Answer:
[tex]\displaystyle \large{x=\pm \sqrt{y}}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle \large{y=x^2}[/tex]
Make ‘x’ the subject of the formula by square root both sides:
[tex]\displaystyle \large{\sqrt{y}=\sqrt{x^2}}[/tex]
Cancel the square root and square in RHS and write plus-minus in LHS:
[tex]\displaystyle \large{\pm \sqrt{y}= x}\\\displaystyle \large{x=\pm \sqrt{y}}[/tex]
Therefore, the solution is [tex]\displaystyle \large{x=\pm \sqrt{y}}[/tex]
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Summary
To make a variable as the subject of equation means to isolate that variable. For an example, if you want to make y as the subject, you’ll have to isolate y-term.
You may also be curious why do you have to add plus-minus on another side when cancelling [tex]\displaystyle \large{\sqrt{x^2}}[/tex] because [tex]\displaystyle \large{\sqrt{x^2}=|x|}[/tex] and [tex]\displaystyle \large{|x|}[/tex] for their positive and their counterparts (opposite/negative) will always give same y-value.
From an example:
[tex]\displaystyle \large{\sqrt{x^2}=4}[/tex] can be rewritten as [tex]\displaystyle \large{|x|=4}[/tex], cancel absolute sign/square root then write plus-minus which the solution is [tex]\displaystyle \large{x=\pm 4}[/tex] and if you substitute x = 4 or -4, the equation will be true for both values.
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Others
Let me know if you have any doubts about my answer, explanation or this question through comment!
what is the parallelogram base b?
Answer:
10
Step-by-step explanation:
The area if a parallelogram is given by the equation, Area = base * height
In this case, area = 200, and the actual height = 20
So, let's say the base is x
Plug these values in to the Area equation
200 = 20 * x
200 = 20x
Divide both sides by 20 to get x alone
200 / 20 = 20x / 20
10 = x
The base is 10
PLEASE HELP
Use the function f(x) to answer the questions.
f(x) = −16x2 + 22x + 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
First graph
y=-16x^2+22x+3(Graph attached)#A
Use quadratic formula
[tex]\\ \rm\rightarrowtail x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm\sqrt{484+192}}{-32}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm\sqrt{676}}{-32}]/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm 26}{-32}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-1}{8}\:or\:\dfrac{3}{2}[/tex]
[tex]\\ \rm\rightarrowtail x=-0.125\:or\:1.5[/tex]
#B
Vertex will be maximum
Coordinates are
(0.688,10.563)#C
We have to find x intercepts (Part A)Then vertex(Part B)Then we can graph it[tex]\sf f(x) = -16x^2 + 22x + 3[/tex]
Part A
To find x-intercepts, the f(x) will be 0
[tex]\sf \hookrightarrow -16x^2 + 22x + 3=0[/tex]
[tex]\sf \hookrightarrow -16x^2 + 24x -2x+ 3=0[/tex]
[tex]\sf \hookrightarrow -8x(2x-3)-1(2x- 3)=0[/tex]
[tex]\sf \hookrightarrow (-8x-1)(2x+ 3)=0[/tex]
[tex]\sf \hookrightarrow -8x-1=0 , \ 2x+ 3=0[/tex]
[tex]\sf \hookrightarrow x=-0.125 , \ x=1.5[/tex]
find y-intercept:
to find y-intercept, x will be 0
[tex]\sf f(x) = -16(0)^2 + 22(0) + 3[/tex]
[tex]\sf f(x) = 3[/tex]
Part B
To find vertex use the formula: x = -b/2(a)
[tex]\sf \rightarrow x = \dfrac{-22}{2(-16)}[/tex]
[tex]\sf \rightarrow x = 0.6875[/tex]
find y coordinates:
[tex]\sf f(x) = -16(0.6875)^2 + 22(0.6875) + 3[/tex]
[tex]\sf f(x) =10.5625[/tex]
coordinates of vertex: (0.6875, 10.5625)
[tex]\bold{\mathrm{If}\:a < 0,\:\mathrm{then\:the\:vertex\:is\:a\:maximum\:value}}[/tex][tex]\bold{\mathrm{If}\:a > 0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}}[/tex]As its positive and greater than 0, the vertex will be Maximum.
part C
To draw the graph, simplify point the vertex on the graph. Then point both the x-intercepts. Also the y-intercept and draw the curve with free hand.
Graph attached:
What is the value of x in the equation –2.4x = 8.4?
Answer:
x = -3.5
Step-by-step explanation:
−2.4x=8.4
Divide both sides by −2.4.
x= 8.4/-2.4
Expand 8.4/-2.4 by multiplying both numerator and the denominator by 10.
x= 84/-24
Reduce the fraction 84/-24 to lowest terms by extracting and canceling out 12.
x= −7/2
-7/2 = -3.5
Answer:
-3.5
Step-by-step explanation:
Hello there?
given such a question,
You have to carry out division on of both RHS and LHS.
Take -2.4 and divide through -2.4{LHS} and 8.4{RHS}.
You are then remained with 1(x) in LHS and -3.5 in RHS
-2.4x /(-2.4)= {8.4}/(-2.4)
= -3.5
I hope this helps. Have a nice studies
This figure is the pre-image of a prism that has undergone a dilation with a scale factor of 3/4.
What is the surface area of the image after the dilation?
185 5/8 m²
219 3/8 m²
247 1/2 m²
292 1/2 m²
The surface area of the image after the dilation is 219 3/8 m²
What is an area?Area is the amount of space occupied by a two dimensional shape or object.
The surface area of the prism = 2(0.5 * 5 * 12) + (5 * 11) + (11 * 12) + (13 * 11) = 390 m²
The surface area of the image after the dilation = scale factor² * 390 m² = (3/4)² * 390 m² = 219 3/8 m²
The surface area of the image after the dilation is 219 3/8 m²
Find out more on area at: https://brainly.com/question/25292087
20. You owe $1,568.00 on a credit card with a limit of $2,200.00 at an interest rate of 11.3% APR. You pay $300.00/month until it is paid off. How many months does it take you to pay it off?
- 6 months
- 9 months
- 4 months
- 7 months
Answer:
(a) 6 months
Step-by-step explanation:
The formula for figuring the monthly payment on an amortized loan can be used for finding the length of time it takes to pay off the loan.
That formula is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where A is the monthly payment, P is the principal value of the loan, r is the annual interest rate, and t is the number of years.
__
Using the given information, we can solve for t:
300 = 1568(0.113/12)/(1 -(1 +0.113/12)^(-12t))
1 -(1 +0.113/12)^(-12t) = 1568(0.113)/(12(300))
(1 +0.113/12)^(-12t) = 1 -(1568·0.113)/(12·300) ≈ 0.950782
Taking logs, we get ...
-12t·log(1 +0.113/12) = log(0.950782)
t = log(0.950782)/(-12·log(1 +0.113/12)) ≈ 0.448739 . . . . years
This fraction of a year is ...
(12 months/year)(0.448739 years) = 5.38 months
It will take you 6 months to pay off the loan.
write the following numbers in words (1) 396 624 (2) 5 200 090 (3) 4 606 220
Answer:
1. three hundred ninety six thousand twenty four
2. five million two hundred thousand ninety
3. four million six hundred six thousand two hundred twenty
Solve the equation:
1. |x-7|=8
2. |x-9|=-14
Answer:
1. [tex]x=-1; x=15[/tex]
2. Impossible
Step-by-step explanation:
About #1.
There are two ways of reasoning.
Algebrically, you split the absolute value in two based on the sign of the quantity [tex]x-7[/tex]
[tex]x-7 = 8; x\ge7\\x=15\\x-7=-8; x < 7\\x=-1[/tex]
Geometrically, and it's a personal preference of mine, you're asking to find the numbers that are 8 units away from 7. One is to the right (15), and the other is to the left (-1).
#2 is impossible. The modulus of a number is by definition non negative, so it can never be equal to a negative number.
If f(x) = 2x² - 5, f(5) =
Answer:
45
Step-by-step explanation:
Put in '5' where 'x' is
2 (5)^2 - 5 = 45
What is the equation: [tex]2x^2-5[/tex]
What do we want to find: f(5)
To find f(5), we must plug the value '5'
⇒ into the 'x' position
⇒ f(x)
So: [tex]f(5) = 2(5^2)-5 = 2 * 25 - 5 = 50 -5 = 45[/tex]
Thus f(5) = 45
Hope that helps!
The sum of two numbers is 35. The smaller number is 11 less than the larger number. What are the numbers?
Answer:
12 & 23
Step-by-step explanation:
Let's make both of the statements into equations by making the numbers x & y.
"The sum of two numbers is 35" which means the two numbers added together is 35. So, x + y = 35.
"The smaller number is 11 less than the larger number." Let's make x the smaller number. So, x = y - 11.
So our equations are x + y = 35 and x = y -11. Using substitution, we can plug in (y-11) for x in the first equation.
y + y - 11 = 35. Combine the (y + y) to get 2y - 11 = 35. Add 11 to both sides of the equation, to get 2y = 46. Divide both sides by 2 to get y = 23.
Now, we can substitute 23 for y in either one of the equations, but I'm going to use the second one. x = y - 11 or x = 23 - 11 which equals 12.
Your 2 numbers are 12 and 23. Hope this helps! :)
h=-16t^2+320, how long will it take to hit the ground
Answer:
It will take 5 seconds
PLEASE HELP ME
A triangle has one angle that measures 29 degrees, one angle that measures 131 degrees, and one angle that measures 20 degrees.
What kind of triangle is it?
Answer:
obtuse angled triangle
Step-by-step explanation:
one angle is more than 90
Pls show work thank you!!!
[tex]|-16-x|=0\\\\\implies -16-x = 0\\\\\implies x = -16[/tex]
I need help with questions two and three I do not understand them at all
Amanda and her best fiend found some money buried in a field. thay split the money evenly, each getting $24.28. how much money did thay find?
Answer:
48.56
Step-by-step explanation:
We have to multiply 24.28x2 because there are 2 people so if we multiply it we will get the answer 48.56.
Find the quotient of 36 and -4.
The quotient of 36 and -4 is -9.
36/-4 = -9
Find the measures of the interior angles?
Answer:
Angle C = 35
Step-by-step explanation:
Angles A and B are already given to you, so I will not be explaining how to find them. If you have any questions, let me know.
There are 2 ways to solve this problem; you can either use the sum of the interior angles or isosceles triangles.
Sum of Interior Angles
The interior angles of all triangles equal 180 degrees. We can use this information to create an equation.
First, set up the equation.[tex]110+35+x=180[/tex]Then, combine like terms.[tex]145+x=180[/tex]Next, subtract 145 from both sides[tex]x=35[/tex]This means that angle C equals 35 degrees.
Isosceles Triangles
The image shows marks on 2 sides. These marks show that the sides are congruent. If a triangle has 2 congruent sides then it is isosceles. Isosceles always have 2 congruent angles as well. In addition, these congruent angles are always the angles opposite of the congruent sides.
In this case, the angles opposite of the congruent sides are angle A and angle C. Thus, angles A and C are congruent. If angle A is equal to 35, then angle C must also be 35.
Irwin rode his bicycle from one end of a trail to another and back at a speed of 20 miles per hour. If the trail is 4 miles long, for how many hours was Irwin riding?
Answer:
it’s C. 2.5
Step-by-step explanation:
At a student café, there are equal numbers of two types of customers with the following values. The café owner cannot distinguish between the two types of students because many students without early classes arrive early anyway (i.e., she cannot price-discriminate).
Students with Early Classes
Students without Early Classes
Coffee 73 63
Banana 53 103
The marginal cost of coffee is 5 and the marginal cost of a banana is 20.
The café owner is considering three pricing strategies:
1. Mixed bundling: Price bundle of coffee and a banana for 166, or just a coffee for 73.
2. Price separately: Offer coffee at 63, price a banana at 103.
3. Bundle only: Coffee and a banana for 126. Do not offer goods separately.
Assume that if the price of an item or bundle is no more than exactly equal to a student's willingness to pay, then the student will purchase the item or bundle.
For simplicity, assume there is just one student with an early class, and one student without an early class.
Price Strategy
Revenue from Pricing Strategy
Cost from Pricing Strategy
Profit from Pricing Strategy
1. Mixed Bundling
$
$
$
2. Price Separately
$
$
$
3. Bundle Only
$
$
$
Pricing strategy yields the highest profit for the café owner.
Based on the prices, the willingness to pay of the students and the costs, the profits will be:
Mixed bundling = 209.Price separately = 199.Bundle Only = 202.The pricing strategy that yields the highest profit is the Mixed bundling strategy.
What is the profit from Mixed bundling?First find the willingness to pay for both the students with early classes and those without.
Student with early classes: Students without early classes:
= 73 + 53 = 63 + 103
= 126 = 166
At a mixed bundling price of 166, only students without early classes will be able to afford the bundle as their willingness to pay is 166.
Student with early classes will only take the coffee at 73 because their willingness to pay of 126 is lower than the 166 bundle price.
Profit is:
= (Bundle price + Coffee price) - (Marginal cost of two coffees + Marginal cost of banana)
= (166 + 73) - (2 x 5 + 20)
= 209
What is the profit from pricing separately?At separate only pricing students without early classes will be able to afford the both things at 166.
Student with early classes will only take the coffee at 63 because their willingness to pay of 126 won't allow them to take both items.
Profit:
= (63 + 63 + 103) - (2 x 5+ 20)
= 199
What is the profit from price separately?At a bundle only price of 126, both the students with early classes and those without early classes will be able to afford the bundle as their willingness to pay, match the price.
Profit will be:
= (126 + 126) - (2 x 5 ) for coffee - (2 x 20) for bananas
= 202
In conclusion, the woman should go with the Mixed bundling as it gives the highest profit of 209.
Find out more on pricing strategies at https://brainly.com/question/7303679.
Find the average of this set of numbers.1, 9, 11, 13, 26
A) 12
B) 13
C) 14
D) none of the above
[tex]\green{ \underline { \boxed{ \sf{Average = \frac{Sum \:of \: observation}{Number \:of \: observation}}}}}[/tex]
[tex]\longrightarrow[/tex]Here, no of observation are 5
Now,
[tex]\begin{gathered}\\\implies\quad \sf Average = \frac{1+9+11+13+26}{5} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf Average = \frac{60}{5} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf Average = 12 \\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]The Average of given set of numbers is 12 .
[tex]\therefore\: [/tex] Option A) is correct ✔️
Michael has a bag with 2 red marbles, 4 white marbles and 3 purple marbles. He will randomly select 2 marbles from the bag one at a time without
replacement. What is the probability that he will choose a red marble first and then a white marble?
O 13/18
8/81
O 1/9
O 2/3
Answer:
1/9
Step-by-step explanation:
Given:
2 red marbles
4 white marbles
3 purple marbles
He will randomly select 2 marbles from the bag one at a time without
replacement.
To Find:
What is the probability that he will choose a red marble first and then a white marble?
Solution:
Since red marbles =2
White = 4
Total = 2+4+3 = 9
Select first time = 2/9
Select second time = 4/8
And then = Multiply
2/9 * 4/8 = 8/72
8/72 Simplify
1/9
[RevyBreeze]
Area compound shapes
Step-by-step explanation:
the area is the sum of the top square of 9×9 and the bottom parallelogram.
we know the length of the parallelogram is still also the square side length : 9ft.
but we don't need to bother about the lengths of the inclined sides, as the area of a parallelogram is
baseline × height
and the height we can see on the right hand side, as the height of the total shape is 14ft. given that the square side length is 9ft, that leaves us with 14-9 = 5ft as the height of the parallelogram.
so, the area of the square is
9×9 = 81 ft²
the area of the parallelogram is
9×5 = 45 ft²
the total area is then
81 + 45 = 126 ft²
calvin and susie baked some cookies in the ratio of 3 : 7. calvin baked 60 fewer cookies than susie. how many cookies did they bake altogether?
Answer:
Acc to ques
7x-3x = 60
x = 15
so they made total of 10x = 150
Hello I need help with number 1-12 please and thank you!!!!!
Answer:
Please see above
Step-by-step explanation:
I have to right stuff here but the answer is above.
What is the value of X?
Answer:
x=7
Step-by-step explanation:
In a 45 45 90 triangle the two legs are equal so you set 33=5x-2 and then solve the equation.
i need helps pls
The net of a square pyramid and its dimensions are shown in the diagram. What is the total surface area in square feet?
5,760 ft²
976 ft²
1,120 ft²
1,040 ft²
The net square pyramid and its given dimension as shown has a total surface area of 1040 ft².
How to calculate surface area of a square pyramidSurface area of a square pyramid = A + 1 / 2 ps
where
A = area of the basep = perimeter of bases = slant heightTherefore,
A = l²
where
l = length = 20 ftA = 20² = 400 ft²
p = 4l = 4 × 20 = 80 ft
s = 16 ft
Therefore,
Surface area = 400 + 1 / 2 × 80 × 16
Surface area = 400 + 1280 / 2
Surface area = 400 + 640
Surface area = 1040 ft²
learn more on surface area here: https://brainly.com/question/2835293
what is the volume of the box with a high of 3/2 inches a length of 7/2 inches and a with of 5/2 inches
Answer: It is 105/8, or 13 1/8 (as a mixed number)
Step-by-step explanation:
To find volume, you do length times width times height (l * w * h)
Hope this helps! :D
Carly needs $149 to buy a skateboard. She already has $52. She earns money washing cars for $20 a car.
Carly says that if she washes 5 cars she will have enough money to buy the skateboard.
Use the drop-down menus to explain how to solve this problem.
First multiply
Choose...
× $20 to find how much money Carly will earn washing cars. Then add this amount to
Choose...
to find how much money Carly has in all. Finally,
Choose...
the total to the cost of the skateboard.
Answer:
$149 - skateboard price
$52 - carly's money
$20 × 5 cars = $100
$100 + $52 = $152
$152 - $149 = $3 left
Question
The sum of four times a number and two is 14. Find the number.
Answer:3
Step-by-step explanation:let the number be x
4x+2=14
4x=14-2
4x=12
divide both sides by 4
4x/4=12/4
x=3
Award: 1.00 point Exercise 6-10A (Static) Why is it important to prepare the benefit analysis report or the total compensation report? [You may select more than one answer. Single flick the box with the question mark to produceea check marka forma correct answer and doubye-click the both with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.) The reports may be used to accompany benefits billing. The reports may be used as employee contracts. The reports promote employee education about the total value of their salary and benefits. The reports inform labor planning and employer cost strategies. References Check All That Apply Difficulty: 1 Easy Exercise 6-10A (Static) Learning Objective: 06-06 Complete Benefit Analysis as a Function of Payroll
Answer:
i think its option one
Step-by-step explanation:
What is the area of this figure?
[tex]a \: = \: square \: area \: + \: triangle \: area \: + \: rectangle \: area \: \\ [/tex]
[tex]a \: = (3 \times 3) + ( \frac{1}{2} \times 3 \times 11) + (3 \times 11) \\ [/tex]
[tex]a = 9 + \frac{33}{2} + 33 \\ [/tex]
[tex]a = 9 + 16.5 + 33[/tex]
[tex]a = 25.5 + 33[/tex]
[tex]a = 58.5 \: \: {ft}^{2} [/tex]