Answer: x=-7
Step-by-step explanation:
please walk me through how to do this so I can di the other questions
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
A car salesperson has already sold 30 cars this year. He sells an average of 13 cars per month. Another salesperson has already sold 50 cars this year. She sells an average of 11 cars per month. After how many months will the salespeople have sold the same number of cars?
Answer:
After 10 months, both salespersons will sell 160 cars.
Step-by-step explanation:
We are given two different salesperson's statistics of sales. We can use this information to set up a system of equations and solve for our variable.
Let us name the first salesperson Person 1 and the other salesperson Person 2.
Person 1 sells 30 cars this year and sells an average of 13 cars a month.We can represent this with a linear equation (form of y = mx + b) to see the linear relationship at which they sell cars.Because they sell an average of 13 cars each month, this is a recurring amount. Therefore, this is m, or our slope.Because they've already sold 30 cars this year, this is our y-intercept, or b, a.k.a. our starting point of sales.Therefore, we are able to set up the equation for Person 1. This equation is [tex]\text{y = 13x + 30}[/tex].Now, for Person 2:
Person 2 sells an average of 11 cars per month and has sold 50 cars already this year.Their sales can be represented the same way - with a linear equation. Therefore, their sales are modeled with the slope-intercept form of an equation of a line (y = mx + b).Considering they have already sold 50 cars, this is where their average sales would start. Therefore, 50 is the y-intercept, or b, of our equation.Since they sell an average of 11 cars per month, they increase their sales by 11 each month. This means that because their sales rise, this is our slope, or m, of our equation.With this information, our equation becomes [tex]\text{y = 11x + 50}[/tex].Now, because we have these equations, we can set up a table that will determine the number of months that will elapse before the salespersons will sell the same amount of cars.
For Person 1, the equation will be the increase of the y-value by 13 cars after an initial sale of 30 vehicles. Therefore, we can create a table of values.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 30 \\ \cline{1-2} 1 & 43 \\ \cline{1-2} 2 & 56 \\ \cline{1-2} 3 & 69 \\ \cline{1-2} 4 & 82 \\ \cline{1-2} 5 & 95 \\ \cline{1-2} 6 & 108 \\ \cline{1-2} 7 & 121 \\ \cline{1-2} 8 & 134 \\ \cline{1-2} 9 & 147 \\ \cline{1-2} 10 & 160 \\ \cline{1-2} \end{array}[/tex]
For Person 2, we can use the same formatting to create a table. However, the rule changes - we must start at 50 cars being sold and increase it by only 11 cars a month.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 50 \\ \cline{1-2} 1 & 61 \\ \cline{1-2} 2 & 72 \\ \cline{1-2} 3 & 83 \\ \cline{1-2} 4 & 94 \\ \cline{1-2} 5 & 105 \\ \cline{1-2} 6 & 116 \\ \cline{1-2} 7 & 127 \\ \cline{1-2} 8 & 138 \\ \cline{1-2} 9 & 149 \\ \cline{1-2} 10 & 160 \\ \cline{1-2} \end{array}[/tex]
Now, we need to see where the y-values are the same in both tables. We can see that we have a value of (10, 160) in both tables, so after 10 months, the salespersons will sell the same amount of cars.
There is an alternative method of solving the problem that is much quicker and will require much less work.
We are given two equations that are both equal to y. Therefore, we can set them equal to each other (dropping the y) and solving for x.
Our value of x will be the amount of months in which the sales are equal.
[tex]\displaystyle{13x+30=11x+50}\\\\2x + 30 = 50\\\\2x = 20\\\\\boxed{x = 10}[/tex]
Therefore, after 10 months of sales, the salespersons will have sold the same amount of cars. We can plug this information into one of the equations to see how many cars will be sold at that point.
[tex]y = 13(10) + 30\\\\y = 130 + 30 \\\\y = 160[/tex]
In 10 months, 160 cars will be sold. If we set the equations equal to each other and substitute x, we should get a true statement.
[tex]13(10)+30=11(10)+50\\\\130 + 30 = 110 + 50\\\\160 = 160[/tex]
Because we get a true statement, each salesperson will sell 160 cars after 10 months of initial sales.
how do you find the measure of an angle?
Answer:
use the corner ofa paper to see if its obtuse it should be long and wide if its acute it should be a corne
Step-by-step explanation:
what is2/3 divided by 4/5
Step-by-step explanation:
2 /4
3. 5
doing reciprocal
2× 5
3. 4
= 8×15
12
= 120
12
=10 ans
hope it help u..
Please help me! Im making the first correct answer brainliest!
Answer:
The answer is most likely c.)
Step-by-step explanation:
It says that they sold 40 scarves and hats at the Winter Festival, but it never told us exactly how many hats total and how many scarves total that they sold. So we leave it as "s+h=40" Next we have the price of the scarves and hats, not the numbers sold. Since the scarves cost $18 and the hats cost $14, we know that a certain amount of each equals $700. Since we don't know the exact number of each that were sold, we leave it at "18s+14h=700." Sorry if you got a bit lost.
After being exposed to an incredible shrinking machine, Halley's height decreased by 108 cm over 6 seco
by the same amount each second. How much did Halley's height change each second?
18 cm
B
108 cm
-18 cm
D
-108 cm
Answer:
it would be -18
Step-by-step explanation:
because you would divide 108 by 6 and you will get -18 each second
The lengths of four insects are 0.02 inch, 1 8 inch, 0.1 inch, and 2 3 inch. List the lengths in inches from least to greatest.
Answer:
0.1,0.2,1.8,2.3
Step-by-step explanation:
Answer:
.02, .1, 1/8, 2/3
Step-by-step explanation:
This month. Quincy buys honey at a price of $8.80 per pound. He sells the honey at a 25% markup. What is the selling price for a pound of honey?
The CD Warehouse is having a clearance sale. A CD player that originally sells for $60 is now priced at $36. What is the percent decrease in the price?
Answer: 24
Step-by-step explanation:
i did the problem and got it right
Mrs. Loar has to grade 75 papers. Mrs. Holt is helping her grade. Mrs. Loar graded 60 papers and Mrs. Holt graded the rest. What percent of the papers did Mrs. Holt grade? Use a double number line to solve the problem.
Answer:
25%
Step-by-step explanation:
Mrs. Loar has to grade 75 papers. Mrs. Holt is helping her grade. Mrs. Loar graded 60 papers and Mrs. Holt graded the rest.
Hence, the amount of papers Mrs Holy graded is = 75 - 60
= 15 papers
What percent of the papers did Mrs. Holt grade?
This is calculated as:
15/60 × 100 = 25%
Hence, Mrs Holy graded 25% of the papers
Pleaseee someone resolve this quick!!!!!!
At the beach, you would like to fill 5 buckets with seashells. You have
8 minutes to do so. If you set a steady pace, how much of a bucket
should you fill in each minute?
A. bucket
2nter your text here
B. bucket
c. bucket
where do i plot the point?
Answer:
This should help
Step-by-step explanation:
1.05, 1.09 and 1.1 are close to each other so I marked where each one should go
What is the absolute value of 8.7
Answer:
absolute value of 8.7 is 8.7
For #11, make sure you answer all parts of the question.
11) The converse of an “if-then” statement reverses the “if” and “then” parts. The converse of a true “if-then” statement may or may not be true.
Write the converse of each true statement below and tell whether it is true or false. If it is false, give a counterexample.
If a polygon is a parallelogram, then it has four sides.
If Gil lives in France, then he lives in Europe.
If a parallelogram has four congruent angles, then it is a rectangle.
If two circles have the same diameter, then they are congruent.
If Daphne has the flu, then she is ill.
Write a true “if-then” geometry statement for which the converse is true. Give the converse.
Write a true “if-then” geometry statement for which the converse is false. Give the converse. Prove the converse is false by giving a counterexample.
1. When one-half of a number is subtracted
from its thrice, it gives 2500. Find the
number.
Answer:
let the number be x
thrice of the number=3x
one-half of the number=(1/2)x
so from the expression we:
3x-x/2=2500
(6x-x)/2=2500
6x-x=2*2500
5x=5000
x=5000/5
x=1000
FIRST, FASTEST CORRECT ANSWER GETS BRAINLIEST
Here is a triangular prism.
7.8 cm
16 cm
5.4 cm
Work out the volume of the prism in cm'.
Give your answer correct to 3 significant figures.
Needed ASAP!
Answer:
124.8
Step-by-step explanation:
Because the formula of a prism is v=bh so you would multiply 16x7.8 and get 124.8
The ratio of goldfish to gallons of water is 7 to 2. how many goldfish can you get if you have 16 gallons of water?
Answer:
56
Step-by-step explanation:
hello everyone.
please answer……
The first water pipe fills the tank in 8 minutes and the second in 16 minutes. If both pipes are open in one minute, what part of the tank will not be filled with water?
have a nice day.good bye
Answer:
13/16 is the answer. Bad handwriting but try to understand .
Is 9 a possible solution for -2x + 4 ≥ -14?
Answer:
Yes
Step-by-step explanation:
-2(9)+4= -14 and -14 is equal to -14.
Y=x^2-10x-18
Write down the information that can be obtained from the equation above?
Determine the vertex form
Answer:
Vertex form is y=(x-5)^2-43
Step-by-step explanation:
Given expression: x^2-10x-18
Take half of b:
-10/2=-5
Square the result:
-5^2=25
Add and subtract into original expression:
x^2-10x+25-25-18
Factor and simplify:
(x^2-10x+25)-25-18
(x-5)^2-25-18
(x-5)^2-43
So the vertex form is y=(x-5)^2-43
HELLLLLLLLLLLLLPPPPPPPPPPPPP please
what is 2 1/9 x 1 1/2
Answer:
3.16
Step-by-step explanation:
Hope this helps!
Choose the slope and y-intercept that
correspond with the graph.
Mr. Austin is driving 390 miles to visit the Gateway Arch in St. Louis, Missouri. He dries at an average rate of 65 miles per hour. How much time will it take Mr. Austin to get to the arch?
Answer:
the time needed to get to the arch is 6 per hour
Step-by-step explanation:
The computation of the time needed to get to the arch is shown below:
As we know that
Speed = distance ÷ time
where,
Speed is 65 miles per hour
And, the distance is 390 miles
So, the time is
= 390 ÷ 65
= 6 per hour
Hence, the time needed to get to the arch is 6 per hour
We simply applied the above formula so that the correct value could come
And, the same is to be considered
If you know trig please help! Will give brainliest!
Answer:
sin^2α
Step-by-step explanation:
I will just pose x instead of alpha here to make things simpler
[tex]\tan ^2\left(x\right)\left(2\cos ^2\left(x\right)+\sin ^2\left(x\right)-1\right)\\\\[/tex]
we know that sin^2x = 1 - cos^2x so...
[tex]=\left(-1+1-\cos ^2\left(x\right)+2\cos ^2\left(x\right)\right)\tan ^2\left(x\right)[/tex]
[tex]=\cos ^2\left(x\right)\tan ^2\left(x\right)[/tex]
we can rewrite using trigonometric identities (tan = sin/cos)...
[tex]=\left(\frac{\sin \left(x\right)}{\cos \left(x\right)}\right)^2\cos ^2\left(x\right)\\= \sin ^2\left(x\right)[/tex]
PLEASE THIS IS URGENT
Answer:
B
Step-by-step explanation:
I am sorry if this is wrong
Given the equation -2x + 8y = 24, determine the x- and y-intercepts. PLZ HELP???
Answer:
[tex]x=(-12,0)[/tex]
[tex]y=(0,3)[/tex]
Step-by-step explanation:
x-intercept
[tex]-2(x-4y)=24[/tex]
[tex]x-4y=-\frac{24}{2}[/tex]
[tex]x-4y=-12[/tex]
[tex]x=4y-12[/tex]
[tex]x=4(0)-12[/tex]
[tex]x=-12[/tex]
y-intercept
[tex]-2(x-4y)=24[/tex]
[tex]x-4y=-\frac{24}{2}[/tex]
[tex]x-4y=-12[/tex]
[tex]-4y=-12-x[/tex]
[tex]y=-\frac{-12-x}{4}[/tex]
[tex]y=-\frac{-12-(0)}{4}[/tex]
[tex]y=\frac{12}{4}[/tex]
[tex]y=3[/tex]
GUYS HELP! IS THIS CORRECT???
ILL MARK YOU BRAINIEST!
Answer:12
Step-by-step explanation:
it’s 12 because 4 x 3 = 12
Answer:
48π units³
Step-by-step explanation:
The volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius of the base and h the height )
Here r = 4 and h = 3 , thus
V = π × 4² × 3
= π × 16 × 3
= 48π units³ ← exact answer
d+7 divided by −3=4.
Answer:
- 19
Step-by-step explanation:
Step 1:
d + 7 ÷ - 3 = 4 Equation
Step 2:
d + 7 = - 12 Multiply
Step 3:
d = - 12 - 7 Subtract
Answer:
d = - 19
Hope This Helps :)