Answers
Answer:
Axis is a vertical line at x = 2
Vertex is (2, -1)
y-intercept is (0, 3)
Solutions are x = 1 and x = 3
Step-by-step explanation:
To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y
Let us do that
Use x = -1, 0, 1, 2, 3, 4, 5
∵ y = x² - 4x + 3
∵ x = -1
∴ y = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8
→ Plot point (-1, 8)
∵ x = 0
∴ y = (0)² - 4(0) + 3 = 0 + 0 + 3 = 3
→ Plot point (0, 3)
∵ x = 1
∴ y = (1)² - 4(1) + 3 = 1 - 4 + 3 = 0
→ Plot point (1, 0)
∵ x = 2
∴ y = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1
→ Plot point (2, -1)
∵ x = 3
∴ y = (3)² - 4(3) + 3 = 9 - 12 + 3 = 0
→ Plot point (3, 0)
∵ x = 4
∴ y = (4)² - 4(4) + 3 = 16 - 16 + 3 = 3
→ Plot point (4, 3)
∵ x = 5
∴ y = (5)² - 4(5) + 3 = 25 - 20 + 3 = 8
→ Plot point (5, 8)
→ Join all the points to form the parabola
From the graph
∵ The axis of symmetry is the vertical line passes through the vertex point
∵ x-coordinate of the vertex point is 2
∴ Axis is a vertical line at x = 2
∵ The coordinates of the vertex point of the parabola are (2, -1)
∴ Vertex is (2, -1)
∵ The parabola intersects the y-axis at point (0, 3)
∴ y-intercept is (0, 3)
∵ x² - 4x + 3 = 0
∵ The solutions of the equation are the values of x at y = 0
→ That means the intersection points of the parabola and the x-axis
∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)
∴ Solutions are x = 1 and x = 3
Related Questions
Michael and Imani go out to eat for lunch. Part A If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill? Enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
25.30*8% tax = 2.02 tax
total 25.30+2.02= $27.32
Answer:
$27.32
Step-by-step explanation:
Multiply $25.30 by 0.08 (8% is equal to 0.08)
2.024
Add 2.024 to $25.30
That would be 27.324
Round to the nearest hundredth
$27.32
Hope this helps :)
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You are starting a savings account for college. You put
$1,000 in as your starting balance. You earn simple
interest at 10% every year. You also must pay 30%
income tax on the interest earned annually. Calculate
the interest, balance, tax paid, and the overall balance
of the account after taxes. To break the code determine
the accounts overall balance for year 5 after taxes after
been paid.
Answers
Answer: $4,000
Step-by-step explanation:
If you have $1,000 dollars, and take ad ten percent ($100) interest you would get $1,100. But If you take away 30 percent ($300) away from 1,100 dollars you would get $800 dollars. The over all balance on the account after five years is, $4,000.
Hope this answer helps! :)
have u ever seen 2 pretty besfrens??
Answers
yea once
they ain't friends no more
bc I stole one
and now there ain't 2 pretty best frens no more
4 A baby's t-shirt requires 5 yards of fabric. How many t-shirts can be made from 48 yards?
Answers
Answer:
9 t-shirts
Step-by-step explanation:
divide 5 by 48 you will get 9.3 but that is not what it is asking it how many t-shirts can they total
Tony hit 9 out of 15 pitches at baseball practice yesterday. The following day at practice 45 pitches were made. How many pitches did Tony miss?
Answers
Answer:
18 pitches.
Step-by-step explanation:
I'm assuming the "9 out of 15" is the fraction of pitches Tony hit at baseball practice.
Hence, Tony missed 6 out of 15 pitches.
6/15 * 45
= 6 * 3
= 18 pitches.
Hope this helped!
Answer:
18
Step-by-step explanation:
You have to start with how many he hit.
Let the number of pitches he hit = x
9/15 = x / 45 Cross multiply
15x = 9 * 45 Combine the right side
15x = 405 Divide by 15
x = 405/15
x = 27
===================
The number he missed is 45 - 27 = 18
2x+3y = 17
2y + z = 1
5x +10z = 25
Find x
Answers
Answer:
x = 7
Step-by-step explanation:
Given the equations
2x + 3y = 17 → (1)
2y + z = 1 → (2)
5x + 10z = 25 → (3)
Rearrange (2) expressing z in terms of y
z = 1 - 2y
Substitute z = 1 - 2y into (3)
5x + 10(1 - 2y) = 25
5x + 10 - 20y = 25 ( subtract 10 from both sides )
5x - 20y = 15 → (4)
Multiply (1) by 20 and (4) by 3, then add to eliminate the y- term
40x + 60y = 340 → (5)
15x - 60y = 45 → (6)
Add (5) and (6) term by term to eliminate y, that is
55x = 385 ( divide both sides by 55 )
x = 7
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
From the equation [tex]2y + z = 1[/tex] , we can separate [tex]z[/tex] so that [tex]z = 1-2y[/tex].
The equation [tex]5x+10z = 25[/tex] can then be turned into:
[tex]5x+10(1-2y) = 25[/tex]
[tex]5x+10-20y = 25[/tex]
[tex]5x -20y = 15[/tex]
[tex]x-4y = 3[/tex] (divide by [tex]5[/tex] on both sides)
We can now use elimination to solve for one of the variable:
[tex]2(x-4y) = 2\times3[/tex] (times 2 to get [tex]2x[/tex] for elimination)
[tex]2x-8y=6[/tex]
[tex]2x+3y-(2x-8y) = 17-6[/tex]
[tex]11y = 11[/tex]
[tex]y = 1[/tex]
Now, we can use substitution to solve for [tex]x[/tex]:
[tex]2x+3y = 17[/tex]
[tex]2x+3 = 17[/tex]
[tex]x = 7[/tex]
Hope this helps :)
Find two integers whose sum is 19 and product is 90
Answers
Answer:
Step-by-step explanation:
The two integers are 10 and 9
10 + 9 = 19
10 x 9 = 90
The two numbers are 9 and 10.
What are integers?A number without a decimal or fractional element is known as an integer, which can be both positive and negative, including zero
Let the two integers be x and y.
Given that, the sum of the integers is 19, therefore,
x + y = 19
x = 19 - y
Given that, the product of the integer is 90:
xy = 90
(19-y)y = 90
19y - y² = 90
y² -19y + 90 =0
y² -10y - 9y + 90 = 0
y(y - 10) -9(y - 10) = 0
(y -9)(y - 10) = 0
y = 9 and y = 10
Hence, the two numbers are 9 and 10.
Learn more about integers:
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HURRYYYYY
Which system of linear inequalities is graphed?
Answers
I would have put C. Because if you look at the triangle it makes then do the math with squared numbers then you should get c.
A number x is greater than 3.
Answers
Answer:
4,5,6,7,8,9..........................
7. What is the mass of 20.6cm3 of iron if iron
has a density of 7.87g/cm3?
A. 162.1 g/cm3
B. 162.1 cm3
C. 162.1 g/mL
D. 162.1 g
Answers
Answer:
Option B
Step-by-step explanation:
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What is the slope of a line with the equation y = 5x + ⅖ ?
Answers
Answer:
The slope would be 5
Step-by-step explanation:
The reason why it would be five is because the slope formula is y=mx+b with m being your slope and b being your y-intercept.
Answer:
slope: 5
Step-by-step explanation:
[tex]y=mx+b[/tex] is the equation used to find the slope of an equation. The slope is ALWAYS the "m" value. So.... in this equation y=5+2/5... the "m" value is 5.... making the slope of the equation 5.
HELP ASAP OTS DUE IN 5 MINUTES!!!!
Find the slope of the line.
0-5
0 -1
O 1
None of the above
Answers
Answer:
0 -1
Step-by-step explanation:
because the line is going down which is negative
2. Count by 5¢ to complete the
pattern.
1
30¢, 35¢, 404,
Pls helpppp
Answers
45,50,55 there
Bill has a large collection of paperback books. He decided to donate 1/3 of them to his local library. If he had 126 to start with, how many does he have left?
Answers
Answer:
42
Step-by-step explanation:
Renee used the values in the table to calculate simple interest.
Principal $750
Interest rate ?
Time 11 years
Interest $412.50
Which interest rate is missing from Renee’s table?
0.05%
0.5%
5%
50%
Answers
Answer:
5% hope its correct
Step-by-step explanation:
The rate of Interest is 55.
What is Simple Interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
Given:
Principal= $750
Time = 11 years
Interest= $412.50
Using Simple Interest
SI= (PRT)/100
412.5 = (750 x R x 11) 100
41250 = 8250R
R= 5%
Hence, the rate of Interest is 55.
Learn more about Simple Interest here:
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Thomas observed that his friend blinked an average of three times every 15 seconds.
How many times should his friend blink in 65 second?
Answers
Answer:
13 blinksStep-by-step explanation:
Step one:
given
number of blinks= 3
time taken to blink=15 seconds
the rate of blink is given as
rate= number of blinks/time taken
rate= 3/15
rate= 1/5 blinks per second, 0.2 blinks per second
Step two:
hence for a 65 second period, the number of blinks is
rate=number of blink/time
0.2=number of blink/9=65
cross multiply we have
number of blink=0.2*65
number of blink=13 blinks
5x +9–3(x-1)=(3x –13)+(4x -30)
Help please
Answers
Answer:
x = 11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
5x + 9 - 3(x - 1) = (3x - 13) + (4x - 30)
Step 2: Solve for x
Distribute 3: 5x + 9 - 3x + 3 = 3x - 13 + 4x - 30Combine like terms: 2x + 12 = 7x - 43Subtract 2x on both sides: 12 = 5x - 43Add 43 on both sides: 55 = 5xDivide 5 on both sides: 11 = xRewrite: x = 11Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 5(11) + 9 - 3(11 - 1) = (3(11) - 13) + (4(11) - 30)Multiply: 55 + 9 - 3(11 - 1) = (33 - 13) + (44 - 30)Subtract: 55 + 9 - 3(10) = 20 + 14Multiply: 55 + 9 - 30 = 20 + 14Add: 64 - 30 = 34Subtract: 34 = 34Here we see that 34 does indeed equal 34.
∴ x = 11 is a solution of the equation.
Answer:
x=11
Step-by-step explanation:
[remember: (-)(-) is (+) , (-)(+) is (-) , (+)(+) is (+)]
5x + 9 – 3(x-1) = (3x –13) + (4x -30)
5x + 9 -3x + 3 = 3x -13 + 4x -30
5x -3x + 9 + 3 = 3x + 4x -13 -30
2x + 12 = 7x - 43
2x - 7x = -43 - 12
-5x = -55
x = -55/-5
x = 11
hope you understood!!
The length of a rectangle is represented by 4 + 6x. The width is half the length. What expression represents the perimeter of the rectangle? Explain your reasoning
Answers
Answer:
12+18x is the perimeter
Step-by-step explanation:
4+6x+4+6x+1/2(4+6x)+1/2(4+6x)=
3(4+6x)=
12+18x
Which set of number is only made up of integers?
Negative 2 and StartFraction 4 Over 7 EndFraction, 0, Two-thirds, 4.6, 24
–7.6, 0, 4.ModifyingAbove 2 with bar, 16, 56
–33.3, –24, 1, 2 , 3
–23, –7, 5, 9, 190
Answers
Answer:
It is D (-23, -7, 5, 9, 190)
Step-by-step explanation:
:)
-3\10d= -4\5 this is just so i can get answer ggggggggggggggggggg
Answers
Answer:
d = 8/3
Step-by-step explanation:
This equation has one solution.
3(x-2) + 4x = 10(x + 1)
What is the solution?
O-5
O-2
-16
3
-16
7
Intro
Answers
Find the slope of the line that contains (1, 6) and (10.-9).
Answers
Answer:
-5/3
Step-by-step explanation:
m=−9−6/10−1
m=−15/9
Slope=
−15/9=−5/3
1. The sum of a number and ten.
Answers
X+10
Explanation:
Break down the information given to you to try and identify what the algebraic expression must looks like. You know that you're dealing with
a sum
→
this means that you are adding something, so you're going to use the
+
sign;
of a number
→
this means that you're dealing with a variable. The most common notation for a variable is
x
.
and 10
→
this is simply an integer that must appear in the algebraic expression along the variable
x
.
So, put all this together to get
x
+
10
You're adding an unknown number,
x
, to an integer,
10
Answer:
x+10
Step-by-step explanation:
sum = addition (+)
number = variable because we don't know what the number is yet (x)
ten=ten
So by this we can get x+10
Will mark brainliest
Answers
Every week, Hector’s 20 hours earns $210.00. He earns a constant amount of money per hour.
Part B
Write an equation that can be used to determine Hector's earnings, in dollars, m, for h hours of work.
Answers
Answer: 20 weeks in 1 week
in 2 weeks 40
Step-by-step explanation:
This proves that the equation is true
What is the surface area of the pyramid
Answers
Answer:
The surface area is 31.85 in.
Step-by-step explanation:
simplify: (-3x^3+2x^2+4x)-(8x^4-5x^3+6x^2-2x
Answers
Answer:
−8^4+2^3−4^2+6
Step-by-step explanation:
Distribute the - to 8x^4-5x^3+6x^2-2x:
-8x^4+5x^3-6x^2+2x
Now simplify:
-3x^3+2x^2+4x-8x^4+5x^3-6x^2+2x= −8^4+2^3−4^2+6
Hope this helps!
Hey again.. Please answer!!
Answers
Answer:
I can't see the question
its too small can you type it out?
Step-by-step explanation:
Answer:
32 cups and 24 cups
Step-by-step explanation:
4x + 3x = 56
7x = 56
x = 8
4(8) = 32 cups of pretzels
3(8) = 24 cups of candy corn
⚠️⚠️What is the output value, if the input value is 30?⚠️⚠️
THIS IS MY LAST ONE HELP
Answers
Answer:
15
Step-by-step explanation:
15 is half of 30, the output values are the input values divided by 2 :)
Gloria pays her insurance three times each year. The first payment is 50% of the annual
premium, and each of the next two payments is 25% of the annual premium. If the annual premium is
$1024, how much is each payment?
Answers
Answer:
First payment (50%) would be 512$
The next two payments would be 32$ each
Explanation:
.5(1024)= 512
.25(512)=128
.25(128)= 32