(1) To find (f ο g ο h)(-2), we first need to find g ο h and then apply f to the result. We have:
g ο h(x) = g(h(x)) = g(2x) = (2x)^2 = 4x^2
So, (f ο g ο h)(-2) = f(g(h(-2))) = f(g(-4)) = f(16) = 3(16) + 1 = 49
Therefore, (f ο g ο h)(-2) = 49.
(2) To find (f o f^-1)(2/3), we need to use the fact that f and f^-1 are inverse functions, which means that f(f^-1(x)) = x for all x in the domain of f^-1. Therefore, we have:
f(f^-1(x)) = 3f^-1(x) + 1 = x
Solving for f^-1(x), we get:
f^-1(x) = (x - 1)/3
So, (f o f^-1)(2/3) = f(f^-1(2/3)) = f((2/3 - 1)/3) = f(-1/9) = 3(-1/9) + 1 = 2/3
Therefore, (f o f^-1)(2/3) = 2/3.
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Is X² always positive?
Yes, the square of any number like X² is always positive.
Define the term positive numbers?Positive numbers are those above zero or to the right of zero on the number line. Be aware that positive numbers can be either integers or fractions, irrational numbers, or both. For instance, the square root of 2 has an infinite number of non-repeating digits.A number can be multiplied by itself to find its square.Example:
The result of two negative numbers is always positive, as explained.When two negative numbers are added together, the result is always positive.If we calculate the square of a negative number, let's say -x, where x > 0, then (-x) (-x) = x².
Here, x² > 0.
Hence, the square of any number like X² is always positive.
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What are the 3 ways in math?
Step-by-step explanation:
Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.
Which of the following is a constant polynomial?a.4x+1b. 3c. 2x2d. 6x+3
A constant polynomial is a polynomial with a degree of 0, meaning it has no variable terms. The only possible constant polynomial is the term with a coefficient of 3, which is 3.
This can be seen by looking at the formula for a polynomial, which is:
P(x) = a0 + a1x + a2x2 + ... + anxn,
where a0 is the constant term, a1 is the linear term, a2 is the quadratic term, and so on. Since this polynomial has no variable terms (x = 0), the only possible constant polynomial is the term with a coefficient of 3.
To calculate the value of a constant polynomial, you simply substitute 0 for x in the equation above. For example, in the polynomial 3, the value would be 3 when x = 0.
P(0) = 3
Therefore, the answer is option b, 3.
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A 8 foot ramp leads from the ground to the tailgate of a truck and forms a 35° angle with the the ground. Find the height of the tailgate from the ground
The height of the tailgate (from the ground), holding the 8 ft ramp inclined at 35° with the ground, found using trigonometric ratios is about 4.59 ft
What are trigonometric ratios?A trigonometric ratio (trig ratio) specifies the relationship between an angle in a right triangle and two sides of the right triangle.
The length of the ramp = 8 ft
The angle the ramp forms with the ground = 35°
The ramp leads from the ground to the tailgate of the truck
The height of the tailgate from the ground can therefore be found using trigonometric ratios as follows;
The trigonometric ratio for the sine of an angle, θ, using SOH CAH TOA therefore is; sin(θ) = Opposite side
Where;
θ = 35°
The opposite side to the angle θ = Height of the tailgate from the ground = h
The hypotenuse side of the right triangle formed by the ramp = The length of the ramp = 8 ft. We get;
sin(35°) = (Height of the tailgate from ground, )/(Length of the ramp)
Therefore;
sin(35°) = h/8
h/8 = sin(35°)
h = 8 × sin(35°) ≈ 4.59
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100 POINTS:
Can someone convert the following to standard form? (Shown work is not required but appreciated"
1. The function f(x) = (x+5)(x-9) in standard form is x²-4x-45.
2. The function f(x) = (x+4)² in standard form is x²+8x+16.
3. The function f(x) = (x+2)²-25 in standard form is x²+4x-21.
4. The function f(x) = 4(x-2)² in standard form is 4x²-16x+16.
5. The function f(x) = 6(2x+1)² in standard form is 24x²+24x+6.
6. The function f(x) = 3(x+4)(x-5) in standard form is 3x²-3x-60.
7. The function f(x) = (x+10)²-100 in standard form is x²+20x.
8. The function f(x) = 9-(x+1)² in standard form is -x²-2x-8.
9. The function f(x) = 2(x+5)²+10 in standard form is 2x²+20x+60.
What is the standard form?
A linear equation can also be written in standard form, slope intercept form, and point slope form.
The formula for standard form is Ax+By=C.
The first function is y = f(x) = (x+5)(x-9).
Simplifying the equation -
f(x) = (x+5)(x-9)
x(x-9)+5(x-9)
x²-9x+5x-45
x²-4x-45
Therefore, the standard form is x²-4x-45.
The second function is y = f(x) = (x+4)².
Simplifying the equation -
f(x) = (x+4)²
Follow the formula - (a+b)² = (a²+2ab+b²)
(x)²+2(x)(4)+(4)²
x²+8x+16
Therefore, the standard form is x²+8x+16.
The third function is y = f(x) = (x+2)²-25.
Simplifying the equation -
f(x) = (x+2)²-25
Follow the formula - (a+b)² = (a²+2ab+b²)
[(x)²+2(x)(2)+(2)²]-25
x²+4x+4-25
x²+4x-21
Therefore, the standard form is x²+4x-21.
The fourth function is y = f(x) = 4(x-2)².
Simplifying the equation -
f(x) = 4(x-2)²
Follow the formula - (a-b)² = (a²-2ab+b²)
4[(x)²-2(x)(2)+(2)²]
4[x²-4x+4]
4x²-16x+16
Therefore, the standard form is 4x²-16x+16.
The fifth function is y = f(x) = 6(2x+1)².
Simplifying the equation -
f(x) = 6(2x+1)²
Follow the formula - (a+b)² = (a²+2ab+b²)
6[(2x)²+2(2x)(1)+(1)²]
6[4x²+4x+1]
24x²+24x+6
Therefore, the standard form is 24x²+24x+6.
The sixth function is y = f(x) = 3(x+4)(x-5).
Simplifying the equation -
f(x) = 3(x+4)(x-5)
3[x(x-5)+4(x-5)]
3[x²-5x+4x-20]
3[x²-x-20]
3x²-3x-60
Therefore, the standard form is 3x²-3x-60.
The seventh function is y = f(x) = (x+10)²-100.
Simplifying the equation -
f(x) = (x+10)²-100
Follow the formula - (a+b)² = (a²+2ab+b²)
[(x)²+2(x)(10)+(10)²]-100
x²+20x+100-100
x²+20x
Therefore, the standard form is x²+20x.
The eighth function is y = f(x) = 9-(x+1)².
Simplifying the equation -
f(x) = 9-(x+1)²
Follow the formula - (a+b)² = (a²+2ab+b²)
9-[(x)²+2(x)(1)+(1)²]
9-x²-2x-1
-x²-2x-8
Therefore, the standard form is -x²-2x-8.
The ninth function is y = f(x) = 2(x+5)²+10.
Simplifying the equation -
f(x) = 2(x+5)²+10
Follow the formula - (a+b)² = (a²+2ab+b²)
2[(x)²+2(x)(5)+(5)²]+10
2[x²+10x+25]+10
2x²+20x+50+10
2x²+20x+60
Therefore, the standard form is 2x²+20x+60.
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PLEASE HELP
Select all the right angles.
What is the coefficient of X²Y in the product 7x² 5y X² 3y?
The coefficient of x²y in the product ( 7x²-5y) ( x²+3y) is 16.
The coefficient of x²y in the product (7x²-5y) (x²+3y) is the numerical factor that is multiplied to x²y when the two polynomials (7x²-5y) and (x²+3y) are multiplied together.
To find the coefficient of x²y in the product, you can use the distributive property of multiplication over addition, also called the FOIL method, which states that to multiply two binomials, you must multiply the first term of the first binomial by the first term of the second binomial, the first term of the first binomial by the second term of the second binomial, the second term of the first binomial by the first term of the second binomial, and the second term of the first binomial by the second term of the second binomial.
The product of (7x²-5y) (x²+3y) can be expanded as follows:
(7x²-5y) (x²+3y) = 7x²x² + 7x²3y -5yx² -5y3y
=7x⁴ + 21x²y -5x²y - 15y²
= 7x⁴ + 16x²y - 15y²
So, the coefficient of x²y in the product ( 7x²-5y) ( x²+3y) is 16.
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If using the method of completing the square to solve the quadratic equation x^2+2x+16=0x , which number would have to be added to "complete the square"?
The number that would complete the square is 1.
What is the completing the square method?We know that the method of completing the square would involve a quadratic equation that does have the general form;
ax^2 + bx + c =0
We have to note that the number that is going to complete the square is the number that is going to correspond to 1/2(b).
This implies that we have to look at the b term in the equation and we b = 2.
Thus;
1/2(2) = 1
Hence, we have found that the square can be completed by 1.
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Determine if the following system of
equations has no solutions, infinitely
many solutions or exactly one solution.
2x + 5y = 4
-4x - 13y
=
-9
One solution exists for the given equation.A linear equation with one variable has only ever one solution.
What is an unique solution?A linear equation with one variable has only ever one solution. The unique solution of a linear equation is the location at which LHS and RHS are identical when substituted.
The solution must be an ordered pair when there are two linear equations operating simultaneously (x, y). In this case, the ordered pair will fulfill the set of equations.
Given:
2x + 5y = 4
-4x - 13y = 9
Now,
a 1 = 2, b1 = 5 , = -4
a2 = -4 , b2 = -13, = 9
Now, = 2 / -4
= 5 / -13
As, a1/ a2 = 2/-4
b1 / b2 = 5 /-13
Thus, the relationship mentioned above reflects intersecting lines.
So, there is only one solution to the given problem.
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if you can write all of the numbers from 30 and 65 including 30 and 65
Answer:
The total number count we are looking at from the numbers 30 to 65 is 36. So that is a total of 72 digits making up this numbers from 30 to 65. Also, we can see that the whole range of numbers 0 to 9 is being used for this range
What polygon has 7 points 7 lines 7 angles?
A polygon having seven sides and seven angles is called a heptagon. Seven straight sides and seven corners, or vertices, make up a heptagon. It's also referred to as a "septagon" at times.
A seven-sided polygon is called a heptagon. A closed figure with seven vertices, it is. Another name for a heptagon is a septagon.
There are various sorts of hexagons, depending on the angles and diagonals.
Regular and Irregular Heptagons
Concave and Convex Heptagon
The following are some heptagon's characteristics:
(1) The inner angles of a heptagon add up to 900 degrees.
(2) A heptagon's outside angles add up to 360 degrees.
(3) The internal angle of a normal heptagon measures approximately 128.57 degrees.
(4) The size of a typical heptagon's central angle is roughly 51.43 degrees.
(5) There are fourteen diagonals in a heptagon.
(6) Convex heptagons are another name for regular heptagons.
(7) A heptagon has a total of five triangles.
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Answer this question Please I need the answer know
Answer:
[tex]y= \frac{x}{2x−1}[/tex]
Step-by-step explanation:
To find the inverse function, swap x and y, and solve the resulting equation for x.
If the initial function is not one-to-one, then there will be more than one inverse.
So, swap the variables: y=x/2x−1 becomes x=y/2y−1.
Now, solve the equation x=y/2y−1 for y.
y=x/2x−1
You have 2.88 meters of copper wire and 5.85 meters of aluminum wire. You need 0.24 meter of copper wire to make one bracelet and 0.65 meter of aluminum wire to make one necklace. Can you make more bracelets or more necklaces? Explain.
Answer: You can make more bracelets than necklaces. ✅
Step-by-step explanation:
You have 2.88 meters of copper wire and 5.85 meters of aluminum wire.
With 2.88 meters of copper wire, you can make 12 bracelets because each bracelet needs 0.24 meters of copper wire.
With 5.85 meters of aluminum wire, you can make 9 necklaces because each necklace needs 0.65 meters of aluminum wire.
So you can make 12 bracelets and 9 necklaces.
Therefore you can make more bracelets than necklaces.
what is the vale of the expression 3devided by 3/4
Answer:
Step-by-step explanation:
0.25
The school that Kyla goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 4 adult tickets and 10 student tickets for a total of $106. The school took in $99 on the second day by selling 4 adult tickets and 9 student tickets. Find the price of an adult ticket. a. $6 b. $9 $7 d $8
The price of the adult ticket is $9
How to determine the price of adult tickets?
Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Set up equations to represent the problem.
Let the A and S represent the prices of adult and student ticket respectively. So we can write:
4A + 10S = 106 --- (1)
4A + 9S = 99 --- (2)
Subtracting (2) from (1) will give:
S = 7
Put S = 7 into (1):
4A + 10S = 106
4A + 10(7) = 106
4A + 70 = 106
4A = 106 - 70
4A = 36
A = 36/4
A = 9
Thus, the price of the adult ticket is $9
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What type of transformation can be defined as moving a figure to a new location with no change to the size or shape of the figure?
Translation type of transformation can be defined as moving a figure to a new location with no change to the size or shape of the figure.
Now, According to the question:
Type of Transformation:
There are four types of transformation in geometry, namely translation, reflection, rotation, and dilation. In translation, it slides the figure in any direction while in reflection, it flips the figure over a point or a line. Also, in rotation the figure turns, while in dilation the figure is either enlarged or reduced.
The type of transformation can be defined as moving a figure to a new location, without any change in the figure's size or shape being called translation. In translation, the figure merely slides or moves in the same direction and distance.
Therefore, the answer is Translation.
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This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form? Graph shows upward parabola plotted on a coordinate plane. The parabola has vertex at (2, minus 8) with the left slope at (0, 0) and the right slope at (4, 0). f(x) = x(x − ) f(x) = (x − )2 +
The quadratic equation written in the vertex form is:
f(x) = 2*(x - 2)^2 - 8
How to find the equation of the parabola?We know that for any parabola whose vertex is (h, k) and the leading coefficient is a, can be written in the vertex-form as:
f(x) = a*(x - h)^2 + k
In this particular case, we know that the vertex of the parabola is the point (2, -8), replacing that in the quadratic equation above we will get:
f(x) = a*(x - 2)^2 - 8
Now we also know that our parabola passes through the point (0, 0), then if we replace these values in the equation we will get:
f(0) = 0 = a*(0 - 2)^2 - 8
0 = a*4 - 8
8 = a*4
8/4 = a
2 = a
Then the quadratic equation in the vertex form is:
f(x) = 2*(x - 2)^2 - 8
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Gas mileage is the number of miles you can drive on a a gallon of gasoline. A test of a new car results in 460 miles on 20 gallons of gas. How far could you drive on 50 gallons of gas? What is the car's gas mileage?
Answer:
1,400
Step-by-step explanation:
y=mx+b
plug in 460 for b
y=mx+460
plug 20 for m
y=20x+460
and when graphed on a graph you would see the answer
I really need help . 28.25 x 9.60
Answer:
271.2
Step-by-step explanation:
Write it down and remove the decimals and do long multiplication. After that, count the decimal points and add them back ro the answer
Answer:
271.2
Step-by-step explanation:
move the decimal point 2 places to the right in the two numbers and multiple
[tex]2825 \times 960 = 2712000 [/tex]
and then move you decimal point 4 places to the left so your finally answer should be 271.2
Find the value of r so that the line through (r,5) and (6,r) has a slope of 5/8
PLEASE HELP ASAP!!
The linear equation for a line made of points (r,5) and (6,r) has slope = 5/8 so r=5.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
As slope (m)=(y2-y1)/(x2-x1)
and m=5/8, (x1,y1) and (x2,y2) are (r,5) and (6,r)
Therefore, 5/8=(r-5)/(6-r) --> 5(6-r)=8(r-5)--->13r=70-->r=5
Hence,
r=5
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The length of a rectangle is 4yd longer than its width. If the perimeter of the rectangle is 40yd , find its area.
The area of rectangle is found to be 117 sq. yd.
Define the term perimeter of the rectangle?If you simply know the width and height, you can easily search all four sides, since two of them are equal to each of the height as well as the width. Add the results after dividing the height and breadth by two.Let the length of rectangle be L:
The, the width is W + 4 = L
Perimeter = 2(length + width)
P = 2(L + B)
P = 2(W + 4 + W)
P = 2(2W + 4)
40 = 4W + 4
4W =36
W = 9
The, L = 9 + 4 = 13 yd.
Area = length * width
Area = 9*13
Area = 117
Thus, the area of rectangle is found to be 117 sq. yd.
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Answer:
Step-by-step explanation:
What is perimeter of a Rectangle:The perimeter of a rectangle is the total circumference of the rectangle.
Perimeter=2(Length + breadth)
Perimeter=40yd
Length=x+4 and breadth=x
40=2(x+x+4);
40=4x+8;
4x=32 and x=8yd
So, length=12yd and breadth=8yd.
Area = length*breadth
So Area = 12*8= 96ydsq
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I need helppp quickkkk
The triangles QRS and TUV are similar. They are similar as ΔTUV = 3ΔQRS.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
There are two similar looking triangles, ΔQRS and ΔTUV.
In ΔQRS, the measure of line segment QR = 9 units
In ΔQRS, the measure of line segment RS = 10 units
In ΔQRS, the measure of line segment QS = 11 units
In ΔTUV, the measure of line segment TU = 27 units
In ΔTUV, the measure of line segment UV = 30 units
In ΔTUV, the measure of line segment TV = 33 units
The pattern here can be seen that -
For the line segment TU -
3 (QR) = TU
3 (9) = 27
Similarly, for the line segment UV -
3 (RS) = UV
3 (10) = 30
Similarly, for the line segment TV -
3 (QS) = TV
3 (11) = 33
Therefore, the triangle TUV is three times scaled version of triangle QRS.
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Identify the initial amount a and the rate of decay r (as a percent) of the exponential function f (t)=475(0.5)^t . Evaluate the function when t=3 . Round the answer to the nearest tenth
When t = 3, the exponential function has a value of 59.375.
What is exponential function?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise indicated, the word refers to a positive-valued function of a real variable, however it can be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras. A mathematical function of the following type is an exponential function: f (x) = an x, where x is a variable and an is a constant known as the function's basis. The transcendental number e, which is about 2.71828, is the most often encountered exponential-function base.
Here,
Given the exponential function h (t) = 475(0.5)^t
When t = 3
h(3) = 475(0.5)^3
h(3) =59.375
h(3) = 59.375
The exponential function when the value of t is 3 is 59.375.
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Plez I need help with this math question
when graphing inequalities, we use an open point when the sign is greater or less than when the sign is ,and a closed point when the sign is greater or less than or equal to
Graph following inequalities.
1) x≥3
2) x<-2
3) x< 7
4) x ≤ -4
explanation
To find the equation of a linear function from its graph:
Find the slope by finding the rise and run.
Find the y-intercept (the point where the line crosses the y-axis)
Substitute the value into the function f(x)= mx+b .
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PERSEVERE ABCD is a parallelogram with side lengths as indicated in the given figure. The perimeter of ABCD is 22. Find AB.
The value of side AB is 6 units for parallelogram ABCD with perimeter is 22 units.
What is an equation?An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic
Parallelogram is a quadrilateral (four angles and sides) in which opposite sides are equal and parallel.
From the diagram:
AB = DC (opposite sides are equal)
2y + 1 = 4 - 4w
2y + 4w = 3 (1)
AD = BC (opposite sides are equal)
3x - 2 = x - w + 1
2x + w = 3 (2)
The perimeter of ABCD is 22:
2(AB + AD) = Perimeter
2(2y + 1 + 3 - 4w) = 22
2(2y - 4w + 4) = 22
4y - 8w + 8 = 22
4y - 8w = 14 (3)
From the three equations:
w = -0.5, x = 1.75, y = 2.5
AB = 2y + 1 = 2(2.5) + 1 = 6 units
The value of side AB is 6 units
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Liam and hi children went into a retaurant where they ell drink for two dollar each in taco for $3. 50 each. Liam i $30 to pend in ma by at leat nine drink and taco all together. If Liam decided to buy five taco, determine the maximum number of drink that he could buy
The maximum number of drinks Liam can buy is 4 without over exceeding his price.
Unitary method:
The unit method is a method of obtaining a single-unit value from a multiple-unit value and obtaining a multiple-unit value from a single-unit value. This is the method used for most calculations in mathematics. This method is useful when solving problems involving proportions and proportions, algebra, geometry, and more.
The unit method allows us to find missing values. For example, if a pack of juice costs $5. Then you can easily see that the cost is 5 packages, or $25.
According to the Question:
If Liam has $30 to spend and he must buy at least 9 drinks and tacos altogether, it means that,
$3.50 for 5 tacos
⇒ 3.50 x 5 = $17.50
Now,
9 - 5 tacos = 4 drinks
Cost of 4 drinks x $2 = $8
The total price :
$17.50 + $8 = $25.50 out of $30 price limit
Thus, the number of drinks that she could buy is 4.
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i need help who knows rhis
Give a algebra equation to represent this pattern
The equation m = 4w + 3 shows the number of days in January.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A pattern shown in the image.
Let m is the number of days in a month.
And w represents the number of days in the weeks.
So, algebraic equation,
m = 4w + 3.
Therefore, the equation is m = 4w + 3.
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The ratio of in-states to out-states visitors at the zoo is approximately 7 to 3. If 2000 people visited the zoo, about how many people were from out the state?
The number of people visited the zoo from the state is 200
How to determine the number of people?Number deals with quantity of people that came to the zoo from the state over the period. These people must be from the state.
The given parameters that will help us to solve the question are:
The ratio is approximately 7 to 3.
The number of people = 2000
The sum of the ratios is equal to 7+3 = 10
This is to say that 10% of the people visited the zoo
10/100*2000/1
Therefore about 200 people visited the zoo
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Find the measures of x and y.
X=
Y=
Answer:
x = 92
y = 92
Step-by-step explanation:
164 + 102 + 90 + x + x = 540
2x + 356 = 540
2x = 184
x = 92