The parabola represented by this graph has the following equation:
y = -16.67(x + 1)² + 2
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
A downward open parabola rises from (-2.4, 4) to (-1,2), and declines through (0.4, -4) on the coordinate plane, hence the vertex is given by:
(-1,2), hence the coefficients are h = -1 and k = 2, and the equation is:
y = a(x - h)² + k
y = a(x + 1)² + 2
We have that when x = -0.4, y = -4, hence the leading coefficient is found as follows:
y = a(x + 1)² + 2
-4 = a(-0.4 + 1)² + 2
a = -6/0.6²
a = -16.67
Hence the equation is:
y = -16.67(x + 1)² + 2
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Mr Lim had a bag of sweets. After giving each pupil 7 sweets, he had 4 sweets left. If he had given only 5 sweets to each pupil, he would have 4 sweets left. If he had given only 5 sweets to each pupil, he would have 80 sweets left.
i.How many pupils were there in the class?
ii. How many sweets did Mr Lim have?
Solving a system of equations we can see that there are 270 sweets and 38 pupils.
How many pupils and sweets are there?
Let's define the variables:
P = number of pupils.
S= number of sweets.
With the given information, we can write:
7*P + 4 = S
5*P + 80 = S
So we have a system of equations, now we can write:
7*P + 4 = S = 5*P + 80
Solving that for P:
7*P + 4 = 5*P + 80
7*P - 5*P = 80 - 4
2*P = 76
P = 76/2 = 38
There are 38 pupils, and the number of sweets is given by:
S = 7*P + 4 = 7*38 + 4 = 270
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Solve the system to answer the questions.
How many premium car washes were ordered?
premium car washes
How many quick car washes were ordered?
quick car washes
The number of quick car and premium car washes ordered are 75 and 50 respectively.
How to find the number of premium and quick car washes ordered?The system of equation models the situation
x + y = 125
5x + 8y = 775
Therefore,
5x + 5y = 625
5x + 8y = 775
3y = 150
divide both sides 3
3y / 3 = 150 / 3
y = 50
Therefore,
x + y = 125
x + 50 = 125
x = 125 - 50
x = 75
Therefore, the number of quick car and premium car washes ordered are 75 and 50 respectively.
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Answer:
50 and 75
Step-by-step explanation:
Determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne. ) an = n2 n3 5n
The sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.
For given question,
We have been given a sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex]
We need to determine whether the sequence converges or diverges.
From given sequence we have, [tex]a_{n+1}=\frac{(n+1)^2}{(n+1)^3+5(n+1)}[/tex]
We use Ratio Test.
According to Ratio Test, [tex]r=\frac{a_{n+1}}{a_n}[/tex], where sequence converges if and only if |r| < 1.
Consider,
[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(n+1)^2}{(n+1)^3+5(n+1)}}{\frac{n^2}{n^3+5n}} |\\\\\\= \lim_{n \to \infty} |\frac{(n+1)^2(n^3+5n)}{n^2[(n+1)^3+5(n+1)]} |\\\\=\infty[/tex]
Since [tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |[/tex] is not defined, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.
Therefore, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.
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Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the π button on your calculator to solve.
The volume of the figure is 1, 005. 4 mi³
Volume of a cylinderNote that the figure is a cylinder
The formula for volume of a cylinder is given as;
Volume = πr²h
Where
h = height = 5 mi
r = radius = 8mi
Substitute into the volume
Volume = 3. 142 × 8 × 8 × 5
Volume = 1,005. 4 mi³
Thus, the volume of the figure is 1, 005. 4 mi³
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A dealer buys oranges for 100000, he sold 60% of them for buying price, he sold 50% of the remaining for profit of 60% then he sold the remaining for a loss of 10%. Find the overall profit
Based on the amount of oranges bought, those sold at a profit and those sold at a loss, the overall profit is 14.2%
What is the overall profit?Assume that the buying price was $1 each.
The amount earned from 60% of them is:
= 60% x 100,000 x 1
= $60,000
The profit from selling 50% of the remaining is:
= (50% x 40,000) x 1.60
= $32,000
The loss from selling the other 50%:
= (50% x 40,000) x 0.90
= $22,222.22
Total selling price:
= 60,000 + 32,000 + 22,222.22
= $114,222.22
Total profit:
= (114,222.22 - 100,000) / 100,000
= 14.2%
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A ________ standard deviation represents an overall wide spread of data points while a ________ standard deviation represents a closely clustered set of points.
Answers are in bold
A larger standard deviation represents an overall wide spread of data points while a smaller standard deviation represents a closely clustered set of points.
Keep in mind the standard deviation cannot be negative. A standard deviation of 0 means that every data value is the same number; hence it is the most clustered set possible. There is no upper limit on how big the standard deviation can be.
If needed, replace "larger" with "large". And if needed, replace "smaller" with "small". I think it will depend on how your teacher wants you to word it. In all honesty, I'm not very good with grammar.
A larger standard deviation represents an overall wide spread of data points while a smaller standard deviation represents a closely clustered set of points.
What is standard deviation?The term "standard deviation refers to a measurement of the data's dispersion from the mean.
A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
The standard deviation cannot be negative, so keep that in mind. The most tightly clustered set of data is one with a standard deviation of 0, which denotes that all the data values are the same.
The size of the standard deviation has no upper bound.
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Pick the correct answer
Thanks so much :)
The linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have that:
Line I is decreasing, hence it has a negative slope.Line K is constant, hence it has a slope of zero.Line J is increasing, hence it has a positive slope.Hence the linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
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Determine whether each pair of triangles is congruent. If yes, include the theorem or
postulate that applies and describe the series of rigid motions that map one triangle onto the
other.
A.
4
B.
ΔΔ
C.
D.
The pair of triangles in option A, C and D are congruent triangles.
Pair of triangles are given.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
A) In the given figure, two angles and one side of the one triangle is equal to two angles and one side of the other triangle
By AAS congruence, two triangles are congruent.
B) In the given figure, one angle and one side is equal
So, two triangles are not congruent
C) Here, two sides and one included angle of the one triangle is equal to two sides and one included angle of the other triangle
D) Here, two angles and one included side of the one triangle is equal to two angles and one included side of the other triangle.
Therefore, the pair of triangles in option A, C and D are congruent triangles.
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Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
According to the developed scale, a radiant day is 16 times brighter than a dim day.
We assume the brightness of a dim day to be x.
According to the developed scale, the brightness of an illuminated day will be 4 times that of a dim day.
Thus, the brightness of an illuminated day = 4*the brightness of a dim day = 4x.
According to the developed scale, the brightness of a radiant day will be 4 times that of an illuminated day.
Thus, the brightness of a radiant day = 4*the brightness of an illuminated day = 4*4x = 16x.
Now, the ratio of the brightness of a radiant day to the brightness of a dim day = 16x:x = 16x/x = 16:1.
Thus, according to the developed scale, a radiant day is 16 times brighter than a dim day.
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The question provided is incomplete. The complete question is:
"Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
Dim=2
Illuminated=3
Radiant=4
Dazzling=5"
A ride at a park has room for 8 children to ride at once.
How many rides are needed to allow 45 children a turn?
Answer:
6
Step-by-step explanation:
45/8=5.625
Since there are .625 children left, we need to add another ride to fill in what's left.
In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square yards, of ΔABC.
a = 12, b = 11, c = 7
Answer:
12 sqrt (10)
Step-by-step explanation:
S = (12 + 11 + 7) / 2 = 15
A = sqrt (s(s-a)(s-b)(s-c))
= sqrt (15(15-12)(15-11)(15-7))
= sqrt (15*3*4*8)
= sqrt (1440)
= 12 sqrt (10)
20 POINTS TO SOLVE THIS ANSWER!!!
Answer:
V₁ = 104 in.³ , S₂ = 650 in. ²
Step-by-step explanation:
⇒ Ratio = 4/10 = 2/5
⇒ V₁ : V₂ = (ratio)³ = 8/125 {geometric scale}
⇒ S₁ : S₂ = (ratio)² = 4/25
∴ V₁ = 8/125 × V₂ = 1,625 in³ × 8/125 = 104 in.³
⇒ S₂ = 25/4 × S₁ = 104 in² × 25/4 = 650 in.²
Solve for x.
°x = 196
Enter your answers in the boxes. Enter the smallest answer first.
x= ____ and x= ____
4 andfirst find x by finding its smallest factor
The solution to the given system of equation is -7 and 7
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Given:
4x² = 196
4x²/4= 196/4
x² = 49
x=√49
x= ±7
Hence, the solution to the given system of equation is -7 and 7
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is (n x (n +1)) / 2 the same as (n/2)(n+1)
Answer:
nope
Step-by-step explanation:
simplify the first equation
Answer:
yes
Step-by-step explanation:
The associative and commutative properties of multiplication allow you to rearrange the product to the form shown in the question.
Division by 2 is effectively multiplication by 1/2.
[tex](n\times(n+1))/2\qquad\text{given}\\\\=\dfrac{n(n+1)}{2}=\dfrac{n}{2}(n+1)\\\\=\boxed{(n/2)(n+1)}[/tex]
__
Additional comment
Evaluation of the expressions according to the order of operations will proceed differently for the two expressions.
For the first expression, evaluation steps are ...
add 1 to nmultiply the sum by ndivide the product by 2For the second expression, evaluation steps are ...
divide n by 2add 1 to nmultiply the results of these two operationsAs we said above, the properties of multiplication ensure the results are the same either way.
As a practical matter, for integer values of n, one of n and (n+1) will be even. It is usually convenient to divide the even number by 2. This means the evaluation might be ...
((n+1)/2)n . . . . for odd n(n+1)(n/2) . . . . for even nFor certain computer representations of the numbers, results may differ depending on the specific numbers and the order of evaluation.
Wynn is 24 years old and has decided to reduce the number of cups of coffee he buys by 2 cups per day. One cup of coffee typically costs $2.50. Assuming 30 days in a month, if he chooses to invest this money at the end of every 6 months into an investment paying 5.50% compounded semi-annually, how much will he have when he turns 69?
The total amount he would have at 69 is $343,347.81.
What is the total amount saved?The formula that can be used to determine the future value of the deferred annuity is:
Future value = annuity factor x monthly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 5.5 /2 = 2.75%n = number of payments = 2 x (69 - 24) = 90Amount he would save every 6 months:
amount saved per day = $2.50 x 2 = $5Amount saved per month : $5 x 30 = $150 Amount saved every 6 months = $150 x 6 = $900Future value : 900 x {[(1.0275^90) - 1] / 0.275}= $343,347.81
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Consider the steps to solve the equation. 2 5 ( 1 2 y + 20 ) − 4 5 = 9 20 (2y − 1)
Distribute: 1 5 y + 8 − 4 5 = 9 10 y − 9 20
What is the next step after using the distributive property?
*Use the multiplication property of equality to isolate the variable term on one side of the equation.
*Use the multiplication property of equality to isolate the constant on one side of the equation.
*Combine the like terms on the right side of the equation.
*Combine the like terms on the left side of the equation.
Answer:
D
Step-by-step explanation:
I did the assignment
hope this helps :)
Find the value of z
A. 50
B. 110
C. 65
D. 130
Need help ASAP! This is due in an hour and this is the last question!!!
the equation with these solutions is:
0 = x^2 - 6x + 6
How to find an equation with the given solutions?
Remember that a quadratic equation with the solutions a and b is written as:
0 = (x - a)*(x - b)
Here we have the solutions:
x = 3 + √3x = 3 - √3Then we can write a quadratic equation of the form:
0 = (x - (3 + √3) )*(x - (3 - √3) )
0 = (x - 3 - √3)*(x - 3 + √3)
Expanding that, we get:
0 = x^2 - 6x + 9 - 3
0 = x^2 - 6x + 6
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Listed below are systolic blood pressure measurements (in mmHg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05.
The regression equation between the variables is y = 1.03x + 62.12 and the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg is 149.67
How to determine the regression equation?From the table of values, we make use of the following representations:
Represent the Right Arm on the x axisRepresent the Left Arm on the y axisUsing the above representations, we can now plot our data values on a graphing calculator
From the graphing calculator, we have the following summary:
Sum of X = 458Sum of Y = 782Mean X = 91.6Mean Y = 156.4Sum of squares (SSX) = 601.2Sum of products (SP) = 618.8The regression equation is
y = bx + a
Where
b = SP/SSX = 618.8/601.2 = 1.02927
a = MY - bMX = 156.4 - (1.03*91.6) = 62.11843
This gives
y = 1.03x + 62.12
Hence, the regression equation between the variables is y = 1.03x + 62.12
To predict the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg, we have
y = 1.03 * 85 + 62.12
Evaluate
y = 149.67
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Louie is trying to find a rectangular canvas for his art project. its height must measure 18 inches and form a 48° angle with the diagonal at the top of the canvas. what is the length of the diagonal of the canvas? round your answer to the nearest inch. 12 inches 14 inches 24 inches 27 inches
The length of the diagonal of the canvas = 27 inches.
The correct option is D.
What is Pythagoras?A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem, or Pythagoras' theorem. The area of the square whose side is the hypotenuse is said to be equal to the total of the areas of the squares on the other two sides.
According to the given information:the Hight of the rectangle = 18 inches
the angle it form sinθ = H/P
H = 18
P =
cosθ = 48
cosθ = H/P
cosθ =18/P
P = 18/cosθ
= 29.60
= 27
The length of the diagonal of the canvas = 27 inches.
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1. Ansley meets her fruends at the movie theter. They had already purchased a bucket of popcorn, and there is only 3/4 left. Ansley eats 1/3 of the remaining popcorn. How much of the bucket did Ansley eat?
2. Jamie bought 6 pool floats to use during the summer. 2/3 of the floats were tellow. How many yellow floats did he buy?
3. Mrs. Jones purchases 2/3 of a pound of cookies for her class. If the cookies are $6.00 per pound, how much did she pay for the cookies?
4.The school band has 24 members. If 1/8 of them play the drums how many members of the band play the drums?
5. Callie spent 1 1/2 hours outside with her sister. They spent half of theat time jumping on their trampoline. How long did they jump on the trampoline?
1. he ate 1/4 of the bucket
2. 4 of the pool floaties are yellow.
3. she paid 4$ for the cookies
4 . 3 members of the band play the drums
5. 45 minutes
Answer:
1. Ansley eats 1/4 of the popcorn bucket
2. He bought 4 yellow floats
3. She pays 4 pounds for the cookies
4. 3 members of the band play the drums
5. They spent 45 minutes jumping on the trampoline
Step-by-step explanation:
If you would like the explanation, I can comment it below (≧∇≦)/ xx
Hope this helps! ♡
Question 9 of 20:
Select the best answer for the question.
9. Select the proper order from least to greatest for 23.76.8.10 -
A. 8,3,10.76.
B.23,10.6.8.
C.8.10 6.2/3.
D.76%10.3.8.
Answer:
Please make the question clearer, but I would say B
Step-by-step explanation:
I am not sure what you mean, to me the question is unclear
evaluate 4 + 6 x 6 / 8
Answer:
8.5
Step-by-step explanation:
4 + (6)(6)/8=
17/2 = 8.5
Answer:
8.5
Step-by-step explanation:
6 x 6 = 36/8 = 4.5 + 4 = 8.5
(6 1/7 divided by x + 3 5/9) / 4 1/6 = 1 1/3 what is x
let's firstly convert the mixed fractions to improper fractions and them proceed.
[tex]\stackrel{mixed}{6\frac{1}{7}}\implies \cfrac{6\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{43}{7}} ~\hfill \stackrel{mixed}{3\frac{5}{9}}\implies \cfrac{3\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{32}{9}} \\\\\\ \stackrel{mixed}{4\frac{1}{6}}\implies \cfrac{4\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{25}{6}} ~\hfill \stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{ ~~ \frac{6\frac{1}{7}}{x}+3\frac{5}{9} ~~ }{4\frac{1}{6}}~~ = ~~1\frac{1}{3}\implies \cfrac{ ~~ \frac{ ~~ \frac{43}{7} ~~ }{x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}\implies \cfrac{ ~~ \frac{43}{7x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}[/tex]
[tex]\cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{25}{6}\cdot \cfrac{4}{3}\implies \cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{50}{9}\implies \cfrac{43}{7x}~~ = ~~\cfrac{50}{9}-\cfrac{32}{9} \\\\\\ \cfrac{43}{7x}~~ = ~~\cfrac{18}{9}\implies \cfrac{43}{7x}=2\implies 43=14x\implies \cfrac{43}{14}=x\implies 3\frac{1}{14}=x[/tex]
A company found that an experienced surveyor can survey a roadbed in 7 hours. An apprentice surveyor needs 8 hours
to survey the same stretch of road. If the two work together, find how long it takes them to complete the job.
***
The number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.
Rate of workHours it takes the experienced surveyor = 7 hoursSurveyors rate of work = 1/7Hours it takes the apprentice = 8 hoursApprentice rate of work = 1/8If the two work together;
Time taken for both to complete the task = Surveyors rate of work + Apprentice rate of work
= 1/8 + 1/7
= (7+8) / 56
= 15/56 hours
Therefore, the number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.
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Area=
What is the area?
Help me asap! Please!! Thanks so much:)
Answer:
area = 10
Step-by-step explanation:
Triangle BOC is a right triangle. You can see this because the slope of BO and OC are negative reciprocals (opposite sign and flipped over) You can calculate the slope, m.
m = (y-Y)/(x-X)
Slope of BO is 4/2,
slope of OC is -2/4.
see image.
So then you can use BO and OC as the base and height in an area calculation.
But first you have to calculate the length of each. Luckily they are the same length. You can use distance formula, but when you have a picture, you can just see to use Pythagorean theorem (distance formula comes from PythagThm anyway)
Both BO and OC have legs length 2 and 4. See image. They are both length sqrt20.
Use Area= 1/2bh to find the area. See image.
3. (x,y) → (x + 2,y) → (x, y)
-10-8
-4-2
10
8
6
2
-2
T
ID
-6
-8
-10
9
10
4. (x,
-10-8
HELPPP PLSSSS
1) A translation 2 units right
2) A reflection over the x-axis
Find the missing segment in the image below.
Answer:
105.
Step-by-step explanation:
x/120 = 56/64 where x is the length of missing segment
64x = 120*56
x = (120*56)/64
= 105.
correct 0.34213 to three significant figures
Answer:
0.342
Step-by-step explanation:
round to the given amount of significant figures
A 2-gallon container of laundry detergent costs $10.24. What is the price per fluid ounce?
Answer:
$0.04
Step-by-step explanation:
The cost per ounce is found by dividing the cost by the number of ounces.
SolutionIn 2 gallons, there are 2×128 fl.oz. = 256 fl.oz. Then the cost per ounce is ...
cost/ounces = $10.24/(256 fl.oz) = $0.04 /fl.oz.
The cost of the laundry detergent is $0.04 per fluid ounce.
__
Additional comment
Keeping the units with the numbers in a calculation can give you confidence that the calculated result has the units you want it to have.