The function H(t) = −16t^2 + 112t + 24 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 5 + 3.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.

Part A: Create a table using integers 4 through 7 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)

Part B: Explain what the solution from Part A means in the context of the problem. (4 points)

Answer:

1. c

Step-by-step explanation:

2. A

Answer:

C and A

Hope This Helps!    Have A Nice Day!!

Answer:

2 points

Step-by-step explanation:

A quadratic equation is in the form of ax²+bx+c. The points at which the graph of the function y = 4x² - 6x + 1 intersects the x-axis is 0.191 and 1.309.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The points at which the graph of the function y = 4x² - 6x + 1 intersects the x-axis can be found by substituting the value of y as 0 in the equation and then solving the equation.

0 = 4x² - 6x + 1

Since the equation is in the quadratic form, the roots of the equation are,

[tex]x = \dfrac{-(-6)\pm\sqrt{(-6)^2-4(4)(1)}}{2(4)}\\\\x = \dfrac{6\pm\sqrt{36-16}}{8}\\\\x = \dfrac{6\pm\sqrt{20}}{8}\\\\x = \dfrac{6\pm2\sqrt{5}}{8}[/tex]

x = 0.191, 1.309

Hence, The points at which the graph of the function y = 4x² - 6x + 1 intersects the x-axis is 0.191 and 1.309.

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Answer:

Step-by-step explanation:

The answer is acd

Answer: A, C, D,

A: 6 (x+7) -2

C: 4f - 2g

D: 3 xyz=-10

Step-by-step explanation:

A difference is the result of a sustraction problem.

In the expression 6( x-7 ) -2, the expressions 6( x-7 ) and 2 are being substracted.

In the expression 4f - 2g. The expresions of 4f and 2g are being substracted.

in the expression 3xyz-10, the expressions 3xyz and 10 are being subtracted.

The following expressions represent the difference of exactly 2 expressions:

6 (x+7) -2

4f - 2g

3 xyz=-10

Answer:

The triangles abc and dbe show that the consistent cost of the pens is 2 dollars for each individual pen

Step-by-step explanation:

The answer is:

The second distance ([tex]distance_{2}[/tex]) is equal to 7.5 feet.

Since we are given two forces acting at distance, torque will be created. We are given two forces and one distance, so, to calculate the other distance required to balance the system (solve this fulcrum problem), we need to write the following equation:

[tex]Torque_{1}=Torque_{2}[/tex]

Where,

[tex]Torque=F*Distance[/tex]

We are given,

[tex]Force_{1}=Weight_{1}=150lb\\Force_{2}=Weight_{2}=30lb\\distance_{1}=15ft\\[/tex]

So, substituting and calculating, we have:

[tex]Torque_{1}=Torque_{2}[/tex]

[tex]Weight_{1}*distance_{1}=Weight_{2}*distance_{2}[/tex]

[tex]150lb*15ft=300lb*distance_{2}[/tex]

[tex]distance_{2}=\frac{150lb*15ft}{300lb}=7.5ft[/tex]

Hence, the second distance ([tex]distance_{2}[/tex]) is equal to 7.5 feet.

It's a logical solution since the second force is twice the first force and it means that the second distance must be equal to half the first distance in order to maintain the equilibrium condition.

Have a nice day!

Final answer:

A 52% chance indicates that it is more likely than not for a player to win a carnival game, expecting roughly 52 wins out of 100 plays.

Explanation:

The likelihood that a player will win a certain carnival game, with a 52% chance, suggests that it is more likely than not that the player will win. This percentage can be interpreted as a probability of 0.52 (where 0 represents an impossible event and 1 represents a certainty). To describe this likelihood in terms of probability theory, if the game were played 100 times, we would expect the player to win approximately 52 times, although the actual outcome could vary due to randomness.

When comparing to other probabilities, such as a child winning one out of five times (20% chance) or the very low probability of winning the grand prize in another carnival game (0.005 or 0.5%), a 52% chance is relatively high, indicating that winning the game is a probable outcome.

The statement that describes the likelihood that a player will win the game is the fourth option

The likelihood of the player winning can be described as follows;

The probability that a player will win the carnival = 52%

The chance of a player winning the carnival is approximately 50%, which indicates that it almost equally likely or unlikely that a player may win the game

The above statement indicates that out of two plays, the player will likely win one and out of 10 palys, the player will likely win five

Therefore, the statement that describes the likelihood of a player will the game is the fourth statement

It is neither likely or unlikely that the player will win the game

Check the picture below.

Answer:

A

Step-by-step explanation:

An excluded value is any value of x that makes the denominator of the rational expression zero as this would make the expression undefined.

For expression A

[tex]\frac{x-3}{x^2-4}[/tex]

The denominator will be zero when x² - 4 = 0

x² - 4 is a difference of squares, thus

(x - 2)(x + 2) = 0

x - 2 = 0 ⇒ x = 2

x + 2 = 0 ⇒ x = - 2

The excluded values of x are x = ± 2 ⇒ A

Option A) is the answer

Answer:

Axis of symmetry is [tex]x=1.5[/tex].

Step-by-step explanation:

Given equation is [tex]y=2x^2-6x+2[/tex].

Now we need to find about what is the axis of symmetry of the given function.

So compare it with [tex]y=ax^2+bx+c[/tex], we get:

a=2, b=-6, c=2

Axis of symmetry is given by the formula

[tex]x=-\frac{b}{2a}[/tex]

[tex]x=-\frac{-6}{2(2)}[/tex]

[tex]x=\frac{3}{2}[/tex]

[tex]x=1.5[/tex]

Hence final answer is given by:

Axis of symmetry is [tex]x=1.5[/tex].

To find another angle in an acute triangle with one angle measuring 38 degrees, any value less than 90 degrees is possible for the second angle, provided that the third angle remains acute as well.

One angle measure in an acute triangle is 38°, and to determine the measure of one of the other angles, we must consider the geometric principle stating that the sum of angles in a triangle is 180°. Since we have one angle measuring 38°, the sum of the remaining two angles must be 180° - 38° = 142°. Given that an acute triangle has all angles measuring less than 90°, one of the other angles could be any value less than 90° but also must leave enough degrees so that the third angle is also acute (less than 90°). For example, if the second angle were 52°, the third angle would be 142° - 52° = 90°, which is the highest possible value without losing the acute property of the triangle.

Your answer is 8

Hope I helped

Answer:

32

Step-by-step explanation:

Answer:

4.575% APEX

Step-by-step explanation:

The new rate would be 3.75% when Peter's bank offered him a 4.95% interest rate for his mortgage. If he purchases 3 points.

A mortgage exists as an arrangement between you and a lender that provides the lender the right to consider your property if you forget to repay the money you've borrowed plus interest.

Mortgage loans exists utilized to buy a home or to borrow money against the significance of a home you already possess.

Purchasing a point simply implies negotiating for a lower rate of interest, which involves paying 1% of the loan in lieu of a 1% interest reduction.

A point implies a reduction in interest rate by 0.25% while 3 points would reduce the interest rate by 0.75%(0.25%*3)

New interest rate = 4.5% - 0.75% = 3.75%

Therefore, the correct answer is option C. 4.575

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Answer:

Length = 24 and Width = 81

Step-by-step explanation:

Let Width be W

then Length = W-57

Perimeter of rectangle = 2(Length + Width)

=2 (W-57+W)= 210

4W- 114= 210

4W= 324

W= 81

Then Length = 81-57 = 24

The length and width of a regulation singles tennis court is 78 feet and 27 feet respectively when the perimeter is 210 feet and length is 57 feet less than five times the width. This can be obtained by using formula of perimeter of a rectangle and algebraic expression.

P = 2(l + b) where P is the perimeter of the rectangle, l is the length of the rectangle and b is the width of the rectangle.

Length of the rectangle is 57 feet less than five times the width, that is, in the form of algebraic expression,

l = 5b - 57 , where l and b are length and width.

Given that, perimeter P=210 feet, length l= 5b - 57, width b = b

P = 2(l + b)

210 = 2((5b - 57) + b)

210 = 2(5b + b -57) =2(6b - 57)

210 = 12b - 114

12b = 210 + 114 = 324

b = 324/12 =27 ⇒b = 27 feet

l = 5b - 57

l = 5(27) - 57

l =135 - 57 =78 ⇒ l = 78 feet

l = 78 feet and b = 27 feet

Hence the length and width of a regulation singles tennis court is 78 feet and 27 feet respectively when the perimeter is 210 feet and length is 57 feet less than five times the width.

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Answer:

B)3

Step-by-step explanation:

to find "x" intercept substitute 0 for y and solve

4x+3(0)=12

4x+0=12

divide by "4" on both sides:

4x/4=12/4

x=3

hope this helps!

Answer: B

Step-by-step explanation: I put it in a website and the answer is b

ANSWER

The value of x is 18.

EXPLANATION

The given expression is

[tex]2x + 3y = 36[/tex]

when y=6, we substitute y=6 into the expression to get:

[tex]2x + 3(6) = 36[/tex]

This gives us:

[tex]2x + 18= 36[/tex]

We group similar terms to obtain:

[tex]2x = 36 - 18[/tex]

We simplify the RHS to get

[tex]2x =18[/tex]

We divide both sides with 2 to get,

[tex]x = \frac{18}{2} [/tex]

x=9

Answer:

The value of x = 9

Step-by-step explanation:

It is given an expression in variables x and y

2x + 3y = 36

To find the value of x

Let 2x + 3y = 36

When y = 6, the expression becomes

2x + (3 * 6) = 36

2x + 18 = 36

2x = 36 - 18  = 18

2x = 18

x = 18/2 = 9

x = 9

Therefore the value of x = 9

Answer:

Option C [tex]10+5x=24+3x[/tex]

Step-by-step explanation:

Let

x ------> the cost of each shirt

we know that

The cost of 5 shirts plus $10 (amount of money that would remain) must be equal to the cost of 3 shirts plus $24 (amount of money that would remain). Considering that the cost of the shirts is the same

The linear equation that represent this scenario is

[tex]10+5x=24+3x[/tex]

Solve for x

[tex]5x-3x=24-10[/tex]

[tex]2x=14[/tex]

[tex]x=\$7[/tex]

To determine the cost of each shirt, set up a system of equations with the given information. By solving the equations, we find that the cost of each shirt is represented by option C.

To determine the cost of each shirt, we can set up a system of equations based on the given information. Let x represent the cost of each shirt. We have the following equations:

We know that Rhonda had $10 left after buying five shirts, so equation A can be rewritten as 5x + 10 = 10. Simplifying this equation, we get 5x = 0, which means x = 0.

Now, let's substitute x = 0 into equation B. We get 3(0) + 24 = 24. Since Rhonda had $24 left after buying three shirts, this is the correct equation.

Therefore, the correct equation to determine the cost of each shirt is 3x + 24 = total amount spent. Option C represents this equation.

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ANSWER

[tex] 10C_5(2)^{5}( - 3)^5[/tex]

EXPLANATION

The given binomial expression is

[tex](2x-3y)^{10} [/tex]

The nth term in this expansion is calculated using the formula,

[tex]T_{r+1} = nC_ra^{n-r}b^r[/tex]

To find the term with coefficient

[tex] {x}^{5} {y}^{5} [/tex]

we substitute r=5, n=10, a=2x, and b=-3y

[tex]T_{6} = 10C_5(2x)^{10-5}( - 3y)^5[/tex]

[tex]T_{6} = 10C_5(2x)^{5}( - 3y)^5[/tex]

[tex]T_{6} = 10C_5(2)^{5}( - 3)^5 {x}^{5} {y}^{5} [/tex]

The coefficient is

[tex] 10C_5(2)^{5}( - 3)^5[/tex]

The second choice is correct.

Answer:

second one

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

Easy-Peasy!

The function is f(x) = z^2 + c, where c=1-3i and z0 = i.

So what you have to do, is to substitute the given values of Z and C into the function:

f(x) = z^2 + c

f(x) = (i)^2 + 1 - 3i

f(x) =  -1 + 1 - 3i = -3i.

Then the first value is z1 = -3i.

Then we substitute new value z1 = -3i into the fuction:

f2(x) = (-3i)^2 + 1 - 3i

f2(x) = -9 + 1 - 3i = -8 - 3i

Then the second value is: z2 = -8 - 3i

Again, we substitute the value z2 = -8 - 3i into the function:

f3(x) = (-8 - 3i)^2 + 1 -3i

f3(x) = 64 + 48i -9 + 1 - 3i = 56 + 45i

Z3 = 56+45i

So, the correct option is: Option A.

Answer:

6

Step-by-step explanation:

Given I varies inversely with R then the equation relating them is

I =  [tex]\frac{k}{R}[/tex] ← k is the constant of variation

To find k use the condition R = 12 when I = 3

k = IR = 3 × 12 = 36

I = [tex]\frac{36}{R}[/tex] ← equation of variation

When I = 6, then

6 = [tex]\frac{36}{R}[/tex], hence

R = [tex]\frac{36}{6}[/tex] = 6

The domain is all real numbers and the range is all the reals at or above the vertex y coordinate (if the coefficient on the squared term is positive) or all the reals at or below the vertex (if said coefficient is negative).

Answer:

The domain is all real numbers, and the range is nonnegative real numbers (y > 0)
-

Step-by-step explanation:

tha pex

Answer:

The length of the pen is [tex]8\ ft[/tex]

The width of the pen is [tex]6\ ft[/tex]

Step-by-step explanation:

Let

x-----> the length of the pen

y----> the width of the pen

we know that

The perimeter of the pen is

[tex]P=2(x+y)[/tex]

[tex]P=28\ ft[/tex]

so

[tex]28=2(x+y)[/tex]

[tex]14=(x+y)[/tex] ------> equation A

[tex]y=2+\frac{1}{2}x[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]14=x+(2+\frac{1}{2}x)[/tex]

[tex]14-2=\frac{3}{2}x)[/tex]

[tex]12=\frac{3}{2}x)[/tex]

[tex]x=12*2/3=8\ ft[/tex]

Find the value of y

[tex]y=2+\frac{1}{2}(8)=6\ ft[/tex]

therefore

The length of the pen is [tex]8\ ft[/tex]

The width of the pen is [tex]6\ ft[/tex]

John's dog pen is solved to have dimensions of 8 feet in length and 6 feet in width by using algebraic expressions to relate the given conditions about the pen's perimeter and the relationship between its length and width.

Let's solve John's problem by denoting the length of the rectangle as L and the width as W. According to the problem, we know that the entire fencing measures 28 feet, so the perimeter of the rectangle can be calculated as 2L + 2W = 28. Furthermore, it's given that the width is two more than one-half the length, which translates to W = ½L + 2.

First, substituting the width's equation into the perimeter equation gives us 2L + 2(½L + 2) = 28. Simplifying this equation leads to L = 8 feet. Plugging the length's value back into W = ½L + 2 gives W = 6 feet.

Therefore, John's dog pen has dimensions of 8 feet in length and 6 feet in width.

Final answer:

The value of 12 + 6/n when N=2 is 15.

Explanation:

The value of 12+6/n when N=2 is found by substituting N=2 into the expression:

12 + 6/2 = 12 + 3 = 15

Therefore, the value of 12 + 6/n when N=2 is 15.

Answer:

what are the answer options?

Step-by-step explanation:

(n-2)*180 divided by n

Answer:

540°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5, hence

sum of interior angles = 180° × 3 = 540°

Answer:

Step-by-step explanation:

-12n - 20

-12n = (-2)(6n)

-20 = (-2)(10)

-12n - 20 = (-2)(6n+10)

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

• cscx = [tex]\frac{1}{sinx}[/tex]

• cot²x = [tex]\frac{cos^2x}{sin^2x}[/tex], sin²x + cos²x = 1

Consider the left side

cscx - sinx

= [tex]\frac{1}{sinx}[/tex] - sinx

=[tex]\frac{1-sin^2x}{sinx}[/tex]

= [tex]\frac{cos^2x}{sinx}[/tex] × [tex]\frac{sinx}{sinx}[/tex]

= [tex]\frac{cos^2x}{sin^2x}[/tex] × sinx

= cot²x × [tex]\frac{1}{cscx}[/tex]

= [tex]\frac{cot^2x}{cscx}[/tex] = right side ⇒ verified

Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The cube root is the number which multiplied by itself 3 times results in 125

Note that 5 × 5 × 5 = 25 × 5 = 125

Thus the cube root of 125 is 5

Answer:

C

Step-by-step explanation:

The angle 160° and the interior angle of the triangle form a straight angle

interior angle = 180° - 160° = 20°

Similarly with angle 131° and the interior angle at the top of the triangle

interior angle = 180° - 131° = 49°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

n is an exterior angle, hence

n = 20° + 49° = 69° → C

Answer:

9/2

Step-by-step explanation:

4* 3/8+6*1/8 divided by 1/4

first dividing a fraction is the same as mutiplying by the recirpocal so you can take 1/4 as times it by 4/1 which equals 4

leaving you with 4* 3/8+6*1/8*4

then you can reduze 4* 3/8 by finign the greatest common factor which is four

so you get 3/2+6*1/8*4

reduce 1/8 * 4 into 1/2

so you get 3/2+6*1/2

then rudce 6* 1/2 and get 3

then add whats left which is 3/2+3

you get 9/2

Answer:

[tex]\large\boxed{S.A.=4500\pi\ in^2\approx14130\ in^2}[/tex]

Step-by-step explanation:

The formula of a surface area of a ball (sphere):

[tex]S.A.=\dfrac{4}{3}\pi R^3[/tex]

R - radius

We have R = 15in. Substitute:

[tex]S.A.=\dfrac{4}{3}\pi(15^3)=\dfrac{4}{3}\pi(3375)=4500\pi\ in^2[/tex]

If you want to get an approximation, then:

[tex]\pi\approx3.14\\\\S.A.\approx(4500)(3.14)=14130\ in^2[/tex]

Answer:

SA=(4⋅3.14⋅225) square inches

Step-by-step explanation:

TTM