The vertex of the function y = x2 - 4x + 3 is at (2,-1). You can find this by using the formula -b/2a for the x-coordinate of the vertex and then substituting this x-value into the original equation to find the y-coordinate.
Explanation:The function you are asking about, y = x2 - 4x + 3, is a quadratic function, and the graph of a quadratic function is a parabola.
The vertex of this parabola can be found using the formula -b/2a for the x-coordinate and then substituting this value into the original equation to find the y-coordinate. For this function, the coefficients a and b (from the general form ax2 + bx + c) are 1 and -4 respectively. Using the formula, the x-coordinate of the vertex is -(-4)/2*1 = 2. We then substitute x = 2 into the original equation to find y = (2)2 - 4*(2) + 3 = -1. Thus, the vertex of the function y = x2 - 4x + 3 is at (2,-1).
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Alexandra is two years older than brad. cecilia is three years younger than alexandra. all three ages added together gives a total of 37 years. how old is each student?
Let us say that:
x = age of brad
x + 2 = age of Alexandra
(x + 2) – 3 = age of Cecilia = x – 1
We are also given that:
x + x + 2 + x – 1 = 37
solving for x:
3x + 1 = 37
3x = 36
x = 12 = age of brad
x + 2 = 14 = age of Alexandra
x – 1 = 11 = age of cecilia
Finding the average values of the representative coordinates of the two endpoints of a line segment in a coordinate plane is also known as using the _______________ formula.
Three member of a tug-of-war team weigh 163 pounds, 148 pounds. and 143 pounds. what must the fourth member weight if the average weight is 150 pounds?
Write the solution to the given inequality in interval notation
If 1 cm = 0.394 inches, how many inches are in 1 kilometer?
Answer: There are 39400 inches in 1 kilometers.
Step-by-step explanation:
Since we have given that
1 cm = 0.394 inches
As we know that
1 m = 100 cm
1 km = 1000 m
1000 m = 100×1000=100000 cm
1 km = 100000 cm
So, it becomes,
[tex]1\ km=0.394\times 100000\\\\1\ km=39400\ inches[/tex]
Hence, there are 39400 inches in 1 kilometers.
How much is 8% of 1249? round the answer to the nearest hundredth
Is the relation a function? (3, 6) (10, 13) (11, 1) (13, 6)
Yes, Given relation is a function.
Here,
Points are given as,
(3, 6) (10, 13) (11, 1) (13, 6)
What is a function?
A function is defined as a relation between a set of inputs having one output each.
Now,
The given relation is a function because we don't have any repeated x values. Each input (x) leads to exactly one output (y). if we plotted all the points, then we would not be able to pass a single vertical line through more than one point. Hence, this graph complies vertical line test.
So, Given relation is a function.
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Janet Fog's uncle, Pete Moore, promised her a gift of $30,000 upon her graduation from law school or $1500 every quarter for the next four years. if the money could be invested at 12% compounded quarterly, which offer should Janet choose?
You randomly select one card from a 52-card deck. find the probability of selecting a blackblack twotwo or a blackblack eighteight
Solve for x
7x-0.15=2x+0.6
Explain
Which of the following describes the graph of {x | 1 < x < 2}? open circles on 1 and 2 open circles on 1 and 2, arrows pointing out open circles on 1 and 2, line segment between no solution
Answer:
open circles on 1 and 2
Erin is 8 years younger than twice Paula’s age. The sum of their ages is 40. How old is Erin
To solve this problem, we set up two linear equations based on the given information and solved them simultaneously. We found that Erin's age is 24 years.
Explanation:This problem is a classic example of a linear equation. We can set up two equations based on the information given:
Erin is 8 years younger than twice Paula’s age. This can be written as E = 2P - 8.The sum of their ages is 40. This can be written as E + P = 40.Upon substituting the value of E (Erin's age) from the first equation into the second, we get: 2P - 8 + P = 40. Simplifying this gives P = 16. Substituting P = 16 into the first equation, we find E = 24. Therefore, Erin is 24 years old.
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The difference of the squares of two positive consecutive even integers is 20 . find the integers. use the fact that, if x represents an even integer, then xplus 2 represents the next consecutive even integer.
The positive even numbers are 4 and 6.
EquationState of quality between two expressions consisting of variable and/or number.
Given
The difference of the squares of two positive consecutive even integers is 20.
To findThe number will be
How do find the numbers?The difference of the squares of two positive consecutive even integers is 20.
Let x be the even number and positive consecutive even is (x+2)
Then according to the condition
[tex]\begin{aligned} (x+2)^{2} -x^{2} &=20\\x^{2} +4x+4-x^{2} &= 20\\4x &= 20-4\\4x &= 16\\x &= \dfrac{16}{4}\\x &= 4\end{aligned}[/tex]
Then the positive even numbers are 4 and 6.
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A regular hexagon rotates counterclockwise around its center. It turns through angles greater than 0° and less or equal to 360°. At how many different angles of a hexagon map onto itself?
there are 6 sides to a hexagon
360/6 = 60 degrees
so it will map onto itself at 60, 120, 180, 240, 300 & 360
there are 6 different angles
Solve each equation. Then check your solution. 3-a/7=-2
Brandon is shopping at Old Navy during a sale. All shorts are $16 each and all t-shirts are $10 each.He has $100 to spend and would like to purchase at least 2 pairs of shorts.
a) Write a system of linear inequalities to represent
this situation, then graph.
b)Using your graph, give two possible combinations
of shorts and Brandon can buy.
Two possible solutions are (a) [tex]3[/tex] pairs of shorts and [tex]5[/tex] t-shirts
(b) [tex]4[/tex] pairs of shorts and [tex]3[/tex] t-shirts.
[tex]x=the\; number\; of shorts\\y=the\; number\; of\ t-shirt\; bought[/tex]
So equation formed is
[tex]16x+10y\leq 100[/tex]
[tex]10y\leq 100-16x\\y\leq 10-1.6x[/tex]---Eq [tex]1[/tex]
Bradon wants at least [tex]2[/tex] pair of shorts.Therefore
[tex]x\geq 2[/tex]--Eq [tex]2[/tex]
Now put,
[tex]x=3 \\y=10-1.6(3)\\y=10-4.8\\y=5\\[/tex]
Hence [tex]3[/tex] shorts and [tex]5[/tex] t-shirts
Now put,
[tex]x=4 \\y=10-1.6(4)\\y=10-6.4\\y=3\\[/tex]
Now graph the equation,
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round 38562.7 to 1 significant figure
Harry's school is selling t-shirts to raise money for the archery team. The school will receive 35% of the total sales which can be modeled by the equation y = 0.35x, where x represents the total number of sales. What is the meaning of the x-intercept in the equation?
Answer:
X-intercept states that the graph crosses the x-axis.
Substitute y = 0 and solve for x.
As per the statement:
Harry's school is selling t-shirts to raise money for the archery team.
The school will receive 35% of the total sales which can be modeled by the equation:
y = 0.35x
where, x represents the total number of sales and y represents the total cost of sale.
By definition of x-intercept:
0 = 0.35x
⇒x = 0
Therefore, the x-intercept in the equation represents:
The number of sales when no money has been raised.
A 150° angle is an obtuse angle. What do you Notice about the statement below? What do you Wonder about the statement?
N is between M and P. if MP=12 and NP=8, then what is the length of MN?
If you live in Dallas, then you live in Texas, what is the contrpositive of this?
Solve for x. x/3≤−6
Answer:
Hence, the value of x is [tex]x\leq -18[/tex]
Step-by-step explanation:
Consider the provided inequity.
[tex]\frac{x}{3}\leq -6[/tex]
We need to solve the above inequity of x.
Multiply both the side by 3.
[tex]3\times\frac{x}{3}\leq 3\times -6[/tex]
[tex]x\leq -18[/tex]
Hence, the value of x is [tex]x\leq -18[/tex]
How would I solve 1/5=125^x
A rectangle has a length of 9.00 inches and a width of 4.25 inches. What is the area in square inches? Round to the correct significant digits. DO I ADD UNITS?????
Evaluate.
3+2⋅6
_____
3
A student has to earn a total of at least 280 points on four tests in his math class to pass the class, and his total on the first three tests is 197 points. set up an inequality necessary to find the minimum number of points that he must earn on the fourth test to pass the class. then solve the inequality.
Toni can carry up to 23 lb in her backpack. Her lunch weighs 1 lb, her gym clothes weigh 2 lb, and her books (
b. weigh 4 lb each. How many books can she carry in her backpack? The inequality is . Toni can carry up to books in her backpack.
I need help with equation number 6
Give the slope intercept form of the equation of the line that is perpendicular to 5x-3y=8
The sum of two numbers is 64 . the larger number is 22 more than the smaller number. what are the numbers?
64-22 = 42
42/2 = 21
21+22 = 43
21 + 43 = 64
the numbers are 21 & 43
The larger number is 43 and the smaller number is 21.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The numbers will be calculated as:-
Let the larger number be L and the smaller number be S.
L + S = 64
From the given data the larger number is 22 more than the smaller number
L = S + 22
Put L = S + 22 in the above equation.
S + 22 + S = 54
2S = 64 -22
2S = 42
S = 42 / 2 = 21
L = S +22 = 21 + 22 = 43
Therefore, the larger number is 43 and the smaller number is 21.
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