A polynomial function can be written as (x - 1)(x - 4)(x + 7). What are the x-intercepts of the graph of this function?
a.(1,0). (4,0), (7,0)
b.(-1,0).(-4,0), (-7,0)
c.(1,0), (4,0), (-7,0)
d.(-1,0), (-4,0), (7,0)​

Answer:

(-1,-2)

Step-by-step explanation:

y=ax^2+bx+c

Find -b/(2a) and you will have found the x-coordinate of the vertex of this parabola.

You can find the y-coordinate that corresponds to it by plugging in your into the original equation.

-b/(2a)=-6/(2*3)=-6/6=-1

Now replace x with -1

3(-1)^2+6(-1)+1

3-6+1

-3+1

-2

So the vertex is (-1,-2)

Answer:

16

Step-by-step explanation:

6+8+10+20=44+16= 60 divided by 5 is 12

Answer:

[tex]8,101\ bears[/tex]

Step-by-step explanation:

we know that

In this problem we have a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

x ----> is the number of years since 2009

y ----> is the population of bears

a ----> is the initial value

b ---> is the base

step 1

Find the value of a

For x=0 (year 2009)

y=1,570 bears

substitute

[tex]1.570=a(b)^{0}[/tex]

[tex]a=1.570\ bears[/tex]

so

[tex]y=1.570(b)^{x}[/tex]

step 2

Find the value of b

For x=1 (year 2010)

y=1,884 bears

substitute

[tex]1,884=1.570(b)^{1}[/tex]

[tex]b=1,884/1.570[/tex]

[tex]b=1.2[/tex]

The exponential function is equal to

[tex]y=1.570(1.2)^{x}[/tex]

step 3

How many bears will there be in 2018?

2018-2009=9 years

so

For x=9 years

substitute in the equation

[tex]y=1.570(1.2)^{9}[/tex]

[tex]y=8,101\ bears[/tex]

Answer:

Step-by-step explanation:

Question 15

1 / 1 pts

In 2009, there were 1570 bears in a wildlife refuge.  In 2010, the population had increased to approximately 1884 bears.  If this trend continues and the bear population is increasing exponentially, how many bears will there be in 2018?

ANSWER = 8,101 GOT IT RIGHT ON TEST

Answer:

156.429

Step-by-step explanation:

52.1428571 in one year x 3

Answer:

156 square inches

Step-by-step explanation:

We are given the two quantities

Let

length = l = 13 inches

and

Width = w = 12 inches

The formula for the area of rectangle is:

[tex]Area=l*w[/tex]

where l is length and w is width

Putting the values of both that are given

[tex]Area = 13*12\\=156[/tex]

so the area is 156 square inches ..

Answer:

5852 deer.

Step-by-step explanation:

That would be 11 * 532

= 5852 (answer).

Answer:

There are 5852 deer live in the county.

Step-by-step explanation:

The population density of deer in the county is 11 deer per square mile.

That means, there are 11 deer in 1 square mile in that county.

Given that, the total area of that county is 532 square miles.

For getting the total number of deer, we just need to multiply the 'population density' by the 'total area'.

So, the total number of deer [tex]=(11\times 532)= 5852[/tex]

Answer:

172.5 mg/dl

Step-by-step explanation:

Given the equation y= -2.5x + 222.5, where 'x' is the time spent exercising in minutes. If we want to know the amount of cholesteron for a person exercising 20 minutes a day, we just have to subtitute 20 into the equation for x.

So we have: y= -2x + 222.5 → y= -2.5(20 minutes) + 222.5 = 172.5 mg/dl

Answer:

172.5

Step-by-step explanation:

Confirmed on test

For this case we must solve the following equation:

[tex]-3 (h + 5) + 2 = 4 (h + 2) -9[/tex]

We apply distributive property to the terms of parentheses:

[tex]-3h-15 + 2 = 4h + 8-9[/tex]

We add similar terms:

[tex]-3h-13 = 4h-1[/tex]

We add 13 to both sides of the equation:

[tex]-3h = 4h-1 + 13\\-3h = 4h + 12[/tex]

Subtracting 4h on both sides of the equation:

[tex]-3h-4h = 12\\-7h = 12\\h = - \frac {12} {7}[/tex]

ANswer:

[tex]h = - \frac {12} {7}[/tex]

Answer:

[tex]h=-\frac{12}{7}[/tex]

Step-by-step explanation:

To solve the equation for h follow the next steps

[tex]-3(h+5)+2=4(h+2)-9[/tex]

Subtract 4(h+2) on both sides of the equality

[tex]-3(h+5)+2-4(h+2)=4(h+2)-4(h+2)-9[/tex]

[tex]-3(h+5)+2-4(h+2)=-9[/tex]

Subtract 2 on both sides of the equality

[tex]-3(h+5)+2-4(h+2)-2=-9-2[/tex]

[tex]-3(h+5)-4(h+2)=-11[/tex]

Apply the distributive property

[tex]-3h-15 -4h-8=-11[/tex]

[tex]-7h-15 -8=-11[/tex]

[tex]-7h-23=-11[/tex]

Sum 23 on both sides of equality

[tex]-7h-23+23=-11+23[/tex]

[tex]-7h=12[/tex]

Divide by -7 on both sides of the inequality

[tex]\frac{-7}{-7}h=-\frac{12}{7}[/tex]

[tex]h=-\frac{12}{7}[/tex]

Remember:

SOH-CAH-TOA

(Sine = [tex]\frac{opposite}{hypotenuse}[/tex] - Cos = [tex]\frac{adjacent}{hypotenuse}[/tex] - tan = [tex]\frac{opposite}{adjacent}[/tex])

For angle H the sin ratio is...

side FG (5) is opposite angle H

side HF (13) is the hypotenuse

so...

sinH = [tex]\frac{5}{13}[/tex]

For angle F the sin ratio is...

side HG (12) is opposite angle F

side HF (13) is the hypotenuse

so...

sinF = [tex]\frac{12}{13}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Part a) The elevation of the road is [tex]6\°[/tex]

Part b) The rise is [tex]0.2\ km[/tex]

Step-by-step explanation:

Part a) What is the elevation of the road to the nearest degree?

Let

y-----> the rise of the road ( vertical distance)

x ----> the run of the road (horizontal distance)

we have

y/x=1/10

we know that

The ratio y/x is equal to the tangent of the angle of the elevation of the road

Let

[tex]\theta[/tex] ---->  angle of the elevation of the road

[tex]tan(\theta)=y/x[/tex]

[tex]tan(\theta)=1/10[/tex]

[tex]\theta=arctan(1/10)=6\°[/tex]

Part b)  If the road is two km long, how much does it rise?

using proportion

[tex]1/10=y/2[/tex]

[tex]y=2/10=0.2\ km[/tex]

Answer:

(- 4, - 10 )

Step-by-step explanation:

Given the 2 equations

y = x - 6 → (1)

x = - 4 → (2)

Substitute x = - 4 into (1) for corresponding value of y

y = - 4 - 6 = - 10

Solution is (- 4, - 10 )

Answer:

the answer is b (-4,-8)

Step-by-step explanation:

i got it right top one is wrong

Answer:36

Step-by-step explanation:

The given parameters include;

The time to complete each trip is calculated as;

distance =[tex]speed $\times$ time[/tex]

forward distance = backward distance

[tex]&20 x=16 x+6 \\[/tex]

[tex]&20 x-16 x=6 \\[/tex]

[tex]&4 x=6 \\[/tex]

[tex]&x=\frac{6}{4} \\[/tex]

[tex]&x=1.5 h r[/tex]

The total time of the motion for the entire trip exists calculated as follows;

Time = time for forward + time for backward

[tex]\text { time } &=1.5 \mathrm{hr} r_{\text {forward }}+1.5 \mathrm{hr} \text { backward }+\frac{6 \mathrm{mi}}{16 \mathrm{mi} / \mathrm{hr}} \text { backward } \\[/tex]

time [tex]&=2(1.5) \mathrm{hr}+0.375 \mathrm{hr} \\[/tex]

time[tex]&=3.375 \mathrm{hr}[/tex]

The time for the entire trip is 3.375 hours.

The total distance of the trip exists calculated as follows;

total distance = forward distance + backward distance total distance [tex]$=20 \times 1.5+16 \times 1.5+6$[/tex] miles

Total distance =60 miles

Therefore, the total distance of the trip is 60 miles.

To learn more about The total distance of the trip refer to:

https://brainly.com/question/1788514

#SPJ2

Answer:

[tex]H'(-3,-18)\\\\J'(3,-9)\\\\K'(-15,-3)\\\\L'(15,-15)[/tex]

Step-by-step explanation:

We know the coordinates of the polygon HJKL:

H(-1,-6), J(1,-3), K(-5,-1), and L(5,-5)

We know that the polygon HJKL is dilated using the scale factor 3. This means that, to find the coordinates of the vertices of polygon H'J'K'L', we need to multiply the x-coordinate and the y-coordinate of each vertex by this scale factor.

Then:

[tex]H'=(-1(3),-6(3))=(-3,-18)\\\\J'=(1(3),-3(3))=(3,-9)\\\\K'=(-5(3),-1(3))=(-15,-3)\\\\L'=(5(3),-5(3))=(15,-15)[/tex]

Konichiwa~! My name is Zalgo and I am here to help you out on this amazing day. I believe the answer that you would be looking for is (x-1)  (6x-1).

I hope that this answer helps! :3

"Stay Brainly and stay proud!" - Zalgo

(By the way, do you mind marking me as Brainliest? I'd greatly appreciate it! Arigato~! XP)

Answer: [tex]x=-5\\y=-7[/tex]

Step-by-step explanation:

Given the system of equations:

[tex]\left \{ {{y=\frac{4}{5}x-3 } \atop {y=-7}} \right.[/tex]

You can apply the Substitution method.

You need to substitute the second equation which gives the value of the variable "y" into the first equation and solve for the variable "x", then:

[tex]y=\frac{4}{5}x-3\\\\-7=\frac{4}{5}x-3\\\\-7+3=\frac{4}{5}x\\\\-4=\frac{4}{5}x\\\\(-4)(5)=4x\\\\x=\frac{-20}{4}\\\\x=-5[/tex]

Answer:

True depending on what you are comparing it to.

Step-by-step explanation:

A pulley would help lighten the load that you are trying to pull up, which may make it easier for you to get the load to your designated area. The more complicated it is, usually the more 'lighter' it becomes, or the less force you have to exert.

For example, you will have to give a 100% energy in trying to life a heavy box. However, if you use a simple pulley (only one), you may only have to exert 75% more energy, for the weight is significantly lower.

~

Answer:

[tex]\frac{sin B}{b} = \frac{sin A}{a}[/tex] should be used to find b.

Step-by-step explanation:

We are given that in a triangle ABC, ∠A = 35°, ∠B = 40° and side a = 9 and we are to find the side length b.

Now using sine rule to find b:

[tex]\frac{sin B}{b} = \frac{sin A}{a}[/tex]

[tex]\frac{sin 40}{b} = \frac{sin 35}{9}[/tex]

[tex]b=\frac{sin 40 \times 9}{sin 35}[/tex]

b = 10.1

Answer:

The equation is 9/sin(35) = b/sin(40) , The length of b = 10.086

Step-by-step explanation:

* Lets explain how to solve the triangle

- In ΔABC

- a, b, c are the lengths of its 3 sides, where

# a is opposite to angle A

# b is opposite to angle B

# c is opposite to angle C

- m∠A = 35°  

- m∠B = 40°  

- a = 9  ⇒ the side opposite to angle A

* To solve the triangle we can use the sin Rule

- In any triangle the ratio between the length of each side  

 to the measure of each opposite angle are equal

- a/sinA = b/sinB = c/sinC

∴ The equation which used to find b is a/sinA = b/sinB  

∵ a = 9 , m∠A = 35° , m∠B = 40°

∴ 9/sin(35) = b/sin(40) ⇒ by using cross multiplication

∴ b = 9 × sin(40) ÷ sin(35) = 10.086

* The length of b = 10.086

Answer:

(x+7) is not a factor

Step-by-step explanation:

we know that

If (x+7) is a factor of f(x)

then

For [tex]x=-7, f(-7)=0[/tex]

Verify

we have

[tex]f(x)=x^{3}-3x^{2} +2x-8[/tex]

Substitute x=-7

[tex]f(-7)=(-7)^{3}-3(-7)^{2} +2(-7)-8[/tex]

[tex]f(-7)=-343-147 -14-8[/tex]

[tex]f(-7)=--512[/tex]

[tex]-512\neq 0[/tex]

therefore

(x+7) is not a factor

Answer:

6 units

Step-by-step explanation:

We require to calculate the absolute value so as to consider the measure both ways, that is

AB = | 1 - (- 5) | = | 1 + 5 | = 6

BA = | - 5 - 1 | = | - 6 | = 6

Answer:

Step-by-step explanation:

-5x+31+3x=3

move everthing to one side

-5+31+3x-3=0

add and subtract common terms

-2x+28=0

divide across by common denominator

-x+14=0

Solve for x

x=14

Answer:

Factor out a -1 from one of the terms so they are the same

Step-by-step explanation:

15x^2 – 3x – 20x + 4

(15x2 – 3x) + (–20x + 4)

3x(5x – 1) + 4(–5x + 1)

Talia should notice that the terms in the parentheses are opposites of each other and factor out a -1 out of the second term

3x(5x-1) +4 (-1) (5x-1)

Now the terms have a common factor

(5x-1) (3x+(-1)4)

(5x-1) (3x-4)

Answer:

Talia needs to factor out a negative from one of the groups so the binomials will be the same.

Step-by-step explanation:

[tex]15x^2 - 3x - 20x + 4[/tex]

Group first two terms and last two terms to factor it

[tex](15x^2 - 3x)+(- 20x + 4)[/tex]

Now we factor out GCF

GCF of 15x^2-3x is 3x

GCF of -20x+4 is -4 because first term should be positive

[tex](15x^2 - 3x)+(- 20x + 4)[/tex]

[tex]3x(5x- 1)-4(5x-1)[/tex]

Talia needs to factor out negative so that the binomials will be same (5x-1)

Answer:

The division was completed in the wrong order

Step-by-step explanation:

To convert [tex]\frac{5}{8}[/tex] to a percent

The numerator is divided by the denominator, that is

    0.625

8 | 5.0

Multiply 0.625 × 100% = 62.5%

Answer:

The number is 25

Step-by-step explanation:

we have

[tex]x^{2} -10x=7[/tex]

we know that

[tex]10/2=5[/tex]

so

Adds [tex]5^{2}[/tex] both sides

[tex]x^{2} -10x+5^{2}=7+5^{2}[/tex]

[tex]x^{2} -10x+25=7+25[/tex]

[tex]x^{2} -10x+25=32[/tex]

Rewrite as perfect squares

[tex](x-5)^{2}=32[/tex]

Answer:

8x+16

Step-by-step explanation:

For this case we have that a quadratic equation is of the form:[tex]ax ^ 2 + bx + c = 0[/tex]

Where:

a: is the main coefficient because it accompanies the quadratic variable.

b: It is the linear coefficient

c: It is the constant term.

Then, a quadratic function with a main coefficient of "3" and a constant term of "-12" is:

[tex]f (x) = 3x ^ 2 + 11x-12[/tex]

Answer:

Option B

[tex]f (x) = 3x ^ 2 + 11x-12[/tex]

Answer:

It is B. f(x) = 3x2 + 11x – 12

Step-by-step explanation:

If this question is on Edg, then it is B, & B is Correct.

Answer:

The distance between both points would be 14.

Step-by-step explanation:

The y coordinate or -8 stays the same for both points on a coordinate grid. However the x coordinate changes from -4 to 10, which is 14 places away on a coordinate grid. Therefore the distance between these two points is 14.

Answer:

14

Step-by-step explanation:

Use the distance equation:

d² = (x₂ − x₁)² + (y₂ − y₁)²

d² = (10 − -4)² + (-8 − -8)²

d² = 14² + 0²

d = 14

Answer:

A.

Only function g is even

Option: A is the correct answer.

  A.   Only function g is even.

Here by looking at the graph we observe that the graph of function g satisfies the condition of even function.

( whereas the graph of function f is not symmetric about the y-axis and hence function f is not even )

     Hence,  the function g is an even function.

Answer:

4 hours at 8 miles an hour: 8(4) = 32 miles in total

8 hours at 2 miles an hour: 2(8) = 16 miles in total

Miles in total: 32 + 16 = 48

The answer is A. 48 miles

Answer: 48

Step-by-step explanation:

8 (MPH) x 4 (H) = 32 miles covered in 8 hours.

2(MPH) x 8 (H) = 16 miles covered in 8 hours.

32 + 16 = 48 MPH

Answer:

Step-by-step explanation:

We have:

two squares 10ft × 10ft

three rectangles 14ft × 10ft

two rectangles 9ft × 14ft

two triangles with base 10ft and height 8ft

The formula of an area of a reactangle l × w  (square s × s) :

[tex]A=lw\qquad(s^2)[/tex]

Substitute:

[tex]A_1=10^2=100\ ft^2\\\\A_2=(14)(10)=140\ ft^2\\\\A_3=(9)(14)=126\ ft^2[/tex]

The formula of an area of a triangle:

[tex]A=\dfrac{(base)(height)}{2}[/tex]

Substitute:

[tex]A_4=\dfrac{(10)(8)}{2}=40\ ft^2[/tex]

The Surface Area:

[tex]SA=2A_1+3A_2+2A_3+2A_4[/tex]

Substitute:

[tex]SA=(2)(100)+(3)(140)+(2)(126)+(2)(40)=952\ ft^2[/tex]

Answer: A is correct (x+2)/(x-1)

Step-by-step explanation:

Divide the top and bottom by 2, to simplify

[2(x^2+x-2)]/[2(x^2+2x+1)]

The 2's cancel each other out, since 2/2 would be 1.

Now factor (x^2+x-2)/(x^2+2x+1)

[(x+2)(x-1)]/[(x-1)(x-1)]

Now you can cancel out one of the (x-1) on top and bottom. All that's left is (x+2)/(x-1) which is your answer. Hope this helps!