Read the story.
Peace Park sets up an outdoor ice-skating rink each winter. Yesterday afternoon, there
were 5 skaters who brought their own skates for every 3 skaters who rented skates.
Pick the diagram that models the ratio in the story.
If there were 12 more skaters who brought their own skates than skaters who rented skates,
how many skaters were there altogether?
skaters
The diagram 2 represents the model that depicts the ratio given in the story.
What is a ratio?Ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Given is that Peace Park sets up an outdoor ice-skating rink each winter. Yesterday afternoon, there were 5 skaters who brought their own skates for every 3 skaters who rented skates.
The given ration of 5 skaters for every 3 skaters is shown in the
diagram 2. In the first column, five blocks are colored and in the second
column, three boxes are colored.
Therefore, the diagram 2 correctly represents the model in the story.
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Evaluate f(x)=2x+5 when x=0, x=1, x=5
Th value of the equation f ( x ) is given as
when x = 0 , f ( 0 ) = 5
when x = 1 , f ( 1 ) = 7
when x = 5 , f ( 5 ) = 15
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given as
f ( x ) = 2x + 5
Now , the values of the function f ( x ) can be determined when we substitute for the values for x in the equation
So , in order to find f ( 0 ) , substituting the value for x as x = 0, we will get the value for the function
a)
when x = 0
The equation is f ( x ) = 2x + 5
f ( 0 ) = 2 x 0 + 5
f ( 0 ) = 5
So , the value of f ( 0 ) = 5
b)
when x = 1
The equation is f ( x ) = 2x + 5
f ( 0 ) = 2 x 1 + 5
f ( 0 ) = 7
So , the value of f ( 0 ) = 7
c)
when x = 5
The equation is f ( x ) = 2x + 5
f ( 0 ) = 2 x 5 + 5
f ( 0 ) = 15
So , the value of f ( 0 ) = 15
Therefore , the values of the equations are f ( 0 ) = 5 , f ( 1 ) = 7 , f ( 5 ) = 15
Hence ,
Th value of the equation f ( x ) is given as
when x = 0 , f ( 0 ) = 5
when x = 1 , f ( 1 ) = 7
when x = 5 , f ( 5 ) = 15
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Tell whether ABC and DCB can be proven congruent.
No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
What is congruent?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Here,
We have to prove whether ΔABC and ΔDCB can be proven congruent.
For this, we examine the given diagram and concluded that there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
Hence, No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
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Matias has a planter that is full of soil. The planter is a rectangular prism that is 1 1/2 ft high, 3 2/3 ft long, and 2 ft wide. Matias pours all the soil into a new planter. The new planter is a rectangular prism that has a base of 8 1/4. What is the height of the soil in the new planter
The height of the soil in the new planter is 4/3 feet
Consider the old planter
The height of the prism = [tex]1\frac{1}{2}[/tex] feet = 3/2 feet
The length of the prism = [tex]3\frac{2}{3}[/tex] feet = 11/3 feet
The width of the prism = 2 feet
The volume of the rectangular prism = Length × width × height
= 11/3 × 2 × 3/2
= 11 cubic feet
The area of the base of the new planter = [tex]8\frac{1}{4}[/tex] square feet = 33/4 square feet
The volume of both planter will be equal
The base area × height = volume
33/4 × h = 11
h = 11 / (33/4)
h = 11 × 4/11
h = 4/3 feet
Therefore, the height of the new planter is 4/3 feet
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The volume of a cylinder having height one and half of the radius is 12,936 m3 what minimum square cm of paper is needed to cover the curved surface area of the cylinder? The answer should be 1848m2. please solve my question.
In ΔPQR, p = 4.7 inches, ∠P=76° and ∠Q=57°. Find the length of q, to the nearest 10th of an inch.
The length of side q to the nearest 10th of an inch is 4.1 inches.
What is the sine rule for a triangle?The sine rule for a triangle ABC is a/sinA = b/sinB = c/sinC.
Given, In ΔPQR, p = 4.7 inches, ∠P=76°, and ∠Q=57°.
∴ the length of q can be obtained by,
p/sinP = 1/sinQ.
4.7/sin76° = q/sin57°.
4.7/0.97 = q/0.84.
q = (4.7×0.84)/0.97.
q = 4.1 inch.
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O A. (2,4) O B. (1,2) O D. (2,2) What is the midpoint of the line segment with endpoints (-1, 7) and (3, -3)?
The midpoint of the line segment is (1, 2). Then the correct option is B.
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoints of the line segment are (-1, 7) and (3, -3). Then the mid-point of the line segment will be given as,
(x, y) = [(-1 + 3) / 2, (7 - 3) / 2]
(x, y) = (2/2, 4/2)
(x, y) = (1, 2)
The midpoint of the line portion is (1, 2). Then the right choice is B.
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18 (a) Reflection: in the x-axis (b) Rotation: 180° 19 20 21 22 Triangle DEF with vertices D(-6, -1), E(-3, -2) and F(-5, -7):
(a)Reflection: in the x-axis
(b) Rotation: 180°
The vertices after reflection will be (-6, 1), (-3, 2), (-5, 7) and the vertices after rotation of 180° will be (6, 1), (3, 2), (5, 7).
What is the reflection of points?A form of Euclidean space isometry in geometry is called a point reflection, also known as a point inversion, center inversion, or asymmetry through a point.
An object is said to have point symmetry if it is unchanged under a point reflection, and central symmetry or being centrally symmetric if it is invariant below a point reflective thinking through its center.
As per the given information in the question,
The given vertices of the triangle are:
D(-6, -1), E(-3, -2), F(-5, -7).
a.
The equation towards reflection in the x-axis: (x, -y)
D = (-6, -1)
Reflected vertex = (-6, 1)
E = (-3, -2)
Reflected vertex = (-3, 2)
F = (-5, -7)
Reflected vertex = (-5, 7)
b.
Now let's find out the rotation of 180° of the given points,
As we can see that the vertices are in the third quadrant because both the points of each vertex are negative, so after rotation of 180° it will move to the 1st quadrant where all the points are positive.
So,
D = (-6, -1)
After rotation, D = (6, 1)
E = (-3, -2)
After rotation, E = (3, 2)
F = (-5, -7)
After rotation, F= (5, 7)
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Find the fourth degree polynomial function with zeros 5, -5, 5i, and -5i. Write the function in factored form.
The fourth degree polynomial function with zeros 5, -5, 5i, and -5i. written in factored form is
(x - 5) (x + 5) (x - 5i) (x + 5i)How to find the function with the given zerosThe zeros of a polynomial function is the the value of x when the function is equal to zero
The zero is also called the root of the polynomial
To find the polynomial we equate to the zeros
the first
x = 5
x - 5 = 0
the second
x = -5
x + 5 = 0
the third
x = 5i
x - 5i = 0
the fourth
x = -5i
x + 5i = 0
Bringing the terms together
(x - 5) (x + 5) (x - 5i) (x + 5i)
Therefore the polynomial of zeros 5, -5, 5i, and -5i is gotten in factored form in the form (x - 5) (x + 5) (x - 5i) (x + 5i)
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At a local print hop, 16 copie can be made for $8. At thi rate, how much would it cot to make 88 copie?
Rate at which 88 copies will get printed is 44 dollars
What is unitary method ?By using the unitary method to find the value of a single unit, we may use that value to calculate the values of the required number of units.
According to the given information :
Applying the unitary method
we get,
Rate at which 16 copies get printed = 8 dollars
Rate at which one copy gets printed = [tex]\frac{8}{16}[/tex]
Rate at which 88 copies get printed = [tex]\frac{8}{16}[/tex]×88
= 44 dollars
Rate at which 88 copies will get printed is 44 dollars.
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.........i need help past due
Answer:
[tex]\frac{85}{17}[/tex]
Step-by-step explanation:
[tex]\frac{8.5}{1.7}[/tex] multiply the top and bottom by 10
[tex]\frac{85}{17}[/tex]
Jeff bicycles 144 miles at the rate of r mph. The same trip would have taken 3 hours longer if he had decreased his speed by 4 mph. Find r (in mph).
His original speed was r =mph.
Jeff bicycles 144 miles at the rate of r mph. The same trip would have taken 3 hours longer if he had decreased his speed by 4 mph. The value of r is 16.
What is speed ?
The speed at which an object's position changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it only has a direction and no magnitude, speed is a scalar quantity.
144/r= t
144/(r-4)-144/r = 3
LCM r(r-4)
144r-144(r-4)/r(r-4)=3
Simplify [tex]$\frac{144 r-144(r-4)}{r(r-4)}: \frac{576}{r(r-4)}$[/tex]
[tex]\frac{576}{r(r-4)}=3[/tex]
Multiply both sides by r(r-4)
[tex]\frac{576}{r(r-4)} r(r-4)=3 r(r-4)[/tex]
Simplify
576=3 r(r-4)
Solve [tex]$576=3 r(r-4): \quad r=16, r=-12$[/tex]
r=16, r=-12
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Literal Equations
help asap !!
Answer:
Step-by-step explanation:
-6y = -5x + 36
y = 5/6x - 6
The first side of a triangle is 3cm longer than the second. The third side is twice as long as the second. The perimeter is 31cm. Find the length of each side.
Answer:
7 cm ; 10 cm ; 14 cm
Step-by-step explanation:
x = y + 3
z = 2y
x + y + z = 31
y + 3 + y + 2y = 31
4y = 31 -3
4y = 28
4/4 y = 28/4
y = 7
z = 7(2) = 14
x = 7 + 3 = 10
PLS HELP EASY EASY EASY
Answer:
x = 30 degrees
Step-by-step explanation:
By Parts-Whole Postulate, x + 100 = 130, meaning that x = 30 degrees.
Answer: 30
Step-by-step explanation: 130-100=30
URGENT HELP PLEASEEE :)
a) The probability of rolling a total of 5 is 1/9.
b) If a pair of fair dice 360 times, then 40 times you will get a total of 5.
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
The number of 5 in the table is 4.
The total number of outcomes is 6 × 6 = 36
The number of outcomes of favorable event is 4.
Total number of outcomes is 36.
The probability getting total of 5 after rolling the pair of dice is
=4/36
Divide the denominator and numerator by 4:
= 1/9
If 360 time the pair of dice rolled, the number of times to get total 5 is
360 × (1/9)
= 40.
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A bag contains 10 red marbles, 7 blue marbles, and 3 green marbles. How many blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4?.
32 more blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4
A bag contains 10 red marbles, 7 blue marbles, and 3 green marbles.
we need to find the numbar of blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4
Let the number of blue marbles added be n,
required probability P = 3/4
Total marbles = 10 + 7 + 3
= 20
Number of blue marbles=7
Using definition of probability,
(7 + n)/(20+n) = 3/4
4(7+n)=3(20+n)
28+4n=60+3n
n = 32
Therefore, we need to add 32 more blue marbles to make the probability of randomly drawing a blue marble be 3/4.
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If they are similar, find the value of x
For figure 2) the value of the 'x' would be x = 14.
and for figure 3) the value of the 'x' would be x = 17 or x = 1 .
What is the Basic Proportionality Theorem?
The Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle that intersects the other sides into two distinct points, then the line divides those sides in proportion.
Figure 2)
By using the Basic Proportionality Theorem, we can write
[tex]\frac{11}{22}=\frac{x}{42-x}\\\\\frac{1}{2}=\frac{x}{42-x}\\\\42-x=2x\\\\3x=42\\\\x=14[/tex]
Now for figure 3)
By using Pythagoras' theorem, we can write
[tex]24^2+(x+7)^2=(2x-10)^2\\\\576+x^2+14x+49=4x^2-40x+100\\\\3x^2-54x+51=0\\\\x^2-18x+17=0\\\\x^2-17x-x+17=0\\\\(x-17)(x-1)=0\\\\x=17 $ or $ x=1[/tex]
Hence, for figure 2) the value of the 'x' would be x = 14.
and for figure 3) the value of the 'x' would be x = 17 or x = 1 .
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a florist has 25 flower arrangements to sell. the amount of money the florist makes for selling x flower arrangements is represented by a function. f(x)
In linear equation, The domain defines the values of numbers of flower arrangements that
can be expected from the florist.
The practical domain of the function is; All integers from 0 to 25, inclusive.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The domain of the function = The possible number of flower arrangements
that can be sold
The possible number of flower arrangements that can be sold = Whole
numbers from 0 to 25
Therefore;
The possible number of flower arrangements that can be sold = 0 ≤ x ≤ 25
Where;
x = An integer
Which gives;
The domain of the function, D = {0 ≤ x ≤ 25 | x ∈ Z}
Therefore;
The practical domain of the function if the florist sells 25 flower
arrangements is D = All integers from 0 to 25, inclusive.
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I really need help with these questions!! Please make it quick!!!
Answer:
The selected answer should be correct!
Step-by-step explanation:
I did the problem step by step and got 1 5/7 which is the simplified version of 1 15/21.
I hope this helped somewhat!!
On a 60-mile road there are 7 rest stops placed at.
equal intervals, including one at each end of the
road, as shown above. What is the distance, in feet,
between two consecutive rest stops?
(Note: 1 mile = 5,280 feet)
A) 31,680
B) 36,960
C) 45,257
D) 52,800
Answer:
C. 45,257
Step-by-step explanation:
5280 * 60 = 316,800
316,800 ÷ 7 = 45,257
The distance between two consecutive rest stops is 45257 feet.
What is division?Division is the process of dividing a number by a given number.
Given that, the 60-mile road is divided into 7 equal parts.
The length of each part is:
60/7 mile
Given that;
1 mile = 5280 feet
Therefore;
60/7 mile = (60/7)5280 feet
60/7 mile ≈ 45257 feet
Hence, the distance between two consecutive rest stops is 45257 feet.
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Need Help for this Answer on this screenshot
Answer:
<
A
Step-by-step explanation:
PLEASE HELP ASAP!!!!
Answer:
#1
Step-by-step explanation:
3x4=12 not 7
PLEASE AWNSER ASAP!!
The Double box plot shows the number of car shows attended by two car clubs each year.
What is the Mean of The Cruisers?
A. 9
B. 10
C. 11
D. Unable to determine given the Data
9 is the mean of clusters
What are equivalent equations?
Equivalent equations are algebraic equations that are having identical roots or solutions. By adding or subtracting the same number or expression to both side of an equation we get an equivalent equation. Also by multiplying or dividing both sides of an equation by the same non zero number we get equivalent equation.
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5/6 X +3 equals 13 
Answer:
Step-by-step explanation:
The answer is 12
Answer:
x=12
Step-by-step explanation:
[tex]\frac{5}{6}x+3=13\\\frac{5}{6}x+3-3=13-3\\\frac{5}{6}x=10\\6(\frac{5}{6}x)=10(6)\\5x=60\\(\frac{1}{5})5x=60(\frac{1}{5})\\x=12[/tex]
how many. roots
f(x) = 4x5 – 3x
The function f(x) is 4x5 – 3x has exactly 5 roots according to the Fundamental Theorem of Algebra.
How to find number of roots ?According to the Fundamental Theorem of Algebra, a polynomial function of degree n has exactly n roots (also known as zeros).In other words, if f(x) is a polynomial function of degree n, then there exist n values of x, called roots or zeros, that satisfy the equation f(x) = 0.The Fundamental Theorem of Algebra is important because it guarantees the existence of solutions to polynomial equations, which are equations that have the form f(x) = 0, where f(x) is a polynomial function.In this case, the polynomial function is f(x) = 4x^5 - 3x, which is of degree 5. Therefore, the function has exactly 5 roots according to the Fundamental Theorem of Algebra.The correct answer is therefore d) 5 roots.
Complete question :
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?
f(x) = 4x5 – 3x
1 root
2 roots
4 roots
5 roots
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A small pool for children has some water in it. Jabari uses a garden hose to add water to it. The total amount of water in gallons, y, is a function of the time in minutes since Jabari turns on the hose, x.
The graph of the linear function passes through the points (2,44) and (5,80). What is the equation of this function?
y=?x+?
The equation for the given linear function is y = 12m + 20.
What is a linear equation?A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.
It can be represented as a straight line on a graph.
The given points for the linear function are (2, 44) and (5, 80) respectively.
The slope can be obtained as,
m = (80 - 44)/(5 - 2)
= 36/3
= 12
Substitute the value of m in the general form y = mx + c to obtain,
y = 12x + c
Now, substitute x = 2 and y= 44 in the above expression as,
44 = 12 × 2 + c
=> c = 44 -24
=> c = 20
Thus the linear function can be written in the form of equation as,
y = 12m + 20
Hence, the equation of the function for the given case is y = 12m + 20.
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The ale price of a wimming pool after a 18. 5% dicount i 1206. 20. Find the original lit price of the pool
The swimming pool was on sale for $1206.2, which is 18.5% less than its initial $1429.35 cost.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
Here,
Sale price after discount=$1206.2
Discount percent=18.5%
Original price=1206.2+18.5%*1206.2
=$1429.35
The original price of the swimming pool was $1429.35 as It was at sale price of $1206.2 with the discount of 18.5%.
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Write a equation for each one please this is urgent!!!
50 points to whoever answers!!!
1. A line with a slope of 0 and a y-intercept of 5.
2. A line with a slope of 2 and a y-intercept of -1.
3. A line with an undefined slope and an x-intercept of -1.
Answer:
1. y = 5
2. y = 2x - 1
3. x = -1
Solve for x. 1+|2+x|=9
Answer: 6
Step-by-step explanation:
Remember:
Anything in | | is considered positive.
Simplified:
1+2+x=9
3+x=9
Solve for x:
x=9-3
x=6