.49

• Transportation: 15%, $357.74

• Debt: 5%, $119.25

• Entertainment: 10%, $238.49

• Medical/Personal Care: 7%, $166.94

• Giving: 10%, $238.49

• Clothing: 3%, $71.55

• Miscellaneous: 5%​, $119.25

Answer:

To find the greatest common factor (GCF) of 8a^3b^2 and 12ab^4, we need to factor each term into its prime factors and then find the common factors.

8a^3b^2 can be written as:

8a^3b^2 = 2^3 * 2 * a * a * a * b * b

12ab^4 can be written as:

12ab^4 = 2^2 * 3 * a * b * b * b * b

The common factors are 2, a, and b^2.

Therefore, the GCF of 8a^3b^2 and 12ab^4 is:

2 * a * b^2 = 2ab^2

Answer:

In that one week, his commision was $896, over all 52 weeks, he made $46592

Step-by-step explanation:

So, he makes 14% commision on any stock he sells. This week, he sold $6,400 worth of stocks, and, hes going to make 14% on it. So, take 6400 and divide that by 14%, and what do you get? $896! So, he made $896 that week. Now, say he made that amount EVERY WEEK. so, all you have to do is know how many weeks are in a year (52) and multiply that by 896, which gives you 46592.

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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Answer:

the first four terms is 3, 0, -3, -6

Therefore , the solution of the given problem of triangle comes out to be  base=4m,16 and height=8m,2m.

In a plane, any three points can be joined to form triangles, which have three sides and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.

Here,

Given :

Triangle area = 16\(m^{2}\)

Thus,

To find the possible base and height of the triangle.

The base can be given by 4 m,16

and height be = 8m or 2m

vice-versa

height = 4m ,16mand base =8m,2m

Therefore , the solution of the given problem of triangle comes out to be  base=4m,16 and height=8m,2m.

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Answer:

see below

Step-by-step explanation:

given that the area of the triangle is 16m² . We need to list all the possible lengths of its base and height. As we know that, the area of triangle is ,

ar(∆) = 1/2 * base* height

substitute the respective values,

16m² = 1/2* b * h

b*h = 32

now here we need to list out all the possible factors of 32 as ,

1 *32

2 *16

4*8

8*4

16 *2

32*1

therefore, all the possible lengths of heights and bases are ,

and we are done!

-Rishabh

The measure of ER given by the equation ER = 21

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 equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The measure of QE = 8x + 3   be equation (1)

The measure of ER = 4x + 1   be equation (2)

The measure of QR = 64

Now , QR = QE + ER   be equation (3)

Substituting the values of QE and ER in the equation (3) , we get

8x + 3 + 4x + 1 = 64

On simplifying the equation , we get

12x + 4 = 64

Subtracting 4 on both sides of the equation , we get

12x = 60

Divide by 12 on both sides of the equation , we get

x = 5

Substitute the value of x in equation (2) , we get

The measure of ER = 4 ( 5 ) + 1

The measure of ER = 21

Hence , the equation is ER = 21

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The ladder will reach a Height of approximately 43.46 meters on the building.

To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.

Using the Pythagorean theorem, we can set up the equation:

(Height of the building)^2 + 7^2 = 44^2

Simplifying the equation, we have:

(Height of the building)^2 + 49 = 1936

Subtracting 49 from both sides, we get:

(Height of the building)^2 = 1887

To find the height of the building, we take the square root of both sides:

Height of the building = √1887

Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.

Therefore, the ladder will reach a height of approximately 43.46 meters on the building.

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Answer:

n = 641

Step-by-step explanation:

Pipe required to provide water is 3846 m

Length of each pipe is 6 m

We need to find the no of tubes required. Let there are n tubes. It can be calculated as follows :

\(n=\dfrac{3846 }{6}\\\\n=641\)

Hence, 641 tubes will be needed.

To know what is the better buy we have to know how much does each GB cost in each case.

For the 4 GB flash drive we have that

then each GB cost $2.

For the 2 GB flash drive we have that

then each GB cost $3.

Finally for the 8 GB we have that

then each GB cost $1.63.

Comparing the prices for each GB we conclude that the best buy is the 8 GB flash drive.

The solution to the problems are;

1.  Area = 108 square feet

2. Area = 342 square feet

3. x = $1, 890, x = $1764

4. Cost, x = $151. 2, $117. 6

The formula for calculating the area of a rectangle is expressed with the equation;

A = lw

Such that;

From the diagram shown, we have that;

The deck is gray

The garden is white

1. The area of the garden in design A

Area = 9(12) = 108 square feet

2. The area of the deck in design A is;

Area = 18(25) = 450 square feet

The area of the deck without the garden = 450 - 108

Area = 342 square feet

3. If $4. 20 = 1 square feet in design A

Then, x = 450 square feet

x = $1, 890

Area of deck of design B = 21(20) = 420 square feet

cost = $1764

4. If $1. 40 = 1 square feet of garden A

Then, x = 108 square feet

Cost = $151. 2

For garden of design B

Area = 1/2 × (12)(14) = 84 square feet

Then, cost = $117. 6

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The distance the duck fly in all is 99 miles

From the question, we have the following parameters that can be used in our computation:

The distance covered in all can be calculated as

Distance = The sum of the product of speed and time

Substitute the known values in the above equation, so, we have the following representation

Distance = 18 * 3 + 15 * 2

Evaluate the products

This gives

Distance = 54 + 45

Evaluate the sum

Distance = 99 miles

Hence, the distance is 99 miles

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Answer:

  x = √65

Step-by-step explanation:

You are given a right triangle with leg lengths 4 and 7, and you are asked for the length of the hypotenuse, x.

The Pythagorean theorem relates the lengths of the sides of a right triangle. It tells you the square of the hypotenuse (x²) is the sum of the squares of the other two sides.

  x² = 4² +7² . . . . . . . . . Pythagorean relation

  x² = 16 +49 = 65 . . . evaluate the expression

  x = √65 . . . . . . . . . . take the square root

Answer:

Answer to your question ; f(t) = 55 = 4t

Answer:

$35

Step-by-step explanation:

This is very easy.

90 / 36 = 2.5

2.5 * 14 = $35

Therefore your answer is $35

Answer:

\(\displaystyle{=-\dfrac{p^5}{6}}\)

Step-by-step explanation:

Given the expression:

\(\displaystyle{\dfrac{1}{-6p^{-5}}}\)

We have to apply the negative exponent law where:

\(\displaystyle{x^{-n} =\dfrac{1}{x^n}}\)

Thus:

\(\displaystyle{\dfrac{1}{-6p^{-5}}= \dfrac{1}{-6\cdot \dfrac{1}{p^5}}}\\\\\displaystyle{=\dfrac{1}{ - \dfrac{6}{p^5} }}\\\\\displaystyle{= 1 \cdot \left(-\dfrac{p^5}{6}\right)}\\\\\displaystyle{=-\dfrac{p^5}{6}}\)

But there's a trick here, consider this:

\(\displaystyle{\dfrac{a}{kb^{-n}}}\\\\\displaystyle{=\dfrac{a}{\dfrac{k}{b^n}}}\\\\\displaystyle{=\dfrac{ab^n}{k}}\)

So the trick is to just move \(p^{-5}\) up then you'll have \(p^5\) as a numerator (top) which still results the same as the answer.

Answer:

See explanation below

Step-by-step explanation:

1. 12x - 18 = 6(2x -3)

2. 15x + 25 = 5(3x + 5)

3. 14x + 21 = 7(2x + 3)

4. 5x - 5 = 5(x - 1)

5. 12x - 30 = 6(2x - 5)

6. 10x + 8 = 2(5x + 4)

7. 27x + 18 = 9(3x + 2)

8. 4x - 20 = 4(x - 5)

9. 20x + 30 = 10(2x + 3)

10. 4(x + 5) = 4x + 20

11. 3(x - 2) = 3x - 6

12. 5(2x + 4) = 10x + 20

13. 5(x - 1) = 5x - 5

14. 1/2(10x + 12) = 5x + 6

15. 4(2x + 4) = 8x + 16

16. 2(5x - 2) = 10x - 4

17. 2(x - 8) = 2x - 16

18. 4(2x + 1) = 8x + 4

The number of months Mark can have the phone is given by the equation

A = 11.4 months

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 number of months be represented as = A

Now , the equation is

Now , the total amount with Mark = $ 146.43

The initial amount for the smartphone = $ 33

The amount per month for 2GB is = $ 9.95

So , the amount for A months = $ 9.95 ( A )

So , the equation will be

Initial amount for the smartphone + the amount for A months = total amount with Mark

Substituting the values in the equation , we get

33 + 9.95 ( A ) = 146.43   be equation (1)

On simplifying the equation , we get

Subtracting 33 on both sides of the equation , we get

9.95 ( A ) = 113.43

Divide by 9.95 on both sides of the equation , we get

A = 11.4 months

Therefore , the value of A is 11.4 months

Hence , the number of months is 11.4 months

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