The yearbook club had a meeting. the meeting had 20 people, which is four-fifths of the club. how many people are in the club? answer
twenty is what percent of 200
A rectangle has the same area as a square. the long side of the rectangle is four times the length of the short side. the perimeter of the square has length 216 mm. how much longer is the perimeter of the rectangle than the perimeter of the square?
The perimeter of the rectangle is 54 mm longer than the perimeter of the square.
Explanation:To find the perimeter of the square, we can use the formula P = 4s, where P represents the perimeter and s represents the length of a side.
Given that the perimeter of the square is 216 mm, we can solve for the length of a side: 216 = 4s ⇒ s = 54 mm.
Since the area of the rectangle is the same as the square, we can calculate the length and width of the rectangle using the given information.
Let's assume the short side of the rectangle is x mm, then the long side would be 4x mm according to the given ratio.
Since the area of a rectangle is length × width, we have:
x × 4x = 54 × 54
4x² = 2916
x² = 729
x = 27 mm.
The perimeter of the rectangle can be calculated using the formula P = 2(length + width). Therefore, the perimeter of the rectangle is
P = 2(27 + 4 x 27) mm
P = 2(27 + 108) mm
P = 2(135) mm
P = 270 mm.
The difference in perimeter between the rectangle and the square is calculated by subtracting the perimeter of the square from the perimeter of the rectangle:
270 mm - 216 mm = 54 mm.
Therefore, the perimeter of the rectangle is 54 mm longer than the perimeter of the square.
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A cube with a side length of 6 mm has a surface area to volume ratio of
Sharon graphed the formula for converting weight from kilograms to pounds. mc024-1.jpg If an item weighs 45 kilograms, what is its weight in pounds? 20 63 90 99
Answer:
45 kilogram = 99.18 pounds
Step-by-step explanation:
In this case, it is required to convert weight in kilograms to pounds. Firstly, we will see the relationship between kilogram and pound. It is as follows :
1 kilogram = 2.204 pounds
The weight of an item is 45 kg. We need to convert it into pounds. So,
45 kilogram = 2.204 × 45 pounds
45 kilogram = 99.18 pounds
So, the weight of the item is 99.18 pounds. Hence, this is the required solution.
If a carton of eggs costs $1.25, how many cartons can be bought for $10?
Answer:
8 cartons
Step-by-step explanation:
Paul plans to put concrete on a rectangular portion of his driveway. The portion is 12 feet long and six inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Paul needs is $108.89. Which of the following is closest to the width of the portion of the driveway on which Paul plans to put concrete?
[1 foot = 12 inches; 1 yard = 3 feet]
a) 3 feet
b) 5 feet
c) 8 feet
d) 10 feet
If you know the ratio of inches to centimeters is 1 to 2.54, how can you find the number of centimeters equivalent to 9 inches? What is the relationship between centimeters and inches?
Ratios are used to show the relationship of variables that are in proportions.
The equivalent of 9 inches is 22.86 centimeterThe relationship between them is: [tex]Centimeter= 2.54 \times Inches[/tex]Given that:
[tex]Inches : Centimeter = 1: 2.54[/tex]
Multiply the ratio by 9, to calculate the equivalent of 9 inches
[tex]Inches : Centimeter = 1 \times 9: 2.54 \times 9[/tex]
[tex]Inches : Centimeter = 9: 22.86[/tex]
Hence, the equivalent of 9 inches is 22.86 centimeter
The relationship between both is as follows:
[tex]Inches : Centimeter = 1: 2.54[/tex]
Rewrite as:
[tex]\frac{Inches}{Centimeter} = \frac{1}{2.54}[/tex]
Cross multiply
[tex]Centimeter \times 1 = 2.54 \times Inches[/tex]
[tex]Centimeter= 2.54 \times Inches[/tex]
Hence, the relationship between them is: [tex]Centimeter= 2.54 \times Inches[/tex]
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Which plot description is the best example of a tragedy?
A. A young married couple begins to grow apart as work and family obligations take their toll on the marriage, causing them to split up.
B. A puppy gets lost during a cross-country move and experiences many dangerous situations as he finds his way back to his family.
C. A billionaire oilman loses his fortune and his family after he fails to see the damage his company is doing to the environment.
D. An old man recounts his amazing experiences during the war, remembering all of the friends he made as well as those he lost.
The base of the triangle is seven less than twice its height. If the area of a triangle is 102cm², find the length of the base.
Answer:
The length of the base is [tex]b=17cm[/tex]
Step-by-step explanation:
We start by writing the equation of the base :
Given that the base of the triangle is seven less than twice its height we can write that
[tex]b=2h-7[/tex] (I)
Where ''b'' is the base and ''h'' is the height.
Now, the area of a triangle is [tex]\frac{bh}{2}[/tex]
We know that the area is [tex]102(cm^{2})[/tex] ⇒
[tex]\frac{bh}{2}=102(cm^{2})[/tex]
Now we can replace ''b'' by the expression in (I) ⇒
[tex]\frac{bh}{2}=102(cm^{2})[/tex]
[tex]\frac{(2h-7)(h)}{2}=102(cm^{2})[/tex]
Rearraging the expression :
[tex]\frac{(2h-7)(h)}{2}=102(cm^{2})[/tex]
[tex](2h-7)(h)=204(cm^{2})[/tex]
[tex]2(h^{2})-7h=204(cm^{2})[/tex]
[tex]2(h^{2})-7h-204(cm^{2})=0[/tex]
We need the values of ''h'' that satisfy the equation.
We can use the quadratic formula with
[tex]a=2\\b=-7\\c=-204[/tex]
The quadratic formula will be
[tex]h1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]
and [tex]h2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
Using [tex]a=2\\b=-7\\c=-204[/tex] in the expression of h1 and h2 we find that
[tex]h1=12\\h2=-8.5[/tex]
Given that ''h'' is a length ⇒ [tex]h\geq 0[/tex]
We conclude that h1 = 12 cm is the correct value of ''h''
With this value of ''h'' we go to the expression of ''b'' ⇒
[tex]b=2h-7\\b=2(12)-7\\b=24-7\\b=17[/tex]
The value of the base ''b'' that satisfies the problem is [tex]b=17cm[/tex]
Rose and Dennis each open a savings account at the same time. Rose invests $2,600 in an account yielding 4.1% simple interest, and Dennis invests $2200 in an account yielding 5.7% simple interest. After nine years, who has the greater total amount of money, and how much greater is it? a. Rose has $230.80 more than Dennis. b. Rose has $559.40 more than Dennis. c. Dennis has $169.20 more than Rose. d. Dennis has $512.00 more than Rose.
Answer:
A homies
Step-by-step explanation:
Which trigonometric ratios are correct for triangle ABC? Check all that apply.
-sin(C) =
-cos(B) =
-tan(C) =
-sin(B) =
-tan(B) =
The correct trigonometric ratios for triangle ABC are sin(C) = 1 if C is the right angle, cos(B) = Adjacent/Hypotenuse, sin(B) = Opposite/Hypotenuse, and tan(B) = Opposite/Adjacent. Additionally, tan(C) is undefined if C is the right angle.
First, it's important to understand basic trigonometric ratios in a right-angled triangle. For triangle ABC, assuming angle C is the right angle:
sin(C) = Opposite/Hypotenuse. Since angle C is the right angle, sin(C) = 1.cos(B) = Adjacent/Hypotenuse. If angle B is one of the non-right angles, cos(B) can be found using the sides adjacent and opposite to angle B.tan(C) = Opposite/Adjacent. Since angle C is 90 degrees, tan(C) = Opposite/0 which is undefined.sin(B) = Opposite/Hypotenuse. This is the ratio of the length of the side opposite angle B to the hypotenuse.tan(B) = Opposite/Adjacent. This is the ratio of the length of the side opposite angle B to the side adjacent to angle B.These trigonometric ratios are correct and fundamental in solving various problems related to triangles.
What is the value of 4p − 2, when p = 8
The value of the expression 4p − 2, when p = 8 is 30.
What is an Expression?An expression is a mathematical statement which consists of variables, constants and mathematical operators.
The expression is :
4p -2
The number p is the variable, 4 is the coefficient of the variable and 4,2 are constants.
The variables are the unknown parameters, whose value is not known.
The coefficients of the variables are the numbers multiplied to the variable.
The constants are integers.
The number p is multiplied by 4 and then 2 is subtracted from it.
Subtraction is the basic mathematical operation.
The value of the expression has to be determined at p =8.
To determine, the value of the p will be substituted in the expression.
=> 4 * 8 -2
=> 32 -2
=> 30
The value of the expression when p=8 is obtained.
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N a trip to his grandparents, donny drove 60 miles per hour for 45 minutes and 50 miles per hour for 30 minutes. how many miles did donny drive?
The solution is, donny drove 70 miles.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
here, we have,
we know that,
Speed: The ratio of distance to time.
To find the distance we use the following formula.
Given that
donny drove 60 miles per hour for 45 minutes and 50 miles per hour for 30 minutes.
so, we get,
In 45 minutes, she traveled = ( 60/60 * 45)
= (1 * 45)
=45 miles.
again, we have,
The she drove 50 miles per hour for 30 minutes.
so, we get,
In 30 minutes, she traveled = ( 50/60 * 30 )
=50/2
= 25 miles
Therefore donny drove (45+25) miles= 70 miles.
Hence, The solution is, donny drove 70 miles.
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A plumber charges $70 per hour plus $40 for the call. What does he charge for 4 hours of work? What's the dependent, solution, independent, and function
I need help with this question.
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: 15x + 10y ≥ 1100
Is (60, 20) a solution? How do you know? What does this point represent?
The coordinate pair (60, 20) is a solution because it satisfies the inequality. The coordinate pair (60, 20) is a solution because Ezra earns 60 x $15 = $900 mowing lawns and 20 x $10 = $200 walking dogs, for a total of $1100. Ezra can spend 60 hours mowing lawns and 20 hours walking dogs to earn enough money for the laptop.
What's the value of X and the measure of angles B and C ? Please help
does this set of ordered pairs represent a function?why or why not? (-5,-5),(-1,-2),(0,-2),(3,7),(8,9)
The set of ordered pairs (-5,-5),(-1,-2),(0,-2),(3,7),(8,9) represent the function.
What is a function?A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.
As per the information provided:
Let's list the x-coordinates and y-coordinates of the ordered pairs:
x: -5, -1, 0, 3, 8
y: -5, -2, -2, 7, 9
There is no x-coordinate that appears more than once in the list, so there are no two or more ordered pairs with the same x-coordinate.
Therefore, the set of ordered pairs represents a function.
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which symbol completes the statement 3/8 ___ 1/4 < > = NEED ANSWER ASAP!!!
The U.S. Mint pays $0.02 to produce every penny. How many pennies are produced when the U.S. Mint pays more than $6 million in production costs?
Answer:
300 millions
Step-by-step explanation:
The U.S. Mint pays to produce every penny = $0.02
When the U.S. Mint pays more than $6 million in production cost.
The number of pennies are produced = [tex]\frac{6,000,000}{0.02}[/tex]
= 300,000,000
U.S. Mint produced 300 million pennies.
The U.S mint pays $0.02 to produce every single penny in the country
Therefore the amount of pennies that will be produced when Mint pays above $6,000,000 can be calculated as follows
= 6,000,000/0.02
= 300,000,000
Hence the number of pennies that will be produced when they pay more than $6 million is 300,000,000
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Which shows the factored form of M^2+ 40m + 400
The factored form of the given quadratic equation M² + 40M + 400 is (M + 20)², achieved by noticing that the equation is a perfect square trinomial.
Explanation:The question asks you to find the factored form of the polynomial equation M² + 40M + 400. We can factor this equation by grouping. Factoring is the process of breaking down a complex equation into its simplest terms or variables.
Factoring the Equation
The first step to factoring is to look for a common factor among all the terms. In this case, we don't have one, so we move to the next step: factoring quadratics. A quadratic is an equation where the highest exponent is 2.
The equation given, M² + 40M + 400, it is a perfect square trinomial because 20² equals 400. Factored form of perfect square trinomial (a + b)² = a² + 2ab + b².
Setting a=M and b=20 (since (20)²=400), hence this polynomial factors to be (M + 20².
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two parallel lines cut by a transversal. What is the value of x?
Answer: x = 37
Explanation: If two parallel lines are cut by a transversal,
then alternate interior angles are congruent.
So we can say that 3x + 4 = 115.
Subtracting 4 from both sides, we have 3x = 111.
Dividing both sides by 3, we find that x = 37.
So the value of x is 37.
Soo.. I'm stuck. On this problem as well :((
What is the expression in radical form?
(5x^4y^3)2/9
Enter your answer, in simplest form, in the box.
if the problem is (5x^4y^3)^2 divided by 9
5^2 = 25
4*2 =8
3*2 =6
so you get (25x^8y^6)/9
if that isn't how the equation was supposed to be written let me know and I will edit my answer.
The given algebraic expression expressed in the simplest radical form is;
25x⁸y⁶/9
The algebraic expression we are given is;(5x⁴y³)²/9
Now, simplifying to a radical form simply means eliminating general square roots, cube roots, squares, cubes e.t.c where possible.Now, from the algebraic expression given, we can see that expanding the bracket gives us;[5² × (x⁴)² × (y³)²]/9
According to laws of indices we will multiply the external exponent by the internal one for the x and y variable. This gives us;
25x⁸y⁶/9
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I really need help please.......
The steps to the simplifying the expression (3x^2 −2)(2x^2 +5x+7) are are listed below. Write out an explanation of how it is being simplified from one step to the next. Use at least 4 -5 complete sentences. Be sure that your explanation includes the following words:
-distribute or distribution or distributive property
-like terms
-binomial
-trinomial
-simplify
(3x^2-2)(2x^2+5x+7)
Step 1: (3x^2*2x^2)+(3x^2*5x)+(3x^2*7)-(2*2x^2)-(2*5x)-(2*7)
Step 2: (6x^4)+(15x^3)+(21x^2)-(4x^2)-(10x)-(14)
Step 3-answer:6x^4+15x^3+17x^2-10x-14
The function f(x) = is shown on the graph.
Which statement is correct?
Answer:
c.
Step-by-step explanation:
In the diagram, the ratios of two pairs of corresponding sides are equal.
To prove that △LMN ~ △XYZ by the SAS similarity theorem, it also needs to be shown that
A.∠N ≅ ∠Z
B.∠N ≅ ∠X
C.∠L ≅ ∠Z
D.∠L ≅ ∠Y
Answer:
A. ∠N ≅ ∠Z
Step-by-step explanation:
I simply aligned both triangles equation. I wish you guys all the luck and love! <3
2. Draw the image of ∆RST under the dilation with scale factor ⅓ and center of dilation at the origin. Label the image ∆R’S’T’.
Arnold walked 3 miles each day for the past 5 days. What is the reasonable range for the total number of miles he walked during this time
Several people form groups with four people in each group. Write an expression for the number of groups from doing by p people. How many groups are formed if there are 28 people?
Answer: 28/p; 7
Step-by-step explanation:
Hope it helps