Answer:
The graph of a quadratic function is a U-shaped curve called a parabola. ... If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value.
Step-by-step explanation:
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The relationship between the vertex and the minimum or maximum value of the parabola is given below.
What is a parabola?A plane curve produced by a moving point such that its separation from a fixed point equals that of a fixed line is a parabola.
Let the vertex be any parabola is (x, y).
When the graph of the parabola opens up,
then the y-value of the vertex is the minimum value.
And when the graph of the parabola opens down,
then the y-value of the vertex is the maximum value.
Therefore, the explanation is given above.
To learn more about the parabola;
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Simplify the expression:
–3(9 − x) =
Answer:
Expand [tex]-3(9-x): -27 + 3x[/tex]
Step-by-step explanation:
[tex]-3(9-x)[/tex]
Apply the distributive law: [tex]a(b-c)=ab-ac[/tex]
[tex]a = -3, b=9, c=x[/tex]
[tex]=-3*9-(-3)x[/tex]
Apply minus - plus rules:
[tex]-(-a)=a[/tex]
[tex]= -3*9+3x[/tex]
Multiply the numbers: [tex]3 * 9 = 27[/tex]
[tex]=-27+3x[/tex]
Hope this helps! If so, may I get Brainliest and a Thanks?
Thank you, have a good one! =)
Which system of equations is represented by this graph?
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[tex]y = 2x + 3[/tex]
[tex]y = - \frac{1}{2} x - 3 \\ [/tex]
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How does your current (or future) employment affect your Social Security or Medicare benefits?
Answer:
Step-by-step explanation:
Receiving Social Security Income While Working. In the year you reach full retirement age, your benefits will be reduced by $1 for every $3 you earn above $48,600 for 2020 and $50,520 for 2021. 6 Starting with the month you attain full retirement age, your benefits will no longer be reduced.
Prove that DE is parallel to BC.
Please help, will award brainliest.
Answer:
see explanation
Step-by-step explanation:
Parallel lines have equal slopes.
To find D and E use the midpoint formula
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(2, - 2) , then
D = ([tex]\frac{4+2}{2}[/tex], [tex]\frac{6-2}{2}[/tex] ) = (3, 2 ) and
let (x₁, y₁ ) = B(2, - 2[tex]\frac{-4+2}{-2-2}[/tex] ) and (x₂, y₂ ) = C(- 2, - 4 ), then
E = ( [tex]\frac{4-2}{2}[/tex], [tex]\frac{6-4}{2}[/tex] ) = (1, 1 )
Use the slope formula to find slopes of DE and BC
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = D(3, 2) and (x₂, y₂ ) = E(1, 1), then
[tex]m_{DE}[/tex] = [tex]\frac{1-2}{1-3}[/tex] = [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
Repeat with (x₁, y₁ ) = B(2, - 2) and (x₂, y₂ ) = C(- 2, - 4), then
[tex]m_{BC}[/tex] = [tex]\frac{-4+2}{-2-2}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]
Since the slopes are equal then DE and BC are parallel lines
Are You Ready for More?
AB is parallel to CD.
Determine the value of x.
Use the sketch tool if it helps you with your thinking.
А
B
degrees
50°
Submit
o
30°
С
D
the ratio the ratio of two numbers is 5:6 . find the sum of two numbers is 55. find the number
Answer:
25 and 30
Step-by-step explanation:
Given the ratio of 2 numbers is 5 : 6 = 5x : 6x ( x is a multiplier ), then
5x + 6x = 55, that is
11x = 55 ( divide both sides by 11 )
x = 5
Thus
5x = 5 × 5 = 25
6x = 6 × 5 = 30
Then the 2 numbers are 25 and 30
I FORGOT HOW TO DO THIS I NEED HELP ASAP!!!
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1. Create your own expression that contains at least one operation and one variable.
example: 5x
2. Describe a situation that your expression can model.
example: x represents the price of a pound of grapes, in dollars. Cheryl buys 5 pounds of grapes. The cost of Cheryl's grapes can be modeled by 5x
Answer:
4x+5
Step-by-step explanation:
4x represents making 4 dollars per hour and 5 represent the amount of money you began with
Answer:
1) 2x
2) x represent how many candy a person have
2 is the amount of person
The total candy canbe modeled by 2x
Step-by-step explanation:
Skyler is buying wings and quesadillas for a party. A package of wings costs $8.00. A package of quesadillas cost $10.00. He must spend no more than $160.00. Skyler's freezer will hold a maximum of 20 packages of wings and quesadillas. Write a system of linear inequalities to represent the situation.
Answer:
The system of inequalities are;
q + w ≤ 20
8w + 10q ≤ 160
Step-by-step explanation:
Let the number of wigs be w and the number of quesadillas be q
Since we have a maximum of 20 packages;
then;
q + w ≤ 20
Let’s now work with the prices
price of w wings is 8 * w =$8w
price of q quesadillas is 10 * q = 10q
The maximum amount to spend is $160
Thus, the addition will be;
8w + 10q ≤ 160
What is the domain and the range for this graph
Answer:
Domain:(0,infinite)
Range:(5,infinite)
Step-by-step explanation:
Answer:
D = 0, 1, 2, 3, 4, 5
R = 20, 40, 80, 160
Solve each triangle using the information provided. If necessary, round to the
nearest tenth.
Answer:
1) B = 66.5° c = 10.9
Step-by-step explanation:
I will do question one as an example. In general, for these questions you want to use the appropriate trigonometric ratios to solve for the variables and/or apply logic using rules regarding triangles. See attached image for all solving steps.
For side c, we can use Cosine of angle A for a ratio between 10 and c. When we write out the equation, we can solve for side c. So when we write it out, we get the equation:
cos23.5 = ¹⁰⁄c
c = ¹⁰⁄cos₂₃.₅
c = 10.9044 (make sure to round to the nearest tenth, which is one decimal place)
For angle B, since they have given two angles, you can solve for B since all angles of a triangle add up to 180 degrees.
So b = 180 - (90 + 23.5) = 180 - 113.5
b = 66.5
It is also possible to solve this using sine of angle B and solve it from there, but applying the theory this way is much simpler. (this is on the image if you're curious about it)I hope this helps you with the other 3 questions.
without using mathematical tables or calculators, evaluate 0.09 * 1.21 / 3.3 * 0.00024 leaving your answer in standard form(scientific notation)
Answer:
Step-by-step explanation:
[tex]0.09* \frac{1.21}{3.3}*0.00024= 0.09 * \frac{1.21*10}{3.3*10}*0.00024\\\\=0.09*\frac{12.1}{33}*0.00024\\\\= 0.09 * \frac{1.1}{3}*0.00024\\\\= 0.09 * 1.1 * 0.00008[/tex]
= 0.00000792
= 7.92 * [tex]10^{-6}[/tex]
1/4 kilometer in 1/3 hour?
Answer:
That means it will take you 1 and 1/3 hour to go a kilometer.
Please help me.......
Answer:
x=206
Step-by-step explanation:
Please Show Your Work All My Points Please Help Me!!!!! 6x^2+8x-6=2-2x-2
Answer:
6x^2+10x-6=0
Step-by-step explanation:
First, you need to add all like terms:
6x^2+8x-6=-2x
Now move the -2x to the other side:
6x^2+10x-6=0
Answer:
x =(-5+√61)/6= 0.468
or:
x =(-5-√61)/6=-2.135
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
6*x^2+8*x-6-(2-2*x-2)=0
Step by step solution :
STEP 1 :
The Equation at the end of step 1
(((2•3x2) + 8x) - 6) - -2x = 0
STEP 2 :
STEP 3 :
Pulling out like terms
3.1 Pull out like factors :
6x2 + 10x - 6 = 2 • (3x2 + 5x - 3)
Trying to factor by splitting the middle term
3.2 Factoring 3x2 + 5x - 3
The first term is, 3x2 its coefficient is 3.
The middle term is, +5x its coefficient is 5.
The last term, "the constant", is -3
Step-1: Multiply the coefficient of the first term by the constant 3 • -3 = -9
Step-2: Find two factors of -9 whose sum equals the coefficient of the middle term, which is 5.
-9 + 1 = -8
-3 + 3 = 0
-1 + 9 = 8
Observation: No two such factors can be found !!
Conclusion: Trinomial can not be factored
The Equation at the end of step 3 :
2 • (3x2 + 5x - 3) = 0
STEP 4 :
Equations which are never true:
4.1 Solve : 2 = 0
This equation has no solution.
A non-zero constant never equals zero.
Parabola, Finding the Vertex:
4.2 Find the Vertex of y = 3x2+5x-3
Parabolas have the highest or lowest point called the Vertex. Our parabola opens up and accordingly has the lowest point (AKA absolute minimum). We know this even before plotting "y" because the coefficient of the first term, 3, is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x-intercepts (roots or solutions) of the parabola. That is if the parabola has indeed two real solutions.
Parabolas can model many real-life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that an object, thrown upwards, can reach. For this reason, we want to be able to find the coordinates of the vertex.
For any parabola, Ax2+Bx+C, the x -coordinate of the vertex is given by -B/(2A). In our case, the x coordinate is -0.8333
Plugging into the parabola formula -0.8333 for x we can calculate the y -coordinate :
y = 3.0 * -0.83 * -0.83 + 5.0 * -0.83 - 3.0
or y = -5.083
Parabola, Graphing Vertex, and X-Intercepts :
Root plot for : y = 3x2+5x-3
Axis of Symmetry (dashed) {x}={-0.83}
Vertex at {x,y} = {-0.83,-5.08}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.14, 0.00}
Root 2 at {x,y} = { 0.47, 0.00}
Solve Quadratic Equation by Completing The Square
4.3 Solving 3x2+5x-3 = 0 by Completing The Square.
Divide both sides of the equation by 3 to have 1 as the coefficient of the first term :
x2+(5/3)x-1 = 0
Add 1 to both side of the equation :
x2+(5/3)x = 1
Now the clever bit: Take the coefficient of x, which is 5/3, divide by two, giving 5/6, and finally square it giving 25/36
Add 25/36 to both sides of the equation :
On the right-hand side we have :
1 + 25/36 or, (1/1)+(25/36)
The common denominator of the two fractions is 36 Adding (36/36)+(25/36) gives 61/36
So adding to both sides we finally get :
x2+(5/3)x+(25/36) = 61/36
Adding 25/36 has completed the left-hand side into a perfect square :
x2+(5/3)x+(25/36) =
(x+(5/6)) • (x+(5/6)) =
(x+(5/6))2
Things which are equal to the same thing are also equal to one another. Since
x2+(5/3)x+(25/36) = 61/36 and
x2+(5/3)x+(25/36) = (x+(5/6))2
then, according to the law of transitivity,
(x+(5/6))2 = 61/36
We'll refer to this Equation as Eq. #4.3.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x+(5/6))2 is
(x+(5/6))2/2 =
(x+(5/6))1 =
x+(5/6)
Now, applying the Square Root Principle to Eq. #4.3.1 we get:
x+(5/6) = √ 61/36
Subtract 5/6 from both sides to obtain:
x = -5/6 + √ 61/36
Since a square root has two values, one positive and the other negative
x2 + (5/3)x - 1 = 0
has two solutions:
x = -5/6 + √ 61/36
or
x = -5/6 - √ 61/36
Note that √ 61/36 can be written as
√ 61 / √ 36 which is √ 61 / 6
Solve Quadratic Equation using the Quadratic Formula
4.4 Solving 3x2+5x-3 = 0 by the Quadratic Formula.
According to the Quadratic Formula, x, the solution for Ax2+Bx+C = 0, where A, B, and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 3
B = 5
C = -3
Accordingly, B2 - 4AC =
25 - (-36) =
61
Applying the quadratic formula :
-5 ± √ 61
x = —————
6
√ 61, rounded to 4 decimal digits, is 7.8102
So now we are looking at:
x = ( -5 ± 7.810 ) / 6
Two real solutions:
x =(-5+√61)/6= 0.468
or:
x =(-5-√61)/6=-2.135
HOPE THIS HELPS!
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solve :
2(3x + 6) = 18
Answer:
2(3x+6)=18
6x+12=18
6x+12-12+18-12
6x=6
6x/6=6/6
x=1
Step-by-step explanation:
Divide 389ten by 44 ten
What is the circumference of a circle
with radius 64 inches? Write your answer
using PI.
Answer:
C≈402.12in
Step-by-step explanation:
The circumference of a circle is equal to pi times the diameter. The diameter is two times the radius, so the equation for the circumference of a circle using the radius is two times pi times the radius
If a bus travels 200 miles in 5 hours what was the average speed of the bus in miles per hour
Answer:
ths answrs is 40 miles pwr hour becUsd 200/5=40
Answer:The average speed the bus was going is 40 mph
Step-by-step explanation: 200÷5=40
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can someone help me pls?
Answer: yes it has gone down 1/5th because the answer would be 27 and that is a lot lower than the other numbers.
Step-by-step explanation:
162 minus 135 = 27
What is the equation of the line with a slope of 2 through (–4, 6) in point-slope form?
The price of an item yesterday was $180. Today, the price rose to $279. Find the percentage increase.
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Step-by-step explanation:
Percentage increase = (279 - 180)/180 x 100% = 55%
this is a topic on percentage. the above question requires a use of a kind of formula if you wish to explore more into this topic you can give me a follow on Instagram (learntionary) I've already posted some notes on this topic and will be doing more on others and also I'll be providing tips on some topics as well!
Answer:
55% increase
Step-by-step explanation:
First I want to say I recommend using sites like Calculator soup, and finding the option "percent increase calculator", for problems like these instead of wasting any points that you could use later on, and Secondly (happy to help), oof and third:
1) subtract the final value minus the starting value
279 - 180= 99
2) Divide that amount by the absolute value of the starting value
99 divided by 180 equals .55
3) Multiply by 100 to get percent increase
changes to 55.00 (final answer 55%)
4) If the percentage is negative, it means there was a decrease and not an increase.
Percentage Increase Formula
someone pls help and dont troll
Answer: A
Step-by-step explanation:
2x + 9 = 15
2x = 6
x = 3
2x+9 = -15
2x = -24
x = -12
Two friends argue over who brushes their teeth more often. To settle the argument, they keep track of the number of mornings and nights they brush and calculate a probability. These are shown in the table.
Using the probability concept, the correct option regarding who is more likely to brush both in the morning and in the evening is:
B. Arabella. She has a 0.64 probability of brushing both times.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering that the events are independent, we just multiply the probabilities, hence the probability of each brushing both times is given as follows:
Braxton: 0.85 x 0.72 = 0.612.Arabella: 0.79 x 0.81 = 0.64.Hence statement B is correct, as 0.64 > 0.612.
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A store owner wants to advertise his store in magazines that most of his shoppers are likely to read. He takes a survey to determine the ratio of females to males that shop at his store each day. The chart represents the number of females and males that shop at his store on average each day. Which statement identifies the ratio of females to males that shop at his store and who he should focu
Answer:
Step-by-step explanation:
Nshsdhdhdhdjsdnddndnd
Answer:
Step-by-step explanation:
5:2
Solve 6x^2-2x+1=0 using any method.
Answer:
[tex]x=\frac{1-\sqrt{-5} }{6}\\x=\frac{1+\sqrt{-5} }{6}[/tex]
There are no real roots.
Step-by-step explanation:
[tex]6x^2-2x+1=0\\x=\frac{2-\sqrt{2^2-4*6} }{2*6} \\x=\frac{2-\sqrt{-20} }{12}\\x=\frac{1-\sqrt{-5} }{6}\\x=\frac{1+\sqrt{-5} }{6}[/tex]
Please answer correctly !!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!
Answer:
15
Step-by-step explanation:
its the same as the other angle on there
Answer:
15
Step-by-step explanation:
They are alternate exterior angles, meaning they are the same!!
Logan weighed two buckets of sand for a geology project. The first bucket weighed 5.19 pounds. The other bucket weighed 9.01 pounds. How much do the two buckets of sand weigh all together?
Answer:
14.2
Step-by-step explanation:
you just have to add both of the numbers shown in the question
A company that makes hair-care products had 9,000 people try the new shampoo. Of the 9,000 people, 36 had a mild allergic reaction. Wht percent of the people had a mild mild allergic reaction?
Answer:
0.4% of the people had a mild allergic reaction.
Step-by-step explanation:
You can find the percent of the people that had a mild allergic reaction using a rule of three as you know that 9,000 people tried the new shampoo which would be the 100% and you can find the percent that represents 36 people:
9,000 → 100%
36 → x
x=(36*100)/9,000
x=0.4%
According to this, the answer is that 0.4% of the people had a mild allergic reaction.
ethansledd17 come here! what is 300 divided by 5?
Answer:
60
Step-by-step explanation: