Answers
Answer: 1308m
Step-by-step explanation:
Top and Bottom: 19 x 16 x 2 = 608
Sides: 16 x 10 x 2 = 320
Front and Back: 19 x 10 x 2 = 380
608 + 320 + 380 = 1308
Related Questions
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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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
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.
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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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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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 + $6,000)
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A 5 -ounce container of Greek yogurt contains 150 calories. Find the unit rate of calories per ounce.
Answers
Answer:
30calories
Step-by-step explanation:
Answer:
30 calories per ounce
Step-by-step explanation:
The answer given by rachelwang2022 is correct.
I am just adding to the explanation
Since there are 150 calories in a 5-ounce container, you can determine the number of calories per ounce by simply dividing 150 by 5.
150/5 = 30 calories per ounce
A block exerts a force of 84 Newtons on a table.
The pressure on the table is 30 N/m².
Work out the area of the box that is in contact with the table.
Total for question 5 is 2 marks)
pressure =
force
area
Answers
Answer:
2.8m²
Step-by-step explanation:
p = F / A
A = F / p
A = 84 / 30
A = 2.8m²
mrs smith had 46$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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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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find all the zeros in y=x^2+2x-24
Answers
Answer:
x = 4 and x = 6
Step-by-step explanation:
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
PLS HELP!!!!!!!!!!! Find x
Answers
Answer:
120
Step-by-step explanation:
The angle below x is 40 degree cause alternate angle. Then you get,
20+x+40=180
60+x=180
x=180-60
x=120
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
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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Por favor ayuda con este ejercicio
Answers
Answer:
-
-
+
+
Step-by-step explanation:
Suppose that Andrea told you that “Blake and I started out with the same number of marbles, but I gave him one of mine. Now Blake has one more marble than me.” Is Andrea’s reasoning incorrect? If so, how can you help Andrea identify her misunderstanding?
Answers
Step-by-step explanation:
i know this but i don't have time now
Andrea has one less than she started with , Blake has one more than he started with. Therefore , Blake has two more than he started with. Therefore, the correct answer is option B.
Andrea told that 'Blake and I started out with the same number of marbles, but I gave him one of mine. Now Blake has one more than me. '
Here Andrea is wrong with her conclusion. Let's understand this by taking some values.
Let's consider that Andrea and Blake both have 4 marbles(Since it is given that 'they have equal number of marbles). And Andrea gave one of her marbles to Blake. So number of marbles of Andrea will become 4-1=3. And number of marbles of Blake = 4+1 =5. If we compare them , Blake has 2 more marbles than Andrea.
Therefore, the correct answer is option B.
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"Your question is incomplete, probably the complete question/missing part is:"
Suppose that Andrea told you that “Blake and I started out with the same number of marbles, but I gave him one of mine. Now Blake has one more marble than me.” Is Andrea’s reasoning incorrect? If so, how can you help Andrea identify her misunderstanding?
A. Blake needs to take one of his marbles away first. Then, Andrea can give him one of hers. Thus, Blake will have one more than Andrea.
B. Andrea has one less than she started with Blake has one more than he started with. Therefore, Blake has two more than Andrea.
C. Andrea meant to say that after giving Blake one of her marbles, show would have one less than Blake.
D. Andrea meant to say that she took one of her marbles away and not give it to Blake. Therefore, Blake would only have one more than her.
What is the perimeter of the figure shown? Round your answer to the nearest tenth.
help asap please
tysm
Answers
If the points of the vertices are (-3,1_,(4,2),(9,-3),(2,-4) then the perimeter of the figure is 28.28 units.
Given points of the vertices of the figure having four sides be (-3,1),(4,2),(9,-3),(2,-4).
We have to find the perimeter of the figure.
Perimeter is the sum of lengths of all the sides of a figure.
First give some name to the points so that it will be easy to understand the sides like A(-3,1),B(4,2),C(9,-3),D(2,-4).
Perimeter of the figure =AB+BC+CD+DA
AB=[tex]\sqrt{(2-1)^{2} +(4+3)^{2} }[/tex]
=[tex]\sqrt{1+49}[/tex]
=[tex]\sqrt{50}[/tex] units
BC=[tex]\sqrt{(9-4)^{2} +(-3-2)^{2} }[/tex]
=[tex]\sqrt{25+25}[/tex]
=[tex]\sqrt{50}[/tex]units
CD=[tex]\sqrt{(2-9)^{2} +(-4+3)^{2} }[/tex]
=[tex]\sqrt{49+1}[/tex]
=[tex]\sqrt{50}[/tex] units
DA=[tex]\sqrt{(2+3)^{2} +(-4-1)^{2} }[/tex]
=[tex]\sqrt{25+25}[/tex]
=[tex]\sqrt{50}[/tex] units
Perimeter=[tex]\sqrt{50} +\sqrt{50} +\sqrt{50} +\sqrt{50}[/tex]
=4[tex]\sqrt{50}[/tex]
=4*5*[tex]\sqrt{2}[/tex]
=20[tex]\sqrt{2}[/tex]
=20*1.411
=28.284
After rounding off we will get 28.28 units.
Hence if the points of the vertices are (-3,1_,(4,2),(9,-3),(2,-4) then the perimeter of the figure is 28.28 units.
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You plan to make a new fenced area in your back yard for your dog. The length of each side of the new dog area is
shown in meters in the diagram below. What is the perimeter of the new dog area?
20 meters
23 meters
29 meters
26 meter
Answers
Step by step
Perimeter is the measurement of all sides added together
3+3+3+4+6+7= 26
i need help pls.............
Answers
Answer:
P = 6750n +7800rn ≤ 19r ≤ 31160n +620r ≤ 8110n = 19r = 8190,650 peopleStep-by-step explanation:
This linear programming problem is described by an objective function and constraints on the variables. A graphical solution works well.
Objective functionThe goal is to maximize the number of people exposed to the company's ad(s). The number of people reached is the sum of the products of the number of ads and the number reached per ad.
For n newspaper ads, we are told that 6750n people are reached.
For r radio ads, we are told that 7800r people are reached.
The total number of people reached is ...
P = 6750n +7800r . . . . . . . the function we wish to maximize
Newspaper adsWe can run at most 19 newpaper ads:
n ≤ 19
Radio adsWe can run at most 31 radio ads:
r ≤ 31
BudgetThe cost of n newspaper ads will be $160n.
The cost of r radio ads will be $620r.
We must stay within a budget for the ads, $8100:
160n +620r ≤ 8110
SolutionThe white area in the first quadrant of the attached graph represents the feasible solution space. (We reversed the inequality symbol in each inequality so the solution space would be white, not triple-shaded.) The corners of the solution space represent possible (n, r) pairs where the objective function might be maximized.
The solid red line on the graph shows the maximum value the objective function might have, and the (n, r) pairs that would give that maximum value. The value of the objective function increases the farther the line is from the origin. Drawing the line on the graph lets us readily identify the (n, r) coordinate pair that will place this line as far as possible from the origin, maximizing P. We find that to be (n, r) = (19, 8).
the number of newspaper ads to run is 19the number of radio ads to run is 8the group exposure is (6750)(19) +(7800)(8) = 190,650HELP PLEASE WITH THIS ASAP ASAP
Answers
Answer:
52
Step-by-step explanation:
62 - 42 = 20
20 / 2 = 10
42 + 10 = 52
52... i think :\
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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Given the following function, find f(-5), f(0), and f(3).
f(x) = x^2+5
Answers
Answer:
f(-5) = 30
f(0) = 5
f(3) = 14
Step-by-step explanation:
=> f(x) = x²+5
for , f(-5) = (-5)² +5
=> 25 +5
=> 30
for , f(0) = (0)² +5
=> 5
for , f(3) = (3)² + 5
=> 9 + 5
=> 14
what is angle JLK?
a. 23 degrees
b. 24 degrees
c. 67 degrees
d. 134 degrees
Answers
Answer:
Answer is c, 67.
Step-by-step explanation:
So angle L and K are going to be the same, and so its going to be:
46+2n=180, since 180* inside a triangle and n= both L and K.
180-46=134
134/2=67
Both K and L will be 67.
Answer is c, 67.
To check, 46+67+67=180
The measure of angle JLK is 67 degree.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
The angle L and K are going to be the same;
46+2n=180,
Since 180 inside a triangle and n= both L and K.
180-46=134
134/2=67
Both K and L will be 67.
The answer is c, 67.
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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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The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, sold by the company:
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x = 1 to x = 4, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
Answers
Based on the given graph relating to the company's profit f(x), the x-intercepts are (0, 0) and (0, 8) and the maximum value is 270.
What does the graph show?The x-intercepts are the points where the graph crosses the x axis. It does so at first at (0,0) and then after going up and coming down, it again intersects at (0, 8).
The maximum value the graph reaches is 270 on the y-axis.
The function is increasing at the interval, (0, 4) and decreasing from (4, 8).
What this shows is that an increase in price between 0 and 4 would lead to an increase in profit but between 4 and 8 results in profits dropping.
In part B, the average rate of change from x=1 to x =4 is:
= (270 - 120) / (4 - 1)
= 50
In part c, the constraints are:
x ≥ 0
f(x) x ≤ 8
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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]
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:
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
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