If a polynomial function f(x) has roots –9 and 7 – i, what must be a factor of f(x)? (x – (7 i)) (x – (–7 – i)) (x (7 i)) (x (7 – i))

The velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s

Velocity is defined as the ratio of the distance moved by the object in a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.  

Here we have a displacement function:-

F(t)=3t⁴-5t³+6t-7

So to find out the velocity we will differentiate the above equation with respect to t.

d(F(t)/dt=12t³-15t²+6

V=12t³-15t²+6

Put the value of t=2 seconds

V=12x(2x2x2)-15x(2x2)+6

V=42 meters per second

Hence the velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s

To know more about Velocity follow

https://brainly.com/question/25749514

#SPJ1

Answer:

y ≤ 45

Step-by-step explanation:

First y must be less than or equal to 45.

y ≤ 45 x + y  ≤  80

And total number of reservations cannot exceed 80:

x + y  ≤  80.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It will take 308 months for Diego to pay the complete loan.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = P×T×R

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

The interest that will be charged on the principal amount is,

SI = $159,000×30×0.0505 = 240,885

Now, the total amount that Diego needs to pay is the sum of interest and principal, therefore,

Total amount = $159,000 + $240,885 = $399,885

Further, since each month Diego is paying $1300, therefore, the number of months it will take to pay the complete loan is,

Number of months = $399,885/$1300 = 307.6 ≈ 308

Hence, it will take 308 months for Diego to pay the complete loan.

Learn more about Simple Interest:

https://brainly.com/question/2793278

#SPJ1

Answer:

106º

Step-by-step explanation:

Because both the base angles are 74º. The known angles so far are 148º.

The top angles also have to be equal as they are on parallel lines so:

360 - 148 = 212º

212 / 2 = 106º

Answer:

x = 106 degrees

Step-by-step explanation:

74 plus 74 = 148

360 is the interior angle sum of all trapezoids

360-148=212

212 is the sum of both x and y

x and y are the same measure.

212/2 = 106

Answer:

the answer is reflected over both axes hope this helped

The value of the np is 10, and the value of the nq is 40 which is less than 5 also the hypothesis H0: p = 0.20 versus H1: p<0.20

The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.

We have:

n = 50

p = 20% = 0.02

q = 1-p = 1- 0.02 = 0.08

[tex]\rm n_p = 50 \times 0.20 = 10\\\\\rm n_q = 50\times 0.80 = 40[/tex]

[tex]\rm n_q > 5\\\\\rm n_p > 5[/tex]

The conditions are verified for this test.

Null hypothesis H0: The number of ships arriving in ports with hazardous cargoes has remained constant.

Alternative hypothesis H1:  The number of ships arriving in port with polluted goods has dropped.

H0: p = 0.20 versus H1: p<0.20

Thus, the value of the np is 10, and the value of the nq is 40 which is less than 5 also the hypothesis H0: p = 0.20 versus H1: p<0.20

Learn more about the null hypothesis and alternative hypothesis here:

brainly.com/question/27335001

#SPJ1

6 full teams will be made.

If you take 62 and divide it by 9, you'll get a value of 6.88... or it can also be notated as 6 remainder 8. You will be able to make 6 full teams but your last team will only have 8 members, which does not have the full 9 members.

Step-by-step explanation:

Rearrange the equations to solve.

cos(-3 • pi) = -1

cos((-3pi) / 4 radians) = -0.707

cos(5 • pi) = -1

cos((5pi) / 4 radians) = -0.707

They are the same because when multiplied, they are the same value, and always will be that way. They also have the same identity if you simplify and compare the results of that equation.

The value of cos (-3π/4) and the value of cos (5π/4) are same.

Trigonometric ratios are the ratios which is described for two sides of a right angled triangle.

The main three trigonometric ratios are sine, cosine and tangent functions.

We know that,

cos (-3π/4) = cos (3π/4)

Now,

cos (3π/4) = cos (π + π/4)

And,

cos (5π/4) = cos (π - π/4)

Now, we know that,

cos (π + x) = -cos (x) and cos (π - x) = -cos (x)

So the value of cos (π + π/4) = -cos( π/4) and cos (π - π/4) = -cos( π/4)

Hence cos (3π/4) = cos (5π/4) = -cos( π/4)

Hence both the values are same.

Learn more about Cosine Functions here :

https://brainly.com/question/17954123

#SPJ2

Answer: the area of the X???

Step-by-step explanation:

the slope is 1/4

because it goes across by 4 and up by 1

Answer:

See the attached graph

Step-by-step explanation:

The solution is the labelled point of intersection in the graph

Answer:

To find the surface area of a rectangular prism, measure the length, width, and height of the prism. Find the area of the top and bottom faces by multiplying the length and width of the prism. Then, calculate the area of the left and right faces by multiplying the width and height.

The correct answer is thermoelectric generator because it transfers heat to electricity directly or converts electrical energy to thermal power for heating or cooling.

Thermoelectric generators are semiconductor solid-state devices that convert a temperature difference and heat flow into a usable DC power source.

The Seebeck effect is used to create voltage in thermoelectric generator semiconductor devices. This voltage is used to drive electrical current and generate usable power at a load.

From the statement given, it is a thermoelectric generator because a thermoelectric power generator transfers heat to electricity directly or converts electrical energy to thermal power for heating or cooling.

Thus, the correct answer is thermoelectric generator because it transfers heat to electricity directly or converts electrical energy to thermal power for heating or cooling.

Learn more about the thermoelectric generator here:

https://brainly.com/question/2289126

#SPJ1

The scale factor of the dilation of triangle def is three-tenths i.e. 3/10

From the complete question, the corresponding sides are:

DE = 10

D'E' = 3

The scale factor k is then calculated using"

DE * k = D'E'

So, we have:

10* k = 3

Divide both sides by 10

k = 3/10

Hence, the scale factor of the dilation of triangle def is three-tenths i.e. 3/10

Read more about dilation at:

https://brainly.com/question/3457976

#SPJ4

Answer: 3/10

Step-by-step explanation:

Answer:

729

Step-by-step explanation:

Answer: x = 0, x = -3, x = 2

Step-by-step explanation:

f(x) = x^3 + x^2 - 6x

f(x) = 0

x^3 + x^2 - 6x = 0

x(x^2 + x - 6) = 0

x = 0 or

x^2 + x - 6 = 0

D = b^2 - 4ac = 1 - 4*(-6) = 25

x = (-b - sqrt(D))/(2a) = (-1 - 5)/2 = -3 or

x = (-b + sqrt(D))/(2a) = (-1 + 5)/2 = 2

Answer:

  (x +4)² +(y -9)² = 121

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

__

We are given that (h, k) = (-4, 9) and r = 11. When we put these values into the equation, it becomes ...

  (x -(-4))² +(y -9)² = 11²

We can simplify this a bit to ...

  (x +4)² +(y -9)² = 121

Answer:

20%

Step-by-step explanation:

Given/To Find:

A $52.50 screen door is on

sale for $42. Find the percent

of discount on the door.

Solve:

Formula: Value 1 - Value 2 ÷ Original Value × 100

Hence we have:

52.50 - 42 = 10.5

10.5 ÷ 52.50 = 0.20

0.20 × 100

=20%

Check Answer:

52.50 × 20% = 10.5

52.50 - 10.5 = 42

Hence, the percent of discount on the door is 20%

Kavinsky

Answer:

3/10

Step-by-step explanation:

The probability of drawing a blue card first is 3/5 (3 blue cards out of a total of 5 cards). Then the probability of drawing a blue card again will be 2/4 (the blue card you drew first is removed so there are only 2 blue cards and 4 total cards). Now we multiply the probabilities together to get the probability of drawing a blue card, not replacing it, and then drawing another blue card = (3/5)(2/4) = 6/20 = 3/10.

Hope this helps! :)

Answer:

Step-by-step explanation:

Answer:

x = 9

y = 116

Step-by-step explanation:

116 and y are vertically opposite angles.

Vertically opposite angles are equal.

So,

y = 116

116 and ( 13x - 53 ) are linear pair angles.

Sum of linear pair angles is 180,

13x - 53 + 116 = 180

13x + 63 = 180

Subtract 63 on both sides,

13x = 180 - 63

13x = 117

Divide 13 on both the sides,

x = 117 / 13

x = 9

Answer:

72 is the closest.The printer will primt 80 pages in one minute

Answer:

72

Step-by-step explanation:

12 pgs in 9 sec

*[tex]\frac{20}{3}[/tex]             *[tex]\frac{20}{3}[/tex]

≈80 pgs in 60 sec

Hope this helps!!!

Please mark me as brainliest!!!

761680

[tex]\sf \boxed{\sum _{n=1}^{44}\:60\left(1.2\right)^{n-2}}[/tex]

Identify the following's:

First Term [a]  =  60(1.2)ⁿ⁻² = 60(1.2)¹⁻² = 50

Common ratio [r]  =  1.2

Total Terms [n] =  44

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

[tex]\sf Geometric \ Sum \ of \ Terms = \dfrac{a(r^n - 1)}{r-1}[/tex]

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

Solving Steps:

[tex]\rightarrow \sf \dfrac{a(r^n - 1)}{r-1}[/tex]

[tex]\rightarrow \sf \dfrac{50(1.2^{44} - 1)}{1.2-1}[/tex]

[tex]\rightarrow \sf 761679.5808[/tex]

[tex]\rightarrow \sf 761680 \ \ \ (rounded \ to \ nearest \ integer)[/tex]

Answer:

The range of the function given in the graph is the values of all y for any input x.

Therefore, as shown in the graph the value of y for any input of x is below y = 1. Therefore, the range is y <= 1

A cylinder's volume is =

π r² h,

and its surface area is =

2π r h + 2π r².

Answer:

whats the question?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Emma has £37 in her bank account she starts putting £7 into her account each week write and solve an equation to find how many weeks it will take for emma to have £100 in her bank account r

(100 - 37) : 7 =

63 : 7 = 9

check

37 + 9 * 7 = 100

the answer is good

Answer:

hope this will help you ( ◜‿◝ )♡

Step-by-step explanation:

[tex]volume = \frac{4}{3} \times \pi {r}^{3} \\ = \frac{4}{3} \times 3.14 \times ( {10}^{3} ) \\ = 4186.666mm {}^{3} [/tex]

[tex]\large\boxed{\bold{Formula:V= \frac{4}{3}\pi{r}^{3}}}[/tex]

[tex]\large\boxed{\bold{\red\pi\red=\red3\red.\red1\red4}}[/tex]

In this question the radius is given so we'll simply have to substitute and solve.

Let's solve!

Instead of π we are asked to use 3.14

Substitute the values according to the formula.

[tex]V= \frac{4}{3}\times 3.14 \times {10}^{3}[/tex]

Calculator value:

[tex]\bold{V= 4186.666667 \: {mm}^{3}}[/tex]

Now, we have to round off to the nearest hundredth.

The value in the thousandths place is greater than 5 so we'll have to round up by adding 1 to the hundredths place.

Final answer:

[tex]\large\boxed{\bold{V= 4186.67 \: {mm}^{3}}}[/tex]

Hence, the volume of the given sphere is 4186.67 cubic millimeters.

For equation 1:

y intercept = (0, 1)

x intercept = (-0.5, 0)

For equation 2:

y intercept = (0, -1)

x intercept = (-1, 0)

Option B is correct

Answer:

Then numbers 7 , 8 , 14 , -6 , 10 are output values of the function