A toy rocket launch can be represented by a parabolic function. Your most
recent launch for the science fair can be modeled by the function
y = -4(x - 5)² + 125 where y is the height of the rocket and x is the
number of seconds since launch. Graph this function and include all of the
points listed above, then discuss in context what the vertex and x-
intercepts mean in context.

The slope-point form of the linear equation with a slope of -3 and the given point is:

y = -3*(x - 3) - 1

Remember that a general linear equation with a slope a and a point (h, k) can be written in the slope-point form as:

y = a*(x - h) + k

In this case, we know that the slope of the linear equation must be -3, so the linear equation can be written as:

y = -3*(x - h) + k

Now we also want this line to pass through the point on the graph, which is (3, -1), then we need to replace the values:

h = 3

k = -1

Replacing that in the linear equation above we will get:

y = -3*(x - 3) - 1

That is the linear equation in the slope-point form.

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On solving the provided question, we  can say that - the give quadratic equation [tex]y = x^2 - 4x - 1[/tex], there are no like terms so it doesn't factor.

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here,

y = [tex]x^2 - 4x - 1[/tex]

so, the above quadratic equation, there no like terms, so it does not give any factor.

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Answer:

Step-by-step explanation:

divide 13 by how many feets u have then what ever you get is the answer

THANK YOU

By solving an inequality, we will see that for more than 12 tons of sugar, the first company will be the cheaper option.

We know that the first company charges a fixed amount of $1503, plus $125.25 for each ton of sugar, then the total cost for x tons of sugar is:

f(x) = $1503 + $125.2*x

While the second company only charges $250.50 for each ton of sugar, then the cost for x tons of sugar is:

g(x) = $250.50*x

The first company will be a better option for all the values of x such that the following inequality is true:

f(x) < g(x)

Replacing the functions we will get:

$1503 + $125.2*x <  $250.50*x

Now we can solve that inequality for x.

$1503 < $250.50*x - $125.25*x

$1503 < $125.25*x

$1503/$125.25 < x

12 < x

So for more than 12 tons of sugar, company one is the best option.

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The meaning of p (10) will be;

⇒ The plant's height in centimeters after 10 weeks.

A relation between a set of inputs having one output each is called a function.

Given that;

The height of a plant in centimeters is a function of its age in weeks, w.

And, p represent this function.

Now,

Since, p represent this function.

Hence, The value of p (10) means is,

⇒ p (10) = The plant's height in centimeters after 10 weeks.

Thus, The correct statement is,

⇒ The plant's height in centimeters after 10 weeks.

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Answer: 4 times

Step-by-step explanation:

35/128 is your chances of getting heads, 8 divided by 2 = 4

Answer:

x = 121 degrees

y = 59 degrees

w = 59 degrees

z = 53 degrees

v = 121 degrees

Step-by-step explanation:

31 + 90 + w = 180  ==> these three angles are in the top left triangle.

                                    Triangles add up to 180 degrees

121 + w = 180  ==> solve for w

w = 59 degrees

y = w ==> these angles are opposite adjacent angles; they are congruent

y = 59 degrees ==> Both angles are equal. So both angles are 59 degrees

68 + y + z = 180 ==> triangles add up to 180 degrees

68 + 59 + z = 180 ==> plugin 59 for y

127 + z = 180 ==> solve for z

z = 53 degrees ==> subtract 137 on both sides

w + x = 180  ==> w and x are on a straight line.

                           Straight lines add up to 180 degrees.

59 + x = 180  ==> plugin 59 for w

x = 121 degrees  ==> subtract 59 on both sides

v + y = 180 ==> v and y are also on a straight line.

v + 59 = 180 ==> plugin 59 for y

v = 121 degrees ==> subtract 59 on both sides

x = 121 degrees

y = 59 degrees

w = 59 degrees

z = 53 degrees

v = 121 degrees

Answer:

-3g+70/7g

I have attached the working as an image file

Answer:

Below

Step-by-step explanation:

Right triangle....use pyhtagorean theorem

c^2 = a^2 + b^2

(2 sqrt5)^2 = 2 ^2 + ?^2

16 = ?^2       ? = 4  units

Area shaded represents the area bounded by both the graphs of the functions y = sin(πx) and y = x³ - 4x.

An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.

Given is the region {r} bounded by the graphs of y = sin(πx) and y = x³ - 4x.

Refer to the graph attached. The shaded region is the area bounded by both the graphs of the functions y = sin(πx) and y = x³ - 4x.

Therefore, area shaded represents the area bounded by both the graphs of the functions y = sin(πx) and y = x³ - 4x.

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The expression can be rewritten as a single logarithm as:

ln|sin x| + ln|cot x| = ln(|sin x||cot x|) = ln|cos x|

This is possible because logarithm function is a monotonically increasing function, meaning that if a > b then log(a) > log(b) and log(a*b) = log(a) + log(b) that's why we can add the two logarithms.

The result is simplified by combining the absolute values of the sin and cot functions into a single term. The absolute value is removed since the product of two positive numbers is always positive. The final result is ln|cos x|, which is the natural logarithm of the product of the sine and cotangent of x.

It is important to note that the cotangent function is defined as 1/tan(x) so that cot(x) = 1/tan(x) and cot(x) is only defined for x where sin(x) is not equal to 0.

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The formula for the nth term of the given function is 3 squared times the difference between 5 and -1, multiplied by the difference between n and 1, divided by the sum of n and 1.

r_n = 3^2 * (5-(-1)) * (n-1)/(n+1)

Step 1: calculate 3 squared

3^2 = 9

Step 2: calculate the difference between 5 and -1

5-(-1) = 6

Step 3: calculate the difference between n and 1

n-1

Step 4: calculate the sum of n and 1

n+1

Step 5: multiply all the above calculations

r_n = 9 * 6 * (n-1)/(n+1)

The formula for the nth term of the given function is 9 times the difference between 5 and -1, multiplied by the difference between n and 1, divided by the sum of n and 1. To calculate this, first calculate 3 squared, which is 9. Then calculate the difference between 5 and -1, which is 6. Then calculate the difference between n and 1, which is n-1. Finally, calculate the sum of n and 1, which is n+1. Multiply all of these calculations together to get the formula for the nth term, which is 9 times the difference between 5 and -1, multiplied by the difference between n and 1, divided by the sum of n and 1.

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The cost for a loaf of bread is $5, the cost for a bag of cookies is $13, and the cost for a cupcake is $2.50.

Cost is the amount of money or resources required to purchase, produce, or maintain something. It can refer to the price of goods or services, the amount of money spent on labor and materials, or the amount of time used to complete a task. Cost is often associated with the decision-making process, as it helps an individual or organization determine the value of a product or service and evaluate if it is worth the investment.

Therefore, the restaurant spent $35 on loaves of bread, $52 on bags of cookies, and $2 on cupcakes in week 1; $24 on loaves of bread, $39 on bags of cookies, and $3 on cupcakes in week 2;

and $40 on loaves of bread, $21 on bags of cookies, and $4 on cupcakes in week 3.

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Thus the angles of the isosceles triangles are 80°, 80° and 20°

An isosceles triangle is a triangle that has two sides of the same length. It also has two equal angles on the right and left (base angles) and one vertical angle, in a total of 180°.

Let's assume the base angle of an isosceles triangle is a, and the vertical angle is b. Then we can apply the total angles of a triangle here.

180° = a + a + b

As we know that a = 4b, then we can rewrite the equation as follows:

180° = a + a + b

180° = 4b + 4b + b

180° = 9b

b      = 20°

Then we calculate the value of a:

a = 4b

  = 4x20°

  = 80°

Thus the angles of the isosceles triangles are 80°, 80° and 20°

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In mathematics, the pattern of association refers to the type of correlation that is found between two variables which includes positive, negative, or no correlation.

The connection between two or more variables is referred to as a pattern of association. There are various variations of this relationship, including a positive correlation, a negative correlation, and no correlation. When both variables rise or fall at the same time, there is a positive correlation. In other words, as one variable rises, the other one rises as well, and vice versa.

When two variables move in the opposing directions, there is a negative correlation. The other variable reduces as one grows, and vice versa. When there is no correlation between the variables, a no correlation exists. This indicates that there is no pattern in the data and that the variables do not change simultaneously.

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Important Formulas:
[tex]s=\dfrac{d}{t}[/tex]

__________________________________________________________

Given:
[tex]d=250mi[/tex] (distance)

[tex]t=5h[/tex] (time)

[tex]s=?[/tex] (speed)

__________________________________________________________

Finding speed:

[tex]s=\dfrac{d}{t}[/tex]

[tex]s=\dfrac{250}{5}[/tex]

__________________________________________________________
[tex]\fbox{s = 50 mi/hr}[/tex]

Answer:

50 miles per hour (mph).

Step-by-step explanation:

250 / 5 = 50 miles per hour (mph).

Answer: 96

Step-by-step explanation:

First we have to find 1/3 of 144. Multiply them together and you get 48.

When one of the factors are less than one, the answer will get smaller.

Then we have to find 2 thirds of 144. Since we know 1 third we can multiply that by 2.
48 x 2 = 96.

Nigel is going to read 96 pages.

The rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers. (option A).

The first step is to determine the number of each type of box shape that would be needed for the pencils.

Number of rectangular prism boxes that would be needed = total number of pencils / capacity of the box

Number of rectangular prism boxes that would be needed = 2400 / 60 = 40 boxes

Number of cylindrical boxes that would be needed = total number of pencils / capacity of the box

Number of cylindrical boxes that would be needed = 2400 / 80 = 30

Now determine the total cost of using each type of box shape.

Total cost of using the  cylindrical boxes = 30 x 0.75 = $22.50

Total cost of using the  rectangular prism boxes  = 40 x 0.50 = $20

Difference in cost = $22.50 - $20 = $2.50

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Answer:

^^ A on edge

Step-by-step explanation:

The first step in constructing a segment congruent to a given segment is to draw a vertex and a ray.

Step 1: draw a vertex and a ray.

Step 2: Draw a line segment that is longer than the specified line segment if we are not given the line segment on which we are to create the congruent section. The portion we just sketched will be known as the second line segment.

Step 3: Place the needle of the compass at an endpoint of the second line segment.

Step 4: Draw an arc of the circle so that it intersects the line segment.

Step 5: Label the point where we placed the needle and the point of intersection using two letters. The congruent line segment we want is the line segment formed by these two endpoints.

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The histogram Illustrated shows that the data is negatively skewed.

Negatively skewed distribution means that the distribution type where more values plot on the graph's right side, the tail of the distribution is longer on the left side.

When a distribution is negatively skewed in statistics, more values are concentrated on the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.

From the histogram we can easily say that most of the population of US are lying on the left of histogram therefore the given data is negatively skewed

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The inverse of the given function is, [tex]f^-^1(x) = \sqrt{x+4} +1[/tex].

What is inverse of the function?

A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f^-1" or "F^-1."

Consider, the given function

f(x) = (x - 1)^2 - 4

We have to find inverse of the function.

Let  y = (x - 1)^2 - 4

Replace x with y in the above equation.

x = (y - 1)^2 - 4

Add 4 on both sides,

x + 4 = (y - 1)^2

Taking square root on both sides,

[tex]\sqrt{x+4} = y - 1[/tex]

Add 1 on both sides,

[tex]\sqrt{x+4}+1 = y[/tex]

[tex]y = \sqrt{x+4} + 1[/tex]

Take [tex]y = f^-^1(x)[/tex]

⇒ [tex]f^-^1(x) = \sqrt{x+4} + 1[/tex]

Hence, the inverse of the given function is, [tex]f^-^1(x) = \sqrt{x+4} +1[/tex].

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Shin splints are a common cause of lower leg pain and can be caused by a variety of factors, such as poorly fitting shoes, weak calf muscles, running on uneven terrain, and overpronation of the foot.

Shin splints is a term used to describe pain that occurs along the shin bone (tibia), which runs down the front of the lower leg. Common causes of shin splints include poorly fitting shoes, weak calf muscles, running on uneven terrain, and overpronation of the foot. Poorly fitting shoes can put excessive pressure on the back of the heel and the front of the foot, leading to inflammation and pain in the shin area. Weak calf muscles can cause the foot to overpronate or roll inward, which can put extra strain on the shin bone and its muscles. Running on uneven terrain can also cause the shin bone to suffer from too much pressure, leading to shin splints. Finally, overpronation of the foot is when the foot rolls inward excessively and puts extra strain on the shin bone and its muscles. Shin splints can cause pain and discomfort and should be treated as soon as possible by rest, stretching, icing, and wearing properly fitting shoes.

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Answer:

can i get brainliest?

Step-by-step explanation:

Garden A started with: 25 weeds

Days after no weeds garden A: 2 days after

Days after no weeds garden B: 6 days after

Rate of weeds dying garden B: -2.5 per day i think

Garden a and b same weeds: Day 1

Note that the two numbers given the equation |n-3| = 5 which are 5 units from 3 on the number line are: -2 and 8.

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in elementary mathematics. Every number line point is assumed to correspond to a real number and every real number to a number line point.

One more quality of number lines that is worth noting is that it stretched to the positive infinity and to the negative infinity with zero as the center point.

Given that we have been given the reference point of 3, this means that both numbers must extend one to the positive infinity constrainted by 5 units and one to the negative infinity constrained by 5 units.

Hence,

To find the two numbers that are 5 units away from 3, we can set up two equations:

n - 3 = 5 and n - 3 = -5

Solving for n in the first equation: n = 8

Solving for n in the second equation: n = -2

Therefore, the two numbers that are 5 units away from 3 on the number line are -2 and 8.

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Answer:

–1 7/15

Step-by-step explanation:

-4/5 - 2/3 = -22/15 or - 1.46

In Fraction, when both denominators are different you multiply them.

Then, multiply the first numerator with the second denominator.

Similarly, multiply the second numerator with the first denominator.

We get,

-4/5 - 2/3 = (-12 - 10)/15

When two numbers have Minus sign, add them both and give the result the same (minus) sign.

we get,

(-12 - 10)/15 = - 22/15

Finally, when - 22 is divided by 15

we get,

- 1.46

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To solve this system, first multiply the first equation by 2 to get 8x+6y=-4.

An equation is a mathematical statement that expresses two values or ideas as equal. It consists of two parts: an expression and an equals sign. The expression on the left side of the equals sign is compared to the expression on the right side of the equals sign. An equation may be used to describe relationships between physical, chemical, and mathematical quantities.

Then add the two equations to get 14x=-8. Therefore,

x=-8/14 and substituting x=-8/14

into the first equation yields y=3/2.

Thus, the solution to the system is x=-8/14 and y=3/2.

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The required functions after transformations are y = -4(x+4)+5, y = (x-o)/14, y = -x+4

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that, the equation for the parent linear value function, f(x)=x, that has been transformed by,

a) Reflecting across the -axis, vertical stretch by a scale factor 4, and a translation of 4 units up and 5 units left :-

Rule for reflection across x-axis = y = f(x) → y = -f(x)

After reflection,

f(x) = -x

And there is a vertical stretch by a scale factor 4, and a translation of 4 units up and 5 units left

f(x) = -4(x+4)+5

Therefore, the function will be f(x) = -4(x+4)+5

b) Vertical shrink by a scale factor of 14 and a horizontal shift O units right.

For vertical shrink = f(x)/14 = x/14

For horizontal shift = (x-o)/14

Therefore, the function will be f(x) = (x-o)/14

c) Reflection in the x-axis, a vertical shift of 4 units up and a horizontal shift 7 units left.

Rule for reflection across x-axis = y = f(x) → y = -f(x)

f(x) = -x

For a vertical shift of 4 units up and a horizontal shift 7 units left =

f(x) = (-x-7)+4

Hence, The required functions after transformations are y = -4(x+4)+5, y = (x-o)/14, y = -x+4

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Answer:

2 miles

Step-by-step explanation:

1/6 × 12 = 2

You can work it as fractions to understand better

1 over 6 × 12 over 1. It's the same as 12÷6