In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equation x2 + y2 = 5, and the path of the bean bag can be represented by y = 0.5x2 – 1.5x – 4. To which points could she have tossed her bean bag?
A. (–1, –2) or (–2, 1)
B. (1, –2) or (2, 1)
C. (–1, 2) or (–2, –1)
D. (1, 2) or (2, –1)

The time at which the population of bacteria will be 25,000 is 2:49 pm.

Given that:-

Population of bacteria at 1:00 PM = 5,400

Population of bacteria at 1:20 PM = 9,000

The rate at which a population of bacteria grows is proportional to the size of the population.

We have to find the time at which the population of bacteria will be 25,000.

The rate at which population of bacteria grows = 3600 bacteria/ 20 min = 180 bacteria/min

Let the population of bacteria takes t minutes to become 25,000.

Hence, we can write,

5400 + 180t = 25000

180t = 25000 - 5400

180t = 19600

t = 19600/180

t = 108.889

t = 109 minutes =  1 hour 49 minutes

Hence, the time will be 2:49 pm.

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Answer: student A

If members of a softball team raised $1,186.50 to go to a tournament they rented a bus for $842.50 and budgeted $21.50 per player for Meals. The  number of players the team can bring to the tournament is 16.

Let x represent the number of players

Formulate an equation

$842.50 + $21.50 × x = $1,186.50

Using the formulated equation to determine the number of players

$842.50 + $21.50 × x = $1,186.50

$842.50 + $21.50 x = $1,186.50

Collect like terms

$21.50 x =  $1,186.50 -$842.50

$21.50 x =  $344

Divide both side by $21.50 x

x = $344 / $21.50

x = 16 players

Therefore the team can bring 16 players to the tournament.

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The absolute functions when matched to the respective vertex is as follows;

(-1, -3/7) → f(x) = (1/2)|x + 1| - (3/7)

(5, 2/3) → f(x) = (-3/5)|x - 5| + (2/3)

(0, -4/5) → f(x) = (1/2)|x| - (4/5)

(2/5, 5/3) → f(x) = (-3/2)|x - (2/5)| + (5/3)

We can solve all of them by writing the equations in a general form;

f(x) = a|x + b| + c

This is a function transformation of f(x) = |x|

where:

a = Factor of vertical stretch

b = Horizontal shift (- shifts right, + shifts left)

c = Vertical shift (+ shifts right, - shifts left)

The original function has its vertex in (0, 0)  so the horizontal shift will be the new x coordinate in the new vertex and the vertical shift will be the new y in the new vertex like this:

f(x) = (1/2)|x + 1| - (3/7)

b = 1 horizontal shift of -1

c = -3/7 vertical shift of -3/7

Thus, (-1, -3/7)

f(x) = (-3/5)|x - 5| + (2/3)

b = -5 horizontal shift of 5

c = 2/3 vertical shift of 2/3

Thus, (5, 2/3)

f(x) = (1/2)|x| - (4/5)

b = 0 horizontal shift of 0

c = -4/5 vertical shift of -4/5

Thus, (0, -4/5)

f(x) = (-3/2)|x - (2/5)| + (5/3)

b = -2/5 horizontal shift of 2/5

c = 5/3 vertical shift of 5/3

Thus, (2/5, 5/3)

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Answer:

83/8 , decimal form 10.375, mixed number form 10 3/8

Step-by-step explanation:

Based on the value of the angles in this triangle, the value of x can be found to be 82 degrees

The interior angles of different polygons always add up to a certain number of degrees. For instance, the interior angles of a heptagon add up to 900 degrees.

In triangles, the the interior angles will always add up to 180 degrees. The value of x can then be found by the formula:

180 = 52 + 46 + x

x = 180 - 52 - 46

x = 82 degrees

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The amount of money Lamonte makes is $22.5 per hour

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let e represent the total earnings in dollars if Lamonte works for h hours. Hence:

e = 22.5h

e/h = $22.5 per hour

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a) 1.4 to the nearest tenth of the place

b) 1.1 to the nearest tenth of the place

c)0.3 to the nearest tenth of the place

d) 0.5 to the nearest tenth of the place

e) 0.4 to the nearest tenth of the place

f) 0.6 to the nearest tenth of the place

The full number and the fraction are expressed simultaneously using decimals. By adding a "." (known as a decimal point) in this instance, we will divide the whole number from the fraction. Think about taking an ice cream cone as an illustration. Your purchase of ice cream will cost $2 and 50 cents, the dealer informs you. Currently, you would state that the ice cream cone costs $2.50 if you were to describe this amount in a single number. You may be utilizing decimals unknowingly in a variety of these real-world situations.

a) [tex]1\frac{5}{16} =\frac{22}{16}[/tex]

= 1.375

=1.4 to the nearest tenth of the place

b) [tex]1\frac{1}{8} = \frac{9}{8}[/tex]

=1.125

=1.1 to the nearest tenth of the place

c)[tex]\frac{1}{4}[/tex]

= 0.25

= 0.3 to the nearest tenth of the place

d) [tex]\frac{1}{2}[/tex]

=o.5

=0.5 to the nearest tenth of the place

e) [tex]\frac{3}{8}[/tex]

=0.375

=0.4 to the nearest tenth of the place

f) [tex]\frac{9}{16}[/tex]

=0.5625

= 0.6 to the nearest tenth of the place

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We need to find the mean salary for the employees:

There are

15 employees with a salary of $21,900, 10

10 employees with a salary of $24,800

3 employees with a salary of $31,200

4 employees with a salary of $37,700

1 employee with a salary of $149, 600

33 total of employees:

The mean formula is given by:

Replacing :

Therefore:

The result is rounded to the nearest hundred.

A list of all the three-element subsets of the given set include the following:

In order to determine the three-element subsets from the given set {1, 2, 3, 4, 5}, we would have to calculate the number of ways to choose the three (3) elements by applying a mathematical model referred to as combination.

Mathematically, combination is given by this mathematical equation:

[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]

Where:

Substituting the given parameters into the formula, we have;

Number of ways = ⁵C₃

Number of ways = 5!/(3! × (5 - 3)!)

Number of ways = 5!/(3! × 2!)

Number of ways = [5 × 4 × 3 × 2 × 1]/[3 × 2 × 2 × 1]

Number of ways = 120/12

Number of ways = 10 ways.

Therefore, there are 10 three-element subsets of this set.

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Complete Question:

List all the three-element subsets of the set {1, 2, 3, 4, 5}

Answer:

arithemetic because of the continuos multiplication

Answer:

A. I'm pretty sure would be geometric. and the next numbers would be 729, 2187, 6561

B. is arithmetic and the next numbers would be 46, 55, 64

C.is also arithmetic, and the next numbers would be 32, 36, 40

Using implicit differentiation, the derivatives of the function are given as follows:

For implicit differentiation, we treat the variables as a function of each other, hence we keep applying the chain rule to find the derivatives.

Supposing a three variable function F(x,y,z) = 0, then the implicit derivatives are given as follows:

In standard format, the function is given as follows:

F(x,y,z) = x^4 + y^2 + z^9 - 8xyz.

Hence the partial derivatives are given by:

Then the implicit derivative relative to x is:

[tex]\frac{\partial z}{\partial x} = -\frac{4x^3 - 8yz}{9z^8 - 8xy}[/tex]

The partial derivative relative to y is:

[tex]F_y = 2y - 8xz[/tex]

Then the implicit derivative relative to y is:

[tex]\frac{\partial z}{\partial y} = -\frac{2y - 8xz}{9z^8 - 8xy}[/tex]

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We can define the translation of building from location C to location E by the following rule -

(x, y) → (x - 4 , y + 6)

A translation is a movement of the graph either horizontally (parallel to the x -axis) or vertically (parallel to the y -axis) without changing its orientation.

Given is a Building C translated to Building E.

In order to translate the building from location C to location E, we will first shift the building near the x - axis vertically upwards. For this we will shift the y coordinate by -

- 7 + y[s] = - 1

y[s] = -1 + 7

y[s] = 6

So the y - coordinate of the translated graph will be -

(y + 6)

Now, we will shift the x coordinate -

1 + x[s] = -3

x[s] = -3 - 1

x[s] = -4

So the x - coordinate of the translated graph will be -

(x - 4)

Therefore, we can define the translation by the following rule -

(x, y) → (x - 4 , y + 6)

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The circle and the elipse in this problem are not congruent because they are of different classes of conics, hence their measures are different.

Congruent figures are figures that are exactly the same, having corresponding sides with the same measure.

In this problem, we have two figures that belong to different groups of conics, which are a circle and an elipse.

The circle has one measure, which is it's radius, while the elipse has two measures, the minor axis and the major axis.

It can be seen visually that the elipse has a horizontal major axis and a vertical minor axis, and the major axis is greater than the minor axis. Since these two measures are not equal, the elipse cannot be congruent with any circle, and it is not congruent with circle B given in this problem.

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Answer: True

Step-by-step explanation:

The equation that represents this relationship is h*n = 24.

How do we solve linear equations?
First order equations include all linear equations as a subset. In the coordinate system, lines are defined as having linear equations. A linear equation in one variable is made up of one homogeneous variable of degree one (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.

Given, number of hours needed to paint a house = h
Number of painters needed to paint the house = n
Also, the relation between h and n is inverse, thus:
h*n = k, where k is the proportionality constant.
Therefore, initial equation derived is h*n = k --(i)
Putting h = 6 and n =4 in (i), we can get the value of k as
k = h*n = 6*4 = 24 --(ii)
Comparing (i) and (ii), we get,
h*n = 24, which is the required equation.

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Answer: Choice A) The average temp is 19/7 or 2.7 degrees Celsius

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

Explanation:

Ignore the ˚C and focus on the numbers only

We have this set of values

15, 1, -4, 3, -10, -7, 21

Add them up to get

15+1+(-4)+3+(-10)+(-7)+21 = 19

Then divide that sum over the total number of items in the set, which in this case is 7.

That's how we get to 19/7 which approximates to 2.7 when rounding to one decimal place.

Answer:

The answer is C.

Step-by-step explanation:

You take 2 values from the graph each for x and y. Use it in finding the gradient:

[tex] gradient = \frac{y2 - y1}{x2 - x1} [/tex]

Your gradient is m. So you replace your answer in the formula:

[tex]y = mx + c[/tex]

where c is the constant

Then you solve solve for x by substituting other values. After finding c, substitute m and c in the equation above but leave x and y like that and you have your equation.

You will need to sell 14 baskets to meet/exceed the goal

Small baskets are sold at $12

Large baskets are sold at $20

The goal is to sell $300 worth of baskets at the upcoming craft show

Let x represent the small baskets and let y represent the large baskets

12x + 20y= 300

7 large baskets are sold, the equates to

7 × 20

= 140

The number of small baskets that must be sold to reach the goal can be calculated as follows

300-140

= 160

160/12

13.33

Hence 14 small basket needs to be sold to meet/exceed the goal

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a) the coordinates of the dilated trapezoid is F'(-3, 2), G'(-2, 3), H'(-1, 3), I'(0, 2)

b) Dilation is reduction.

In this question, we have been given a trapezoid has coordinates F (−9, 6), G (−6, 9), H (−3, 9), and I (0, 6).

a. We need to dilate the trapezoid by a scale factor of 1/3 with a center of dilation at the origin.

The scale factor is 1/3

so, the coordinates of the image would be,

F' = 1/3 (-9, 6)

   = (-3, 2),

G' = 1/3(-6, 9)

    = (-2, 3),

H' = 1/3 (−3, 9)

    = (-1, 3),

and I' = 1/3 (0, 6)

         = (0, 2)

b. We know that a dilation is a geometric transformation that either enlarges or reduces a figure in size.

As we know, if the scale factor is between 0 to 1 then the image is reduction and if the scale factor is greater than 1 then the image is enlargement.

Here, scale factor is 1/3 which is 0 < 1/3 < 1

So, in this case the dilation is reduction.

Therefore, a) the coordinates of the dilated trapezoid is F'(-3, 2), G'(-2, 3), H'(-1, 3), I'(0, 2)

b) Dilation is reduction.

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Answer:

z=16

Step-by-step explanation:

1/4 *16=4

and 4 +8=12

Answer:

is that a z or 2?

[tex]\begin{array}{ccll} scarves&\$\\ \cline{1-2} 2 & 22.80\\ 3& x \end{array} \implies \cfrac{2}{3}~~=~~\cfrac{22.80}{x} \\\\\\ 2x=3(22.80)\implies x=\cfrac{3(22.80)}{2}\implies x=34.2[/tex]

Answer: $34.20

Step-by-step explanation:

2 scarves = $22.80

22.80 ÷ 2 = $11.40

11.40 x 3 = $34.20

To check your work you could do:

$22.80 + $11.40 = $34.20

or

$34.20 ÷ 3 = $11.40

Answer:

9*x³ or 9x³

Step-by-step explanation:

a number = x

cubed = to the power of 3

not really much to explain here

The undefined terms are parallel lines are line and plane.

What is parallel lines?

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. In this essay, let's study more about parallel lines. No matter how far we extend a parallel line, it will never meet another parallel line. See the parallel lines in the following illustration. Lines "a" and "b" are parallel, while lines "p" and "q" are also parallel.

Given that,

Parallel lines are two or more lines in a plane that are the same distance apart and will never intersect.  

This definition uses two undefined terms, line and plane.

Therefore,  undefined terms are parallel lines are line and plane.

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The graph is about a tangent function.

We have to find the parameters a and b.

The period formula is

If we find the period, we can find b.

Remember that the period is the distance between two consecutive asymptotes. In this case, the period is 2pi.

a.) The expression of the sketch is:

2 - 1 + 2 - 1 - 1 + 1 = 2

So, the value of the expression is 2.

b.) The expression of the sketch is:

4 - 6 = -2

So, the value of the expression is -2.

c.) The expression of the sketch is:

-1 + 2 - 1 + 1 - 2 + 1 = 0

So, the value of the expression is 0.

d.) The expression of the sketch is:

- 4 + 7 = 3

So, the value of the expression is 3.

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Looking at the graph

the value is currently increasing, because the slope of the line is positive

so

I agree with Mr. Alvarez reasoning

Answer:

Range is called a set of possible outputs..in an realtion or function.

Every relation is not function but all function is relation

Actually some specified relations are called function.

Thanks

Here Range= {5}