Simplify, if possible.
8ab² +3ab+2a-3b+5
A. The expression is in its simplest form.
B. -10ab² +5
2
C. 8ab² + 2ab +5
D.
8ab²-3ab+5
Please select the best answer from the choices provided

The distance in feet between the ground and the top of the ladder  is 16.7 feet.

Let the distance in feet between the ground and the top of the ladder be x.

According to the given question.

Length of the ladder = 17 foot

The distance of the ladder from the base of the wall is 3 feet.

From the given data we can say that we have a right angle triangle in which the hypotenuse is the length of the ladder, base is the distance between the ladder and wall. And the distance between ground and ladder is our perpendicular.

Now according to the Pythagoras theorem,the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

Therefore,

17^2 = 3^2 + x^2

⇒ 289 = 9 + x^2

⇒ 280 = x^2

⇒ x = 16.7 feet

Hence, the distance in feet between the ground and the top of the ladder  is 16.7 feet.

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The radius of the sprinkler is approximately 7 yards.

In this situation we find the case of a sprinkler that rotates until a complete revolution is done, that is, the area of complete circle is covered due to the rotation. That area can be found by using this formula:

A = (θ / 360) · π · r²

Where:

If we know that A = 171 yd² and θ = 360°, then the radius is approximately:

171 = π · r²

r = √(171 / π)

r ≈ 7.378 yd (approx. 7 yd)

The radius of the sprinkler is approximately 7 yards.

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Answer:

-4.2

Step-by-step explanation:

Check the attached photo for work.

Answer:

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

The missing statement is:

Justification is:

All the other options have mismatching or wrong statements or justifications:

Explanation:

Draw a vertical number line (see below). Mark -2 on it. Then move up 2 units to arrive at 0. Move up the remaining 13 units to arrive at 13

This shows that -2+15 = 13

The solution to the equation and the explanation for each step is given below.

Given the equation, -3/4(x + 4) - 6 = 54, the steps to find the value of x is given below:

-3/4(x + 4) - 6 = 54 [given]

-3/4(x) -3/4(4) - 6 = 54 [Distributive property]

-3/4x + (-3) - 6 = 54 [Use multiplication to simplify]

-3/4x - 9 = 54 [Simplify using addition]

-3/4x = 63 [Add 9 to each side and simplify]

x = -84 [Multiply each side by -4/3 and simplify]

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Answer:

  x = 25

Step-by-step explanation:

The given angles, x° and (6x+5)° form a linear pair. You want the value of x.

Two angles that together form a straight line are called a linear pair. A linear pair of angles has a total measure of 180°.

  x° +(6x +5)° = 180°

  7x +5 = 180 . . . . . . . . . divide by °, collect terms

  7x = 175 . . . . . . . . . . subtract 5

  x = 25 . . . . . . . . . . divide by 7

The value of x is 25.

Answer:

for first question the answer will be .. 5

Step-by-step explanation:

easily,

[tex] \frac{1}{5} \times 5 = 1 [/tex]

There are [tex]6\frac{1}{4}[/tex] groups of 1/5 in 5.

The simplified value of  5 ÷ 4/5 is also [tex]6\frac{1}{4}[/tex].

A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.

From the bar given above the number line, each group has subgroups of 4.

Therefore, The number of groups of (1/5) in 5 is [tex]6\frac{1}{4}[/tex] groups.

We know when a fraction is in the division we can reciprocate the fraction and the division changes to multiplication,

Therefore, 5 ÷ 4/5 = 5×5/4 = 25/4 = [tex]6\frac{1}{4}[/tex]

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The total cost  is  $616.98.

The amount he has left to spend is  $43.02.

The total cost to Douglas is the sum of the total cost of the thirteen doors and the sum of the six bags of fertilizers

The total cost of the thirteen doors = (cost of one door x total number of doors that would be bought)

$43.44 x 13 = $564.72

The total cost of six bags of fertilizers = (cost of one bag x total number of bags)

$8.71 X 6 = $52.26

Total cost = $564.72 +  $52.26 = $616.98

Amount he has left to spend = $660 - $616.98 = $43.02

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Answer:

Number of orchestra tickets = 8

Number of balcony tickets = 22

Step-by-step explanation:

Let the number of orchestra tickets be x and number of balcony tickets be y.

So, cost of x orchestra tickets = $148 × x = $148x

Cost of y balcony tickets = $65 × x = $65y

Also given, total number of tickets = 30

Cost of 30 tickets = $2,614

So, the system of equations that can ne formed is :

x + y = 30     ....eq 1

148x + 65y = 2614    ....eq 2

Multiplying eq 1 by 148 and subtracting eq 2 by it,

148x + 148y - 148x - 65y = 4440 - 2614

83y = 1826

y = 1826/83 = 22

Substituting y = 22 in eq 1,

x + 22 = 30

So, x = 30 - 22 = 8

Thus,

Number of orchestra tickets = 8

Number of balcony tickets = 22

Answer:

I am pretty sure it is a i think.

Step-by-step explanation:

just subtract the fractions and you will get 6\10 and the you will simplify and get 3\5. so 3\4 is closest to 3\5.

Step-by-step explanation:

it made £12,858.56.

the costs were £6,429.28

so, the profit was

12,858.56 - 6,429.28 = £6,429.28

since cost and profit are equal, that means they are both exactly half of the total income.

and half means 50%.

formally, to do the full % calculation :

100% = 12,858.56

1% = 100%/100 = 12,858.56/100 = 128.5856

how many % are 6,429.28 ?

as many % as times that 1% fits into 6,429.28 :

6,429.28 / 128.5856 = 50

so, it is 50%.

The linear function that gives the monthly cost E for x > 300 is given by:

E(x) = 44 + 0.04x.

A linear function is modeled by:

y = mx + b

In which:

When x > 300, we have that:

Hence the intercept is given by:

b = 8 + 0.12 x 300 = 44.

The slope is the cost per kWh of 4 cents, hence the function is:

E(x) = 44 + 0.04x.

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The equation of the two-step problem is 2x = x + 2/3

The conditions are given as

Let the variable in the equation be x

So, a possible equation is as follows

2x = x + 2/3

The solution to the equation is as follows

2x = x + 2/3

Subtract x from both sides

x = 2/3

Hence, the equation of the two-step problem is 2x = x + 2/3

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Answer: 89.21g

Step-by-step explanation:

36.81g + 52.40g = 89.21g

[tex]\begin{array}{ccll} \stackrel{recipe}{batch}&\stackrel{recipe}{flour}\\ \cline{1-2} 1&4\frac{2}{3}\\[1em] \frac{3}{4}&f \end{array}\implies \cfrac{1}{ ~~ \frac{3}{4}~~ }~~ = ~~\cfrac{ ~~ 4\frac{2}{3} ~~ }{f}\implies \cfrac{4}{3}~~ = ~~\cfrac{ ~~ \frac{4\cdot 3+2}{3}~~ }{f}\implies \cfrac{4}{3}=\cfrac{ ~~ \frac{14}{3} ~~ }{f} \\\\\\ \cfrac{4}{3}=\cfrac{14}{3f}\implies 12f=42\implies f=\cfrac{42}{12}\implies f=\cfrac{7}{2}\implies f=3\frac{1}{2}[/tex]

Check the picture below.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad A(\stackrel{x_2}{0}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ BA=\sqrt{(~~0 - (-3)~~)^2 + (~~0 - 6~~)^2} \implies BA=\sqrt{(0 +3)^2 + (0 -6)^2} \\\\\\ BA=\sqrt{( 3 )^2 + ( -6 )^2} \implies BA=\sqrt{ 9 + 36 } \implies BA=\sqrt{ 45 }\implies BA\approx 6.7[/tex]

Answer: 0.681818

Hope this helps!

The height of the density curve is 1/5

From the graph, we have the following parameter

Base = 5 units

As a general rule, the area under the density curve must have a value of 1

This means that

Area = 1

So, we have

Area = Base * Height

So, we have

1 = 5 * Height

Evaluate

Height = 1/5

Hence, the height of the density curve is 1/5

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Answer:

$28.00

Step-by-step explanation:

Set up an equation:

$22.40 = y(1 - 0.20)

Solve the contents of the parentheses first:

$22.40 = y(0.80)

Divide by 0.80 on both sides to isolate y:

($22.40)/0.80 = y

Solve:

$22.40 / 0.80 = $28.00

The measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.

We are given a ray diagram.

In the diagram, the measure of angles are given as:

∠ ACB = 25°

∠ ACG = 90°

We need to find the measure of angle ∠ DCE​ when CE bisects ∠ DCEF.

Now, we know that:

∠ BCG = ∠ DCF ( Vertically opposite angles.)      … (1)

Now,

∠ BCG = ∠ ACB + ∠ ACG

∠ BCG = 25° + 90°

∠ BCG = 115°     … (2)

∠ DCF = ∠ DCE + ∠ CEF

∠ DCF = ∠ DCE + ∠DCE ( as ∠ DCE = ∠ CEF since CE bisects them)

∠ DCF = 2 ∠ DCE   … (3)

Now, put (2) and (3) in (1), we get that:

115° = 2 ∠ DCE

∠ DCE = 115 / 2°

∠ DCE = 57.5°

Therefore, we get that, the measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.

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Answer:

2 [tex]\frac{2}{5}[/tex] hours or 2.4 hours or 2 hours and 24 minutes

Step-by-step explanation:

Answer:

The information that I do not need is how much the customer gave the parking attendant.

The garage charged $5.00

Step-by-step explanation:

2 + .75h       h stands for the number of hours the car was parked.

2 + .75 (4)

2 + 3 = 5

Answer:

  51%

Step-by-step explanation:

Given P(passing math) = 59%, P(passing physics) = 26%, and P(passing both) = 17%, you want to find the probability of passing only one of the courses.

We can record the given probabilities in a 2-way table (values shown in blue). The table is completed by making sure the totals add up (values shown in black).

The probability of passing one course and failing the other is the sum of the probabilities with a yellow background:

  42% +9% = 51%

The probability of passing one or the other is 51%.

__

Additional comment

We can also get there using the relation ...

  P(A+B) = P(A) +P(B) -P(AB)

The union of A and B also includes their overlap:

  P(A+B) = P(AB') +P(A'B) +P(AB)

In other words, the probability of interest is ...

  P(AB') +P(A'B) = P(A) +P(B) -2×P(AB) = 59% +26% -2(17%)

  P(AB') +P(A'B) = 51%

Answer:

Equation: (14.71-4.48) [divided by] 3 =x

"Answer x": 3.41

Explanation:

14.71-4.48=10.23

10.23/3 = 3.41

3.41

76 degrees n 83 degrees it's div

Answer: 111 + 222 = 333

Puja is not right to claim that any fraction can be thought of as a division problem and any division problem can be thought of as a fraction.

As seen by the definition of fraction, in terms of division problem, it involves only the the dividend and the divisor and not the quotient.

Hence, the two cannot be used inter-changeably, i.e., a fraction is not a division problem and vice versa.

Hence, Puja is not right to claim that any fraction can be thought of as a division problem and any division problem can be thought of as a fraction.

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Answer:

Step-by-step explanation:

yesterday