Answer:
vertex = (- 4, - 3 ), equation is x = - 4
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = 6(x + 4)² - 3 ← is in vertex form
with (h, k ) = (- 4, 3 ) ← vertex
The equation of the axis of symmetry is a vertical line passing through the vertex, with equation
x = - 4
Factor the following trinomial completely. Look first for the greatest common factor.
6r^2+14r−12
Answer:
[tex]2(3r-2)(r+3)[/tex]
Step-by-step explanation:
Factor [tex]6r^2+14r-12[/tex]
[tex]6r2+14r-12[/tex]
[tex]=2(3r-2)(r+3)[/tex]
Answer:
[tex]2(3r-2)(r+3)[/tex]
Step-by-step explanation:
[tex]6r^2+14r-12[/tex]
Start by factoring out the greatest common factor, [tex]2[/tex]:
[tex]2(3r^2+7r-6)[/tex]
Factor out the trinomial in the parentheses using the "Reverse FOIL" method (Write 2 parentheses and factor out the trinomial into them):
[tex]2(3r-2)(r+3)[/tex]
_
To check:
(Multiply First, Outside, Inner, Last):
[tex]2(3r^2+9r-2r-6)[/tex]
Combine like terms:
[tex]2(3r^2+7r-6)[/tex]
Distribute the [tex]2[/tex]:
[tex]6r^2+14r-12[/tex]
Write 2.08 x 10^2 in standard form.
Answer:
208
Step-by-step explanation:
If you multiply 2.08 by ten to the second power (100) Then you get 208
Scientific notations are the way through which a very small or a very large number can be written in shorthand. The given expression can be written in the standard form as 208.
What are Scientific notations?Scientific notations are the way through which a very small or a very large number can be written in shorthand. In scientific notations when a number between 1 and 10s is multiplied by a power of 10.
For example, 6,500,000,000,000 can be written as 6.5e+12.
The given expression can be written in the form of an expression as shown below.
2.08 x 10²
= 2.08 × 100
= 208
Hence, the given expression can be written in the standard form as 208.
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Sydney is a salesperson who sells computers at an electronics store. She makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from her sales that day. Let P represent Sydney's total pay on a day on which she sells "x" dollars worth of computers. Write an equation that represents P as a function of X
Answer:
P=0.025x+100
Step-by-step explanation:
The y-intercept of the function is 100 which represents the base pay Sydney makes regardless of computer sales.
that's the correct answer^^^
y = 1/40x + 100 is an equation that represents P as a function of X
What is Linear function?A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.
Given, Sydney is a salesperson who sells computers at an electronics store. She makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from her sales that day.
Let the equation of line y = kx + b
Where b is 100
Since the given line passes through (0, 100) and (4000,200)
since For a line k = (y₂ - y₁)/(x₂ - x₁)
Thus, k = (200 -100)/(4000-0)
k = 1/40
Thus,
y = 1/40x + 100
Therefore, an equation that represents P as a function of X is y = 1/40x + 100.
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Complete question:
A survey was conducted of students at a highschool and at a college to determine students favorite subjects. The results are shown in the table. What percentage of the students are college students that prefer history?
Highschool-
history(80)
math (50)
science (70)
total(200)
College-
history (70)
math(60)
science (70)
total (200)
History total (150)
Math total (110)
science total (140)
Answer:35%
Step-by-step explanation:
So I’m not sure this is high school math because i’m still in grade school but...
So what you have to do is make a ratio
so if 70 students out of 200 in college prefer history the ratio should be 70 to 200 or 70:200
Then you want to do 70 * 200 which then you get a answer of .35
then to make .35 into a percent you move the decimal two spaces to the left for a answer of 35%
Hope this helps!
A total of 17.5% of students are college students that prefer history.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Percentage is usually denoted by the symbol '%'.
Total number of students = 400
Number of college students that prefer history = 70
Percentage is the division of the required number with the whole.
Percentage of students who are college students that prefer history is,
= (70 / 400) × 100
= 17.5%
Hence the percentage of students who are college students that prefer history is 17.5%.
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Earth is 148.61 million km from the sun in scientific notation it is
Answer:
1.48x10^2 ten to the second
Step-by-step explanation:
4. Complete the following two-column proof.
Given: 5x - 2 = -12
Prove: x = -2
help please.
Answer:
x does equal -2
Step-by-step explanation:
Substitue x = -2:
[5(-2) -2 = -12]
Simplify:
[-10-2 = -12]
Add/Subtract from left to right:
[-12 = -12]
Therefore:
x = -2
can someone who KNOWS WHAT theyre doing and is good at angles please help
m1=51
m2=18
m3=123
m4=39
***remember the 180 rule, and supplementary/complementary angles!
180 rule: all triangle's internal angles add up to 180, this means if you know any two angles you can always find the last one
supplementary angles:
angles that add up to 180, 180 is a straight line so they can be found on almost all triangle problems.
if there is a straight line and you know one of the angles that is on the line, you can find the other one by subtracting it from 180
complementary angles:
same thing ^ but with 90
i hope my explanations make sense! let me know if you have any more questions :)
PLEASEEE HURRY!!! And please show work thank youuu
Caleb is a junior at JA Enterprise High School and plays rugby on the school team. He has a part-time job at a local fast-food restaurant and works 20 hours a week for $7.60 an hour. His gross monthly income is $608.00, and his take-home pay is $501.64. In his spare time, Caleb walks a dog belonging to an elderly neighbor. He earns an additional $40.00 per month for that chore.
Caleb's parents gave him a used car, and he pays his own insurance, which is $110 per month. His gas and maintenance expenses usually run $65 a month. He also has a cell phone and pays his parents $30 each month for his share of the family plan.
In three weeks, Caleb plans to take a day trip to Six Flags amusement park. His admission will cost $50, and he plans to have $35 for meals and another $50 for incidentals.
Caleb needs to start saving for Christmas, which is in four months, and he usually spends around $200 on gifts for his family and friends. He also would like to buy a new $80 e-reader this month.
Though Caleb's parents will help pay for his college tuition, he knows that in two years, he will have to pay for his books and earn his own spending money. He is estimating that each semester, he will spend $300 on books and $600 on personal needs.
How much are Caleb's regular monthly expenses?
Answer:
Caleb's net monthly income would be $541.64
Step-by-step explanation:
His monthly take home pay from restaurant is $501.64
Since he earns additional $40 per month for dog walk,
Therefore, his monthly pay would be ;
= $501.64 + $40
Caleb's net monthly income =$541.64
Caleb's monthy regular expenses including car insurance and books is
$355.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
From the given information, The total net earnings of Caleb is,
= $(501.64 + 40).
= $541.64.
Now, The expenses for Car insurance, Gas, and cell phone recharge is,
= $(110 + 65 + 30).
= $205.
Again, For books and personal needs, he have to spend $(300 + 600).
= $900.
Monthly it is,
= 900/6.
= $150.
Therefore, Caleb's regular expenses is,
= $(205 + 150).
= $355.
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2. Jonas measured ZDCG to be 56° and ZDCF to be 124. He wants to verify that DCF is
124° using the Angle Addition Postulate.
O
124° + 180°
D
124-56°
180°-56°
7
180° +56°
CLEAR ALL
Which is the correct calculation Jonas must use?
Answer:
The correct calculation is 180 - 56
Step-by-step explanation:
From the question, we have DCG and DCF
looking at the diagram, we can see that both lie on a straight line and are a linear pair
So the addition of both will give 180
But DCG is 56
So;
DCF + 56 = 180
So;
DCF = 180 - 56
what expression is equivalent to -0.2-4.9?
A rock garden is in the shape of a triangle as shown. Which equation could be used to find the area of the rock garden
Answer1/2(8x15)=60ft2
Step-by-step explanation: hope this helps you
The area of the rock garden will be represented by the equation 1/2 x 15 x 8 = 60. The correct option is D.
What is the area of a triangle?The entire area filled by a triangle's three sides in a two-dimensional plane is referred to as the triangle's area. The fundamental equation for a triangle's area is A = 1/2 x b x h, where b and h are the product of the triangle's base and height.
The area of the triangle will be calculated as,
Area = 1/2 x 15 x 8
Area = 15 x 4
Area = 60 square feet
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The following scores represent students' test grades in Ms. Orr's science class. Test Scores 78 81 78 81 78 81 78 81 78 87 91 87 91 87 91 87 91 87 What is the median score for Ms. Orr's science class?
plsss help mee
Answer:
Its definitely B 84.5
I took the test
Step-by-step explanation:
Answer:
87
Step-by-step explanation:
The median score is the score that appears in the middle of the graph and the set of numbers. 87 is the median score.
i need help.please help me
Answer:
1) r >-5 2) x >9
Step-by-step explanation:
Charlie's homemaking class makes aprons to give to a local soup kitchen. Each apron requires 2 1/4 yards of fabric, and the cost of fabric per apron is $9. What is the cost of 1 yard of fabric?
Answer:
4 dollars to get 1 yard
Step-by-step explanation:
Kayla wanted to buy a sweatshirt. The original price was $45. When she went to the store the sale price was $37. What is the percent discount on the sale price?
can someone explain how to solve this question.. it would mean a lot to me, thanks :)
Answer:
you would need to cross multiply 37/45 = x/100
Step-by-step explanation:
The first part represents the 37 dollars out of the original 45 and the second part represents x= the unknown percent out of 100 percent.
Two expressions are shown below. Which of the following is the DIFFERENCE obtained when subtracting expression II from expression I?
I. y2−4xz+z2
II. x2+xz+2y2
A. 3y2−3xz+z2−x2
B. 3y2−3xz+z2+x2
C. −y2−5xz+z2−x2
D. y2+5xz−z2+x2
Answer:C.
−y2−5xz+z2−x2
Step-by-step explanation:
Took the test got it right
The solution is Option C = ( -y² - 5xz + z² - x² )
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Given data ,
Expression 1 = y² - 4xz + z²
Expression 2 = x² + xz + 2y²
Let Expression 1 - Expression 2 = A
To find Expression 1 - Expression 2 = A
A = y² - 4xz + z² - ( x² + xz + 2y² )
By grouping the like terms , we get
A = ( y² - 2y² ) - ( 4xz + xz ) + z² - x²
Therefore,
A= - y² - 5xz + z² - x²
Hence , the solution is ( -y² - 5xz + z² - x² )
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Price reduced
25% off
Now £14 625
Work out the price of the car before it was reduced.
Step-by-step explanation:
let x be the original.price
so x * 75/100= 14625
x=19500
so the price of car before it was reduced was 19500
The price of the car before it was reduced is £19500.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given that the price of the car with 25% price reduced is £14625.
Now to find the price of the car before it was reduced,
for that we will find the price of car to 100 - 25 = 75 percentage.
Let P be the price of the car before it was reduced.
P × 75 / 100 = 14625
P = 14625 × 100 / 75
P = £19500
Therefore, the price of the car before it was reduced is £19500.
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Suppose jefferson middle school had 616 students and averaged 28 students per teacher during the year. If Jefferson Middle Schools student population increases by 18% this year and 9% of last years teacers left, how many new teachrs does Jefferson need to hire to keep its average of 28 students per teacher
Answer:
6 more teachers are required.
Step-by-step explanation:
Total number of students = 616
No of teachers = 616/28= 22
Increase in students = 18%
= 18/100*616= 110.88= 111
Total number of students = 616+111= 727
Decrease in teachers = 9%
= 9/100*22= 1.98= 2
New number of teachers= 20
Now Average is 28 students per teacher so
727/28= 25.96= 26 teachers are required for the total number of 727 students. The school has already 20 teachers so they need 6 more teachers.
A 2000-gallon metal tank to store hazardous materials was bought 15 years ago at cost of $100,000. What will a 5,000-gallon tank cost today if the power–sizing exponent is 0.57 and the construction cost index for such facilities has increased from 180 to 600 over the last 15 years? Choose the closest value.
Answer:
The value is [tex]P_o = \$ 561958.9 [/tex]
Step-by-step explanation:
From the question we are told that
The capacity of the metal tank is [tex]C = 2000 \ gallon[/tex]
The duration usage is [tex]t = 15\ years \ ago[/tex]
The cost of 2000-gallon tank 15 years ago is [tex]P = \$100,000[/tex]
The capacity of the second tank considered is [tex]C_1 = 5,000[/tex]
The power sizing exponent is [tex]e = 0.57[/tex]
The initial construction cost index is [tex]u_1 = 180[/tex]
The new construction after 15 years cost index is [tex]u_2 =600[/tex]
Equation for the power sizing exponent is mathematically represented as
[tex]\frac{P_n}{P} = [\frac{C_1}{C} ]^{e}[/tex]
=> Here [tex]P_n[/tex] is the cost of 5,000-gallon tank as at 15 years ago
So
[tex]P_n = [\frac{5000}{2000} ] ^{0.57} * 100000[/tex]
[tex]P_n = \$168587.7[/tex]
Equation for the cost index exponent is mathematically represented as
[tex]\frac{P_o}{P_n} = \frac{u_2}{u_1}[/tex]
Here[tex]P_o[/tex] is the cost of 5,000-gallon tank today
So
[tex]\frac{P_o}{168587.7} = \frac{600}{180}[/tex]
=> [tex]P_o = \frac{600}{180} * 168587.7[/tex]
=> [tex]P_o = \$ 561958.9 [/tex]
Help please! Only answer if you know for sure.
Answer:
c I am 100% sure
Step-by-step explanation:
can u simplify 18/56 into a fraction?
Answer:
9/28
Step-by-step explanation:
just divide by 2
Answer: 9/28
Steps: 18/56
Factor the number: 8 = 2 · 9
Factor the number: 56 = 2 · 28
Cancel the common factor: 2
9/28
Plz mark brainliest:)
Think about the methods you have for comparing two probabilities to decide which is greater. In your Learning Log, create an example and explain two different strategies for comparing probabilities. Title this entry "Comparing Probabilities" and label it with today's date.
Answer:
Step-by-step explanation:
Probabilities are basically values determining how likely something is to happen. These values are usually represented in fractions or percentages which are the two main strategies as well for comparing probabilities. For comparing probabilities through fractions we would try to make sure the denominators are equal and then compare the numerators. The higher numerator is the probability with the highest chance of something happening. For example...
[tex]\frac{3}{4} > \frac{1}{4}[/tex] ... 3/4 is a much higher probability than 1/4
The second strategy would be using percentages in the same way. The higher percentage is the one with the highest probability while the lower percentage is the one with the lower probability.
96% > 54%
What is the solution to the system of equations?
Answer:
(2, - 4 )
Step-by-step explanation:
Given the 2 equations
x + 2y = - 6 → (1)
3x + y = 2 → (2)
Multiplying (2) by - 2 and adding to (1) will eliminate the term in y
- 6x - 2y = - 4 → (3)
Add (1) and (3) term by term to eliminate y
- 5x = - 10 ( divide both sides by - 5 )
x = 2
Substitute x = 2 into either of the 2 equations and solve for y
Substituting into (1)
2 + 2y = - 6 ( subtract 2 from both sides )
2y = - 8 ( divide both sides by 2 )
y = - 4
Solution is (2, - 4 )
856 divided by 57 somebody please help?
Answer:
15.0175439
Step-by-step explanation:
856/57 = 15.017
Please tell me if it is correct! :)
Find FG. (idk how to write the question but apparently it needs to be longer)
Answer:
FG = 18
Step-by-step explanation:
FG + GH = FH
FG + 31 = 49
Subtract 31 from each side
FG +31-31 = 49-31
FG = 18
Answer: FG is 18
Step-by-step explanation: FG + GH is FH, GH is 31 and then you substitute 31 in for GH which makes the equation FG+31=49 49-31 is 18 which means FG is 18
*PLEASE ANSWER, I NEED HELP I DONT GET IT*
Answer:
the third graph
Step-by-step explanation:
2x<6/÷2 we get x<3
3x+2>-4
3x>-4-2
3x>-6/÷3
x>-2
Answer:
Basically how inequalities work is that they restrict equations into certain parts of graphs. So the answer would be C.
Step-by-step explanation:
You can do normal division on inequalities so you can do 2x<6 and then divide both sides by 2 to get the unit value of x. You get x<3
When something is < or >, the inequality graph will be an open circle.
When something is ≥ or ≤, the sign is a closed circle which basically means a filled in circle. Since both inequalities have the > or < sign, you know that both graphs have to have open circles, which basically mean a circle where you can see the center as a different color. It will be a circle like an o.
You now know that it is either A or C, but how to know which one?
You can simplify the inequalities as you know from before that 2x<6 is equal to x<3 so you can graph that on a number line. X is less than three, so the line should run away from three down to 0 and the infinity of negative numbers. C is the only answer that fits it. You may wonder though, "Why in C, does the line stop at -2 with another open circle?" That is because are two inequalities.
The first is x<3
but the other is 2x+2>-4
You can simplify that by subtracting 2 from both sides to get 2x isolated on the left side. You get 2x>-6.
Now you can divide both sides by 2, as we did previously at the beginning. You get x>-3 from dividing.
Finally you can graph that on the number line, but you know that x is greater than -3, so it should be an open circle starting from -3 heading out to the infinite cosmos of positive numbers.
BUT...
The two inequalities are separated by "and," meaning that they are related by the fact that they are directly connected. There are two possible words that separate inequalities, "and," and, "or."
In "or" statements, the two inequalities are not related, so the two inequalities would keep on going forever without regard to the other.
In "and" statements, the two inequalities are related, so the two inequalities would depend on each other to end off each other.
SO
Because they are connected with the word And,
They would end off at each other, so the original inequalities would depend on each other to continue, or to end off.
That is why the two inequalities would be a line from anything greater than -2 all the way to all the numbers below 3. The numbers could be anything from -1.999999999999999... forever, as long as they do not equal or go less than -2. The numbers could be anything from 2.99999999... forever, as long as they do not equal or go over 3.
Hope this helps!
The formula to convert °F to °C is C = C equals StartFraction 5 Over 9 EndFraction left-parenthesis F minus 32 right-parenthesis.(F – 32).
Convert 50°C to °F.
Answer:
122
Step-by-step explanation:
Roberto has run the first 16 miles of a race, means he is 72% finished. How long is the race?
Answer:
22.22222222
Step-by-step explanation:
Answer:
the race is 22 miles long.
Step-by-step explanation:
p %
~~ = ~~
w 100
What is the value of 120?