What are the vertex and x intercepts of the graph of the function below
y=(x-4)(x + 2)
Answer:
x - intercepts: (4,0) and (-2,0)
vertex: (1/2 , - 17/2)
Step-by-step explanation:
Part A
To find the x-intercepts you have to set y=0
(x-4) (x+2) = 0
Separate the parenthesis. Solve for x
x-4 = 0
x= 4
x+2 = 0
x= -2
x - intercepts: (4,0) and (-2,0)
-------------------------------------------------
Part B
vertex formula for the x: coordinate : -b/2a
Expand the function.
y = 2x^2-2x-8
a = 2
b = -2
c= -8
-b/2a = -(-2)/2(2) = 1/2
vertex x- coordinate: 1/2
Substitute 1/2 back into every "x" in the function to find the "Y" for the vertex.
y = 2(1/2)^2 -2(1/2) -8
y = -17/2
vertex: (1/2 , - 17/2)
WORTH 100 POINTS IF YOU GET IT RIGHT IN THE NEXT FIVE MINUTES
Evaluate the expression when x=1/4 and y=1/2.
2(1/16+x2)+5y
Enter your answer as a mixed number in simplest form.
[tex]\displaystyle \sf Find : \\\\ 2 \left( \frac{1}{16}+x^2 \right)+5y =? \ \ ; \ \ If : x=\frac{1}{4} \ ; \ y=\frac{1}{2} \\\\\\ 2\left( \frac{1}{16} +\bigg(\frac{1}{4} \bigg) ^2\right)+5\cdot \frac{1}{2} =2\cdot \frac{2}{16} +\frac{5}{2} =\frac{1}{4} +2+\frac{1}{2} =\boxed{2\frac{3}{4} }[/tex]
Find the value of k so that the remainder is 1 when x^3+5x^2+kx-8 is divided by (x-3)
K=
By the remainder theorem, the remainder upon dividing [tex]x^3+5x^2+kx-8[/tex] by [tex]x-3[/tex] is given by the value of this expression when x = 3 :
[tex]3^3 + 5\cdot3^2 + 3k - 8 = 1[/tex]
Solve for k :
[tex]27 + 45 + 3k - 8 = 1 \\\\ 3k = -63 \\\\ \boxed{k = -21}[/tex]
calculate the shaded area
Answer:
640[tex]cm^{2}[/tex]
(I hope that I am right)
Step-by-step explanation:
The bigger shape :1. First, look at the triangle as a whole -Area of a triange : [tex]\frac{Base x Height}{2}[/tex]
30 x 48 = 1440[tex]cm^{2}[/tex]
1440 ÷ 2 = 720[tex]cm^{2}[/tex]
2. Now let's look at the small triangle -20 x 16 = 320[tex]cm^{2}[/tex]
320 ÷ 2 = 160[tex]cm^{2}[/tex]
The area of the bigger shape -720 - 160 = 560[tex]cm^{2}[/tex]The smaller shape :1. Let's look at the shape as a rectangle first -Area of a rectangle = Base x Height
20 x 16 = 320[tex]cm^{2}[/tex]
2. Now let's do the little triangle -20 - 30 = 10
10 x 16 = 160[tex]cm^{2}[/tex]
160 ÷ 2 = 80[tex]cm^{2}[/tex]
The area of the smaller shape -80[tex]cm^{2}[/tex]The Area Of The Shaded Area :560 + 80 = 640[tex]cm^{2}[/tex]can someone please explain this
Answer:
D) 70 degrees
Step-by-step explanation:
A triangle angle's has a total of 180 degrees
180 - 40 = 140
140/2 = 70 (the other 2 angles are equvilent angles)
Brainly plz :)
Answer:
answer below
Step-by-step explanation:
every triangle has angle that, added together, equal 180 degrees.
if the given angle is 40 and the red lines tell you the sides are equal in length (both lines have only one red line so they are the same.), calculate the angles. (hint they are both the same amount of degrees.)
My process:
180-40=140
?+?=140
70+70=140
solution= 140 degrees
can someone please help me with this
Answer: 780
Step-by-step explanation: if right please mark as brainlest
Write the slope intercept form of the equation of the line through the given point with the given slope
(0,3) Slope=1/4
adding decimals
the sum of 32.11 + 109.14+ 3.67 =
Answer:
144.92
Step-by-step explanation:
32.11 = 032.11
3.67 = 003.67
032.11
109.14 +
003.67 +
______
144.92
______
find the measure of each angle
m angle QRT
and
m angle TRS
Rational numbers can be written as either terminating or nonterminating decimals. What kind of nonterminating decimals are rational numbers?
Answer:
Non terminating recurring decimals
Step-by-step explanation:
Decimals can be categorised into two groups: Terminating and non-terminating. Terminating decimals are rational, and non terminating can be further divided into: Non terminating Recurring (which are rational) and Non terminating Non recurring (which are irrational).
in the expression 8 ( x-y +b(x-y ; the common binomial factor is
Step-by-step explanation:
the common binomial factor is (x-y).
hope this helps you.
what is the diameter of 12mm and 8mm
Answer:
diameter 12mm
Step-by-step explanation:
please help!!
-69 + 63t = 9( 77 - 8) + 3
Brandon is going to the Sutter County Fair. Admission to the fair is $7, and each ride costs $2.
Write an equation that shows how the total amount Brandon spends, y, depends on the number of rides he takes, x.
The Answer: y = 2x + 7
Which of the statements below are true? Select all that apply. A) (2, 2) is a point on the line shown B) (3,6) is a point on the line shown C) Each pack of gum costs $2.00 D) Each pack of gum costs $0.50.
Answer:
C)
Step-by-step explanation:
The purpose of this document is to provide proof of identity and employment eligibility for the person being hired.
I-9 form
W-4
application
resume
Find the GCF of 72 and 108.
Answer: the gcf of 72 and 108 is 36!
Please help!
What system of linear equations is shown in the graph? Enter your answers in the box.
Answer:
The equation of the line with a bold line:
slope = ( 0 - ( -1 ) ) / ( ( 2 - 0 ) )= 1/2
c = -1
Therefore, y <= ( 1 / 2 ) x - 1
The equation of the line with the dotted line:
slope = ( 1 - ( - 2 ) ) / ( 0 - 1) = - 3
c = 1
Therefore, y < - 3x + 1
Step-by-step explanation:
If there is any confusion please leave a comment below.
The mean of 5 scores is 75, four of the numbers are 60, 70, 80, & 85. What is the 5th score?
Answer:
80
Step-by-step explanation:
Your 4 given numbers equal 295. 5x75 is 375. So take 375-295 and you get 80, your 5th number.
Please help!
A restaurant sells tea for
$1.50 per drink. The cost of drinks, F(d), can be found by using the function F(d) = 1.5d. If the restaurant sells no more
than $150 in drinks in a day, what is a reasonable domain and range
Thank you!
Domain:
Range:
Answers:
Domain is [tex]0 \le d \le 100[/tex]
Range is [tex]0 \le F(d) \le 150[/tex]
==============================================
Explanation:
The most money made from selling drinks is $150. Divide this over the cost per drink to get 150/(1.50) = 100; indicating that at most 100 drinks are sold per day. This is the largest that d can get because d represents the number of drinks sold.
The smallest d can get is d = 0 to mean that no drinks are sold.
In short: d is between 0 and 100, including both endpoints. We write [tex]0 \le d \le 100[/tex] to indicate this. This is the domain because the domain represents all the possible inputs allowed.
---------------------------------------------------
The range is the set of allowed outputs.
If we plugged in d = 0, then you would find F(d) = 0 as well. If you don't sell any drinks, then you earn $0. This is the smallest item in the range.
On the other side of things, the largest item in the range is 150 because this value was given to us. It's the upper limit or ceiling value of how much money is made from drinks. You can also find this by plugging d = 100, the largest domain value, into the function to get F(d) = 150.
Therefore the range is [tex]0 \le F(d) \le 150[/tex] to indicate that F(d) is between 0 and 150 inclusive of both endpoints.
Heeeeelppp please help
Answer:
.98 L / b * .4 b = .392 L amount contained in sample
.99 L / b * .25 b = .248 L this was rounded from .2475
1.00 L / b * .3 b = .30 L
1.01 L / b * .05 b = .05 L
---------------------------------------
3.98 L / 4 b * 1.0 b = .99 L
Actual measurements might be 40 bottles at .98 L/b, 25 bottles at .99 etc
Then the total liters would be divided by the total number of bottles
Please I got 25 Brainly points (03.03)
The table below represents a linear function f(x) and the equation represents a function
g(x)
х
f(x)
-9
-1
0
-1
1
1
7
g(x) = 3x-2
Part A: Write a sentence to compare the slope of the two functions and show the steps
you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
Evaluate the function
f(x) = - 2x^2 + 2x + 4
Find f(1)
Answer:
f(1) = 4
Step-by-step explanation:
f(x) = - 2x^2 + 2x + 4
f(1) = - 2(1)^2 + 2(1) + 4
f(1) = -2 + 2 + 4
f(1) = 4
how many distinct 9-digit numbers can you make from four "1", three "2", and two "3"?
Answer:
2520
Step-by-step explanation:
If a nine digit number contains exactly 4 one's, 3 two's and 2 three's
We can choose the positions of the 1's in P(9/4) ways.
We can choose the positions of the 2's from the five remaining positions in P(5/3) ways
We can choose the positions of the 3's from the two remaining positions in P(2/2) ways
In this problem order doesnt matter..
= (9!/5!×4!) × (5!/3!×2!) × (2!/2!×0!)
= 2520
8/y = 2/y-2 +1 Answer fast please.
Answer:
Given equation is (8/y) = 2/(y-2) +1
=> (8/y)- 2/(y-2) = 1
=> [8(y-2)-2y]/(y-2)y = 1
=> (8y-16-2y)/(y²-2y) = 1
=> (6y-16)/(y²-2y) = 1
=> y²-2y = 6y-16
=> y²-2y -6y+16 = 0
=> y²-8y+16 = 0
The standard form is y²-8y+16 = 0.
Answer:
-6
Step-by-step explanation:
8/y = 2/y - 2 + 1
8/y = 2/y - 1
8 = 2 - y
6 = -y
y = -6
Expand the linear factors of f(x), where f(x) = (x - 10)(x + 2).
1 9) y=--x + 3 3 *x y 2 # 54 B X there
the slope is -1/3 and since the slope is negative, the line goes the opposite way and you start at (3,0)
Given f(x)=3x^2-5x+k and the remainder when f(x) is divided by x-4 is 38, then what is the value of k? brainliest for correct answer( and fastest, obviously).
Answer:
the answer is 30
when you substitute x = 4
solve for K
Step-by-step explanation:
the answer is 30
please brainlist
The perimeter, p, of an equilateral triangle varies directly as the length of a side, s, if
the perimeter is 153 cm when the side length is 51 cm, what would be the perimeter if
the side length is 81 cm.
Variation can be direct, inverse or joint.
The perimeter is 243 cm
Represent perimeter with P and side lengths with L.
So, we have:
[tex]\mathbf{P\ \alpha\ L}[/tex]
Express as an equation
[tex]\mathbf{P = kL}[/tex]
Where k is the constant of variation.
Make k the subject
[tex]\mathbf{k = \frac PL}[/tex]
So, we have:
[tex]\mathbf{\frac{P_1}{L_1} = \frac{P_2}{L_2}}[/tex]
Make P2 the subject
[tex]\mathbf{P_2 = L_2 \times \frac{P_1}{L_1} }[/tex]
Substitute the given parameters
[tex]\mathbf{P_2 = 81 \times \frac{153}{51} }[/tex]
[tex]\mathbf{P_2 = 81 \times 3 }[/tex]
[tex]\mathbf{P_2 = 243}[/tex]
Hence, the perimeter is 243 cm
Read more about variations at:
https://brainly.com/question/16510700
describe how the pattern is changing
as you can see in the pattern he adds 1 in each time to the height and 2 to the width