Answer:
F ................................
Derive the equation of the parabola with a focus at (-5,5) and a directix of y = -1
Answer:
D
Step-by-step explanation:
From any point (x, y) on the parabola the focus and directrix are equidistant
Using the distance formula
[tex]\sqrt{(x+5)^2+(y-5)^2}[/tex] = | y + 1 |
Squaring both sides
(x + 5)² + (y - 5)² = (y + 1)^2 , that is
(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides
(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify
y² + 2y + 1 - y² + 10y - 25 = (x + 5)²
12y - 24 = (x + 5)² ← factor left side
12(y - 2) = (x + 5)² ← divide both sides by 12
y - 2 = [tex]\frac{1}{12}[/tex] (x + 5)² ← add 2 to both sides
y = [tex]\frac{1}{12}[/tex] (x + 5)² + 2
or
f(x) = [tex]\frac{1}{12}[/tex] (x + 5)² + 2 → D
Henry recorded the number of miles he biked each day for a week. His miles were 25, 40,35, 25, 40, 60, and 75,
Enter the data into the statistics calculator,
What is the standard deviation of the miles Henry biked to the nearest tenth?
Answer:
SD = 17.1 miles
Step-by-step explanation:
In order to find the SD we have to calculate mean first
So,
[tex]Mean = \frac{sum}{no.\ of\ items} \\=\frac{25+40+35+25+40+60+75}{7}\\ =\frac{300}{7}\\ =42.86[/tex]
Now mean will be subtracted from each value and the answers will be squared
So,
X X-mean (X-mean)^2
25 -17.86 318.9796
40 -2.86 8.1796
35 -7.86 61.7796
25 -17.86 318.9796
40 -2.86 8.1796
60 17.14 293.7796
75 32.14 1032.9796
So,
Sum of squares = 2042.8572
As SD is the square root of variance
so,
Variance = Sum of squares / number of data values
=2042.8572/7
=291.84
Hence,
[tex]SD = \sqrt{Variance} =\sqrt{291.84} \\=17.083\\to\ the\ nearest\ tenth\\SD=17.1\ miles[/tex] ..
Answer:
17.1
Step-by-step explanation:
The standard deviation of the miles Henry hiked is 17.1
I have nooooo clue, please help
Answer:
case a) [tex]x^{2}=3y[/tex] ----> open up
case b) [tex]x^{2}=-10y[/tex] ----> open down
case c) [tex]y^{2}=-2x[/tex] ----> open left
case d) [tex]y^{2}=6x[/tex] ----> open right
Step-by-step explanation:
we know that
1) The general equation of a vertical parabola is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
a is a coefficient
(h,k) is the vertex
If a>0 ----> the parabola open upward and the vertex is a minimum
If a<0 ----> the parabola open downward and the vertex is a maximum
2) The general equation of a horizontal parabola is equal to
[tex]x=a(y-k)^{2}+h[/tex]
where
a is a coefficient
(h,k) is the vertex
If a>0 ----> the parabola open to the right
If a<0 ----> the parabola open to the left
Verify each case
case a) we have
[tex]x^{2}=3y[/tex]
so
[tex]y=(1/3)x^{2}[/tex]
[tex]a=(1/3)[/tex]
so
[tex]a>0[/tex]
therefore
The parabola open up
case b) we have
[tex]x^{2}=-10y[/tex]
so
[tex]y=-(1/10)x^{2}[/tex]
[tex]a=-(1/10)[/tex]
[tex]a<0[/tex]
therefore
The parabola open down
case c) we have
[tex]y^{2}=-2x[/tex]
so
[tex]x=-(1/2)y^{2}[/tex]
[tex]a=-(1/2)[/tex]
[tex]a<0[/tex]
therefore
The parabola open to the left
case d) we have
[tex]y^{2}=6x[/tex]
so
[tex]x=(1/6)y^{2}[/tex]
[tex]a=(1/6)[/tex]
[tex]a>0[/tex]
therefore
The parabola open to the right
How do I solve this?
Answer:
60.3
Step-by-step explanation:
opposite = 14
adjacent = 8
Tan(B) = opposite / adjacent
Tan(B) = 14 / 8
Tan(B) = 1.75
B = tan-1(1.75)
B = 60.3
An exam was given to a group of freshman and sophomore students. The results are below: Freshman: 106 got A’s, 130 got B’s, and 149 got C’s. Sophomore: 192 got A’s, 118 got B’s, and 168 got C’s. If one student is chosen at random from those who took the exam, find the probability that: a) the student was a sophomore. round to 4 decimal places as needed.
Answer:
106 + 130 + 149 + 192 + 118 + 168 =
863 total students
192 + 118 + 168 = 478 sophomores
P(sophomore) = 478/863
= about .5539
The probability that a randomly chosen student was a sophomore is approximately [tex]\(0.5538\)[/tex] .
To find the probability that a randomly chosen student was a sophomore, we need to calculate the total number of students and the total number of sophomores. Then we use the probability formula:
[tex]\[ P(\text{Sophomore}) = \frac{\text{Number of Sophomores}}{\text{Total Number of Students}} \][/tex]
Step-by-Step Calculation
1. Number of Freshmen:
- A's: 106
- B's: 130
- C's: 149
Total Freshmen:
[tex]\[ 106 + 130 + 149 = 385 \][/tex]
2. Number of Sophomores:
- A's: 192
- B's: 118
- C's: 168
Total Sophomores:
[tex]\[ 192 + 118 + 168 = 478 \][/tex]
3. Total Number of Students:
[tex]\[ 385 + 478 = 863 \][/tex]
4. Probability Calculation:
[tex]\[ P(\text{Sophomore}) = \frac{478}{863} \][/tex]
Let's calculate this probability and round to 4 decimal places:
[tex]\[ P(\text{Sophomore}) \approx \frac{478}{863} \approx 0.5538 \][/tex]
How many times does 4 go into 89
4 goes exactly 22.25 times. That means that it goes in 22 FULL times
Hope this helped!
~Just a girl in love with Shawn Mendes
15. Read the following statement.
Shari rode the bus to work.
What is the negation of this statement?
Shari did not go to work.
Shari may not have ridden the bus to work.
Shari did not ride the bus to work.
Shari rode her bike to work.
Shari did not ride the bus to work.
Answer:
Shari did not ride the bus to work.
Step-by-step explanation:
Shari rode the bus to work. What is the negation of this statement?
Negation of a statement means putting a 'not' in the sentence, to make it overall negative.
So, here, the negation of the above given sentence is -
Shari did not ride the bus to work.
Which functions are even? Check all of the boxes that apply.
f(x) = x4 – x?
f(x) = x2 – 3x + 2
f(x) = (x - 2)
f(x) = x
DONE
Answer:
None of the functions are even.
Step-by-step explanation:
Even FunctionsAn even function is a function that appears unchanged if reflected upon the y axis.
An example of such function is the function y = x^2, which would not appear to have been changed if we were to reflect it across the y axis.
The core property of even functions is that for any even function f(x), the following condition is always true:
[tex]f(x) = f(-x)[/tex]
Thus, if we'd like to identify whether or not a function is even, we can check if that condition is true. If it is, the function is even.
Breaking Down The OptionsNow that we know how to identify even functions, we can apply this method to all of the given options and identify whether or not they're even.
[tex]$\begin{enum}\begin{align}\text{1) }&f(x) = x^4-x\\&f(-x)= (-x)^4-(-x)=x^4+x\\\\&\implies f(x)\neq f(-x) \textbf{ Not even!}\\\\\text{2) }&f(x)=x^2-3x+2\\&f(-x)=(-x)^2-3(-x)+2=x^2+3x+2\\\\&\implies f(x)\neq f(-x) \textbf{ Not even!}\\\\\text{3) }&f(x)=x - 2\\&f(-x)=-x-2=-(x-2)\\\\&\implies f(x)\neq f(-x) \textbf{ Not even!}\\\\\text{4) }&f(x)=x\\&f(-x)=-x\\\\&\implies f(x)\neq f(-x) \textbf{ Not even!}\end{align}\end{enum}$[/tex]
None of the functions are even.
How do u write a function for the reflection across the y axis
The function for the reflection across the y-axis can be written as: f(x,y)=(−x,y)
To reflect a point across the y-axis, we multiply its x-coordinate by -1. This means that if a point has coordinates (x,y), its reflection across the y-axis will have coordinates (−x,y).
We can use this to define a function for the reflection across the y-axis. Let f(x,y) be the function that reflects a point across the y-axis. Then, for any point (x,y), we have:
f(x,y)=(−x,y)
In other words, f(x,y) takes a point (x,y) and returns its reflection across the y-axis.
We can also write this function in terms of components. Let x and y be the coordinates of a point. Then, the reflection of this point across the y-axis has coordinates (−x,y). Therefore, the function for the reflection across the y-axis can be written as:
f(x,y)=(−x,y)
This function takes the coordinates of a point as input and returns the coordinates of its reflection across the y-axis as output.
which expression is equivalent -4×4×4×4×4×4×4×4?
Answer:
[tex]-\underbrace{4\times4\times4\times4\times4\times4\times4\times4}_{8}=-4^8[/tex]
The guy below is correct!
Sumone please help I need helpp
Can someone help me plz
Answer:
The answer is 4.
Step-by-step explanation:
8/3 ÷ 2/3 = 8/3 x 3/2 = 4
4
Step-by-step explanation:Change this to multiplication by flipping the second fraction to [tex]\frac{3}{2}[/tex].
Multiply the numerators. [tex]8*3=24[/tex]
Multiply the denominators. [tex]3*2=6[/tex]
Simplify. Divide 24 by 6. [tex]\frac{24}{6} = 4[/tex]
What is the slope of the line that contains the points (4, 3) and (2, 7)?
Answer:
-2
Step-by-step explanation:
given 2 points on a line (x1, yx) and (x2,y2)
the formula for slope, m = (y2-y1) / (x2-x1)
in this case,
x1 = 4, y1 = 3, x2 = 2, y2 = 7
Hence,
m = (7-3) / (2-4) = 4 / -2 = -2
The slope of the line that contains the points (4, 3) and (2, 7) is -2.
How to estimate the slope of the line?To estimate the slope of the line that has the points (4,3) and (2,7)
Slope formula = y₂ - y₁ / x₂ - x₁
From the question, the points given are; (4,3) and (2,7)
So, x₁ = 4, y₁ = 3, x₂ = 2 and y₂ = 7
Slope of the line = 7 - 3 / 2- 4
= -2
The slope of the line is -2.
therefore, the correct answer is option D. -2.
To learn more about slope equation
https://brainly.com/question/10400643
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If ABD= CBD then AD=CD
Picture is above !
Answer: A. True.
Step-by-step explanation:
Considering the given figure,
Given : ∠ABD ≅ ∠CBD
In Δ ABD and Δ CBD , we have
∠ABD ≅ ∠CBD [given]
∠A≅ ∠C ≅90° [right angle]
BD ≅ BD [Reflexive property]
⇒ Δ ABD ≅ Δ CBD
⇒ AD=CD [By CPCTC]
CPCTC is property of congruent triangle that means that Congruent parts of congruent is congruent.
Hence, the correct answer is "True".
HELP Geometry Find X
Answer: 8
Step-by-step explanation: We are dealing with a 30 60 90 triangle which has special side lengths that I will attach.
The short leg, in this case 4, is half of the hypotenuse in 30 60 90 triangles, therefore x = 8
Answer: Last option.
Step-by-step explanation:
You need to remember the following identity:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
In this case, we can observe that:
[tex]\alpha=30\°\\opposite=4\\hypotenuse=x[/tex]
Now you must substitute these values into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for the hypotenuse. Then:
[tex]sin(30\°)=\frac{4}{x}\\\\(x)(sin(30\°))=4\\\\x=\frac{4}{sin(30\°)}\\\\x=8[/tex]
Help!! The table shows how many males and females
Answer:
frequency of females watching action movie is 99
total participants 479
joint relative frequency of females and action movie = 99/479
your answer is D: divide 99 by 479
Step-by-step explanation:
Answer:
option d is right.
Step-by-step explanation:
Given is a table showing the list of males and females who attended two different movies.
Relative frequency of attending an action movie and being a female is required
First let us find joint frequency
This is represented by 2nd row I column i.e. 99
Relative frequency is obtained by dividing 99 by total of 479
Hence option d is right.
what is the slant asymptote y=x^2-x+1/x+1
Answer:
Step-by-step explanation:
let : f(x) = (x²-x+1)/x+1
limf(x) = lim(x²/x) = limx = - -∞ and limf(x) =+ ∞
x → - -∞ x → +∞
lim/f(x)/ = ∞ ....... x = 1 is the line asymptote
limf(x)/x = 1
x → + -∞
lim (f(x) -x ) = -1 .....so y =x -1 is the second line asymptote
x → + -∞
x → 1
Which is a perfect square?
A.5
B.8
C.36
D.44
Answer:
I believe the answer is C. 36
Step-by-step explanation:
Because a perfect square is everything that equals the same number
Ex: all of the sides of a square is 6, you can't do that with any of the other numbers.
Hope my answer has helped you!
What is the domain of the of the exponential function shown below?
You're right. It is D All real numbers
There are no restrictions to the value of x
The domain of the given function is "All real numbers". So, option D is correct.
What is the domain of a function?The domain of a function is the set of possible values as inputs to the function. The Domain of the exponential function is the set of all real numbers represented by R.Finding the domain of the given function:The given function is f(x) = 2×[tex](\frac{1}{10})^x[/tex]
Since this function has the variable x in the exponent, this is an exponential function.
So, its inputs are of all real numbers. And the domain is {x:x ∈ R}.
Thus, option D is true.
Learn more about the domain and range of a function here:
https://brainly.com/question/1942755
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What is the equation of a line with a slope of 4 and a y-intercept of -3
Answer:
y=4x-3
Step-by-step explanation:
Answer: It would be y=4x-3
Step-by-step explanation:
The format this is under is called slope intercept and we have our slope which is 4 and the Y-Intercept of -3. So the equation for this is y=mx+b and m is your slope and b is your y intercept always. Hope this helps :)
A container of fruit punch serves 16 cups how many quarts of punch are in the container
Answer:
4
Step-by-step explanation:
16 cups = 4 quarts
Please mark brainliest and have a great day!
Answer:
4 quarts
Step-by-step explanation:
We are given that a container of fruit punch serves 16 cups and we are to find the number of quarts that are in a container.
For this, we will use the ratio method.
We know that, 1 cup = 0.25 quarts, so:
[tex] \frac { 1 cup } { 1 6 cups } = \frac { 0 . 2 5 quarts } { x } [/tex]
[tex] x = 1 6 \times 0 . 2 5 [/tex]
[tex]x=4 quarts[/tex]
Therefore, there are 4 quarts of fruit punch in the container.
What device is being shown in the above photograph?
A. Factory scan tool
B. Generic type scan tool
C. PCM programming device
D. Laptop computer adapter
Answer:
option is c)
Step-by-step explanation:
the answer is option is c) PCM programming device.
The device shown in the figure shows is PCM programming device.
PCM programming device is powertrain control module which is used as the mini computer in the cars.
It is used to improve the performance of car.
It is also used to fix the negative bug in the car which can effect the performance of the car.
Which equation represents a line that has a slope of 1/3 and passes through the point (–2, 1)?
Step-by-step explanation:
The pointl-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have
[tex]m=\dfrac{1}{3},\ (-2,\ 1)\to x_1=-2,\ y_1=1[/tex]
Substitute:
[tex]y-1=\dfrac{1}{3}(x-(-2))[/tex]
[tex]y-1=\dfrac{1}{3}(x+2)[/tex] → the point-slope form
Convert to the slope-intercept form:
[tex]y-1=\dfrac{1}{3}(x+2)[/tex] use the distributive property
[tex]y-1=\dfrac{1}{3}x+\dfrac{2}{3}[/tex] add 1 = 3/3 to both sides
[tex]y=\dfrac{1}{3}x+\dfrac{5}{3}[/tex] → the slope-intercept form
Convert to the standard form:
[tex]y=\dfrac{1}{3}x+\dfrac{5}{3}[/tex] multiply both sides by 3
[tex]3y=x+5[/tex] subtract x from both sides
[tex]-x+3y=5[/tex] change the signs
[tex]x-3y=-5[/tex] → the standard form
Convert to the general form:
[tex]x-3y=-5[/tex] add 5 to both sides
[tex]x-3y+5=0[/tex] → the general form
2.
You are going to go to the grocery store. You have $25 to spend. There are several items on your list that you must purchase and some are “for fun” items that you can purchase if you have enough money.
Your list: 2 gallons of milk for $3.50 each; 2 loaves of bread for $2.75 each; 1 pot roast for $10.45 each.
You want to also purchase some candy bars. The candy is on sale for 43 cents each. Ignore sales tax and answer the following questions.
a. Write an equation representing your shopping experience and use x for the number of candy bars.
b. Solve the equation to determine how many candy bars can you purchase?
c. How much change would you have left?
Answer:
Part a) [tex]22.95+0.43x \leq 25[/tex]
Part b) The maximum number of candy bars that you can purchase is 4
Part c) The change would be [tex]\$0.33[/tex]
Step-by-step explanation:
Part a) Write an equation representing your shopping experience and use x for the number of candy bars
Let
x -----> the number of candy bars
we know that
The inequality that represent this problem is equal to
[tex]2(3.50)+2(2.75)+10.45+0.43x \leq 25[/tex]
[tex]22.95+0.43x \leq 25[/tex]
Part b) Solve the equation to determine how many candy bars can you purchase?
[tex]22.95+0.43x \leq 25[/tex]
Solve for x
Subtract 22.95 both sides
[tex]0.43x \leq 25-22.95[/tex]
[tex]0.43x \leq 2.05[/tex]
Divide by 0.43 both sides
[tex]x \leq 2.05/0.43[/tex]
[tex]x \leq 4.8[/tex]
The maximum number of candy bars that you can purchase is 4
Part c) How much change would you have left?
If you purchase 4 candy bars
then
[tex]22.95+0.43(4)=\$24.67[/tex]
therefore
[tex]\$25-\$24.67=\$0.33[/tex]
The equation representing the shopping experience is 3.50*2 + 2.75*2 + 10.45 + 0.43x = 25. The maximum number of candy bars you can purchase is 4. You would have $1.05 in change left.
Explanation:a. The equation representing your shopping experience can be written as: 3.50*2 + 2.75*2 + 10.45 + 0.43x = 25, where x represents the number of candy bars.
b. To determine how many candy bars you can purchase, we need to solve the equation for x. First, combine like terms: 7 + 5.50 + 10.45 + 0.43x = 25. Subtracting 22.95 from both sides gives 0.43x = 2.05. Dividing both sides by 0.43 gives x ≈ 4.77. Since you can't purchase a fraction of a candy bar, the maximum number of candy bars you can buy is 4.
c. To find out how much change you would have left, subtract the total cost of items from your budget. The cost of items is 3.50*2 + 2.75*2 + 10.45 = 23.95. Subtracting this from your budget of $25 gives 25 - 23.95 = $1.05 in change.
Which of the following represents the solution of 3/2 = 3x/2x minus 6/5X
a) x=1/5
b)x=5/9
c)all real numbers
d)no solution
(im pretty bad at math)
Answer: d) No solution.
Step-by-step explanation:
Given the equation:
[tex]\frac{3}{2}=\frac{3x}{2x}-\frac{6}{5x}[/tex]
The denominator of the fractions cannot be zero, then, the Domain is:
[tex]x\neq 0[/tex]
Simplify:
[tex]\frac{3}{2}=\frac{3}{2}-\frac{6}{5x}[/tex]
Subtract [tex]\frac{3}{2}[/tex] from both sides of the equation. Then you get:
[tex]\frac{3}{2}-(\frac{3}{2})=\frac{3}{2}-\frac{6}{5x}-(\frac{3}{2})\\\\0=-\frac{6}{5x}[/tex]
Multiply both sides of the equation by [tex]5x[/tex] ([tex]5x \neq 0[/tex]), then:
[tex](5x)(0)=(-\frac{6}{5x})(5x)[/tex]
Since the multiplication of [tex]5x[/tex] by zero is zero, you get:
[tex]0=-6[/tex] (This is FALSE)
Therefore, since there is no value for the variable that makes the equation true, the equation has NO SOLUTION.
Answer:
CORRECT ANSWER IS 1/5
Step-by-step explanation:
Please help me really urgent !!!
Answer:
C) 360π
Step-by-step explanation:
Note the formula for the volume of Cylinder:
V(olume) = πr²h
π = 3.14
r = radius
h = height of the cylinder
V = (3.14)(6²)(10)
Simplify. First, solve the power, then multiply
V = (3.14)(36)(10)
V = 3.14 * 360
V = 1130.97
However your answer choices all shows π, so just back track a bit.
V = 360π is your answer, or C).
~
Answer:
360π
Step-by-step explanation:
formula for finding the volume of a cylinder is
πr²h
3.14 x 6² x 10 =1130.4
you take the answer you get and divide it to the pi to get the pie answer
1130.4/3.14 = 360π
Hope this helps and if it does mark as branliest answer thx
Which points are solutions to the linear inequality y < 0.5x + 2? Check all that apply.
(–3, –2)
(–2, 1)
(–1, –2)
(–1, 2)
(1, –2)
(1, 2)
Answer:
(-1, -2), (1, -2), (1, 2)Step-by-step explanation:
[tex]y<0.5x+2\\\\\text{Put the coordinates of the points to the inequality, and check it:}\\\\(-3,\ 2)\\2<0.5(-3)+2\\2<-1.5+2\\2<0.5\qquad\bold{FALSE}\\\\(-2,\ 1)\\1<0.5(-2)+2\\1<-1+2\\1<1\qquad\bold{FALSE}\\\\(-1,\ -2)\\-2<0.5(-1)+2\\-2<-0.5+2\\-2<1.5\qquad\bold{CORRECT}\\\\(-1,\ 2)\\2<0.5(-1)+2\\2<-0.5+2\\2<1.5\qquad\bold{FALSE}\\\\(1,\ -2)\\-2<0.5(1)+2\\-2<0.5+2\\-2<2.5\qquad\bold{CORRECT}\\\\(1,\ 2)\\2<0.5(1)+2\\2<0.5+2\\2<2.5\qquad\bold{CORRECT}[/tex]
the average number of cars that pass through an intersection is 45 cars every minute. what is the rate of cars passing through in a day?
Answer:
64,800 cars
Step-by-step explanation:
45 cars times 60 = 2700 cars per hour
2700 times 24 hours = 64,800 cars per day
64,800
Basically i put into the calculator 45 times 60 then that times 24 and thats how i got 64,800.
Necesito ayuda con esto . La suma de dos numero consecutivos es 49 cual es el número menor?
Answer:
24
Step-by-step explanation:
x + x + 1 = 49
x + x = 2x = 48
x = 48 ÷ 2 = 24
Give the domain and range.
a.
domain: {0, 2, 4}, range: {2, 6, 10}
b.
domain: {0}, range: {2}
c.
domain: {2, 6, 10}, range: {0, 2, 4}
d.
domain: {2}, range: {0}
Answer:
a. domain: {0, 2, 4}, range: {2, 6, 10}
Step-by-step explanation:
The given diagram depicts a function.
Let us define function:
A function is a mapping of inputs to output.
The left ones are the input of the function while the right side values are the output of the function.
The domain of the function is the set of values that are given as input to the function while the outputs are called range.
so, in the given question
The domain is: {0,2,4} and the range is: {2,6,10}
So, Option A is correct ..