f(x) = -2(x+3)(x - 1)
What is the vertex

Answer:

Well if we were to graph this quadratic equation. We would be looking for places on that graph where Y is equal to zero. Well those are places where the graph crosses the x axis.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You graph a quadratic the way you graph any equation.

The solution is generally where the graph crosses the x-axis, depending on what you're graphing.

__

We assume you want to graph an equation of the form ...

  y = ax^2 +bx +c

Often, we are interested in the values of x that make y = 0. Sometimes, we want other solutions, for example, the one(s) that make y = 194. That is why I say "depending on what you're graphing" in the text above.

__

For a quadratic, it is helpful to start at the line of symmetry. The line of symmetry for this equation is the vertical line at ...

  x = -b/(2a)

The graph will be symmetrical about this line. Points on either side of this line will be the same distance from it.

So, once you find the x-value for this line of symmetry, you evaluate the quadratic for that value of x. The resulting y-value will be the y-value of the vertex, the most extreme point on the curve. If a>0, it will be the lowest point on the curve. The curve will open upward from there. If a < 0, it will be the highest point on the curve, which will open downward.

__

Another point you can plot is the y-intercept. The value of that is 'c' in the above equation, so (0, c) is a point on the curve. Of course, another point on the curve is found where this one is reflected across the line of symmetry.

__

Personally, I usually find it convenient to choose values of x that differ from the line of symmetry by 1, 2, 3, or some other small integer value. You will find for these values of x, the corresponding y-values differ from the vertex by a, 4a, 9a. Of course, for some quadratics, it is appropriate to choose a different set of points than these.

_____

Worked-out Example

Consider ...

  y = 2x^2 -x -6

The values of a, b, c are: a=2, b=-1, c=-6.

One point you can graph right away is the y-intercept: (0, -6).

The line of symmetry is ...

  x = -b/(2a) = -(-1)/(2(2)) = 1/4

The corresponding value of y is ...

  y = 2(1/4)^2 -1(1/4) -6 = 2/16 -1/4 -6 = -(6 1/8)

So, the vertex of this graph is (1/4, -6 1/8).

As we noted above, we can add points at ±1, ±2, ±3 from the vertex fairly easily.

For x = 1/4 ±1, y will be -6 1/8 +2(1^2) = -4 1/8. So, two more points are ...

  (1 1/4, -4 1/8) and (-3/4, -4 1/8)

For x = 1/4 ±2, y will be -6 1/8 +2(2^2) = 1 7/8. So, two more points are ...

  (2 1/4, 1 7/8) and (-1 3/4, 1 7/8)

You will notice that the graph crosses the x-axis between -3/4 and -1 3/4, and also between 1 1/4 and 2 1/4. You might reasonably guess that values of x of 2 or -1 1/2 would give y-values of zero. You would be right.

For x=2, we have ...

  y = 2(2^2) -(2) -6 = 8 -2 -6 = 0

For x = -1.5, we have ...

  y = 2(-1.5)^2 -(-1.5) -6 = 2(2.25) +1.5 -6 = 4.5 +1.5 -6 = 0

So, the solutions are also points on the graph:

  (2, 0) and (-1.5, 0)

_____

Additional comment

Graphing calculator apps are available for smartphones, tablets, and desktop computers. I personally like to use one of those for making graphs of equations. One that is reasonably easy to learn is shown in the attachment. Desmos provides this one.

The attachment shows part of the table we computed, and a plot of those points and the curve through them. The x-intercepts are also shown.

This are the right steps

Step 1: first you divide the both size by 7 because there is 7 a's

7a/7 = 28/7

Step 2: You solve the equation

7a/7= a. 28/7 = 4

So, the answer is a = 4

not 7 = 4

Carly did a mistake in Step 1, as she divides the two sides of the equation by different quantities (she divided the left side of the equation by a and the right side of the equation by 7), but we are supposed to follow the same operations on both sides of the equation. Hence, option A: Step 1 is the right choice.

To solve linear equations in one variable, we isolate the variable to one side of the equation and simplify the other side to get the solution for the equation.

In the process of isolation, the operations performed on one side of the equation have to be performed on the other side too.

In the question, we are informed that Carly tried to solve an equation step by step. 7a=28 Step 1: 7a/a = 28/7 Step 2: 7 = 4.

We are asked to find the mistake that Carly did in solving the equation.

We first try to solve the equation: 7a = 28.

Step 1: 7a/7 = 28/7 {Dividing both sides by 7}

Step 2: a = 4 {Simplifying}.

Thus, we can see that Carly did a mistake in Step 1, as she divides the two sides of the equation by different quantities (she divided the left side of the equation by a and the right side of the equation by 7), but we are supposed to follow the same operations on both sides of the equation. Hence, option A: Step 1 is the right choice.

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This triangle is isosceles. The bottom 2 angles are the same.

180= 54+2y

126=2y

y=63

Answer:follow key h!gh on tik tok

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Area is the number of square units it tales to fill the inside of a polygon.

Answer:

50 Years

Step-by-step explanation:

175.5 million (The difference) divided by 3.51 million equals 50.

Answer:

-50 feet

Step-by-step explanation:

The trout is swimming 30 ft below sea level,if it were above sea level it would be positive but since its below it is negative. It then swims 20 feet lower so it would be -50 as a short cut you can use in problems like this one is to ignore the sign's and add it regularly then add the sign after the equation is done.

Answer:

-50 is the answer

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

First add like terms: 5x+90=360

Then subtract 90 from both sides: 5x=270

Then divide both sides by 5: x=54

Answer:

1.8

Step-by-step explanation:

3 * 0.6 = 1.8

Step-by-step explanation:

0.40 ___0.04

We are given with two decimal numbers. Compare the numbers and complete the blank by < or > or =

To compare the decimals , compare each digit from left to right

0 is equal to 0

4 is greater than 0

so we can say 0.40 is greater than 0.04

0.40 > 0.04

Both decimal numbers are not equal

Answer:

0.40 > 0.04

Answer: B

Step-by-step explanation:

To find r, we need to use the formula to find slope. The formula is [tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]. Since we are given the coordinates and slope, we can plug them into the formula and solve for r.

[tex]\frac{2}{3} =\frac{3-5 }{r-4}[/tex]               [multiply both sides by r-4]

[tex]\frac{2r-8}{3}=3-5[/tex]        [subtract]

[tex]\frac{2r-8}{3}=-2[/tex]           [multiply both sides by 3]

[tex]2r-8=-6[/tex]        [add both sides by 8]

[tex]2r=2[/tex]                 [divide both sides by 2]

[tex]r=1[/tex]

Now that we found that r=1, we know that the answer is B.

Step-by-step explanation:

(hog)(x) = h(g(x))

= h(3x + 7)

h(x) = x + 8

h(3x + 7) = 3x + 7 + 8

h(3x + 7) = 3x + 15

(hog)(x) = 3x + 15

Answer:

Step-by-step explanation:

First of all, your question is very clear. Excluding 0 is a needed restriction.

f(1) = 3*1 + 1 = 3 + 1 = 4

f(2) =3*2 + 1 = 6 + 1 = 7

f(3) = 3*3 + 1 = 9 + 1 = 10

f(4) = 4*3 + 1 = 12 + 1 = 13

4,7,10,13

Notice that you are just adding 3 to the previous term.

Answer:

m = 0 or slope = 0

Step-by-step explanation:

Answer:

x = 3/8

Step-by-step explanation:

Answer:

exact form:

[tex]x=\frac{11}{5}[/tex]

Decimal:

[tex]x=2.2[/tex]

Mixed Number Form:

[tex]x=2\frac{1}{5}[/tex]

Step-by-step explanation:

simplify [tex]2(x + 6) + 4[/tex]

[tex]2(x + 6) + 4 = 12x - 6[/tex]

Move all terms containing  x  to the left side of the equation.

[tex]-10x+1=-6[/tex]

Move all terms not containing  x  to the right side of the equation.

[tex]-10x=-22[/tex]

Divide each term by  − 10  and simplify.

[tex]x=\frac{11}{5}[/tex]

the result can be shown in multiple forms

Exact Form: [tex]x=\frac{11}{5}[/tex]

Decimal Form: [tex]x=2.2[/tex]

and Mixed Number Form: [tex]x=2\frac{1}{5}[/tex]

The probability that the two selected students for  both men,1 men and 1 Women, Both are women , Both are women and The same gender are 7/15,7/15 ,1/15 and 8/15 respectively.

It is required to find the probability.

probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0(impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.

Given:

There are 7 men and 3 women on a coed volleyball team.

We have to find the probability.

According to given question we have

Possibilities are

both men= 7c2=[tex]\frac{7!}{2!5!} =21[/tex]

1 men and 1 Women=7c1*3c1

                            =[tex]\frac{7!}{6!1!} *\frac{3!}{2!1!} =21[/tex]

Both are women=3c2=

[tex]\frac{3!}{2!1!} =3[/tex]

The same gender=7c2+3c2

                              =21+3=24

Total possibilities =10c2

                              =45

The probabilities are

A) both men=21/45=7/15

B)1 men and 1 Women=21/45=7/15

C) Both are women==3/45=1/15

D)The same gender=24/45=8/15

Therefore, the probability that the two selected students for  both men,1 men and 1 Women, Both are women , Both are women and The same gender are 7/15,7/15 ,1/15 and 8/15 respectively.

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n+8<13

n=4

If n=4, then n+8 is equal to 4+8.

4+8=12

12<13

True

hope it helps!

Answer:

12 < 13

Step-by-step explanation:

n = 4

n + 8 < 13

4 + 8 < 13

12 < 13

Answer:

B

Step-by-step explanation:

Rise over run

Answer:

3 divided by (1+2)=1

Step-by-step explanation:

bc u do parthensis first so 1+2 is 3 therfore if u divide 3 by 3 gives u one

An expression that is equivalent to 3(5x-4) is: D. 15x-12.

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.

Mathematically, the distributive property of multiplication is given by this expression:

a(b + c) = ab + ac.

By applying the distributive property of multiplication to the given expression, we have:

3(5x - 4) = 3(5x) - 3(4)

3(5x - 4) = 15x - 12

Therefore, the correct answer option is: D.) 15x - 12.

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Complete Question:

Which expression is equivalent to 3(5x-4)

A 8x-4

B 8x-1

C 15x-4

D 15x-12

Answer:  The numbers are 172  and 43

Step-by-step explanation:

We will represent the numbers by x and y  

where x is the positive number and y is the other number.

So x the positive number is 4 times the other number which could be represented by the equation x = 4y  

And the difference between x and y is 129  which could also be represented by the equation  x - y = 129  

Now use both equations to solve for y and x  

x = 4y  

x-y = 129   Substitute the value for x into the second equation

4y - y = 129

 3y = 129  

   y =  43  so we know that y is 43  and  x is 4 times it

x = 4(43)

x= 172  

So the numbers are 172 and 43 .

Check:

172 - 43 = 129

   129 = 129

Answer:

2546

Hope this helps

Answer:

The perimeter is quadrilateral Q is 3 times the perimeter of quadrilateral P.

Step-by-step explanation:

Using a scale factor of 3, every dilated side is 3 times longer then the original side. Then, the perimeter is also 3 times greater.

The perimeter is quadrilateral Q is 3 times the perimeter of quadrilateral P.

The perimeter of a shape is the sum of its side lengths. The perimeter of quadrilateral Q is 186 units

The sides of quadrilateral P (see attachment) are:

[tex]Sides = \{7, 15, 15, 25\}[/tex]

So, the perimeter of P is:

[tex]P_p = 7 + 15 + 15 + 25[/tex]

[tex]P_p = 62[/tex]

Given that:

[tex]k = 3[/tex] --- the scale factor from P to Q

This means that the sides of Q are 3 times the sides of P. So, the perimeter of Q will also be 3 times the perimeter of P

So, we have:

[tex]P_Q = P_p \times k[/tex]

This gives

[tex]P_Q = 62 \times 3[/tex]

[tex]P_Q = 186[/tex]

Hence, the perimeter of Q is 186 units

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Answer:

Length = 6.1 inches and Width = 3.4 inches

Step-by-step explanation:

We are told that the diagonal measures 7 inches.

We are also told that the length of the screen is 2.7 inches more than the width.

Let the length be L and width be W.

Thus, L = W + 2.7

Now, since length = W + 2.7 and width = W and diagonal = 7 inches, we can use pythagoras theorem to solve.

Thus;

W² + (W + 2.7)² = 7²

W² + W² + 5.4W + 7.29 = 49

2W² + 5.4W - 41.71 = 0

Using quadratic formula, we have;

W = [-5.4 ± √(5.4² - 4(2 × -41.71))]/(2 × 2)

W = [-5.4 ± √(362.84)]/4

W = -5.4/4 ± 19.05/4

W = (-1.35 + 4.7625) or (-1.35 - 4.7625)

W ≈ 3.4 inches or -6.1

W cannot be negative, thus, W = 3.4 inches

From earlier, we saw that L = W + 2.7

Thus,L = 3.4 + 2.7 = 6.1 inches

So, Length = 6.1 inches and Width = 3.4 inches

Answer:

$98.55

Step-by-step explanation:

Answer:

he has to pay 108.55

Step-by-step explanation:

Answer:

Non-response bias

Step-by-step explanation:

Selection bias in a survey occurs when individuals are selected in a disproportionate way such that the samples obtained do not represent the true population to be studied or interviewed. An example of a selection bias that can occur from Random-digit dialing is the non-response bias.

Participants who are to be selected for surveys must be eligible or suitable for the purpose of the experiment. If the survey is trying to measure the effect of stress on parents, there is a possibility that through random-digit dialing, homes might be called at times when parents are on a work trip. This inability to get the response of eligible subjects for the survey is a form of selection bias.