A parallelogram is cut out of a 12-inch by 8-inch sheet of paper. There are four right triangle remnants. Two have the dimensions 2 inches by 9 inches, and the other two have the dimensions 3 inches by 6 inches. The resulting parallelogram has a base of approximately 9.22 inches. Complete the following steps to calculate the altitude of the parallelogram using area methods. The area of the sheet of paper is square inches. The combined area of the triangle cutouts is square inches. The area of the parallelogram is square inches. The altitude of the parallelogram rounded to two decimals is square inches.
Answer:
96
36
60
6.51
Step-by-step explanation:
The area of a shape is the amount of space it occupies.
The area of the paper is 96 square inchesThe combined area of the triangle cutouts is 36 square inchesThe area of the parallelogram is 60 square inchesThe altitude of the parallelogram is 6.51 inchesThe dimension of the paper is given as: 12-inch by 8-inch
So, its area is:
[tex]\mathbf{A_1 =12 \times 8}[/tex]
[tex]\mathbf{A_1 =96}[/tex]
The dimensions of the 4 right triangles are: Two 2 inches by 9 inches, and two 3 inches by 6 inches
So, the combined area is:
[tex]\mathbf{A_2 = 2 \times \frac 12 \times 2 \times 9 + 2 \times \frac 12 \times 3 \times 6}[/tex]
[tex]\mathbf{A_2 = 36}[/tex]
The area of the parallelogram is the difference between the areas of the paper and the four right triangles.
So, we have:
[tex]\mathbf{A_3 = A_1 - A_2}[/tex]
[tex]\mathbf{A_3 = 96 - 36}[/tex]
[tex]\mathbf{A_3 = 60}[/tex]
The area of a parallelogram is:
[tex]\mathbf{Area = Base \times Altitude}[/tex]
The base is given as 9.22
So, we have:
[tex]\mathbf{60 = 9.22\times Altitude}[/tex]
Divide both sides by 9.22
[tex]\mathbf{6.51 = Altitude}[/tex]
Rewrite as:
[tex]\mathbf{Altitude = 6.51}[/tex]
Hence, the altitude of the parallelogram is 6.51 inches
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Which trinomial is a perfect square trinomial?
A) a^2 - 12a + 36
B) a^2 - 8a + 64
C) a^2 - 6a + 36
D) a^2 - 4a + 64
Answer:
d is the answer
How long will it take a $800 investment to be worth $900 if it is continuously compounded at 11% per year?
It takes approximately 1.083 years, or around 1 year and 1 month for an $800 investment to grow to $900 when continuously compounded with an 11% yearly interest rate.
Explanation:To calculate how long it will take for an $800 investment to grow to $900 with continuous compounding at an 11% yearly interest rate, we use the formula for continuously compounded interest, P = Pert, where P is the final amount, Pe is the original principal, r is the interest rate, and t is time in years.
Rearranging the equation to find t, we have, t = ln(P/Pe) / r.
Substitute P as $900, Pe as $800, and r as 0.11 into the formula.
Therefore, t = ln(900/800) / 0.11 = approximately 1.083 years or around 1 year and 1 month.
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what is 8m-3-7m???????
Answer:
i personally think it's 4
Step-by-step explanation:
even tho this was 4 years ago ehhhhhhh
Tomas's grandfather is 100 years old.Tomas's grandfather is 10 times as old as Tomas.How old is Tomas? Can someonegive me the answer to this plz
the directions for mixing water and powdered milk say that one should use 3 cups of water for each cup of powdered milk. how many cups of powdered milk are needed if 5 cups of water are used
If a company has 5 employees with annual salaries of $30,000, $50,000, $30,000, $80,000, and $70,000, respectively, what is the mean annual salary at the company?
Answer:
Annual mean salary at the company is $52,000
Step-by-step explanation:
Given : If a company has 5 employees with annual salaries of $30,000, $50,000, $30,000, $80,000, and $70,000, respectively.
We have to determine the mean annual salary at the company.
Consider the given salaries of 5 employee of the company
$30,000, $50,000, $30,000, $80,000, and $70,000
The annual mean salary at the company is the sum of salary of the employees divided by the number of employees.
Annual mean salary =[tex]\dfrac{30,000+50,000+30,000+70,000+80,000}{5}=\frac{2,60,000}{5}[/tex]
Thus, Annual mean salary at the company is $52,000
f(x)=2× if x<0
|x| if x>0
I don't understand what the question is asking?
which situation could be modeled by using a linear function
The figure has ____ lines of symmetry. A. 0 B. 4 C. 6 D. 8
Answer:
B. 4
Step-by-step explanation:
Vertical and horizontal lines through the vertices farthest from center are two of the lines of symmetry.
The other two lines of symmetry are the diagonal lines through the vertices closest to center.
There are a total of 4 lines of symmetry.
Answer:
4
Step-by-step explanation:
hope it helps
The number of chicken legs depends on how many chickens are in the coop. This is modeled by y=2x and is an example of _____ variation.
Answer:
y=2x is an example of direct variation.
Step-by-step explanation:
Direct variation is mathematical relationship in between two variables which can be expressed by an equation where one variable is equal to a constant multiplied by the other variable.
In the equation y=2x, x and y are the variables and 2 is a constant.
Here it is expressed as an equation where the variable y is equal to the constant 2 multiplied by the other variable x.
Thus we can say that it is an example of direct variation.
find the x-intercepts of the parabola with vertex (2,13) and y intercept (0,5)
round to the nearest hundredth
i have no idea how to do this problem please help!
Answer:
What is the vertex of the parabola?
Round to the nearest hundredth.
✔ (8.33, 236.67)
Step-by-step explanation:
1. The function f(x) = –0.05(x2 – 26x – 120) represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent? (1 point)
2. What do the zeros of this function represent? Remember the zeros are where f(x) = 0. (1 point)
3. Will the zeros tell you where the net should be placed? Why or why not? (1 point)
4. To find the zeros, set the function equal to 0, and then factor the polynomial. Start by setting the function equal to 0. (1 point)
Factor the polynomial.
The polynomial (x2 – 26x – 120) is in the form x2 + bx + c which can be factored as (x + p)(x + q) .
5. Next factor the polynomial x2 – 26x – 120. To identify the factors, complete the table: Note: This table does not contain all the factors of –120, but it has enough to let you factor the polynomial. (2 points: 0.5 points for each row)
p q p + q
10 –12
–10 12
30 –4
4 –30
6. Which values of p and q give the correct factors? (1 point)
7. Factor the polynomial completely: (2 points: 1 point for each factor)
0 = –0.05(x2 – 26x – 120)
8. Find the roots of the equation by setting each factor equal to 0 and solving for x.
Hint: There are three factors, but the constant factor, –0.05, does not equal zero. Solve for x with the other two factors. (2 points: 1 point for each factor)
9. Identify the roots. (2 points: 1 point for each root)
10. What are the zeros of this function? Circle them on the graph. (1 point)
11. Are these zeros the same as the roots you found? (1 point)
12. What does a negative zero mean in terms of this problem? (1 point)
13. Following this trajectory, will Nik hit a net that is 30 feet from the cannon? How do you know? (1 point)
The motion of the projectile (cannonball), given by the (quadratic)
polynomial function is the path of a parabola.
Response:
Vertical heightThe point the projectile is at ground levelYes, because is it where the projectile will landx² - 26·x - 120 = 0(x - 30)·(x + 4) = x² - 26·x - 120 p = -30, and q = 4-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4) x - 30 = 0 and x + 4 = 0 Which gives; x = 30 or x = -4x = 30 or x = -4The zeros of the function are x = 30, and x = -4YesThe negative zero (x = -4) means that the ground level is a point before the location at which the cannonball is launched (x = 0). It also means that the cannonball was launched above ground level.Yes, because the projectile hits the ground 30 feet from the cannonWhich methods can be used to evaluate the polynomial?1. f(x) is the output of the projectile function, where;
x = The input which is the distance
Therefore;
f(x) = The vertical distance (height) of the cannonball at point x.2. The zeros are the points where the height, f(x) = 0
Therefore;
The zeros represent the points at which the cannonball is at ground level3. The net should be placed where the cannonball is expected to reach ground level.
Therefore;
The zeros indicates where the net should be placed4. The given polynomial can be equated to 0 as follows;
x² - 26·x - 120 = 0
5. x² - 26·x - 120 = x² - 30·x + 4·x- 120
Which gives;
x·(x - 30) + 4·(x- 30) = (x - 30)·(x + 4)
(x - 30)·(x + 4) = x² - 26·x - 1206. Where; (x + p)·(x + q) = a·x² + b·x + c
We have;
The values of p and q that give the correct factors are;
p = -30, and q = 47. The polynomial, -0.05·(x² - 26·x - 120) = 0 in factored form is therefore;
-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4)8. From the factors, we have;
-0.05·(x² - 26·x - 120) = -0.05·(x - 30)·(x + 4)
The roots of the equations, are given as follows;
x - 30 = 0 and x + 4 = 0
Which gives;
x = 30 or x = -49. The roots of the equation are therefore;
x = 30, and x = -410. The zeros for the function, are the values of x at which f(x) = 0
At x = 30 f(30) = -0.05 × (30² - 26 × 30 - 120) = 0
At x = -4, f(-4) = -0.05 × ((-4)² - 26 × (-4) - 120) = 0
The zeros of the function are x = 30, and x = -411. Yes. The zeros are the same as the roots found given that at the roots, f(x) = 0
12. The zeros of the function are x = 30 and x = -4, which are points at
which the projectile (cannonball) is at ground level. The negative zero, x
= -4, means that, apart from the point x = 30, the projectile can (also/only)
be at ground level at a point before the location where the projectile is
launched, (-4) which means that at the point at which the cannonball is
launched, which is at x = 0, the cannonball was not on the ground, but
at the lip of the barrel or at a more elevated position.
What the negative zero means are therefore;
It is a location before the point where the cannonball is launchedThe cannonball is launched from a height above ground level13. At 30 feet, x = 30, which is a zero of the function, and the cannonball
is at ground level, such that a net placed at 30 feet from the cannon
will be hit by the cannonball.
Therefore;
Yes Nik will hit a net that is 30 feet from the cannonLearn more about quadratic functions and projectiles here:
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A map scale has a scale of 1 inch equals 35 miles what is the actual distance if the distance on the map is 3.5 in
Jessica and Franklin are volunteering to paint one of their community member’s fences for service hours. If Jessica could complete the job in 6 hours and Franklin could complete the job in 4.5 hours, how long would it take them to complete the job together, to the nearest minute?
The best leaper in the animal kingdom is the puma, which can jump to a height of 12 ft when leaving the ground at an angle of 45 degrees. with what speed in si units, must the animal leave the ground to reach that height?
Sonya can walk 6 km in 3 hours. If she has to walk 10 km, how much time will it take her?
The area of Desert A is nine times the area of Desert B. If the sum of their areas is 2,000,000 square miles, find the area of each desert.
Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
a.Divide all terms in the equation by a.
b.Subtract the constant (the term without an x) from both sides.
c.Add a constant (in terms of a and b) that will complete the square.
d.Take the square root of both sides of the equation.
e.Solve for x.
Answer:
See below.
Step-by-step explanation:
We are going to take the quadratic formula ax²+bx+c=0
a.Divide all terms in the equation by a.
[tex]\frac{ax^{2} }{a} +\frac{b}{a}x+\frac{c}{a}=0\\\\x^{2} +\frac{b}{a}x+\frac{c}{a} =0[/tex]
b.Subtract the constant (the term without an x) from both sides.
[tex]x^{2} +\frac{b}{a}x+\frac{c}{a} -\frac{c}{a} =\frac{-c}{a} \\\\x^{2} +\frac{b}{a}x=-\frac{c}{a}[/tex]
c.Add a constant (in terms of a and b) that will complete the square.
[tex]x^{2} +\frac{b}{a}x=-\frac{c}{a}\\\\[tex]x^{2} +\frac{b}{a}x+\frac{b^{2} }{4a^{2} } =-\frac{c}{a} +\frac{b^{2} }{4a^{2}}\\\\(x+\frac{b}{2a}) ^{2} =\frac{-4ac+b^{2} }{4a^{2} }[/tex]
d.Take the square root of both sides of the equation.
[tex]x+\frac{b}{2a} =[tex]\\x+\frac{b}{2a} =\frac{\sqrt{-4ac+b^{2} } }{2a}\\x=\frac{\sqrt{-4ac+b^{2} } }{2a}-\frac{b}{2a} [/tex]
e.Solve for x.
[tex]x=-b+\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
How tall is a building that casts a 73 foot shadow when the angle of elevation of the sun is 29
The height of the building is approximately 40.39 feet.
Explanation:To find the height of the building, we can use the concept of similar triangles. The height of the building is proportional to the length of its shadow. We can set up a proportion using the angle of elevation of the sun and the length of the shadow.
Let x be the height of the building. The proportion can be set up as:
(x / 73) = tan(29°)
Using a calculator, we can find the value of tan(29°) to be approximately 0.5543. Solving for x, we get:
x = (73 * 0.5543)
Therefore, the height of the building is approximately 40.39 feet.
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Assume that the risk-free rate is 8 percent the required rate of return on the market is 13 percent and the required rate of return on acme healthcare stock is 15 percent what is the implied beta coefficient
We deal from a well-shuffled 52-card deck. calculate the probability that the 13th card is the first king to be dealt.
Final answer:
The probability that the 13th card is the first king to be dealt is 1/52.
Explanation:
To calculate the probability that the 13th card is the first king to be dealt from a well-shuffled 52-card deck, we need to consider the number of favorable outcomes and the total number of possible outcomes. There are 4 kings in the deck, so the probability of the first king being the 13th card is 1/52.
Final answer:
The probability that the 13th card is the first king to be dealt in a shuffled 52-card deck is 1/13.
Explanation:
In a well-shuffled 52-card deck, the probability that the 13th card is the first king to be dealt can be calculated as follows:
First, let's determine the number of favorable outcomes. Since there are 4 kings in the deck, there are 4 possible kings that can be the first king dealt.
Next, let's determine the number of possible outcomes. Since there are 52 cards in the deck, there are 52 possible cards to be the 13th card dealt.
Therefore, the probability is calculated as:
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 4 / 52
Probability = 1 / 13
So, the probability that the 13th card is the first king to be dealt is 1/13.
If a cow has a mass of 9×1029×102 kilograms, and a blue whale has a mass of 1.8×1051.8×105 kilograms, which of these statements is true?
A.) The blue whale has about 200200 times more mass.
B.)The blue whale has about 500500 times more mass.
C.)The cow has about 200200 times more mass.
D.)There is no way to compare the masses.
Answer:
The blue whale has about 200 times more mass.
On average, Donna's Cafe has 84 customers, which represents 24% of the total approved occupancy by the fire department. a. What is the total approved occupancy of the cafe by the fire department?
The RideEm Bicycles factory can produce 160 bicycles in a day at a total cost of $10,100. It can produce 180 bicycles in a day at a total cost of $11,000. What are the company's daily fixed costs
Answer:
$2,900
Step-by-step explanation:
The additional 180 - 160 = 20 bicycles cost an additional $11,000 - 10,100 = $900. That means the 180 bicycles cost 9·$900 = $8100, and the fixed costs are $11,000 - 8,100 = $2,900.
_____
Each group of 20 bikes costs $900, so 9 groups of 20 (180 bikes) cost 9×$900 = $8100.
To find the daily fixed costs of RideEm Bicycles factory, subtract the variable cost from the total cost.
Explanation:To find the daily fixed costs of RideEm Bicycles factory, we need to determine the fixed cost component of the total cost. We can do this by subtracting the variable cost from the total cost. The formula for calculating fixed cost is:
Fixed Cost = Total Cost - (Variable Cost per Unit x Number of Units)
Using the given information:
By plugging in the values and solving the equations, we can find the daily fixed costs of the company.
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identity the two rational numbers
Which input value produces the same output value for the two functions on the graph?
x = −3
x = −2
x = −1
x = 3
x = -2
Explanation:The line represents the output value (y) for a given input value (x). Where the lines cross, the output values are equal. These lines cross at x=-2.
Answer:x=-2
Step-by-step explanation:
got it right on edg
Allen's monthly take-home pay is $3000, and his monthly rent is $750. If both his monthly take-home pay and his rent increase by $200, what percentage of Allen's take-home pay will be used to pay rent?
Answer:
29.68%
Step-by-step explanation:
Allen's monthly take-home pay is $3000
His monthly rent is $750
Now both his monthly take-home pay and his rent increase by $200
So, After increase Allen's monthly take-home pay =$3000+$200= $3200
After increase His monthly rent = $750+200=$950
Now we are supposed to find what percentage of Allen's take-home pay will be used to pay rent
So, percentage = [tex]\frac{\text{Rent after increase}}{\text {Take- home pay after increase}} \times 100[/tex]
= [tex]\frac{950}{3200}\times 100[/tex]
= [tex]\frac{950}{32}[/tex]
= [tex]29.68\%[/tex]
Hence 29.68% of Allen's take-home pay will be used to pay rent.
To be eligible for a basketball tournament, a basketball team must win at least 60% of its remaining games. If the team has 21 game remaining, how many games must the team win to qualify for the tournament?
The basketball team must win at least 13 out of their 21 remaining games to qualify for the tournament, as they need to win at least 60% of the games.
Explanation:To determine how many games a basketball team must win out of 21 to qualify for a tournament, given they must win at least 60%, we perform the following calculation:
First, multiply the total number of remaining games, which is 21, by 60% (or 0.60) to find the minimum number of games they need to win.Next, solve for the number: 21 games × 0.60 = 12.6.Since a team can't win a fraction of a game, they must win at least the next whole number of games, which is 13.Therefore, the team must win at least 13 games out of the remaining 21 to be eligible for the tournament.