Answer:
The dimensions that will produce a maximum area of the rectangular region is 50 meters or 5000/Pi
Step-by-step explanation:
From the question given, let us recall the following formula
The perimeter = 200 which is,
P=2L + C
where L is = length of the rectangular region
The circumference of a circle denoted as C
The Circumference of the semi-circle is denoted as,
C=Pi x D, which is D=C/Pi.
Thus the equation becomes,
200 = 2L+C
A=L x (C/Pi)
We now have Two equations and three variables, from these two equations, we can get a single equation,
200=2L+C means that C = 200-2L
For C in the Area equation. Substitute 200-2L:
A=Lx (C/Pi) which is A = Lx (200-2L)/Pi.
We Simplify: A = (1/Pi)(-2L<sup>2</sup> + 200L)
Now take a derivative of A with respect to L: dA/dL = (1/Pi)(-2L + 200)
(1/Pi)(-2L+200)=0
Let Solve for L: L = 50.
when L is 50 we have the MAXIMUM area. this is a negative quadratic so it MUST therefore not be a minimum but maximum
Then,
Plug in L=50 into the formula for A: A = 50(200-2(50))/Pi = 5000/Pi.
Final answer:
To find the dimensions that maximize the area of the rectangular region for a 200-meter running track with semicircle ends, we can use the perimeter constraint and optimization techniques to solve for the variable x that will give the maximum area when substituted back into the area formula. Therefore, the dimensions of the rectangular region that yield the largest area are [tex]\( x = 50 \) and \( y = \frac{100}{\pi} \).[/tex]
Explanation:
The student is asking about optimizing the area of a rectangular region with semicircles on each end, with a constraint on the perimeter. This is a typical optimization problem that can be solved using calculus, where we need to maximize the area function A(x) = x*y subject to the perimeter constraint P = 2x + πy = 200, considering y as the diameter of the semicircles.
To maximize the area, we'd typically take the derivative of the area function with respect to one of the variables, substitute the relationship given by the perimeter constraint, and solve for the variable that will give us the maximum area. However, since this is a high school level question, it might be expected that the student uses algebraic methods instead of calculus.
To find the value of \( x \) that maximizes the area [tex]\( A(x) = \frac{x(200 - 2x)}{\pi} \)[/tex], we'll follow the steps you provided.
1. Express \( y \) in terms of \( x \) using the perimeter constraint:
Given that the perimeter of the rectangle is \( 200 \), we have:
[tex]\[ P = 2x + 2y = 200 \][/tex]
Rearranging for \( y \):
[tex]\[ 2y = 200 - 2x \] \[ y = \frac{200 - 2x}{2} \] \[ y = \frac{200 - 2x}{\pi} \][/tex]
2. Substitute \( y \) in the area formula:
Now, we substitute the expression for \( y \) in terms of \( x \) into the formula for the area:
[tex]\[ A(x) = x \times \left( \frac{200 - 2x}{\pi} \right) \][/tex]
3. Maximize the area:
To maximize \( A(x) \), we'll find the critical points by taking the derivative of \( A(x) \) with respect to \( x \), setting it equal to zero, and solving for \( x \).
[tex]\[ A'(x) = \frac{dA}{dx} = \frac{d}{dx} \left( x \times \frac{200 - 2x}{\pi} \right) \] Using the product rule, we get: \[ A'(x) = \frac{d}{dx} \left( x \right) \times \frac{200 - 2x}{\pi} + x \times \frac{d}{dx} \left( \frac{200 - 2x}{\pi} \right) \] \[ A'(x) = \frac{1}{\pi} (200 - 2x) - \frac{2x}{\pi} \][/tex]
Setting \( A'(x) \) equal to zero and solving for \( x \):
[tex]\[ \frac{1}{\pi} (200 - 2x) - \frac{2x}{\pi} = 0 \] \[ 200 - 2x - 2x = 0 \] \[ 200 - 4x = 0 \] \[ 4x = 200 \] \[ x = \frac{200}{4} \] \[ x = 50 \][/tex]
So, \( x = 50 \) maximizes the area. To find the corresponding value of \( y \), we substitute \( x = 50 \) into the expression we found for \( y \):
[tex]\[ y = \frac{200 - 2 \times 50}{\pi} = \frac{200 - 100}{\pi} = \frac{100}{\pi} \][/tex]
Therefore, the dimensions of the rectangular region that yield the largest area are [tex]\( x = 50 \) and \( y = \frac{100}{\pi} \).[/tex]
Sadie is making punch for her soccer team picnic. She uses 8 quarts of lemon lime soda, 4 pints of vanilla ice cream and 8 cups of orange juice. How many gallons of punch will she have.
Answer:
[tex]3\text{ gallons}[/tex]
Step-by-step explanation:
GIVEN: Sadie is making punch for her soccer team picnic. She uses [tex]8[/tex] quarts of lemon lime soda, [tex]4[/tex] pints of vanilla ice cream and [tex]8[/tex] cups of orange juice.
TO FIND: How many gallons of punch will she have.
SOLUTION:
Amount of lemon lime soda punch [tex]=8\text{ quarts}[/tex]
Amount of vanilla ice cream punch [tex]=4\text{ pints}[/tex]
Amount of orange juice punch [tex]=8\text{ cups}[/tex]
Now,
[tex]1\text{ gallon}=4\text{ quarts}[/tex]
total lemon lime soda punch [tex]=2\text{ gallon}[/tex]
[tex]1\text{ gallon}=8\text{ pint}[/tex]
total vanilla ice cream punch [tex]=0.5 \text{gallon}[/tex]
[tex]1\text{ gallon}=15.77\text{ cups}[/tex]
total orange juice punch [tex]=0.51\text{ gallon}[/tex]
Hence total gallon of punch [tex]=2+0.5+0.51[/tex]
[tex]\approx3\text{ gallon}[/tex]
Hence sadie has total [tex]3\text{ gallons}[/tex] of punches
Hector puts a principal of $5,600 in a savings account with a simple interest rate of 8%. After several years, he
withdraws the balance of $11,424. How many years did he leave his investment in this particular savings account?
Simple interest: I = Pirit
11 years
12 years
13 years
14 years
Done
Answer:
13 years
first calculate interest and use formula
SI=ptr/100.
Answer:
13
Step-by-step explanation:
Question: here is a spinner with 6 pink shaded areas and 6 white shaded areas. If you spin the spinner ONCE, What is the probability (P) your spinner will land on a pink shaded area?
—-I NEED HELP ASAP!!
Answer: 6/12
Step-by-step explanation:
You have a 50% percent chance of landing on the shaded area
The table shows the distance, y, a cheetah can travel in feet in x seconds.
Speed of a Cheetah
Time, x
(seconds)
5
10
Distance, y
(feet)
470
940
1,410
1,880
2,350
15
|
20
25
Based on the information in the table, which equation can be used to model the relationship between x and y?
a
Ob
OC
O d
y = 5x
y = x + 5
y = x + 470
y = 94x
what is the answer
Answer:D.y=94x
Step-by-step explanation:
Final answer:
The relationship between time and distance for the cheetah can be modeled by y = 94x.
Explanation:
The relationship between the time, x, and distance, y, for the cheetah can be modeled by the equation y = 94x. This equation corresponds to the pattern shown in the table where the distance traveled increases by 470 feet as the time increases by 5 seconds.
Elena divided a decimal by a whole number. 84.36 ÷ 12 = ? Part A: Explain each step needed to divide 84.3y by 12. Part B: What is the correct qoutient?
Answer:
Part A. [tex]\frac{84.3y}{12} = 7 +\frac{0.1\cdot y}{4}[/tex]
Part B. The correct quotient is (3 × 4)
Step-by-step explanation:
Part A.
To divide 84.36 by 12 we look for the Highest Common Factor of the whole number and the decimal portions of the numerator and the denominator individually as follows;
[tex]\frac{84.36}{12} = \frac{84+0.3636}{12} = \frac{2 \times 2 \times 3 \times 7+0.01\times 12\times 3}{12} = \frac{12 \times 7+0.03\times 12}{12}[/tex]
Therefore, dividing 84.36 by 12 gives [tex]\frac{12 \times 7+0.03\times 12}{12} = 7+0.03[/tex] = 7.03
When dividing 84.3·y by 12, therefore, we have;
[tex]\frac{12 \times 7+0.3\times y}{12} = 7 +\frac{0.1\cdot y}{4}[/tex]
Part B.
The correct quotient should have factors of the numerator
Therefore the divisor 12 should be represented as follows
[tex]\frac{12 \times 7+0.3\times y}{12} =\frac{12 \times 7+0.3\times y}{3 \times 4}[/tex]
The correct quotient therefore = (3 × 4)
Elena divided the decimal 84.36 by the whole number 12 to get the correct quotient of 7.03. The division process is similar to dividing whole numbers but includes placing the decimal point correctly in the quotient.
To answer the question, Elena divided a decimal by a whole number. Specifically, the division problem is 84.36 ÷ 12. Dividing a decimal by a whole number follows the same process as dividing two whole numbers, with the additional step of placing the decimal point in the quotient.
Set up the division problem with 84.36 inside the division bracket and 12 on the outside.
Start dividing from the left. 12 goes into 84 seven times (12 x 7 = 84), so put 7 above the 84 in the quotient.
Subtract 84 from 84, which leaves 0, and bring down the next digit, which is 3 (from the decimal part).
Since 12 does not go into 3, we place a 0 in the quotient above the 3 and bring down the next digit, which is 6.
Now we have 36. 12 goes into 36 three times (12 x 3 = 36), so place a 3 in the quotient above the 36.
Again, we subtract 36 from 36, leaving 0, with no more digits to bring down, so we have our answer.
The correct quotient is 7.03. Multiplying or dividing by powers of ten, as seen when working with decimals, involves shifting the decimal point. For example, when multiplying 45.86 by 100, you would move the decimal point two places to the right, giving 4586. Conversely, dividing 1.9436 by powers of 10 shifts the decimal point to the left. The significance of this process is underlined by the fact that in scientific fields, calculations often require adjusting the decimal by powers of ten to maintain precision and correct significant figures.
It should be noted that a calculator provides the raw numerical result of a division and doesn't account for the significant figures involved; therefore, it's essential to consider how many decimal places are appropriate for the situation.
Mrs. Barto has a pet rabbit and wants to build a pen for it. She has 3 pieces of lumber: one is 3 ft, one is 7 ft, and the other is 8 ft long. Can she build a closed triangular pen with these three boards (will the boards form a triangle)?
Answer:
Yes, it is possible
Step-by-step explanation:
In a triangle, the length of the longest side of the triangle cannot be larger than the sum of the lenghts of the two shortest sides.
In formula, this means that:
[tex]c\leq a+b[/tex]
where
c is the length of the longest side
a, b are the lengths of the shortest side
In this problem, we want to build a triangle using 3 pieces of lumber, each of length:
a = 3 ft
b = 7 ft
c = 8 ft
We can verify that the length of the longest piece of lumber is less than the sum of the lengths of the other two sides, so:
[tex]8\leq 3+7 = 10[/tex]
Therefore, yes, it is possible to build a closed triangular pen.
The question is about the Triangle Inequality Theorem in Geometry. It asks if a triangle can be formed with given lengths of 3 ft, 7 ft, and 8 ft. By verifying with the theorem, we can confirm that a triangle can be formed.
Explanation:The subject of the question is determining if a triangle can be formed with three given lengths. This topic belongs to Geometry, a branch of Mathematics. To form a triangle, the lengths must satisfy the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. In this case, we can plug our given lengths into this theorem:
3 ft + 7 ft > 8 ft3 ft + 8 ft > 7 ft7 ft + 8 ft > 3 ftAll these inequalities hold true, so yes, Mrs. Barto can build a closed triangular pen for her pet rabbit with the three pieces of lumber.
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The circumference of a circle is 3 pi miles. What is the diameter?
Answer:
3 miles
Step-by-step explanation:
The circumference of a circle can be found using:
c=[tex]\pi d[/tex]
We know the circumference is [tex]3\pi[/tex], so we can substitute that in for c
[tex]3\pi[/tex]=[tex]\pi d[/tex]
We want to find the diameter. To do this, we need to get d by itself. It is being multiplied by pi. To undo this, divide both sides by pi. This will cancel pi, and leave d by itself.
[tex]3\pi /\pi =\pi d/ \pi[/tex]
3=d
So, the diameter is 3 miles
Answer:
Diameter is 3
Step-by-step explanation:
C=2πr
3π = 2πr
3π / 2π = r (Divide each side by 2π)
3/2 = r (Simplify π)
3/2 *2 = d (d = 2r)
d = 6/2 = 3
use the venom diagram to calculate probabilities. which probability is correct?
Answer:
Wheres the diagram?
Step-by-step explanation:
A Venn Diagram is commonly used in probability theory to visualize and calculate probabilities. The probability of two conditions being met can be found by taking a sum of the probabilities of both conditions and their intersection, and subtracting the probabilities of each condition occurring separately. A Tree Diagram is another tool used to easily represent and calculate probabilities of multiple outcomes.
Explanation:The use of a Venn Diagram is a common strategy in probability theory to help visualize and calculate probabilities effectively. To begin solving these problems, label each piece of the Venn Diagram clearly and note the probability or frequency of each part. Start by labeling the overlapping section first.
In the case of calculating the probability that a student belongs to a club and works part-time, identify the overlapping section of the Venn Diagram that represents both these conditions. The probability of this will be the sum of the probabilities of the student belonging to a club, working part-time, and both these conditions minus the probabilities of each of these conditions occurring separately.
Another tool that can be useful for visualizing and calculating probabilities is a Tree Diagram. A tree diagram uses branches to represent the possible outcomes of a scenario, which makes it easier to visually work through and solve probability problems. For instance, to visualize the probability of a man developing cancer in his lifetime and having at least one false-positive test, a tree diagram could be used where one branch represents the man developing cancer and the other branch represents the man having a false-positive.
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help ASAP pls :) brainly to whoever has the right answer first :D
Answer:
0.02 (rational)
2 (rational)
Square root of 2 (irrational)
Square root 1/2 (irrational)
Step-by-step explanation:
Rational numbers are numbers that can be in form of a/b such that a and b are not zeros. In other words, a and b are integers ranging from 1 to infinity.
Conversely, irrational numbers are numbers that are endless and are non repeating digits after decimal point.
Thus, from the questions above;
[tex]0.02 = \frac{2}{100} = rational \: number[/tex]
[tex]2 = \frac{2}{1} = rational \: number[/tex]
[tex] \sqrt{2} = 1.41421356 = irrational \: number[/tex]
[tex] \sqrt{ \frac{1}{2} } = 0.70710678 = irrational \: number[/tex]
A recent study found that the life expectancy of a people living in Africa is normally distributed with an average of 53 years with a standard deviation of 7.5 years. If a person in Africa is selected at random, what is the probability that the person will die before the age of 65?
Answer:
P(X<65)=0.9452
Step-by-step explanation:
This is a normal distribution problem.
-Given the mean age is 53 years and the standard deviation is 75, the probability of dying before age 65 is calculated as:
[tex]z=\frac{\bar x-\mu}{\sigma}\\\\\\=\frac{65-53}{7.5}\\\\=1.60[/tex]
#We check the value of z=1.60 on the z table:
[tex]P(X<65)=0.5+0.4452\\\\=0.9452[/tex]
Hence, the probability of dying before 65 is 0.9452
the probability that the person will die before the age of 65 is 0.9452.
The calculation is as follows:[tex]P(X<65 ) = P[(X- \mu ) \div \sigma < (65 -53) \div 7.5][/tex]
= P(z <1.6 )
Now here we Using z table
So,
= 0.9452
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When bands play at the arena the money made from ticket sales is split in an agreed ratio. When Phillip Cage played, £21,000 was split at a ratio of 2:5 between the arena and Phillip Cage. How much money did the arena make from Phillip Cage's concert?
Answer:
£6000
Step-by-step explanation:
Given:
Phillip Cage played, £21,000 was split at a ratio of 2:5 between the arena and Phillip Cage.
Question asked:
How much money did the arena make from Phillip Cage's concert?
Solution:
Ratio Arena and Philip cage in which money distributed = 2 : 5
Let ratio be [tex]x[/tex]
Money earned by Arena = [tex]2x[/tex]
Money earned by Phillip Cage = [tex]5x[/tex]
Phillip Cage played total for = £21,000
Money earned by Arena + Money earned by Phillip Cage = £21,000
[tex]2x+5x=21000\\7x=21000\\[/tex]
Dividing both sides by 7
[tex]x=3000[/tex]
Money earned by Arena = [tex]2x[/tex] = [tex]2\times3000=6000[/tex]
Thus, Arena made £6000 from Phillip Cage's concert.
Please help me idk this
Answer:
37.68
Step-by-step explanation:
C=2[tex]\pi[/tex]r
C=2*6*3.14
C=12*3.14
C=37.68
Answer:
C = 2 π r
Step-by-step explanation:
2*3.14*6=37.69911=37.7
the answer is 37.7
Simplify (32)2
A) 9
B) 18
C) 27
D) 81
Answer:
D)81
Step-by-step explanation:
which expressions are equivalent ? A. 3v+5-9v+2 and 6v+6 B. -6n+3-2n+2 and -8n+6 C. -4n+8+9n-2 and 5n+6 D. 10n-5-2n+3 and 5n-2
Answer:
C. -4n+8+9n-2 and 5n+6
Step-by-step explanation:
The equivalent expression is found by combining like terms:
-4n +8 +9n -2 = n(-4+9) +(8-2)
-4n +8 +9n -2 = 5n +6 . . . . . matches choice C
__
The other answer choices have flaws in the work:
A. 3v -9v ≠ 6v
B. +3 +2 ≠ +6
D. 10n -2n ≠ 5n
Answer:
C. -4n+8+9n-2 and 5n+6
Step-by-step explanation:
Hope this helps, and holy cow! the person above me deserves brainliest!
Solve the equation -3/13 - 2/5 =
To solve the equation -3/13 - 2/5, find the common denominator, convert both fractions and then subtract them. The answer is -41/65.
Explanation:The question asks to solve the equation -3/13 - 2/5. To solve this, we need to find a common denominator for the fractions, which in this case is 65. We then convert each fraction to have this common denominator and subtract them.
Here is the step-by-step solution:
Find the Least Common Denominator (LCD) of 13 and 5, which is 65.Convert -3/13 to a fraction with a denominator of 65: (-3/13) imes (5/5) = -15/65.Convert 2/5 to a fraction with a denominator of 65: (2/5) imes (13/13) = 26/65.Now subtract the two fractions: -15/65 - 26/65 = -41/65.The answer to the equation is -41/65.
find x. round our answer to the nearest tenth of a degree.
Answer:
Step-by-step explanation:
From the given right angle triangle,
the hypotenuse of the right angle triangle is 6
With m∠x as the reference angle,
the adjacent side of the right angle triangle is the unknown side.
the opposite side of the right angle triangle is 4
To determine m∠x, we would apply
the sine trigonometric ratio.
Sin θ = opposite side/hypotenuse. Therefore,
Sin x = 4/6 = 0.67
x = Sin^-1(0.67)
x = 42.1° to the nearest tenth.
PLEASE HELP
Circle A has circumference 2 2/3 m. Circle B has a diameter that is 1 1/2 times as long as Circle A’s diameter. What is the circumference of Circle B?
The circumference of Circle B is 4 meters.
Convert mixed number to fraction:
Circumference of Circle A = 2 2/3 m = 8/3 m
Find the diameter of Circle A:
Circumference = π * diameter
8/3 m = π * diameter_A
diameter_A = 8/3π m
Find the diameter of Circle B:
diameter_B = 1 1/2 * diameter_A = 3/2 * (8/3π) m
diameter_B = 4 / π m
Find the circumference of Circle B:
Circumference = π * diameter_B
Circumference of Circle B = π * (4 / π) m
Circumference of Circle B = 4 m
Therefore, the circumference of Circle B is 4 meters.
What is the volume of the triangular prism? Round to the nearest tenth.
A triangular prism. The triangular base has a base of 12 inches and height of 10.4 inches. The height of the prism is 19 inches.
118.6 inches cubed
748.8 inches cubed
1,085.6 inches cubed
1,185.6 inches cubed
Answer:
A= 1/2 Bh
1/2 (12)(10.4)
A=62.4
V= 62.4x19= 1185.6
Final answer is 1185.6
Step-by-step explanation:
You first need to find the area of the Prism than multiply with the height.
The solution is, Correct option D) 1,185.6 inches cubed, is the volume of the triangular prism.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
given that,
A triangular prism. The triangular base has a base of 12 inches and height of 10.4 inches. The height of the prism is 19 inches.
We need to find the volume of the triangular prism .
Let's find out:
We have following parameters :
b = 12
h = 10.4
l = 19
now, we know,
A= 1/2 Bh
so, we have,
A = 1/2 (12)(10.4)
A=62.4
We know that , Volume of triangular prism is :
⇒ V = 1/2 * bh* l
= A * l
so, we get,
V= 62.4x19
= 1185.6
Final answer is 1185.6
Hence, The solution is, Correct option D) 1,185.6 inches cubed, is the volume of the triangular prism.
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HELPPPP!!!!
Need the answer ASAP!!
Given that the functions [tex]f(x)=x+4[/tex] and [tex]g(x)=x^{3}[/tex]
We need to determine the value of the function [tex](g \ {\circ} f)(-3)[/tex]
First, we shall determine the composition of the function [tex](g \circ f)(x)[/tex]
Function [tex](g \circ f)(x)[/tex]:
Let us determine the function [tex](g \circ f)(x)[/tex]
Thus, we have;
[tex](g \circ f)(x)=g[f(x)][/tex]
[tex]=g[x+4][/tex]
[tex]=(x+4)^3[/tex]
[tex](g \circ f)(x)=x^3+3x^2(4)+3x(4)^2+(4)^3[/tex]
[tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]
Thus, the function is [tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]
Value of the function [tex](g \ {\circ} f)(-3)[/tex]:
The value of the function can be determined by substituting x = -3 in the function [tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]
Thus, we have;
[tex](g \circ f)(-3)=(-3)^3+12(-3)^2+48(-3)+64[/tex]
Simplifying the terms, we get;
[tex](g \circ f)(-3)=-27+12(9)+48(-3)+64[/tex]
[tex](g \circ f)(-3)=-27+108-144+64[/tex]
[tex](g \circ f)(-3)=1[/tex]
Thus, the value of the function [tex](g \ {\circ} f)(-3)[/tex] is 1.
What is the volume of this cylinder if its circumference is 125.7 feet
(the height is 80 ft) use 3.14 for pi
A) 100,681.06
B) 100,053.1
C) 10048
D) 32,032
To find the volume of a cylinder given its circumference and height, divide the given circumference by 2π to find the radius then use the formula for the volume of a cylinder πr²h. In this case, the volume of the cylinder is approximately 100,530.4 cubic feet.
Explanation:The volume of a cylinder can be calculated using the formula V = πr²h where V is the volume, r is the radius of the base, h is the height, and π is a constant that is approximately 3.14. Firstly, we need to find the radius. The circumference of the circle, which is the base of the cylinder, is given by the formula C = 2πr where C is the circumference and r is the radius. Given the circumference as 125.7 feet, we can calculate the radius (r) by dividing the circumference by 2π. Therefore, r = 125.7/(2*3.14) = 20 feet. Once we have the radius, we can calculate the volume of the cylinder using the formula V = πr²h. Substituting r = 20 feet and h = 80 feet, we get V = 3.14 * (20)^2 * 80 which equals 100,530.4 cubic feet. Hence, the closest answer would be option (B) 100,053.1.
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help me find
2/9 + something = 1
Answer:
7/9
Step-by-step explanation:
There are 9/9 in one whole, so if we have 2/9 now, we need another 7/9 to make 9/9: 2/9 + 7/9 = 9/9 = 1
Answer:
7/9
Step-by-step explanation:
1-2/9=7/9
Solve for x: −2x − 4 > 8
Answer:
x < -6
Step-by-step explanation:
-2x -4 > 8
-2x +4 >+4
-2x >12
/-2 > /-2
x < -6
remember to flip the inequality sign whenever you divide by a negative number :)
What do I dots solve this
[tex]8y - 72 = 8 \times y - 8 \times 9 = \\ = 8 \times (y - 9) = 8(y - 9)[/tex]
If the vertex of a parabola is (8,10) , what is the axis of symmetry?
Answer:
x = 8
Step-by-step explanation:
The axis of symmetry for graph is always set up as "x="
So, if the x in this ordered pair is 8, then the axis of symmetry is also 8.
(I have posted a picture below as proof...)
Un grupo de turistas gasta $ 153 para alquilar tubos y aletas. Se alquilan un total de 12 snorkels y 15 pares de aletas. Alquilar un snorkel cuesta tres veces más que alquilar un par de aletas. ¿Cuánto cuesta alquilar un snorkel? Cuesta $ alquilar un snorkel.
Answer:
The cost to rent a snorkel is 9$
(espanol) el costo de un snorkel es de 9$
Step-by-step explanation:
(English)Given that the group of tourists have spent $153 in renting snorkels and fins and there are 12 snorkels and 15 pairs of fins being rented, allow x to be the amount paid for the rent of the snorkels and y to be the rent for pairs of fins then 12x + 15y = 153. Given also that the rent for a snorkel is three times the rent of a pair of fins then x = 3y then, 12(3y) + 15y = 153. Simplify the equation, 36y + 15y = 153. 51y = 153. Solve for y by dividing both sides of the equation by 51 then, y = 153/51 = 3. Therefore, renting a pair of fins costs $3. To compute for the rent of a snorkel, use the equation x = 3y then, x = 3($3) = $9.
(Espanol) Dado que el grupo de turistas han gastado $153 en el alquiler de snorkels y aletas y hay 12 snorkels y 15 pares de aletas que se alquilan, permitir x para ser la cantidad pagada por el alquiler de los snorkels y y para ser el alquiler para pares de aletas entonces 12x + 15y 153. Dado también que el alquiler para un snorkel es tres veces el alquiler de un par de aletas y luego x a 3y, entonces, 12 (3y) + 15y a 153. Simplifique la ecuación, 36y + 15y a 153. 51y a 153. Resuelva para y dividiendo ambos lados de la ecuación por 51 entonces, y á 153/51 a 3. Por lo tanto, alquilar un par de aletas cuesta $3. Para calcular el alquiler de un snorkel, utilice la ecuación x á 3y, a continuación, x a 3($3) a $9.
10, 4, 1.6, 0.64.. what’s next
Answer:
0.256 or 0.26
Step-by-step explanation:
The common ration is being multiply by 0.4
Consider the system of equations below. What could be the first step in solving the
system of equations using elimination?
2x + 3y = 8
2x + 6y = 12
Add the two equations.
Add 4 to both sides of the first equation.
Multiply the first equation by -1
Multiply the second equation by 2.
Answer:
(A) Add the two equations.
Step-by-step explanation:
Solved by addition/elimination method.
Let me know if I'm wrong.
<3
A soda factory packages 10 soda cans per box. How many boxes are needed to ship 120,450 soda cans?
boxes
Answer: 12,045 boxes
Step-by-step explanation:
120,450 divided by 10
= 12,045
Answer:
12,045
Step-by-step explanation
If you need to ship 120,450 soda divide that by 10 (the number of cans in a box) and that gives you 12,045.
what 1/6 divided by 5
Answer:
1/30
Step-by-step explanation:
Answer:
1.2
Step-by-step explanation:
(simplified)
2. Jessica's grandparents gave her $2000 for college to put in a savings account until she starts
college in four years. Her grandparents agreed to pay her an additional 7.5% simple interest on
the $2000 for every year. How much extra money will her grandparents give her at the end of
four years?
Answer:
I =2000(0.075)4= $600
Step-by-step explanation: