The height, h (in meters above ground), of a projectile at any time, t (in seconds), after the launch is defined by the function h(t) = −5t2 + 13t + 6. The graph of this function is shown below. When rounded to the nearest tenth, what is the maximum height reached by the projectile, how long did it take to reach its maximum height, and when did the projectile hit the ground?

Given,

The function is:

Taking x = -x then,

The function is odd.

Step-by-step explanation:

The leading term is -5x^4, which tells us the highest degree of the polynomial.

The leading term in the equation tells us about the degree and whether the curve opens outwards on inwards

What is an equation in one variable?

An equation is a polynomial in one variable with a finite degree

We are given an equation

[tex]-5x^4+4x^3-6x^2+8[/tex]

In this the leading term is -5x^4

Here the coefficient is negative this tells us that the curve opens downwards. if the coefficient has been positive then the curve would open outwards.

Also from the leading term we can find out the degree of the highest variable. the degree of highest variable in this case is 4

Hence, The leading term in the equation tells us about the degree of the variable and whether the curve opens outwards on inwards

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The inverse of the function f(x) = 10 (√x + 9) is  f⁻¹(x) = (x - 90)² / 100

Given,

The function, f(x) = 10 (√x + 9)

We have to find the inverse of the function, f⁻¹(x)

Here,

f(x) = 10 (√x + 9)

f(x) = 10√x + 90

Replace f(x) with y.

y = 10√x + 90

Swap x with y;

x = 10√y + 90

Solve for y

That is,

x = 10√y + 90

x - 90 = 10√y

(x - 90) / 10 = √y

Square both sides

((x - 90) / 10)² = √y²

(x - 90)² / 100 = y

Replace y with f⁻¹(x)

That is,

f⁻¹(x) = (x - 90)² / 100

Therefore,

The inverse for the function  f(x) = 10 (√x + 9) is  f⁻¹(x) = (x - 90)² / 100

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The correct answer to this question is that m is the dependent variable and h is the independent variable.

The amount of money Trevor earns can be formulated in the form of linear equation. A Linear equation is the one which can be expressed in the form of y = ax + b where y is dependent, and x is independent variable whereas a, b are coefficients. According to question amount of money Trevor earns will depend on the number of houses he paints. If m is the amount of money Trevor earns and h is the number of houses Trevor paints. This can be formulated as

m = hx + b and in this expression, m is dependent variable and h is independent variable as his earning will depend on the number of houses he paints.

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The number sand bags required are 84 approximately.

Given, we have:

Diameter of garden = 38 yd

Width of path = 5 yd

Diameter of garden with path = 38 + 2 x 5 = 48 yd

We need to find area of path.

Area of path = Area of garden with path - area of garden

Area of path = π × 48²/4 - π × 38²/4

Area of path = 7234.56/4 - 4534.16/4

Area of path = 1808.64 - 1133.54

Area of path = 675.1 yd²

Area covered by one sand bag = 8 yd²

Number of sand bags required =  Area of path/Area covered by one sand bag

=675.1/8

= 84.38 ≈ 84

Number of sand bags needed = 84

Therefore, number of sand bags required are 84.

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Answer:

42 1/6 square inches

Step-by-step explanation:

253=6x

x=42 1/6

42 1/6 square inches

:]

x^6

Step-by-step explanation:

I don't know how to explain but I think this is what you mean

Consider that the Bob's Golf Palace bought the set of golf clubs by $390.

Moreover, take into account that the golf clubs were markes on sale for $840.

The profit is only the difference between the marked on sale and the money Bob's Golf Palace payed:

$840 - $390 = $450

Hence, the profit was $450

Answer:

first draw the line edges and vertical

second put the dot every no.

And put the y=2000×+4000

Answer:

A is the answer :))))))))))))))))))

We will ahve the following:

The probability that they are the 5 oldest people in the group is 1/6.

Given that we have a group of 6 people, and we randomly select 5 of them.

We need to find the probability that they are the 5 oldest people in the group.

The total number of ways to select 5 people from a group of 6 people is given by 6C5 which is equal to 6.

This means that there are only 6 possible outcomes when we randomly select 5 people from a group of 6 people.

We know that the 5 oldest people in the group can be selected only in one way.

So, the number of favorable outcomes is 1.

Hence, the probability of selecting the 5 oldest people from the group when 5 people are randomly selected is: Probability = favorable outcomes/total outcomes Probability = 1/6

Therefore, the probability that they are the 5 oldest people in the group is 1/6.

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Answer:

  12.123

Step-by-step explanation:

You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.

When the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.

The area we want is the sum ...

  f(0) +f(1) +f(2) +f(3)

As the attachment shows, that sum is ...

  area ≈ 12.123 . . . square units

__

Additional comment

The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.

Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.

For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.

The area of the shaded triangle is equal to:

the base of the shaded triangle is 4 in and the height is 5 in, then:

Therefore the shaded area is 10 squared inches.

Answer: It would be Answer D

Step-by-step explanation: He Subtracted from both sides in an incorrect order

Given,

A population doubles every 27 years.

a. Let initial population be 1 and after 27 years it becomes 2.

Considering r as the rate of annuall growth we have,

Thus annual growth rate is 2.6%

b. For continuous growth,

The continuous growth rate is _2.5___% per year

Given

Equation

Procedure

The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are

The discriminant b^2 - 4ac < 0

so, there are two complex roots.

To find the area of the running track that goes around the field, we need to follow the formula:

area of running track = outside area - inside area

1. Outside Area:

outside area = area of rectangle + 2× area of the semi- circle

= 92.52× 84.39 + π × 46.26² = 14527.32m²

2. Inside Area:

inside area = area of rectangle + 2× area of the semi- circle

= 73 × 84.39 + π × 36.5² = 10343.74m²

So, area of running track = 14527.32 m² - 10343.74m² = 4183.58m² ≈ 4184m²

Answer:

a because 8.508

Step-by-step explanation:

0.625 so it easy 0.5:0.8

Given equation:

Solve the equation to find the value of x,

Hence, x=-2/3

Answer: option B) is correct

Answer:

2(3×+6) is 96 _6 by (2×4=5) with A.X

Answer:

Hello! The answer is A) B=3

Step-by-step explanation:

Hope I helped! Please mark brainiest if get chance.

(Ps: Are you an army?)

Answer:

d = 3

Step-by-step explanation:

I took different numbers, like 1 and 2, and multiplied them to themselves 3 times, for example, 2 x 2 x 2, but since that answer was wrong, I decided to try a different number, which was 3 and that was correct.

Given the following question:

We know the two triangles are similar

We also have the bases of the two triangles which means we can find how bigger the second triangle is, compared to the first triangle.

The following congruence statements a, b, e, f are correct.

Triangle congruence: If all three corresponding sides and all three corresponding angles seem to be equal in size, two triangles are said to be congruent.

When two triangles are congruent, their sides and corresponding angles are identical.

Therefore, if GHI is congruent to LMN, then GH =LM, HI=MN and GI=LN, and also angle G=angle L, Angle H=angle M, while angle I = angle N, therefore the correct answers is f) ∠M= ∠H, (a) GH = LM b) ∠L=∠G. and e)IH=NM.

Therefore, option a, b, e, f are correct.
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Answer:

10 - 3 = 7

10 - 7 = 3

Step-by-step explanation:

Given two triangles, ADB and CBD

So,

1. the measure of < D = the measure of angle < B

2. CB = AD

3. BD = DB

so, the triangle ADB is congruent to the triangle CBD by SAS [ side - angle - side ]

So, the corresponding parts are congruent :

So,

1. the measure of angle A = the measure of angle C

2. the measure of angle B = the measure of angle D

3. AB = CD

[tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-8\leq 10-2x < 28 } \end{gathered}$} }[/tex]

Separate the inequality compound in the inequality system.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{{\left\{ \begin{array}{r}10-2x\geq -8 \\ 10-2x < 28 \ \end{array} \right.} } \end{gathered}$} }[/tex]

Order the unknown terms to the left side of the equation.[tex]\boxed{\bf{-2x < 28-10 }}[/tex]

Calculate the sum or difference.

[tex]\boxed{\bf{-2x < 18 }}[/tex]

Divide both sides of the equation by the coefficient of the invariable.[tex]\boxed{\bf{x > -\frac{18}{2} }}[/tex]

Clear the common factor

[tex]\boxed{\bf{x > -9} }}[/tex]

Order the unknown terms to the left side of the equation.

  [tex]\boxed{\bf{-2x\geq -8-10 }}[/tex]      

Calculate the sum or difference.

[tex]\boxed{\bf{-2x\geq -18 }}[/tex]

Divide both sides of the equation by the coefficient of the invariable.

[tex]\boxed{\bf{x\leq \frac{-18}{-2} }}[/tex]

Determine the sign of multiplication and division.

[tex]\boxed{\bf{x\leq \frac{18}{2} }}[/tex]

Clear the common factor

[tex]\boxed{\bf{x\leq 9}}[/tex]

[tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{x > -9 \ and \ x\leq 9 } \end{gathered}$} }[/tex]

We find the intersection.

Answer = [tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-9 < x\leq 9 } \end{gathered}$} }[/tex]

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ L(\stackrel{x_1}{1}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{9}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ LC=\sqrt{(~~9 - 1~~)^2 + (~~-3 - (-8)~~)^2} \implies LC=\sqrt{(9 -1)^2 + (-3 +8)^2} \\\\\\ LC=\sqrt{( 8 )^2 + ( 5 )^2} \implies LC=\sqrt{ 64 + 25 } \implies LC=\sqrt{ 89 }\implies LC\approx 9.43[/tex]

The probability distribution is given in the table.

The condition for the probability distribution is

1. The sum of the probability distribution is 1.

2. The probabilities value range between 0 and 1.

Condition to check the probability distribution

The sum of the probability is not equal to 1.

Hence the distribution does not represents a discrete probability distribution.

Given:

Total amount of hamburger meat = 5½ pounds

Let's find how many ¼ pound hamburgers could be made from 5½ pounds of hamburger meat.

To find how many pound hamburger could be made divide 5½ by ¼.

Thus, we have:

To perform the division, take the following steps:

Step 1:

Convert the mixed fraction to improper fraction

Step 2:

Flip the fraction on the right and change the division symbol to multiplication

Therefore, 22 of ¼ pound of hamburger could be made from 5½ pounds of hamburger meat.

ANSWER:

22