Jasmine is studying the polynomial function f(x)=-x^2+8x+18. Which of the following statement(s) about this function are true?
I. The polynomial function will open down.
II. The polynomial function has a minima of (4, 34).
III. The polynomial function has two roots.
IV. The axis of symmetry of the function is x=–4.

A. I and IV
B. II and III
C. I and III
D. lII and IV

Answer:

The correct option is C) Yes; the change in x is constant and the change in y is constant.

Step-by-step explanation:

Consider the table shown.

x     y

0    8

1     1

2   -6

3   -13

Now observe the changes in x and y coordinates, if changes are constant then the given function is linear.

Consider the change in x coordinate.

1-0=1,  2-1=1 and 3-2=1

Now consider the change in y coordinate.

1-8=-7,  -6-1=-7  and -13-(-6)=-13+6=-7

Since the change in x and y is constant the given relationship is linear.

Therefore, the correct option is (C) Yes; the change in x is constant and the change in y is constant.

Answer:

The 2 angles are supplementary.  This means they have to add up to 180 degrees.  The first angle is 8x and the second is x+27.  So set both of them equal to 180.

8x + x + 27 = 180

9x = 153

x = 17

Angle 1 = 8(17) = 136

Angle 2 = (17) + 27 = 44

Check: Angle 1 + Angle 2 = 180

136 + 44 = 180

Step-by-step explanation:

Answer:

Answer choice D

Step-by-step explanation:

So we need to get r to the right side. First we can multiply by 3 to get rid of the fraction:

3V=4[tex]\pi[/tex][tex]r^{3}[/tex]

Then we can divide both sides by 4[tex]\pi[/tex] to get r by itself:

[tex]\frac{3V}{4\pi } = r^{3}[/tex]

Then cube both sides:

[tex]\sqrt[3]{\frac{3V}{4\pi } } =r\\[/tex]

Answer choice D

9514 1404 393

Answer:

  2.89 m

Step-by-step explanation:

The attached shows the figure drawn accurately. It also shows that the angle of the line of sight is 102° -90° = 12° below the horizontal. The sine relation is useful in this situation.

The side opposite the angle in the triangle of interest is the difference in building heights, 5.3 -4.7 = 0.6 m. So, the useful relation is ...

  Sin = Opposite/Hypotenuse

  sin(12°) = (0.6 m)/(PR)

  PR = (0.6 m)/sin(12°) ≈ 2.886 m

  PR ≈ 2.89 m

The distance to the subject is about 2.89 meters.

Answer:

5

Step-by-step explanation:

y-x

8-5 = 5

The value of the expression y - x is 5.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

y - x

The value of y - x when x = 3 and y = 8.

= y - x

= 8 - 3

= 5

Thus,

The value of the expression is 5.

Learn more about expressions here:

https://brainly.com/question/3118662

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Step-by-step explanation:

25/-15×9

The answer is -15

Answer:

Function

Step-by-step explanation:

These coordinates do represent a function. For a relation to be a function every y-value must have an x-value, this means x's cannot repeat. In this relation x's never repeat, they simply increase by one every time. Therefore, this is a function.

Answer:

The longest length of the similar triangle is 7 inches

Step-by-step explanation:

If two triangles are similar, the ratio of their sides are equal

We shall be working the shortest and longest side of both

What we have here will be that;

The shortest length/ the longest length ratio in both triangles will be the same

Let the longest side of the similar triangle be x

8/14 = 4/x

8x = 4 * 14

x = (4 * 14)/8

x = 7 inches

Answer:

This is NOT a graph :)

Step-by-step explanation:

Answer:

The solutions for both system of equations are as follows:

Step-by-step explanation:

The first set of equations is:

[tex]4x+6y=32\\3x-6y=3\\[/tex]

It can clearly be seen that the coefficients of y are already same in magnitude with different signs so we have to add both equations

So adding both equations, we get

[tex]4x+6y+3x-6y = 32+3\\7x = 35\\\frac{7x}{7} = \frac{35}{7}\\x = 5[/tex]

Putting x=5 in equation 1

[tex]4(5)+6y = 32\\20+6y = 32\\6y = 32-20\\6y = 12\\\frac{6y}{6} = \frac{12}{6}\\y = 2[/tex]

The solution is (5,2)

The second set of simultaneous equations is:

[tex]-3x+5y=-113x+7y=-1[/tex]

We can see that the coefficients of x in both equations are same in magnitude with opposite signs so

Adding both equations

[tex]-3x+5y+3x+7y = -11-1\\12y = -12\\\frac{12y}{12} = \frac{-12}{12}\\y = -1[/tex]

Putting y= -1 in first equation

[tex]-3x+5(-1)=-11\\-3x-5=-11\\-3x=-11+5\\-3x=-6\\\frac{-3x}{-3} = \frac{-6}{-3}\\x = 2[/tex]

The solution is: (2,-1)

Hence,

The solutions for both system of equations are as follows:

Answer:

see explanation

Step-by-step explanation:

Given f(x) then the derivative f'(x) from first principles is

f'(x) = lim ( h tends to 0 ) [tex]\frac{f(x+h)-f(x)}{h}[/tex]

      = lim ( h to 0 ) [tex]\frac{3(x+h)^3+2-(3x^3+2)}{h}[/tex]

      = lim ( h to 0 ) [tex]\frac{3(x^3+3x^2h+3xh^2+h^3)+2-3x^3-2}{h}[/tex]

      = lim ( h to 0 ) [tex]\frac{3x^3+9x^2h+9xh^2+3h^3-3x^3}{h}[/tex]

      = lim ( h to 0 ) [tex]\frac{9x^2h+9xh^2+3h^3}{h}[/tex]

      = lim ( h to 0 ) [tex]\frac{h(9x^2+9xh+3h^3)}{h}[/tex] ← cancel h on numerator/ denominator

      = lim ( h to 0 ) 9x²+9xh+3h² ← let h go to zero

f'(x) = 9x²

Answer:

-4

Step-by-step explanation:

Answer:s

slope of -4x-3: m=-4

YOU WILL NOT FAIL, YOU SHALL PASS

Answer: w^6/9

Step-by-step explanation:

first, i evaluated the powers.

3^-2 x 1 x 1/w^-6

then, i calculated those products.

3^-2/w^-6

then, i just expressed it with a positive exponent.

w^6/3^2

finally, i evaluated that.

w^6/9

Answer:

The answer is not 1 or 0

I think its D. infinitely many

Step-by-step explanation:

Answer:

H in terms of c is H = 5c³.

Step-by-step explanation:

Given that:

H = 40 and c = 2

H varies directly to the cube of c.

Which means that,

H ∝ c³

Let,

k be the proportionality constant.

H = kc³

Putting H=40 and c=2

[tex]40=k(2)^3\\40=k(8)\\40=8k\\8k=40[/tex]

Dividing both sides by 8,

[tex]\frac{8k}{8}=\frac{40}{8}\\k=5[/tex]

Now,

H in terms of c.

H = 5c³

Hence,

H in terms of c is H = 5c³.

Answer:

y=5

Step-by-step explanation:

Any equation that's y=c (or any other constant) is a horizontal line. Imagine a parabola and a horizontal line plotted on a graph.

There are three possibilities of where the horizontal line can be:

It may not touch the parabola at all,

It may touch the parabola at one specific point (it's a tangent line)

Or it may touch the parabola at two points (it's a secant line)

The question prompt tells us that the horizontal line y=c touches the parabola at exactly one point; so for it not to touch two points it has to touch the parabola at the vertex point, right?

If we graph the parabola (or we could just look at the equation and it should be intuitive), we find out that the y-intercept is 5. In other words the point where the function reaches its maximum value (maxima) is at y=5.

For this reason, the value of c is 5 since if it was any value below that it would touch more than one point and if it was above it it wouldn't touch any point.

Here's an image so that it'll be a bit clearer hopefully:

Good luck!

Answer:

x= -1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Brainly plss?

Answer:

x=-1

use math papa calculator it helps :)

Answer:

89.03

Step-by-step explanation:

29x3.07=89.03

According to values of a function we can plot the points on a graph.

What is domain?

Domain is the value which we used to enter in a function to get the value of a function.

We have been given the domain of the function and we have to plot the value in the graph.

F(1/2)=log1=0

F(1)=log2=0.3

F(2)=log4=0.6

F(4)=log8=0.9

F(8)=log16=1.2

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Answer:

its C

Step-by-step explanation:

Answer: Friday

Step-by-step explanation:

If February 29th is on a Sunday, then, the day that the next February 29th will fall on will be Friday.

First and foremost, we should realise that February has 28 days but in leap years which takes place every 4 years, it has 29 days.

We should realise that the dates in the calendar are arranged in such a way that if a particular date falls on a particular day this year, the date will fall on the next day next year. e.g. since January 20 falls on. Wednesday this year, it will fall on a Thursday next year.

Since February 29 is a date for a leap year, following the above explanation, if February 29th is on a Sunday, then, the day that the next February 29th will fall on will be Friday which is in the next four years.

Answer:

4,500 different codes.

Answer:

0.8= 2.1448=2.1379

Step-by-step explanation:

Answer:

0.8/2.1448/2.1379

Step-by-step explanation:

I got right(Plato/Edmentum

Answer:

y=1/3x-4

Step-by-step explanation:

Answer:

y=1/3x-4

Step-by-step explanation:

4 is negative cause it says less than..