Answers
The equation of the parabola from its focus and vertex is 5x = 4y² .
A parabola is a mirror-symmetrical, roughly U-shaped planar curve. The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.
A line and a point (the focus) are two components of one definition of a parabola (the directrix). There is less emphasis on the directrix. The parabola is the location of the endpoints in that plane that are equally spaced away from the directrix and the focus.
Another approach to define a parabola is as a conic section formed by the union of a right circular conical area with a plane parallel to another axis perpendicular to the conical surface.
from the figure the parabola is opening on the right side.
Hence the general equation of the parabola is is y² = 4ax
Now from the focus we get 4a = 5
or, a = 5/4
Hence the equation of the parabola is 5x = 4y².
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Related Questions
What value of x makes this equation true?x+7------7A. 6B. 8C. 35 D. 42
Answers
We have
[tex]\begin{gathered} \frac{x+7}{7}=6 \\ x+7=6\times7 \\ x+7=42 \\ x=42-7 \\ x=35 \end{gathered}[/tex]Option C
need help with these parts. both parts use the same table
Answers
Given:
[tex]f(x)=h(2x)[/tex]And the values in the table.
Required:
The equation of a normal line to f at x=3.
Explanation:
The equation of the line that passes through from point (x,y) and has slope m
is given by the formula
[tex]y-y_1=m(x-x_1)[/tex]From the table at x=3, f(x)=h(2x)
that is f(3)= h(6)=9
And the slope from the table at x=3 is 1/2.
Now the equation of the line is:
[tex]\begin{gathered} y-9=\frac{1}{2}(x-3) \\ 2(y-9)=(x-3) \\ 2y-18=x-3 \\ x-2y=-15 \end{gathered}[/tex]Final answer:
Thus the equation of the normal line is
[tex]x-2y+15=0[/tex][tex] 4 ^{ \frac{1}{3} } \times 4 ^{ \frac{1}{5} } = [/tex]pls answer this
Answers
The given Expression is :
[tex]4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}[/tex]From the property of exponents
If the base value of the exponents are same then during the process of multiplication powers will add up.
Since in the given expression 4 is the base value on both base of the exponents
Thus, base value are equal
The powers will add up:
[tex]\begin{gathered} 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}} \\ 4^{\frac{1}{3}+\frac{1}{5}} \end{gathered}[/tex]Simplify the farction of the exponents :
[tex]\begin{gathered} \frac{1}{3}+\frac{1}{5} \\ \text{Taking LCM of the 3 \& 5} \\ \frac{1}{3}+\frac{1}{5}=\frac{5+3}{15} \\ \frac{1}{3}+\frac{1}{5}=\frac{8}{15} \end{gathered}[/tex]So, the value of the given expression will be :
[tex]\begin{gathered} 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}=4^{\frac{1}{3}+\frac{1}{5}} \\ 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}=4^{\frac{8}{15}} \end{gathered}[/tex]Answer : 4 ^8/15
- The Freedom Tower in New York City is 1776 feet
tall. The equation f(t) = -16t² + 1776 models the
height f(t) (in feet) of an object t seconds after it is
dropped from the top of the tower.
a. After how many seconds will the object hit the
ground? Round your answer to the nearest
hundredth of a second.
b. What is the height of the object 3 seconds after
it has been dropped from the top of the tower?
A golf ball is hit from the ground, and its height
can be modeled by the equation h(t) ==16t² + 128t,
where h(t) represents the height (in feet) of the ball
t seconds after contact. What will the maximum
height of the ball be?
WILL GIVE BRAINLIEST PLSSS
Answers
Part a: time when object hit the ground is 10.5 sec.
Part b: The height of the object 3 seconds is 1632 ft.
What is termed as the equation of motion?A mathematical formula which describes this same position, velocity, as well as acceleration of a body in relation to a specific frame of reference is known as an equation of motion. The equation of motion is second law, that also states that the force that acts on an object is equivalent to the mass m of a body multiplied by the acceleration an of its center of mass.For the given question;
The equation that models the height f(t) (in feet) of an object t seconds after it is when dropped from the top of the tower is,
f(t) = -16t² + 1776
Part a: time when object hit the ground.
When the object hit the ground, height will be zero.
Put f(t) = 0.
0 = -16t² + 1776
-16t² = -1776
t² = 111
t = 10.5 sec.
The, time after which the object will hit the ground is 10.5 sec.
Part b: The height of the object 3 seconds;
Put t = 3 in the equation.
f(3) = -16(3)² + 1776
f(3) = 1632 ft
The height of the object after 3 sec will be 1632 ft.
Thus, the values for the object hitting the ground are found.
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For what values of m does the graph of y = 3x² + 7x + m have two x-intercepts?
0 m> 25
O
Om<25
3
49
Om 12
49
m> 12
Answers
The graph of y = 3x² + 7x + m will have two x-intercepts if m < 49/12.
The given function is,
y = 3x² + 7x + m
Having two x-intercepts means that the value of y should be 0.
So, we can write,
3x² + 7x + m = 0
Now, this has become a quadratic equation and it will have two zeroes according to the question,
As we know, the condition of quadratic to have two different values of x is,
0 < √(b²-4ac)
Where,
a = 3
b = 7
c =m
Putting all the values,
√(7²-4(3)(m)) > 0
Squaring both sides,
7²-4(3)(m) > 0
49-12m > 0
49/12 > m.
So, the graph will have two intercepts if m < 49/12.
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12+212+25,432*5,000+
Answers
Answer:
127160224
or use a calculator
A 2-column table with 4 rows. The first column has entries glass, baby oil, maple syrup, wax. The second column has entries 2.40 grams per centimeter cubed, 0.83 grams per centimeter cubed, 1.37 grams per centimeter cubed, 0.93 grams per centimeter cubed.
Use the information in the table to predict whether each substance will sink or float in water. Note that the density of water is 1.0 g/cm3.
Glass:
Baby oil:
Maple syrup:
Wax:
Answers
The Glass and Maple syrup will sink , Baby Oil and Wax will float in water.
We are provided with the following data mentioned below:
Glass Baby oil Maple syrup Wax
2.40 0.83 1.37 0.93
The density of water = 1.0 [tex]g/cm^{3}[/tex]
The material with the lower density floats and the material having higher velocity sinks. As the density of glass is 2.40 [tex]g/cm^{3}[/tex] which is larger than the density of water , so glass will sink in water. As the density of baby oil is 0.83 [tex]g/cm^{3}[/tex] which is less than the density of water , so glass will float in water.
As the density of Maple syrup is 1.37 [tex]g/cm^{3}[/tex] which is larger than the density of water , so Maple syrup will sink in water. As the density of Wax is 0.93[tex]g/cm^{3}[/tex] which is less than the density of water ,so Wax will float in water.
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Answer:
Step-by-step explanation:
what is the correct order of operations for the expression below
Answers
Given:
[tex](7-4)\div(5-2)[/tex]Required:
To choose the correct order of operations for the given expression.
Explanation:
Consider the given exprsesion
[tex](7-4)\div(5-2)[/tex]Here subtract 4 from 7, subtract 2 from 5, and divide the first difference by the second.
Final Answer:
Subtract 4 from 7, subtract 2 from 5, and divide the first difference by the second.
Graph the following function.
f(x)=2(x-2)²-4
Answers
The graph of the given expression f(x)=2(x-2)²-4 is shown (refer to the graph attached below.)
What is a graph?In mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way. The relationships between two or more things are frequently represented by the points on a graph. Charts and graphs come in a variety of styles.Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types. A graph's function representation can be determined using the vertical line test. All points with a certain x value are included in a vertical line. Output for a given input x value is represented by the y value of the point on a graph where a vertical line intersects it.So, f(x)=2(x-2)²-4:
Now, graph the function f(x)=2(x-2)²-4 as follows.(Refer to the graph attached below)Therefore, the graph of the given expression f(x)=2(x-2)²-4 is shown (refer to the graph attached below.)
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what is this answer i need it asap!
Answers
Answer:
The answer is 3.375
Step-by-step explanation:
You just multiply 1.5 by itself 3 times
Consider the rectangle with width 20 in and length 26 in, write a ratio of the width to length
Answers
The ratio of the width of the rectangle to the length of the rectangle is 10/13
We are provided with the rectangle. The dimensions of the rectangle are mentioned below;
Width of rectangle = 20
Length of rectangle = 26
We were asked to calculate the ratio of width of the rectangle to the length of the rectangle. So, to calculate the ratio of width of the rectangle to the length of the rectangle we need to divide the width of rectangle to the length of the rectangle as mentioned below;
( Width of rectangle/Length of rectangle ) = 20 / 26
( Width of rectangle/Length of rectangle ) = 10/13
So, we can finally conclude that the ratio of width of the rectangle to the length of the rectangle is 10/13 .
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If you roll a die, find the probability that you: (Enter your answers in exact form or round to 3 decimalplaces.)(a) roll at least 4 or an odd number,Answer:(b) roll an even number or a number at most 5.Answer:
Answers
A.
The question asks us to find the probability of getting at least 4 or an odd number after throwing a die.
This is easily gotten using the OR probability of two events which states:
[tex]\begin{gathered} P(A\text{ OR B) = P(A) + P(B) - P(A AND B)} \\ \text{if A = rolling at least 4} \\ B\text{ = rolling odd number,} \\ \\ P(\text{rolling at least 4 OR rolling odd number) = } \\ P(\text{at least 4) + P(odd number) - P(at least 4 AND odd number)} \end{gathered}[/tex]To get at least 4, it means the possible values we can have are: 4, 5, 6.
To get an odd number, it means the possible values we can have are: 1, 3, 5.
From both set of possibilities, 5 is common. We need to subtract the probability of getting a 5 in both situations to prevent duplication.
Thus, we can compute each probability:
[tex]\begin{gathered} P(any\text{ number)= }\frac{1}{6} \\ \\ P(at\text{ least 4)= P(4) OR P(5) OR P(6) = P(4) + P(5) +P(6)} \\ \therefore P(at\text{ least 4)= }\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{3}{6} \\ \\ P(\text{odd number) = P(1) OR P(3) OR P(5) = P(1)+P(3)+P(5)} \\ \therefore P(\text{odd number)= }\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{3}{6} \\ \\ P(\text{at least 4 AND odd number) = }\frac{1}{6} \\ \\ \\ \therefore P(\text{at least 4 or odd number)=}\frac{3}{6}+\frac{3}{6}-\frac{1}{6}=\frac{5}{6} \end{gathered}[/tex]Therefore, the probability of getting at least 4 or an odd number is 5/6
B:
This part of the question asks us to find the probability of rolling an even number or a number at most 5.
We, once again, take a look at the possibilities to solve this question.
Possibilities of getting an even number are: 2, 4, or 6
Possibilities of getting at most 5 are: 1, 2 , 3, 4, 5.
Therefore, we can compute the probabilities as:
[tex]undefined[/tex]Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
h(x) = x−1⁄3 (x − 12)
Answers
The critical value of the given function is = -11/2
The x values for which f'(x) = 0 are the crucial values of a function f(x).
The function in this quandary is:
h(x) = x−1⁄3 (x − 12)
The derivative is discovered using the quotient rule as follows:
[tex]h(x) = \frac{x - 1}{3(x - 12)} \\\\h'(x) = \frac{ (x-1) (3x - 36)' - (x - 1)'(3x - 36)}{(3x - 36)^{2} }\\\\h'(x) = \frac{ (x-1) (3) - (-1)(3x - 36)}{(3x - 36)^{2} }\\\\On equating it to 0\\\\\frac{ (x-1) (3) + 1(3x - 36)}{(3x - 36)^{2} } = 0\\\\3x - 3 + 3x + 36 = 0\\\\6x + 33 = 0\\\\x = \frac{-11}{2}[/tex]
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Assume the annual day care cost per child is normally distributed with a mean of $8000 and a standard deviation of $1500. In a random sample of 300 familles, how many pay morethan $6440 annually for day care per child?Of the 300 families, approximately pay more than 56440 annually for day care per child(Round to the nearest whole number as needed.)
Answers
Let's begin by listing out the information given to us:
Mean = $8,000, SD = $1,500
In a sample of 300, how many pay more than $6440?
Arc Length S. Central Angle 0 82 miles. 135°Find the radius and radians r of a circle with an arc length s and a central angle 0.
Answers
Central angle of 135 degrees = 135 (Pi/180) = (3/4)Pi = 2.356 radians
First answer:
Central angle = 2.356 radians
Arc lenght = 2 Pi r (angle/360), in this case:
82 = 2 Pi r (135/360) = 2 Pi r (3/8) = (3/4) Pi r
82 = (3/4) Pi r
r = 82/(3/4)Pi = 82/2.35619449
r = 34.80188089
Second answer:
Radius = 34.8 miles
Which expression is equivalent to (sin 2θ)(sec2θ)? 2sin θ sin θ tan θ 2tan θ
Answers
Answer:
Explanation:
Here, we want to get the expression that is equivalent to the given expression
We have this as follows:
[tex]\begin{gathered} \text{ sec 2}\theta=\text{ }\frac{\sec^2\theta}{2-\sec^2\theta} \\ \\ \sin 2\theta\text{ = 2sin}\theta\cos \theta \end{gathered}[/tex]Now, we can rewrite the overall expression as:
[tex]undefined[/tex]Thad needs to buy dirt for his children's playground. The dirt costs $15 per ton, and there is a delivery cost of $12 with each order. What types of numbers are possible in the domain? -All positive rational numbers -All rational numbers greater than 15 -All positive rational numbers less than 12 -All rational numbers
Answers
The domain is the set input values, it means the number of tons that can be deliver.
The type of numbers that are possible are the positive rational numbers. This is because you can order 1, 2, 2.5, 1/3 tons but you can not order -6, -4.4 or -0.3 tons.
It means that the type of numbers that are possible for the domain are the possitive rational numbers.
Which equation has a constant of proportionality equal to 1? Choose 1 answer: A y 10 1 11 B y 7 8 3 y = 15 D y = 2
Answers
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constan of proportionality
therefore
in this problem
the answer is the option Dy=x
because, the value of k =1
You are trying to memorize a speech for your public speaking class. After 1 day, you memorized 200 words. Each of the following days, you memorized an additional 30 words.
Use the given information to write a linear equation in point-slope form. Then use the equation to find the number of words will you have memorized after 8 days.
__words
can someone help me find the formule pls
Answers
The linear equation in point-slope form of the given condition is y = 30x + 170. The number of words after 8 days will be 410.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
Let's represent the number of days by x and the number of words by y.
At day 1 (x = 1) ⇒ Number of words (y = 200)
At day 1 (x = 2) ⇒ Number of words (y = 230)
The point-slope form of a linear equation is given as,
y = mx + c
Where m is the slope, while c is the y-intercept.
Substitute,(1,200) in y = mx + c
200 = m(1) + c
Now slope m = (230 - 200)/(2 - 1) = 30
200 = 30(1) + c
c = 170
Therefore, the equation become,
y = 30x + 170
The number of words after 8 days will be,
y = 30(8) + 170 = 410
Hence "The linear equation in point-slope form of the given condition is y = 30x + 170. The number of words after 8 days will be 410".
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20 PTS GET MAKED BRAINLIEST IF CORRECT
Answers
a) the probability that event A occurs but event B does not occur = 0.33
b) the probability that either B occurs without A occurring or A and B both occur = 0.04
In this question, we have been given two mutually exclusive events A and B.
event A has probability 0.33 and the event B has probability 0.04
P(A) = 0.33 and P(B) = 0.04
We need to compute the probability that event A occurs but event B does not occur.
i.t., to find = P(A ∩ B')
We know that, P(A ∩ B') = P(A) - P(A ∩ B)
For mutually exclusive events, P(A ∩ B) = 0
So, P(A ∩ B') = P(A)
P(A ∩ B') = 0.33
Also, we need to compute the probability that either B occurs without A occurring or A and B both occur.
P(B ∪ A') + P(A ∩ B)
= P(B) + 0
= 0.04
Therefore, a) the probability that event A occurs but event B does not occur = 0.33
b) the probability that either B occurs without A occurring or A and B both occur = 0.04
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please answer this anybody
Answers
Answer:
5 is a vertical angle. 1 is a vertical angle. 3 is a corresponding angle.
Step-by-step explanation:
Let me know if i got anything wrong!
it says determine how to rewrite one of the two equations above in the form ax + by=c. where a B and C are consistent so that the sum of the new equation in the unchanged equation from the original system results in an equation of one variable
Answers
Solution
-3x +4y = 24 (1)
6x +2y =-18 (2)
We can multiply equation (1) by 2 and we got:
-6x + 12y = 48
6x +2y =-18
_____________
14 y= 30
y = 30/14= 15/7
And the value of x would be:
x= 4y-24/3
x= (60/7 -24)/3
QUESTION IN ATTACHMENTS
Answers
Answer:
C.
Step-by-step explanation:
Since you are missing a side, use the Pythagorean Theorem:
[tex]a^{2}+b^{2}=c^{2}\\ 5^{2}+8^{2}=c^{2}\\ 25+64=c^{2}\\ 89=c^{2}\\ \sqrt{89}=c Answer[/tex]
Answer:
the answer is C.
[tex] \sqrt{89} [/tex]
Solve for X. 70 degreeright angle 6solve
Answers
ANSWER:
The value of x is 16.49
STEP-BY-STEP EXPLANATION:
We can calculate the value of x by means of the tangent trignometric function, which is the following
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \theta=70\text{\degree} \\ \text{opposite = x} \\ \text{adjacent = 6} \end{gathered}[/tex]Replacing and solving for x:
[tex]\begin{gathered} \tan 70=\frac{x}{6} \\ x=6\cdot\tan 70 \\ x=16.49 \end{gathered}[/tex]
Find the common factors and the highest common factor of each of the following
a. 6, 8 and 10
b. 4, 8 and 12
c. 10, 15 and 20
d. 6, 12 and 24
e. 8, 12 and 16
f. 13, 26 and 39
h. 16, 32 and 40
g. 12, 14 and 16
i. 16, 56 and 64
j. 8,24 and 40
k. 7, 35 and 42
l. 22,44 and 66
Answers
a:2
b:4
c:5
d:6
e:4
f:13
h:8
g:2
i:8
j:8
k:7
l:22
Put in simplest radical form: -√3 + 4√3
Answers
Answer:
3√3
Step-by-step explanation:
You want the simplest radical form of -√3 + 4√3.
Like termsWe can consider these "like terms" in the sense that each is an integer multiple of √3. As such, they can be combined by combining coefficients.
-√3 + 4√3 = (-1 +4)√3 = 3√3
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that
each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 18 couples.
Find the expected number of girls in groups of 18 births
Answers
Answer:
since the method is deemed to have no effect
which means probability of having a girl child is same as having a boy child which is 0.5
Total births = 18
Therefore, expected number of girls in groups should be equal to = 0.5 × 18 = 9
I hope this is helpful
4. A student asks, “If the average income of 10 people is $10,000 and one person gets a raise of $10,000, is the median or the mean changed and, if so, by how much?
Answers
Since we don't know the specific income of each person in the sample, we don't know for sure if the median will change. Nevertheless, the mean will surely raise.
Since the current average income is $10,000, if one of them gets a raise of $10,000, then the sum of all incomes would be $100,000+$10,000=$110,000. And the new average income will be:
[tex]\frac{110,000}{10}=11,000[/tex]Then, the mean increases by $1,000, and we can't say anything about the median.
In the diagram below, the circle has a radius of 25 inches. the area of the unshaded is 500pi in^2Determine and state the degree measure of angle Q, the central angle of the shaded sect
Answers
1) In this question, we are going to make use of the formula for the area of that sector, to find the central angle.
2) So, let's write it out an expression involving the area of a circle, the unshaded area, and the shaded one and then plug into that the given data:
[tex]\begin{gathered} A=\frac{\alpha}{360^{\circ}}\times\pi r^2 \\ A_{Unshaded}+A_{shaded}=A_{Circle} \\ 500\pi+\frac{\alpha}{360}\times\pi r^2=\pi r^2 \\ \\ 500\pi+\frac{α}{360}\pi25^2=25^2\pi \\ \\ 500\pi+\frac{125\piα}{72}=625\pi \\ \\ 500\pi +\frac{125\pi α}{72}-500\pi =625\pi -500\pi \\ \\ \frac{125\pi α}{72}=125\pi \\ \\ \frac{72\times \:125\pi α}{72}=72\times \:125\pi \\ \\ \frac{125\pi α}{125\pi }=\frac{9000\pi }{125\pi } \\ \\ α=72^{\circ} \\ \\ \end{gathered}[/tex]Thus, the centra angle of that shaded area is 72º
Solve for brainliest and 20 points
Answers
Answer:
x = 50
Step-by-step explanation:
50 x 3 - 15 = 135
an octagon has 8 sides & 8 angles. 135 x 8 = 1,080 which is the amount of degrees an octagon equals.
Answer:
50
Step-by-step explanation:
Total angles in an octagon is 1080
Because there are 8 sides you must divide 1080/8 to find the angle of one side ... 1080/8 = 135
3x-15=135
1) 135+15 = 150
2)150/3=50
Hope this helps, have a great day!