Answer:
B) The vertex will shift down.
Step-by-step explanation:
In the equation of a parabola, (y - k)² = 4p(x - h), (h, k) is the vertex.
The original parabola's vertex was (3, -2).
In the new parabola, the y-coordinate changed to -10, making the new vertex (3, -10).
So, the parabola's vertex shifted down 8 units from -2 to -10.
How does it do? thank you very much
sorry this subject is physic.
Which function is the inverse of f(x) = -5x-4?
1
4
1
4
O 8(x)3x -
F () --3x+
O F1(x) = -4x+5
Of '(x) = 4x+4
Answer:
The inverse is -1/5x -4/5
Step-by-step explanation:
f(x) = -5x-4
y = -5x-4
Exchange x and y
x = -5y -4
Solve for y
Add 4 to each side
x+4 = -5y
Divide by -5
-1/5x -4/5 = -5y/-5
-1/5x -4/5 = y
The inverse is -1/5x -4/5
Answer:
[tex]\huge\boxed{f^{-1}(x) = -\frac{x+4}{5}}[/tex]
Step-by-step explanation:
[tex]f(x) = -5x-4[/tex]
Replace y = f(x)
[tex]y = -5x-4[/tex]
Exchange values of x and y
[tex]x = -5y -4[/tex]
Solve for y
[tex]x = -5y - 4[/tex]
Adding 4 to both sides
[tex]x + 4 = -5y[/tex]
Dividing both sides by -5
[tex]y = -\frac{x+4}{5}[/tex]
Replace y = [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x) = -\frac{x+4}{5}[/tex]
Please answer ASAP
Randomly pick 6 points from a square of side = 1. Show that you can always find 2 points from these 6 that their distance is less or equal to [tex]\frac{\sqrt{2} }{2} }[/tex]
Randomly pick 5 points from a sphere. Show that you can always find a closed semi-sphere ( half a sphere and boundary) that contains 4 points.
Problem 1.
My thinking is that the furthest you can get is have two points at each opposite corner, so the distance between them is sqrt(2). If we have two other points with this property, then all four corners are filled up. It is possible to pick two points where the distance is 1 unit.
Then a fifth point can be placed at the center such that the distance from it to any of the corners is sqrt(2)/2. We placed the fifth point at the center to try to get as far away as possible from the other four points.
Basically we're trying to find the worst case scenario (leading to the largest distance possible) and seeing how we can fill up the square. This establishes the upper bound. Any other kind of scenario will have a distance less than the upper bound.
===================================================
Problem 2.
For this one, I'm not sure what to make of it. The terminology is a bit strange so I'm not going to be fairly helpful here. Sorry about that.
If I had to guess, I'd assume it has something to do with the fact that a plane is uniquely defined by 3 points. That fourth point is not coplanar with the other three, which helps define the semi-spherical portion. The fifth point is just extra. The points can't be all collinear or else a plane won't form. Though to be honest, I'm still not sure about problem 2. I'd get a second opinion.
All changes saved
2. The ratio of "D"s to "A"s in the school was 8 to 21. If there were 572 As in the school this term, how many Ds
were there?
Answer:
218
Step-by-step explanation:
572/21 = 27.23
8 x 27.23 = 217.9
Answer Check:
21/8 = 2.6
572/218 =2.6
8/21 = .38
218/572 = .38
Solve for x: 2(10-2x) = 4(3x + 1). Write your answer as a fraction.
Answer:
[tex]\boxed{x=1}[/tex]
Step-by-step explanation:
[tex]2(10-2x) = 4(3x + 1)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]20 - 4x = 12x + 4[/tex]
[tex]\sf Subtract \ 12x \ and \ 20 \ from \ both \ sides.[/tex]
[tex]20 - 4x - 12x - 20 = 12x + 4 - 12x - 20[/tex]
[tex]-16x = -16[/tex]
[tex]\sf Divide \ both \ sides \ by \ -16.[/tex]
[tex]\displaystyle \frac{-16x}{-16} =\frac{-16}{-16}[/tex]
[tex]x=1[/tex]
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 1
▹ Step-by-Step Explanation
2(10 - 2x) = 4(3x + 1)
Simple terms are written last:
2(-2x + 10) = 4(3x + 1)
Distributive Property:
-2 * 2x + 2 * 10 = 4 * 3x + 4
x = 1
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Find the equation of the parabola with focus (2, 3) and directrix y = -1.
es
Answer:
Below in bold.
Step-by-step explanation:
Let (x, y) be a point on the parabola. As the graph is a parabola, the distance of this point to the focus is equal to the distance of this point from the directrix. So:
√(( x - 2)^2 + (y - 3)^2) = y - (-1)
Squaring both sides:
(x - 2)^2 + (y - 3)^2 = (y + 1)^2
x^2 - 4x + 4 + y^2 - 6y + 9 = y^2 + 2y + 1
x^2 - 4x + 4 + 9 - 1 = 2y + 6y
8y = x^2 - 4x + 12
y = 1/8(x^2 - 4x + 12)
or we can write it as
y = 1/8x^2 - 1/2 x + 3/2.
A company determined that for each $1 increase in the price of their product, the
number of items sold will decrease by 2. Their predicted weekly profit with a
price increase of x dollars is represented by the function
f(x)= – 2x2+20x +150.
By how many dollars
should they increase the price of their product to
maximize their weekly profits?
15
200
150
5
Answer:
To have maximum profit, the price must be increased by 5,
Step-by-step explanation:
Given that the price increase function is:
f(x) = -2x² + 20x + 150,
For maximum profit, then f(x) = 0.
Putting f(x) = 0, we have
-2x² + 20x + 150 = 0
Or
x² - 10x - 75 = 0
(x + 5)(x - 15) = 0
x = -5
Or
x = 15
Again, differentiating f(x) and equating to zero, we have
-4x + 20 = 0
4x = 20
x = 20/4
= 5
To have maximum profit, the price must be increased by 5,
An isotope of lead, 201Pb, has a half-life of 8.4 hours. How many hours ago was there 70% more of the substance? (Round your answer to one decimal place.) hr
Step-by-step explanation:
half life time-50%-8.4hr
so for 10%- 8.4/5=1.68 hr
now for 70%
1.68 × 7 = 11.76 hrs
to one decimal place - 11.8hrs
11.8 hours ago, there were 70% more of the substance if an isotope of lead has a half-life of 8.4 hours.
What is half-life?Half life is the time that it takes for half of the original value of some amount of a radioactive element to decay.
Half-life period - 50% -8.4hours
so for 10%- 8.4/5 = 1.68 hour
now for 70%
1.68 × 7 = 11.76 hours
To one decimal place - 11.8hours
Hence, 11.8hours is the answer.
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The tee for the fifth hole on a golf course is 355 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
Answer:
184
Step-by-step explanation:
what is 10% of $14,580
Answer:
1458
Step-by-step explanation:
10% * 14580
Change to decimal form
.10 * 14580
1458
Answer:
1458
Step-by-step explanation:
14,580 multiply that by .1
Help me throughout this question please!!!!!!
[tex] \cos(2A)=\cos^2 A-\sin^2A=(\cos A+ \sin A)(\cos A-\sin A)[/tex]
substitute the second term in LHS to get
[tex]{ (\cos A - \sin A)^2 \over \cos(2A))}[/tex]
expand the square, [tex] \frac{1-2\sin A \cos A}{\cos 2A}= \sec2A- \tan 2A[/tex]
([tex] \sin (2\theta)=2 \sin\theta\cos\theta[/tex])
Answer:
Both sides can take the same identity
Step-by-step explanation:
Sec 2A - tan 2A
Express with sin and cos
1/cos (2A) - sin (2A)/cos (2A)
= 1 - sin (2A) / cos (2A)
=
1 - sin (x) = 1-sin (x) = 1 - sin^2 ( x ) / 1 + sin (x)
=
1 - sin ^2 (x) = cos ^2 (x)
=cos ^2 (2A) / 1+sin (2A)/Cos (2A)
simplified
cos (2A) / 1+sin 2A
identity x used = cos 2x = cos ^2 x - sin ^2 x
= 1 + sin (2x) + (cos (x)) + (sin (x))^2
= cos ^2A - sin ^2A / (cos A - sin A) ^2
= cos A - sin A / cos A +sin A
Both sides are true.
what is the value of a?
a. 55
b. 110
c. 50
d. 100
Answer:
a i think
Step-by-step explanation:
Explain in detail the steps for solving multi-step equations.
i just need the steps no problem is included . Thank you sm !
Answer:
1) Get rid of grouping symbols like square brackets and parentheses
2) Simplify both sides of the equation. Combine like terms if possible.
3) Choose where you want to keep the variable because that will help you decide where to place the constant.
4) Eliminate numbers or variables by using opposite operations. Remember that addition and subtraction are opposites and so are multiplication and division.
Step-by-step explanation:
What is 22% of $900?
Answer:
198
Step-by-step explanation:
Of means multiply and 22% as a decimal is 0.22, so multiply 0.22 by 900.
900*0.22=198
Answer:
198
Step-by-step explanation:
22% of 900
of means multiply
22% * 900
Change to decimal form
.22 * 900
198
If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f+g)(x) = 0?
O -4
O-2
O 2
O 4
Answer:
x = -2
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask ;)
The value of the function (f+ g)(x) = 0 then x = -2.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given:
f(x) = x² - 2x and g(x) = 6x + 4
As, (f+g)(x) = 0
x² - 2x + 6x + 4 = 0
x² + 4x + 4 =0
x² + 2x + 2x + 4 = 0
x(x+2) + 2 (x +2 )= 0
(x + 2)(x+2) = 0
(x+ 2)²= 0
x+ 2= 0
x = -2
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Kaitlyn can build a shed in 6 days. Mark can build the same shed in 8 days. Which equation can be used to find d, the number of days it would take Kaitlyn and Mark to build the shed together? Rate (Sheds per Day) Time (Days) Fraction Completed Kaitlyn One-sixth d One-sixth dd Mark One-eighth d One-eighth dd One-sixth d minus one-eighth d = 48 One-sixth d + one-eighth d = 48 One-sixth d minus one-eighth d = 1 One-sixth d + one-eighth d = 1
Answer:
One-sixth d + one-eighth d = 1
Step-by-step explanation:
When they work together, their rates of completion add. They want to build one shed, so the number of sheds being built is ...
(Kaitlyn's sheds per day)×(days Kaitlyn works) +(Mark's sheds per day)×(days Mark works) = 1 shed
(1/6)d + (1/8)d = 1 . . . . matches the last choice
calculate the size of angle x. the sides are 8cm, 11cm and 15cm
Answer:19.93
Step-by-step explanation:
11 x 8 x 15 = 1320
then u would simplify
The value is: angle x is approximately 103.95 degrees.
Here, we have,
To calculate the size of angle x, you can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
In this case, the sides of the triangle are given as follows:
a = 8 cm (adjacent to angle x)
b = 11 cm (opposite to angle x)
c = 15 cm (hypotenuse)
The Law of Cosines states:
c² = a²+ b² - 2ab*cos(x)
Substituting the given values:
15² = 8² + 11² - 2(8)(11)*cos(x)
225 = 64 + 121 - 176*cos(x)
Simplifying:
225 = 185 - 176*cos(x)
Rearranging the equation:
176cos(x) = 185 - 225
176cos(x) = -40
Now, divide both sides by 176 to isolate the cosine term:
cos(x) = -40/176
cos(x) ≈ -0.2273
To find the value of angle x, take the inverse cosine (cos⁻¹) of -0.2273:
x ≈ cos⁻¹(-0.2273)
x ≈ 103.95 degrees
Therefore, angle x is approximately 103.95 degrees.
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3. State the general version of the recursive formula.
72,54, 36, 18,0
Answer:
a(1) = 72
a(n) = a (n-1) - 18
Step-by-step explanation:
This is a simple series of multiplication of 18 . If we divide all the numbers by 18 we get
72/18, 54/18, 36/18. 18/18, 0/18
4 , 3 , 2 , 1 , 0
So we can see that the numbers are in decreasing order as the multiples of 18.
in other words the first term is a= 72
from which we subtract 18 and get 54 and so on.
So the general rule would be
a(1) = 72
a(n) = a (n-1) - 18
Where n and (n-1 ) are subscripts. We are just subtracting 18 from the number to get the answer.
72-18= 54
54-18= 36
36-18= 18
18-18=0
Reflections, rotations, and translations are types of transformations. A reflection flips an image, a rotation spins an image, and a translation slides an image. Draw a shape on a piece of paper and cut it out. Then, flip it, spin it, and slide it. Explain how each transformation affects the size and shape of the image you drew. IDK how to answer this PLS HELP
Answer:
Hey there!
A "flip" can be considered a reflection.
A "spin" is a rotation.
A "slide" is a translation.
None of these transformations change the way a shape looks, or the size of the shape. They only change how the shape is oriented.
Let me know if this helps :)
In this exercise we have to differentiate three geometric terms, in this way we can say that;
Flip is considered a reflection. Spin is a rotation. Slide is a translation.
So in a more in-depth way these geometric terms can be described as:
Flip: the established term, exist a static or exciting concept namely produce by a mirror-reversal of an original across a lying flat point around which something revolves (a fail miserably image happen reflect across the upright point around which something revolves)Spin: When two surfaces bear many point correspondences, they equal. Taken together, the familiarize points and befriend figure create our surface repre-sentation. Because the image era process maybe visualized as a page make go around about the common of a point, the counterpart fashionable our likeness happen named spin-images.Slide: A move smoothly show happen a presentation of a succession of still figure (slides) ahead of a projection screen or photoelectric display symbol, usually fashionable a prearranged series. The changes grant permission exist automatic and repeatedly or they grant permission happen manually controlled by a person who entertains or the witness.See more about geometry at brainly.com/question/7558603
The box plots display the same data set for the number of touchdowns a quarterback threw in 10 seasons of play. Including outlier: A number line goes from 5 to 30. The whiskers range from 5 to 29, and the box ranges from 18 to 26. A line divides the box at 21.5. Excluding outlier: A number line goes from 5 to 30. The whiskers range from 17 to 29, and the box ranges from 19 to 27. A line divides the box at 21. There is an asterisk at 5. Complete the statements describing the effect of the outlier on the measures of variability. The outlier of the data set is . The range of the data set including the outlier is more than the one excluding the outlier. The interquartile range of the data set including the outlier is more than the one excluding the outlier. The outlier had the most effect on the .
Answer:
5
12
0
range
Step-by-step explanation:
i just did it, these are the right answers.
Answer:
5,12,0, and the last answer is range
Step-by-step explanation:
Did it on Edge2021. Hope this helps!
Find the perimeter of the triangle
Answer:
26 units
Step-by-step explanation:
Answer:
657.88 i guess becuz by using pythagoras i got 320 for the hypotenous
Jemma has 24 balls. Out of the 24 balls, 12 are yellow, 4 are pink, and the rest are red. What is the ratio of the number of red balls to the number of balls that are either yellow or pink? arrowRight
Answer:
1 :2
Step-by-step explanation:
12 are yellow, 4 are pink
To find the number of red
24 -12 -4 = 8
There are 8 red balls
We want the ratio of
red: yellow or pink
8 : 12+4
8 :16
Divide each side by 8
8/8 : 16/8
1 :2
Answer:1:2
Step-by-step explanation: 12 yellow + 4 pink= 16
24 balls total minus 16 =8 red balls so 8:16=1:2
Determine what type of model best fits the given situation: The height of a tree twenty feet tall increases by 2 feet per year.
Answer:
linear model
Step-by-step explanation:
This is a linear function. The initial value is 20 ft, and the yearly growth is 2ft/yr. Thus, the function is
height(t) = (20 ft) + (2 ft/yr)t, where t is the number of years.
PLEASE HELP PLEASE WILL MARK BRAINLY
Answer:
Every 18 miles he uses 3 gallons
divide this:
18 ÷ 3 = 6 miles per gallon
30 miles = 30 ÷ 6 = 5 gallons
7 gallons = 7 x 6 = 42 miles
48 miles = 48 ÷ 6 = 8 gallons
10 gallons = 10 x 6 = 60 miles
Hope this helps :D
Given the regular decagon, what is the measure of each numbered angle? A. m∡1 = 72°; m∡2 = 18°; m∡3 = 36° B. m∡1 = 18°; m∡2 = 36°; m∡3 = 72° C. m∡1 = 36°; m∡2 = 72°; m∡3 = 18° D. m∡1 = 36°; m∡2 = 18°; m∡3 = 72°
Answer:
D. m∡1 = 36°; m∡2 = 18°; m∡3 = 72°
Step-by-step explanation:
The 10 central angles are all the same for the regular decagon, so each is 1/10 of 360°. Angle 1 is 36°.
Angle 2 is half of angle 1, since the altitude shown is an angle bisector. Angle 2 is 18°.
Angle 3 is the complement of angle 2. It is the other acute angle in the triangle that has angle 2 marked. Angle 3 is 72°.
The university theater uses a combination of one letter (A - Z) and two digits (0 - 9) to identify their reserved seats. How many reserved seats are
possible using a combination of one letter followed by two digits. EXPLAIN how to solve this problem in your own words.
Answer:
Hey There!! The answer to this is Correct option: 1) 2600 The letter has a total of 26 possible values (from 'a' to 'z'), and each digit has a total of 10 possible values (from 0 to 9).
So, to find the number of reserved seats possible, we just need to multiply the number of possible values of each letter and digit.
We have one letter and two digits, so we have:
26 * 10 * 10 = 2600 possible reserved seats
Thus, Correct option: 1)
Hope It Helped!~ ♡
ItsNobody~ ☆
The total number of combinations of one letter followed by two digits is 2600 option (1) 2600 is correct.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
The missing options are:
1.) 26002.) 2343.) 2604.) 2106We have:
The university theater uses a combination of one letter (A - Z) and two digits (0 - 9) to identify their reserved seats
As we know, in the alphabet(A to Z) there are the 26 letters and total number of digits (0 to 9) is 10
A total number of combinations of letters followed by two digits can be calculated as follows:
As we have one letter and two digits
= 26×10×10
= 2600
, so we have:
26 * 10 * 10 = 2600 possible reserved seats
Thus, the total number of combinations of one letter followed by two digits is 2600 option (1) 2600 is correct.
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Find the percent of change if the original price is $246.95 and the new price is $199.95. Round to nearest tenth of a percent if necessary. Show your work and state whether this is an increase or decrease.
Answer:
Percentage change = 19%Step-by-step explanation:
Since the new price is lesser than the original price the percentage change will be a decrease.
To find the percentage change use the formula
[tex]Percentage \: \: change = \frac{change}{original \: \: quantity} \times 100[/tex]
To find the change subtract the new price from the original price
new price = $199.95
original price = $246.95
Change = $246.95 - $ 199.95 = $47
[tex]Percentage \: \: change = \frac{47}{246.95} \times 100[/tex]
Percentage change = 19%Hope this helps you
HELP ME PLEASE !! A duck paddles 4 yards downstream in 24 seconds. It takes the duck 40 seconds to paddle the same distance upstream. How fast can the duck paddle in still water ? What is rate of the current? Duck speed: _____ Current: ________ And if possible you can show me the steps?
Answer:
1. duck will travel in still water paddles 4 yards = 38,7 sec
up stream speed = 0,63 mph
down stream speed = 0,68 mph
The sum of 4 consecutive integers is 130 what is the third number in the sequence
PLZ HELP!!!
Answer:
33
Step-by-step explanation:
We can write an equation:
x+x+1+x+2+x+3=130
x represents the smallest number of the consecutive integers
By the way, an example of consecutive would be 2, 3, 4, 5 or 10, 11, 12, 13
We can combine like terms from our equation:
4x+6=130
4x=124
x=31
The smallest number is 31. The second number would be 31+1=32, which means the third number is 33!
Hope this helps! :) :)
Answer:
[tex]\huge\boxed{3rd\ number = 33}[/tex]
Step-by-step explanation:
Let the consecutive numbers(Coming one after another) be x, x+1, a+2 and x+3
So,
x+x+1+x+2+x+3 = 130
4x + 6 = 130
Subtracting 6 to both sides
4x = 130-6
4x = 124
Dividing both sides by 4
x = 32
So,
1st number = x = 31
2nd Number = x+1 = 31+1 = 32
3rd number = x+2 = 31+2 = 33
4th number = x+3 = 31+3 = 34
You buy a new computer for $1,500. The value of the computer decreases by 6%
every year. How much is the computer worth after 4 years?
$999.80
$1,171.05
$1,008.50
$1,225.35
Answer:
$1171.05
Step-by-step explanation:
1500 × (1-(6 / 100))⁴
Answer:
Hey there!
Each year, the computer is (100-6), or 94% of it's original value.
Thus, we have:
Original: 1500
First year: 1500(0.94)
Second year: 1500(0.94)(0.94)
Third year: 1500(0.94)(0.94)(0.94)
Fourth year: 1500(0.94)(0.94)(0.94)(0.94)
Fourth year: 1171 dollars.
Hope this helps :)
