If the length of one side of Rory's garden is [tex]5^{2}[/tex] then the area of the garden will be equal to 625 [tex]feet^{2}[/tex].
Given that Rory' garden is square in shape and the length of one side of the garden is [tex]5^{2}[/tex] feet.
We are required to find the area of the garden.
Area is basically the quantity that expresses the extent of a region on the plane or on a curved surface.
Area of square=Side*Side
Area=[tex]5^{2}[/tex]*[tex]5^{2}[/tex]
=[tex]5^{4}[/tex]
=625 [tex]feet^{2}[/tex]
Hence if the length of one side of Rory's garden is [tex]5^{2}[/tex] then the area of the garden will be equal to 625 [tex]feet^{2}[/tex].
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the function f multiplies it’s input by 2 and then subtracts 17 to produce its output. What is the symbolic representation of this operation
Answer:
f(x)= 2x-17
Step-by-step explanation:
Let, input be x,
Multiplying input by 2: 2x
then subtracting it by 17: 2x-17
Therefore, Symbolic representation required is : f(x)= 2x-17
The symbolic representation of the function defined is f(x) = 2x-17
What is function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that, the function f multiplies it’s input by 2 and then subtracts 17 to produce its output. we need to express the operation into symbolic representation.
Let the input be x, then the output will be the value of f(x).
Therefore, it is given, the input is multiplied by 2, that mean,
f(x) = 2x
Then 17 is subtracted from it, that will give,
f(x) = 2x-17
Hence, the symbolic representation of the given operation is f(x) = 2x-17
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Question 6 (10 points)
=) Listen
The ratio of outdoor outdoor swimmers to indoor swimmers at the recreation center
is 3:2. If the center has 55 swimmers altogether, how many of them are indoor
swimmers?
22
44
none
33
Answer:
22
Step-by-step explanation:
The ratio tells us 2/5 of the swimmers are indoor swimmers.
55(2/5)=22
Question Write an equation of the line that passes through point (−3, 8) and has the slope m=−2.
Answer:
y = - 2x + 2
Step-by-step explanation:
[tex]y-8=-2(x-(-3))\\y-8=-2(x+3)[/tex]
[tex]y-8=-2x-6[/tex]
[tex]y=-2x-6+8[/tex]
[tex]y=-2x+2[/tex]
Hope this helps
HELP PLEASE I WILL GIVE BRAINLYEST! ALGEBRA 1 HW
expressions that are equivalent to k/2
A: k-2
B: 2/k
C: 1/2 k
D: k/2
E: k+k
The correct option is D: k/2 is the expression that is equivalent to the expression, K/2.
What is defined as the equivalent expressions?Two equations are equivalent unless and until they produce the same result for all matching variable values. As a result, we can determine whether 2 expressions seem to be equivalent by putting in many distinct corresponding values of the variables to ensure that each expression returns the same value in every instance.If we enter matching variable values into two mathematical expressions and get a different result from each expression, the two expressions really not equivalent.In response to the question;
We must determine the expression that is equivalent to k/2.
Among the options, Option D: k/2 is same as expression K/2.
Choice C, when written as (1/2)k, is equivalent to k/2 since they both imply half of k.
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Please help, I don’t know how to solve this!
A group of exchange students from Japan went to a convalescent home to sing songs for the seniors and to demonstrate origami. Groups of students and seniors sat together at tables so the students could teach the seniors to fold some origami figures. As it turned out, at each table there was either 1 student and 3 seniors, or 2 students and 4 seniors. There were 23 students and 61 seniors in all. How many tables were being used?
Answer:
19 tables
Step-by-step explanation:
Let X represent the number of tables that have 1 student and 3 seniors
Let Y represent the number of tables that have 2 student2 and 4 seniors
Therefore number students total
1X + 2Y =23 (1)
Number of seniors total
3X + 4Y = 61 (2)
Multiply equation (1) by 2 giving
2X + 4Y = 46 (3)
Subtract (3) from (2)
3X + 4Y - (2X+4y) = 61-46
3X + 4Y - 2X -4Y = 15
3X-2X = 15
X = 15
Plugging this value into equation (1) gives
1(15) + 2Y = 23
15 + 2Y = 23
Subtract 15 from both sides
2Y = 23 - 15
2Y = 8
Divide by 2 both sides
Y = 4
Thus total number of tables used = X +Y = 15+4 = 19
How many jelly beans are in a 2-liter jar? HELP ME PLEASE
1. The number of sample size 1 jelly beans in a 2-liter jar is 645.
2. The number of sample size 2 jelly beans in a 2-liter jar is 640.
3. The number of sample size 3 jelly beans in a 2-liter jar is 637.
What is a mathematical operation?A mathematical operation is an expression involving the use of mathematical operands and operators to compute values.
Mathematical operations use variables, numbers, and operators (addition, subtraction, division, and multiplication).
Data and Calculations:Total weight = 1,150g
Weight of the jar = 440g
The total weight of the jelly beans = 710g (1,150 - 440)
Sample Size 1: the number of jelly beans = 645 (710/22.0 x 20)
Sample Size 2: the number of jelly beans = 640 (710/22.2 x 20)
Sample Size 3: the number of jelly beans = 637 (710/22.3 x 20)
Thus, the number of jelly beans in a 2-liter jar depends on the sample size of the jelly beans.
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When a constant force acts upon an object, the acceleration of the object varies Inversely with its mass. When a certain constant force acts upon an object with
mass 7 kg, the acceleration of the object is 10 m/s². If the same force acts upon another object whose mass is 5 kg, what is this object's acceleration?
The acceleration of the object is found as 14 m/s².
What is defined as the Newton's second law of motion?Newton's second law states that acceleration of an object is determined by two variables: the net force acting on it and its mass.
The acceleration of the body is proportional to the net force exerting on it and inversely proportional to its mass. This implies that as the force that acts on an object increases, so does the object's acceleration. Similarly, as an object's mass increases, the object's acceleration decreases.The formula for the Newton's second law is;
F = ma
F = acting force in Newton
m = mass of the body in Kg.
a is the acceleration in m/s².
The mass of 7 kg accelerates with 10m/s².
Force acting on it is;
F = ma
F = 7×10
F = 10 N.
The same force is acting on the body of mass 5 kg.
F = ma
a = F/m
a = 70/5
a = 14 m/s².
Therefore, the acceleration of the body is found as 14 m/s².
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Which situation describes a non-proportional relationship?
The circumference of a circle with a radius of x units can be represented by y = 2zx.
The perimeter of an equilateral triangle with a side length of x units can be represented by y = 3x.
The total surface area of a cylinder with a radius of 1 unit and height of x units can be represented by
y = 2x + 2.
The radius of a circle with a diameter of x units can be represented by y=x.
Situation of non- proportional relationship :
The circumference of a circle with a radius of x units can be represented by = 2nx.
The perimeter of an equilateral triangle with a side length of x units can be represented by y = 3x
The total surface area of a cylinder with a radius of 1 unit and height of x units can be represented by y = 2xx + 2x
The radius of a circle with a diameter of x units can be represented by y = [tex]\frac{1}{2}x[/tex]
a proportional relationship is a relationship between two quantities in which the ratio of one quantity to the other quantity is constant. The graph of a proportional relationship is a line through the origin.
When ratios between quantities are not constant, a relationship may be linear but not proportional and the graph does not pass through the origin.
The graph shows the sales tax charged based
on the amount spent at a video game store in
a particular city. Does the graph show a linear
relationship? Is the relationship proportional
or nonproportional?
The graph shows a linear proportional
relationship because it is a line that contains
the origin.
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How many centimeters are in 2 miles?
Answer:
321,800 cm. (Rounded)
Step-by-step explanation:
2 × 160,900 = 321,800
There are 160,900 centimeters in one mile, so you must multiply that by 2 and round.
is 7 1/2 equal to 1/10, 1/5 or 4/5?
7y+2=3x-5 is the given equation. Finding the point that does not lie on the specified line, 7y+2=3x-5, is the next step.
To determine whether or not the point meets the provided equation, we will simply enter in the supplied point.
Check for (2,-1/7)
Connect it to 7y+2=3x–5.
7(-1/7)+2=3(2)-5
-1+2=6-5
1=1
Which is correct; as a result, this point is on the line 7y+2=3x-5.
Verify (3,-2/7)
Connect it to 7y+2=3x–5.
7(-2/7)+2=3(3)-5
-2+2=09-5
1=4
Which is False; as a result, the supplied line 7y+2=3x-5 does not include this point.
Connect it to 7y+2=3x–5.
7(-1)+2=3(0)-5
-7+2=0-5
-5=-5
Which is correct; as a result, this point is on the line 7y+2=3x-5.
Verify (1, -4, 7)
Connect it to 7y+2=3x–5.
7(-4/7)+2=3(1)-5
-4+2=3-5
-2=-2
This is why I'm making this point
lies on the line 7y+2=3x-5 that is presented.
Verify (-1, -10/7)
Connect it to 7y+2=3x–5.
7(-10/7)+2=3(-1)-5
-10+2=-3-5
-8=-8
Which is correct; as a result, this point is on the line 7y+2=3x-5.
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The product of 0.61 and 4 please
Answer:
4.61
Step-by-step explanation:
4.00 is the same as 4
4.00
0.61
--------+
4.61
Please help solve…………………
Answer:
22.5
Step-by-step explanation:
∠EAB=2x (alternate interior angles)
∠AEB=180°-4x (linear pair)
2x+180-4x=6x (exterior angle theorem)180-2x=6x180=8xx=22.5How is subtracting integers related to adding integers
Integer addition is the addition of integers with the same signs, whereas integer subtraction is the addition of integers with the opposite signs.
Are there any consistent rules for adding and subtracting integers?
Integer addition and subtraction formulas: 1) Subtract the two numbers and indicate the sign of the larger number if the two numbers have different signs, such as positive and negative. 2) Add the two numbers and give the common sign if the two numbers have the same sign, that is, either positive or negative signs.What in math is an integer?
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.Learn more about integer
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A couch with a list price of $2200 will be discounted 35 % at the time of purchase. What is the sale price before taxes?
The sale price before taxes and after discount is $1,430.
Given that A couch with a list price of $2200 will be discounted 35 % at the time of purchase and asked to find the sale price before taxes.
The original cost of the couch=$2200
The discount percentage=35 %
I.e. 35 % of $2200 is $770
The discount given to the customer will be 35% i.e. $770
⇒The selling price will be $770 less than the original cost price.
As a result, the selling price will be =$2200-$770
The Selling price of the couch is $1,430
Therefore,The sale price before taxes and after discount is $1,430.
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A rectangular garden is 6 ft longer than it is wide. Its area is 667 ft2. What are its dimensions?
The dimensions of the rectangular garden are 29 feet by 23 feet .
A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are a lot of rectangular objects all around us. Any rectangular form's two defining characteristics are its length and width. A rectangle's longer and shorter sides are its width and length, respectively.
The area of a rectangle is given by length × width
Now the given area of the rectangle is 667 ft² .
Let the width of the rectangle is x ft. Therefore length = x + 6
Now area of the rectangle is x (x+6) = x² + 6 x
Therefore x² + 6 x = 667
or, x² + 6 x - 667 = 0
or, (x-23)(x+29) = 0
Either x = 23 or x = -29(not possible)
Hence the width is 23 feet.
Length = 23 + 6 = 29 feet
Therefore the dimensions of the rectangle are 29 feet by 23 feet .
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describe a sequence of transformation that takes abcd to a'b'c'd'
The quadrilateral A'B'C'D' is the result of reflecting and translating the quadrilateral ABCD.
What kind of rigid transformations were done to transform ABCD to A'B'C'D'?
In this problem we find a representation of a quadrilateral and its image on a Cartesian plane. That image is the result of the following rigid transformations, that is, transformations applied on geometric loci such that Euclidean distance is conserved at every point of the locus.
After a careful inspection, we find that the following two rigid transformations were done:
Reflection about the x-axis.Translation 7 units in the + x direction.Now let is prove this steps:
Given: A(x, y) = (- 5, - 7), B(x, y) = (- 5, - 2), C(x, y) = (- 3, - 4), D(x, y) = (- 3, - 7)
Reflection:
A''(x, y) = (- 5, - 7) + (0, 14)
A''(x, y) = (- 5, 7)
B''(x, y) = (- 5, - 2) + (0, 4)
B''(x, y) = (- 5, 2)
C''(x, y) = (- 3, - 4) + (0, 8)
C''(x, y) = (- 3, 4)
D''(x, y) = (- 3, - 7) + (0, 14)
D''(x, y) = (- 3, 7)
Translation
A'(x, y) = (- 5, 7) + (7, 0)
A'(x, y) = (2, 7)
B'(x, y) = (- 5, 2) + (7, 0)
B'(x, y) = (2, 2)
C'(x, y) = (- 3, 4) + (7, 0)
C'(x, y) = (4, 4)
D'(x, y) = (- 3, 7) + (7, 0)
D'(x, y) = (4, 7)
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A company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. What is the implied valuation of the business?
If a company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. The implied valuation of the business is: $4,533,333.
Implied valuationFirst step is to calculate the equity valuation
Using this formula
Equity valuation=Amount invested/Equity rate
Let plug in the formula
Equity valuation=$800,000/.15
Equity valuation=$5,333,333
Second step is to calculate the implied valuation
Implied valuation=Equity valuation-Amount invested
Let plug in the formula
Implied valuation=$5,333,333-$800,000
Implied valuation=$4,533,333
Therefore If a company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. The implied valuation of the business is: $4,533,333.
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If f(x) = -2x² + 4 and g(x) = 3x - 3, find f (4) + g(-6).
Answer:
(-2[tex]x^{2}[/tex]+3x+1)
Step-by-step explanation:
f(x) = -2x² + 4 g(x) = 3x - 3 find f (4) + g(-6).
f(x)+g(x)
(-2[tex]x^{2}[/tex]+4) +(3x-3)
(-2[tex]x^{2}[/tex]+3x+4-3)
(-2[tex]x^{2}[/tex]+3x+1)
SOS, is for today!!!!
Given that the total length of the piece of steel is 25in, the numerical lengths of the first, second and third piece of the steel are 3in, 6in and 16in respectively.
What is the numerical length of each piece of the steel?Given the data in the question, let x represent the length of the first piece.
Length of first piece = xLength of second piece = 2xLength of third piece = 5x + 1Total length of the steel = 25 inTo determine the length of each piece, we equate the sum of the pieces to the total length of the steel ( 25in ).
x + 2x + ( 5x + 1 ) = 25
3x + 5x + 1 = 25
8x + 1 = 25
8x = 25 - 1
8x = 24
x = 24/8
x = 3
Hence,
Length of first piece = x = 3 inch
Length of second piece = 2x = 2(3) = 6 inch
Length of third piece = 5x + 1 = 5(3) + 1 = 15 + 1 = 16 inch
Given that the total length of the piece of steel is 25in, the numerical lengths of the first, second and third piece of the steel are 3in, 6in and 16in respectively.
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Mathematical connection A lighthouse casts a revolving beam of light as far as the pier
The light's coverage area is given mathematically as i.e. Area=[tex]\pi d^{2}[/tex]
Given that a lighthouse casts a revolving beam of light as far as they peir and asked the area is covered.
The revolving beam of light covers the whole space i.e entirely 360°
I.e. it forms a circle-like region
Area of circle = [tex]\pi r^{2}[/tex]{ where r is the radius of circle}
Let's assume the distance traveled by light as "d"
as it forms a circular region, it forms a circle of radius "d"
Mathematical connection i.e. area of the region
⇒area of circular region=[tex]\pi d^{2}[/tex] {where d is the radius of region}
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49.95 pair of shoes;5% tax
Two friends are playing with water balloons. They each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other. Joy walked 15 steps forward, and Shaunte walked 6 steps backwards. Which expression correctly represents the distance between the friends?
Answer choices
|−15| + 6 = 21 steps
|−15| + |−6| = 21 steps
15 + 6 = 21 steps
15 + |−6| = 21 steps
Answer: 15 + |−6| = 21 steps
Its stated that Joy walked 15 steps forward, meaning it would be a positive value. Shaunte walking backwards would give a negative value.
????????????????????
Answer: 120 minutes, 105 km, proportional
Step-by-step explanation:
90 km/hr
180 km * 1 hr/90 km=
180 km/90 km * 1 hr=
2 hours=120 minutes
1 hour=60 minutes
70/60=x/90
7/6=x/90
7*90/6=x
x=7*15
x=105 km
li has a jar full of marbles. In the jar there are 15bblue marbles, 10 red marbles and 16 purple marbles. a. She selects a marble at random from the jar. She does not replace the marble. She selects a second marble from the jar. What is the probability that both marbles are red? What is the correct interpretation of this question?
The probability that both marbles are red will be 0.055.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences. The probability is given as,
P = (Favorable event) / (Total event)
A jar full of marbles is kept by Li. There are 16 purple marbles, 10 red marbles, and 15 blue marbles in the jar. A stone is chosen at random by her from the jar. She leaves the marble alone. She takes another stone out of the jar.
The total number of event = 16 + 10 + 15 = 41
Then the probability of both marble should be red will be given as,
P = (10 / 41) x (9 / 40)
P = 0.055
Thus, the probability that both marbles are red will be 0.055.
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What is the value of this expression if h 8, j = -1, and k = -12?
Value of the given expression j³k/h0 is 12
h = 8
j=-1
h = 8
In order to do this, we need to change the values of h, j, and k in the given statement = (-1)^3 (-12) / 8^0 ....(1)
Find the denominator by using (1)
(-1)³ (-12) / 1
Analyze each exponent.
= 12/1
Hence, j³k/h0 = 12
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Complete Question -
What is the value of this expression if h=8 ,j= -1 , and k= -12? j³k/h0
Help on this question please
A 20-year U.S. Treasury bond has a 3.50 percent interest rate, while a same maturity corporate bond has a 5.25 percent interest rate. Real interest rates and inflation rate expectations would be the same for the two bonds. If a default risk premium of 1.50 percentage points is estimated for the corporate bond, determine the liquidity premium for the corporate bond.
The liquidity premium for the corporate bond is 0.25%.
What is liquidity?Any additional compensation needed to stimulate investment in assets that cannot be quickly and effectively converted into cash at fair market value is known as a liquidity premium. For instance, due to its relative illiquidity, a long-term bond will have a higher interest rate than a short-term bond.
Liquidity premium for corporate bond will be:
= 5.25 - 3.5 - 1.5
= Interest - Treasury - Default risk
= 0.25%.
Therefore, the liquidity is 1.25%.
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Determine if the following radical expression is a real number. If it is, you are to evaluate the expression.
3√-27
Answer
Selecting an option will display any text boxes needed to complete your answer.
Real Number
O Not a Real Number
