Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x = − 8 x=-8 and x = − 4 x=-4 and passes through the point ( 0 , − 7 ) (0,-7) .
Answers
.. y = a(x +8)(x +4)
At x=0, this is
.. -7 = 32a
.. a = -7/32
The formula is
.. f(x) = (-7/32)(x +8)(x +4)
The formula for a parabola with roots at x=-8 and x=-4, and which passes through the point (0,-7), is y = -7/32(x + 4)(x + 8).
Explanation:The formula we're looking for is in the form of a quadratic function, generally expressed as
y = ax² + bx + c. Our roots are -8 and -4, which we represent in the factors of the equation as (x + 4) and (x + 8). As coefficients multiply to a, we seek a that makes our function pass through the specific point (0, -7). Thus, we substitute the point into the function giving -7 = a(0+4)(0+8) leading us to a = -7/32. So, the equation of the parabola asked is
y = -7/32(x + 4)(x + 8).
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Related Questions
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What is the trigonometric ratio for sin S?
Enter your answer, as a simplified fraction, in the boxes.
Answers
Answer: [tex]\frac{8}{17}[/tex] or 8:17
Step-by-step explanation:
For any angle x (other than right angle) in a right triangle ,the trigonometric ratio of sin x is given by :-
[tex]\sin x=\frac{\text{side opposite to x}}{\text{Hypotenuse}}[/tex]
Given: A right triangle with hypotenuse = 68 units
The side adjacent to S = 60
Let h be the side opposite to S, then using Pythagoras in the given right triangle, we get
[tex](68)^2=60^2+h^2\\\\\Rightarrow\ h^2=68^2-60^2\\\\\Rightarrow\ h^2=1024\\\\\Rightarrow\ h=\sqrt{1024}=32[/tex]
Thus, the side opposite to S = 32 units
Now, the trigonometric ratio for sin S is given by :-
[tex]\sin S=\frac{\text{side opposite to S}}{\text{Hypotenuse}}\\\\\Rightarrow\sin S=\frac{32}{68}=\frac{8}{17}[/tex]
Hence, the trigonometric ratio for sin S =[tex]\frac{8}{17}[/tex] or 8:17
Trigonometric Identities and Applications?
Answers
[tex]\bf 8cos^2(\theta )-3cos(\theta )=0\implies \stackrel{common~factor}{cos(\theta )}[8cos(\theta )-3]=0\\\\ -------------------------------\\\\ cos(\theta )=0\implies \measuredangle \theta =cos^{-1}(0)\implies \measuredangle \theta =90^o\\\\ -------------------------------\\\\ 8cos(\theta )-3=0\implies 8cos(\theta )=3\implies cos(\theta )=\cfrac{3}{8} \\\\\\ \measuredangle \theta =cos^{-1}\left( \cfrac{3}{8}\right)[/tex]
22)
[tex]\bf \begin{cases} y=cos(2x)\\ y=cos^2(x)-1 \end{cases}\implies \stackrel{intersection~at}{cos(2x)=cos^2(x)-1} \\\\\\ 2cos^2(x)-1=cos^2(x)-1\implies 2cos^2(x)-1-cos^2(x)+1=0 \\\\\\ 2cos^2(x)-cos^2(x)=0\implies cos^2(x)=0\implies cos(x)=0 \\\\\\ \measuredangle \theta =cos^{-1}(0)\implies \measuredangle \theta =180^o~~,~~270^o[/tex]
Trigonometric identities are equations that hold true for all permissible values of the involved variables. They are fundamental to many areas of mathematics and have applications in various fields such as physics and engineering.
Explanation:Trigonometric identities are equations that are true for all values of the variables where both sides of the equation are defined. They are fundamental to the study of mathematics, particularly in geometry, calculus and physics.
Some of the basic trigonometric identities include:
Reciprocal identities:sin = 1/csc θcos = 1/sec θtan = 1/cot θPythagorean identities:sin² θ + cos² θ = 11 + tan² θ = sec² θ1 + cot² θ = csc² θ...Trigonometric identities are widely used in solving trigonometric equations and proving other identities, and in many fields such as engineering, physics and computer science.
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What is 5(7h+3m) equal to?
Answers
5(7h)=35h
5(3m)=15m
you should then have 35h+15m and since you cannot combine the variables that should be your final answer
5(7h) + 5(3m)
35h + 15m
Find f(1/4) when f(x)=2x^2+9x-7
Answers
To find f(1/4) when f(x)=2x^2+9x-7, substitute x=1/4 into the function and simplify.
Explanation:To find f(1/4) when f(x) = 2x² + 9x - 7, we substitute x = 1/4 into the function.
Plugging in the value of x, we have f(1/4) = 2(1/4)² + 9(1/4) - 7.
Simplifying the expression, we get f(1/4) = 2/16 + 9/4 - 7. Evaluating the fractions and subtracting, we find that f(1/4) = -45/16.
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A circle has an area 324 pi cm. What is the radius?
Answers
if area is given as [tex]324 \pi [/tex]
then r² = 324
r = √324
r = 18 cm
Ans: The radius is 18 cm
The radius of the circle with an area of 324π sq cm is 18 cm.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know, The area of a circle is πr².
So, We can equate the given area with the general formula,
324π = πr².
r² = 324.
r = 18 cm.
A clock can be thought of as a circle having 12 steps and we know that circle is 360°,
So, the measure of each integer step of a clock is 30°.
Also, If we want to find some portion(arc) of the circumference we use the formula, s = rФ.
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find the height of each pyramid square pyramid: volume 297 ft cubed area of the base 81 ft squared
Answers
The formula for the volume of a right pyramid is V=1/3Bh, where B is the area of the base and h is the height. Substituting the known information, we have:
297=1/3(81)h
297=27h
Divide both sides by 27:
297/27 = 27h/27
11 = h
I don't know if this is right but I got 0.14
True Or False
The term software refers to everything from the machine’s operating system (OS) to the individual programs and applications you use to write, listen, speak, sing, or learn.
Answers
Akira Chang's uncle dies without a will, leaving an estate of $945,000. His heirs consist of a wife and two adult children. His state requires that, in the absence of a will, each child is to receive two-thirds as much as a spouse. How much will his wife receive?
Answers
.. w +2*(2/3*w) = 945,000
.. 7/3w = 945,000
.. w = (3/7)*945,000 = 405,000
The wife will receive $405,000.
a leatherback turtle swims at a constant rate of 2.5 kilometers per hour, at its constant rate of speed how long will it take for a leatherback turtle to swim 10 kilometers?
Answers
So, if this turtle is only going 2.5 miles per hour. This would mean that (EACH) hour, this turtle only arrived 2.5 miles. So, we do,
[tex]\boxed{10.0 \left \{ {{2.5+2.5=5.0} \atop {2.5+2.5=5.0}} \right.}[/tex]
We would have to count how many ("2.5's" they are above.)
We count only 4.
I would take this turtle 4 miles to swim 10 kilometers.
A box contains 3 red balls, 2 white balls, and 5 black balls. two balls are drawn at random from the box (with replacement of the first before the second is drawn). what is the probability of getting a red ball on the first draw and a white ball on the second?
Answers
Katie filled a measuring cup with 9/10 of a cup of vegetable oil. Then she poured 1/4 of a cup of the oil into a frying pan. How much oil is left in the measuring cup? Simplify your answer.
Answers
The answer is "4/5".
Reason:
First write the equation:
9*4=36
10*4=40
-
1*4=4
4*10=40
36-4=32
32/2=16/2=8/2=4
40/2=20/2=10/2=5
=4/5
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During a two week period, Norm worked 85.6 hours. His hourly wage is $6.92. How much did he earn? (Round the answer to the nearest cent)
Answers
an athlete is training to run a marathon. she plans to run 2 miles the first week. she increases the distance by 8% each week. whixh function models how far she will run in the nth week
Answers
nth=ae^(bx)
nth=2e^(0.08x)
where x is the nth time.
Omar uses 1/6 of his tickets to ride the water slide. How many tickets does he use he has 24 in total?
Answers
Have a brainy day.
[tex] \frac{24}{1} [/tex] × [tex] \frac{1}{6} [/tex] = [tex] \frac{24}{6} [/tex] = 4
They could mow the lawn in how many hours if they work together
Answers
Jack can mow 10% of the yard in 0.3 hours
Marilyn can mow 10% of the yard in 0.7 hours
Jack will mow 70% of the yard : 0.3 hours ( 10% ) × 7
= 2.1 hours . Jack can mow 70% of the yard in 2.1 hours
Marilyn will mow 30% of the yard : 0.7 hours ( 10%) × 3 = 2.1 hours. Marilyn can mow 30% of the yard in 2.1 hours.
John mowwing for 2.1 hours + Marilyn mowwing for 2.1 hours = 100% of the yard in 4.2 hours.
Awnser : 4.2 hours
First, figure out their mowing rates per hour.
Jack's is [tex] \frac{1}{3} [/tex] since he mows 1 lawn in 3 hours; Marilyn's is [tex] \frac{1}{7} [/tex] since she mows 1 lawn in 7 hours.
We now know that their combined rate of mowing 1 lawn is [tex] \frac{1}{3} + \frac{1}{7} [/tex]. Use the variable t for time and multiply it by their combined rate to figure out their combined time of mowing 1 lawn.
[tex]( \frac{1}{3} + \frac{1}{7})t =1[/tex]
[tex]( \frac{7}{21} + \frac{3}{21} )t=1[/tex]
[tex] \frac{10}{21} t =1[/tex]
[tex]t= \frac{21}{10} [/tex]
Answer:
Jack and Marilyn could mow the lawn in [tex] \frac{21}{10} [/tex] or 2.1 hours if they work together.
Write a mixed number for p so that 3 1/4 x p is more than 3 1/4
Answers
The value of p just needs to be greater than 1. It could be 43 million (and 2/7, since you want a mixed number).
Given: ΔXYZ
AB is a midsegment parallel to XZ. The slope of XZ is 4.
What is the slope of AB?
Answers
we know the slope of XZ, and we know AB is parallel to XZ, well, parallel lines have the same slope.
Since AB is a midsegment parallel to XZ, its slope and the slope of XZ are the same.
which number is least to greatest 42%,0.43,17/40
Answers
Hope I helped!
Let me know if you need anything else!
~ Zoe (Rank:'Genius')
solve equations using addition x+y=5 and x-y=3
Answers
x - y = 3 ----------- (2)
(1) + (2):
2x = 8
x = 4 ----------- sub into (1)
4 + y = 5
y = 5 - 4
y = 1
Ans: x = 4, y = 1
Mark’s father drove the family car 32,143 miles last year. He drove the car 29,675 miles this year.
How many fewer miles did Mark’s father drive the car this year?
A. 2,468 mi
B. 2,578 mi
C. 3,468 mi
D. 3,478 mi
Answers
your water hose is leaking at a rate of 0.25 cups per hour. how many gallons did you hose leak in a full 24 hour day
Answers
Solution:
we are given that
water hose is leaking at a rate of 0.25 cups per hour.
We have been asked to find that
how many gallons did you hose leak in a full 24 hour day.
Since water hose is leaking at a rate of 0.25 cups per hour.
It mean the tank will leak by [tex] 0.25*4=1 \ Cup [/tex] in 4 Hours.
So in 24 Hours the tank will leak by [tex] \frac{24}{4}*1=6*1=6 \ Cups [/tex] .
As we know that 1 Gallon=16 Cups.
It mean in 24 Hours the tank leaked by [tex] \frac{1}{16}*6= 0.375 \ Gallon [/tex]
which of the following statements are true? check all that apply
Answers
Answer with explanation:
Mean of this data set
[tex]=\frac{\text{sum of all the observation}}{\text{Total number of observation}}\\\\=\frac{30+37+37+41+22+69+45+64+51+22+63+31+64+65+25+51+26+48+28+49}{20}\\\\=43.4[/tex]
Arranging the data set in ascending order
22, 22,25, 26, 28,30,31,37,37,41,45,48,49,51,51,63,64,64,65,69
Median =Middle observation ,if number of terms is odd
and if number of terms is even, divide number of terms by ,2 and then follow the procedure
[tex]=\frac{10^{th term}+11^{th term}}{2}\\\\=\frac{41+45}{2}\\\\=43[/tex]
To find the Outlier
[tex]Q_{1}=\frac{28+30}{2}=29,Q_{3}=\frac{51+63}{2}=57[/tex]
Interquartile range = 57 - 29=28
Data values are approximately equally distributed on both sides of median.
That is, 43-22=21, and ,69 -43=26
So,we can say that there will be no outliers.
Graph will be positively skewed.
Mean > Median
So,mean will be better measure of central tendency because, 43.4-22=21.4, and 69-43.4=25.6
Option A: There are no outliers.
And, Option C: The Mean is good measure of central tendency.
The stopping distance s of a car varies directly as the square of its speed v. If a car traveling at 20 mph requires 28 ft to stop, find the stopping distance for a car traveling at 55 mph
Answers
Marlena is making fruit salad she will choose from 6 of the 11 different fruits offered at a fruit stand. How many different fruit salads can she make
Answers
The Correct answer is 462
Compare the Triangle Proportionality Theorem and the Triangle Midsegment Theorem.
Answers
If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the sides into segments of proportional lengths.
Question 10 an urn contains two white marbles and one black marble. a marble is drawn from the urn without replacement and put aside without my seeing it. then a second marble is drawn, and it is white. what is the probability that the unknown removed marble is white, and what is the probability that it is black?
Answers
Final answer:
The probability that the unknown removed marble is white is 1/2, and the probability that it is black is also 1/2. This is calculated by considering the outcomes of the draws, their probabilities, and the fact that drawing a white marble after another without replacement affects the outcomes.
Explanation:
The question involves calculating conditional probabilities in a scenario where marbles are drawn from an urn without replacement. Initially, the urn contains two white marbles and one black marble. A marble is drawn and set aside (its color unknown), and then a second marble is drawn, which is observed to be white. We are asked to find the probability that the first marble drawn was white, and the probability it was black.
To solve this, we consider the two possible scenarios for the first draw: drawing a white marble or drawing a black marble, and then drawing a white marble in the second draw. The probability of drawing white then another white (WW) equals, the probability of drawing a white marble first (2/3) multiplied by the probability of drawing the second white marble given the first was white (1/2). This gives (2/3)*(1/2) = 1/3. Alternatively, the probability of drawing a black then a white marble (BW) equals the probability of drawing a black marble first (1/3) multiplied by the probability of drawing a white marble given the first was black (2/2) = 1/3, simplifying to (1/3)*(1) = 1/3
To find the probability that the unknown marble is white, we see that both scenarios WW and BW result in drawing a white marble second, so we only need to calculate the probability of the WW scenario over the total probability of drawing a white marble in the second draw. This gives us 1/3 / (1/3 + 1/3) = 1/2. Therefore, the probability that the unknown marble is white is 1/2, and by complement, the probability it is black is also 1/2
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One side of a square is 2^3 inches.
What would be the area of the square?
*Solve the equation of 2^3 first*
Answers
First solving the equation 2^3 . . .
To solve 2^3, multiply the number 2 three times:
2 x 2 x 2 = 8
To find area, multiply the two sides . . .
(Since a square has all sides the same length, multiply 8 x 8)
8 x 8 = 64 <-------
The area of the shape is 64 inches.
Hope this helps you.
Have a great day!
A store sells two kinds of candles, scented and unscented. The scented burns 1/12 inches in 20 minutes and the unscented burns 1/6 inches in 30 minutes. Which type of candle burns in 1 hour and what is its burn rate?
Answers
Given :The scented burns [tex] \frac{1}{12} [/tex] inches in 20 minutes
The scented candle will burn [tex] \frac{1}{12} times 3 =\frac{1}{4} [/tex] inches in one hour.
The unscented candle burns [tex] \frac{1}{6} [/tex] inches in 30 minutes
In one hour it will burn [tex] \frac{1}{6} times 2=\frac{1}{3} [/tex] inches .
Burn rate of scented is [tex] \frac{1}{4} [/tex] inches per hour.
Burn rate of unscented is [tex] \frac{1}{3} [/tex] inches per hour.
△ABC is reflected to form △A′B′C′ .
The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) .
Which reflection results in the transformation of △ABC to △A′B′C′ ?
A)reflection across the x-axis
B) reflection across the y-axis
C)reflection across y = x
D)reflection across y=−x
Answers
Answer:
The correct option is A.
Step-by-step explanation:
The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) .
The relation between coordinates of preimage and image is defined as
[tex](x,y)\rightarrow (x,-y)[/tex]
Sign of y-coordinate changes but x-coordinate remains the same. It is possible it the figure is reflection across the x-axis.
Therefore the correct option is A.
Calculate the effective rate of interest (to the nearest hundredth percent) of the following Treasury bill. Given: $10,000 Treasury bill, 3.85% for 13 weeks.
Answers
.. (effective rate) = r/(1 -rt)
If we assume a 52-week year, the t = (13 weeks)/(52 weeks) = 1/4.
.. (effective rate) = 0.0385/(1 -0.0385/4) ≈ 0.038874 ≈ 3.89%