Answers
Step-by-step explanation:
these are both quadratic curves, parabolas, and factorization means to express the 2 terms as multiplication with each other, so that the result would be the simplified function. in other words : find the two factor terms that make the whole function.
the advantage of factorization is to see the 2 solutions for y=0 right away.
the general form is
y = (x + a)(x + b)
and the y=0 solutions are then simply x = -a and x = -b.
in example 3 we have 2 different y=0 solutions, seemingly at x = 1 and x = 5.
that makes the factorization :
y = (x - 1)(x - 5)
when x becomes one of these values, the corresponding factor becomes 0 and therefore y becomes 0 too.
in example 4 we have only one y=0 solution (or so it seems; in fact there are still formally 2 solutions, they are just equal).
it is seemingly at x = -2.
since both solutions are equal, we have also two equal factors.
that makes the factorization
y = (x + 2)(x + 2) = (x + 2)²
Related Questions
You are playing a game where you draw a card from a standard deck, and you will win $13 if you draw a face card,
$3 if you draw an ace and lose $5 if you draw any other card. What is the expected gain from this game?
Round your final answer to the nearest cent.
Answers
Answer:
Step-by-step explanation:
win
There are 3 face cards / suit. Every suit contains a Jack, Queen, and king.
There are 4 suits so the number of face cards is 3*4 = 12
There is 1 ace / suit
There are 4 suits so the number of aces is 1 * 4 = 4
The gain from the face cards = 12 * 13 = 156
The gain from the aces = 4 * 3 = 12
Total gain = 168
Losses
Any other card costs you $5
How many cards is that? 52 - 16 = 36
Each one costs 5 dollars
Total loss = 5 * 36 = 180
So each time you play the game, you can expect to lose 180 - 68 = 12 dollars. You should walk away quickly from this one.
graph the solution of the inequality 2.25k≤−9
Answers
Answer:
Wouldn’t negative 9 be the inequality because its less than 2.25
Step-by-step explanation:
Hey budddy if i got this wrong im soooooo, sorry
Help ASAP Homework Due Tomorrow
Answers
Answer:
Its definitely D
Step-by-step explanation:
Your welcome ♀️
A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained the wishes the estimate to be within three percentage points
with 90% confidence, assuming that
(a) he uses the estimates of 21.3% male and 19.5% female from a previous year?
(b) he does not use any prior estimates?
(a)n (Round up to the nearest whole number)
(b) (Round up to the nearest whole number.)
Answers
Using the z-distribution and the formula for the margin of error, it is found that:
a) A sample size of 54 is needed.
b) A sample size of 752 is needed.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
Item a:
The estimate is [tex]\pi = 0.213 - 0.195 = 0.018[/tex].
The sample size is n for which M = 0.03, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.018(0.982)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.018(0.982)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.018(0.982)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.018(0.982)}}{0.03}\right)^2[/tex]
[tex]n = 53.1[/tex]
Rounding up, a sample size of 54 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.05[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
[tex]n = 751.7[/tex]
Rounding up, a sample of 752 should be taken.
A similar problem is given at https://brainly.com/question/25694087
Write an equation with slope of -2 and goes through the point (-3,7)
Answers
Answer:
y = -2x + 1
Step-by-step explanation:
Substitute the slope and the given point into y = mx + b and solve for "b".
y = mx + b
7 = -2(-3) + b
7 = 6 + b
1 = b the y-intercept is 1
The equation of the line is y = -2x + 1
write this number in expanded form three hundred thirty nine thousand six
Answers
Answer:
339,006
Step-by-step explanation: i think
Answer:
300,000 + 30,000 + 9,000 + 6
Step-by-step explanation:
hope this helps. . . <3
good luck! UwU
Write (-3,-9) and (4,-2) in slope intercept form
Answers
Answer:
Slope intercept form is y = x - 6 (you don't write 1 in front of x in this case btw)
Slope = 1
Y-intercept = -6
Step-by-step explanation:
Slope intercept form looks like this y=mx+b, where m is slope and b is y-intercept.
To find slope, we will do y2 - y1 over x2 - x1.
This is how coordinates are written btw (x,y)
So we will do:
-2 - (-9) = -2 + 9 = 7
4 - (-3) = 4 + 3 = 7
Since 7/7 is the same as 7÷7, the slope is going to be 1. (It's also a positive slope btw)
Now, in order to find what the y-intercept is, you should use the point slope formula⤵⤵⤵:
[tex]y - y _{1} = m(x - x _{1})[/tex]
We'll use point (4,-2) for this:
y + 2 = 1 (x - 4)
Now we solve:
Distribute the 1 among everything inside the parenthesis to get y + 2 = x - 4, then subtract 2 on both sides to get y = x - 6.
Hope this helps :)
Similar Triangles
In the figure below, AB has length 6 feet, BC has length 8 feet and CD has length 7 feet.
If angles B and D are right angles, what is the length of DE rounded to the nearest tenth foot?
Answers
Answer:
5.3 ft
Step-by-step explanation:
Because CD corresponds to BC, the scale factor from triangle ABC to triangle CDE, is 7/8. Now, DE corresponds to AB, so to get DE, we must multiply the value of AB by 7/8. 6 times 7/8 is 5.25, and rounding to the nearest tenth of a foot, the value of DE is 5.3.
A company has launched a Business App. for smart mobile phones, the users who installed the application in 2015 were 10000 users, and they increase by 10% each succeeding year.
a) Determine the number of users in the year 2020.
b) If the company gains on average annual revenue of OMR 12 per user, what is the total revenue gained until the end of the year 2021?
Answers
Answer: a) 15000 b) OMR 192,000
In this problem, I did part a) correctly, but I got 7 points off in part b) but I don’t know why?
Answers
Answer: You need to prove that ABCD is a rhombus because it's diagonals are always perpendicular, no matter what.
A rhombus is a quadrilateral and:
- its opposite angles have equal measure.
- The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral.
- Its diagonals bisect opposite angles.
Using 7 what is the angle measure represented by the expression (2x+45)°?
PLEASE HELP ITS URGENT
Answers
If you plug 7 as x into:
(2x+45)
then you get
(2(7)+45)
(14+45)
(59)
ed says a decimal grid shows 10 tenths monica says a decimal grid shows 100 hundredths who is correct explain PLEASE HELP I NEED TBIS DONE IN 30 minutes
Answers
Answer:
will i need a picture but its probably 10 count by 5s
Step-by-step explanation:
9 - 3 ÷ 1/3 + 1 = x
pls help
Answers
Answer:
Step-by-step explanation:
x=9
what is 10 2/1 divided by 2 1/4
Answers
Answer:
5.3 but the three is repeated
Step-by-step explanation:
Answer:
[tex]10 \frac{2}{1} \div 2 \frac{1}{4 } = \frac{48}{9} [/tex]
Penjelasan
[tex]10 \frac{2}{1} = \frac{12}{1} [/tex]
[tex]2 \frac{1}{4} = \frac{9}{4} [/tex]
[tex] \frac{12}{1} \div \frac{9}{4} = \frac{12}{1} \times \frac{4}{9} = \frac{48}{9} [/tex]
Then the answer is 48/9
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[tex] \green{ \boxed{ \boxed{ \sf{Lusi \: Adriana} } } } [/tex]
The diameter of a circle 18cm
Answers
Answer:
[tex]\text{Circumference}~ = 2 \pi r = 2 \pi \cdot \dfrac{18} 2 = 18 \pi =18 \times 3.14=56.52~ cm[/tex]
Step-by-step explanation:
Lyra is designing a model of a solar system with a planet and a comet. The planet has a circular orbit, centered at the origin with a diameter of 100. The comet follows a parabolic path with directrix x = 70 and vertex at (60, 0).
Part A: Write the equation of the planet's orbit in standard form. Show your work. (2 points)
Part B: Write the equation of the comet's path in standard form. Show your work. (4 points)
Part C: Identify all points where the planet's orbit intersects the path of the comet. Show your work and round answers to the hundredth place. (4 points)
Answers
The equation of the circular orbit and the parabolic path of the comet are
given by the center, diameter, vertex, and directrix.
Part A: The equation of the planet's orbit is; x² + y² = 50²
Part B: The equation of the comet's orbit is; [tex]\underline{x = -\dfrac{y^2}{280} + 60}[/tex]
Part C: The planet's orbit and the comet's path do not intersect.
Reasons:
Part A: The center of the orbit = The origin (0, 0)
The diameter of the orbit = 100
Therefore;
[tex]Radius \ of \ orbit = \dfrac{100}{2} = 50[/tex]
The radius of the planet's orbit, r = 50
The equation of a circle with center (h, k) is; (x - h)² + (y - k)² = r²
Therefore, the equation of the circle is (x - 0)² + (y - 0)² = r²
Which gives;
x² + y² = 50²
Part B: The directrix of the parabolic path is x = 70
The vertex = (60, 0)
Therefore, -p = 70
[tex]The \ equation \ is \ x = \dfrac{1}{4\cdot p} \cdot (y - k)^2 + h[/tex]
Which gives;
[tex]The \ equation \ is \ x = \dfrac{1}{4\times (-70)} \times (y - 0)^2 + 60 = -\dfrac{y^2}{280} + 60[/tex]
[tex]x = \mathbf{ -\dfrac{y^2}{280} + 60}[/tex]
The equation of the comet's path in standard form is [tex]\underline{x = -\dfrac{y^2}{280} + 60}[/tex]
Part C: At the point where the path intersect, we have;
[tex]x^2 = \left( -\dfrac{y^2}{280} + 60 \right)^2[/tex]
Therefore;
[tex]\mathbf{\left( -\dfrac{y^2}{280} + 60 \right)^2} = 50^2 - y^2[/tex]
Let y² = a, we get;
[tex]\left( -\dfrac{a}{280} + 60 \right)^2 = 50^2 -a[/tex]
a ≈ -2015.693 and a ≈ -42784.31
y ≈ √(-2015.693) or y ≈ √-42784.31) (imaginary numbers)
The planet's orbit does not intersect the path of the comet.
Learn more here:
https://brainly.com/question/20743199
Paul received a bonus of $750, which was 5% of his annual salary. His annual salary is a. A$37,500 b. $25,000 c. $22,500 d. $15,000 e. $7,500
Answers
What is 8.981 times 1.981
Answers
Answer:
17.791361
Step-by-step explanation:
Hope this helps!
Can I get Braineist Pls?
Answer:
17.791361
You can cross multiply. I am almost sure this is the method. Put the first number over each other. Then multiply the numbers across. Hope this is helpful!
(-x+ 4) (3х^2 + 3х + 5)
Answers
Answer:
-3x^3 + 9x^2 + 7x + 20
Step-by-step explanation:
this is the expression simplified
I have more question
Answers
Answer:
you would need three wholes because each whole would represent a loaf of pumpkin bread
PASSCODE DECODER RING SHRI o If it takes 6 hours to bake 3 cakes, then at that rate, how many cakes could be baked in 12 hours? If Ava makes $15 in 2 hours, what is her rate of pay? 3nt took 5 hours to mow 6 yards. At that rate, how many yards can be mowed in 20 hours? co malaya $ o 94 If 10 bags of ice cost $12, how much does 1 bag cost? 5 A car gets 30 miles per gallon of gas. At that rate, how many gallons would it take for the car to go 360 If you type 75 words in 3 minutes, at what rate do you type? RECORD PASSCODE Directions Complete the questions, match each answer on the decoder eing, med record the letter from that spot When complete, go back to The Nission page te access the posscode reader to check your answer and solve another part of the mystery
Answers
The rate is a fraction that compares the values of two quantities. The expected answers to the questions are given below:
1. Given that 3 cakes takes 6 hours to bake, then:
1 cake = [tex]\frac{6}{3}[/tex]
= 2 hours
So that;
the number of cake to be baked in 12 hours = [tex]\frac{12 hours}{2 hours}[/tex]
= 6
The number of cake to be baked in 12 hours is 6.
2. Ava's rate of pay = [tex]\frac{15}{2}[/tex]
= $7.5 pr hour
Thus Ava's rate of pay is $7.5 per hour.
3. It took 5 hours to mow 6 yards. Thus;
To mow 1 yard = [tex]\frac{5}{6}[/tex] hours
The number of yards to be mowed in 20 hours = 20 ÷ [tex]\frac{5}{6}[/tex]
= 20 x [tex]\frac{6}{5}[/tex]
= 24
The number of yards to be mowed in 20 hours is 24.
4. Given that 10 bags of rice cost $12, then;
1 bag = [tex]\frac{12}{10}[/tex]
= 1.2
1 bag = $1.2
The cost of a bag of rice is $1.2.
5. Rate = 30 miles per gallon
The number of gallons required = [tex]\frac{360}{30}[/tex]
= 12
Thus 12 gallons would be required by the car to travel 360 miles.
6. Rate = [tex]\frac{75}{3}[/tex]
= 25
Rate = 25 words per minute
The typing speed is 25 words per minute.
For more on rate, check: https://brainly.com/question/119866
GIVING OUT BRAINLIEST!!
Answers
Answer:
Jill plz tell if i am right
Step-by-step explanation:
give me schoology website
Choose the end behavior of the graph of each polynomial function
Answers
Answer:
D, A, B
Step-by-step explanation:
The sign of the leading coefficient always tells you the end behavior on the right: positive = rises; negative = falls.
The degree of the polynomial tells you how the left- and right-end behaviors compare: even = they are the same; odd = they are opposites.
__
A) negative leading coefficient, even degree:
falls to the left, falls to the right (D)__
B) positive leading coefficient, odd degree:
falls to the left, rises to the right (A)__
C) negative leading coefficient, odd degree
rises to the left, falls to the right (B)3/15 as an improper fraction
Answers
Answer:
3/15 cannot be simplified as an improper fraction because ethe denominator is greater than the numerator. However, we can simplify 3/15 as a fraction
=> 3/15 = 1/5
Step-by-step explanation:
Hoped this helped.
Answer:3/15 as an improper fraction is 1/5
Step-by-step explanation:1 over 5
Use the image above for question ^^
Answers
A reflection over y = x, the coordinates reverse: (x,y) becomes (y,x)
Using point A which is located at (5,2) reflection y = x A' would become (2,5)
On the graph shown the location of A' is (2,5) so the answer is
4. a reflection over the line y = x
WILL GIVE BRAINLIEST
(5x-7)
(10x-32)
14
the perimeter of the pictured triangle is _____ in.
Answers
By converse of isosceles triangle theorem:
5x - 5 = 10x - 32
add 32 and -5x at both sides
27 = 5x (divide 5 both sides)
x = 5.4
5(5.4) - 5 = 27 - 5 = 22 inches
22 + 22 + 14 = 58 inches
Plss help me! I’m so confused! Brainlist! Pls no links and deleting!
Answers
$60
Step-by-step explanation:
The unit rate can be determined by dividing $24 by 8 attendees to get
[tex]\dfrac{\$24}{8\:\text{attendees}} = \$3/\text{attendee}[/tex]
so when 20 people are attending the graduation picnic, his total cost is going to be
[tex]20\:\text{attendees}×\dfrac{\$3}{\text{attendee}} = \$60[/tex]
Can someone please explain to me how to solve this?
Will give brainly if you answer the question
Answers
Answer:
D.12
Step-by-step explanation:
College brother told me its 12 which is D.
Answer:x=1
Step-by-step explanation:
Find the sum of this problem.
Answers
Answer:
34
Step-by-step explanation:
i think
What is m + 5n where m = 1 and n = 5?
CHOOSE THE RIGHT ANSWER:
A. 26
B. 52
C. 25
D. 62
HELP! (T^T)
Answers
Answer:
A. 26
Step-by-step explanation:
substitute the number in for the variables (letters).
[tex]m + 5n \\ \\ 1 + 5(5) \\ 1 + 25 \\ 26[/tex]