Answers
Answer:
Y= -1/3x + 8/3
Step-by-step explanation:
Related Questions
A quadratic function has an axis of symmetry at x=4 and contains the points (2, -6) and (7, -11). Find the equation in standard form (y=ax2+bx+c). Then state the "a" value in the equation.
Answers
Answer:
The equation in standard form is [tex]y = -x^{2}+8\cdot x -18[/tex]. The "a" value is -1.
Step-by-step explanation:
A quadratic function is the standard form of the parabola. We can take advantage of the symmetry property of the parabola by using the following formula from the Analytical Geometry:
[tex]y - k = C\cdot (x-h)^{2}[/tex] (1)
Where:
[tex]C[/tex] - Parabola constant, dimensionless.
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Depedent variable, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex of the parabola, dimensionless.
If we know that [tex](x_{1},y_{1})=(2,-6)[/tex], [tex](x_{2},y_{2})=(7,-11)[/tex] and [tex]h = 4[/tex], then we have the following system of linear equations:
[tex](x_{1},y_{1})=(2,-6)[/tex]
[tex]-6-k = C\cdot (2-4)^{2}[/tex]
[tex]4\cdot C +k = -6[/tex] (2)
[tex](x_{2},y_{2})=(7,-11)[/tex]
[tex]-11-k =C\cdot (7-4)^{2}[/tex]
[tex]9\cdot C + k = -11[/tex] (3)
By clearing [tex]k[/tex] in (2) and (3) and equalizing each other, we get that:
[tex]-6-4\cdot C = -11-9\cdot C[/tex]
[tex]5\cdot C = -5[/tex]
[tex]C = -1[/tex]
And the remaining variable is calculated by substituting directly on (3):
[tex]k = -11-9\cdot C[/tex]
[tex]k = -11-9\cdot (-1)[/tex]
[tex]k = -2[/tex]
Then, the equation of the parabola is:
[tex]y+2 = -(x-4)^{2}[/tex]
And the standard form of the equation is obtained by algebraic handling:
[tex]y+2 = -(x^{2}-8\cdot x + 16)[/tex]
[tex]y + 2 = -x^{2}+8\cdot x -16[/tex]
[tex]y = -x^{2}+8\cdot x -18[/tex] (4)
The equation in standard form is [tex]y = -x^{2}+8\cdot x -18[/tex]. The "a" value is -1.
Which scatterplot would have a trend line with a negative slope?
Answers
65.6g of sugar is needed to make 8 cakes how much is needed to make 5
Answers
Answer:
41g
Step-by-step explanation:
65.6/8= 8.2g per cake
8.2*5 cakes= 41g
Answer:
41g of sugar.Step-by-step explanation:
65.6g = 8 cakes
We need to find the sugar for 1 cake:
65.6 ÷ 8= 8.2 (gram for 1 cake)
The sugar for 5 cakes:
8.2 × 5= 41 (gram for 5 cakes)
Michael has a set of 24 math problems to do for homework. Michael completed 1/4 of his homework in 3/4 of an hour. If he continues at this rate , what fraction of his homework would he complete in one hour ? A. 3/8 B. 2/3 C. 4/3 D. 3/2
Answers
Given:
Total number of problems = 24
Michael completed [tex]\dfrac{1}{4}[/tex] of his homework in [tex]\dfrac{3}{4}[/tex] of an hour.
To find:
What fraction of his homework would he complete in one hour.
Solution:
We have,
Part of work done in [tex]\dfrac{3}{4}[/tex] of an hour [tex]=\dfrac{1}{4}[/tex]
Part of work done in an hour [tex]=\dfrac{4}{3}\times \dfrac{1}{4}[/tex]
[tex]=\dfrac{1}{3}[/tex]
Therefore, he complete [tex]\dfrac{1}{3}[/tex] of his homework in 1 hour. Hence, all options are incorrect.
WILL MARK branniest answer if gotten right
Answers
Answer:
Line MN is the answer
Step-by-step explanation:
Image SQ as a line that extends forever, if you took line segment and also made it extend forever, then it would become parallel to line segment SQ, never touching or intersecting and going at the same angle.
PLEASE HELP QUICK
The costume jewelry and accessories for the show are bought from sales racks at two different stores on different days. Use x to represent the price of each item on the sales rack at the first store and y to represent the price of each item on the sales rack at the second store.
On the first day, the students spent $30 on 4 items from the first store and 7 items from the second store. On the second day, the students spent $22 on 3 items from the first store and 5 items from the second store. On the third day, the students need to buy 10 items from the first store and 17 items from the second store.
What is the amount of money the students will need on the third day? Find your answer by creating and solving a system of linear equations based on the first day and the second day. Explain your reasoning.
Answers
Answer:
74
Step-by-step explanation:
Using linear equations, we are given two equations from the questions:
4x +7y=30 from day one and 3x +5y=22 from day two
Multiply the first equation by 3 and second by 4 giving us
12x +21y=90 and 12x +20y=88. Minus both equations.
12x - 12x +21y - 20y= 90 - 88, Gives you y=2,
You can now use the value of y to find x.
4x + 7y = 30
4x + 7(2)= 30
4x + 14= 30. Minus 14 on both sides giving you
4x=16. Divide both sides by 4.
x=4
Now use both values to find how much money is needed on the third day.
10x + 17y
=10(4) + 17(2)
=40 +34
=74
25 POINTS!!!! AND BRAINLIEST!
1. An internet company surveyed their users. The first 25 people who responded gave the ages shown below. Answer the following questions and create a histogram to display the data.
(You may want to make a frequency table to help organize the data)
What intervals would you use to make the histogram?
Find the mean, median and mode of the data
Find the mean absolute deviation for the data
Identify skew of the data (normal or asymmetric)
Identify any peaks, gaps or clusters in the data from the histogram
Age of internet users:
25, 43, 65, 12, 8, 30, 44, 68, 18, 21, 25, 33, 37, 54, 61, 29, 31, 38, 22, 48, 19, 34, 55, 14, 21
2. What does it mean for data to have variability as it refers to statistical questions? Give an example.
Answers
.... hope this helps?
Factor the algebraic equation
36a+20
Answers
Answer:
4(9a+5)
Step-by-step explanation:
Answer:
4(9a+5)
Step-by-step explanation:
Their common factor is 4 so divide both by 4 and put it in parentheses times 4
if triangle ABC=triangle DEC, and angle b=3x and angle e=6x-39, what is x
Answers
So you’ll have :
3x = 6x - 39
0 = 6x - 3x - 39
39 = 3x
x = 39/3
x = 13
The value of x in the expression is 13.
What is a Triangle?A polygon which has three sides and three vertices is called as triangle.
The sum of all the angles of the triangle is 180°.
Given:
The triangle ABC = triangle DEC,
and angle b=3x and angle e=6x-39.
To find the value of x:
We know,
b = e
So, substituting the values,
3x = 6x - 39
3x = 39
x = 13.
Therefore, the value of x is 13.
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whats 851,708 to the nearest hundred-thousand
Answers
Answer:
900,000
Step-by-step explanation:
because when you round number from 1-4 you put it down example: 1223
round to nearest thousand it is 1000 but when 5-9 is higher example: 1566 it is 2000
Answer:
900,000
Step-by-step explanation:
Bc The Ten Thousandths place is over 4
Jada has time on the weekends to earn some money. A local bookstore is looking for someone to help sort books and will pay $12.20 an hour. To get to and from the bookstore on a work day, however, Jada would have to spend $7.15 on bus fare.
how would I write an equation for this? use e for her earnings and h for hours worked
Answers
PLEASE ANSWER ASSAP!!! IF CORRECT WILL GIVE BRAINLY!!!!! Which one of these relationships is different than the other three? Explain how you know.
Answers
Answer:
The relationship B is different than the other three, because it has a different proportionality constant.
Step-by-step explanation:
All available options show direct relationships, which are defined as follows:
[tex]y\propto x[/tex]
[tex]y=k\cdot x[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]k[/tex] - Proportionality constant, dimensionless.
We proceed to use the following strategy based on the proportionality constant, that is:
[tex]k = \frac{y}{x}[/tex]
A different relationship must indicate a different proportionality constant:
Option A ([tex]x = 0.8[/tex], [tex]y = 4[/tex])
[tex]k = \frac{4}{0.8}[/tex]
[tex]k = 5[/tex]
Option B ([tex]x = 10[/tex], [tex]y = 55[/tex])
[tex]k = \frac{55}{10}[/tex]
[tex]k = 5.5[/tex]
Option C ([tex]x = 4[/tex], [tex]y = 20[/tex])
[tex]k = \frac{20}{4}[/tex]
[tex]k = 5[/tex]
Option D ([tex]x = 10[/tex], [tex]y = 50[/tex])
[tex]k = \frac{50}{10}[/tex]
[tex]k = 5[/tex]
The relationship B is different than the other three, because it has a different proportionality constant.
Draw triangle ABC by first drawing segment BC six inches long. Then draw a 60° angle at vertex B and a 60° angle at vertex C. Extend the segments so that they intersect at point A.
Answers
Answer:
Step-by-step explanation:
Given that segment BC is the base of the triangle, this drawing shows that triangle ABC is an equilateral triangle.
Since;
<B = <C = 60°
Then,
<A + <B + <C = [tex]180^{o}[/tex]
<A + 60° + 60° = [tex]180^{o}[/tex]
<A = [tex]180^{o}[/tex] - [tex]120^{o}[/tex]
= 60°
Thus,
AB = BC = AC = 6 inches
The construction is attached to this answer.
If the sinø=7/12, what is cosø?
Answers
Answer:
If the sinø=7/12, cosø is [tex]\frac{\sqrt{95} }{12}[/tex]
Step-by-step explanation:
We are given sinФ = 7/12
We need to find cosФ
The basic trigonometric functions of right triangle are:
[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]
[tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex]
We need values of adjacent and hypotenuse to find cosФ
Using Pythagoras theorem we can find the value of adjacent
[tex](Hypotenuse)^2= (Opposite)^2+(Adjacent)^2[/tex]
We have Hypotenuse= 12 and Opposite = 7 (because [tex]sin\theta=\frac{opposite}{hypotenuse}[/tex] and we are given [tex]sin\theta=\frac{7}{12}[/tex]
Inserting values and finding adjacent:
[tex](Hypotenuse)^2= (Opposite)^2+(Adjacent)^2\\(12)^2=(7)^2+(Adjacent)^2\\144=49+(Adjacent)^2\\144-49=(Adjacent)^2\\95=(Adjacent)^2\\\sqrt{(Adjacent)^2} =\sqrt{95}\\Adjacent=\sqrt{95}[/tex]
So, value of Adjacent is [tex]\sqrt{95}[/tex]
Now finding cosФ
[tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex]
Adjacent = [tex]\sqrt{95}[/tex], hypotenuse = 12
[tex]cos\theta=\frac{\sqrt{95} }{12}[/tex]
So, If the sinø=7/12, cosø is [tex]\frac{\sqrt{95} }{12}[/tex]
please help and if you don't know the answer the don't put a random one thank you :(
Answers
hi i think the answers C z<=16.1 good luck:)
pls don't hate on me if im wrong:(
Answer:
Your answer will be C z<=16.1
Step-by-step explanation:
How to solve this would be to divide -4 from both sides and because you are dividing a negative you have to flip the sign.
the square root of 84 is it closer to 9 or 10
Answers
Answer: It is closer to 9
Step-by-step explanation: The square root of 84 is 9.16515139
Answer:
9
Step-by-step explanation:
The square root of 84 rounded the hundredth is 9.17, making it closer to 9 than 10.
Graph the equation.
y-1 = -2(x-2)
Answers
Answer:
y-1 = -2(x-2) graph:
Answer:
Graph is below
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope:
−
2
y-intercept:
(
0
,
5
)
x
y
0
5
5
2
0
A bus is traveling at a constant speed. If the bus travels 15 1 2 15 1 2 miles in 1 3 1 3 of an hour, how many miles will the bus travel in one hour?
Answers
Answer:
46 1/2 miles
Step-by-step explanation:
Given that:
Bus traveled at a constant speed ;
Miles traveled = 15 1/2 miles
Time taken for the travel = 1/3 of an hour
Number of miles bus will travel in 1 hours :
Let number of miles traveled in 1 hour = n
15 1/2 miles = 1/3 hour
n miles = 1 hour
Cross multiply :
1/3 * n = 15 1/2 * 1
1/3n = 31/2
Divide both sides by 1/3
n = 31/2 ÷ 1/3
n = 31/2 * 3/ 1
n = 93/2
n = 46.5 miles = 46 1/2 miles
A blueprint of a plot of land has a scale of 1 1/4 cm to 3 1/4 m the length of the land is 20 cm on the blueprint if i represents the length of the actual peace of land. What is i
Answers
Answer:
52metre
Step-by-step explanation:
Let us use proportion in solving this question, the land has a scale of 1 1/4 cm to 3 1/4 m then the proportion is
( 1 1/4)/ (3 1/4 ) =[blueprint of the plot of land/length of the actual peace of land]
But we need to convert those mixed fractions to improper fraction for easy simplification
1 1/4= [(4×1)+4]= 5/2
3 1/4=[(4×3)+1)]=13/4
Then we can proceed with simplification as
(5/2)/(13/4)=[blueprint of the plot of land/length of the actual peace of land]
But we were given length of the actual peace of land as 20 cm, then
(5/2)/(13/4)=[blueprint of the plot of land/20]
If we cross multiply we have
[blueprint of the plot of land] ×13/4 =5/2 ×20
[blueprint of the plot of land] =(5/2 ×20)÷(13/4)
= 50/(13/4)
=(4×13)/50
= 52
Therefore, the length of the actual peace of land is 52metre
Answer: B) 52 miles
Step-by-step explanation:
393.3 in 10 years investment
Answers
Step-by-step explanation:
The question is not well structured. We can say;
$393.3 in 10 years investment at rate of 10% is equivalent to what?
Given
Amount invested = $393.3 (principal)
Time = 10years
Rate = 10% (assumed rate)
Required
Amount after 10 years
Amount = Principal + Interest
First we need to get the simple interest using the formula
SI = PRT/100
SI = $393.3 * 10 * 10/100
SI = $393.3*100/100
SI = $393.3
Amount in 10years = $393.3 + $393.3
Amount in 10years = $786.6
Hence $393.3 in 10 years investment at rate of 10% is equivalent to $786.6.
Note that the rate was assumed. Any value of the rate can be used. Just employ the same calculation steps.
Sonia and Layla are both running for class president. The senior class has 220 students. After 60% of
the students have voted, Sonia has received 25% of the casted votes, and Layla has received 75%. How
many more votes does Sonia need to receive 50% of the total votes?
Answers
Answer: 33 votes
Step-by-step explanation:
First, we have to calculate 60% of 220 to Kno.the number of people who voted. This will be:
= 60% × 220
= 0.6 × 220
= 132 students
Sonia has received 25% of the casted votes. The number of votes Sonia got will be:
= 25% × 132
= 0.25 × 132
= 33 votes
Layla has received 75%. Her votes will be:
= 75% × 132
= 0.75 × 132
= 99 votes.
50% of the total votes will be:
= 50% × 132
= 0.5 × 132
= 66 votes
The number of votes needed by Sonia to receive 50% of the total votes will be:
= 66 - 33
= 33 votes
Carson just lit a new candle and then let it burn all the way down to nothing. The
candle burned at a rate of 1.25 inches per hour and its initial length was 10 inches.
Make a table of values and then write an equation for L, in terms of t, representing
the length of the candle remaining unburned, in inches, t hours after the candle was
lit.
Number of Hours Burning Length of Candle Remaining (Inches)
0
10
1
1
2
3
Answers
Answer:
Step-by-step explanation:
L = 10 - 1.25t
t = 1 ⇒ L = 10 - 1.25 = 8.75 inches
t = 2 ⇒ L = 10 - 1.25(2) = 7.5 inches
t = 3 ⇒ L = 10 - 1.25(3) = 6.25 inches
i’ll give brainliest if it’s right
Answers
Answer:
bruh i cant see it
Step-by-step explanation:
Answer: what does the display say
A solid cylindrical metal is melted and recast into cubes of metal of side 3cm the base radius of the initial cylindrical metal is 10.5 and height is 63cm . how many cubes will be Madeline
Answers
Answer:
A solid cylindrical metal is melted and recast into cubes of metal of sides 3cm . The base radius of the initi… Get the answers you need, ... is melted and recast into cubes of metal of sides 3cm . The base radius of the initial cylindrical metal is 10.5cm and height is 63cm. How many cubes will be made.
Step-by-step explanation:
hope this is right!
At a certain bookstore, you get a $5 coupon for every 4 books you buy. What is the least number of books you could buy to get $15 in coupons? Show your work.
Answers
Answer:
12books
Step-by-step explanation:
4 books → 1 $5 coupon
$15 coupon = $15 / $5 = 3times of $5 coupons
3 $5 coupons → 4 x 3 = 12 books
this is a topic on forming and solving equations. If you wish to explore more into this topic you can give me a follow on Instagram (learntionary) I'll be posting notes for many topics and will also be posting some tips :)
The number of books for $ 15 coupon is 12 books
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
From the bookstore :
Number of books for $ 5 coupon = 4 books
So ,
Number of books for $ 15 coupon = Number of books for $ 5 coupon x 3
Number of books for $ 15 coupon = 4 x 3 books
Number of books for $ 15 coupon = 12 books
Therefore , the number of books is 12
Hence , the number of books for $ 15 coupon is 12 books
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Write a rule for the translation of ABC to A' B' C'
Answers
Answer:
(x-2,y-4)
Step-by-step explanation:
Here, we want to calculate the rule for the translation
From the question, we can see that the new image was just formed as a movement of the old image by some particular units
The x-axis was move sideways while the y-axis was moved further down
The number of units is thus;
Y from 12 to 8
A movement of -4
For the x-axis
we have a movement of two units toward the left
So the rule is;
(x,y) to (x-2, y-4)
To control an infection, a doctor recommends that a patient who weighs 92 pounds be given 320 milligrams of antibiotic. If the antibiotic is given proportionally according to the patient's weight, how much antibiotic should be given to a patient who weighs 138 pounds?
A 400 milligrams
B 480 milligrams
C 550 milligrams
D 600 milligrams
Answers
Answer:
480 milligrams
Step-by-step explanation:
92 pounds → 320 milligrams
138 pounds → 320/92 x 138 = 480 milligrams
Last year, Summerfield Steel sold 6.5×104 pounds of steel to private businesses and 2.5×105 pounds of steel to government agencies. This year, they expect to sell 3 times that amount. How much steel would that be?
Answers
Answer:
9.45 × 10⁵ pounds of steel
Step-by-step explanation:
Last year, Summerfield Steel sold 6.5×10⁴ pounds of steel to private businesses and 2.5×10⁵ pounds of steel to government agencies.
Total amount of steel sold last year = (6.5 × 10⁴ + 2.5 × 10⁵) pounds = 315000 pounds = 3.15 × 10⁵ pounds
This year, they expect to sell 3 times that amount.
This year = 3 × 3.15 × 10⁵ pounds
= 9.45 × 10⁵ pounds of steel
What is the cost of making one burrito? (Remember that costs are negative.) Explain how you found your answer.
Answers
Answer:
it cost 5.99
Step-by-step explanation:
it all depends on the type of burrito
Help plz!!!! I will give brainliest!!
Caroline is going to invest in an account paying an interest rate of 5.2% compounded continuously. How much would Caroline need to invest, to the nearest dollar, for the value of the account to reach $940 in 6 years?
Answers
Answer:
688
Step-by-step explanation: