for the function f(x)=3(x-1)^2+2 identify the vertex, domain, and range.

Answer:

0

Step-by-step explanation:

The first equation is for when t = 8.

The second equation is for when t = 10.

The third equation is for all other values of t.

For t = 2, we use the third equation.

f(t) = t² − 3t + 2

f(2) = 2² − 3(2) + 2

f(2) = 4 − 6 + 2

f(2) = 0

Answer:

This has one real solution, x=4

Step-by-step explanation:

8 - 4x = 0

Add 4x to each side

8 - 4x+4x = 0+4x

8 =4x

Divide each side by 4

8/4 = 4x/4

2 =x

This has one real solution, x=4

Answer:

This equation has 1 real solution, x=2....

Step-by-step explanation:

8- 4x=0

Move 8 to the R.H.S

-4x=0-8

-4x=-8

Divide both sides by -4

-4x/-4 = -8/-4

x=2

Thus this equation has 1 real solution, x=2 ....

Answer:

x=1

Step-by-step explanation:

So we are talking about parabola functions.

All parabolas (even if they aren't functions) have their axis of symmetry going through their vertex.

For parabola functions, your axis of symmetry is x=a number.

The "a number" part will be the x-coordinate of the vertex.

The axis of symmetry is x=1.

Answer:

x=1

Step-by-step explanation:

The vertex of a parabola is the minimum or maximum of the parabola.

This is the line  where the parabola makes a mirror image.

Assuming the equation for the parabola is ( since this is a function)

y= a(x-h)^2 +k

where (h,k) is the vertex

Then x=h is the axis of symmetry

y = a(x-1)^2+5

when we substitute the vertex into the equation

The axis of symmetry is x=1

Answer:

Options A) and E)

Step-by-step explanation:

If you use Ruffini's method for polynomials, you can find the roots.

The given picture shows us the first root of the polynomial [tex]5x^{2}-16x+12=0[/tex] wich is 2.

Thus, the original polynomial can be written as

[tex](x-2)*(5x-6)=0[/tex]

Here, you can notice that (x-2) is a factor

Answer:

y + 4 = 5(x - 3)

Step-by-step explanation:

In the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are.

Answer:

D. The Equation is y - ( - 4 ) = 5 ( x - 3 )

Step-by-step explanation:

Got It right on Edg.

Answer:

[tex]5(4)^{x}[/tex]

That's the exponential function.

Step-by-step explanation:

Simply just use a graphing calculator (there's plenty of apps and websites that are graphing calculators) and follow these steps.

1) Clear out calculator RAM

2) Press STAT button

3) Press ENTER on EDIT

4) Type the X's in L1 and type the Y's L2.

5) Press STAT again

6) Press the RIGHT ARROW once

7) Press 0

8) Press ENTER

9) There's your exponential function!

To find the formula for the exponential function passing through given points (-3,5/64) and (2,80), we assume the function to be y=ab^x, substitute both points into the equation and solve it for a and b. This will provide the desired formula.

To find the formula for the exponential function through given points (-3,5/64) and (2,80), we firstly assume the function to be of the form y=ab^x. After that, we substitute the given points into this assumed equation, resulting in a system of two non-linear equations and solve it for the unknowns a and b.

Using our initial guess for the formula, substitute the first point (-3,5/64), we get: 5/64=a*b^-3

Substitute the second point (2,80) into the equation we get: 80=a*b^2

Solving these equations using substitution or elimination methods we will derive the appropriate values for a and b, which we can then substitute back into the y=ab^x to get the desired formula.

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For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

By definition, if two lines are perpendicular then the product of their slopes is -1.

We have the following line:

[tex]y = 2x-6[/tex]

Then[tex]m_ {1} = 2[/tex]

The slope of a perpendicular line will be:

[tex]m_ {1} * m_ {2} = - 1\\m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = - \frac {1} {2}[/tex]

Thus, the equation of the line will be:

[tex]y = - \frac {1} {2} x + b[/tex]

We substitute the given point and find "b":

[tex]-3 = - \frac {1} {2} (0) + b\\-3 = b[/tex]

Finally the equation is:

[tex]y = - \frac {1} {2} x-3[/tex]

Answer:

[tex]y = - \frac {1} {2} x-3[/tex]

Answer:

[tex]y=-\frac{1}{2}x -3[/tex]

Step-by-step explanation:

The slope-intercept form of the equation of a line has the following form:

[tex]y=mx + b[/tex]

Where m is the slope of the line and b is the intercept with the y axis

In this case we look for the equation of a line that is perpendicular to the line

[tex]y = 2x - 6[/tex].

By definition If we have the equation of a line of slope m then the slope of a perpendicular line will have a slope of [tex]-\frac{1}{m}[/tex]

In this case the slope of the line [tex]y = 2x - 6[/tex] is [tex]m=2[/tex]:

Then the slope of the line sought is: [tex]m=-\frac{1}{2}[/tex]

The intercept with the y axis is:

If we know a point [tex](x_1, y_1)[/tex] belonging to the searched line, then the constant b is:

[tex]b=y_1-mx_1[/tex] in this case the poin is: (0,-3)

Then:

[tex]b= -3 -(\frac{1}{2})(0)\\\\b=-3[/tex]

finally the equation of the line is:

[tex]y=-\frac{1}{2}x-3[/tex]

Answer:

x = 5

Step-by-step explanation:

Given

6 = 3x - 9 ( add 9 to both sides )

15 = 3x ( divide both sides by 3 )

5 = x

Answer:

x = 5

Step-by-step explanation:

6 = 3x - 9

If you add 9 to both sides 6 + 9 = 3x - 9 + 9. You would get the equation 15 = 3x because adding 9 to both sides cancels out the 9 on the right side of the equation. Then you would divide by 3 on both sides 15/3 = 3x/3 which would give you 5 = x your answer

If the table below shows values for x and y. If y varies directly as x, The constant of variation will be 4.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that, The value of y and x are,

y  12  24  36  48

x   3   6    9   12

Suppose k is the constant of proportionality,

Lineae equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

y=kx

k=12/3

k=4

Thus, if the table below shows values for x and y. If y varies directly as x, The constant of variation will be 4.

Learn more about the proportional here:

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Answer: Option A

[tex]x=\frac{3+i}{2}[/tex] or [tex]x=\frac{3-i}{2}[/tex]

Step-by-step explanation:

Use the quadratic formula to find the zeros of the function.

For a function of the form

[tex]ax ^ 2 + bx + c = 0[/tex]

The quadratic formula is:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

In this case the function is:

[tex]2x^2-6x+5=0[/tex]

So

[tex]a=2\\b=-6\\c=5[/tex]

Then using the quadratic formula we have that:

[tex]x=\frac{-(-6)\±\sqrt{(-6)^2-4(2)(5)}}{2(2)}[/tex]

[tex]x=\frac{6\±\sqrt{36-40}}{4}[/tex]

[tex]x=\frac{6\±\sqrt{-4}}{4}[/tex]

Remember that [tex]\sqrt{-1}=i[/tex]

[tex]x=\frac{6\±\sqrt{4}*\sqrt{-1}}{4}[/tex]

[tex]x=\frac{6\±\sqrt{4}i}{4}[/tex]

[tex]x=\frac{6\±2i}{4}[/tex]

[tex]x=\frac{3\±i}{2}[/tex]

[tex]x=\frac{3+i}{2}[/tex] or [tex]x=\frac{3-i}{2}[/tex]

Answer:

f(x) = 48(0.5)^n - 1 ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The number of alligators changes each week

∵ The number in week 1 is 28

∵ The number in week 2 is 24

∵ The number in week 3 is 12

∵ The number in week 4 is 6

∴ The number of alligators is halved each week

∴ The number of alligators each week = half the number of alligators

   of the previous week

- The number of alligators formed a geometric series in which the

  first term is 48 and the constant ratio is 1/2

∵ Any term in the geometric series is Un = a r^(n - 1), where a is the

  first term and r is the constant ratio

∴ f(n) = a r^(n - 1)

∵ a = 48 ⇒ The number of alligators in the first week

∵ r = 1/2 = 0.5

∴ f(x) = 48(0.5)^n - 1

the answer is f(x) = 48(0.5)^n - 1

Answer:

0

Step-by-step explanation:

0 would be the individual function because 0 is only one number so if you were to multiply 0x(x) then it would be 0x.

Answer:

4

Step-by-step explanation:

if we see the table as being a numerical representation of a graph in the x-y plane, the first column will represent the x-values (i.e the domain) and the second column will represent the y-values (i.e the range).

That is to say, the x-values are the inputs into the function that will spit out the y-values as outputs.

By observation, we can see that when x = 0 (i.e the initial value of the input), that the resulting function output is y =4 (i.e the initial value of the output).

Hence the initial value of the function (i.e the output) is 4

Answer:

The numbers of toys per hour is 60c/m toys

Step-by-step explanation:

* Lets explain how to solve the problem

- an algebraic expression is an expression formed from integer

 constants, variables, and the algebraic operations like addition,

  subtraction, multiplication, division

- Ex: 5x² − 7xy + a is an algebraic expression

* Lets solve the problem

- Kevin makes c toys in m minutes

∴ His rate is c/m toy per minute

- To find the number of toys in one hour multiply his rate by the time

  in minutes

∵ In one hour there are 60 minutes

∵ His rate = c/m (toy/minute)

∵ The time is 60 minutes

∴ The number of toys = c/m × 60 = 60c/m toys

∴ The numbers of toys per hour is 60c/m toys

Answer:

Hey, You have chosen the correct answer.

the correct answer is C.

12. 1.625 [terminating]; 13. 0.83 [bar notation over 3 (repeating)]; 14. 900 cm = 9 m; 15. 0.23 cm = 2.3 mm

Repeating decimals are parts of decimals that have repetitive digits; terminating decimals are decimals whose digits end.

Whether you are using Metric or Imperial, you have to determine whether you are going from a small unit to a big unit or vice versa. Then perform your operation. So, in exercise 14, the smaller unit is centimeters, so you would be going from big to small. Exercise 15 has you going from small to big.

There are centimeters in one meter, so multiply 9 by to get 900 centimeters.

There are 10 millimeters in one centimeter, so divide 2.3 by 10 simply by moving the decimal point ONCE to the left [Power of 10].

small to BIG → Division

BIG to small → Multiplication

I am joyous to assist you anytime.

The down payment is 25 percent of 57000. Taking 1/4 of 57000 gives 14250 dollars in down payment. Closing cost is just 2.8 percent. This costs 1596 dollars, so your answers are 14250 and 1596.

Hope this helps!

Answer: it goes down (decreases) steadily

Step-by-step explanation:

Answer:

It goes down/decreases in a steady way.

Answer:

= 8.33 inches

Step-by-step Explanation

First add 49 + 16, which equals 65, and subtract that result from 180, since a triangle equals 180 degrees and you find out angle C is equal to 115 degrees.

Now using the formula sinA/a = sinB/b = sinC/c, plug in values and you'd get the equation sin49 x 10/sin115. After solving the equation you'd get about  8.32729886047258 inches.

= 8.33

Answer:

13.2 units

Step-by-step explanation:

∠A = 16°

∠B = 49°

∠C = 180-(16+49)

∠C = 115°

a = 4

Now, from sine rule we get

[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]

[tex]\frac{sinA}{a}=\frac{sinC}{c}\\\Rightarrow \frac{sin16}{4}=\frac{sin115}{c}\\\Rightarrow c=\frac{sin115}{ \frac{sin16}{4}}\\\Rightarrow c=13.2[/tex]

∴ c is 13.2 units

Answer:

Um

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

note (f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 4x + 1 - (x² - 5) ← distribute by - 1

= 4x + 1 - x² + 5 ← collect like terms

= - x² + 4x + 6 ← in standard form → C

For this case we have the following functions:

[tex]f (x) = 4x + 1\\g (x) = x ^ 2-5[/tex]

We must find [tex](f-g) (x).[/tex] By definition we have to:

[tex](f-g) (x) = f (x) -g (x)[/tex]

So:

[tex](f-g) (x) = 4x + 1- (x ^ 2-5)[/tex]

We take into account that:

[tex]- * + = -\\- * - = +\\(f-g) (x) = 4x + 1-x ^ 2 + 5\\(f-g) (x) = - x ^ 2 + 4x + 6[/tex]

Answer:

[tex](f-g) (x) = - x ^ 2 + 4x + 6[/tex]

Option C

Answer:

Step-by-step explanation:

Look at the picture.

C. The hypotenuse is √2 ties as long as either leg

Answer:

-38z

Step by step explanation:

You’d Combine Like Terms:

- 10z + -28z

= (-10z + -28z)

= -38z

Answer:

Louisa needs 28 more pounds of dog food to reach 100 pounds

Step-by-step explanation:

=100 - 20.5 + 18.75 + 32.75

=28

Answer:

Louisa needs 28 pounds more of dog food.

Step-by-step explanation:

We need to find how much dog food she had collected in three weeks. In order to do this we need to add the number of pound collected in each week.

Notice that the pounds collected are given in different notations, so we need to write them ‘‘uniformly’’, in particular we must write the mixed number of the second week in decimal notation:

[tex]18\frac{3}{4} = \frac{18\times 4+3}{4}=\frac{75}{4} = 18.75[/tex]

Now, we add the three numbers:

[tex]20.5+18.75+32.75 = 72[/tex]

Finally, as she wants to collect 100 pounds and already has 72, Louisa only has to collect 28 pound more to complete her goal.

Answer:

Option 1: {-7,5,18,24,32}

Step-by-step explanation:

Observing the number line we can see that the solution is

x≤18 and x>22

So we will check the options one by one

For {-7,5,18,24,32}

The number set satisfies the solution translated from the number line.

For {-9,7,15,22,26}

As this number set includes 22 which is not included in the solution so this option is not correct.

For {16,17,22,23,24}

This number set also includes 22 so the option is not correct.

For {18,19,20,21,22}

This number set includes 19,20,21,22 which is not a part of the solution. Therefore, this option is also not correct ..

Answer:

The price for one student ticket is $8

Answer:

im say your answer is between 1 choice and last choice but I'm say last choice 2.2

Answer:

B. 1.6 yards

Step-by-step explanation:

For the given triangle ABC,

We have ∠BAC = 36° and ∠BCA = 28° and side BC = 2 yards

We have to find length of side labeled as c, so using the sine rule we can say

[tex]\frac{c}{sin28} = \frac{2}{sin36} \\\frac{c}{0.4694} = \frac{2}{0.5877}\\c = 3.4030*0.4694\\c = 1.59\\[/tex]

c is equal to 1.59 which is nearly equal to 1.6 yards so the correct option would be D.

1 meter = 1000 mm

so then 5 meters is just 5 * 1000 = 5000 mm.

Answer:

Satish will pay $64.8

Step-by-step explanation:

Kilometres when Satish is alone

150 kilometres in the beginning

150 kilometres in the end

Total: 300 kilometres

Kilometres when Satish is with friends

Total km: 2100

Satish Travelled alone: 300

Kilometres when Satish is with friends: 2100-300 = 1800 km

Litres of gas when Satish is alone

6 litres of gas per 100 kilometres

6 x 3 for 300 kilometres = 18 litres

Litres of gas when Satish is with friends

6 litres of gas per 100 kilometres

6 x 18 for 1800 kilometres = 108 litres

Cost of gas when Satish is alone

$1.2 per litre

18 x 1.2 = $21.6

Cost of gas when Satish is with friends

$1.2 per litre

108 x 1.2 = $129.6

Cost for each friend = $129.6/3 = $43.2

Satish will pay: Cost when travelled with friends + Cost when travelled alone

=$43.2+ $21.6

=$64.8

So, Satish will pay $64.8

Answer:

He will pay $ 64.8

Step-by-step explanation:

Given,

The total distance of the trip = 2100 km,

∵ Sathish pick up his 2 friends 150 kilometers after he begins the trip and drop off when there are 150 kilometer remaining.

So, the number of kilometres for which he and his friends pay the costs = 2100 - (150+150)

= 2100 - 300

= 1800 km,

Now, the quantity of gas for 100 km = 6 liters,

So, the quantity of gas for 1800 km = 18 × 6 = 108 liters,

If the cost of gas is $ 1.20 per liters,

Then the total cost paid by them ( when satish is not alone )  

[tex]=\text{gas consumed in liters}\times \text{cost per liters}[/tex]

[tex]=108\times 1.2[/tex]

[tex]=\$ 129.6[/tex]

∵ they split this cost evenly,

So, the share of satish ( when he is with his friend ) = [tex]\frac{129.6}{3}[/tex] = $ 43.2

For the remaining 300 km, he paid the cost of gas,

Again, the quantity of gas for 100 km = 6 liters

⇒ The quantity of gas for 300 km = 18 liters,

Thus, the cost he paid when he was alone = 18 × cost of gas for 1 liter

= 18 × 1.2

= $ 21.6

Hence, the total amount paid by satish = $ 43.2 + $ 21.6 = $ 64.8

Answer:

y = -(2/3)*x - 11

Step-by-step explanation:

To convert a point-slop equation into a linear function, there are certain steps which have to be followed. The primary aim is to make y the subject of the equation. By making sure that y is on the left hand side of the equation and x is on the right hand side of the equation, our goal will be achieved. To do that, first of all do the cross multiplication. This will result in:

3(y+7) = -2(x+6).

Further simplification results in:

3y + 21 = -2x - 12.

Keeping the expression of y on the left hand side and moving the constant on the right hand side gives:

3y = -2x - 33.

Leaving y alone on the left hand side gives:

y = -(2/3)*x - 33/3.

Therefore, y = -(2/3)*x - 11!!!

Answer:

See below.

Step-by-step explanation:

The first is a reflection in the y-axis.

Then a downward translation of 10 units.