Match each of the equations with their corresponding graph.
a) y= x^3 +2x^2-1
b) 2x^2-x-3
c) 1/x +1
d) 2-3x^2 -x^3

Answer: To solve this problem, we can use algebra. Let x be the smaller page number. Then, the larger page number is x + 1, since the pages are facing each other. We know that the sum of these two numbers is 553, so we can set up the equation:

x + (x+1) = 553

Next, we will solve for x by combining like terms:

2x + 1 = 553

Now we will subtract 1 from both sides of the equation:

2x = 552

Finally, we will divide both sides by 2:

x = 276

So the smaller page number is 276.

Step-by-step explanation:

Answer:

-----------------------------

The numbers that are at least a distance of 3 away from -7 are the numbers 3 units or more away from -7 either side on the number line :

or

This is same as:

Answer:

Have a good day!:)

Step-by-step explanation:

When two lines intersect at a point, they form two pairs of angles that do not share a side. These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.

The correct brackets for the equations are added as follows:

a) (42 - 8) x 3 - 22 = 80

b) 75+ (5 x 4) -70 = 25

c) (160 ÷ 4) x (3 + 2) = 200

d) 120 ÷ (2 x 3) + 5 = 25.

Equations are mathematical statements that equate or show that two or more mathematical expressions are equivalent or equal.

Equations use the equation symbol (=) to show the equality of the algebraic expressions.

Using parentheses in equations enable the use of the distributive property to solve the equation.

Thus, the correct parentheses have been added to the equations to prove them correct when solved.

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Answer:

$1,100

Step-by-step explanation:

The cost of the summer camp for the youngest child is around $500, when rounded to the nearest hundred.

The cost of the summer camp for the middle child is around $200.

The cost of the summer camp for the oldest is around $400.

500+200+400=1100

Answer:

C. 43

A. 40

C. 37

E. Other

A rectangle with sides of length 84 and 45 has the same perimeter asa hexagon. If the sides of the hexagon all have the same length then what is the length of a side of the hexagon

Ans:

The perimeter of a rectangle is given by 2length + 2width. In this case, the perimeter of the rectangle is 284 + 245 = 258.

Since the perimeter of the hexagon is the same as the rectangle, and the sides of the hexagon are all the same length, we can find the length of a side of the hexagon by dividing the perimeter by the number of sides.

A hexagon has 6 sides, so the length of a side of the hexagon is 258/6 = 43.

So the answer is (C) 43.

A square has an area of 25. Two opposite side of the square each have their length tripled what is the perimeter of the new figure.

Ans:

The perimeter of the new figure would be 40. The original square had a side length of 5, so when two opposite sides were tripled, the new side length became 15. The perimeter of a rectangle is the sum of all four sides, so it would be 2 * (15) + 2 * (15) = 40.

(A).40

A rectangle measures 6 centimeters by 25 centimeters the probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 is p/q are relatively prime positive whole numbers what is the sum of p and q.

Ans:

The probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 can be found by comparing the areas of the two triangular regions formed by the point and the two sides. The area of the triangular region formed by the point and the side of length 25 is (1/2) * 6 * (distance from point to side of length 25) while the area of the triangular region formed by the point and the side of length 6 is (1/2) * 25 * (distance from point to side of length 6).

For the point to be closer to the side of length 25, the area of the triangular region formed by the point and the side of length 25 must be greater than the area of the triangular region formed by the point and the side of length 6. This means (1/2) * 6 * (distance from point to side of length 25) > (1/2) * 25 * (distance from point to side of length 6). Therefore, the probability that the point is closer to the side of length 25 is (1/2) * (6/25) = 3/25. The sum of p and q is 3 + 25 = 28.

Therefore, the answer is (C) 37.

The three values of x that are solutions to X^3 + mx = 37x^2 +n are positive whole numbers that form a geometric sequence what is the sum of the possible values of the common ration of the geometric sequence.

Ans:

It is not possible to determine the sum of the possible values of the common ratio of the geometric sequence without more information about the values of m and n in the equation X^3 + mx = 37x^2 +n. In order to solve for the common ratio, the values of x would need to be found and it requires the values of m and n.

The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.

A linear equation is an algebraic equation where the highest exponent of the variable is one. There are linear equations with one, two, or three variables, but not all linear systems have three equations. Typically, a system of linear equations has a single solution, but occasionally there is no solution or an infinite number of solutions.

A relationship in which the value of one variable, say "x," depends on the value of the other variable, say "y," is described by a two variables linear equation. A linear equation's graph will be a straight line if there are only two variables.

Given that cost for 5 tickets is $174.45

Let x be the cost of each ticket and y be the processing fee

5x + y = 174.45

And for the cost for 8 tickets is $271.95

8x + y = 271.95

Subtract the terms

 8x + y = 271.95

- 5x + y = 174.45

 3x + 0 = 97.5

If 3x = 97.5

Then,

x = 97.5/3

x = 32.5

Each ticket costs $32.5 then processing fees

5(32.5) + y = 174.45

y = 174.45 - 162.5

y = 11.95

8(32.5) + y = 271.95

y = 271.95 - 260

y = 11.95

Thus, The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.

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Answer:

The simplest algorithm (a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.) to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1. For example, by prime factorizing the number 30 we get, 30/2 = 15, 15/3 = 5, and 5/5 = 1. Since we received the remainder, it cannot be further factorized.

Step-by-step explanation:

pls tell me if wrong have a good day/night<3

There are two typical approaches to prime factorization. The Prime Factor Tree and the Upside-Down Division are the first and second, respectively.

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Answer: So, after 3 years and 5 months, the total amount of simple interest earned on an investment of $2500 at a 6% interest rate would be $525.

Step-by-step explanation:

To calculate the simple interest on an investment of $2500 at a 6% interest rate for 3 years and 5 months, you would use the formula:

Simple Interest = (Principal x Interest Rate x Time in Years)

In this case, the time in years would be 3.5 (3 years and 5 months)

Simple Interest = (2500 x 0.06 x 3.5) = $525

So, after 3 years and 5 months, the total amount of simple interest earned on an investment of $2500 at a 6% interest rate would be $525.

The constant of proportionality will be $0.79

It is defined as the rate or the ratio of two proportional values which are known to be at the same value.

The two variable values are said to have a proportional association if or when either of their ratio or their product are known to bring about a constant.

Hence, the proportionality constant's value is known by the proportion between the two said quantities.

Jason bought 4 pounds of bananas for $3.16.

k = $3.16/4

k = $0.79

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Answer:

There are few possible ways to find the complex zeros

You can find the complex zeros by using quadratic formula

[tex]x^2-6x+13=0[/tex]

[tex]=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:13}}{2\cdot \:1}[/tex]

[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \:4i}{2\cdot \:1}[/tex]

[tex]x_1=\frac{-\left(-6\right)+4i}{2\cdot \:1},\:x_2=\frac{-\left(-6\right)-4i}{2\cdot \:1}[/tex]

[tex]x=3+2i,\:x=3-2i[/tex]

Answer: The scale of the billboard is 1 foot = 8 inches, so to find the actual height of the woman, we need to multiply the height on the billboard by 8.

8 3/8 feet x 8 inches/foot = 66 inches (8 x 8) + (3 x 8) = 66

So the woman's actual height is 66 inches.

Step-by-step explanation:

The median margin for victory will be 1.89.

The median of the data is the value of the middle observation discovered after the data are organized in ascending order. The median is useful in situations where it is difficult to express anything while taking into account all of the data.

One of the easy to calculate statistical summary metrics is the median. Since it bases its value on the data that is in the middle of a sequence, the median is often referred to as the place average.

Given Data:-

1.89,2.32,0.08,4.74,0.30

Mean margin of victory= 1.866

Median margin of victory= 1.89

So the median margin for victory will be 1.89.

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Complete question -

Answer:

  x = 18.3

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle given the side opposite the 41° angle is 12 units.

The sine relation is ...

  Sin = Opposite/Hypotenuse

This can be rearranged to ...

  Hypotenuse = Opposite/Sin

  x = 12/sin(41°) ≈ 18.3 . . . . units

The value of x is about 18.3.

__

Additional comment

This is the SOH relation from the mnemonic SOH CAH TOA, which is intended to remind you of the relation between trig functions and sides of a right triangle. The others tell you ...

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

In the attached, note the calculator mode is set to DEG (degrees) so the argument of the Sin( ) function will be interpreted properly.

Part (a)

Reason:

There are 7 items inside set A. The notation n(A) counts the number of elements in a set.

==========================================

Part (b)

It's not clear what your teacher is asking. It seems this part is incomplete. Please revise.

Answer:

y - 9

Step-by-step explanation:

(y-9)²/4÷(4y-36)/16

is a fraction divided by a fraction.

When you have one or two fractions with a division, use Keep-Change-Flip.

Keep the first term:

(y-9)²/4

then Change the ÷ to a times.

(Y-9)²/4•

then Flip the second term.

(y-9)²/4 • 16/(4y-36)

You can factor the term (y-9)² into

(y-9)(y-9).

The other term (4y-36) can also be factored into

4(y-9).

see image.

The 4's and the y-9 terms can be "cancelled".

see image. The only term left is y-9.

Answer:

let's see jssjsjnsjsjsjsjsjsjsjsjsjs

The x-intercepts and the y-intercept of the cubic function f(x) = x³ - 9·x² + 20·x - 12 for which (x - 6) is a factor are;

A function is a rule that uniquely maps each value from the set of input variables to exactly one value in the set of the output variables.

The specified cubic function is; f(x) = x³ - 9·x² + 20·x - 12

A factor of f(x) = x - 6

The x-intercepts are the points on the graph of the function, where the value of the function, f(x) = 0, which are found as follows;

At the x-intercept, f(x) = x³ - 9·x² + 20·x - 12 = 0

x³ - 9·x² + 20·x - 12

Dividing the cubic function by the factor (x - 6), we get;

          x² - 3·x + 2

(x - 6) | x³ - 9·x² + 20·x - 12

   [tex]{}[/tex]       x³ - 6·x²

[tex]{}[/tex]                 -3·x²

[tex]{}[/tex]                 -3·x² + 18·x

                    [tex]{}[/tex]       2·x  

[tex]{}[/tex]                            2·x - 12

[tex]{}[/tex]                                      0

The other factor of the cubic function is; x² - 3·x + 2

x² - 3·x + 2 = (x -2)·(x - 1)

Therefore;

f(x) = x³ - 9·x² + 20·x - 12 = (x - 6)·(x - 2)·(x - 1)

From which at the x-intercepts, we get;

f(x) = (x - 6)·(x - 2)·(x - 1) = 0

x = 6, x = 2, and x = 1

The y-intercept are the points the x-values is zero, therefore, at the y-intercepts, we get;

f(0) = 0³ - 9·0² + 20·0 - 12 = -12

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The angles are 36,118,62

If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.

Given: m and n are parallel lines with 3 transversals

We can observe that a=36 (vertically opposite angles)

and b =180-(36+26)     ∵  They all lie on a line .

          =118

and c= 180-118               ∵They all lie on a line.

         =62

Hence, The angles are 36,118,62

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Check the picture below.

An equation of a given parabola that is translated by 4 units left, 5 units up and is compressed by a factor of one-quarter is y=  1/4 ((x-3)²-6).

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Translation rules:

When the shape is moved towards the left by k units, then replace x with x - k.

When the shape is moved up by k units, then replace y with y + k.

3) Given that, the equation of the parabola is y=(x-3)²-7

The equation is translated by 4 units left, 5 units up and is compressed by a factor of one-quarter.

Here, 1/4 ((x-3)²-7-4+5)

y=  1/4 ((x-3)²-6)

4) The given equation is h=-4.9t²+180t+2

a) the maximum height of the rocket

Use the formula

x =-b/2a to find the maximum and minimum.

(18.36734693,1655.06122448)

b) the time required for the rocket to reach its maximum height

Find where the first derivative is equal to 0 to find the local maxima and minima.

(18.36734693, 1655.06122448) is a local maxima

c) the time required for the rocket to reach the ground

Solve the equation for t by finding a, b, and c of the quadratic then applying the quadratic formula.

t=900+3.16227766√(81098−49h)/49

t=900-3.16227766√(81098-49h)/49

Therefore, an equation of a given parabola that is translated by 4 units left, 5 units up and is compressed by a factor of one-quarter is y=  1/4 ((x-3)²-6).

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Answer:

The zeroes of the equation are -2 and -6.

Step-by-step explanation:

(x + 2)(x + 6) = 0

=> x = -2, -6

Hope it helps.

Answer:

Step-by-step explanation:

Assuming that there are no sidewalks or other obstructions, the estimated size of the crowd along a 3-mile section of the parade route would be approximately 3,780,400 people. This calculation is based on the assumption that people will be standing shoulder to shoulder and that each person will take up an area of 5 feet by 11 feet. This would mean that for each mile of the parade route, there would be 1,260,800 people standing (12 people x 10 feet x 5280 feet). Multiplying this by 3 gives us 3,780,400 people.

Answer:

12 people fitting in an area of 5*5 = 25 ft². Area of the street: 3 miles = 3*5280 ft = 15840 ft 25 feet on both sides. So, the total area in which the crowd is sparsed is: A = 15840*25*2= 792000 ft². Now we apply the ratio: People over area. Applying cross multiplication: 25x = 12*792000 x = (12*792000)/25 x = 380160

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solution:- this is question of subtraction , so 18712-9412=9300(Answer)

Answer:

Step-by-step explanation:

This problem can be represented by the equation: x + (x/2 - 1) + (x/4 - 1) + (x/8 - 1) + ... + (x/128 - 1) + 1 = x, where x is the total number of apples gathered.

This equation represents the process described in the problem, where the man gives half of his remaining apples (x/2, x/4, x/8, etc.) to each guard, minus 1 apple each time, until he is left with 1 apple.

Using the mathematical operations of addition and subtraction, the weight of the bag of grapefruit is 3¹¹/₁₆.

The basic mathematical operations we have studied so far include addition, subtraction, division, and multiplication.

In addition operation, two or more addends are added to obtain a result known as the sum or total.

Using subtraction operation, the minuend, subtrahend, and difference are the major parts, including the subtraction operator (-).

There are two ways of solving this problem, we can add the fractional weights of apples and bananas and subtract the sum from the total weight of fruits Lynne bought.

We can also subtract each fractional weight from the total weight of fruits to arrive at the fractional weight of the bag of grapefruit.

The total weight of Lynne's purchases = 7¹/₂ pounds

The weight of apples = 1⁵/₈ pounds

The weight of bananas = 2³/₁₆ pounds

The weight of grapefruit = x

= 7¹/₂ - 1⁵/₈ - 2³/₁₆

= 3¹¹/₁₆

Add fractional weights:

1⁵/₈ + 2³/₁₆ = 3¹³/₁₆

Subtract the sum of the fractional weights from the total weight:

7¹/₂ - 3¹³/₁₆ = 3¹¹/₁₆

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Answer:

11

Step-by-step explanation:

we know this because there are 5 people saying they have 3 and 6 people saying they have between 4-7