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:
\(\implies 2x+6=-2x^2+18\)
\(\implies 2x^2+2x-12=0\)
\(\implies 2(x^2+x-6)=0\)
\(\implies x^2+x-6=0\)
\(\implies x^2+3x-2x-6=0\)
\(\implies x(x+3)-2(x+3)=0\)
\(\implies (x-2)(x+3)=0\)
\(\implies x=2, -3\)
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:
\(\begin{aligned} \textsf{Point A}: \quad 2x+6 & =y\\2(2)+6 & =10\\ \implies & (2, 10)\end{aligned}\)
\(\begin{aligned} \textsf{Point B}: \quad -2x^2+18 & =y\\-2(-3)^2+18 & =0\\ \implies & (-3,0)\end{aligned}\)
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:
\(\textsf{Equation 1}: \quad y=2x+6\)
\(\textsf{Equation 2}: \quad y-28=-2x^2+18\)
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:
\(\implies 2x+6-28=-2x^2+18\)
\(\implies 2x^2+2x-40=0\)
\(\implies 2(x^2+x-20)=0\)
\(\implies x^2+x-20=0\)
\(\implies x^2+5x-4x-20=0\)
\(\implies x(x+5)-4(x+5)=0\)
\(\implies (x-4)(x+5)=0\)
\(\implies x=4,-5\)
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:
\(\begin{aligned} \textsf{Point C}: \quad 2x+6 & =y\\2(-5)+6 & =-4\\ \implies & (-5,-4)\end{aligned}\)
\(\begin{aligned} \textsf{Point D}: \quad -2x^2+18 & = y \\ -2(-5)^2+18 & =-32\\ \implies & (-5, -32)\end{aligned}\)
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.
\(2x + 6 = -2x^2 + 18 + 28\)
\(-2x^2 + 18 + 28-2x - 6 = 0\)
\(-2x^2-2x+40=0\)
\(-2x^2-10x+8x+40=0\)
\(-2(x+5)+8(x+5)=0\)
\((-2x+8)(x+5)=0\)
\(x = -5, 4\)
\(\leftrightarrow \sf C(-5, y_2), \ D(-5, y_2)\)
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
\(\sf \rightarrow Point \ C = (-5, -4)\\ \\\rightarrow Point \ D = (-5, -32)\)
Related Questions
Problem is in the picture
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So, now to find the cost of agricultural exports, we can use the equation provided.
E(x) = 1.1x - 1.47
E(5) = 1.1(5) - 1.47
E(5) = 5.5 - 1.47
E(5) = 4.03
What are the domain and range of the function
Answers
Therefore, the domain is (-∞, ∞) and the range is (-∞, ∞) for the given function.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is associated with exactly one output. In other words, a function is a rule that assigns a unique output value to each input value.
Here,
To find the domain and range of the function f(x) = -1/4(x³ + 6x² + 5x - 4), we need to consider the restrictions on x and the possible values of f(x).
Domain:
Since the function involves a cubic expression in the numerator, there are no restrictions on x, and the domain of the function is all real numbers, or (-∞, ∞).
Range:
To find the range of the function, we need to consider the behavior of the cubic expression as x goes to positive infinity or negative infinity. As x becomes very large or very small, the dominant term in the expression becomes x³, and the other terms become negligible. The coefficient of x³ is negative, which means that the cubic expression approaches negative infinity as x goes to negative infinity and approaches positive infinity as x goes to positive infinity.
Therefore, as x approaches negative infinity, f(x) approaches positive infinity, and as x approaches positive infinity, f(x) approaches negative infinity. Hence, the range of the function is all real numbers, or (-∞, ∞).
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PLEASE HELP! 30 POINT!!!
What is the value of y when x = 3 in this equation
Y = 2x + 2
Answer:
5
7
8
12
Answers
Answer:
Step-by-step explanation:
8
What's is the quotient of 5/7 ÷ 2/7
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Answer:
5/2 or 2.5
Step-by-step explanation:
PLEASE HELP ME OR I WILL DIE...WHAT IS THE VALUE OF Y?!!!!!! I WILL BRAINLY, THANK FOR HELP AND FRENNNDDDDD
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Answer:
Y = -128
Step-by-step explanation:
X is 36
F(x) = ׳+3
Help meee
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Answer:
4
Step-by-step explanation:
Im smart and goatified
Answer:4x^2–3>0
Step-by-step explanation:
Xavier is buying fencing to surround his garden if his garden has a perimeter of 30 yards and fencing cost six dollars a yard how much money will he need for the fencing
Answers
Answer:
$180
Step-by-step explanation:
If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180
The time it takes to drive to Myrtle Beach varies inversely with the speed you drive. If it takes you 4 hours to reach Myrtle Beach when driving at a speed of 60 mph, how much time would it take if you drove at a speed of 80 mph?
Answers
If you drove at 80mph it would take you approximately 3 hours
This is because 60 is 75% of 80 and 3 hours is 75% of 4 hours.
25% of 4 hours is 1 hour
4 hours - 1 hour = 3 hours
 Please tell me what question 4
Answers
Step-by-step explanation:
In my opinion I think the answer for this question is B you don't have to choose it because it might be wrong
which expression is equivalent to g^2/3h
Answers
The given expression \(g^2/3h\) is equivalent to the option (c) \(8g^2/24h\)as we have multiplied 8 in both numerator and denominator.
The given expression is \(g^2/3h\).
Now, to further simplify the expression, we can multiply both numerator and denominator by 8. This gives us:
\((g^2/3h) * (8/8)\)
Simplifying further, we get:
\((8g^2)/(24h)\)
Therefore, the expression equivalent to \(g^2/3h\) is \((8g^2)/(24h)\).
Thus, the given expression \(g^2/3h\) is equivalent to the option (c) \(8g^2/24h\) as we have multiplied 8 in both numerator and denominator.
The numerator is the top part of a fraction, which represents the number of equal parts being considered. It is the value that is above the fraction bar and represents the quantity being divided into equal parts.
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The complete question is :
Which expression is equivalent to \(g^2/3h\)?
Click on the correct answer.
(A) \(g^2+5/3h+5\)
(B) \(6g^2/15h\)
(C) \(8g^2/24h\)
The following selected information was extracted from the records of B Solomon.
1. B Solomon, the owner of Solomon Traders, bought a new Machine for R250 000 on 1 July 2013.
2. On 1 October 2014, he purchased a second Machine for R350 000 cash.
3. On 30 June 2015, the Machine bought during 2013 was sold for R120 000 cash.
4. It is the business’ policy to depreciate Machines at 20% per annum on cost.
REQUIRED:
Prepare the following ledger accounts reflecting all applicable entries, in the books of Solomon Traders, properly balanced/closed off, for the years ended 31 March 2016:
1.1. Accumulated depreciation.
1.2. A Machines realisation.
NB: Show all calculations as marks will be awarded for calculations.
Answers
1.1. Accumulated depreciation:
The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.
1.2. Machine realization:
The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.
1.1. Accumulated Depreciation:
To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.
Machine bought on 1 July 2013:
Cost: R250,000
Depreciation rate: 20% per annum on cost
Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000
Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000
Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000
Accumulated depreciation for the machine bought on 1 July 2013:
As of 31 March 2014: R50,000
As of 31 March 2015: R100,000
As of 31 March 2016: R150,000
1.2. Machine Realisation:
To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.
Machine's original cost: R250,000
Accumulated depreciation as of 30 June 2015: R100,000
Net book value as of 30 June 2015:
R250,000 - R100,000 = R150,000.
On 30 June 2015, the machine was sold for R120,000.
Realisation amount: R120,000
To record the sale:
Debit Cash: R120,000
Debit Accumulated Depreciation: R100,000
Credit Machine: R250,000
Credit Machine Realisation: R120,000
Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).
These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.
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21/64 Marks
Work out the perimeter of a semicircle with radius 3 cm.
Give your answer in terms of it.
I
3 cm
Answers
What is the answer to 156 x 13
Answers
Answer:
2028
Step-by-step explanation:
156 x 13 = 2028
When treated with an antibiotic, 92% of all the dolphins are cured of an ear infection. If 7 dolphins are treated, find the probability that exactly 4 are cured.
The probability is
(Round your answer to 4 decimal places.)
Answers
The probability that exactly 4 are cured from 7 dolphins is 0.0128
What is Probability ?Probability is the likeliness of an event to occur and it has a range of 0 to 1, where 0 means unlikely and 1 indicates certainty of the event to happen.
It is given that the 92% of all the dolphins are cured of an ear infection ,When treated with an antibiotic
If there are total dolphins given as 7
On the basis of given data
The dolphin that cannot be cured is given by
1 - p = 1 - (92/100) = 0.08 = 8/100
q = (8/100)
n= 7
r = 4
Therefore by Binomial Distribution
\(P = ^nC_r p^r q^{n-r}\)
Putting the values
\(P = ^7C_4 (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}\)
\(P = \dfrac{7!}{4! \;3!} (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}\)
P = 0.0128
Therefore the probability is 0.0128.
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At a carnival game, there is a 38% probability of winning a prize. What is the probability of not winning a prize?
A) 62%
B) 76%
C) 38%
D) 50%
Answers
Answer:
A
Step-by-step explanation:
Answer:
Step-by-step explanation:
its 62
62 plus 38= 100
Help please no one helps me
Answers
Answer:
The answer would be B because Ms. Shah's class planted four more trees so you would subtract 36 by 4 to get your answer
Select all of the following tables which represent y as a function of and are one-to-
one.
Answers
Answer:
Option 3
Step-by-step explanation:
Each value of x maps onto one value of y and vice versa.
Find the rule and complete the
expression.
[?]
m
m -
8
1
24
0w
48
72
9
Please be fast will mark brainliest
![Find the rule and complete theexpression.[?]mm -81240w48729 Please be fast will mark brainliest](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/l5uk5whOmgf51pupiroT5FeRhVp7rDlF.png)
Answers
Answer:it’s divided by 8
Step-by-step explanation:
Hope it help
Solve the following quadratic inequality x^2+x-6>0
Answers
Answer:
x < -3 or x > 2
Step-by-step explanation:
x² + x - 6 > 0
Convert the inequality to an equation.
x² + x - 6 = 0
Factor using the AC method and get:
(x - 2) (x + 3) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x - 2 = 0
x = 2
x + 3 = 0
x = -3
So, the solution is x < -3 or x > 2
What is the value of x? Enter your answer in the box. X = cm 5 cm 48 cm 40 cm
Answers
The value of x in the similar triangle is 6 units.
How to find side of similar triangle?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Therefore, let's use the similarity ratio to find the value of x in the similar triangle as follows:
Hence,
5 / 40 = x / 48
48 × 5 = 40x
240 = 40x
divide both sides by 40
x = 240 / 40
x = 6
Therefore,
x = 6
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If f(x) = 8- 10x and g(x) = 5x + 4, what is the value of (fg) (-2)?
O -196
O -168
O 22
O 78
Answers
= 8-50x-40
= -50x-32
So F(g(-2)) = -50(-2)-32
= 100-32
= 68
I think the choices are wrong.
Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without
replacement from a standard deck. If both cards are hearts, your friend will pay you $35. Otherwise, you have to pay your friend $5.
Step 1 of 2: What is the expected value of your bet? Round your answer to two decimal places. Losses must be expressed as negative values.
Answers
Answer:
\(-2.65\)
Step-by-step explanation:
\(x\\\\ P(x)\) \(35\\ \\ \frac{156}{2652}\) \(-5\\\\\frac{2496}{2652}\)
\(E(x)=\frac{156}{2652}\times35-\frac{2496}{2652}\times5\\ =-2.65\)
I hope this helps you
:)
4 + √2 divided by 3 - 5√2
Answers
Answer:
-2.59966329107
Step-by-step explanation:
Compare the expressions 7+3^2-2⋅5 and (3/4+1/8)÷1/8 using , =, or . Show your work. Answer:
Answers
\(A=7+3^2 -2 \cdot 5 = 7 + 9 - 10 = 9-3=6\\\\\\B = \left(\dfrac 34 + \dfrac 18\right) \div \dfrac 18 = \dfrac 78 \times 8 =7\\\\\\B>A\)
The expression relation is 7+3²-2⋅5 > (3/4+1/8)÷1/8.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
First, 7+3²-2⋅5
Solving the above expression
= 7 + 9 -2.5
= 16 - 2.5
= 13.5
Second,
(3/4+1/8)÷1/8
= (6/8 + 1/8) ÷ 1/8
= 7/8 ÷ 1/8
= 7/8 x 8/1
= 7
Hence, 7+3²-2⋅5 > (3/4+1/8)÷1/8.
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A 40-inch piece of rope is cut into 4 equal pieces. How long is each piece in feet?
Answers
Answer:
10!
Step-by-step explanation:
Because 40*10= 4
and we all know 4/10=40 so there you go! Go succeed!
Answer: 5/6
Step-by-step explanation:
If you chose \(\frac{5}{6}\) foot, you are correct. If you chose 10 feet, you forgot to convert inches to feet. If you chose 1 foot, you thought that there were 10 inches in a foot. If you chose \(\frac{1}{10}\)foot, you wrote 1 over the number of inches because you were unsure how to write fractions in terms of feet.
Help for Pre Calc please
Answers
The correct statement regarding the inverse function of f(x) = 4x^4 is given as follows:
\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\); f^(-1)(x) is not a function.
How to obtain the inverse function?The function in this problem is defined as follows:
f(x) = 4x^4.
To obtain the inverse of a function y = f(x), first the variables y and x are exchanged, as follows:
x = 4y^4.
Isolating the variable y, we have that:
y^4 = (x/4).
The inverse operation of the fourth power is the fourth root, hence:
\(y = \pm \sqrt[4]{\frac{x}{4}}\)
\(f^{-1}(x) = \pm \sqrt[4]{\frac{x}{4}}\)
\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\)
The plus/minus symbol means that for each input of x, the inverse function gives two outputs, meaning that there are multiple outputs mapped to each input, and thus the inverse is not a function.
This means that the second statement is correct.
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Three pizza are shared equally among 12 people.what fraction of a pizza will each person get?
A
4/1
B
3/1
Answers
Answer:
d) 1/12
Step-by-step explanation:
What percent is
16 of 500?
Answers
Answer:
3.2
Step-by-step explanation:
please mark me brainliest
8. Find the solution of the following equation: 7-√√4 - x = 4a. -13b. 13c. -5d. 5e. 6
Answers
c. -5
Explanation
given
\(7-\sqrt{4-x}=4\)Step 1
a) subtract 7 in both sides
\(\begin{gathered} 7-\sqrt{4-x}=4 \\ 7-\sqrt{4-x}\text{ -7}=4-7 \\ -\sqrt{4-x}=-3 \end{gathered}\)b) divide both sides by -1
\(\begin{gathered} -\sqrt{4-x}=-3 \\ \frac{-\sqrt{4-x}}{-1}=\frac{-3}{-1} \\ \sqrt{4-x}=3 \end{gathered}\)c) now, toeliminate the root, power two sides to 2
\(\begin{gathered} \sqrt{4-x}=3 \\ (\sqrt{4-x})^2=3^2 \\ 4-x=9 \end{gathered}\)d) subtract 4 in both sides
\(\begin{gathered} 4-x=9 \\ 4-x-4=9-4 \\ -x=5 \\ x=-5 \end{gathered}\)therefore, the answer is
c. -5
I hope this helps you
write the greatest and smallest four digit number by using 7,8,0,9 digit
Answers
9870 is the largest