To find the height of a sail shaped as a right triangle, utilize the area formula A = (base x height) / 2, rearranged to solve for height, leading to the solution of 7 feet for the given area of 42 square feet and base of 12 feet.
To find the height of a sail that is shaped as a right triangle with an area of 42 square feet and a base of 12 feet, we can use the formula for the area of a triangle, which is A = (base x height) / 2. Therefore, we can rearrange the formula to solve for the height:
Height = (2 x Area) / base
By plugging in the values we have:
Height = (2 x 42) / 12 = 84 / 12 = 7 feet
The height of the sail is therefore 7 feet.
What is the value of the expression? 3(6/8−1/2)+0.25
Which numbers are a distance of 3 units from 12 on a number line?
Select each correct answer.
3
15
0
9
−9
−15
Answer:
15 and 9 are the correct answers.
Step-by-step explanation:
The numbers that are at a distance of 3 units from 12 on a number line are given as:
We will add 3 to 12 and also subtract 3 from 12 to get both numbers on the left side an right side on the number line.
[tex]12+3 = 15[/tex]
[tex]12-3 = 9[/tex]
So, the correct answers are 15 and 9.
Tanya is printing a report. There are 100 sheets of paper in the printer, and the number of sheets of paper p left after t minutes of printing is given by the function p(t) = -8t + 100. How many minutes would it take the printer to use all 100 sheets of paper?
Using the function p(t) = -8t + 100, where t is time and p(t) is the amount of paper left, we set p(t) to 0 and solve for t. This reveals that it will take 12.5 minutes for the printer to use all 100 sheets of paper.
Explanation:In this problem, we're told that the printer uses paper according to the function p(t) = -8t +100, where t is the time it takes to print and p(t) is the amount of paper left in the printer. We want to find how much time it will take for the printer to use all the 100 sheets of paper, meaning we need to set p(t) to 0 and solve for t.
Therefore, we set up and solve the equation as follows: 0 = -8t + 100. If we solve this equation for t, we get t =100/8, which simplifies to t = 12.5 minutes.
This means it will take the printer 12.5 minutes to use all the 100 sheets of paper. The previous suggestions about other solutions and negative time are not applicable in the context of this problem because time cannot be negative in this instance, and this equation yields only one solution.
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Determine the digits of Y from these clues. The digits of Y add to 16. The first digit is 4 times the third digit. The second digit is 3 times the third digit. Y is a three digit number. 268 826 628 862
Answer: 862
Step-by-step explanation:
Let the third digit of Y be x .
Then , the first digit will be 4x and the second digit will be 3x.
Since , the digits of Y add to 16.
Then we have
[tex]3x+4x+x=16\\\\\Rightarrow\ 8x=16\\\\\Rightarrow\ x=\dfrac{16}{8}=2[/tex]
Thus , the third digit of Y = 2
Then the first of Y digit will be [tex]4(2)=8[/tex]
The second digit of Y will be [tex]3(2)=6[/tex]
Hence, the digits of Y must be 862
Which ordered pairs lie on the graph of the exponential function f(x)=4(5)2xf(x)=4(5)2x ?
Select each correct answer.
(−1,425)(−1,425)
(0,0)
(1,4)
(2,2500)
The ordered pairs lie on the graph of the exponential function [tex]\rm f(x) = 4(5)^{2x}[/tex] is (2,2500) and this can be determined by using the arithmetic operations.
Given :
Exponential Function --- [tex]\rm f(x) = 4(5)^{2x}[/tex]
The following steps can be used in order to determine the ordered pairs lie on the graph of the exponential function:
Step 1 - Write the exponential function.
[tex]\rm f(x) = 4(5)^{2x}[/tex]
Step 2 - Substitute the value of (x = -1425) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times -1425}[/tex]
[tex]\rm f(x) = 4(5)^{-2850}[/tex]
By simplifying the above function it does not give the value of f(x) = -1425, therefore, option (A) is incorrect.
Step 3 - Substitute the value of (x = 0) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times 0}[/tex]
f(x) = 4
Therefore, option (B) is also incorrect.
Step 4 - Substitute the value of (x = 1) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times 1}[/tex]
f(x) = 100
Therefore, option (C) is also incorrect.
Step 5 - Substitute the value of (x = 2) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times2}[/tex]
f(x) = 2500
Therefore, option (D) is correct.
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How many of the first 10,000 positive integers contain the digit pair “43” in that order?
Final answer:
There are 209 numbers among the first 10,000 positive integers that contain the digit pair '43' in that order, when considering the different placements of the digit pair in a four-digit number.
Explanation:
To find out how many of the first 10,000 positive integers contain the digit pair "43" in that order, let's consider the different places this pair can occur. The '43' pair can be in the units and tens place, the tens and hundreds place, or the hundreds and thousands place.
For the units and tens place, we have '43' fixed and two remaining places that can be any digit from 0 to 9, so there are 10 times 10 = 100 possibilities. However, we need to exclude the combination '043' as it is not a four-digit number but rather '43', giving us 100 - 1 = 99 combinations.
For the tens and hundreds place, we again have 10 possibilities for the other two places (thousands and units). We do not need to exclude any numbers here because even '043x' represents a valid four-digit number. Thus, we have 10 imes 10 = 100 combinations.
For the hundreds and thousands place, there are only 10 possibilities for the units place, as '430x' represents a valid four-digit number, which results in 10 combinations.
Adding them up, we have a total of 99 + 100 + 10 = 209 numbers that contain the '43' pair in the first 10,000 positive integers.
How do i do 4/7 divided by 1 3/4
make 1 3/4 an improper fraction:
1 3/4 = 7/4
now you have 4/7 divided by 7/4
now reverse the 7/4 and multiply:
4/7 x 4/7 = 16/49
What is the product? Enter your answer as a fraction, in simplified form, in the box. 3/8⋅(−3/6)
The product of the given expression of a fraction is [tex]\frac{-3}{16}[/tex].
Given:
An expression : [tex]\frac{3}{8}.(\frac{-3}{6})[/tex]
To find:
The product of the given expression of fractions in simplified form.
Solution:
[tex]\frac{3}{8}.(\frac{-3}{6})\\\\= \frac{3}{8}\times (\frac{-3}{6})\\\\=\frac{-9}{48}\\\\=\frac{-3}{16}[/tex]
The product of the given expression of a fraction is [tex]\frac{-3}{16}[/tex].
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A farmer has 212 acres of land for sale.He divides the land into 18 equal sections.About how many acres are in each section?
name three quaderlateral that only sometimes have right angle
What did the doctor say to the guy who thought he was a wigwam one day and tepee the next?
Amy class went the fair they saw 22 horses and 18 ponies they also saw 18 rabbits and 37 hares compare the the number of horses and ponies to the number of rabbits and hares that the class saw.
Amy's class saw a total of 40 horses and ponies and 55 rabbits and hares at the fair,
The question involves comparing the numbers of two sets of animals seen at the fair: horses and ponies versus rabbits and hares. To solve this, we will first add the number of horses and ponies together and then do the same for rabbits and hares.
Number of horses and ponies combined:
22 horses + 18 ponies = 40
Number of rabbits and hares combined:
18 rabbits + 37 hares = 55
Comparing the two totals:
40 horses and ponies is less than 55 rabbits and hares. Therefore the class saw more rabbits and hares combined than horses and ponies combined at the fair
The amounts that two partners invested in a new business are given below. If the partners share the profits in the same ratio as their investment, what is partner B's share in a $3600 profit?
Partner A $4300 Partner B $7700
Pls help!! will give brainiest to best answer!
Kevin tries to climb a wall with a ladder. The length of the ladder is 15 feet and it reaches only 12 feet up the wall. What is the distance between the base of the ladder and the wall?
The solution is Option A.
The distance between the base of the ladder and the wall is 9 feet
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ABC
Now , the height of the wall = 12 feet
The measure of AB = 12 feet
The length of the ladder = 15 feet
The measure of AC = 15 feet
Now , the distance between the base of the ladder and the wall = BC
The measure of BC is given by the Pythagoras Theorem , where
Hypotenuse² = base² + height²
AC² = AB² + BC²
Substituting the values in the equation , we get
15² = 12² + BC²
Subtracting 12² on both sides of the equation , we get
BC² = 15² - 12²
BC² = 225 - 144
BC² = 81
Taking square roots on both sides of the equation , we get
BC = 9 feet
Therefore , the value of BC is 9 feet
Hence , the distance is 9 feet
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Help there are 4 screen shots
1. A video cassette recorder uses 2m of tape in 3 minutes when set on extended play. The tape is about 240 m long. How many hours can be recorded at this setting?
2. You would burn about 200 calories by walking for 60 minutes. About how many calories would you burn if you walk or 15 minutes?
3. A 17 minute phone call from Boston to Chicago costs $2.38. What is the cost per minute?
a quiche with a diameter of 12 inches can feed 6 people. can a quiche with a diameter of 10 inches feed 4 people, assuming the same serving size explain your thinking
Final answer:
The area per person served by a 12-inch quiche, it was determined that a 10-inch quiche can indeed feed 4 people with the same serving size, as the area available per person in the 10-inch quiche is sufficient.
Explanation:
To determine whether a quiche with a diameter of 10 inches can feed 4 people at the same serving size as a 12-inch quiche that feeds 6 people, we need to compare the areas of the two quiches. The area of a circle is calculated using the formula A = πr² where A is the area and r is the radius. Since the radius is half of the diameter, the 12-inch quiche has a radius of 6 inches and the 10-inch quiche has a radius of 5 inches.
For the 12-inch quiche:
A12 = π(6²) = 36π
For the 10-inch quiche:
A10 = π(5²) = 25π
So, the 12-inch quiche has an area of 36π square inches and the 10-inch quiche has an area of 25π square inches. To find out if the smaller quiche can serve 4 people, we calculate the area per person for the larger quiche: 36π/6 = 6π square inches per person.
Now, we check to see if the 10-inch quiche provides at least that much area for 4 people: 25π/4 ≈ 6.25π square inches per person. Since 6.25π is greater than 6π, we can conclude the 10-inch quiche can indeed feed 4 people with the same serving size as the 12-inch quiche fed 6 people.
simplify 50 1/2 + 12.3
If the side of a square is doubled and then increased by 7, the new perimeter is 8 more then 3 times the old perimeter. What is the side of the original square?
To find the side of the original square, we can set up an equation and solve for x.
Explanation:To solve this problem, let's assume that the side length of the original square is 'x'. If we double it, the new side length would be '2x'. Adding 7 to it gives us '2x + 7'.
The new perimeter of the square is 8 more than 3 times the old perimeter, so we can set up the equation: 2(2x + 7) = 3(4x).
Simplifying this equation, we get 4x + 14 = 12x. By rearranging the equation, we find that 8x = 14, which leads to x = 1.75.
Therefore, the side length of the original square is 1.75 units.
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The diameter of a spherical basketball is 10in, what is the volume of the basketball?
Answer:
21
Step-by-step explanation:
hard wok
talent
Abbey gets paid a flat rate of $10.00 to mow her neighbor's lawn plus an additional $5 per hour to rake the leaves. The money she earns is represented by the equation m = 5h + 10, where m represents the amount of money she earns, in dollars, and h is the number of hours she rakes leaves for. Which of the following equations can be used to find h, the number of hours she rakes leaves for?
The answer choices are:
A. h= m -2
B. h=m -10
C. h= m/5
D. h= m-10/5
The prices of two radios are in the ratio x:y
When the prices are both increased by £20, the ratio becomes 5:2
When the prices are both reduced by £5, the ratio becomes 5:1
Express the ratio x:y in it's lowest terms.
The concept of linear equation and ratios is used to solve for the price of radios. The price of two radios are [tex]x=\pounds 80[/tex] and [tex]y=\pounds 20[/tex].
Given information:
The ratio of prices of two radios is [tex]x:y[/tex].
If the price of both the radios is increased by [tex]\pounds20[/tex], the ratio of price would become 5:2.
The above condition can be written mathematically as,
[tex]\dfrac{x+20}{y+20}=\dfrac{5}{2}\\2x+40=5y+100\\2x-5y=60.........(1)[/tex]
If the prices are both reduced by [tex]\pounds 5[/tex], the ratio will become 5:1.
The above condition can be written mathematically as,
[tex]\dfrac{x-5}{y-5}=\dfrac{5}{1}\\x-5=5y-25\\x-5y=-20\\-x+5y=20.........(2)[/tex]
Add equation (1) and (2), to get the value of [tex]x[/tex] and [tex]y[/tex] as,
[tex]2x-x=60+20\\x=80[/tex]
Solve for [tex]y[/tex] as,
[tex]2x-5y=60\\2\times 80-5y=60\\5y=100\\y=20[/tex]
Therefore, the price of two radios is [tex]x=\pouns 80[/tex] and [tex]y=\pounds 20[/tex].
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Which equation is in standard form?
x + 2y = 8
x = -2y + 8
2y = -x + 8
name a segment skew to Wy
Which equation shows y=34x−52 in standard form? 4x−3y=−10 3x−4y=10 3x−4y=−10 4x−3y=10
Answer: The equation that shows y=(3/4)x-5/2 is standard form is:
Second option: 3x-4y=10
Solution:
y=(3/4)x-5/2
Standard form of the equation Ax+By=C, with A, B, and C integer numbers
The coefficient of "x" and the independent term are fractions. To simplify them, let's multiply both sides of the equation by 4:
4y=4 [ (3/4)x-5/2]
4y=4(3/4)x-4(5/2)
4y=(4/1)(3/4)x-(4/1)(5/2)
4y=[(4*3)/(1*4)]x-(4*5)/(1*2)
4y=(12/4)x-20/2
4y=3x-10
The two variables must be in the same side of the equation and the independent term in the other side, but the coefficient of "x" must be positive, then subtracting 4y and adding 10 both sides of the equation:
4y-4y+10=3x-10-4y+10
10=3x-4y
3x-4y=10
Answer:
its B i took the test explanation:
Audrey needs to cut 1 meter of yellow ribbon and 28 centimeters of blue ribbon. In total, how many centimeters of ribbon does she need?
centimeters
Answer: She needed 128 cm of ribbon.
Step-by-step explanation:
Since we have given that
Length of yellow ribbon needed to be cut = 1 meter
Length of blue ribbon needed to be cut = 28 cm
We need to find the number of centimeters she needed to be cut.
First of all, we convert meter into centimeter.
As we know that
1 meter = 100 centimeter
So, Total number of centimeters of ribbon she needed is given by
[tex]100+28\\\\=128\ cm[/tex]
Hence, She needed 128 cm of ribbon.
Write the algebraic expression representing the length and width of Marliens house. Someone please tell me the process of how to do this
Answer:
Length of Marliens house = [tex](\frac{7}{2}x-4)\text{ or }(\frac{9}{2}x-18)[/tex] .
Width of Marliens house = [tex](2x-2)[/tex].
Step-by-step explanation:
We need to find the length and width of Marlien's home in algebraic expressions.
Add length of living room, hallway and kitchen, to find the length of Marlien's home.
Length of Marlien's home = [tex](2x+2)+(\frac{1}{2}x-4)+(x-2)=\frac{7}{2}x-4[/tex]
Or we can add Master bedroom,guest room, hallway and bathroom, to find the length of Marlien's home.
Length of Marlien's home = [tex](2x-10)+(x-2)+(\frac{1}{2}x-4)+(x-2)=\frac{9}{2}x-18[/tex]
Add width of living room and Master bedroom to find the width of Marlien's home.
Width of Marlien's home = [tex]x+(x-2)=2x-2[/tex]
Hence, the length of Marliens house is either [tex](\frac{7}{2}x-4)\text{ or }(\frac{9}{2}x-18)[/tex] and width of Marliens house is [tex](2x-2)[/tex].
A theater seats 1860 people the last 6 shows have been sold out estimate the total number of people attending the last 6 shows
Please help me Simplify 3x-2x+x-9. I was told my answer was wrong
Someone plz tell me if my answers for the two questions are correct.Also help me with question f without telling the answer.