What is the answer to this question

The graph of the quadratic function x² + 3x - 108 is given by the image shown at the end of the answer.

Three features have to be considered to obtain the graph of a quadratic function.

The function for this problem is defined as follows:

a = 1, b = 3, c = -108.

Hence the coefficients of the function are given by:

a = 1, b = 3, c = -108.

Inserting these points into a calculator, the x-intercepts of the function are:

Hence the function crosses the x-axis at x = -12 and at x = 9, and it is a concave up parabola, as the coefficient a is positive.

The y-intercept of the function is given as follows:

f(0) = 0² + 3(0) - 108 = -108.

Hence the graph crosses the y-axis at y = -108.

The axis of symmetry of the function is:

x = -b/2a = -3/2 = -1.5.

The y-coordinate of the vertex is:

f(-1.5) = (-1.5)² + 3(-1.5) - 108 = -110.25.

Which is the turning point of the graph.

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If a chemist wants to make 671 milliliters of the drug, then 305 milliliters of compound A are needed.

Given that:

A certain drug is made of compound A and compound B.

There are 5 milliliters of compound A used for every 6 milliliters of compound B.

So, A and B are in the ratio of 5:6.

Let a chemist will use 5x milliliters of compound A and 6x milliliters of compound B to make 671 milliliters of the drug.

So, we equate the total amount and find the value of x.

i.e. 5x + 6x = 671

=> 11x = 671

=> x = 61

Putting the value of x = 61. We get the value of compound A and compound B.

The value of compound A = 5x = 5 x 61 = 305 milliliters.

The value of compound B = 6x = 6 x 61 = 366 milliliters.

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The correct function represented in the table given is y=2x+3.

Given table:

x            y

0           3

1            5

2           7

3           9

Take any two points suppose take (0,3) and (1,5)

slope m = 5 - 3 / 1 - 0

= 2/1

m = 2.

(0,3) passes through y = mx + c

3 = m*0 + c

m value substitute

3 = 2*0 + c

3 = 0+c

c = 3.

y = mx+c

y=2x+3.

Therefore the correct function represented in the table given is y=2x+3.

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The given expression 81x[tex]^2-[/tex] 36 is a multiply of conjugates.

In the given question we have to find expression is a result of multiplying conjugates together, squaring binomials, or neither.

The given expression is 81x[tex]^2-[/tex]36.

If we simplify the expression, then it is written as;

81x[tex]^2-[/tex] 36=(9x)^2-(6)^2

We write it as

81x[tex]^2-[/tex] 36=(9x-6)(9x+6)

It is a multiply of conjugates.

Hence, the given expression 81x[tex]^2-[/tex] 36 is a multiply of conjugates.

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In a group of 50 people, 20 are vegetarian. If two people are selected at random, the expected number of vegetarians is 0.8.

In mathematics, the mean is the average of a set of data, which is calculated by adding all the numbers together and then dividing the result by the total number of numbers. There are various mean types in mathematics, particularly in statistics. Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.

Given,

In a group of 50 people, 20 are vegetarian. If two people are selected at random,

For proportion,

p = x/n

p = 20/50

p = 0.4

n = 2

Mean:

x = np

x = 2 × 0.4

x = 0.8

In a group of 50 people, 20 are vegetarian. If two people are selected at random, the expected number of vegetarians is 0.8.

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Answer:

mAngleT = 60°

mAngleU = 60°

TS = 13cm

SU = 13cm

Step-by-step explanation:

Since two of the sides are the same the two base angles are also the same. One is 60° so the other one is 60° also. But if they are both 60° and all the angles add up to 180° the last one has to be 60° also.

One side is marked 13cm. It is marked congruent to the left side so they are both 13cm.

But we saw from the angles all being the same, that this is actually an equilateral triangle. So all three sides are the same.

Answer:

2067.5

Step-by-step explanation:

divide each number and when you get to the end add a zero for the decimal.

Answer:

Q36 this is geometry if anyones good at it can someone help me pls

(3⁴)² can be written as 3² × 3⁶.

Exponentiation is the operation of doing multiplication repeatedly and it is written in the form aᵇ.

We have to write the given expression (3⁴)² as product of two numbers.

Now, (3⁴)² = 3⁸

We have the property of exponentiation,

aⁿ × aˣ = a^(n + x)

Thus 3⁸ = 3^(2+6) = 3² × 3⁶

Hence, (3⁴)² can be expressed as 3² × 3⁶.

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Answer:
x = 48/3

when Jack got 50 chocolates and has left 2, then Jack gave away 50-2=48 chocolates. When each friend got 3 chocolates, the number of friends x is equal to 48 divided by 3.

Answer:

x=16 (friends)

Step-by-step explanatn

50/3 = 16.6666

take away the .66666

so 16x3=48

meaning u would have 2 left over

The probability that tails appears on the next toss is 0.5

Given,

In the question:

If I toss a fair coin five times and the outcomes are TTTTT,

To find the probability that tails appears on the next toss is.

Now, According to the question:

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.

A sequence of five fair coin flips has a sample space that contains all potential outcomes. [tex]2^3[/tex] {H, T}  is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .

The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH}  or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5

Hence,  the probability that tails appears on the next toss is 0.5

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Answer:

-31

Step-by-step explanation:

-31 add 7 on a calculator equals -24

Answer:

Step-by-step explanation:

Ok: Hi

1. First Isolate the x on the left side of equation. Remember that if a variable or number goes over the equal sign, it becomes opposite!

x+7=-24

x=-24-7

x=-31

2. Always double check equations!

-31+7=-24 TRUE

Answer x=-31 or choice B

The points that showed a negative trend is

A graph with a negative trend line slope is said to have a negative trend.

The variables are shown to be negatively correlated, meaning that when one increases, the other decreases and vice versa.

An instance of such graphs would be a graph illustrating the relationship between a car's age and value.

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The constant of variation of the distance is 13.5 miles

From the question, we have the following parameters that can be used in our solution:

Distance cycled = 9 miles

Number of hours = 2/3 of an hour

From the above parameter, we can calculate the constant of variation

The constant of variation is calculated as

Constant of variation = Distance cycled/Number of hours

Substitute the known values in the above equation

So, we have the following equation

Constant of variation = 9/(2/3)

Evaluate the quotient

Constant of variation = 13.5

Hence, the constant of variation is 13.5 miles per hour

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In statistics, a confidence interval defines the possibility that a population parameter will fall between a set of values for a certain proportion of the time. Analysts commonly incorporate confidence zones that encompass 95% or 99% of the expected data. Thus, if a point estimate of 10.00 is derived using a statistical model with a 95% confidence interval of 9.50 - 10.50, there is a 95% chance that the real value falls within that range.

What is the need for Confidence Intervals?

Confidence intervals are one technique to illustrate how "accurate" an estimate is; the higher the 90% confidence interval for a certain estimate, the more the precaution advised when employing the estimate. Confidence intervals serve as a crucial reminder of the estimates' limitations.

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Answer:

17/10 (1.7)

Hope this helps!

The mass of mass of 'you' and the skateboard together will be 60 kg.

According to the question,

We have the following information:

You push yourself on a skateboard with a force of 30N and accelerate at 0.5m/s².

We know that the following formula is used to find the force applied:

Force = mass*acceleration

(More to know: force is denoted by F, mass is denoted by m and acceleration is denoted by a.)

Putting the given values in this formula:

30 = m*0.5

m = 30/0.5

m = 60 kg

Hence, the mass of mass of 'you' and the skateboard together will be 60 kg.

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The x-intercept would be 5.6, and the y intercept would be 4, if that helps.

The number of phones sold would be 20

And, the number of accessories sold would be 26.

Used the concept of an equation that states,

An equation is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.

Given that,

Kylie earns a $15 commission for every phone she sells and a $2 commission for every accessory she sells.

And, On a given day, Kylie made a total of $352 in commission and sold 6 more accessories than phones.

Let us assume that,

The number of phones sold = x

And, the number of accessories sold = y

Hence, the equation becomes,

15x + 2y = 352   .. (i)

And, y = x + 6  .. (ii)

Substitute the value of y in (i);

15x + 2y = 352  

15x + 2 (x + 6) = 352

15x + 2x + 12 = 352

17x + 12 = 352

17x = 352 - 12

17x = 340

x = 340/17

x = 20

From (ii);

y = x + 6

y = 20 + 6

y = 26

Therefore,  The number of phones sold = 20

And, the number of accessories sold = 26

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Of the given options, the correct options are [1], [4], [6], [7].

The general equation of a exponential function is -

y = aeˣ

It's graph is plotted and attached below.

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the [x] or [y] approaches zero.

Given is the population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year.

We have the graph in the question as shown. Of the given options, the correct options are [1], [4], [6], [7].

Therefore, Of the given options, the correct options are [1], [4], [6], [7].

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Answer:

This can go both ways but out of 124 black women and only 10 selected you have a chance at least one experienced IPV

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation

y = x^2 + 8x + 7                      Put brackets around the first two terms

y = (x^2 + 8x) + 7                    Take 1/2 the linear term's coefficient  (8)

8/2 = 4                                    Put this result inside the brackets and  square

y = (x^2 + 8x + 4^2) + 7          Take - 4^2 and add it to the seven.

y = (x^2 + 8x + 16) + 7 - 16       What you did, did not change the eqiuation

Y = (x^2 + 8x + 16) - 9              The first 3 terms make a perfect square

y = (x + 4)^2 - 9

The minimum should be at - 4,-9  Just to make sure it is, I'll graph the original equation. The y intercept should be at 7 and the two x roots should x = + 3 - 4 and x = -3 - 4. or x = -1 and x = - 7

Let's see if this all checks out.

Graph of original equation.

Answer: 6 zeros

Step-by-step explanation: 30 x 10^5

using P.E.M.D.A.S

you do exponents first

10^5 = 100000

then 100000 x 30 = 3000000

and there is 6 zeros

Answer:

1. 95=8x+55  8x=40  x=5  Reason: Since m and n are parallel, and a line traverse through it, they are corresponding angles, meaning that their angle is the same.

2. 200-2x=130  200-130=2x  2x=70  x=35  Reason: The two angles are the same because the "130-degree" angle's corresponding angle is the vertical angle of the "200-2x" angle.

3. Yes, we can use the corresponding angle theorem to prove that m and n are parallel.

4. No, there's not enough information to determine because both given angles are on line m, we need an angle on line n as well.

5. No, the same explanation as 4^^^ Vertical angles do not necessarily prove that two lines are parallel.

6. Yes, we can use the corresponding angles theorem, and then use the vertical angles theorem.

Good luck, and comment on anything you don't understand. I suggest you watch some help videos.

Answer:

In the equation of a straight line (when the equation is written as "y = MX + b"), the slope is the number "m" that is multiplied by the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis).

Answer: The equation defines the relationship between the angle of inclination of the line relative to the x-axis and the point at which the line passes through the y-axis on a graph.

Step-by-step explanation:

Imagine a line, L, that passes through the y-axis of a graph at some point B=(0,b), where the 0 is the x-coordinate of B and b is the y-coordinate of B. In this case, we will use the variable m to represent the slope of the line. Geometrically, the slope of a line is said to be tangent to its angle of inclination, the smaller of the two angles formed by the line L and the x-axis. In trigonometry, the tangent of an angle in a right triangle is defined as the ratio of the side opposite of it over the side adjacent to it. This relationship can be illustrated by constructing a right triangle where the hypotenuse is formed by the segment of the line L between the point B and an arbitrary point P somewhere along the line with the coordinates (x,y).

This triangle can be seen in the attached jpg. The side opposite of the angle of inclination is the imaginary vertical line formed between the point P and the x axis and the side adjacent to it is formed by the imaginary horizontal line between the point B and the vertical line from P. The point where these imaginary lines intersect forms the right angle of the triangle. The length of the opposite side, l1, can be expressed as the difference in y between points P and B:

l1 = y-b

Likewise, the length of the adjacent side, l2, can be expressed as the difference in x between points P and B:

l2 = x-0

The tangent of the angle of inclination, labled as [tex]\alpha[/tex] in the picture, can then be expressed as:

tan([tex]\alpha[/tex]) = [tex]\frac{(y-b)}{(x-0)}[/tex]

simplified as:

tan([tex]\alpha[/tex]) = [tex]\frac{y-b}{x}[/tex]

Because we know that slope m = tan([tex]\alpha[/tex]), we can say that

m =  [tex]\frac{y-b}{x}[/tex]

solving by algebra for y,

mx + b = y              or             y = mx + b

in single variable calculus, the slope of a line is described as the rate of change of its y coordinates with respect to the rate of change of its x coordinates, referred to as the derivative of y with respect to x. This relationship is used to describe things like the speed of an object as it relates to the change in the objects position. The important thing to realize here is the connection between the slope, which we expressed as the difference in the y values of two points on a line over the difference in their x values, and the behavior of the coordinates of points as you move along the line.

Hope that helps! If the last bit is confusing, don't worry, as long as you understand why y=mx+b is the slope intercept form you've got the right idea.

Answer:

16(x+5)

Step-by-step explanation:

16x+80

=8(2x+10)

=16(x+5)

The algebraic factor of the given expression 16x + 80 will be 16(x + 5).

An algebraic factor is the multiplication of two algebraic terms.

That term could be in form of summation multiplication or in subtraction.

The root of the quadratic equation formed by the algebraic factor is always real.

As per the given expression,

⇒ 16x+80

Take 8 as common

⇒ 8(2x + 10)

Take 2 as common

⇒ 8 × 2 (x + 5)

⇒ 16 (x + 5)

Hence "The algebraic factor of the given expression 16x + 80 will be 16(x + 5)".

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