the function h=14t²+56t+60 represents the height of an object that is launched directly up into the air, where h represents the height in feet of the object and t represents time in seconds
What is the maximum height in feet of the object?
How long will it take the object to reach its maximum height?

Answer:

175% increase

Step-by-step explanation:

(3.5 / 2) * 100 = 175%

Answer:

C

Step-by-step explanation:

Total number of rolls = 96

There are three even numbers: 2, 4 and 6.

Number 2 was rolled 13 times

Number 4 was rolled 17 times

Number 6 was rolled 20 times

Hence, even number was rolled [tex]13+17+20=50[/tex] times.

The experimental probability is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.

Therefore,

[tex]P=\dfrac{50}{96}=\dfrac{25}{48}[/tex]

Answer: x = 15

Step-by-step explanation: The first thing to note is that what we have here are two similar triangles. First we have triangle ABC and secondly we have triangle EDC. Line BD is a transversal that cuts line AE at point C. Hence we can deduce that angle ACB is equal in measurement to angle ECD (opposite angles). Next we also observe that the other two angles are right angles, that is, 90° in size. Therefore we can conclude that the other two angles (angle ABC and angle EDC) are also of the same measurement.

We can now establish the ratio of the similar sides.

Line AB = Line ED

Line AC = Line EC

AB/ED = AC/EC

24/40 = 2x/3x + 5

3/5 = 2x/3x + 5 {the left hand side has been reduced to it's simplest form}

Next we cross multiply and that gives us

3(3x + 5) = 5(2x)

9x + 15 = 10x

Subtract 9x from both sides of the equation

15 = 10x - 9x

15 = x

Answer:

6<8

Step-by-step explanation:

This is actually simple since the 6 is less than 8 the thing will face away from the 6 and towards the 8.

Answer:

7.41%

Step-by-step explanation:

16/216 =

16 ÷ 216 =

0.074074074074074 =

0.074074074074074 × 100/100 =

0.074074074074074 × 100% =

(0.074074074074074 × 100)% ≈

7.407407407407% ≈

7.41%;

Answer:

-80

Step-by-step explanation:

The answer is -80 because 80 feet below sea level would be a negative number. So you just add a negative sign to 80 and voila! You get the answer. Your welcome, by the way!

Elevation 80 feet below sea level can be represented by the negative number -80 in mathematics. This is because negative numbers are used to represent depths or locations below sea level.

In mathematics, when we talk about locations below sea level, we represent them with negative numbers. So, an elevation of 80 feet below sea level will be represented as -80. This numerical representation helps us have an accurate and easy understanding of above and below sea level elevations. Such as, 0 represents sea level, positive numbers represent elevations above sea level, and negative numbers represent depths below sea level.

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Answer:

k = 4

Step-by-step explanation:

-8|4k-10|=-48

|4k-10|=-48/-8

|4k-10|= 6

4k = 6+10

4k = 16

k = 4

Answer:

C 147in2

Step-by-step explanation:

Formula: [tex]\frac{bh}{2}[/tex]

b=base

h=height

21*14=294

294/2=147

Answer: 20m³

Step-by-step explanation:

From the statement

V <> 1/p --------------------- 1

V = k/p --------------------- 2

K. = VP ---------------------- 3

V = 60 , p = 1

To find k which is a constant, we put those values in equation 3

K = 60 x 1

= 60.

Now from the second statement

V = k/p where p is 3

Therefore,

V = 60/3

= 20m³

Question:

A width of a rectangular painting is 3 in. More than twice the height. A frame that is 2.5 in. Wide goes around the painting

a. write an expression for the combined area of the painting and frame.

b. use the expression to find the combined area when the height of the painting is 12 in.

c. use the expression to find the combined area when the height of the the painting is 15 in.

Answer:

a) (h + 5)(2h + 8) is the expression for the combined area of the painting and frame

b) The combined area when h = 12 is 544 square inches

c) The combined area when h = 15 is 760 square inches

Solution:

Given that,

A frame that is 2.5 inches wide goes around the painting

The frame will go around all 4 sides of the painting.

That means that the length of each side of the painting will increase by 2.5 inches

Therefore,

The height of painting and frame is:

h = h + 2.5 + 2.5

h = h + 5

(2.5  inches on the top and the bottom)

Also given that,

Width of a rectangular painting is 3 inches more than twice the height

w = 3 + 2h

Now the width of painting and frame is:

w = 3 + 2h + 2.5 + 2.5

(Again, 2.5 inches on the top and the bottom)

w = 2h + 8

Thus the combined area of the painting and frame is:

[tex]Combined\ area = (h+5)(2h+8)[/tex]

B) Substitute h = 12 inches

[tex]Combined\ area = (12+5)(2(12)+8)\\\\Combined\ area = 17 \times (24+8) = 17 \times 32\\\\Combined\ area = 544[/tex]

Thus the combined area when h = 12 is 544 square inches

C) Substitute h = 15 inches

[tex]Combined\ area = (15+5)(2(15)+8)\\\\Combined\ area = 20 \times (30+8) = 20 \times 38\\\\Combined\ area = 760[/tex]

Thus combined area when h = 15 is 760 square inches

The answer is B, 7i.

sqrt(-49)

Pull out an i.

i*sqrt(49)

Take the square root to get 7i.

⭐ Answered by Hyperrspace (Ace) ⭐

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Answer:

d

Step-by-step explanation:

Answer:

24 hours

24 hours is the solution to 300=10(2)^t/15

Answer:

Step-by-step explanation:

18x+8=14

18x=6

x=1/3

When ƒ(x) is equal to 14, the value of x is 1/3.

To find the value of x when f(x) is equal to 14, we can set up the equation:

f(x) = 18x + 8

We know that f(x) is equal to 14, so we substitute that into the equation:

14 = 18x + 8

We isolate the variable x by subtracting 8 from both sides of the equation:

14 - 8 = 18x

6 = 18x

To solve for x, we divide both sides of the equation by 18:

6/18 = x

1/3 = x

Therefore, when f(x) is equal to 14, the value of x is 1/3.

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Answer:

3x^2 - 10x - 1 = 0 $OPTION D ON EDGE$

Step-by-step explanation:

Answer:

3x2 – 10x + 6 = 0

Step-by-step explanation:

Givena general quadratic equation

ax²+bx+c = 0

The general formula for finding x is;

x = -b±√b²-4ac/2a

Where a,b and c are the coefficient of x², x and x° respectively

Given the solution in question to be;

x = 5±2√7/3

The quadratic equation that has thw above general solution will be;

3x²-10x+6 = 0

From the equation, a = 3, b= -10 and c = 6

Substituting this value in the general formula to get x we have;

x = -(-10)±√(-10)²-4(3)(6)/2(3)

x = 10±√100-72/6

x = 10±√28/6

x = 10±√7×4/6

x = 10±2√7/6

Dividing through by 2 gave;

x = 2(5±2√7)/6

x = 5±2√7/3 (which gives the solution in question)

Answer:

Circumference of circle= 37.68 units

Circumference of sector= 6.28 units

Step-by-step explanation:

The given figure is a circle with given radius OB= 6 units.

The circumference of a circle is the total length of its boundary.

For the complete circle its circumference can be calculated by;

           Circumference= [tex]2\pi r[/tex]

                                 [tex]=2*3.14*6\\=37.68[/tex] units

For the circumference of the Sector with 60° in the figure, the circumference can be calculate by:

                              [tex]=\frac{60}{360}* 2*\pi*6\\\\=\frac{1}{6}*12*3.14\\\\ =2*3.14\\\\=6.28[/tex] units

So, the circumference of the full circle is 37.68 units and the circumference of the sector is 6.28 units.

Answer:

1/2

Step-by-step explanation:

2(x+1.25)=3.5

2x+2.5=3.5

2x=3.5-2.5

2x=1

x=1/2

You will need 119 cups to sell all of the lemonade.

Step-by-step explanation:

Given,

Diameter of cups = 9 cm

Radius of cup = [tex]\frac{Diameter}{2}=\frac{9}{2}=4.5\ cm[/tex]

Height of cups = 12 cm

We will find volume of cup.

[tex]Volume = \frac{1}{3}\pi r^2h\\[/tex]

Putting all the values

[tex]Volume=\frac{1}{3}(3.14)(4.5)^2(12)\\\\Volume=\frac{1}{3}(3.14)(20.25)(12)\\\\Volume= \frac{763.02}{3}\\\\Volume= 254.34\ cm^3[/tex]

Therefore;

Each cup can hold 254.34 cubed centimeter of lemonade.

Number of gallons = 8

1 gallon = 3785 cm³

8 gallons = 3785*8 = 30280 cm³

Let,

x = Number of cups

Volume of lemonade in one cup * Number of cups = Volume of 8 gallons

254.34x=30280

Dividing both sides by 254.34

[tex]\frac{254.34x}{254.34}=\frac{30280}{254.34}\\x=119.05[/tex]

Rounding off to nearest whole number

x = 119

You will need 119 cups to sell all of the lemonade.

Keywords: volume, division

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Answer:

35

Step-by-step explanation:

Total number of students in class is 40

87.5% of the class = 87.5/100 *40 =35

The students in Ms. Carr's class that live less than 10 miles from school are 35 students.

To find out how many students in Ms. Carr's class live less than 10 miles from school, we can use the percentage provided in the question.

1. Identify the total number of students in the class:

  Ms. Carr has a total of 40 students in her class.  

2. Determine the percentage of students living less than 10 miles from school:

  We know that 87.5% of these students live less than 10 miles from school.  

3. Convert the percentage to a decimal for calculation:

To convert 87.5% to a decimal, we divide by 100:  

[tex]\[ 87.5\% = \frac{87.5}{100} = 0.875 \][/tex]

4. Calculate the number of students:  

Now, multiply the total number of students by the decimal:  

Number of students = 0.875 × 40 = 35

5. Conclusion:

Therefore, 35 students in Ms. Carr's class live less than 10 miles from school.

Evaluate the inside absolute values first:

17-|16*9|

17-|144|

17-144

-127

Hope this helped!

Answer:

X = 0

Y = 2

so Option A (0,2) IS CORRECT

Step-by-step explanation:

Y = -1/3 x + 2 equation 1

Y = x+ 2 equation 2

from equation 2 we have

y = x+ 2 Put in equation 1

x + 2 = -1/3 x + 2

x +1/3x = 2 -2

0.67 x = 0

X = 0

so put x =0 in equation 2 then we have

y = x +2

Y = 0+ 2

Y = 2

If you add 10 and then subtract 1, you get the same result as if you just added 9.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

We have to add 24+9 by making 10s.

As per the given question, the required solution would be as:

24 + 10 - 1 = 33

Therefore, if you add 10 and then subtract 1, you get the same result as if you just added 9.

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Final answer:

To add 24 and 9 using tens, break 9 into 6 and 3, add 6 to 24 to get 30, and then add the remaining 3 to reach 33.

Explanation:

To add 24 and 9 by making 10s, you can first break down the number 9 into 6 and 3.

Add 6 to 24 to make a round number, which is 30.

Now you have made a '10' because 30 is a multiple of 10.

Next, add the remaining 3 to get 33.

So, 24 + 9 = 33.

Answer:

5/1, 25/5

Step-by-step explanation:

Answer:

[tex]\delta=\frac{\epsilon}{3}[/tex]

The proof is in the explanation.

Step-by-step explanation:

Compare [tex]\lim_{x\rightarrow 7}(3x-2)=19[/tex] to [tex]\lim_{x\rightarrow a}f(x)=L[/tex].

We want to find  [tex]\delta[/tex] such that whenever [tex]0<|x-a|<\delta[/tex] we have [tex]|f(x)-L|<\epsilon[/tex].

We want to find [tex]\delta[/tex] such that whenever [tex]0<|x-7|<\delta[/tex] we have [tex]|3x-2-19|<\epsilon[/tex].

[tex]|3x-2-19|<\epsilon[/tex]

Simplify:

[tex]|3x-21|<\epsilon[/tex]

Factor on left side inside the | |:

[tex]|3(x-7)|<\epsilon[/tex]

|ab|=|a||b|:

[tex]|3||x-7|<\epsilon[/tex]

|3|=3:

[tex]3|x-7|<\epsilon[/tex]

Divide both sides by 3:

[tex]|x-7|<\frac{\epsilon}{3}[/tex]

So we will need to choose [tex]\delta=\frac{\epsilon}{3}[/tex].

We want to prove there exists a [tex]\delta[/tex] such that whenever [tex]0<|x-7|<\delta[/tex] we have [tex]|f(x)-L|<\epsilon[/tex].

Proof:

Let [tex]\epsilon>0[/tex]. We will choose [tex]\delta=\frac{\epsilon}{3}[/tex] such that [tex]0<|x-7|<\delta[/tex] will give us [tex]|f(x)-L|<\epsilon[/tex].

[tex]|f(x)-L|=|(3x-2)-19|[/tex]

        [tex]=|3x-21|[/tex]

        [tex]=|3||x-7|[/tex]

        [tex] =3|x-7|<3\delta=3\frac{\epsilon}{3}=\epsilon[/tex].

Therefore, we have for all [tex]\epsilon>0[/tex], [tex]\delta=\frac{\epsilon}{3}[/tex] is the number that satisfies the definition.

Answer:

The length of the blue rope is 80.25 meters.

Step-by-step explanation:

B = Blue Rope

G = Green Rope

R = Red Rope

B=3R (Blue is 3 x as long as Red)

G=5B (Green is 5 x as long as Blue)

B+G+R = 508.25 (The three ropes together are 508.25 meters)

Since B=3R, I will rewrite the equation above

3R + G + R = 508.25

Now, I will write G in terms of R:

G=5B

B=3R, so 5B = 15R (multiply both sides by 5) which means that G=5B=15R, so G=15R.

Rewrite the equation again in terms of R:

3R + 15R + R = 508.25

19R = 508.25 (combine like terms)

R = 26.75 (divide both sides by 19 to solve for R)

Now, use the value 26.75 (R, which is the length of the red rope) to solve for B (the length of the blue rope):

B=3R

B=3(26.75)

B=80.25 meters

Use this formula to get the total angle measurement of the figure:

T=180(n-2)

Since there are 7 sides, the total measurement must be:

180(7-2)

180(5)

900 degrees

Set up an equation and solve for x:

123+121+127+128+139+125+x=900

763+x=900

x=137

So the missing angle is 137 degrees.

Hope this helped!

Answer:

-10k-28

Step-by-step explanation:

-19+4k-15k+k-9

-28-11k+k

-10k-28

Answer:

12k+ -10

im not truely sure if this is correct... but i went off my knowlage

Answer:

Explanation:

The average cost is found dividing the total cost by the number of hot dogs:

         [tex]Average\text{ }cost=Total\text{ }cost/Number\text{ }of\text{ }hot\text{ }dogs[/tex]

The total cost is the the sum of amount that you invest plus the product of the cost of producing each hot dog times the number of hot dogs:

[tex]Total\text{ }cost=investment+Number\text{ }of\text{ }hot\text{ }dogs\times cost\text{ }to\text{ }produce\text{ }each\text{ }hot\text{ }dog[/tex]

           [tex]Total\text{ }cost=15,000+0.65x\\ \\ Averate\text{ }cost=(15,000+0.65x)/x=1.15[/tex]

Where x is the number of hot dogs.

         [tex](15,000+0.65x)/x=1.15\\ \\ 15,000+0.65x=1.15x\\ \\ 15,000=1.15x-0.65x\\ \\ 15,000=0.5x\\ \\ 15,000/0.5=x\\ \\ 30,000=x\\ \\ x=30,000[/tex]

Which shows you how you can find that the answer is 30,000 hot dogs.

Final answer:

To find the number of hot dogs needed to achieve an average cost of $1.15, including a fixed investment of $15,000 and a variable cost of $.65 per hot dog, the calculation reveals that 30,000 hot dogs must be sold to reach this target.

Explanation:

The question asks how many hot dogs must be sold before the average cost per hot dog is $1.15, given an initial investment of $15,000 and a production cost of $.65 per hot dog. To find the break-even point in terms of units sold to reach the target average cost, we use the formula to calculate average cost: Average Cost = (Fixed Costs + Variable Costs) / Quantity. Here, the fixed cost is the initial investment of $15,000, and the variable cost is $.65 per hot dog.

To find the number of hot dogs needed to achieve an average cost of $1.15, we set up the equation: $1.15 = ($15,000 + $.65Q) / Q. Solving for Q gives us 30,000 hot dogs as the break-even point where the average cost per hot dog would be $1.15.

This calculation allows the business owner to understand how many units need to be sold to overcome the initial investment and start making a profit on each hot dog sold at or above $1.15.

Answer:

-2x-5

Step-by-step explanation: