The vertex is (-2, 11), then the vertex form of the quadratic is:
f(x) = 5*(x + 2)^2 - 11
How to write the quadratic equation in vertex form?A quadratic equation with a leading coefficient a and a vertex (h, k) can be written in vertex form as:
y = a*(x - h)^2 + k
And for a quadratic equation of the form:
y = a*x^2 + b*x + c
The vertex is at:
h = -b/2a
In this case, our equation is:
f(x) =5x^2 + 20x + 9
Then:
h = -20/2*5 = -2
Evaluating in x = -2 we get:
f(-2) = 5*(-2)^2 + 20*-2 + 9
f(-2) = 5*4 - 40 + 9
f(-2) = 20 - 40 + 9 = -20 + 9 = -11
The vertex is (-2, -11), and the leadin coefficient is a = 5, then the vertex form is:
f(x) = 5*(x + 2)^2 - 11
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In the first five math quizzes, Patty had an average score of 8. She got a 7 and a 5 on the next two quizzes. After the eighth quiz, her
average stood at 7.5. What was her score on the eighth quiz?
*
Answer: 8
Step-by-step explanation:
(Sum of first 5 quizzes) / 5 quizzes = 8
Sum of 1st 5 quizzes = 8 x 5 = 40
let x = score on the 8th quiz
(40 + 7 + 5 + x) / 8 = 7.5
52 + x = (7.5)(8) = 60
x = 60 - 52 = 8
How would you investigate the complaints from renters who are
unhappy about their monthly rents?
What statistical measurement would be used?
To investigate the complaints from renters who are unhappy about their monthly rents, the mean rents can be collected
The statistical measurement that would be used is the ANOVA.
What is a mean?A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."
ANOVA is an abbreviation for Analysis of Variance. It is a statistical test invented by Ronald Fisher in 1918 that has been in use ever since. Simply said, ANOVA determines whether or not there are statistical differences between the means of three or more independent groups. The most basic type is one-way ANOVA. To know of the meansare the same, the ANOVA can be used.
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Pedro walks 3/8 of a mile in a 1/4 of an hour. How many miles does he walk in an hour
Answer:
S=3/8 miles
T=1/4 hour
V=S/T = 3/8 ÷ 1/4 = (3×4)÷8 = 3/2 miles in an hour
(2,y) and (x,−3).
4x+2y=14
the table shows the number of pounds that 10 students in gary langs weight training class could bench press and squat. make a scatterplot to display the relationship between the bench press and squat weights for this sample. (use squat as the explanatory variable). describe the relationship shown in the scatterplot
The scatter plot that displays the relationship between the bench press and squat weights for this sample is given by the second image at the end of the answer.
From the scatter plot, it can be taken that the relationship is that the variables have a positive association, as when the bench press weight increases, so does the squat weight. The relationship, however, is not strong, as the scatter plot is not 100% increasing.
How to built the scatter plot?The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:
(bench press weight, squat weight).
From the table given by the first image at the end of the answer, the points are listed as follows:
(95, 141), (111, 208), (113, 100), (125, 218), (135, 284), (145, 275), (165, 338), (180, 338), (140, 420), (196, 420), (95, 141), (111, 208).
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Convert 0.8 grams to grains
Answer:
12.3459 grains
Step-by-step explanation:
Answer:
12.346 grains
Step-by-step explanation:
for an approximate result, multiply the mass value by 15.432
( which is basically 0.8 times 15.432)
Lorna Hall’s real estate tax of $2,010.88 was due on December 14, 2017. Lorna lost her job and could not pay her tax bill until February 27, 2018. The penalty for late payment is 61/2% ordinary interest. (Use Days in a year table.)
a. What is the penalty Lorna must pay? (Round your answer to the nearest cent.)
b. What is the total amount Lorna must pay on February 27? (Round your answer to the nearest cent.)
a) The penalty Lorna must pay for the late payment of her real estate tax is $26.50.
b) The total amount Lorna must pay on February 27 is $2,037.38.
How is the penalty for unpaid taxes computed?The penalty for unpaid taxes is computed by determining the number of days the taxes remained unpaid.
Then the penalty rate is applied to the unpaid taxes multiplied by the number of days taxes were outstanding, divided by 365 days.
The product of the above multiplication and division operations is the penalty.
Outstanding real estate tax = $2,010.88
Due date for the tax = December 14, 2017
Payment date for the tax = February 27, 2018
Number of days, tax outstanding = 74 days
Penalty rate for late payment = 6.5%
Penalty = $26.50 ($2,010.88 x 6.5% x 74/365)
Total payment on February 27 = $2,037.38 ($2,010.88 + $26.50)
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Eugene has a collection of 140 pet rocks. Of these rocks, 35% are sedimentary, 40% are igneous, and the rest are metamorphic. How many are metamorphic?
Answer:
25% or 35 rocks.
Step-by-step explanation:
To find this answer, simply add up 40% and 35% to get 75%. Now, 100% is the most we can have. So, 100 - 75 = 25%.
To find even more in depth of exactly how much 25% of 140 is, we can simply move the decimal point from 25 over twice to get 0.25. The term "of" means multiply:
0.25 x 140 = 35 rocks.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane.
y> 2x+4
x+y≤6
The graph of inequalities equation on coordinate plane is given below ↓↓↓
Difference between equality and inequality equations
Both mathematical phrases, equality and inequality , are created by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.
The inequalities equation is ,
y> 2x+4
x+y≤6
so, the graph is ↓↓↓
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Which ordered pair is a solution of the equation? 2 x + 4 y = 6 x − y 2x+4y=6x−y
The solution to the equation given as 2x + 4y = 6x − y has the ordered pair of (3, 4)
How to determine the ordered pair of the solution?From the question, we have the following equation that can be used in our computation:
2x+4y=6x−y
Solving further, we need to collect the like terms
So, the equation becomes
2x - 6x = -4y - y
Next, we evaluate the like terms in the above equation
So, we have the following representation
-4x = -3y
Divide both sides by -3
The equation becomes
x = 3/4y
At this point, we assume any value for y and then solve for x
Assume that the value of y is 4
So, we have the following representation
x = 3/4 * 4
Evaluate the products
x = 3
So, we have
x = 3 and y = 4
Express as ordered pairs
(x, y) = (3, 4)
Hence, the ordered pair of the solution is (3, 4)
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Man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and she wants to order between 15% and 20% extra of the material
The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².
How to calculate the value?From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.
It should be noted that 15% of the material will be:
= 15% × 115.4
= 17.31 ft²
It should be noted that 20% of the material will be:
= 20% × 115.4
= 23.08 ft²
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Chris works at an electronics store. He earns $10 per hour plus 12.5% commission on his computer sales. Today, Chris worked 5.5 hours and sold $1100 in computers. How much did Chris earn in total today?
By solving a simple equation we can see that Chris earned $192.50.
How much did Chirs earn Today?
We know that Chris wins $10 per hour plus the 12.5% of the total amount he solds in computers.
So, if he works 5.5 hours and sold $1,100 in computers, the amount that he earns is given by the equation:
E = $10*5.5 + $1,100*( 12.5%/100%)
E = $10*5.5 + $1,100*(0.125) = $192.50
Then we conclude that Chris earned $192.50 today.
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What is the equation of this graphed line
Answer: y = -9/8 + 7
Step-by-step explanation:
point a = (0,7), point b = (8,-2)
y = mx + b
b = 7
y = mx + 7
-2 = 8m + 7
-9 = 8m
m = -9/8
y = -9/8 + 7
Answer:
y= -9/8x+7
Step-by-step explanation:
find the slope
y2-y1/x2-x1
-2-7/8-0
-9/8
y=mx+b
m=slope
b=y intercept
y= - 9/8x + b
y= -9/8x+7
Ken spends $344.76 before tax at a hardware store. If the sales tax rate in his city is 7.5%, what is the total cost of his purchase? Round to the nearest cent if necessary.
Answer:
$318.90
Step-by-step explanation:
Turn the percent into a decimal and multipy it by 344.76
0.075 × 344.76 = 25.857
after you get your answer you subtract 344.76 and 25.857
$344.76 - 25.857 = $318.903
round you answer to the nearest cent
= $318.90
The assets and liabilities of a landscaping business are listed below.
Owned Inventory
$30,500
Cash
$75,420
Building Mortgage
$154,265
Savings Account
$28,000
Owned Equipment
$15,670
Small Business Loan
$25,652
Credit Cards
$11,450
Accounts Receivable
$11,560
Investments
$178,925
Which balance sheet correctly shows the assets, liabilities, and net worth of the landscaping business?
The total value of the ice cream shop owner's business assets would be; $286,898.
What are business assets?Business assets are the value of the assets of the Ice Cream Shop. The business assets consist of liabilities (amounts owed outsiders) and equity (the difference between assets and liabilities).
Business Assets:
Owned Inventory $30,500
Cash $75,420
Savings Account $28,000
Owned Equipment $15,670
Accounts Receivable $11,560
Property Value $125,768
Total assets = $286,898
Business Liabilities:
Small Business Loan $25,652
Other Debt $1,235
Building Mortgage $154,265
Total liabilities = $171,152
Equity = $115,746 ($286,898 - $171,152)
The total value of the ice cream shop owner's business assets would be; $286,898.
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Answer:
The net worth of the landscaping business is $148,708.
Step-by-step explanation:
Assets:
(Owned Inventory) $30,500
(Cash) $75,420
(Savings Account) $28,000
(Owned Equipment) $15,670
(Accounts Receivable) $11,560
(Investments) $178,925
30500+75420+28000+15670+11560+178925 = 340075
Liabilities:
(Building Mortgage) $154,265
(Small Business Loan) $25,652
(Credit Cards) $11,450
154265+25652+11450= 191367
Assets - liabilities = net worth
340075 - 191367 = 148708
So, the net worth of the landscaping business is $148,708.
Factor 64+ 60. Write your answer in the form a(b + c) where a is the GCF of 64 and 60
Z-Grand Shipping Company manufactures boxes in the shape of a cube.
The formula for the surface area of a cube is 6s, where s is the length of one side.
Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is
square feet
The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is
square feet
The surface area of the large box is times larger than the small box.
Please Help?
Answer:
Z-Grand Shipping Company manufactures boxes in the shape of a cube.
The formula for the surface area of a cube is 6s, where s is the length of one side.
Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is 216
square feet
The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54
square feet
The surface area of the large box is 4 times larger than the small box.
{So for the first line which is The surface area of each large box is
square feet.}
Ans;216
{The second line which is The surface area of each small box is
square feet.]
Ans;54
{The Third line which is The surface area of the large box is times larger than the small box.}
Ans;4
Thank you So much Hope this helps you! Please Mark Brainleast looking forward to help everyone ty!
Answer:
Z-Grand Shipping Company manufactures boxes in the shape of a cube.
The formula for the surface area of a cube is 6s, where s is the length of one side.
Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is 216
square feet
The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54
square feet
The surface area of the large box is 4 times larger than the small box.
{So for the first line which is The surface area of each large box is
square feet.}
Ans;216
{The second line which is The surface area of each small box is
square feet.]
Ans;54
{The Third line which is The surface area of the large box is times larger than the small box.}
Ans;4
Whats ?? Also right an addition expression to get the same answer Answer ASAP
Answer:
p=-10
Step-by-step explanation:
-10-20=-30
Subtracting a negative from a negative will result in a higher negative, the same can be said for -10-20. Removing 10 from -20 will result in a lower answer. This is 20.
Write the linear equation when given the following information.
m = -2 and b = -5
Answer:
y=-2x-5
Step-by-step explanation:
m =-2 and b=-5 so when substituted it will get you y=-2x-5
Find the difference between the sums to ten terms of the AP and GP whose first two terms are-2 and 4.
The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932
What is Arithmetic Progression and Geometric Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
First term = -2
Second term = 4
A)
For Arithmetic Progression
First term a = -2
Second term = 4
Common difference d = Second term - First term
= 4 - ( -2 )
= 6
And Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
n = 10 terms
Sₙ = ( 10/2 ) [ (2x- 2) + ( 9 ) x 6]
Sₙ = 5 [ -4 + 54 ]
Sₙ = 5 x 50
Sₙ = 250
Therefore , Sum of first 10 terms of an AP is 250
B)
For Geometric Progression
First term a = -2
Second term = 4
Common ratio = Second term / First term
= 4 / -2
= -2
And Sum of first n terms of an GP : Sₙ = a( 1 - rⁿ ) / ( 1 - r )
n = 10
Sₙ = 2( 1 - ( -2 )¹⁰ ) / 1 - ( -2 )
Sₙ = 2 ( 1 - 1024 ) / 3
Sₙ = ( 2 x (-1023) ) / 3
Sₙ = 2 x ( - 341 )
Sₙ = - 682
Therefore , Sum of first 10 terms of an GP is -682
The difference between the sum of first 10 terms of AP and GP is GP - AP
= -682 - 250
= -932
Hence , The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932
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11. Corey bought 25 gallons of gas to fill up his pickup truck. He paid for the part of the total with a $25 gift card and was left owing $26. How much did he pay per gallon for the gas?
Answer:
I believe that the answer is $2.04, per gallon.
Step-by-step explanation:
I added the $25 he paid with the gift card, and the $26, which was $51 that Corey paid in total. Corey had gotten 25 gallons and they want to figure out how much he paid for each gallon. So we take the total he spent divided by the number of gallons he had gotten. So 51/25=2.04
Hope this helps!!!!
What should be added to 5/6 to get 41/24
Answer: 26/24
Step-by-step explanation:
First we have to convert 5/6 with a denominator of 24 so 6 times what makes 24, that is 4 & whatever you do with the denominator, you have to do it with the numerator. So 5 times 4 is 20, the new fraction is 20/24. Now, we need to find what we need to add with 20/24 to get 41/24, so we subtract 20/24 from 41/24 & that is 21/24. We can check if it's correct by adding both 21/24 and 20/24 & that makes 41/24.
Choose from the drop-down menus to match the trigonometric expression with its value
The values that match the various trigonometric identity are;
1) sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀ = 1
2) cos 13 cos 47 + sin 13 sin 47 = 0.5
3) sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π = 0
How to solve Trigonometric Identities?Trigonometric identities are defined as the equations that involves the trigonometric functions that are true for every value of the variables involved.
1) We know that the trigonometric identity sin(A + B) is expressed as;
sin(A + B) = sinAcosB + cosAsinB
We are given;
sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀
Applying the trigonometric identity above, gives us;
sin(²/₅π + π/₁₀)
= sin(5π/10)
= sin(π/2)
= 1
2) We know that the trigonometric identity sin(A + B) is expressed as;
cos(A + B) = cosAcosB − sinAsinB.
We are given;
cos 13 cos 47 + sin 13 sin 47
Applying the trigonometric identity above, gives us;
cos(13 + 47)
= cos 60
= 0.5
3) We know that the trigonometric identity sin(A + B) is expressed as;
sin(A + B) = sinAcosB + cosAsinB
We are given;
sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π
Applying the trigonometric identity above, gives us;
sin(²/₅π + ⁸/₅π)
= sin(¹⁰/₅π)
= sin(2π)
= 0
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How do I solve this question
Answer:
the answer is down there
A shoe store is offering a series of markdowns for its customers due to its need for quick cash. The shoe store is offering the markdowns in the following order: 35%, 20%, and 10%. What would be the sale price of a pair of boots, if it originally costs $165.00?
The final price of the shoes after successive discounts is $77.22.
What is a discount?
A discount is a reduction in the regular selling price of a good or service, either in terms of money or as a percentage.
Main Body:
Sale price = Original price - discount
The formula for successive discount is given by=
Cost price*(1 - discount₁/100)*(1 - discount₂/100)*(1 - discount₃/100)
Now calculating:
According to the question , Cost price = $165
sale price = 165*(1-0.35)*(1-0.20)*(1-0.10)
= 165*0.65*0.8*0.9
= $77.22
Hence the answer to sale price of the shoe would be $77.22
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A sample of size 39 will be drawn from a population with mean 23 and standard
deviation 10. Find the probability that will be greater than 25.
The probability that X will be greater than 25 is 0.42
Given,
The sample size, n = 39
The mean of the population, μ = 23
The standard deviation of the population, σ = 10
We have to find the probability for X > 25.
Here,
Z score = (X - μ) / σ
Z score = (X - 23) / 10
Now,
We have to find P(X > 25)
Then,
P(X > 25) = P(z > (25 - 23) / 10)
P(X > 25) = P(z > 2/10)
That is,
P(X > 25) = P(z > 0.2)
Here,
0.5 - P(0 ≤ z ≤ 0.2)
= (0.5 - 0.0792)
= 0.42
Therefore,
The probability that X will be greater than 25 is 0.42
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Does anyone know the answer to this problem?
It is a scalene triangle .
What is a scalene triangle?A triangle called a Scalene Triangle in geometry is one with equally spaced-apart sides. It indicates that all three angles and all three sides of a scalene triangle are of different sizes. According to sides, there are three different kinds of triangles.The sides and angles of the triangles are used to define them. A triangle is represented as a three-sided polygon in geometry and is a closed, two-dimensional plane object having three sides and three angles. There are three edges and three vertices.acc to our quesion-
all the sides of triangle are unequal
if all sides are unequal ,it is called scalene triangle.
hence,It is a scalene triangle .
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how many groups 1/4 are in 3/4
There are 3 1/4's in 3/4, hope this helps.
Answer: 3
Step-by-step explanation: since they are the same denominator it is basically asking how many 1s go in 3
Last week, the total weight of the members of a weight loss support group was 2,500 pounds. This week, it was 2,525 pounds. What percent heavier is the group now? %
The percent increase from 2,500 pounds this week to 2,525 pounds is 1% increase
How to find the percent increase of the weights?From the question, we have the following parameters that can be used in our computation:
Initial weight = 2500 pounds
New weight = 2525 pounds
The percentage increment is then calculated as
Percentage = (Final value - Initial value)/Initial value * 100%
Substitute the known values in the above equation
Percentage = (2525 - 2500)/2500 * 100%
Evaluate the difference
So, we have
Percentage = 25/2500 * 100%
Evaluate the quotient
So, we have
Percentage = 0.01 * 100%
Evaluate the product
So, we have
Percentage = 1%
Hence, the percent increase is 1% increase
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You accidentally inhale some mildly poisonous fumes. From a blood sample poison concentration exponentially
The exponential function giving the concentration after t hours is given as follows:
[tex]C(t) = 0.00372(0.9359)^t[/tex]
What is an exponential function?The standard modelling of an exponential function is presented as follows:
[tex]y = a(b)^x[/tex]
The meaning of the variables of the equation are given as follows:
a is the initial value of the exponential function, that is, the numeric value of y when x = 0.b is the rate of change of the exponential function, giving by how much y is multiplied when x increases by one.The initial value of the exponential function is given as follows:
a = 0.00372.
After eight hours, the concentration is given as follows:
C(8) = 0.00219.
Hence the rate of change is obtained as follows:
[tex]C(t) = 0.00372b^t[/tex]
[tex]0.00219 = 0.00372b^8[/tex]
[tex]b^8 = \frac{0.00219}{0.00372}[/tex]
[tex]b = \sqrt[8]{\frac{0.00219}{0.00372}}[/tex]
[tex]b = \left(\frac{0.00219}{0.00372}\right)^{\frac{1}{8}}[/tex]
b = 0.9359.
Hence the equation is:
[tex]C(t) = 0.00372(0.9359)^t[/tex]
Missing InformationThe problem is given by the image at the end of the answer, and it asks for the exponential function modelling the situation.
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