Answers
Answer:
Coordinates A and B: (1, 0) and (3, 0)
Coordinates of P: (0, 3)
Coordinates of Q: (2, -1)
Step-by-step explanation:
You're pretty much given the x-intercepts from the original equation.
y = (x - 1)(x - 3). So to get the x-intercepts (points A and B), y has to equal 0. So,
0 = (x - 1)(x - 3).
and y = 0 when x equals 1 and 3. Because anything multiplied by 0 equals 0. So substituting 1 for the value of x, for example, we get:
0 = (1 - 1)(1 - 3)
0 = 0 * (-2)
So there are your x-intercepts, points A and B.
Now,
Expand the brackets of the equation.
y = (x - 1)(x - 3) becomes
y = x^2 - 4x + 3
You get the y-intercept (point P) by substituting 0 for the value of x. Doing so gives:
y = 0^2 - 4*0 + 3
y = 0 - 0 + 3
y = 3
So, we have our y-intercept (0, 3).
Point Q, the x-coordinate of the vertex is calculated with the equation -b/2a
Taking our expanded equation: x^2 - 4x + 3
which is of the form ax^2 + bx + c
So we find the values of a, b and c and input the values into the equation
a = 1
b = -4
c = 3
So, inputting these into the vertex equation, gives:
-(-4) / 2 * 1
4 / 2
2
So we have the x-coordinate of the vertex. Now that we know that, we can just substitute it into the expanded equation to give the y-coordinate:
y = 2^2 - 4*2 + 3
y = 4 - 8 + 3
y = -1
So there's our y-coordinate, and now we have both the x and y coordinate for the vertex, point Q. (2, -1).
Related Questions
what is the sum of 71/5 + 2 4/5 = N
A.9 5/5
B. 10
C. 10 5/5
D. 9 1/2
Answers
Answer:
A
Step-by-step explanation:
71/5 + 24/5 = N
Since the denominator is the same for both values, we can add them together.
71+24 / 5 = 95/5
We can prove this since 71/5 = 14.2 and 24/5 = 4.8
14.2 + 4.8 = 19
95/5 = 19
A submarine dove to a level of 450 meters below the surface of the ocean. Later it
climbed 270 meters and finally dove 80 meters more. At what depth did it stop?
Answers
Answer:
260 Meters Below the Surface
Step-by-step explanation:
"Dove 450 meters" = - 450
"Climbed 270 meters" = +270
"Dove 80 meters more" = - 80
-450+270-80
-180-80
-180+(-80)
-260 or 260 Meters Below the Surface
Solve the photo displayed above ⬆️
Answers
Answer: 216
Step-by-step explanation:its just 6x6x6
ecuacion primer grado para hoy 7x+2=8x+5
Answers
Answer:
[tex]7x + 2 = 8x + 5 \\ collecting \: like \: terms \: \\ 7x - 8x = 5 - 2 \\ - 1x = 3[/tex]
(ecuacion primer grado para hoy. ). what does this mean..
Answer:
7x+2=8x+5Recopilar términos semejantes
7x - 8x = 5 - 2-1x = 3x = 3/-1x = - 3Write an equation that represents the line.
Use exact numbers.
Answers
Answer:
y = 1.5x + 3
Step-by-step explanation:
Take the two points marked by the blue dots.
(0,3), (2,6)
Start with (0,3). The zero makes the other number with it = to the y intercept.
So far what you know is
General equation: y = mx + b
b = 3
Partial equation: y = mx + 3
Givens
To get m, you need both points.
y2 = 6
y1 = 3
x2 = 2
x1 = 0
Equation
m = (y2 - y1) / (x2 - x1)
m = (6 - 3) / (2 - 0)
m = 3 / 2
Entire equation
y = 3/2 x + 3
or
y = 1,5x + 3
What is jk? Please help asap!!!
Answers
Answer:
20 m
Step-by-step explanation:
We can see from the hatch marks that JK is equal to one half of HG
2(6x - 4) = 10x
12x - 8 = 10x
2x - 8 = 0
2x = 8
x = 8/2
x = 4
therefore to find JK we will substitute x with 4
JK = (6(4)-4) = 24 - 4 = 20m
Help help please math math please
Answers
Answer:
n = 6
Step-by-step explanation:
6÷4 = 9÷n
6n = 9*4
6n = 36
n = 6
A jar contains 0.65 liter of lime juice and 0.40 liter of orange juice. Meg poured 0.35 liter of cranberry juice into the jar. She then drank 0.10 liter of the mixture.
Part A: Write an expression to represent the total amount of juice left in the jar. (5 points)
Part B: Simplify the expression and identify which property is used in each step. (5 points)
Answers
Answer:
Part A: 0.65+0.4+0.35-.1
Part B: 1.3L left and basic maths
Answer:
Step-by-step explanation:
Solve by elimination, ordered pair also
4x + 6y = 12
6x + 9y = 12
Answers
[tex]\large\underline{\sf{Solution-}}[/tex]
Solving by Eliminating method:
[tex]\sf \leadsto 4x + 6y = 12\:\:- - - (i)[/tex]
[tex]\sf \leadsto 6x+9y = 12 \:\: - - -(ii)[/tex]
Step 1: Multiply Eqⁿ (I) by 3 and Eqⁿ (ii) by 2 to make the coefficients of y equal. Then we get the equations.
[tex]\sf \leadsto 12x + 18y = 36\:\: - - - (iii) [/tex]
[tex]\sf \leadsto 12x + 18y = 24\:\:- - - (iv)[/tex]
Step 2: Subtract Eqⁿ (iii) from Eqⁿ (iv) , we get
[tex]\sf \leadsto (12x + 18y)-(12x + 18y) = 36-24[/tex]
[tex]\sf \leadsto 0 =12, Which is a false statement. [/tex]
Therefore, the pair of equations has no solution.
Hope this helps!!
I don’t wanna fail if you know the answer pls tell me
Answers
If an object accelerates at a rate of 3 m/s2, it will exert a force of 15 N. How much force will the same object exert if it accelerates at a rate of 7 m/s2?
Answers
Answer:
13 newtons
Step-by-step explanation:
21 N force will the same object exert if it accelerates at a rate of 7 m/s².
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to define force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Given:
F = 15N
a= 3 m/s²
Now, Force = mass x acceleration
15 = mass x 3
mass = 5Kg
Now, the acceleration is 7 m/s²
F = m x a
F = 3 x 7
F = 21 N
Hence, the force exerted is 21 N.
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1. The miles traveled in 5 hours at a rate of 189 miles in 3 hours?
Special gift if you answer it right!
Answers
Answer:
312 miles were traveled in 5 hours
Step-by-step explanation:
What is P55 ? 5 25 1 120
Answers
Answer:
120
Step-by-step explanation:
I took the test
HELP! DUE SOON! X^2=6
Answers
Answer:
x² = 2
x = sqrt. of 6
x = (+-)2.449
Step-by-step explanation:
brainliest plz
I NEED URGENT HELP PLSS
Answers
Answer:
try b or c hop this help have a good day
Answer:
D
Step-by-step explanation:
the answer is D.. nothing to say step by step
what are 2 different ways to rewrite 3/8
Answers
Answer:
3/8 can be 3:8 or 3n:8n or 3n/8n where n is not zero
Step-by-step explanation:
Solve.
−0.4x−3.1=5.9
Enter your answer as a decimal or as a mixed number in simplest form in the box.
x =
Answers
The solution to the algebraic equation, −0.4x − 3.1 = 5.9, is: x = -22.5
Given the algebraic equation, −0.4x−3.1 = 5.9, to solve for x, follow the steps below:
−0.4x − 3.1 = 5.9
Add 3.1 to both sides−0.4x − 3.1 + 3.1 = 5.9 + 3.1
-0.4x = 9
Divide both sides by -0.4-0.4x/-0.4 = 9/-0.4
x = -22.5
Therefore, the solution to the algebraic equation, −0.4x − 3.1 = 5.9, is: x = -22.5
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8.
In February, you have a balance of $270 in your bank account. Each month you deposit $45. Let January = 1, February = 2, and so on. Write an equation for this situation. Use the equation to find the balance in June.
A. y – 270 = 45x; $45
B. y = 45(x – 4); $180
C. y = 45(x – 4); $270
D. y – 270 = 45(x – 2) ; $450
Answers
Answer:
D. y – 270 = 45(x – 2) ; $450
Step-by-step explanation:
GradPoint answer
I got it correct on the quiz.
PLEASE HELP
A. Anna's route is about 4 miles shorter than Alex's route, but he gets home about 20 minutes before she does because he
is traveling faster.
B. Anna's route is about the same length as Alex's route, but he will get home first because he is driving.
C. Alex's route is about the same length as Anna's route, but his stop for pizza allows Anna to get home about 30 minutes
before him
D. Alex's route is about 4 miles longer than Anna's route, but his stop for pizza allows Anna to get home just minutes before him
Answers
Answer:
A. Anna's route is about 4 miles shorter than Alex's route, but he gets home about 20 minutes before she does because he
is traveling faster.
Step-by-step explanation:
Distance word problems are a common type of algebra word problems. They involve a scenario in which you need to figure out how fast, how far, or how long one or more objects have traveled. These are often called train problems because one of the most famous types of distance problems involves finding out when two trains heading toward each other cross paths
What is the radius of a hemisphere with a volume of 6496 (cm to the third power) to the nearest tenth of a centimeter?
Answers
Answer:
14.6cm
Step-by-step explanation:
The volume of a hemisphere is 2/3 × π × r³ → 6496 = 2/3 × π × r³. You can divide both sides by 2/3π to get r³ on its own → 3103.611531 = r³. To find r, cube root both sides → r = ∛3103.611531 = 14.5835... ≈ 14.6cm.
Hope this helps!
The radius of a hemisphere with a volume of 6496 is 14.5 cm
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The volume of a hemisphere is given by the formula V = (2/3)πrr³.
Since we are given the volume of the hemisphere, we can solve for the radius as follows:
V = (2/3)πr³
6496 = (2/3)πr³
Multiplying both sides by 3/2π, we get:
r³ = 6496 × (3/2π)
=6496×3/2×3.14
=19488/6.28
=3103.1
=∛3103.1
radius=14.5
Hence, the radius of a hemisphere with a volume of 6496 is 14.5 cm
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The equation y = 18x describes the amount of money Spongebob earns as a fry cook, where x is the
number of hours he works and y is the amount of money he earns. Show work. Complete sentence.
The table shows the amount of money Squidward earns as a cashier for different numbers of hours worked.
Squidward’s Earnings
Time (h) 3 5 8 10
Money earned
($) 48 80 128 160
(a) How much money does Spongebob earn per hour?
(b) How much money does Squidward earn per hour?
pls help and explain
Answers
Answer:
a. 18 dollars per hour
b. 16 dollars per hour
Step-by-step explanation:
for a, 18 is the slope of y=18x, meaning spongebob earns 18 dollars per hour
for b, since it seems like squidward earns 32 dollars every 2 hours, it can be guessed that he earns 16 dollars per hour, since 32/2 = 16
Write the expression in rational exponent form.[tex](\sqrt[4]{x}+5)^{3}[/tex]
Answers
[tex] = \: \: \: \sqrt[4]{ {x}^{3} + 15 \sqrt{x} + 75 \sqrt[4]{x} + 125 } [/tex]
hope it helps
see the attachment
for which values of a, b, and c will Ax+ By=C be a horizontal line through the point (-4,2)
Answers
Answer:
A = 0, B = 1 and C = 2
Step-by-step explanation:
The slope of a horizonal line is zero.
y = mx + b Use the slope intercept form with m = 0 and point (-4, 2).
2 = 0(-4) + b Solve for "b"
2 = 0 + b
2 = b
The equation in slope intercept form is y = 0x + 2 ; y = 2.
The equation in standard form: Ax + By = C has the value 0x + y = 2
Write the point slope form of the equation with the given characteristics:
Slope = 1/2; x intercept = 3
Answers
Answer:
point-slope form: y - 0 = ½(x - 3)
Step-by-step explanation:
Given the slope, m = ½, and the x-intercept, (3, 0):
We can substitute these values into the point-slope form:
y - y1 = m(x - x1)
y - 0 = ½(x - 3) ← This is the point-slope form.
If ever you need to transform the point-slope form into its slope-intercept form, y = mx + b:
Distribute ½ into the parenthesis:
y - 0 = ½(x - 3)
y = ½x - 3/2 (this is the slope-intercept form).
To form the blue parallelogram, the red parallelogram is dilated using point A as the
center of dilation. Which statement is true?
Answers
Answer:
option b
Step-by-step explanation:
have a great day
pls mark as brainliest
Answer:
B
Step-by-step explanation:
crows are migrating and travel 35 km on a bearing of 047°. Then then fly 15 km of a bearing of 105°. How far , and on wha…
Answers
Answer:
American Crows can be considered partially migratory. That is, some populations migrate, others are resident, and in others only some of the crows migrate. Crows in the southern parts of their range appear to be resident and not migrate. They may make some changes in their use of space at this time, spending more time off the territory to forage and roost. Crows migrate out of the northern most parts of their range. It has been stated that crows migrate out of those areas where the minimum January temperature averages 0 ° F. Certainly crows leave the northern Great Plains in the fall, leaving Saskatchewan and Alberta to winter in the lower Plains states of Nebraska, Kansas, and Oklahoma (Kalmbach, E. R., and S. E. Aldous. 1940. Winter banding of Oklahoma crows. Wilson Bull. 52: 198-206). Crows can be seen crossing the Great Lakes in spring and fall, and these birds undoubtedly are migrating to and from parts of Canada.
Step-by-step explanation:
because They may make some changes in their use of space at this time, spending more time off the territory to forage and roost. Crows migrate out of the northern most parts of their range. It has been stated that crows migrate out of those areas where the minimum January temperature averages 0 ° F.
A scale model of the Great Pyramid of Giza is being installed in a museum. The edges of the square base have lengths of 5.6 feet and the height of the pyramid is 7.86 feet. Using these measurements, to how many significant figures could the volume of the pyramid be reported? Please help !!!
A. 1 significant figure
B. 2 significant figures
C. 3 significant figures
D. 4 significant figures
Answers
The answer to the question to how many significant figures could the volume of the pyramid be reported is B. 2 significant figures.
Since in multiplication, we cannot have more significant figures than the number with the least significant figures. So, the number of significant figures in our volume of the pyramid will be 2 since, the length of side of its square base measures 5.6 feet which is one significant figure less than that of its height which is 7.86 feet.
Since volume = area of base × height
volume = 5.6 × 5.6 × 7.86 ft³
So, the answer volume of the pyramid will have 2 significant figures.
The answer to the question to how many significant figures could the volume of the pyramid be reported is B. 2 significant figures.
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Need Help ASAP! Not too hard
Answers
Answer:
Step-by-step explanation:
What are the domain and range of the function below?
A. Domain: (-∞,-5)
Range: (5,∞)
B. Domain = (-∞,∞)
Range: (-10,5)
C. Domain: (-5,10)
Range: (-10,5)
D. Domain: (-∞,∞)
Range: (-∞,∞)
Answers
Answer:
D
Step-by-step explanation:
the graphic does not indicate any limitation in any form in any direction.
compared to a default y = x function this function is just shifted a bit. but that does not block x or y from "running" all the way from -infinity to +infinity.
need help with homework plz and thank u :)
Answers
Answer:
B
Step-by-step explanation:
The zeros are where the function crosses the x-axis. In this case, it is 5/2 and -3, which eliminates options C and D. Next, the y-intercept is the point as to where the function crosses the y-axis. Here, it is (0,15), but does not help us to narrow down our options. Finally, the maximum is the highest y-value that the function touches. If you observe the graph at its highest point, it can be inferred that it's y-value is slightly above 15, and so it is at 15.1 (x-value has no importance in this context).