Answer:
width: 9 cmlength: 13 cmStep-by-step explanation:
Integer factors of 117 include ...
... 117 = 1×117 = 3×39 ≈ 9×13
The last factor pair is two factors that differ by 4. We can take these to be the dimensions of the rectangle.
_____
If you want to write an equation for width (w), it might be ...
... w(w+4) = 117
... w² +4w -117 = 0
The factorization problem for this quadratic is the problem of finding two factors of 117 that differ by 4. That is what we have done, above.
If you want to solve this by completing the square, you can to this:
... w² +4w = 117
... w² +4w +4 = 121 . . . . . add 4 = (4/2)² to complete the square
... (w+2)² = 121
... w + 2 = ±√121 = ±11 . . . . take the square root
... w = -2 ± 11 . . . . . we're only interested in the positive solution
... w = 9, then w+4 = 13 and the dimensions are 9 cm by 13 cm.
Joel has 210 baseball and football cards. He has 50 more baseball cards than football cards. How many of each does he have?
Need to explain this to a 3 rd grade without dividing?
Suppose that factory a produces 12 tables and 6 chairs an hour while factory b produces 8 tables and 4 chairs and hour. how many hours should each factory work to produce 48 tables and 24 chairs? how many different solutions are there to this problem?
Factory A should work for 4 hours, while factory B should work for 6 hours to produce 48 tables and 24 chairs
The rates of both factories are given as:
Factory A = 12 tables and 6 chairs in an hour
Factory B = 8 tables and 4 chairs in an hour
To produce 48 tables and 24 chairs, we make use of the following equation
[tex]h = \frac{Produce}{Rate}[/tex]
Where h represents time (in hours)
So, we have:
Factory A
[tex]h = \frac{48\ tables, 24\ chairs}{12\ tables, 6\ chairs}[/tex]
[tex]h = 4[/tex]
Factory A
[tex]h = \frac{48\ tables, 24\ chairs}{8\ tables, 4\ chairs}[/tex]
[tex]h = 6[/tex]
Hence, factory A should work for 4 hours, while factory B should work for 6 hours to produce 48 tables and 24 chairs
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Factory A should work for 0 hours and Factory B should work for 6 hours to produce 48 tables and 24 chairs. There is only one solution to this problem.
Explanation:To find out how many hours each factory should work to produce 48 tables and 24 chairs, we can set up a system of equations. Let's say that factory A works for x hours and factory B works for y hours. From the information given, we can write the following equations:
12x + 8y = 48 (equation 1, for tables)
6x + 4y = 24 (equation 2, for chairs)
We can solve this system of equations using substitution or elimination method. Let's solve it using the substitution method:
From equation 1, we can isolate x by subtracting 8y from both sides:
12x = 48 - 8y
x = (48 - 8y) / 12
Substituting this value of x in equation 2:
6((48 - 8y) / 12) + 4y = 24
Simplifying the equation:
3(48 - 8y) + 4y = 24
144 - 24y + 4y = 24
-20y = -120
y = (-120) / (-20)
y = 6
Substituting the value of y in equation 1:
12x + 8(6) = 48
12x + 48 = 48
12x = 0
x = 0
Therefore, factory A should work for 0 hours and factory B should work for 6 hours to produce 48 tables and 24 chairs. There is only one solution to this problem.
Find the dimensions of a rectangle with perimeter 100m area of 336
A 12 ounce can of lemonade costs $1.32. How much would a 16 ounce can of lemonade cost
The amount of cost of the lemonade of 16 ounces will be $1.76.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
A 12-ounce can of lemonade costs $1.32.
Then the cost of 1 ounce will be
⇒ $1.32 / 12
⇒ $0.11 per ounce
Then the amount of the cost of the lemonade of 16 ounces will be
⇒ $0.11 x 16
⇒ $1.76
The amount of cost of the lemonade of 16 ounces will be $1.76.
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Divide then check using multiplcation
1056÷37=
With continuous compounding, a principal of P dollars accumulates to an amount A given by the equation
A = Pe^rt
where r is the interest rate and t is the time in years.
a) suppose you start with a principal of $1000 and an interest rate of 7%. how much work will you have in ten years
b)suppose you start with a principal of $1000 and an interest rate of 75. how long will it be until you have $2000? round to the nearest tenth of a year. PLEASE HELP
540 less than the product of 54 and a number is 918
You are scheduled to receive $16,500 in three years. when you receive it, you will invest it for nine more years at 9.5 percent per year. how much will you have in twelve years?
The total amount you will have in twelve years is calculated by multiplying your initial amount of $16,500 with (1 + 0.095) raised to the power of 9 (years of investment). This is a demonstration of the future value concept in finance.
Explanation:This question is about the concept of future value in finance. First, you receive $16,500 after three years. Following this, you invest this amount at an interest rate of 9.5% for nine more years. To calculate the future value of an investment, you can use the formula: Future Value = Present Value * (1 + Interest rate)^numbers of years. In this case, it would be $16,500 * (1 + 0.095)^9. This calculation will give you the total amount you will have in twelve years after the investment.
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Reteach to build to understand 10-4
What is the range of arcsinx
Final answer:
The range of the inverse sine function, or arcsin(x), is the set of angles from -π/2 to π/2 radians, which is the same as -90° to 90° degrees. This defines the possible output values of the function for all real numbers in the interval [-1, 1].
Explanation:
The question "What is the range of arcsinx" concerns itself with the inverse trigonometric function, specifically the inverse of the sine function. The range of a function is the set of all possible output values it can produce. For the inverse sine function, or arcsin(x), the range is the set of angles that can produce all possible sine values, which are within the closed interval [-1, 1].
The sine function itself has a range from -1 to 1, so the arcsine function, being its inverse, takes on values that are angles that correspond to these sine values. In terms of angles, the range of the arcsin function is [-π/2, π/2] or [-90°, 90°] in degrees. This means that for any input value x within [-1, 1], the output of arcsin(x) will always be an angle measured in radians (or degrees) that falls within this range.
HELP MEEEE!!!!!!!!! I BEG YOU !!!!!!
A store discounts the price of a beanbag chair by 20%. The price of the beanbag chair is marked as $16. What was the original price of the beanbag chair?
original price of the beanbag chair was $20 before the 20% discount was applied.
To find the original price of the beanbag chair that has been discounted by 20%, we set up an equation. Let's denote the original price as P. A 20% discount on the original price means the chair is being sold for 80% (100% - 20%) of P. This is represented by the equation 0.80P = $16.
To find P, we simply divide both sides of the equation by 0.80:
P = $16 / 0.80
This gives us:
P = $20
Therefore, the original price of the beanbag chair was $20 before the 20% discount was applied.
Becky bought 4 pounds of grapes for $8.24.How much did the grapes cost per pound?
Please help and explain how you got it
Draw cubes to show the number. Write the number different ways. Love has seven ones Nick has 5 ones they put all their once together what number did they make
7/8m +9/10-2m-3/5 how to do this question
4.1 Find the Least Common Multiple
The left denominator is : 8
The right denominator is : 10
Least Common Multiple:
40
4.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 5
Right_M = L.C.M / R_Deno = 4
4.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
4.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 40 as the denominator :
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
5.2 Adding up the two equivalent fractions
7.1 Pull out like factors :
36 - 45m = -9 • (5m - 4)
7.2 Find the Least Common Multiple
The left denominator is : 40
The right denominator is : 5
Least Common Multiple:
40
7.3 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 1
Right_M = L.C.M / R_Deno = 8
7.4 Rewrite the two fractions into equivalent fractions
7.5 Adding up the two equivalent fractions
8.1 Pull out like factors :
12 - 45m = -3 • (15m - 4)
One number is twice another number and their sum is 36. which system of equations represents the word problem? 2x y = 36 and x y = 36 x y = 36 and y = 2x y = 2x and 2x y = 36
Let
y------>one number
x------> another number
we know that
[tex]y=2x[/tex] ------> equation A
[tex]x+y=36[/tex] ------> equation B
substitute equation A in equation B
[tex]x+2x=36[/tex]
[tex]3x=36[/tex]
[tex]x=12[/tex]
Find the value of y
[tex]y=2x[/tex]
[tex]y=2*12=24[/tex]
the numbers are [tex]24[/tex] and [tex]12[/tex]
therefore
the answer is
The system of equations are
[tex]x+y=36[/tex] and [tex]y=2x[/tex]
In right triangle ABC, AB = 10, AC = 6 and BC = 8 units. What is the distance from C to the midpoint of segment AB?
Grammy's apple orchard is selling apple cider in 34.7-ounce bottles for $2.09. Grammy's competitor is selling 24.6- ounce bottles of cider for $1.99. What is Grammy's competitor's price per ounce for cider?
Find the volume v of the described solid s. the base of s is the triangular region with vertices (0, 0), (5, 0), and (0, 5). cross-sections perpendicular to the y-axis are equilateral triangles.
Final answer:
To find the volume of the solid with a triangular base and equilateral triangular cross-sections, we integrate the area of the cross-sections along the y-axis from 0 to 5 based on the changing side length, which is a linear function of y.
Explanation:
The problem requires finding the volume of a solid with a triangular base and equilateral triangular cross-sections perpendicular to the y-axis. The base of the solid, S, is a right triangle with vertices at (0, 0), (5, 0), and (0, 5). The height of each equilateral triangular cross-section at any point y is the distance from the point (y, 0) to the hypotenuse of the triangular base, which is linear and can be described by the equation x + y = 5. Because cross-sections are equilateral triangles, each side of a cross-section is twice the length of the height. Therefore, the area of a cross-section is ½∙height²∙√3.
As we move along the y-axis from 0 to 5, the length of a side of each cross-section decreases linearly from 5 to 0. We can integrate the area of these cross-sections from y = 0 to y = 5 to find the total volume of the solid. The integral for the calculation of volume is:
∫ (2∙(5-y))² × √3/4 dy from y=0 to y=5
Upon integrating, this gives us the volume of the solid S.
Write a situation in which positive and negative numbers are used to describe values that have the opposite meaning.
what is 5879 rounded to the nearest hundredth
The volume of a box of soup broth is 972 cubic centimeters. The box is 20 centimeters high and 10.8 centimeters long. How wide is the box?
The width of the rectangular prism will be 4.5 centimeters.
What is the volume of the rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
The volume of a box of soup broth is 972 cubic centimeters. The box is 20 centimeters high and 10.8 centimeters long.
Then the width of the rectangular prism is calculated as,
972 = 20 x W x 10.8
Simplify the equation, then we have
972 = 20 x W x 10.8
972 = 216W
W = 4.5 centimeters
The width of the rectangular prism will be 4.5 centimeters.
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Which sentence explains the correct first step in the solution of this equation?
2(x−4)=12
A. Subtract 12 from both sides.
B. Add 4 to both sides.
C. Apply the distributive property to get 2x - 8 = 12
D. Apply the distributive property to get 2x - 4 = 12
Answer: like 5 years late but wtv
Step-by-step explanation:
A right triangle has sides 5.0 m, 12 m, and 13 m. the smallest angle of this triangle is nearest:
Final answer:
To find the smallest angle in a right triangle with side lengths of 5.0 m, 12 m, and 13 m, we use the inverse tangent function with the shortest leg over the adjacent leg, yielding an angle of approximately 22.6 degrees.
Explanation:
The subject of the question is mathematics, and it pertains to high school level geometry. The question is asking to determine the smallest angle in a right triangle with sides measuring 5.0 m, 12 m, and 13 m. To find the smallest angle, we can use trigonometry, specifically the inverse tangent function.
Step-by-Step Explanation
Identify the sides of the triangle. In this case, we know that the sides are 5.0 m, 12 m (which could be interpreted as legs), and 13 m (the hypotenuse).
Because we are looking for the smallest angle, we will use the smallest leg, which is 5.0 m, and the next largest leg, which is 12 m.
Use the tangent function, which relates the opposite side to the adjacent side in a right triangle. The smallest angle, which we will call θ, will have the opposite side of 5.0 m and an adjacent side of 12 m.
Calculate θ using the inverse tangent function (also known as arctangent). θ = tan-1(5.0/12).
Perform the calculation using a calculator to find the nearest degree. θ = tan-1(5.0/12) ≈ 22.6°.
Therefore, the smallest angle in the triangle is approximately 22.6 degrees.
A 12 lb shankless ham contains 16 servings. What is the rate in servings per pound?
What happened to the glass blower who inhaled
Answer: he got pane in his stomach
Step-by-step explanation:
because he ate glass
Benjamin solved the equation 3 + x over 2 = 10 and justified each step as shown.
Identify Benjamin’s error and fix his mistake
Step:
3 + x/2 = 10
X/2 = 7
X= 14
Justification:
Given
Multiplication Property of Equality
Subtraction Property of Equality
Answer:
The equation itself is fine but the justification looks wrong step2 is subtraction property of equality and step3 is Multiplecation property of equaliity
I could be wrong but im 95% sure
Good luck!
A refrigerator has a volume given by the trinomial y^3 + 5y^2 – 14y. What are the possible dimensions of the refrigerator? Use factoring
A recipe for krispy rice treats calls for 6 cups of rice cereal and 40 large marshmallows. You want to make a larger batch of goodies and have 9 cups of rice cereal. How many large marshmallows do you need? However, you only have the miniature marshmallows at your house. You find a list of substitution quantities on the internet that suggests 10 large marshmallows are equivalent to 1 cup miniatures. How many cups of miniatures do you need?