Find the perimeter of the following rectangle. Write your answer as a mixed number in simplest form. Be sure to include the correct unit in your answer. length is 7/10 and 2 1/4
1 2 3 4 5 6 7 8 9 10
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Which are the solutions of the quadratic equation?
x2 = 9x + 6
The solutions of the quadratic equation x^2 = 9x + 6 are (9 + sqrt(105))/2 and (9 - sqrt(105))/2.
Explanation:To find the solutions of the quadratic equation x^2 = 9x + 6, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b +- sqrt(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -9, and c = -6. Plugging in these values, we get:
x = (-(-9) +- sqrt((-9)^2 - 4(1)(-6))) / (2(1))
Simplifying further:
x = (9 +- sqrt(81 + 24)) / 2
x = (9 +- sqrt(105)) / 2
So the solutions of the quadratic equation x^2 = 9x + 6 are:
x = (9 + sqrt(105)) / 2
x = (9 - sqrt(105)) / 2
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The solutions to the quadratic equation x² = 9x + 6 are x = 3 and x = 6. This is done by rearranging the equation and then factoring into two binomials (x - 3) and (x - 6) equals 0, then set each binomial equal to zero.
Explanation:The given quadratic equation is x² = 9x + 6. To find the solutions of the quadratic equation, we first move all the terms to one side. This gives us: x² - 9x - 6 = 0. This is now a standard quadratic equation, and can be solved by either factoring or using the Quadratic Formula.
If we opt to solve via factoring, we're looking to factorize the original expression into two binomial expressions, essentially looking for two numbers which both add up to -9 and multiply to -6. These two numbers are -3 and 6. Therefore, the quadratic equation can be factored as follows: (x - 3)(x - 6) = 0. Setting each factor equal to 0 gives the possible solutions for x, in this case, x = 3 and x = 6.
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Which of the following are good ideas to use when gathering your resources? Check all that apply
A. List potential formulas.
B. Draw a diagram.
C. Guess at the solution and see if you are close.
D. Write down the facts.
E. Form an equation.
F. Organize into a table.
When gathering resources for problem-solving, the following ideas can be helpful:
A. List potential formulas.B. Draw a diagram.D. Write down the facts.E. Form an equation.F. Organize into a table.The given options are all effective strategies that can assist in organizing and understanding the problem, as well as formulating a solution.
Option C, guessing at the solution, might not always be reliable or effective in all scenarios and is not considered a systematic approach.
Therefore, it may not be considered a recommended idea when gathering resources for problem-solving.
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Write 12.5% as a fraction or mixed number in simplest form
Answer: 1/8
Step-by-step explanation: A percent is a ratio that compares a number to 100. So we can write 12.5% as 12.5/100.
Next, we need to get rid of the decimal. We can multiply the numerator and denominator of a fraction by the same number without changing the value of the fraction.
So to get rid of the decimal, we can multiply the numerator and the denominator of 12.5/100 by 10 and we have 125/1000.
Now, notice that 125/1000 is not in lowest terms because we can divide the numerator and the denominator by 125 to get 1/8.
So 12.5% can be written as the fraction 1/8.
if you had a fraction strip folded into twelfths what fractional lengths could you measure with the strip
the picture shows a barn door what is the distance BC between two horizontal parallel bars?
one stae leads the country in tart cherry production producing 78 out of every 100 tart cherries each year what percent of tart cherries are produced in this state
The state in question produces 78% of the country's total annual tart cherry production.
Explanation:The state in question produces 78 out of every 100 tart cherries annually, which is the same as 78 out of 100 or 78/100. When written as a fraction, this can be turned into a decimal by dividing the numerator (78) by the denominator (100). This will give 0.78. To convert this decimal into a percentage, we then multiply by 100 which leads to 78%. This means the state produces 78% of the total tart cherries grown in the country each year.
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If $3000 is deposited in an account that pays 5% interest, what is the difference in the amount after 4 years between the amount earned if the principal is compounded annually and the amount earned calculated using simple interest?
A. $30.72
B. $41.12
C. $46.52
D. $53.76
Can someone show me how to do this pleases?!.
solve the equation.
- 2 = 3x/5 + 1
1. -2=1/2x
2.1/2x=-2
3. 2*(1/2x)=(2)*(-2)
4. x=-4
Hope this helps :)
-2=1/2x
1/2x=-2
2*(1/2x)=(2)*(-2)
x=-4
I hope this helped! :)
Factor 27x+9y
using the GCF.
The greatest common factor for the expression 27x+9y will be 9.
What is the greatest common factor?The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers. The largest factor that splits both numbers is said to be the greatest common factor.
List the prime factors of each integer before calculating the greatest common factor.
It is given that the expression is,
27x+9y
We can take out 9 commons in the expression because it does not affect the expression,
The greatest common factor is,
9( 3x + y)
We obtain 9 as the value that we can take commonly from the complete expression. As a result, it is the greatest common factor.
Thus, the greatest common factor for the expression 27x+9y will be 9.
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What is the value of this expression? (−8)3
=-24
Use the Rules for Signs for Multiplication
then multiply the numbers
bird leaves its nest and travels 18 miles per hour downwind for x hours. On the return trip, the bird travels 3 miles per hour slower and has 5 miles left after x hours. What is the distance of the entire trip?
Charlie is making a scale model of his kitchen. If the kitchen measures 12 feet by 11 feet, and his scale is two inches = three feet, what is the scale measure of the kitchen? Round to the nearest tenth.
A. 8 in by 7.3 in
B. 18 in by 16.5 in
C. 0.5 in by 0.4 in
D. 10 in by 9 in
Answer:
Option A. is the answer.
Step-by-step explanation:
Charlie is making a scale model of his kitchen.
The kitchen measures 12 feet by 11 feet.
We can use the unitary method to get the scale measures.
Since his scale is 3 feet = 2 inches.
So 1 feet = [tex]\frac{2}{3}[/tex] inches
and 12 feet = [tex]\frac{(2)(12)}{3} = 8[/tex] inches
Similarly 11 feet = [tex]\frac{(11)(2)}{3}=7.3[/tex] inches
Therefore, scale measures of the kitchen will be = 8 in by 7.3 in
Option A. is the correct answer.
How many diameters can a circle have?
Please help me solve 9x+16=4x-19
find decimal notation 75 percent
How many solutions does 25-4x=15-3x+10-x have
Answer: The given equation will have infinite number of solutions.
Step-by-step explanation: We are given to check the number of solutions to the following equation :
[tex]25-4x=15-3x+10-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the number of solutions, we must solve the given equation.
The solution of equation (i) is
[tex]25-4x=15-3x+10-x\\\\\Rightarrow 25-4x=25-4x\\\\\Rightarrow 4x-4x=25-25\\\\\Rightarrow 0=0,[/tex] which is always true.
Thus, the given equation will have infinite number of solutions.
What is 3/7 divided by 6?
2.) Simplify a fraction:
342 = 1 × 314 × 3 = 1143/7 divided by 6 is equal to 1/14.
To divide 3/7 by 6, you can multiply the numerator (3) by the reciprocal of the denominator (6).
The reciprocal of 6 is 1/6.
So, (3/7) divided by 6 can be calculated as:
(3/7) × (1/6)
= (3 × 1) / (7× 6)
= 3/42
Divide numerator and denominator by 3:
= 1/14
Therefore, 3/7 divided by 6 is equal to 1/14.
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How to find the least common denominator of 10x/x-3 and 4x/x-2
evaluate the function
can someone please explain how I would solve this please?
A conical tent made of canvas has a base that is 34 feet across and a slant height of 12 feet. To the nearest whole unit, what is the area of the canvas, including the floor? Use 3.14 for π.
Answer:
The area of the canvas, including the floor is 1548 sq. feet.
Step-by-step explanation:
Given : A conical tent made of canvas has a base that is 34 feet across and a slant height of 12 feet.
To find : What is the area of the canvas, including the floor?
Solution :
A conical tent made of canvas has a base that is 34 feet.
The diameter of the base is D=34 feet.
The radius of the base is [tex]r=\frac{34}{2}=17[/tex]
The slant height l=12
The area of the canvas, including the floor is
[tex]A=\pi r l+\pi r^2[/tex]
[tex]A=\pi r(l+r)[/tex]
[tex]A=3.14\times 17(17+12)[/tex]
[tex]A=3.14\times 17\times29[/tex]
[tex]A=1548.02[/tex]
In nearest whole unit, A=1548 sq. feet.
Therefore, The area of the canvas, including the floor is 1548 sq. feet.
find factors of 14y^2+41y+15
How long should the metal stripping be to protect the edge of circular table top if the radius of the top is 2 feet
A) 1.26 feet
B) 4 feet
C) 122 feet
D) 6.28
E) none
There are 25 squares in the pattern. What fraction of the squares have these number of edges free?
The function y_p(t) = \ln(1 + 2 t), \ t > -\frac{1}{2}, is a particular solution to the differential equation y^{\,\prime\prime} + 3 y = g(t). find g(t)
the costume designer decides to make the sashes a little smaller, so that each of the 8 dresses can have a sash. What fraction of fabric should the costume maker use to make each sash
The fraction that the costume maker should use for each sash is 1/8 of the total fabric available, as the fabric is being evenly divided among the 8 dresses.
Explanation:
If the costume designer is making sashes for 8 dresses and aims to use each bit of fabric equally, then each sash should consist of 1/8 of the total fabric. This is because the total fabric is being divided evenly among the 8 dresses. For example, if the costume designer has 8 yards of fabric, then each sash would use 1 yard of fabric (8 divided by 8 equals 1).
In fraction terms, each sash uses 1/8 of the fabric available. So for each dress, the costume designer should use 1/8 of the total fabric to make a sash.
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A publishing company has a weekly cost equation of C=96,000+20x and a weekly revenue equation of R=26x, where x is the number of books produced and sold in a week. The company loses money when R
To find when a publisher makes or loses money, compare the cost function C=96,000+20x to the revenue function R=26x. The break-even point is at x=16,000 books produced and sold weekly. Below this, the company incurs losses.
When determining when a publishing company makes or loses money, we investigate the relationship between cost and revenue functions. The cost function given is C=96,000+20x and the revenue function is R=26x, with x representing the number of books produced and sold per week. A company loses money when costs exceed revenues, that is when C > R.
To find the quantity of books where this happens, we equate the two equations:
C = R96,000 + 20x = 26x96,000 = 26x - 20x96,000 = 6xx = 96,000 / 6x = 16,000Therefore, at the production and sale of 16,000 books, the company will break even. Producing fewer than 16,000 books would result in a loss because the cost would be higher than the revenue generated.
nearly 4 of 5 people choose vanilla as their favorite ice cream flavor. if 120 people attend an ice cream social, how many would you expect to choose vanilla?
Line l passes through the origin and point (3,4).What is the slope of a line parallel to line l
Forty percent of all registered voters in a national election are female. a random sample of 5 voters is selected. the probability that there are no females in the sample is
To calculate the probability of selecting no female voters in a sample of 5, given that 40% of the registered voters are female, we multiply the probability of selecting a male voter (60%) five times, which equals to (0.6)⁵ or 7.776% probability.
The question involves calculating the probability that none of the five randomly selected voters are female, given that 40% of registered voters are female. To find this probability, we need to use the complementary probability, which is the probability of the opposite event occurring (that is, selecting a male voter).
The probability of selecting one male voter randomly is 60% (or 0.6), as females account for 40% of the registered voters. When we select 5 voters independently, we multiply the individual probabilities together because the events are independent. Therefore, the probability of selecting no female voters in 5 trials is calculated as:
(0.6) × (0.6) × (0.6) × (0.6) × (0.6) = (0.6)⁵ = 0.07776 or 7.776%.
This is the probability that a random sample of 5 voters will contain no females.