Find the value of a. A. 57 B. 104 C. 26 D. 52​

Answer:

Martin family: 20 hours

Lewis family: 35 hours

Step-by-step explanation:

Let's say that the Lewis family sprinklers were out for L hours and the Martin family's sprinklers were out for M hours. We know that for each hour that the Lewis family sprinkler was on, 30L of water was put out. We can thus write the Lewis family sprinkler water output as 30L per each hour of L = 30 * L. Similarly, the Martin family sprinkler water output = 15 * M .

We know that the total hours for the sprinklers is 55, so L + M = 55. The total water output for the sprinklers is the sum of the sprinkler outputs, so 30 * L + 15 * M = 1350

L + M = 55

30 * L + 15 * M = 1350

One way to solve this would be to solve for L in the first equation and substitute that into the second

subtract M from both sides in the second equation

55 - M = L

30 * (55-M) + 15 * M = 1350

30 * 55 - 30 * M + 15 * M = 1350

1650 - 15M = 1350

subtract 1650 from both sides to isolate the M and its coefficient

-15M = -300

divide both sides by -15 to isolate M

M = 20

L = 55-20 = 35

Answer: A = 833.66 in^2

Step-by-step explanation:

Area of the base = (7^2)(pi) = 49 pi = 153.9 in^2

Height of the cylinder = 12 in

Circumference of the base = (2)(pi)(r) = 44in

Surface area = (2)(pi)(7)(12) + (2)(pi)(7) = 833.66 in^2

A midpoint is a point that divides a given line into two equal halves.The answers to the questions are:

1. BC = 89

b. AB = 45

c. AC = 44

2. The coordinate of I is 2.5

3. J = 19

4. MQ = 32

5. NO = 13

6. NO = 23

b. MN = 25

A line segment can be divided into different fractions. Where the point that divides the line segment into equal parts is the midpoint. however, number line is a system that shows the location or positions of all directed numbers.

The given questions can be solved as follows:

1. Given that point A is between BC and AB = 4x -3, BC = 7x + 5, AC = 5x - 16

But,

BC = AB + AC

7x + 5 = (4x -3) + (5x - 16)

          = 9x - 19

7x + 5 = 9x - 19

19 + 5 = 9x - 7x

24 = 2x

x = [tex]\frac{24}{2}[/tex]

x = 12

So that;

a. BC = 7x + 5

         = 7(12) + 5

BC = 89

The value of BC is 89.

b. AB = 4x -3

         = 4(12) - 3

AB = 45

Thus AB has a value of 45.

c.  AC = 5x - 16

          = 5(12) -16

 AC = 44

The value of AC is 44.

2. Given that H is the mid point of GI, and G = 8, I = -3.

Then;

I = 2.5

The coordinate of I is 2.5

3. A midpoint is a point that divides a line segment in to two equal halves. Given that J is the midpoint of KL. KL = 38

J = [tex]\frac{KL}{2}[/tex]

  = [tex]\frac{38}{2}[/tex]

J = 19

The value of the midpoint J is 19.

4. It can be deduced from the conditions given in the question that:

  MQ = MN + NO + OP + PQ

          = 8 + 8 + 16      (NB: OP + PQ = 16)

MQ = 32

Thus, value of MQ is 32.

5. Since P is the mid point of NQ, and OP = 11, OQ = 35

 Then;

PQ  = OQ - OP

      = 35 - 11

PQ = 24

Since, PQ = NP =24

Then;

NO = NP - OP

      = 24 - 11

NO = 13

NO has a length of 13.

6. NO = 2y + 11, OP = 3y - 2, NP = 6y + 3 and MP = 64.

But,

NO + OP = NP

(2y + 11) + (3y - 2) = 6y + 3

5y + 9 = 6y + 3

9 - 3 = 6y - 5y

y = 6

So that;

a. NO = 2y + 11

          = 2(6) + 11

NO = 23

Here, the value of NO is 23.

b. MN = MP - NP

But,

NP = 6y + 3

     = 6(6) + 3

NP = 39

Then;

MN = 64 - 39

MN = 25

So that MN has a value of 25.

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Answer:

[tex]2^{\frac{1}{6} }[/tex]

Step-by-step explanation:

(2^1/3)^1/2 = 2^(1/3 x 1/2) =2^1/6

Answer:

13 and 17 units

Step-by-step explanation:

explaination is in pic.

The length of the diagonals of the quadrilateral AC and BD are 13 units and 17 units respectively, as per length between two points.

The length between two given points (x₁, y₁) and (x₂, y₂) will be:

√[(x₂ - x₁)² + (y₂ - y₁)²] units

Given, the vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).

Therefore, the diagonals of the quadrilateral will be AC and BD.

The coordinates of the diagonal AC are (4, - 3) and (- 8, 2).

Now, the length of the diagonal AC will be:

= √[(-8 - 4)² + (2 - (- 3))²] units

= √[(- 12)² + (5)²] units

= √[144 + 25] units

= √(169) units

= 13 units                                  (length can't be negative)

Similarly, the coordinates of the diagonal BD are (7, 10) and (- 1, - 5).

Now, the length of the diagonal BD will be:

= √[(-1 - 7)² + (- 5 - 10)²] units

= √[(- 8)² + (- 15)²] units

= √[64 + 225] units

= √(289) units

= 17 units                                  (length can't be negative)

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Answer:

0 is the answer . The explanation is in the attachment .

Answer:

100000 = 8 (4) ^t

Step-by-step explanation:

We are multiplying by 4 each time

y = a (4)^t

The initial amount is 8

y = 8 (4)^t

We want to get to 100000

100000 = 8 (4) ^t

Answer:

B

8 ⋅ 4^t  = 100,000

Step-by-step explanation:

the answer to this question is the slope is 43

Answer:

Therefore, the slope is 3/4

Step-by-step explanation:

An x -intercept is the value of x when y=0 , so an x-intercept of 4 can be written as a coordinate on the graph as (4,0)

Likewise, an

y -intercept is the value of y when x=0 , so an y -intercept of −3can be written as a coordinate on the graph as (0,-3)

Now we have two points(4,0) (0,-3)

To find the slope given two points, we use the formula

rise÷run , or y2−y1÷x2−x1 .

Plug in the given points into the formula

-3-0/0-4

-3/-4

3/4

Therefore, the slope is 3/4

Hope this helps!

Answer:

x=6, y=4, z=8

I hope this is helpful!

Answer:

x = 8/3

Step-by-step explanation:

Copy the right side of the given to the right side of the equation.

sqrt(x - 5) = sqrt(3 - 2x)            Square both sides.

x - 5 = 3 - 2x                             Add 2x to both sides

2x + x - 5 = 3                            Combine

3x - 5 = 3                                  Add 5 to both sides.

3x = 3 + 5                                 Combine

3x = 8                                       Divide by 3

x = 8/3

The Annuity payment will be "65,209.35 Taka". A further solution is provided below.

Given:

Monthly payment,

= 3000 Taka

Interest rate,

= 6% (compounded monthly)

Time,

= 18 years

The Future value will be:

→ [tex]FV = PMT\times \frac{((1+r)^{nt}-1)}{r}[/tex]

By putting the values, we get

         [tex]=3000\times \frac{((1+\frac{6}{12\times 100} )^{12\times 18}-1)}{\frac{6}{12\times 100} }[/tex]

         [tex]=3000\times \frac{((1+\frac{6}{1200} )^{216}-1)}{\frac{6}{1200} }[/tex]

         [tex]=1,162,059.58 \ Taka[/tex]

hence,

The Annuity payment will be:

→ [tex]P=\frac{PV(\frac{r}{n\times 100} )}{1-(1+\frac{4.5}{4\times 100} )^{-4\times 5}}[/tex]

      [tex]=P=\frac{PV(\frac{r}{n\times 100} )}{1-(1+\frac{4.5}{4\times 100} )^{-20}}[/tex]

By substituting all the values, we get

      [tex]=65,209.35 \ Taka[/tex]

Thus the correct answer is "65,209.35 Taka".

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Answer:

B. 56

Step-by-step explanation:

x + (x + 7 ) + ( x + 14 ) + ( x + 21 ) + ( x + 28 ) = 350

( x + x + x + x + x ) + ( 7 + 14 + 21 + 28 ) = 350

5x + 70 = 350

     - 70    - 70

_____________

5x = 280

x = 56

Hope this helps!

The smallest number is 56, the correct option is B.

The sum is the output of the mathematical operation, Addition.

Let the first number is x, they are multiples of 7,

As they are multiples of 7, the consecutive numbers will be added by 7 for next term.

The 5 consecutive numbers can be written as x, (x+7), (x+14), (x+21), (x+28).

The equation can be formed for the numbers that are given as,

An equation is a mathematical statement that relates an algebraic expression with other expression by an equal sign.

The sum of the multiples is 350

x + (x + 7 ) + ( x + 14 ) + ( x + 21 ) + ( x + 28 ) = 350

Grouping the variables and the constants separately

( x + x + x + x + x ) + ( 7 + 14 + 21 + 28 ) = 350

5x + 70 = 350

Adding (-70) to both sides of the equation

5x = 280

Dividing both sides by 5

x = 56

The value of the first number of the series is obtained.

The first value is the smallest number of the series.

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Answer:

1) a³b⁴/ ab³ = a²b

2)2 (x³ )² = 2x^6

3)3x*2x³ y² = 6x⁴y²

Answer:

x=14.2

Step-by-step explanation:

AC = BD

The diagonals of a rectangle are equal

7x-9 =  2x+62

Subtract 2x from each side

7x-9-2x = 2x+62-2x

5x-9 = 62

Add 9 to each side

5x-9+9 = 62+9

5x= 71

Divide by 5

5x/5 = 71/5

x=14.2

Answer:

the answer is the number 6

Step-by-step explanation:

+ Both equations

You will get : 5x=13 ; x=13/5

and put x to the first equation

2*13/5-y=4

y=6/5

(13/5;6/5)

Answer is C

Answer:

48.5 and 34.5

Step-by-step explanation:

83 divided by 2 and then subtract 7

Answer:

45 and 38 equal 83 and 45 is 7 more than 38

[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{16}{26}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{8}{13}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=0.5[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{5}{10}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto sin\Theta=sin30[/tex]

[tex]\\ \sf\longmapsto \Theta\approx30°[/tex]

Answer:

9/8 = n

Step-by-step explanation:

9 = 8n

Divide each side by 8

9/8 = 8n/8

9/8 = n

Answer:

(x, y) → (y, -x)

Step-by-step explanation:

The coordinates of the vertices of parallelogram ABCD are; A(2, 5), B(5, 4), C(5, 2), and D(2, 3)

The coordinates of the vertices of parallelogram A'B'C'D' are; A'(5, -2), B'(4, -5), C'(2, -5), and D'(3, -2)

The rule that escribes the transformation of the rotation of parallelogram ABCD to create the image A'B'C'D' is presented, by observation, is therefore;

(x, y) → (y, -x)

The resulting transformation used will be (x, y) -> (y, -x)

Transformation are rules applied to an object to change its orientation

For the given parallelogram, in order to know the rule used, we need the coordinate of the image and preimage

The coordinate of A is (2, 5) while that of A' is (5, -2).

From both coordinates, you can see that the coordinate was switched and the resulting y coordinate negated.

Hence the resulting transformation used will be (x, y) -> (y, -x)

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Answer:

C(x)=40x+14, 6 days

Step-by-step explanation:

C(x)= payment per day*x + initial payment. the payment per day is $40 while the initial payment is $14. so C(x)=40x+14.

C(x)=254=40x+14, 40x=240, x=6

Answer:

Step-by-step explanation:

25*-30= -$750

Second: He sells 22 of those calculators for $35 each, so he is making money.

22*35= $770

Third: With the remaining three calculators, he must pay $2 each for returned calculators, so he is losing money again.

3*-2= -6

Add all the costs and sales together, and you get 770-750-6= $14 profit

However, the problem does not say if he gets his money back for the 3 returned calculators. In that case if he did, you would add the cost of each of those calculators to his profit. 30*3= 90

$90+$14= $104 profit

here u go

Answer:

Line segments A'B' and C'D' do not intersect and are the same distance apart as AB and CD.

Step-by-step explanation:

Answer:

8a^3-64p^3-36a^2+54a-27

Step-by-step explanation:

since it no common variable so it can not be further solved

The answer is : [tex]\left(m+n^2\right)\left(m-n^2\right)[/tex]

Here are the steps below to help you! ^^

Answer:

$290

Step-by-step explanation:

We are told that 1 out of 5 buyers change to a more expensive sofa than the one in the sale advertisement.

Now we are told that the advertised sofa is $250 and the more expensive sofa is $450.

Thus;

P(x) for expensive sofa = 1/5

P(x) for sofa in sale advertisement = 4/5

Thus, expected value is;

E(X) = (1/5)450 + (4/5)250

E(x) = 90 + 200

E(x) = $290

Answer:

Step-by-step explanation:

Cost of advertised sofa = [tex]\$250[/tex]

Cost of more expensive sofa = [tex]\$450[/tex]

So, the average cost of sofa,

[tex]E(x) = (450*\frac{1}{5})+ (250*\frac{4}{5})\\\\E(x) = 90 + 200\\\\E(x) = 290[/tex]

Hence,

The average cost of a sofa = [tex]\$290[/tex]

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Complete question :

At the city museum, child admission is $6.30 and adult admission is $9.80. On Wednesday, three times as many adult tickets as child tickets were sold, for a total sales of $ 1178.10 . How many child tickets were sold that day?

Answer:

33 children ticket

Step-by-step explanation:

Let :

Number of Child admission = x

Number of Adult admission = y

On Wednesday ;

y = 3x

9.80y + 6.30x = 1178.10

9.80(3x) + 6.30x = 1178.10

29.40x + 6.30x = 1178.10

35.70x = 1178.10

x = 1178.10 / 35.70

x = 33

question 3

Step-by-step explanation:

i only able to show you the step of question 3..so sorry

Answer:

Answer for this is 62 * 2 = 126

Step-by-step explanation:

Answer:

14×9=126

Step-by-step explanation:

how do you explain it lol

Answer:  (-1, -2)

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

Explanation:

Plot (3,-2) on the xy grid. Then draw a vertical line through 1 on the x axis.

Note that the horizontal distance from the point to the line is exactly 2 units. We move 2 units to the left to go from (3,-2) to (1,-2). Then we move another 2 units to the left to arrive at the final destination of (-1, -2)

In short, (3,-2) reflects over the vertical line x = 1 to get to (-1, -2)

See the diagram below.