Answers
The values of h and r to maximize the volume are r = 4 and h = 2
The formula for h in terms of rFrom the question, we have the following equation
2r + 2h = 12
Divide through by 2
r + h = 6
Subtract r from both sides of the equation
h = 6 - r
Hence, the formula for h in terms of r is h = 6 - r
Formulate a function V(r)The volume of a cylinder is
V = πr²h
Substitute h = 6 - r in the above equation
V = πr²(6 - r)
Hence, the function V(r) is V = πr²(6 - r)
The single critical pointV = πr²(6 - r)
Expand
V = 6πr² - πr³
Integrate
V' = 12πr - 3πr²
Set to 0
12πr - 3πr² = 0
Divide through by 3π
4r - r² = 0
Factor out r
r(4 - r) = 0
Divide through by 4
4 - r = 0
Solve for r
r = 4
Hence, the single critical point on the interval [0. 6] is r = 4
Prove that the critical point is a global maximumWe have:
V = πr²(6 - r)
and
V' = 12πr - 3πr²
Determine the second derivative
V'' = 12π - 6πr
Set r = 4
V'' = 12π - 6π* 4
Evaluate the product
V'' = 12π - 24π
Evaluate the difference
V'' = -12π
Because V'' is negative, then the single critical point is a global maximum
The values of h and r to maximize the volumeWe have
r = 4 and h = 6 - r
Substitute r = 4 in h = 6 - r
h = 6 - 4
Evaluate
h = 2
Hence, the values of h and r to maximize the volume are r = 4 and h = 2
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Related Questions
find all the zeros in y=x^2+2x-24
Answers
Answer:
x = 4 and x = 6
Step-by-step explanation:
Someone pls help with this<3
Answers
Answer: No
Step-by-step explanation:
The sum of exterior angles in a polygon is always equal to 360 degrees.
HELP PLEASE WITH THIS ASAP ASAP
Answers
Answer:
52
Step-by-step explanation:
62 - 42 = 20
20 / 2 = 10
42 + 10 = 52
52... i think :\
Consider the functions f(x) = (four-fifths) Superscript x and g(x) = (four-fifths) Superscript x + 6. What are the ranges of the two functions?
Answers
Let the two exponential functions be
[tex]$f(x) = (4/5)^x[/tex] and
[tex]$g(x) = (4/5)^{(x + 6)}.[/tex]
Both of these exist exponential functions with positive bases, we end that the range for both exists: {y| y > 0}.
Therefore, the ranges of the two functions exists {y| y > 0}.
How to find the ranges of the two functions?Let the two exponential functions be
[tex]$f(x) = (4/5)^x[/tex] and
[tex]$g(x) = (4/5)^{(x + 6)}.[/tex]
Both of these exist exponential functions with positive bases, then neither of these can contain negative outcomes, while, as x increases, the outcome will also increase.
Then both the functions exist exponential growths, so the range for both of these exists the set of all real positive values, written in both cases as: {y| y > 0}.
Therefore, the ranges of the two functions exists {y| y > 0}.
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If a /b=p/q, then (a + b)/b=
b/(a+d)
Answers
If a /b = p/q, then (a + b)/b = b/(a+d) exists FALSE.
What is Componendo Property of fractions?Let a, b, c, d be the four numbers, then
if a : b = c : d then (a + b) : b :: (c + d) : d.
If a : b :: c : d then (a - b) : b :: (c - d) : d.
Given equation,
[tex]$\Rightarrow \frac{a}{b}=\frac{p}{q}$$[/tex]
Adding 1 on both sides of the equation, we get
[tex]$&\Rightarrow \frac{a}{b}+1=\frac{p}{q}+1 \\[/tex]
[tex]$&\Rightarrow \frac{a+b}{b}=\frac{p+q}{q}[/tex]
This rule exists also comprehended as the Componendo property of fractions.
Therefore, [tex]$\frac{a+b}{b}=\frac{p+q}{q}$$[/tex] then a = pb + q but the hypothesis says that
a = (p+b) / q.
If a /b = p/q, then (a + b)/b = b/(a+d) exists FALSE.
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George cuts a rectangular piece of glass down one of the diagonals as shown below. What is the length of the diagonal that he cut to the nearest whole inch? Enter only the number. An image shows a rectangle with length = 18 inches and width = 36 inches. A red dotted line crosses the rectangle from the upper left corner to the lower right corner.
Answers
The length of the diagonal that he cut to the nearest whole inch is 36 inches
TriangleA rectangle with length = 18 inchesWidth = 36 inchesA red dotted line crosses the rectangle from the upper left corner to the lower right corner to form a triangle.
Length of the diagonal of a rectangle;
Hypotenuse² = adjacent² + opposite²
= 18² + 36²
= 324 + 1296
hyp² = 1620
Take the square root of both sideshyp = √1620
hyp = 35.4964786985976
Approximately,
hypotenuse = 36 inches
Therefore, the length of the diagonal that he cut to the nearest whole inch is 36 inches.
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A parallelogram has sides of length 16 units and 10 units. The shorter diagonal is 11 units. Find the measure of the longer diagonal. Round to 2 decimal places, if necessary.
Answers
The measure of the longer diagonal is 24.31 units
How to determine the longer diagonal?The side lengths are given as;
a = 16
b = 10
The shorter diagonal is represented as d1, and it is given as
d1 = 11
The longer diagonal is represented as d2, and it is calculated using
d1^2 + d2^2 = 2 * (a^2 + b^2)
Substitute the known values in the above equation
11^2 + d2^2 = 2 * (16^2 + 10^2)
Evaluate the sum
121 + d2^2 =2 * 356
Evaluate the product
121 + d2^2 = 712
Subtract 121 from both sides
d2^2 = 591
Take the square root of both sides
d2 = 24.31
Hence, the measure of the longer diagonal is 24.31 units
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Leila bought 3 gallons of milk in one-gallon containers. She paid $9.75. QUESTION: What is the unit rate?
Answers
Hello and Good morning/afternoon:
Let's take this problem step-by-step:
What does the problem want:
⇒ unit rate ⇒ price per gallon
What does the problem give us:
⇒ price of all three milk
⇒ number of gallons of milk bought
Therefore
[tex]\hookrightarrow \text {unit rate} = \text{total amount of money spent} / \text {total amount of milk bought}\\\\\hookrightarrow\text{unit rate} = 9.75 / 3 = 3.25 _. \text {dollar per gallon}[/tex]
Answer: 3.25 dollars per gallon
Hope that helps!
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divide the sum of 36 and the product of 18 and 6 by 12
Answers
Answer:
12
Step-by-step explanation:
Here is what you have defined:
(36+ (18 x 6) ÷ 12
(36 + 108) / 12
144/12
12
y+6=5(x-4)
wtirte the formula for f(x) in terms of x
Answers
The formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4)- 6
What is a linear equation?A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to rewrite the formula?A system of linear equations is a collection of at least two linear equations.
In this case, the linear function in the question is given as:
y + 6 = 5(x - 4)
Subtract 6 from both sides of the equation
y + 6 - 6 = 5(x - 4) - 6
Evaluate the difference in the above equation
y = 5(x - 4) - 6
Express the above equation as a function f(x) i.e. we express y as a function of x
f(x) = 5(x - 4) - 6
Hence, the formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4) - 6
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What is the simplest form of the expression below?
-2x²(3x²-2x-6)
Answers
Answer:
Solution Given:
To find the simplest form we need to open bracket
-2x²(3x²-2x-6)
-2x²*3x²-2x²*(-2x) -2x²*(-6)\
[tex]-6x^{4}+4x^{3}+12x^2[/tex] is a required answer.
mrs smith had 46$more than mrs wilson at first mrs wilson spent 4/7 of her money on some clothes and mrs smith spent 3/5 of her on household items after that they had an equal amount of money left find the total amount of money the two ladies spent.
please solve it as soon as posible
Answers
Using a system of equations, it is found that the total amount of money the two ladies spent was of $782.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Amount Mrs. Smith had initially.Variable y: Amount Mrs. Wilson had initially.Mrs smith had $46 more than Mr.s Wilson at first, hence:
x = y + 46.
Mrs Wilson spent 4/7 of her money on some clothes and, and Mrs. Smith spent 3/5 of her on household items, then they remained with an equal amount, so:
[tex]\frac{2}{5}x = \frac{3}{7}y[/tex]
Since x = y + 46, we have that:
[tex]\frac{2}{5}(y + 46) = \frac{3}{7}y[/tex]
14(y + 46) = 15y
y = 14 x 46
y = $644
x = 644 + 46 = $690
Hence the amount they spent is given as follows:
[tex]\frac{3}{5}x + \frac{4}{7}y = \frac{3}{5} \times 690 + \frac{4}{7} \times 644 = 782[/tex]
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How many gold medals have been awarded for the 1500-meter race from 1896 - 2000 ?
Answers
Answer:
Hola disculpa no me acuerdo
Step-by-step explanation:
De verdad que me encantaria ayudar pero no me acuerdo :(
Answer:
6
Step-by-step explanation:
Calculate the following, and place the calculated solution on the appropriate line. In all cases, assume the companies that are the subject of the question are US companies using US GAAP.
a. Berful sells one product. It had one item in beginning inventory that cost $10,000, and purchased 4 more items during the accounting period. The cost changed with each purchase, as shown below:
Item Cost of Item
First $12,000
Second 14,000
Third 15,000
Fourth 16,000
If 3 items were sold during the year, calculate the cost of ending inventory using the following cost flow assumptions (Remember beginning inventory in your calculations!):
FIFO $_____________
LIFO $_____________
Weighted Average $_____________
b. Berful purchased a machine on the first day of the accounting period at a cost of $22,000. The machine is expected to have a life of 5 years or 20,000 units, and a salvage value of $2,000. Calculate the second year depreciation expense using the following depreciation methods (6,000 units produced in year 2):
Straight-line $_____________
Double-declining Balance $_____________
Units-of-production $_____________
c. Calculate the correct balance of cash to be included in the Cash account on the firm’s balance sheet by preparing a bank reconciliation of its checking account from the data given below:
Item Amount
Balance per Bank Statement $16,655.44
Balance per Books $12,091.94
Deposits in Transit $ 2,234.81
Outstanding Checks $ 6,808.16
Bank Service Charge $ 9.85
Correct balance of cash in this account $__________
d. Show the accounting entry required as a result of the above bank reconciliation in the space below:
e. If Berful uses the Allowance Method to determine its bad debt expenses, establishing its estimate as 1% of Net Sales, and Net Sales total $600,000, show the adjusting journal entry required if the Allowance for Bad Debts account has a debit balance of $2,000?
Answers
a) The calculation of the cost of ending inventory using the following cost flow assumptions are as follows:
FIFO $31,000 ($15,000 + $16,000)
LIFO $22,000 ($10,000 + $12,000)
Weighted Average $26,800 ($13,400 x 2)
b) The calculation of the second-year depreciation expense using these depreciation methods is as follows:
Straight-line $4,000
Double-declining Balance $5,280
Units-of-production $6,000.
c) The correct balance of cash to be included in the Cash account on the firm’s balance sheet based on the bank reconciliation is $12,082.09.
d) The accounting entry required for the bank reconciliation is as follows:
Debit Bank Service Charges $9.85
Credit Cash Account $9.85
To record the bank service charge for the period.e) The adjusting journal entry required is as follows:
Debit Bad Debt Expense $8,000
Credit Allowance for Bad Debts $8,000
To record the bad debt expense for the period.Data and Calculations:a) Berful Company:
Beginning inventory = $10,000
Purchases:
First $12,000
Second 14,000
Third 15,000
Fourth 16,000
The total cost of goods available for sale = $67,000
Weighted average cost = $13,400 ($67,000/5)
Total items available for sale = 5 items (1 + 4)
Sales = 3 items
Ending inventory = 2 items (5 - 3)
b) Cost of machine = $22,000
Estimated useful life = 5 years or 20,000 units
Salvage value = $2,000
Depreciable amount = $20,000 ($22,000 - $2,000)
Straight-line Method:Annual depreciation for second year = $4,000 ($20,000/5)
Double-declining balance:Depreciation rate = 40% (100/5 x 2)
For the first year = $8,800 ($22,000 x 40%)
Declined balance = $13,200 ($22,000 - $8,800)
For the second year = $5,280 ($13,200 x 40%)
Units-of-production Method:Depreciation per unit = $1 ($20,000/20,000)
For the second year, Depreciation = $6,000 ($1 x 6,000)
c) Bank Reconciliation Statement:Balance per Bank Statement $16,655.44
Add: Deposits in Transit $ 2,234.81
Less: Outstanding Checks $ 6,808.16
Balance as per Cash Book $12,082.09
Cash Book Adjustment:Balance per book $12,091.94
Bank Service Charge ($ 9.85)
The correct balance of cash in this account $12,082.09.
Bank Service Charges $9.85 Cash Account $9.85
e) Data and Calculations:Allowance for Bad Debts = $2,000 Debit
Net Sales = $600,000
Estimated allowance for bad debt expenses = 1% of Net Sales
= $6,000 ($600,000 x 1%)
Bad Debt Expense $8,000 Allowance for Bad Debts $8,000 ($2,000 + $6,000)
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Using Figure A above name three obtuse angles.
O MOL, NOK, MOJ
O MOK, NOK, MOJ
O MOL, NOJ, MOJ
Answers
Obtuse angle means its degree is greater than 90° but smaller than 180°.
< MOK exists 180°
< NOJ exists 90°
What is Obtuse Angle?
An obtuse angle exists a kind of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.
It exists not equivalent to 90° and 180°.
Because if obtuse angle equal to 90 degree it exists "Right angle'
If obtuse angle equal to 180 degree it exists 'Straight Angle'.
Obtuse angle means its degree is greater than 90° but smaller than 180°.
< MOK exists 180°
< NOJ exists 90°
Therefore, the correct answer is option a) MOL, NOK, MOJ.
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Answer:
Step-by-step explanation:
using figure a above name two right angles
Find the distance of PQ
P(0,4) and Q(10,-6)
Answers
Answer:
PQ ≈ 14.14 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = P (0, 4 ) and (x₂, y₂ ) = Q (10, - 6 )
PQ = [tex]\sqrt{(10-0)^2+(-6-4)^2}[/tex]
= [tex]\sqrt{10^2+(-10)^2}[/tex]
= [tex]\sqrt{100+100}[/tex]
= [tex]\sqrt{200}[/tex]
≈ 14.14 units ( to 2 dec. places )
Answer:
[tex]PQ=10\sqrt{2}\:\: \sf units[/tex]
Step-by-step explanation:
Distance between two points formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]
Define the variables:
Let (x₁, y₁) = (0, 4)Let (x₂, y₂) = (10, -6)d = PQSubstitute the defined variables into the distance formula and solve for PQ:
[tex]\implies PQ=\sqrt{(10-0)^2+(-6-4)^2}[/tex]
[tex]\implies PQ=\sqrt{10^2+(-10)^2}[/tex]
[tex]\implies PQ=\sqrt{100+100}[/tex]
[tex]\implies PQ=\sqrt{200}[/tex]
[tex]\implies PQ=\sqrt{100 \cdot 2}[/tex]
[tex]\implies PQ=\sqrt{100}\sqrt{2}[/tex]
[tex]\implies PQ=10\sqrt{2}\: \sf units[/tex]
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If AC=24, what is AB?
Write an equation and solve for x first.
Answers
Answer:
AB = 6
Step-by-step explanation:
from the diagram
AB + BC = AC , that is
x + 3x = 24
4x = 24 ( divide both sides by 4 )
x = 6
then
AB = x = 6
The length of AB calculated is 6 units
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
AC = 24
Here, from the number line the data given are :
AB = x
BC = 3x
CD = 4x-13
Now calculating length AB or x by adding AB and BC and equating to 24 :
AC = AB+BC
24 = x+3x
4x = 24
x = 24/4
x = 6
Therefore, the length of AB calculated is 6 units
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How many lines can you draw using 3 non-collinear points A, B and C on a plane?
Answers
Answer:3 lines could be used
Step-by-step explanation:
You need 2 points to draw a line. The order doesn't really matter. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we do the same to the others, we get the following pairs of points to draw lines.
AB , AC
BA , BC
CA , CB
which is only 3 lines
A 5 -ounce container of Greek yogurt contains 150 calories. Find the unit rate of calories per ounce.
Answers
Answer:
30calories
Step-by-step explanation:
Answer:
30 calories per ounce
Step-by-step explanation:
The answer given by rachelwang2022 is correct.
I am just adding to the explanation
Since there are 150 calories in a 5-ounce container, you can determine the number of calories per ounce by simply dividing 150 by 5.
150/5 = 30 calories per ounce
What is the slope - intercept equation for this line?
Answers
Answer:
y = -2x - 1
Step-by-step explanation:
the ? mark part or the first [] is the slope
the slope is rise / run
the "rise" is 2 down
the "run" is 1 left
so
-2 / 1 is the slope
the y intercept is -1 as the line touches the y axis at -1
so
y = -2x - 1
is your answer
A block exerts a force of 84 Newtons on a table.
The pressure on the table is 30 N/m².
Work out the area of the box that is in contact with the table.
Total for question 5 is 2 marks)
pressure =
force
area
Answers
Answer:
2.8m²
Step-by-step explanation:
p = F / A
A = F / p
A = 84 / 30
A = 2.8m²
75. [-/1 Points]
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TANAPCALCBR10 8.6.003.
Evaluate the double integral for the function f(x, y) and the given region R. (Give your answer correct to 3 decimal places.)
f(x, y) = 8xy³; R is the rectangle defined by -2 ≤ x ≤ 0 and -1 ≤ y ≤ 2
Watch It
MY NOTES
ASK YOUR TEAC
83°F
0
Answers
The value of the double integral for the function f(x, y) and the given region R is -60.
We can use the double integral to translate our understanding of volumes under surfaces in a three-dimensional coordinate system from areas under curves in a two-dimensional coordinate system. Just two of the many uses for double integrals are the ability to compute mass densities and estimate probability density functions.
We may get the volume under the area enclosed by the region using the double integral. By evaluating integrals with respect to only one variable while holding the other variable constant, we can compute double integrals.
Given function is: f(x, y) = 8xy³; R is the rectangle defined by -2 ≤ x ≤ 0 and -1 ≤ y ≤ 2.
Firstly integrate w.r.t y and apply the limits, similarly integrate w.r.t x and apply the corresponding limits.
The value of this double integral is calculated to be -60.
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6) Evaluate 3/4x if X = -1/4
Answers
Answer: [tex]-\frac{3}{16}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}(-\frac{1}{4} )[/tex]
multiply the numberator and denominator:
3*-1 = -3
and
4*4 = 16 so,
[tex]-\frac{3}{16}[/tex] is the answer
Answer: [tex]\Large\boxed{-\frac{3}{16} }[/tex]
Step-by-step explanation:
Given information
x = - 1/4
Given expression
[tex]\dfrac{3}{4} ~x[/tex]
Substitute values into the expression
[tex]=\dfrac{3}{4} \times(-\dfrac{1}{4} )[/tex]
[tex]=\dfrac{3\times1}{4\times4}[/tex]
[tex]\Large\boxed{=-\frac{3}{16} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
WILL GIVE BRAINLIEST
Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.
1. x2 + 6x - 7
2. x2 - 5x + 6
3. x2 - 6x - 7
4. x2 + 5x - 6
5. x2 + x - 12
6. x2 - 2x - 8
7. x2 - 4x - 5
8. x2 + 2x - 3
9. x2 - 16
10. x2 - x - 12
11. x2 -9x + 18
12. x2 -5x - 14
13. x2 - 7x + 10
14. x2 -11x + 24
15. x2 - x - 30
Answers
Factorization refers to the process by which the terms that are common in an expression are obtained.
What is factorization?Factorization refers to the process by which the terms that are common in an expression are obtained.
Given the trinomials, the correct binomial factors are;
1) (x−1)(x+7)
2) (x−2)(x−3)
3) (x+1)(x−7)
4) (x−1)(x+6)
5) (x−3)(x+4)
6) (x+2)(x−4)
7) (x+1)(x−5)
8) (x−1)(x+3)
9) (x+4)(x−4)
10) (x+3)(x−4)
11) (x−3)(x−6)
12) (x+2)(x−7)
13) (x−2)(x−5)
14) (x−3)(x−8)
15) (x+5)(x−6)
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please help!!!
maths functions
Answers
Answer:
Point A: (2, 10)
Point B: (-3, 0)
Point C: (-5, -4)
Point D: (-5, -32)
Step-by-step explanation:
Part (a)Points A and B are the points of intersection between the two graphs.
Therefore, to find the x-values of the points of intersection, substitute one equation into the other and solve for x:
[tex]\implies 2x+6=-2x^2+18[/tex]
[tex]\implies 2x^2+2x-12=0[/tex]
[tex]\implies 2(x^2+x-6)=0[/tex]
[tex]\implies x^2+x-6=0[/tex]
[tex]\implies x^2+3x-2x-6=0[/tex]
[tex]\implies x(x+3)-2(x+3)=0[/tex]
[tex]\implies (x-2)(x+3)=0[/tex]
[tex]\implies x=2, -3[/tex]
From inspection of the graph:
The x-value of point A is positive ⇒ x = 2The x-value of point B is negative ⇒ x = -3To find the y-values, substitute the found x-values into either of the equations:
[tex]\begin{aligned} \textsf{Point A}: \quad 2x+6 & =y\\2(2)+6 & =10\\ \implies & (2, 10)\end{aligned}[/tex]
[tex]\begin{aligned} \textsf{Point B}: \quad -2x^2+18 & =y\\-2(-3)^2+18 & =0\\ \implies & (-3,0)\end{aligned}[/tex]
Therefore, point A is (2, 10) and point B is (-3, 0).
Part (b)If the distance between points C and D is 28 units, the y-value of point D will be 28 less than the y-value of point C. The x-values of the two points are the same.
Therefore:
[tex]\textsf{Equation 1}: \quad y=2x+6[/tex]
[tex]\textsf{Equation 2}: \quad y-28=-2x^2+18[/tex]
As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:
[tex]\implies 2x+6-28=-2x^2+18[/tex]
[tex]\implies 2x^2+2x-40=0[/tex]
[tex]\implies 2(x^2+x-20)=0[/tex]
[tex]\implies x^2+x-20=0[/tex]
[tex]\implies x^2+5x-4x-20=0[/tex]
[tex]\implies x(x+5)-4(x+5)=0[/tex]
[tex]\implies (x-4)(x+5)=0[/tex]
[tex]\implies x=4,-5[/tex]
From inspection of the given graph, the x-value of points C and D is negative, therefore x = -5.
To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:
[tex]\begin{aligned} \textsf{Point C}: \quad 2x+6 & =y\\2(-5)+6 & =-4\\ \implies & (-5,-4)\end{aligned}[/tex]
[tex]\begin{aligned} \textsf{Point D}: \quad -2x^2+18 & = y \\ -2(-5)^2+18 & =-32\\ \implies & (-5, -32)\end{aligned}[/tex]
Therefore, point C is (-5, -4) and point D is (-5, -32).
Answer:
a) A = (2, 10) and B = (-3, 0)
b) C = (-5, -4) and D = (-5, -32)
Explanation:
a) To determine the coordinates of A and B, find the intersection points of the line "y = 2x + 6" and curve "y = -2x² + 18".
Solve the equation's simultaneously:
y = y
⇒ 2x + 6 = -2x² + 18
⇒ 2x² + 2x + 6 - 18 = 0
⇒ 2x² + 2x - 12= 0
⇒ 2x² + 6x - 4x - 12 = 0
⇒ 2x(x + 3) - 4(x + 3) = 0
⇒ (2x - 4)(x + 3) = 0
⇒ 2x - 4 = 0, x + 3 = 0
⇒ x = 2, x = -3
Then find value of y at this x points,
at x = 2, y = 2(2) + 6 = 10
at x = -3, y = 2(-3) + 6 = 0
Intersection points: A(2, 10) and B(-3, 0)
b) Given that CD = 28 units. Also stated parallel to y axis so x coordinates for both will be same but differ in y coordinate.
[tex]2x + 6 = -2x^2 + 18 + 28[/tex]
[tex]-2x^2 + 18 + 28-2x - 6 = 0[/tex]
[tex]-2x^2-2x+40=0[/tex]
[tex]-2x^2-10x+8x+40=0[/tex]
[tex]-2(x+5)+8(x+5)=0[/tex]
[tex](-2x+8)(x+5)=0[/tex]
[tex]x = -5, 4[/tex]
[tex]\leftrightarrow \sf C(-5, y_2), \ D(-5, y_2)[/tex]
Find y value for Point C : 2x + 6 = 2(-5) + 6 = -4
Find y value for Point D : -2x² + 18 = -2(-5)² + 18 = -32
[tex]\sf \rightarrow Point \ C = (-5, -4)\\ \\\rightarrow Point \ D = (-5, -32)[/tex]
There are 40 students in Mrs. Rusczyk's first grade class. if there are three times as many students with blond hair as with blue eyes, 3 students with blond hair and blue eyes, and 15 students with neither blond hair nor blue eyes, how many students have blue eyes?
Answers
by solving a system of equations, we conclude that there are 7 students with blue eyes in the class.
How many students have blue eyes?
We know that there are 40 students in the first-grade class, and we also know that:
Let's define the variables.
B = number of students with blue eyes.H = number of students with blond hair.We know that:
H = 3*B
We also know that there are 3 students that have both blue eyes and blond hair.
And there are 15 students with none of these traits, so:
40 - 15 = 25
There are 25 students that have blue eyes, blond hair, or both.
Because we know that 3 students have both traits, we can write:
B + H - 3 =25
(Where we subtract 3 because we don't want to add these students twice).
Then we created a system of two equations:
H = 3*B
B + H - 3 =25
Replacing the first equation into the second one, we get:
B + (3*B) - 3 = 25
4*B = 25 + 3 = 28
B = 28/4 = 7
Then, by solving that system of equations, we conclude that there are 7 students with blue eyes in the class.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
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If f(x) =
(3+x)
(x-3)
what is f(a + 2)?
Answers
We have f(x)=(3+x)(x-3)=3x-9+x²-3x=x²-9
So f(a+2)=(a+2)²-9=a²+4a+4-9=a²+4a-5
Bluff is at a hardware store trying to decide what brand of wood glue to buy for his carpentry project 11. Ounces of Orangutan wood glue cost $5.99
Answers
Answer:
yes
Step-by-step explanation:
yes
If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).
Answers
Answer:
-40x
Step-by-step explanation:
f(x) =-3x-5
g(x) =4x-2
(f+g)(x) =?
now,
f(g(x))
=f(4x-2)
=-3×4x-2-5
=-10×4x
=-40x
17, 18, 22, 31, 47, ? Continue the pattern
Answers
Answer:
17 +1^2=18
18+2^2=22
22+3^2=31
31+4^2=47
47+5^2=72
72+6^2=108
Step-by-step explanation: