The area of a garden is (x² + 7x + 10)
square yards. Find the dimensions of the
garden if x= 14.

Answer:

14/27

Step-by-step explanation:

Let x be the unknown number

-2/3 * x = -28/81

Multiply each side by -3/2

-3/2*-2/3 * x = -28/81 * -3/2

x = 28/2 * 3/81

x =14*1/27

x = 14/27

Answer:

14/27

Step-by-step explanation:

Let x be the other number

x × -2/3 = -28/81

x = -28/81 × -3/2

x = 14/27

Answer:

The answer is D

Step-by-step explanation:

Answer:

Shota's speed = 5 m/s

In total, it take 6 seconds to reach the edge of the volcano.

Step-by-step explanation:

Given;

Total height below the edge of the volcano = 30 m

(Note that he climbed at constant rate)

After 4.5 seconds, he was 7.5 meters below the edge of the volcano.

Time = 4.5 s

Distance covered = 30 - 7.5 = 22.5 m

His speed = distance covered/time

Substituting the values;

Speed = 22.5/4.5

Speed = 5 m/s

Time needed to reach the edge;

Time = distance/speed

Speed = 5m/s

Distance = 30 m

Substituting;

Time = 30/5 = 6 seconds

Answer:

1 an -5/2

Step-by-step explanation:

Answer:

The answer is D

I hope this is right

Answer: f(120°) = (√3) + 1/2

Step-by-step explanation:

i will solve it with notable relations, because using a calculator is cutting steps.

f(120°) = 2*sin(120°) + cos(120°)

           =2*sin(90° + 30°) + cos(90° + 30°)

here we can use the relations

cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)

sin(a + b) = cos(a)*sin(b) + cos(b)*sin(a)

then we have

f(120°) = 2*( cos(90°)*sin(30°) + cos(30°)*sin(90°)) +  cos(90°)*cos(30°) - sin(90°)*sin(30°)

and

cos(90°) = 0

sin(90°) = 1

cos(30°) = (√3)/2

sin(30°) = 1/2

We replace those values in the equation and get:

f(120°) = 2*( 0 +  (√3)/2) + 0 +  1/2 = (√3) + 1/2

Step-by-step explanation: To find the x-intercept, substitute in 0 for y and solve for x.

x-intercept(s): (2.30581496,0)

y-intercept(s): None

Answer:

32 cubic feet

Step-by-step explanation:

To know the volume of a figure we have to calculate the area of its "base" and then multiply it by its height.

In this case we have a rectangular hole that has an area of 8 square feet.

As we said before:

Volume = Area x height.

If we substitute the value of the area of the rectangle and the height (or depth in this case) we would get:

Volume = 8 x 4 = 32 cubic feet.

Thus, the volume of John's hole is 32 cubic feet.

Answer:

32 cubic feet

Step-by-step explanation:

The volume of a rectangular prism is given by;

Length*width*Height

or, Area*height

Height = 4 feet

Area= 8 square feet

Conversion to Cubic feet is given by;

(cubic feet) = (square feet) × (height in feet)

Therefore,

Cubic feet = 8 square feet*4 feet

= 32 cubic feet.

Answer:Regina recieved $14 dollars of change

Step-by-step explanation:

12+14=26

40-26=14

The change received by Regina is $14.

A word problem is a verbal description of a problem situation. It consists of  few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Regina bought a book for price = $12

Regina bought a game for price = $14

Total amount paid by Regina = $40

The Regina should receive the change,

⇒ [tex]Change = 40-(12+14)[/tex]

⇒ [tex]Change = 40-26[/tex]

⇒ [tex]Change = 14[/tex]

Hence we can conclude that the change received by Regina is $14.

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Answer:

To be done in time, he would need to solve 6 questions per day on the days that he is not on trip

Step-by-step explanation:

If he solves the problems 5 per day, the total number of days that would be required to finish solving the problem would be 120/5 = 24 days

Now, he has 4 free days which would be for a family trip. The number of questions that he would miss during those trip days will be 4 * 5 = 20 questions

Now since he wants to still finish on time, what is needed to be done is to share the 20 left overs amongst the 20 days which he has to work

This makes a total of 1 question per day

Adding this to the 5 questions per day he has before will be = 6 questions per day

Answer:

6 problems

Step-by-step explanation:

Answer:

Option "A" is the correct answer to the following question.

Step-by-step explanation:

Given:

Total number of experiment = 50

Find:

Probability to get less then 4:

Computation:

⇒ Total number can be get less then 4 = 4+2+3

⇒ Total number can be get less then 4 = 9

⇒ Probability of an outcome = Total number of outcomes /  Total number of experiment

⇒ Probability to get less then 4 = Total number can be get less then 4 / Total number of experiment

⇒ Probability to get less then 4 = 9 / 50

Answer:

I believe your favorite subject maybe Science and World geography

Step-by-step explanation:

I am not sure : )

Answer:

B

Step-by-step explanation:

hope this helps.......

Answer:

my answer is B

Step-by-step explanation:

I know this because I just took a test on this and got it right.

Answer:

65.97

Step-by-step explanation:

Answer:

Step-by-step explanation:

If 2 men take 6 hrs to paint the fence, then

  3 men would  obviously take  less time to paint the same fence;

            2 men= 6 hrs

            3 men= ?

thus, the time taken by three men to paint the same fence=2/3 ×6 hrs

                                                                                                = 4 hrs

Answer:

y=-2x+9

Step-by-step explanation:

1. Make m value opposite of og m value.

2. Then plug in variables x and y into the equation

3. Solve for b

-1 = -2(5) + b

9 = b

4. You have the answer

Answer:

157.48

Step-by-step explanation:

Answer:

(x+2)(x+4)

Step-by-step explanation:

Answer:

( x + 2 ) ( x + 4 )

Step-by-step explanation:

Question

A student solved this problem and said the answer was [tex]5\frac{1}{4}[/tex] miles. Danielle ran [tex]3\frac{1}{8}[/tex] miles on Tuesday, [tex]4\frac{1}{2}[/tex] miles on Wednesday, and [tex]5\frac{1}{4}[/tex] miles on Thursday. How far did Danielle run altogether? Is the student's answer reasonable?

- No, the answer is not reasonable. It should be about 13 miles.

- Yes, the answer is reasonable.

- No, the answer is not reasonable. It should be about 2 miles.

- No, the answer is not reasonable. It should be about 20 miles.

Answer:

- No, the answer is not reasonable. It should be about 13 miles.

Step-by-step explanation:

Given

Student solution = [tex]5\frac{1}{4}[/tex] miles.

Miles covered on Tuesday = [tex]3\frac{1}{8}[/tex] miles

Miles covered on Wednesday = [tex]4\frac{1}{2}[/tex] miles

Miles covered on Thursday = [tex]5\frac{1}{4}[/tex] miles

Required

- Total distance covered by the student

- Is the student answer reasonable?

To calculate the actual distance covered by Danielle, we simply add the distance covered on each day,

This goes thus

Distance = [tex]3\frac{1}{8}[/tex] + [tex]4\frac{1}{2}[/tex] + [tex]5\frac{1}{4}[/tex]

Convert to Improper Fractions

Distance = [tex]\frac{25}{8}[/tex] + [tex]\frac{9}{2}[/tex] + [tex]\frac{21}{4}[/tex]

Take LCM

Distance = [tex]\frac{25 + 36 + 42}{8}[/tex]

Distance = [tex]\frac{103}{8}[/tex]

Distance = 12.875

From the calculations above, we can conclude that the student's answe is not reasonable because his calculation ([tex]5\frac{1}{4}[/tex] miles) is much more smaller than the actual result 12.875 miles

From option A through D, Only option A is correct because 12.875 miles cam be approximated to 13 miles.

Hence,

A. - No, the answer is not reasonable. It should be about 13 miles.

is the right answer

Answer:

a

Step-by-step explanation:

Answer:

The area of the circle is [tex]153.94meters^2[/tex]

Step-by-step explanation:

The formula for the area of a circle is : [tex]\pi *radius^{2}[/tex]

To work this out you would first need to divide the diameter of 14 by 2, this gives you 7. This is in order for us to calculate the radius. The radius of a circle is the length from one side to the centre.

Now that we know the radius the next step is to multiply pi by the radius of 7 squared, this gives you 153.94. This is because in order for you to calculate the area you would substitute the values into the formula.

1) Divide 14 by 2.

[tex]14/2=7[/tex]

2) Multiply pi by 7 squared.

[tex]\pi *7^2=153.94 meters^2[/tex]

153.94 square meters is the area of the triangle.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

The formula to calculate the area of a circle is A = πr², where A is the area and r is the radius of the circle.

Since the diameter is given as 14 meters, the radius can be calculated by dividing the diameter by 2:

r = d/2 = 14/2 = 7 meters

Now, we can substitute this value of radius into the formula for the area of a circle:

A = πr² = π(7)² = 49π square meters

Therefore, the area of Fiona's circle is 49π square meters (or approximately 153.94 square meters if π is approximated to 3.14).

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Answer:

It's B.

Step-by-step explanation:

Z=-3, z=6

Answer:

120

Step-by-step explanation:

by using the basic counting rule, there are 5 positions first, then 4, then ,3 and so on down to one. so when you multiply them all together, you get 120. Also i took  a test with the same qeustion, and that was the anwer :)

Answer:

120

Step-by-step explanation:

5 times 4 times 3 times 2 times 1= 120

5 choices for first

1 choice already taken so 4 for the other model

3 for the other

2 for the other

and 1 for the other

=120

Its correct, trust me!

Answer:

44t + 11

Step-by-step explanation:

[tex]11(4t + 1) \\ = 11 \times 4t + 11 \times 1 \\ = 44t + 11 \\ [/tex]

Answer:

the answer is attached to the picture

Please consider the complete question.

A student is deriving the quadratic formula. Her first two steps are shown. Step 1: [tex]-c = ax^2 + bx[/tex]

Step 2: [tex]-c = a[x^2+\frac{b}{a}x][/tex]

Which best explains or justifies Step 2?

A. division property of equality

B. factoring the binomial

C. completing the square

D. subtraction property of equality

We can see that in step 2 student has factored the right side of equation.

The student factored our a from the right side of equation. To factor our a from right side, student has divide the bx term by a.

We can multiply and divide by same quantity in an equation.

[tex]-c = ax^2+a\cdot \frac{b}{a}x[/tex]

Now we can factor out a as:

[tex]-c = a(x^2+\frac{b}{a}x)[/tex]

Therefore, the 2nd step is known as factoring of binomial and option B is the correct choice.

Answer:

it b factoring a binomial on

Step-by-step explanation:

thats on edge

Answer:

7110 books

Step-by-step explanation:

5%*15800=0.05*15800=790

790*11=8690

15800-8690=7110

Therefore, 7110 books

Answer: 86,900

Step-by-step explanation:

I changed the 5% into decimal form and made it 0.5. Next, I multiplied 0.5 by 11, which gave me 5.5.

15,800 x 5.5 = 86,900

So, the author would’ve sold 86,900 books in the first 11 months.

(Sorry if wrong. Yeah I think I’m wrong now because I’m not even in high school. Just ignore this lol)

Answer:

The shaded segment  = The arc area - The triangle

The arc area = pi x radius^2 x angle/360

                     = pi x 9^2 x (360-270)/360 = 63.61 (m2)

The triangle area = 9 x 9/2 = 41.5 (m2)

(because this is right triangle)

=> The shaded segment = 63.61 - 41.5 = 22.11 (m2)