How do you graph
Y=x^2-4x+3
Answers
Answer:
Answer is below
Step-by-step explanation:
Use 3 as the y-intercept. Factor the equation to find the solutions
(x - 1) (x - 3) so 1 and 3 are the x-intercepts. The vertex of the graph is at (2,-1).
I also graphed the equation below.
If this answer is correct, please make me Brainliest!
The graph of [tex]y = x^2 - 4x + 3[/tex] is a parabola that opens upward with its vertex at (2, -1). It intersects the x-axis at x = 3 and x = 1 and the y-axis at y = 3.
How to graph this equationThe equation is [tex]y = x^2 - 4x + 3.[/tex]
Use the formula x = -b / (2a) to find the x-coordinate of the vertex. In this case, a = 1, b = -4.
x = -(-4) / (2*1)
= 4 / 2
= 2.
So, the x-coordinate of the vertex is 2.
Subtitute x = 2 into the equation:
[tex]y = (2)^2 - 4(2) + 3[/tex]
= 4 - 8 + 3
= -1.
The y-coordinate of the vertex is -1.
The vertex is at (2, -1).
The y-intercept, we will set x = 0 in the equation:
[tex]y = (0)^2 - 4(0) + 3[/tex]
= 0 - 0 + 3
= 3.
The get x-intercepts, we set y = 0 in the equation:
[tex]0 = x^2 - 4x + 3.[/tex]
(x - 3)(x - 1) = 0.
x = 3 or x = 1.
The x-intercepts are 3 and 1.
Now, we will plot the y-intercept and x-intercepts. The y-intercept is at (0, 3), and the x-intercepts are at (3, 0) and (1, 0).
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Related Questions
A multiplier is the amount by which a change in any component of _____ is magnified or multiplied to determine the change in _____ and _____ that it generates.
Answers
Answer:
Autonomous Expenditure ; Equilibrium expenditure ; Real GDP
Step-by-step explanation:
A multiplier is the amount by which a change in any component of Autonomous Expenditure is magnified or multiplied to determine the change in Equilibrium Expenditure and Real GDP that it generates.
Multiplier = Change in Equilibrium Expenditure of Real GDP
Change in autonomous expenditures
(government expenditure, autonomous taxes)
The parallel sides of a trapezoid measure 13.5 inches and 6.5 inches. The legs of the trapezoid are 4 inches and 7 inches. The height of the trapezoid is 3 inches. Find the perimeter of the trapezoid. *
Answers
Answer:
31 inches. Add all the sides together. The height is not needed. 6.5+13.5+4+7=31 inches.
Step-by-step explanation:
Answer:
Perimeter = 13.5 + 6.5 + 4 + 7
= 31 inches
Step-by-step explanation:
given that y varies directly with x in the table find the value of y if the value of x is 5
Answers
Answer:
15
Step-by-step explanation:
Alejandro ha hecho 3 exámenes. El primero tenía 8 preguntas, el segundo 9 y el tercero 12. Las preguntas correctas de cada uno de ellos han sido 7, 8 y 10, respectivamente. Si en cada examen todas las preguntas tenían la misma calificación ¿en cuál de ellos ha obtenido un mejor resultado?
Answers
encuentras el mínimo común denominador para que todas las fracciones tengan el mismo y te da nuevas fracciones que serían: 63/72, 64/72, y 60/72 respectivamente
Quadrilateral RSTV is a rectangle, and the diagonal intersect at W. Find the value of X and Y.
Answers
Answer:
x = 3
y = 14
Step-by-step explanation:
VR = TS VT = RS (Rectangle)
y = x + 11
y - 3x = x + 2
y = 4x + 2
x + 11 = 4x + 2
3x = 9
x = 3
y = 14
dentify the parts of the following algebraic expression.
-8z + 1
2
y - 7.7
Term:
Variable:
Coefficient:
Constant:
Answers
The algebraic expression -8z + 1 consists of terms (-8z and 1), a variable (z), a coefficient (-8), and a constant (1), enriching the understanding of algebraic expressions.
Explanation:The question identify the parts of the following algebraic expression: -8z + 1 is focused on dissecting an algebraic term to its fundamental components. The expression – 8z + 1 has several parts to be identified:
Term: The terms in the expression are – 8z and 1. Terms are individual parts of an expression separated by + or – signs.Variable: The variable in the expression is z. Variables represent unknown values and can change.Coefficient: The coefficient in the expression is –8. Coefficients are numbers used to multiply a variable.Constant: The constant in the expression is 1. Constants are fixed numbers that do not change.The identification of each part of an algebraic expression helps in understanding and solving mathematical equations effectively.
The algebraic expression -8z + [tex]\frac{1}{2}[/tex]y - 7.7 has -
Terms: -8z, [tex]\frac{1}{2}[/tex]y, and -7.7Variables: z and yCoefficients: -8 and [tex]\frac{1}{2}[/tex]Constant: -7.7In the algebraic expression -8z + [tex]\frac{1}{2}[/tex]y - 7.7, we can identify the terms, variables, coefficients, and constants as follows:
Terms: These are the individual parts of the expression separated by plus or minus signs. In this expression, the terms are -8z, [tex]\frac{1}{2}[/tex]y, and -7.7.Variables: These are the symbols representing unknown values in each term. Here, the variables are z and y.Coefficients: These are the numerical factors multiplied by the variables. In the expression, the coefficients are -8 (for the term -8z) and [tex]\frac{1}{2}[/tex] (for the term [tex]\frac{1}{2}[/tex]y).Constant: This is a term without any variable, which is just a fixed number. In the given expression, the constant is -7.7.Understanding these parts is essential for simplifying expressions and solving algebraic equations effectively.
Complete question:
Identify the parts of the following algebraic expression.
-8z + [tex]\frac{1}{2}[/tex]y - 7.7
Term:Variable:Coefficient:Constant:According to the annual Summer Vacation Survey conducted by Myvesta, a nonprofit consumer education organization, the average summer vacation costs $2252. If $1650 of this amount is charged on a credit card, what percent of the vacation cost is charged?
Answers
Answer:
The answer is : 73.3% (to 1 decimal place)
Step-by-step explanation:
The question is asking us to convert the proportion of a certain amount into percentage, and this is done as shown below:
vacation cost = $2252
amount charged = $1650
%of vacation cost that was charged = X%
∴ X% of 2252 = 1650
[tex]\frac{X}{100}[/tex] × 2252 = 1652
[tex]\frac{2252X}{100} =1650[/tex]
2252X = 165000 (dividing both sides by 2252)
[tex]\frac{2252X}{2252}=\frac{165000}{2252}[/tex]
∴ X = 165000 ÷ 2252
X = 73.3%
Is the product of two positive numbers negative?
Answers
Answer:
Product (Multiplication) always needs a negative to be negative
Step-by-step explanation:
Andrea makes the claim that 20% of the states have
populations of at least 10 million people.
Is she correct?
Yes
No
Explain your thinking.
Share with Class
Answers
In order to confirm Andrea's claim that 20% of U.S. states have populations of 10 million or more, we'd need to refer to updated population census data. The number of states that comply to this number would validate or invalidate her claim.
Explanation:To determine whether Andrea's claim that 20% of the states have populations of at least 10 million people is correct, we would need to refer to updated census data. As of the most recent U.S. census, there are 50 states in the United States. If 20% of them had populations of at least 10 million, that would mean that 10 states meet this criteria. Checking the census data, we can see whether this number is accurate or not and thus confirm or deny Andrea's claim.
For example, if only 8 states had a population of over 10 million, Andrea's claim would be incorrect. On the other hand, if 15 states had a population of over 10 million, her claim would also be incorrect, but it would be an underestimation rather than an overestimation. Therefore, without specific data, we cannot unequivocally say whether Andrea's claim is correct.
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A machine drops 74 milliliters of liquid into a beaker every minute. Using an empty beaker, Sarah started the machine and left the room. When she returned, the beaker had 1,850 milliliters of liquid in it. Select the correct operation that can be used to find the time in minutes, m, that Sarah was out of the room, and then find the value of m. Sarah was out of the room for minutes.
Answers
Answer:
Division, you can divide the total amount of total milliliters buy the number of milliliters dropped every minute. 1850/74= 25. So m= 25. Sarah left the room for 25 minutes
Step-by-step explanation:
pls mark me brainliest
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 9898% confidence interval for p is 59 plus or minus 0.08 .59±0.08. Interpret this interval. A. We are 9898% confident that between 5151% and 6767% of the sampled students receive some sort of financial aid. B. We are 9898% confident that the true proportion of all students receiving financial aid is between 0. 51.51 and 0. 67..67. C. 9898% of the students receive between 5151% and 6767% of their tuition in financial aid. D. We are 9898% confident that 59% of the students are on some sort of financial aid.
Answers
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 200
x = 118
p = 118/200 = 0.59
q = 1 - 0.59 = 0.41
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.01 = 0.9
The z score corresponding to the area on the z table is 2.326. Thus, confidence level of 98% is 2.326
Therefore, the 98% confidence interval is
0.59 ± 2.326√(0.59)(0.41)/200
= 0.59 ± 0.08
The lower boundary is
0.59 - 0.08 = 0.51
The upper boundary is
0.59 + 0.08 = 0.67
The correct option is
B. We are 98% confident that the true proportion of all students receiving financial aid is between 0. 51 and 0. 67
Sarita is selling lemonade in 400 milliliter bottles she made two batches of lemonade each batch made 16.3 liters of lemonade how much lemonade will she have left over after filling the bottles
Answers
Answer: She will have 200 milliliters of lemonade left after filling the bottles.
Step-by-step explanation:
Hi, since 1 liter = 1000 milliliters
For 16.3 liters: 16.3 x 1000 = 16,300 milliliters (1 batch)
She made 2 batches.
16,300ml x2 = 36,600 milliliters
We have the total amount of lemonade in two batches; we have to divide it by the capacity of each bottle (400 ml), to calculate how many bottles she can fill.
36,600 milliliters / 400 milliliters = 81.5 bottles
She can fill 81 bottles and she will have a leftover of half a bottle.
Since each bottle is 400 milliliters, half of it:
400/2 = 200 milliliters
She will have 200 milliliters of lemonade left after filling the bottles.
Jacob makes 20 baskets for every 35 times he shoots the ball. What is the ratio of baskets he makes to baskets he misses? Write an equivalent ratio by simplifying.
Answers
Answer:
ratio = 4/3 = 1.3333
Step-by-step explanation:
If Jacob makes 20 baskets for every 35 times he shoots the ball, that means he misses 35 - 20 = 15 shoots for every 35 shoots.
So, to calculate the ratio of baskets he makes to baskets he misses, we just need to divide these values:
baskets he makes = 20 for every 35
baskets he misses = 15 for every 35
ratio = 20 / 15 = 4 / 3 = 1.3333
What is the value of z so that’s -9 and 9 are both solutions of x^2+z=103
Answers
Answer:
we have been given that x=-9 and x=9 then putting two values of x in the given equation we can find the value of z. I've got the value of z as 22
Step-by-step explanation:
The given equation is :
x^2+z=103
If we put x as (-9) ,
(-9)^2+z = 103
or, 81 +z = 103
or, z= 103-81
or,z=22 (Answer)
Now , again if we put x as 9,
9^2+z=103
or, 81+z=103
or,z=103-81
or,z=22 (Answer)
THEREFORE THE VALUE OF Z IS 22
True or False?
You can use an equilateral triangle in front of the three letter points to name a triangle.
Answers
True.
I'm not sure if it's right or not
Answer:
True
Step-by-step explanation:
I am not sure if it's right or not
Part A
If you spin the spinner 11 times, what is the prediction for the number of times it will land on red?
Each section is equal in size.(it's talking about the spiner)
Answer:
Part B
What is the probability of green?
A: 3/11
B:4/11
C:1/11
D:7/11
Answers
Since all sectors have the same area, the spinner is equaly likely to land on each of them. There are:
3 yellow sectors3 red sectors4 green sectors1 blue sectorObviously, this implies that there are 11 sectors in total.
So, the spinner will land on a certain color with probability
[tex]p=\dfrac{\text{\# of sectors for that color}}{\text{11}}[/tex]
Use this formula to deduce the probability of green.
Finally, you can multiply the probability of red by 11 to get the expected number of reds in 11 spins.
What is the value of n when (9)^2n-1 =(27)^n+2
Answers
Answer:
n = 8
Step-by-step explanation:
Using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
Given
[tex](9)^{2n-1}[/tex] = [tex](27)^{n+2}[/tex], then
[tex](3^2)^{2n-1}[/tex] = [tex](3^3)^{n+2}[/tex]
[tex]3^{4n-2}[/tex] = [tex]3^{3n+6}[/tex]
Since the bases on both sides are equal, both 3 then equate the exponents
4n - 2 = 3n + 6 ( subtract 3n from both sides )
n - 2 = 6 ( add 2 to both sides )
n = 8
Answer:
n = 8
Step-by-step explanation:
9²ⁿ⁻¹ = 27ⁿ⁺²
(3²)²ⁿ⁻¹ = (3³)ⁿ⁺²
3⁴ⁿ⁻² = 3³ⁿ⁺⁶
4n - 2 = 3n + 6
4n - 3n = 6 + 2
n = 8
After stepping into a room with unusual lighting, Erik's pupil has a radius of 4 millimeters. What is the pupil's area?
Answers
The area of the pupil can be found using the formula for the area of a circle (Area = π × r²). When you substitute the given radius (4mm), the pupil's area comes out to be approximately 50.27 square millimeters.
Explanation:To calculate the area of a circle which in this case is the pupil, you need to use the formula, Area = π × r², where r is the radius of the circle. Here, the radius (r) of the pupil is 4 millimeters. Substituting r = 4 mm in the formula we get:
Area = π × (4 mm)²
Area = π × 16 mm²
So, the area of the pupil is 16π mm², which is about 50.27 mm² when calculated. Please note that the unit of the area is square millimeters since we are calculating the area.
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The pupil's area can be calculated using the formula A = πr^2, where r is the pupil's radius, the area is 50.27 square millimeters.
Explanation:The area of a circle can be calculated using the formula A = πr2, where A is the area and r is the radius of the circle. In this case, the pupil's radius is given as 4 millimeters, so we can substitute this value into the formula.
A = π(4 mm)2 = π16 mm2
Therefore, the pupil's area is approximately 50.27 square millimeters.
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which factors can be multiplied together to make the trinomial 5x^2+8x-4
Answers
Answer:
Step-by-step explanation:
hello :
5x²+8x-4 quadratic expression when : a = 5 and b=8 and c= -4
∆ = b²-4ac ∆ = 8²-4(5)(-4) = 64 +80 = 144 = 12²
X1 = ( -b -√∆)/2a X1 = (-8-12)/10 = -20/10= -2
X2 =(-b+√∆)/2a X2 = (-8+12)/10 = 4/10 = 2/5
us factorisation : a(X-X1)(X-X2)
5x²+8x-4= 5(x+2)(x-2/5) = (x+2)(5x-2)
you can verify ; (x+2)(5x-2) = 5x²-2x+10x-4 = 5x²+8x-4
The trinomial [tex]5x^2+8x-4[/tex] can be factored into two binomials (5x + 4) and (x - 1), which when multiplied together, produce the original trinomial.
To factor the trinomial [tex]5x^2+8x-4[/tex], we are looking for two binomials that when multiplied together will give us this trinomial.
The process of factoring involves reversing the distributive law and turning the expression back into factors (multiples). To do this, we look for two numbers that multiply to give the product of the coefficient of x² term (which is 5) and the constant term (which is -4), and that also add up to give the coefficient of the x term (which is 8).
Let's find the factors:
Factors of 5x² are 5x and x.
Factors of -4 that add up to +8 when multiplied by the corresponding factors of 5 can be 4 and -1, since (5x)(-1) + (x)(4) = -5x + 4x = -1x.
Therefore, the binomials we are looking for are (5x + 4) and (x - 1).
When you multiply (5x + 4) and (x - 1) together, it will result in the original trinomial 5x²+8x-4.
Mr.smith and mr.Stein We’re driving to a business meeting 100 miles from their office. Mr.smith Drove the first y miles ,then mr. Stein Drove the rest of the way.
Answers
Answer:
mrs smith drove 50 miles and mr stein drove 50 mile
Step-by-step explanation:
An object is dropped from 43 feet below the tip of the pinnacle atop a 527-ft tall building. The height h of the object after t seconds is given by the equation h equals negative 16 t squared plus 484. Find how many seconds pass before the object reaches the ground.
Answers
Answer:
5.5 seconds
Step-by-step explanation:
The function that gives the height of the object after t seconds falling is:
h = -16t^2 + 484.
To find the time when the object reaches the ground, we just need to use the value of h = 0 in the equation, and then find the value of t:
0 = -16t^2 + 484.
16t^2 = 484
t^2 = 30.25
t = 5.5 seconds
So the object will reach the ground after 5.5 seconds
Answer:
5.5 sec
Step-by-step explanation:
The height h of the object after t seconds is given by the equation
h =- 16 t²+ 484
The height would be zero when the object hits the ground. therefore equating the above equation to zero
0 = - 16 t²+ 484 (solving for t)
16 t²= 484
t² = 484/16
t²= 30.25
taking square root on B.S
t= 5.5 sec
Jen rode her bike 1/5 of a mile to her friend's house. It took her 5 minutes to get there. What was Jen's speed?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
Answers
Jen's speed was 1/25 miles per minute or 2.4 miles per hour. This was found by dividing the distance travelled by the time it took.
Explanation:To find Jen's speed, we need to divide the distance she rode by the time it took her. In this case, Jen rode 1/5 of a mile in 5 minutes. To get her speed in miles per minute, we perform the division:
1/5 mile ÷ 5 minutes = 1/25 miles per minute
This means that Jen's speed was 1/25 miles per minute. You could also convert this to miles per hour if you prefer, by multiplying the result by 60 (since there are 60 minutes in an hour). In that case:
1/25 miles per minute x 60 minutes/hour = 2.4 miles/hour.
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Jen's speed was 1/25 miles per minute, calculated by dividing the distance traveled, 1/5 mile, by the time taken, 5 minutes.
Explanation:To determine Jen's speed, we would divide the distance she traveled by the time it took her to get there. Jen rode her bike for 1/5 of a mile, and it took her 5 minutes. To find her speed in miles per minute, we perform the following calculation:
Speed = Distance ÷ Time
Speed = (1/5) mile ÷ 5 minutes = 1/5 ÷ 1/5 = 1/25 miles per minute.
We don't need to convert the units since we are asked to provide the answer as a proper fraction. Therefore, Jen's speed was 1/25 miles per minute.
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HELP
Find the value of two numbers if their sum is 5 and their difference is 30
Answers
Answer:
The 2 numbers are -12.5 and 17.5.
Step-by-step explanation:
Let 1 number be x then x - y = 30 where the other number is y.
y = x - 30 so the sum is:
x - 30 + x = 5
2x = 35
x = 17.5
and y = 17.5 - 30 = -12.5.
Answer:
17.5 and -12.5
Step-by-step explanation:
Kel has 6 nickels, 2 dimes and 4 quarters in his pocket. What is the likelihood that Kel will choose a nickel from his pocket?
A. impossible
B. likely
C. as likely as not
D. certain
Answers
Answer:
B likely
Step-by-step explanation:
the probability is 1/2 because there are 12 coins and 6 of them are nickels
Find the perimeter of the shape
5cm
6cm
17cm
8cm
Perimeter = [perimeter] cm
Answers
PLEASE HELP!!!! What is the absolute value of 5.9?
Answers
Answer:
5.9
Step-by-step explanation:
The absolute value of a number is its distance from zero on the number line, without considering direction. Hence, the absolute value of 5.9 is 5.9 itself.
Explanation:The absolute value of a number is its distance from zero on the number line, regardless of direction. In other words, it's the number without any sign (either positive or negative).
As for your question, the absolute value of 5.9 is simply 5.9.
That's because 5.9 is already a positive number, and its distance from zero is 5.9 units on the number line. Absolute values are always non-negative (0 or positive), so the absolute value of any positive number is the number itself.
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Hey need help asap :):):):
Answers
Answer:
C Option is the right one. (•‿•)(•‿•)(•‿•)(•‿•)
Answer:
Its B
Step-by-step explanation:
Distribute and do not forget the minus in the middle and the 4 is negative
Find the circumferences of both circles to the nearest tenth.
I need to The circumference of the blue circle and The circumference of the orange circle please and thank you!
Answers
Answer:
Step-by-step explanation:
C=pi (d) circumference = pi (3.14) times the diameter which is 10, because the radius 5 and diameter is twice the radius..........
you can also use Formula C=2pi r which will give you the same answer.
31.4 cm for orange circle
the diameter (all the way through the center of the circle) for blue circle would be 20
C=pi (d) 3.14 times 20= 62.8 cm for blue circle
The circumferences of both circles to the nearest tenth is 31.4 cm for the orange circle and 62.8 cm for the blue circle.
Calculation of the circumference:Since the diameter is 10 so the radius is 5
Now for the orange, it should be
= 2(3.14) (5)
= 31.4 cm
And, for the blue circle, it should be
= 2(3.14) (20)
= 62.8
Hence, The circumferences of both circles to the nearest tenth is 31.4 cm for the orange circle and 62.8 cm for the blue circle.
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16 is what percent of 25?
Answers
Answer
64%
Step-by-step explanation:
cross multiply
16/25 = x/100
16 X 100 = 1600
25x=1600
/25 /25
that = 64 which is 64%
16 is 64.0% of 25.
To determine what percent 16 is of 25, follow these steps:
Identify the given values:
• The part (numerator): 16
• The whole (denominator): 25
Set up the percentage formula:
[tex]\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100[/tex]
Substitute the given values into the formula:
[tex]\text{Percentage} = \left(\frac{16}{25}\right) \times 100[/tex]
Perform the calculation:
[tex]\text{Percentage} = \left(0.64\right) \times 100 = 64.0[/tex]
How do you construct a box plot?
Answers
Answer:
to draw a box plot? The median, mean and standard deviation. The minimum, maximum, median, first and third quartiles. The median and interquartile range.
Step-by-step explanation: