A football is thrown from the stadium. The height of this football can be represented by the polynomial -16t2 +32t + 20, where t is the time in seconds. Find the factored form of the polynomial.

A) 4(2t+5)(2t-1)
B) 4(2t-5)(2t+1)
C) -4(2t-5)(2t+1)
D) -4(2t+5)(2t-1)​

Answer:

Rs 968

Step-by-step explanation:

Given :-

To Find :-

Solution :-

We know CI as ,

> CI = P ( 1 + R/100)ⁿ

> CI = Rs 800 ( 1 + 10/100)²

> CI = Rs 800 × 11/10 × 11/10

> CI = Rs 968 .

Answer:

D

Step-by-step explanation:

Hello,

A: no since (1/3)^3=1/27 not 1/9

B: no since (-1)^3=-1 not 1

C: no since (-2)^3=-8 not -6

D: yes since (-1/2)^3=-1/8

Answser D

Answer: 60 miles

Step-by-step explanation:

Given

It takes ferry 2 hours to travel to town A and only [tex]1.5\ hr[/tex] to travel back to town B.

Speed of current is [tex]u=5\ mph[/tex]

Suppose the speed of the ferry is [tex]v[/tex] mph

Distance traveled in both the cases is same, but it took more time traveling to city A that is, ferry is moving upstream and downstream for returning time.

[tex]\Rightarrow 2(v-5)=1.5(v+5)\\\Rightarrow 2v-10=1.5v+7.5\\\Rightarrow 0.5v=17.5\\\Rightarrow v=35\ mph[/tex]

Distance between the towns is [tex]2\times (35-5)=60\ \text{miles}[/tex]

Answer:

The distance between the two towns is 60 miles.

Step-by-step explanation:

Let the distance between A and B is d.

A to B , t = 2 hour

B to A , t' = 1.5 hour

Speed of current, u = 5 mph

Let the speed of ferry is v.

distance = speed x time

d = (v - 5) x 2 = (v + 5) x 1.5

2 v - 10 = 1.5 v + 7.5

0.5 v = 17.5

v = 35 mph

So, the distance is

d = (35 - 5) x 2 = 60 miles.

Even function:

A function is said to be even if its graph is symmetric with respect to the , that is:

Odd function:

A function is said to be odd if its graph is symmetric with respect to the origin, that is:

So let's analyze each question for each type of functions using examples of polynomial functions. Thus:

FOR EVEN FUNCTIONS:

1. When  becomes  

1.1 Effects on the y-intercept

We need to find out the effects on the y-intercept when shifting the function  into:

We know that the graph  intersects the y-axis when , therefore:

So:

So the y-intercept of  is one unit less than the y-intercept of

1.2. Effects on the regions where the graph is increasing and decreasing

Given that you are shifting the graph downward on the y-axis, there is no any effect on the intervals of the domain. The function  increases and decreases in the same intervals of

1.3 The end behavior when the following changes are made.

The function is shifted one unit downward, so each point of  has the same x-coordinate but the output is one unit less than the output of . Thus, each point will be sketched as:

FOR ODD FUNCTIONS:

2. When  becomes  

2.1 Effects on the y-intercept

In this case happens the same as in the previous case. The new y-intercept is one unit less. So the graph is shifted one unit downward again.

An example is shown in Figure 1. The graph in blue is the function:

and the function in red is:

So you can see that:

2.2. Effects on the regions where the graph is increasing and decreasing

The effects are the same just as in the previous case. So the new function increases and decreases in the same intervals of

In Figure 1 you can see that both functions increase at:

and decrease at:

2.3 The end behavior when the following changes are made.

It happens the same, the output is one unit less than the output of . So, you can write the points just as they were written before.

So you can realize this concept by taking a point with the same x-coordinate of both graphs in Figure 1.

FOR EVEN FUNCTIONS:

3. When  becomes  

3.1 Effects on the y-intercept

We need to find out the effects on the y-intercept when shifting the function  into:

As we know, the graph  intersects the y-axis when , therefore:

And:

So the new y-intercept is the negative of the previous intercept shifted one unit upward.

3.2. Effects on the regions where the graph is increasing and decreasing

In the intervals when the function  increases, the function  decreases. On the other hand, in the intervals when the function  decreases, the function  increases.

3.3 The end behavior when the following changes are made.

Each point of the function  has the same x-coordinate just as the function  and the y-coordinate is the negative of the previous coordinate shifted one unit upward, that is:

FOR ODD FUNCTIONS:

4. When  becomes  

4.1 Effects on the y-intercept

In this case happens the same as in the previous case. The new y-intercept is the negative of the previous intercept shifted one unit upward.

4.2. Effects on the regions where the graph is increasing and decreasing

In this case it happens the same. So in the intervals when the function  increases, the function  decreases. On the other hand, in the intervals when the function  decreases, the function  increases.

4.3 The end behavior when the following changes are made.

Similarly, each point of the function  has the same x-coordinate just as the function  and the y-coordinate is the negative of the previous coordinate shifted one unit upward.

Answer:

A

Step-by-step explanation:

The first thing we have to do here is to subtract g(x) from f(x)

We have this as;

2x + 4 -(3x-7)

= 2x + 4-3x + 7

= -x + 11

Now, we substitute the value of x for 5

We have -5+ 11 = 6

Hello!

2x - 3 > 11 - 5x

2x + 5x > 11 + 3

7x > 11 + 3

7x > 14

x > 14 : 7

x > 2

x = 4 → the solution

Good luck! :)

Answer:

n = 12$    x = 8$   y = 10$     where n, x, and y are number of tickets

12 n + 8 x + 10 y = 3920     and n + x + y = 420

12n + 8 (x + y) + 2 y = 3920

12 n + 8 (5 n) + 2 y = 3920        since 5 (x + y) = n

52 n + 2 y = 3920   or  y = 1960 - 26 n

Also, n + x + y = 420   or n + 5 n = 420   since x + y = 5 n

n = 70    so 70 of the $12 were sold

And since y = 1960 - 26 n     we have y = 140 tickets

Now 12 * 70 + 8 x + 140 * 10 = 3920

This gives x = 210 tickets

Check:   210 + 140 + 70 = 420 tickets

Also, 12 * 70 + 210 * 8 + 140 * 10 = 3920

Answer:

(8.7×100)cm=870cm

870cm/20cm=43.5

so 43 20cm can be cut

Answer:

160 cm³

Step-by-step explanation:

→ Write down the formula for the volume

Length × Width × Height

→ Find each value

Length = 4, Width = 4 and Height = 10

→ Substitute into formula

4 × 4 × 10 = 160 cm³

Answer:

1/36

Step-by-step explanation:

Since Tess rolled 2 different dices, there are 36 different possibilities. Rolling two 4's is 1 of them.

Therefore, the probability of Tess rolling 2 fair dice is 1/36

Hope this helped have a great rest of your day!

Answer:

1 out of 36 chance because add what a dice equals to then divide

Answer:

Difference between average day temperature and average night temperature = 70°

Step-by-step explanation:

Given;

Average day temperature = 43° C

Average night temperature = -30° C

Find:

Difference between average day temperature and average night temperature

Computation:

Difference between average day temperature and average night temperature = Average day temperature - Average night temperature

Difference between average day temperature and average night temperature = 43 - (-30)

Difference between average day temperature and average night temperature = 70°

Answer:

desculpa mas não sei essa

Answer:

3 by 2

Step-by-step explanation:

3+2+3+2=10

3*2=6

Hope this Helps!!!

1.f(0) = 6

2.f(4)=5

3.f(-3)=-5

4. V(r) represent volume of basketball when radius is r

5.f(9) =5

Answer:

Step-by-step explanation:

1.

[In the attachment]

2.

again taking 4 as x and 5 as y.

since,

y = f(x)

5 = f(4)

that is option 3.

3.

x = -3

y = -5

y = f(x) = -5

f(-3) = -5

1st option

4.

V(r) = 4/3 pi r³

here the ou.tput is V(r) when the input is r.

and since V(r) denotes volume of air inside the basketball

V(r) is the volume of basketball when the radius is r.

that is option 2.

5.

given that:-

x = 9, f(x) = 5

•°• f(9) = 5

that is the 1st option

Answer:

A

Step-by-step explanation:

We have the equation:

[tex]\displaystyle \frac{3}{8}y=2+x[/tex]

And we want to determine whether or not this represents a direct proportion.

First, let's solve for y. Multiply both sides by 8/3:

[tex]\displaystyle y=\frac{16}{3}+\frac{8}{3}x[/tex]

Remember that direct proportions must pass through the origin point on a graph. In other words, their y-intercept or constant value is zero.

Since the constant value here is not zero (it is 16/3), the equation is not direct proportion.

Our answer is A.

Answer:

29 av

Step-by-step explanation:

Answer:

The answer is 3x-y-2=0

Step-by-step explanation:

Answer:

2nd option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate the slope using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (2, 4) ← 2 points on the line

m = [tex]\frac{4-1}{2-1}[/tex] = 3

The line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = 3x - 2 ← in slope- intercept form

subtract y from both sides

0 = 3x - y - 2 , that is

3x - y - 2 = 0 ← in general form

Answer:

Step-by-step explanation:

[tex]\sqrt[5]{(3y)^{4}} = [(3y)^{4}]^{\frac{1}{5}}=(3y)^{4*\frac{1}{5}}=(3y)^{\frac{4}{5}}[/tex]

Answer:

well your answer should be "F"

Step-by-step explanation:

we have

Y<-2x+10  -----> inequality A

The solution of the inequality A is the shaded area below the dashed line

Y = -2x+10

The y-intercept of the dashed line is (0,10)

The x-intercept of the dashed line is (5,0)

Y<1/2x-2 ----> inequality B  

The solution of the inequality B is the shaded area below the dashed line

Y= 1/2x-2

The y-intercept of the dashed line is (0,-2)

The x-intercept of the dashed line is (4,0)

The solution of the system of inequalities is the shaded area between the two dashed lines

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution

therefore

The solution are the points

E, F and G

i hope this helps

Answer:

-1 Not in domain

0 In domain

1 In domain

Step-by-step explanation:

The domain for the square root function is all positive numbers including (0). The domain is the set of real numbers which when substituted into the function will produce a real result. While one can substitute a negative number into the square root function and get a result, however, the result will be imaginary. Therefore, the domain for the square root function is all positive numbers. It can simply be expressed with the following inequality:

[tex]x\geq0[/tex]

Therefore, one can state the following about the given numbers. Evaluate if the number is greater than or equal to zero, if it is, then it is a part of the domain;

-1 => less than zero; Not in domain

0 => equal to zero; In domain

1  => greater than zero: In domain

Answer:

-1.540

Step-by-step explanation:

H0 : μ = 18

H0 : μ ≠ 18

The sample size, n = 48

Sample mean, xbar = 17

Sample standard deviation, s = 4.5

α = 0.05

The test statistic :

(xbar - μ) ÷ (s/√(n))

(17 - 18) ÷ (4.5 / √48))

-1 ÷ 0.6495190

= -1.5396

= -1.540 (3 decimal places ).

Answer:

7 and 13

Step-by-step explanation:

let the 2 numbers be x and y , x > y , then

x = y + 6 → (1)

[tex]\frac{1}{4}[/tex] (x + y) = y - 2 ( multiply both sides by 4 to clear the fraction )

x + y = 4y - 8 ( subtract 4y from both sides )

x - 3y = - 8 → (2)

Substitute x = y + 6 into (2)

y + 6 - 3y = - 8

- 2y + 6 = - 8 ( subtract 6 from both sides )

- 2y = - 14 ( divide both sides by - 2 )

y = 7

Substitute y = 7 into (1)

x = 7 + 6 = 13

The 2 numbers are 7 and 13

Answer:

150 + (.05x) = 355

.05x = 205

x = $4100

Step-by-step explanation:

Subtract to find amount of commission made:

355 - 150 = 205

She made $205 in commissions

Divide the amount she made in commission by the percentage she gets:

205 / 0.05 = 4,100

Her sales was $4,100

Answer:

x > 4

Step-by-step explanation:

4x + 3 > 19

4x + 3 - 3 > 19 - 3

4x > 16

4x/4 > 16/4

x > 4

Hope this helps.

[tex]4x + 3 > 19 \\ = > 4x > 19 - 3 \\ = > 4x > 16 \\ = > x > \frac{16}{4} \\ = > x > 4[/tex]

Answer:

x > 4

Hope you could understand.

If you have any query, feel free to ask.

[tex]\large\boxed{ \sf{Answer}} [/tex]

[tex]4x - ( - 2) = 18 \\ 4x + 2 = 18 \\ 4x = 18 - 2 \\ 4x = 16 \\ x = \frac{16}{4} \\ x = 4[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Step-by-step explanation:

4x-1-2=18

4x+2=18

4x=18-2

4x=16

x=16/4

x=4

Answer:

300 seconds

Step-by-step explanation:

The first dog run at v₁ = 15 m/sec     the second one run at  v₂ = 12 m/sec

we know that  d = v*t  then  t  =  d/v

Then the first dog will take  300/ 12  =  25 seconds to make a turn

The second will take   300 / 15   =   20 seconds to make a turn

Then the first dog in 12 turns 12*25 will be at the start point, and so will the second one at the turn 15.

To check  first dog    12 *  25 = 300

And the second dog 15 * 20 = 300

That means that time required for the two dogs to be at the start point together is

300 seconds, in that time the first dog finished the 12 turns, and the second had ended the 15.

Another procedure to solve this problem is as follows:

between  12  m/sec and  15 m/sec   the minimum common multiple  is 300 ( 300 is the smaller number that accept 12 and 15 as factors         12*15 = 300) Then when time arrives at 300 seconds the two dogs will be again in the starting point

Answer:

Dominio de una Raíz cuadrada

Cuando tenemos una raíz, para estudiar su existencia debemos saber que una raíz existe si y solo sí el radicando (lo que está dentro de la raíz) sea mayor o igual a cero.

Por lo tanto deberemos estudiar el signo de lo que se encuentra dentro de la raíz; y determinar las zonas positivas y las raíces que son las zona de existencia de la función raíz o dominio de esta función.

Step-by-step explanation:

qsy

Answer:

A

Step-by-step explanation:

The domain is all real numbers and the range is all real numbers greater than zero

The domain is {x| all real numbers} and the range is {y| y > 0}

The domain of a function is the set of inputs that we can use in the function. To find it, we initially assume that it is the set of all real numbers, and then remove the problematic values of x.

For example, a problematic point would be a value of x that causes the denominator to be equal to zero.

In this particular case, we can see that the variable is in the exponent, thus it can take any real value and it will not cause any problem, so the domain is the set of all real numbers.

The range is the set of possible outputs. Because in this case, the base is a positive number, the outcomes will only be positive, then the range is given by:

y > 0.

So the correct option is A.

If you want to learn more about range and domain, you can read:

https://brainly.com/question/1770447