The length and width of rectangle is 160 feet and 100 feet.
The perimeter of the rectangle is calculated by the formula -
Perimeter = 2 × (length + width)
As per the given information, length = (60 + width)
Keep the values in formula to find the breadth of rectangle.
520 = 2 × (60 + width + width)
520 = 2 × (60 + 2 × width)
(60 + 2 × width) = [tex]\frac{520}{2}[/tex]
(60 + 2 × width) = 260
2 × width = 260 - 60
2 × width = 200
Width = [tex]\frac{200}{2}[/tex]
Width = 100 feet
Keep the value in formula to find the length of perimeter
520 = 2 × (length + width)
Length + 100 = [tex]\frac{520}{2}[/tex]
Length = 260 - 100
Length = 160 feet
Hence, the length and width of rectangle is 160 feet and 100 feet.
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a fitness club with 100 members offers one free training session per member in either running, swimming, or weightlifting. Thirty of the fitness center members sign up for a free session. The running and swimming sessions are each twice as popular as the weightlifting session. What is the probability that a randomly chosen fitness club member signs up for a free running session?
The probability that a randomly chosen fitness club member signs up for a free running session is 0.4.
Let total s members sign up for the weightlifting session.
So, the total members for the running session is 2x.
And the total members for the swimming session be 2x.
Also here it is given that, thirty of the fitness center members sign up for a free session.
⇒ x + 2x + 2x = 30
⇒ 5x = 30
⇒ x = 30/5
⇒ x = 6
Thereofre, the probability that a randomly chosen fitness club member signs up for a free running session
= total number of members in running session/ number of members sign up for a free session
= 12/30
= 0.4
Hence, the probability that a randomly chosen fitness club member signs up for a free running session is 0.4.
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A recycling center claims to give 96
cents for every 12 aluminum cans
turned in.
Using the cross-multiplication formula we conclude that 768 cents will be given for 96 can recycled.
What is cross-multiplication?Cross multiplying is the process of multiplying the denominator of the second fraction on the other side of the equals to sign by the numerator of the first fraction on the same side.
In a similar manner, the numerator of the second fraction is multiplied by the denominator of the first fraction. Cross-multiplication is another name for the butterfly method. We employ the cross-multiply approach to identify one or more variables in a fraction. Cross multiplying is another method for comparing fractions.
We will do simple cross-multiplication here
given that for 12 cans we get 96 cents, that is
⇒ 12/96
and for 96 cans we get x cents, that is
⇒ x/96
Now, we do cross-multiplication here
⇒ 12/96 = 96/x
⇒ 12x = 96 × 96
⇒ x = (96 × 96)/12
⇒ x = 768 cents
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Correct question
A recycling center claims to give 96 cents for every 12 aluminum cans turned in. How much cents will they give if u recycled 96 cans?
what is the parent function of () =− 2| − 3| + 1 ????
Answer:
|x|
Step-by-step explanation:
Review your parent functions and how to identify them. They are the fundamentals of algebra and pre calc
the sum of two numbers is 16 and their diffrence is 14
Answer:
15, 1
Step-by-step explanation:
I'm assuming the answer should be limited to only positive integers. Either way, looking at 16 and 14, they are 2 apart and their average is 15. Since 15 is one from 16 and 14 both, the answer is 15 and 1.
15-1 = 14
15+1 = 16
Mia buys a car for $12500 She sells it to Chen for $16000 (a) Calculate Mia's percentage profit.
15 points
Answer:
3500
Step-by-step explanation:
1600-12500=3500
3500/12500*100% = 28%
so the percentage profit is 28%
2x² + 12x + 16
what is it
Answer:
2(x+2)(x+4)
Step-by-step explanation:
ANSWER QUICK PLS
Follow the steps to solve 15 / 4 – (-41/3)
a. Rewrite as addition
b. State whether the answer will be positive or negative
c. Solve
How to find slope for 1.5
Answer:0
Step-by-step explanation:The slope-intercept form is
y=mx+b, where m is the slope and b is the y-intercept
y=mx+b Using the slope-intercept form, the slope is 0
i need helpppppppppp
Answer: XYW = 32, WYZ = 85
Step-by-step explanation:
We are looking for what x is, which we can find with the formula:
117 = (6x+44) + (-10x+65)
117 = -4x + 109
8 = -4x
x = -2
We can verify this is correct by plugging it in and seeing if they add up to 117.
6x + 44 (XYW)
= 6(-2) + 44
= -12 + 44
= 32
-10x + 65 (WYZ)
= -10(-2) + 65
= 20 + 65
= 85
32 + 85 = 117
1. J(1, 9), K(7, 4), L(8, 13), M(-2, 1)
The image of the points after they are reflected across the x-axis are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)
How to determine the image of the points?From the question, we have the following parameters that can be used in our computation:
J(1, 9), K(7, 4), L(8, 13), M(-2, 1)
Also from the question we have the transformation to be
Transformation: reflection across the x-axis
The rule of the reflection across the x-axis is represented as
(x, y) = (x, -y)
Substitute the known values J(1, 9), K(7, 4), L(8, 13), M(-2, 1) in the above equation, so, we have the following representation
J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)
Hence, the image of the points are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)
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Triangle ABC has the following vertices:
A(7,-2)
B(-1,-8)
C(5,0)
Is triangle ABC an isosceles triangle, and why?
Calculate the lengths of the 3 sides of the triangle:
AB =
[tex] \sqrt{(7 - ( - 1)) ^{2} + (( - 2) - ( - 8))^{2} } = 10[/tex]
BC =
[tex] \sqrt{(( - 1) - 5) ^{2} + (( - 8) - 0)^{2} } = 10[/tex]
AC =
[tex] \sqrt{(7 - 5) ^{2} + (( - 2) - 0)^{2} } = 2 \sqrt{2} [/tex]
Because AB = BC
=> ️ABC is an isoscelea triangle at B
home prices in a neighborhood vary every year. in 2021, the following nine home prices were listed. (in thousands)
H 120 166 173 H H H 123 127 L
Where L indicates a Home below $110 and H indicates a Home above $190. The median home price is:
A) 166
B) 169.5
C) 170
D) 173
E) Cannot be determined
Based on the prices of the homes in the neighborhood, the median home price is A) 166
What is the median home price?
L is for a home below $110 and H is for a home above $190. The distribution of home prices can therefore be shown as:
190, 120, 166, 173, 190, 190, 190, 123, 127, 110
In an ordered list, this becomes:
= 110, 120, 123, 127, 166, 173, 190, 190, 190
The median is the price in the middle and we can see this price is $166
In conclusion, the median home price is $166.
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Find the equation of the linear function represented by the table below in slope-intercept form.
The equation of the linear function represented by the table below in slope-intercept form is y = 7x + 4
Linear equationsThe equation of a line in point-slope form is expressed as y = mx + b
where
m is the slope
b is the intercept
Using the coordinate points (0,4) and (1, 11)
Slope = 11-4/1-0
slope = 7
The y-intercept is at the point (0,4)
Determine the equation
y = mx + b
y = 7x + 4
Hence the equation of the linear function represented by the table below in slope-intercept form is y = 7x + 4
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Determine whether the following numbers are divisible by 2, 3, 4, 5, 6, 8, 9, and/or 10. Then,
explain why.
1. 450
2. 168
Explain why
Which ordered pair, when graphed, would be on the same line as
(
1
,
3
)
and
(
4
,
9
)
?
Multiple choice question.
cross out
A)
(
−
1
,
−
3
)
cross out
B)
(
−
2
,
−
3
)
cross out
C)
(
2
,
4
)
cross out
D)
(
3
,
6
)
The required ordered pair, when graphed, would be on the same line as (1,3) and (4,9) is (-2,-3).
Option (B) is correct.
What is co-ordinate geometry?
Coordinate geometry is defined as the study of geometry using the coordinate points. Coordinate geometry is required to provide a link between algebra and geometry through the use of line and curve graphs.
Given:
The given points is
(1,3) and (4,9)
According to given question we have
The points is
(1,3) and (4,9)
Plot the ordered pairs Draw a line through the points to indicate all of the points on the line.
The points lie on the given point is (-2,-3).
Therefore, the required ordered pair, when graphed, would be on the same line as (1,3) and (4,9) is (-2,-3).
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if you have a mixture of 10 lb. sunflower seeds which cost 32c per pound and 16 lb. of cracked corn which cost 18¢per pound, how much would this mixture cost per pound?
By unitary method, we get that the total cost of mixture per pound = 50 cents.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given:
Cost of 1 pound sunflower seeds = 32 cents.
Cost of 1 pound cracked corn = 18 cents.
Available sunflower seeds = 10lb = 10 pounds
Available cracked corn = 16lb = 16 pounds
To find: Cost of the mixture per pound
Finding:
By unitary method, Cost of 1 pound sunflower seeds = 32 cents.
Cost of 10 pounds sunflower seeds = 32(10) = 320 cents.
Again, by unitary method,
Cost of 1 pound cracked corn = 18 cents.
Cost of 16 pound cracked corn
= 18(16) cents
= 288 cents.
Therefore, total cost of mixture per pound
= 32 + 18 = 50 cents.
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The main courses at a restaurant all contain rice or onion. of the 23 choices, 17 contain onion and 14 contain rice. how many dishes contain both rice and onion?
If the main courses at a restaurant all contain rice or onion and of the 23 choices, 17 contain onion and 14 contain rice, then the number of dishes containing both rice and onion will be equal to 8.
The number of dishes that contain both rice and onion at the restaurant can be calculated by using an algebraic expression.
An algebraic expression can be defined as an equation in which both numerals and letters are present.
An algebraic expression for this problem can be given as,
(14 - x) + x + (17 - x) = 23
Here x is equal to the number of dishes containing both rice and onion.
14 + 17 - x + x - x = 23
31 - x = 23
x = 31 - 23
x = 8
Hence, the number of dishes that contain both rice and onion is calculated to be 8.
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Write 28 as a product of primes.
Use index notation when giving your answer.
HELP
Answer:
28 = 2² × 7
Step-by-step explanation:
28 = 4 × 7 = 2² × 7
Find the value of c in the equation c3 = 1,728
Answer:
c = 576
Step-by-step explanation:
3 c = 1728
divide both sides by 3
c = 576
If 14 inches of wire cost 42 cents how many inches of wire can be bought with 21 cents
If 14 inches of wire cost 42 cents, with 21 cents can be bought 7 inch of wire
Information about the problem:
Inches bought= 14Inches bought cost = 42 centsAmount = 21 centsInches with 21 cents = ?Calculating how much 1 inch cost, we have:
1 inch cost= Inches bought cost / Inches bought
1 inch cost= 42 cents / 14 inches
1 inch cost= 3 cent/inch
Calculating how much can be bought with 21 cents:
Inches of wire= Amount / 1 inch cost
Inches of wire= 21 cent / 3 cent/inch
Inches of wire= 7 inch
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
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Help me with number 59 and 60 :)
Answer:
59. a₁ = 4
60. a₁ = 10
Step-by-step explanation:
The general equation for the sum of the first n terms Sₙ of a geometric sequence with common ratio r and first term a₁ is
[tex]S_n = a_1 \dfrac{1-r^n}{1-r}[/tex]
Problem 59
Here we are given
[tex]S_n = \dfrac{31}{4}\\\\r = \dfrac{1}{2}[/tex]
So we can plug these values into the above equation and get [tex]a_1[/tex]
Let's first compute [tex]1 - r^n[/tex]
[tex]1 - r^n = 1 - \left(\dfrac{1}{2}\right)^5\\\\\left(\dfrac{1}{2}\right)^5 = \dfrac{1}{32}\\\\1 - r^n = 1 - \left(\dfrac{1}{2}\right)^5 = 1-\dfrac{1}{32} = \dfrac{32}{32}-\dfrac{1}{32} = \dfrac{31}{32}[/tex]
[tex]1- r = 1 - \dfrac{1}{2} = \dfrac{1}{2}[/tex]
So
[tex]\dfrac{1-r^n}{1-r} = \dfrac{31}{32} \div \dfrac{1}{2} = \dfrac{31}{32} \times \dfrac{2}{1} = \dfrac{31}{16}[/tex]
Substituting this value into [tex]S_n = a_1 \dfrac{1-r^n}{1-r}[/tex] we get
[tex]\dfrac{31}{4} = a_1\dfrac{31}{16}[/tex]
Multiplying both sides by [tex]\dfrac{16}{31}[/tex]
[tex]\dfrac{31}{4} \times\dfrac{16}{31} = a_1\dfrac{31}{16} \times\dfrac{16}{31}\\\\4 = a_1 \textrm{or alternatively }\\ \\\boxed{a_1 = 4}[/tex]
Problem 60
Use the same technique as above
[tex]S_8 = 2550, r = 2\\\\S_8 = a_1 \times \dfrac{1-r^8}{1-r}\\\\\\2550 = a_1 \times \dfrac{1-2^8}{1-2}\\\\2550 = a_1 \times \dfrac{1 - 256}{1-2}\\\\2550 = a_1 \times \dfrac{-255}{-1}\\\\2550 = a_1 \times255\\\\== > a_1 = \dfrac{2550}{255}\\\\\boxed{a_1=10}[/tex]
Brandy and mark are selling magazines. Brandy has sold half as many as mark. Together they have sold 747 magazines. How many did each sell? Elimination
Answer 1120.5
Step-by-step explanation:
4(5x+3)=14x+30 not sure if i understand
Answer:
x = 3
Step-by-step explanation:
Use the distributive property to multiply 4 by 5x+3. Subtract 14x from both sides. Combine 20x and −14x to get 6x. Subtract 12 from both sides. Subtract 12 from 30 to get 18. Divide both sides by 6. Divide 18 by 6 to get 3.
Answer:
20x+12=14x+30
6x=18
x=3
Step-by-step explanation:
First, apply the distributive property:
4(5x+3) = 4 · 5x + 4 · 3 = 20x+12
Now, we have this equation
20x+12=14x+30
We need to group the elements now.
So, to bring all the elements with an "x," we subtract 14x from both sides.
20x-14x+12=14x+30-14x
We have this now
6x+12=30
Now, let's subtract 12 on both sides
6x+12-12=30-12
6x=18
Divide both sides by 6
x=3
Can someone please help me with this proof? I don't get how to do it.
2) BA and CD are parallel (segments that are collinear with parallel segments are parallel)
3) CDAB is a parallelogram (a quadrilateral with two pairs of parallel sides is a parallelogram)
4) ∠B is congruent to ∠D (opposite angles of a parallelogram are congruent)
5) m∠B = m∠D (congruent angles)
6) m∠D=115° (transitive property)
7) m∠EDA=65° (linear pair)
8) m∠EAD=65° (base angle of an isosceles triangle)
9) m∠E = 50° (sum of angles in a triangle)
Find the equation of this line.
y =
[?]
x + [
Answer:
Step-by-step explanation:
15 Write an expression for the
gradient of the line
perpendicular to the line
segmentjoining
(3p, 6) to (-2p, 10).
5p/6 an expression for the gradient of the line perpendicular to the line segment joining (3p, 6) to (-2p, 10).
Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values. The coordinates of the first point represent x1 and y1
gradient of the line segment joining (3p, 6) to (-2p, 10)
m=(y2-y1)/(x2-x1)
m =( 10 -4)/ ( -2p - 3p)
m= 6/ (-5p)
m= -6/5p
we know that
Gradient of a line perpendicular to a line with a gradient of m = -1/m
Gradient of a line perpendicular to a line with a gradient of -6/5p = 5p/6
Hence 5p/6 an expression for the gradient of the line perpendicular to the line segment joining (3p, 6) to (-2p, 10).
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What is the quotient of 2 3/4 and 7/8?
Pls help fast
The quotient of the given expression 2 3/4 and 7/8 is 22/7
Quotient of an expressionQuotient refers to a number resulting from the division of one number by another. 12 ÷ 2 = 6 the quotient is 6
Dividend is number or expression that is to be divided by another. 12 ÷ 2 = 6 the dividend is 12
Divisor is the number or expression that is to be divided by another. 12 ÷ 2 = 6 the divisor is 2
Quotient of 2 3/4 and 7/8?
= 2 3/4 ÷ 7/8
= 11/4 ÷ 7/8
multiply by the reciprocal of 7/8= 11/4 × 8/7
= (11 × 8) / (4 × 7)
= 88/28
= 22/7
Therefore, the quotient of the given expression 2 3/4 and 7/8 is 22/7
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terra writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: terra's proof ao
Vertical angles or contrary angles are the statement that Terra's proof is still absent. The angles formed opposite to each other when two lines cross each other are equal.
The missing word in Terra's proof is described as :Terra describes the parallelogram nature of the diagram. Because they are vertical or opposite angles, these angles are equal.
The angles formed opposite to each other when two lines cross each other are equal. As a result, we have discovered that either vertical angles or opposite angles make up Terra's proof.
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PLS HELP ASAP
DONT JUST USE FOR POINTS
WILL MARK BRAINLIST
ANSWER NEEDS TO BE CORRECT TYSM
THIS IS FROM IXL BTW
Answer:
6,720
Step-by-step explanation:
Answer:
31 square miles
Step-by-step explanation:
We basically have three shapes here.
The top rectangle:
A= l x w = 7 x 2 = 14
The middle rectangle:
A= l x w = 4 x 2 = 8
The triangle
A = 1/2 x b x h = (3 x 6)/2 = 18/2 = 9
Add the area of all three: 14 + 8 +9 = 31
An expression is shown below.
2√51x
Which value of x makes the expression
equivalent to 10√51 ?
1. 6
2. 25
3. 59
4. 100
The required value of x in the expression 2√51x is 25.
Given that,
An expression 2√51x,
To determine the value of x when the expression is equivalent to 10√51.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
2√51x = 10√51
√51x = 5√51
√x = 5√51 / √51
√x = 5
squaring both sides
x = 25
Thus, the required value of x in the expression 2√51x is 25.
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