In the figure, ABCD and EFGF are rectangle. ABCD and EFGH are similar.(a) If the length of AB is a cm, try to use a to Indicate the length of EF(b) Find the ratio of the areas of ABCD and EFGH.(English isn't my native language. Please correct me if I have any grammatical mistakes.)

The lateral surface area is the total surface area minus the area of the two triangular faces at the top and bottom of the prism. t

Current trees = 25

trees when workers are finished = 80

Subtract the number of current trees (25) to the number of trees that are when the workers are finished:

80-25 = 55

The workers planted 55 trees today

x = 44

Note that:

Opposite angles of a cyclic quadrilateral are supplementary

m

mm

(3x + 10) + 38 = 180

3x + 10 + 38 = 180

3x + 48 = 180

3x = 180 - 48

3x = 132

x = 132/3

x = 44

ANSWER:

5

STEP-BY-STEP EXPLANATION:

The perfect square trinomial is given as follows:

Therefore, in this case would be:

Therefore the value of k is 5

In a parallelogram, opposite sides are equal.

ON = LM

OL = NM

OL = y-6

NM= 1/3 x

ON= 5x-8

LM= 9x-26

First, solve for x

ON = LM

5x - 8 = 9x - 26

-8 + 26 = 9x - 5x

18 = 4x

18/4 = x

x = 4.5

Replace x=4.5 on NM, and solve for y:

OL = NM

y-6= 1/3x

y-6 = 1/3 (4.5)

y-6= 1.5

y= 1.5 + 6

y= 7.5 = 15/2

8x^2 + 19 = 54 + 3x^2

Solving for x:

8x^2 - 3x^2 = 54 - 19

5x^2 = 35

x^2 = 35/5 = 7

x^2 = 7

x = sqrt(7) = 2.6458

x = -sqrt(7) = -2.6458

Answer:

It has two solutions:

x = 2.6458 and x = -2.6458

The data that represent the number of flying saucers that are owned by each alien on planet nowhere is given below:

(a)We sort the data from the least to greatest below.

(b)The median is the middle number.

In this case, we have two numbers in the middle: 4 and 8

Therefore we find their average:

Answer:

6 is the correct answer.

Step-by-step explanation:

Given:

The sum of two numbers is 21, and their difference is 9.

Let x and y be the two numbers.

Equation 1: The sum of two numbers is 21.

Equation 2: Their difference is 9.

The two graphs that reserve congruence are in the option A and option D

Congruent refers to something that is "absolutely equal" in terms of size and shape.

The shapes hold true regardless of how we rotate, flip, or turn them.

Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another. We will see that they will superimpose, or be positioned entirely on top of, one another. This demonstrates the congruence of the two circles.

The images on the graphs in the options A and options D both maintains congruence, The sizes are identical and has a rigid transformation

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In the picture we see that between 10 and 20 years old there are two rectangles . One goes to the 11% aproximately

the other rectangle reach 10% in the Y axis .

So then finally we have to add both percentages to obtain

10% + 11%= 21 %

21 percent are between ages 10 and 20 years old

The vertical line test consists in tracing various vertical lines throughout the function and checking wheter this lines will touch the function more than once.

As we can see none of the lines touch the graph more than once, therefore this graph is a function.

Answer

B) 8 or D) 17

Step-by-step explanation

Let's call x to one unknown number and y to the other number.

If one number is 9 more than another number, then:

Given that the sum of the numbers is 25, then:

Substituting equation 1 into equation 2 and solving for x:

Substituting x = 8 into the first equation:

Then, one of the numbers is 8 and the other one is 17

To find the domain of the rational function we need to equate the denominator to zero and solve the equation, as follows:

Then, all the x-values are valid except x = -14, which makes the denominator equal to zero. Therefore, the domain of R(x) is:

In order to calculate the rate of cups of flour to stick of butter, just calculate the following quotient:

(1 1/4)/(7/8) = (5/4)/(7/8) = 5·8/7·4 = 40/28 = 20/14 = 10/7

Hence, the required rate is 10/7 or 10:7

that is, 10 cups of flour for 7 sticks of buttter

The value of k for which the inequality has the given solution set is:

k = 8.5.

The inequality is presented as follows:

0.5 < -4x + k ≤ 12 - k.

Two inequalities compounded, hence the and operation is applied, which means that the solution set is composed by the elements that respect both conditions.

The solution set of the inequality is:

1.25 ≤ x < 2.

The lower bound of the solution is of 1.25, hence:

-4x + k ≤ 12 - k.

-4x + 2k ≤ 12

4x ≥ 2k - 12

x ≥ 0.5k - 3

Hence:

0.5k - 3 = 1.25

0.5k = 4.25

k = 4.25/0.5

k = 8.5.

The upper bound of the solution is of 2, hence:

-4x + k > 0.5

-4x > 0.5 - k

x < -0.125 + 0.25k

Hence:

-0.125 + 0.25k = 2

k = 2.125/0.25

k = 8.5. -> Which confirms the solution.

The problem is given by the image shown at the end of the answer.

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Explanation

The salary with regular pay rate is calculated as:

S is the salary, R is the regular pay rate and h is the number of hours worked.

The salary with over time is:

Because it pays double after 40 hours.

So the first 40 hours worked you'll get

The amount of overtime hours is 15 (55-40 = 15), so the overtime salary is:

The total Salary is the sum of the regular and the overtime salaries:

If the total salary was $840, then the regular pay rate R is:

Answer

Your regular pay rate is $12 / hour

Let's define the next variable:

t: number of toys that Quinn still needs to collect

The number of toys that he already collected plus the number of toys that Quinn still needs to collect is: 16 + t

Quinn needs to collect at least 90 toys, then 16 + t must be greater than or equal to 90, that is,

16 + t ≥ 90

or

90 ≤ 16 + t

Subtracting 16 at both sides, we get:

90 - 16 ≤ 16 + t - 16

74 ≤ t

area = side x side = 20 x 30 =600 ft

we want to double the area, this is 1200 ft, therefore:

but, We don't measure in negative numbers, so we disregard this answer. and the other

therefore, the patio is now 30ft x 40ft

Answer:

wind speed 35 miles per hour

plane speed 210 miles per hour

Explanation:

Let us call p the place speed and w the wind speed.

We know that

p + w = 1225/5 = 245

p - w = 1225/7 = 175

adding the two equations above gives

2p = 245 + 175

2p = 420

dividing both sides by 2 gives

p = 210 miles per hour.

putting in the value of p in p + w = 245 gives

210 + w = 245

w = 245 - 210

w = 35 miles per hour

The given expression is

5m+3m + 3n - m + 6n + 8​

We would simplify the expression by collecting like terms.

The terms containing m are like terms

The terms containing n are like terms

8 is a constant

Thus, we have

5m + 3m - m + 3n + 6n + 8

7m + 9n + 8

The final expression is

7m + 9n + 8

Given,

The principal amount is 20k.

The rate of interest is 8.3%.

The time period is 6 Years.

Required

The amount of investment after 6 years.

The amount is calculated as,

Hence, the amount after 6 years is 2000 x (1 + 0.083)^6.

apply the distributive property

apply the substraction property

Answer:

Step-by-step explanation:

1260+11200=12460

so its, 1.246 x 10^4

9)

Let x represent the amount that she gets for 1/7 of a working day.

From the information given, she gets $35 for 1 working day. Thus, we can set up the equations as follows

35 = 1

x = 1/7

By crossmultiplying, we have

x = 35 x 1/7

x = 5

Ariel will earn $5 for working 1/7 of a day

To get the required combining pairs : B, C , D, E , F

B (1, 10) = Pattern A - 1 and pattern B = 10

C (3, 6) = pattern a = 3 and pattern b = 6

D (5, 4)= pattern A = 5 and pattern B = 4

E (5, 6) = Pattern A = 5 and pattern B = 6

F (7, 4) = Pattern A = 7 and pattern B = 4

Given ; Pattern A : 1, 3, 5, 7, 9

Pattern B: 10, 8, 6, 4, 2

To get ;  A (1, 3) B (1, 10) C (3, 6) D (5, 4) E (5, 6) F (7, 4)

Thus to get the required pair we have to match it the following way

A ( 1, 3 ) = Pattern A - 1 and pattern B - ? thus not correct

B (1, 10) = Pattern A - 1 and pattern B = 10

C (3, 6) = pattern a = 3 and pattern b = 6

D (5, 4)= pattern A = 5 and pattern B = 4

E (5, 6) = Pattern A = 5 and pattern B = 6

F (7, 4) = Pattern A = 7 and pattern B = 4

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To evaluate the expression:

We can use PEMDAS. We can start from the parenthesis, then, since we have divisions and multiplications, and they have the same precedence, we can start doing the evaluation from the left to the right. Then, we have:

The answer is 54 (option D).

From the question,

The two triangles that are congruent are :

Triangle CDM = Triangle ABM --------- Option C

C(x) = 3x³ − 9x² − 243x + 1229

500 = 3x³ − 9x² − 243x + 1229

Subtract 500 on each side, as follows:

0 = 3x³ − 9x² − 243x + 729

(3x³ − 9x²) - (243x - 729) = 0

3x² (x - 3) - 243 (x - 3) = 0

(x - 3)(3x² - 243) = 0

x = 3, x = 9, x = -9; in the context of this problem, where x is the number

of units produced, negative values of x must be omitted, so x = 3 and x = 9

So we can say that if either 3 units or 9 units are produced the total cost

for the product will be at least $50000

[0, 3] U [9,∞)

Answer

11 gallons of the 25% alcohol is required for the mixture.

4 gallons of the 10% alcohol is required for the mixture.

Explanation

Let the number of gallons of 25% alcohol required be x

Let the number of gallons of 10% alcohol required be y

The total amount of gallons required is 15 gallons. In mathematical terms,

x + y = 15

The alcohol content of the 15 gallons is to be 21%.

21% of 15 gallons = 3.15 gallons

From the first statements,

Let the number of gallons of 25% alcohol required be x

Let the number of gallons of 10% alcohol required be y

25% of x gallons = 0.25x gallons

10% of y gallons = 0.10y gallons

0.25x + 0.10y = 3.15

We can then bring these two equations together to solve simultaneously

x + y = 15

0.25x + 0.10y = 3.15

Solving this simultaneously with the calculator, we obtain

x = 11 gallons

y = 4 gallons

Hope this Helps!!!