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Answer the following:
20 points
The area of a rectangular garden is 168 ft2. The length of the garden is
2 ft greater than the width of the garden. This situation can be
represented by the equation w2 + 2w - 168 = 0.
What is the width of the garden in feet?

The values of h and k would be =2 and 2 respectively.

The value of x would be = 5.2

A horizontal distance is the distance that is be covered by a moving object through a horizontal pathway.

y = h + kx - 0.5x^2

When X = 2 and y = 5 is the centre of the hoop.

To calculate for y;

X max = -k/2× (-0.5)

X max = k = 2

y max = 5

Substitute the given variables into the equation and make h the subject of formula.

5 = (h + 2×2) - (0.5x^2)

5= (h + 4)- 1

h +4 = 5+1

h +4 = 6

h = 6-4

h = 2

Also from the graph, the value for x as the ball hits the ground would be = 5.2

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A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.

For a triangle the circumcentre is a point equidistant from each of the three vertices. Every non-degenerate triangle has such a point. This result can be generalised to cyclic polygons: the circumcentre is equidistant from each of the vertices. Likewise, the incentre of a triangle or any other tangential polygon is equidistant from the points of tangency of the polygon's sides with the circle.

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Answer:

If you want to learn something without me directly giving you the answer, then here's the explanation

Step-by-step explanation:

You are given two points with unclear coordinates. Because they are equal to each other, you know that they are both the exact same point, meaning that the x and y coordinate of each point is equal to eachother. Therefore,

[tex]3x/4=3\\y/6=2[/tex]

If you understand basic algebra, the rest should be easy.

Answer:

x = 1

Step-by-step explanation:

f(x) = 5 - 6x         g(x) = 3x -4

5 -6x = 3x - 4

5 = 9x - 4

9 = 9x

x = 1

(50/34.2)^1.5=10-t this equation is proved.

An equation is a formula that is express the equality of two equation.

(50/34.2)^1.5=10-t

Covert decimal to integers

(500/342)^1.5 =10-t

Rearrange the variables to left side of the equation

t=10-(500/342)^1.5

Covert decimal to fraction

t=10(500/342)15/10

Simplify using a^n/m

Simplify using exponent rule with the same exponent(ab)^n=a^n.b^n

t=10-√250^3/171^3

Factor and rewrite the redicant in expotential form

T=10-√250^2×250/√171^2×171

Simplify the radical expression

t=10-1250√10×√19/513×19

Multiply number with radicals

t=1250√190/9747

Rewrite fraction using the latest common denominator

t=97470-1250√190/9747

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Answer:

There is no way to answer this question without more information about the amounts of orange juice and lemon-lime soda in Martha's fruit punch the last time.

Step-by-step explanation:

Answer:

3/4 = 15/20

3/4 = 8/10

Step-by-step explanation:

Answer:

To solve this problem, we need to first find the length of each side of the sandbox. Since the sandbox is an octagon with 8 equal sides, we know that the perimeter of the sandbox is 8 times the length of each side. Thus, we can use the formula for perimeter to find the length of each side:

Perimeter = 8 * Side Length

Substituting the given values into this formula, we get:

18.8 feet = 8 * Side Length

Dividing both sides of the equation by 8, we get:

Side Length = 2.35 feet

Therefore, each side of the sandbox has a length of 2.35 feet.

________________________________________________________

To find the amount of money that each person pays to fill the sandbox, we need to divide the total cost by the number of people involved. In this case, there are 4 people in total, so each person pays 1/4 of the total cost. Thus, the cost per person is $59.48 / 4 = $14.87.

Answer:

80

Step-by-step explanation:

The total answers count 30 - it's 100%, so we to get a 1% value, divide 30 by 100 to get 0.30. Next, calculate the percentage of 24: divide 24 by 1% value (0.30), and you get 80.00% - it's your percentage grade

The truck is propelled forward by force D of 2.769 * 10⁴ N and acceleration of 0.78 m/s2.

The definition of force is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.

Given, Mass of the truck = 5000 kg

Mass of car = 1600 kg

Force applied = 25000 N

As we know Force (F)  =m.a

Where m = mass of the body

a = acceleration of the body

25000 = (5000  + 1600) * a

a = 25000/ 6600 = 3.7878.

a = 3.79 m/s²

According to diagram D = ma

m = 27000 + 8500 = 35500 kg

a = 0.78 m/s²

so D = 35500 * 0.78 = 27690N

Therefore, Force D that moves the truck forward is 2.769 * 10⁴ N, and acceleration is  0.78 m/s².

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We can create charts in microsoft Excel by using new tab on the view menu.

It is a software programe created by Microsoft that uses spreadsheet to display numbers and data with formulas.It enables the users to format,organize and calculate data easily in a spreadsheet.

Open Microsoft Excel and select new tab.

Enter the data you want to create a chart.

Click the insert tab.

Click the recommended charts.(chart type)

Create chart.(once you select the chart preview and description appear at the right).

Click OK.(The recommended chart inserted into worksheet).

Hence we can create Excel chart into worksheet or microsoft word.

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The net salary of Charles in the month of January is 8100.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, 'x' be the total salary of Charles in January.

Charles spent 1/4 of his net salary on school fees so the reaming amount is,

= {x - (1/4)x}

= (3/4)x.

(1/3)rd of the remainder on electricity and water bills which is,

= (1/3)×(3/4)x.

= (3/12)x.

= (1/4)x.

Now, The remaining amount is {(3/4)x - (1/4)x}.

= (2/4)x.

He then spent 1/9 of what was left on transport which is,

= (2/4)x×(1/9).

= (1/18)x.

Now, The remaining amount is {(2/4)x - (1/18)x}.

= [(18 - 2)/36]x.

= (16/36)x.

= (4/9)x.

So, as he left with 3600 it is equal to (4/9)x.

Therefore,

(4/9)x = 3600.

4x = 32400.

x = 8100.

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The value of b when the system has an infinite number of solutions is 12.

The Given equations are

y=6x-b ---(1)

6=3x+3y ----(2)

If the system has an infinite number of solutions, then equation 1 is equal to equation 2

If a pair of linear equations have unique or infinite solutions, then the system of equation is said to be a consistent pair of linear equations

Isolate variable y in equation 2

2=x+y

Multiply by 6 on both sides

y=6x-12 -----(3)

To find the value of b, equate equation 1 and equation 3

6x-b=6x-12

b=12

Thus the value of b=12.

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The probability that the offices will be assigned to 2 of the men and 1 of the women will be 3/5

Lets find all the combinations of 2 men and 1 woman that can be chosen

(men, men, women) m m w

3/5 x 2/4 x2/3

(men, women, men) m w m

3/5 x 2/4 x 2/3

(women, men, men) w m m

2/5 x 3/4 x2/3

then just add those probabilities together:

= 3/5x2/4x2/3+3/5x2/4x2/3+2/5x3/4x2/3

= 12+12+12/60

this simplifies to 3/5

Simply put, probability measures how probable something is to occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics explains the examination of events that can occur subject to probability.

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Answer:

30 seats

Step-by-step explanation:

For every row, there are 2 seats on the left and 3 seats on the right.

If there are 45 seats total on the right side, then there must be 45/3 = 15 rows. Therefore, there are 15*2= 30 seats on the left.

Answer: [-11, 11)

Step-by-step explanation:

Because the point is closed and shaded in at x = -11, we know that the value is included in the domain. So, in interval notation, we will use a "[".

Because the point is empty and not shaded in at x = 11, we know that values approaching x = 11 are included, but not x = 11 itself. So, in interval notation, we will use a ")".

The third binomial formula is given by ( a + b )( a - b) = a² - b².

Binomial theorem in the standard form is given by :

( a + b )ⁿ = ⁿC₀aⁿb⁰ +  ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+  ⁿCₙa⁰bⁿ

Binomial formula starts from n = 2

First binomial formula of the binomial theorem is given by :

( a ± b )² = a ² ± 2ab + b²

Second binomial formula is given by:

( a ± b )³ = a³ ± 3a²b + 3ab² ± b³

Third binomial formula is given by :

( a + b) ( a - b) = a² - b²

Therefore, the third binomial formula is equal to ( a + b )( a - b) = a² - b².

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We can represent the number of apples purchased by Adrian as the variable "a" and the number of mangos purchased by Adrian as the variable "m". The total cost of apples can be represented as $2.25 * a, and the total cost of mangos can be represented as $2 * m. The inequality that represents the possible values for the number of apples and mangos that Adrian can purchase is $2.25 * a + 2 * m <= 25.

Note that in the word problem above, the number of Pawns that you have is 14 pawns.

To solve this problem, you can use the equation:

Number of pawns = (Number of pawns in the largest possible square) + (Number of pawns needed to fill in the square) + 1

Substituting the given information, we get:

Number of pawns = (7 pawns) + (6 pawns) + 1 pawn

Simplifying, we get:

Number of pawns = 14 pawns

Therefore, you have 14 pawns.

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The numeric value with no sign is positive so 1 is positive.

Can numeric value be negative?

There are whole numbers and fractional numbers, for instance, in the world of numerical data. There are both positive and negative numbers.

What is positive and negative in numbers?

Positive numbers are those that are greater than zero. It is possible to write positive numbers with or without a sign in front of them. A negative number is one that is less than zero. The minus symbol (-) is always written in front of negative values.

As 1 have no sign with it so it means 1 is positive. If any numeric value is negative it must have negative sign with it else numeric value is positive.

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Answer:

B

Step-by-step explanation:

The [tex]x[/tex] intercepts are where [tex]f(x)=0[/tex].

[tex]2x^2+7x-9=0 \\ \\ (2x+9)(x-1)=0 \\ \\ x=-\frac{9}{2}, 1[/tex]

The [tex]y[/tex] intercept is where [tex]x=0[/tex].

[tex]f(0)=2(0)^2+7(0)-9=-9[/tex]

Answer:

Step-by-step explanation:

if you move over from 2. 3 full lines you get to 2.6. draw the x in between 2.6 and 2.8.

each line is 0.2 so 3.5 lines is 2.7

The equation of the function in vertex form is f(x) = 1/4(x-1)²+2.

What is vertex form?

A different way to express the equation of a parabola is in its vertex form. A quadratic equation is typically represented as an x 2 + b x + c, and when graphed, it will look like a parabola.

Here, we have

Given

The vertex (1, 2) and the point (-3, 6).

we have to find the equation of the function in vertex form.

We know that

The vertex form of the equation is :

f(x) = a (x-h)² +k

Now, we put the value of x, h, and k and we get

6 = a(-3-1)² + 2

6 = 16a + 2

4 = 16a

a = 1/4

Now, we put the value of a in the vertex form equation and we get

f(x) = 1/4 (x-1)²+2.

Hence, the equation of the function in vertex form is f(x) = 1/4(x-1)²+2.

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Answer:

Step-by-step explanation:

No solution.

y=x

-1(y=x)

-1y=-1x

+1y=1x+2

-1y and 1y cancel each other out. -1x and 1x cancel each other out.

Leaving +2..so it's a no solution. Solved using elimination it's easier..

Answer:

A reasonable range for the function y=0.1x+12 would be all real numbers greater than or equal to 12. This is because the minimum monthly phone bill that Ben could have would be $12 (if he does not use any minutes), and the monthly bill can increase to any higher value depending on the number of minutes he talks. In set builder notation, this range would be written as {y | y >= 12}.

Step-by-step explanation:

The size of  image if magnification m  is equal to 1 is calculated to be 2m.

Given

Height of object = 1 m

Height of image = h'

Magnification = m = 2

The formula to calculate magnification is

m = h'/h

2 = h'/1

h' = 2 m

Therefore , the height of the image formed will be 2m.

Magnification is a concept of physics which refers to the process of enlarging an object ,  the object itself does not become physically larger, but just appears larger as projected on a screen.

The magnification can take two forms, microscopic magnification and telescopic magnification. When we insert a small thing, it appears larger due to microscopic magnification.

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The relationship between area and sides of rectangle is Area = product of length and breadth.

The geometrical shape which has four right angles and four straight sides. The identical sides are parallel to each other.

the sides of rectangle which are situated along the horizontal axis and parallel to each other are called length. The other parallel sides which situated along the vertical axis are called breadth. The area of rectangle = length× breadth

hence, area of rectangle is the product of two unequal side length.

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The correct option is C. It is safe to apply the central limit theorem, even if the sample size for each sample is 15, if the sample population is normally distributed.

The central limit theorem states that, if you take repeated samples of a population and calculate the mean of each sample, the distribution of the means of those samples will tend to be normally distributed, provided that the sample size is large enough. This means that, even if the original population is not normally distributed, the distribution of the means of the samples will tend towards a normal distribution as the sample size increases.

However, if the original population is already normally distributed, then you can apply the central limit theorem with a smaller sample size and still expect the distribution of the means of the samples to be normally distributed. Therefore, in order for it to be safe to apply the central limit theorem with a sample size of 15, the sample population must be normally distributed.

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The function is in the form of linear equation in two variables where y is the cost and x are number of games played.

Linear equation in two variables is referred to a function that can be expressed in the form y = ax + b where a, b are constant values and x and y are variables. x is the independent variable and y is the dependent variable. Here we have the function y = 3.5x + 4 and the independent variable x is the number of games played and dependent variable y is the cost of the games that are played. Now in the equation the additional fee is represented by the constant value 3.5 and the fee for shoe is represented by the number 4 and is not dependent as the shoe rent fee is constant and not depends on number of games played.

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Answer: 12-pound bag of cat food

Step-by-step explanation:

12 pounds bag of cat food = $18

15 pounds bag of cat food = $24

Let's find the cost per pound of the 12-pound bag first

Take 18 divided by 12 = $1.50 per pound

Now find the cost per pound of the 15-pound bag

Take 24 divided by 15 = $1.60 per pound

So, buying a 12-pound bag of cat food is better because it is cheaper per pound.