STEM:

If you can rewrite a quadratic equation as a product of factors that equals zero, you
can solve the equation. To solve equations in this manner, you must use all your
factoring skills.

Example:

What are the solutions of the equation x2– x = 20?

First rewrite the equation so that one side equals zero.



x2– x = 20

x2 – x – 20 = 20 – 20

x2 – x – 20 = 0

Subtract 20 from each side.

Simplify.

Now, factor to rewrite the equation as a product of factors equal to zero. Find two
integers whose product is –20 and whose sum is –1. The product of 4 and –5 is
–20, and the sum of 4 and –5 is –1.






x + 4 = 0


x + 4 – 4 = 0 – 4


x = –4

x2 – x – 20 = 0

(x + 4)(x – 5) = 0

or

or

or




x – 5 = 0


x – 5 +5 = 0 +5


x = 5

The solutions are –4 and 5.

These "solutions" tell us where our quadratic function passess through the x-axis (ie this tells us the "roots" aka "x -intercepts" aka "zeros" aka "solutions" aka "zeros" are)





Question:

In the graph provided in the example, what do the coordinates (-4,0) and (5,0) represent?



A
The y- intercept of the function (ie where the function passes through the y-axis)

B
The x-intercept of the function (ie where the function passes through the x-axis)

C
The vertex of the function

D
none of the above

E
the zeros of the quadratic function

F
the roots of the quadratic function

Answers

Answer 1

9514 1404 393

Answer:

  A, E, F

Step-by-step explanation:

Every point on the graph has coordinates (x, f(x)). This means a point such as (-4, 0) or (5, 0) is a point on the x-axis where f(x) = 0. It is all of ...

an x-intercepta root of the functiona zero of the function

These terms are used essentially interchangeably.


Related Questions

(a) If (x - 2)(x-5) <0 and x e N then find x.​

Answers

Answer:

x = 3 or x = 4.

Step-by-step explanation:

We are given the following inequality:

[tex](x - 2)(x - 5) < 0[/tex]

It is a product, and a product is negative when one term is positive and the other is negative.

First case:

[tex]x - 2 > 0 \rightarrow x > 2[/tex]

And

[tex]x - 5 < 0 \rightarrow x < 5[/tex]

Thus, in the natural set: x = 3 and x = 4.

Second case:

[tex]x - 2 < 0 \rightarrow x < 2[/tex]

And

[tex]x - 5 > 0 \rightarrow x > 5[/tex]

Empty set.

Union of the cases:

Second case is the empty set, so we only count the first case. Thus x = 3 or x = 4.

In each turn of a game you toss two coins. If 2 heads come up, you win 2 points and if 1 head comes up you win one point

Answers

Answer:

I don't understand pls explain

Ariel has a plastic ice cream cone in her food playset. The ice cream cone is a half-sphere sitting on top of a cone. What is the
approximate volume of the toy ice cream cone? Use 3.14 for x.

Answers

52 Step-by-step explanation:

What is the volume of a cube whose sides are each 1 3/4 ft?

Answers

Answer:

5.4 (rounded)

Step-by-step explanation:

the volume of a cube is length*width*height so here all three are 1 3/4 (same as 1.75) and so you multiply 1.75 * 1.75 * 1.75 and that gives you 5.4 when rounded.

HELP EDCITEE !! PLEASE !!!

Answers

Answer:

75.3074525 dgrees

Step-by-step explanation:

law of sines

29/sin(115 degrees) = 13/sin(B)

==> B = 0.418374736 rad

or 75.3074525 dgrees

Which table represents a linear function?
c
2
0
1
2
y
0
-1
4
-9
0
1
2
3
y
3
1
1
-3
2
0
y
0
1
4
9
y
1
3
0
1
2
3
1
--3
2
3
-1

Answers

Answer:

Table C is the answer

Step-by-step explanation:

In how many ways can 10 people be seated in 10badjacenr seats in a theater​

Answers

3,628,800 is the correct answer

ratios that are equivalent to 7/6

Answers

Answer:

14 : 12 , 21 : 18 and 28 : 24 .

Step-by-step explanation:

Answer:

14 : 12 , 21 : 18 and 28 : 24 .

Step-by-step explanation:

Therefore, 14 : 12 , 21 : 18 and 28 : 24

how are they the same

Answers

Answer:

Step-by-step explanation:

The ways that they are the same are.

The slope is the same.Since the slope is the same for both of them, there is no possible solution meant for both of them. The slope is 1/4They are both written in slope y intercept form.The only difference is the y intercept is different. y intercept for y = 1/4 x is 0,0y intercept for y = 1/4 x is 0,5

onathan collects postcards and stamps. The number of postcards in his collection is 12 more than the number of stamps. He has 39 postcards in all. If Jonathan has x stamps, which equation represents this situation and how many stamps does he have?

Answers

equation: 39 - 12 = x

x = 27 (stamps)

find two numbers whose ratios is 3 to 5 and whose sum is 88​

Answers

Answer:

33 and 55

Step-by-step explanation:

[tex]\frac{x}{y}: \frac{3}{5}[/tex]

x + y = 88

3 + 5 = 8

[tex]y(\frac{x}{y}): y(\frac{3}{5})[/tex]

[tex]x= \frac{3}{5}y[/tex]

[tex]y+\frac{3}{5}y=88[/tex]

[tex]\frac{8y}{5}=88[/tex]

[tex]5(\frac{8y}{5})=5(88)[/tex]

8y = 440

8y ÷ 8 = 440 ÷ 8

y = 55

x + y = 88

x + 55 = 88

x + 55 - 55 = 88 - 55

x = 33

Which statement is true about the graphed function?
O Fx) < 0 over the interval (-0, 4)
OFx) < 0 over the interval (-0, -3)
O F(x) > 0 over the interval (-00, -3)
O F(x) > 0 over the interval (-0, 4)

Answers

Answer:

D is the answer to the question

Suppose we are interested in bidding on a piece of land and we know one other bidder isinterested. The seller announced that the highest bid in excess of $10,000 will be accepted.Assume that the competitor’s bid x is a random variable that is uniformly distributedbetween $10,000 and $15,000.a. Suppose you bid $12,000. What is the probability that your bid will be accepted?b. Suppose you bid $14,000. What is the probability that your bid will be accepted?c. What amount should you bid to maximize the probability that you get theproperty?d. Suppose you know someone who is willing to pay you $16,000 for the property. Wouldyou consider bidding less than the amount in part (c)? Why or why not?

Answers

Answer:

a. 0.4 = 40% probability that your bid will be accepted

b. 0.8 = 80% probability that your bid will be accepted.

c. $15,000.

d. Bidding $15,000 guarantees you a profit of $1,000, while trying to bid less than $15,000, you can end up without a profit, thus, you should not consider bidding less than the amount in part (c).

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

Assume that the competitor’s bid x is a random variable that is uniformly distributed between $10,000 and $15,000.

This means that [tex]a = 10, b = 15[/tex], considering the measures in thousands of dollars.

a. Suppose you bid $12,000. What is the probability that your bid will be accepted?

Probability that the other bidder's bid is less than 12000(X < 12). So

[tex]P(X < 12) = \frac{12 - 10}{15 - 10} = \frac{2}{5} = 0.4[/tex]

0.4 = 40% probability that your bid will be accepted.

b. Suppose you bid $14,000. What is the probability that your bid will be accepted?

Probability that the other bidder's bid is less than 14000(X < 14). So

[tex]P(X < 14) = \frac{14 - 10}{15 - 10} = \frac{4}{5} = 0.8[/tex]

0.8 = 80% probability that your bid will be accepted.

c. What amount should you bid to maximize the probability that you get the property?

The upper bound of the uniform distribution, that is, $15,000.

d. Suppose you know someone who is willing to pay you $16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not?

Bidding $15,000 guarantees you a profit of $1,000, while trying to bid less than $15,000, you can end up without a profit, thus, you should not consider bidding less than the amount in part (c).

PLEASE HELP MEEEEEEEEEEEEEE
triangle area ?​

Answers

25 root 3 divided by 2
Base is 5. Height is 5 root 3
Multiply then divide by 2

Answer:

A= 21.65063509

Step-by-step explanation:

triangle area is =base*hight/2

Because we have a right triangle we can apply the trigonometric functions

sin30 =base/hypothenuse = base/10

cos 30 = hight/hypothenuse =hight/10

sin30 = base /10  ; multiply both sides by 10

base = 10*sin30

cos 30 = hight /10 ; multiply both sides by 10

hight = 10 cos 30

A= 10*sin30*10*cos30/2 =

      100*sin 30*cos 30/2=

            50*sin30*cos30 = ; use calculator make sure is set up in degrees

A= 21.65063509

HELP Will mark brainlist

Answers

Answer:

Its B since the decimals are lower than the data.


Which point on the x-axis lies on the line that passes point C and is parallel to line AB

Answers

Answer:

(2,0)

Step-by-step explanation:

Ali surveyed his classmates to see who liked tennis. In all, 32 males liked tennis, and 6 males did not like tennis; 13 females liked tennis, and 4 females did not like tennis. How many females did Ali survey

Answers

Answer:

Ali surveyed 17 females.

Step-by-step explanation:

From Ali's survey:

13 females liked tennis, while 4 did not.

This means that Ali's surveyed 13 + 4 = 17 females.

How many females did Ali survey?

Ali surveyed 17 females.

help me find the answer

Answers

d because it’s right

PLEASE HELP !! WILL MARK BRAINLIEST !!!

Answers

Answer:

5

Step-by-step explanation:

We can write the equation 7y=3y+20, because the top and bottom lemgths are equivalent

Now isolate x:

7y=3y+20

7y-3y=3y+20-3y (subtract 3y, subtraction property of equality)

7y-3y=20

4y=20 (simplify)

4y/4=20/4 (divide by 4, division property if equality)

y=5

The sum of two numbers is 67. The difference of the two numbers is 41. What are the two numbers.
Let 3 be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 67."
Write an equation that expresses the information in the sentence "The difference of the two numbers is 41."
Solve the system you have written above.
The larger number, 2 is
The smaller number, y is

Answers

Answer:

32

Step-by-step explanation:

Which of the expressions below could be factored quickly using the "difference of squares"? Select all that apply.
O 81x² - 12
O x^2 + 25
O 4x^2 – 25
O 9x^2 – 16
O x^2-50
O x^2-81
O x^2-100

Answers

Answer:

81x² - 12, no as 12 is not a perfect square x^2 + 25, no as it is a sum of squares 4x^2 - 25, yes 9x^2 - 16, yes x^2 - 50, no as 50 is not a perfect square x^2 - 81, yes x^2 - 100, yes

A bicycle wheel has a diameter of 26 inches. What is the circumference?

Answers

Answer:

81.64 Inches

Step-by-step explanation:

Given :

Diameter of wheel =26 inches

Radius of wheel (r)=26/2=13 inches

Circumference (C) of wheel can be calculated as :

C=  2πr

C=6.28(13)

C=81.64 Inches

Does -5 + 7 - 8 = 6?

Answers

Answer:

-6

Step-by-step explanation:

-5+7=2

2-2=0

0-the remaining 6 of the 8=-6

What is the horizontal distance between (−5/3, -2) and (4, -2)?


ANSWER QUICK GIVING BRAIN LEST

Answers

Answer:

-2?

Step-by-step explanation:

use y2-y1 over x2-x1 to find the answer. So you would do -2--5/3 over 4--2. The two negitives turn into a positive. SO it is now -2+5/3 over 4+2. -2+5/3= -1/3 over 4+2=6 it is now -1/3/6 which equals -2. So I think the answer is -2. I do not know if you should trust me on this but I tried.

What is the x-intercept of the line y = 2x – 10?

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

(5,0)

»»————- ★ ————-««  

Here’s why:  

I have graphed the equation in a program. When graphed, the point crosses through the point (5,0). This means that (5,0) is the x-intercept. See the graph attached below.  

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Use the formula for simple interest to help solve the following questions

Answers

Answer:

1. ₹ 382.50

2. 14,583.33

3. 6%

Step-by-step explanation:

Interest  = p × r × t

p = principal amount

r = rate of interest

t = time in years

(1) Interest = 10,200 × 0.025 × 1.5

                 = ₹ 382.50

(2) Principal = [tex]\frac{I}{(r\times t)}[/tex]

                   = [tex]\frac{1750}{(0.04 \times 3)}[/tex]

                   = [tex]\frac{1750}{0.12}[/tex]

                  = ₹ 14,583.33

(3)  [tex]Rate=\frac{(I \times 100)}{(p \times t)}[/tex]

              [tex]=\frac{(1186.5 \times 100)}{(5650 \times 3.5)}[/tex]

              [tex]=\frac{118650}{19775}[/tex]

              = 6%

find the value of x and y in the parallelogram ​

Answers

Answer:

x=14

y=40

Step-by-step explanation:

A parallelogram is like a rectangle 2 parallel sides are equal.

so x+3=17 and y-2=38

x+3=17

x=17-3

x=14

y-2=38

y=38+2

y=40

Tessellations (image below)

Answers

9514 1404 393

Answer:

  regular octagon

Step-by-step explanation:

In order for a shape to tessellate a plane, there must be a way to arrange the shapes so that the sum of angles at a node is 360°. An arrangement of kites is shown in the attachment. Of course, squares are used to tile planes all the time, as their four 90° corners fit together nicely.

An octagon has internal angles of 135°, which is not a sub-multiple of 360°. Hence there is no way for octagons to fit together to tile a plane.

Octagons will not tessellate a plane.

a) Two thirds of the class are freshman

Is it parameter or statistic

Answers

Answer:

parameter

Step-by-step explanation:

Parameter is the answer

4 lemons required to make 6 cups of lemonade

Answers

Answer:

If you are looking for a fraction, it would be 2/3 lemon per cup of lemonade

Step-by-step explanation:

If you simplify 4/6 it would be 2/3

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