Sandy was given this function. f(x)=3x2−24+1/3 She used the method of completing the square to rewrite the function. In this second step of her process, r and s are real numbers. f(x)=3(x2−8x+r)+1/3+s What are the values of r and s? Enter your answers in the boxes.
Answer:
[tex]r = 16[/tex], [tex]s = -48[/tex]
Step-by-step explanation:
The values of [tex]r[/tex] and [tex]s[/tex] can be found with the help of algebraic manipulation on the second-order polynomial described on statement:
[tex]f(x) = 3\cdot x^{2} - 24\cdot x + \frac{1}{3}[/tex]
[tex]f(x) = 3\cdot (x^{2} - 8\cdot x) + \frac{1}{3}[/tex]
[tex]f(x) = 3\cdot (x^{2} - 8\cdot x + 16 - 16) + \frac{1}{3}[/tex]
[tex]f(x) = 3\cdot (x^{2}-8\cdot x + 16) + \frac{1}{3} - 48[/tex]
By comparing each expression, the results are presented below:
[tex]r = 16[/tex], [tex]s = -48[/tex]
Prove that DJKL~ DJMN using SAS Similarity Theorem. Plot the points J (1,1), K(2,3), L(4,1) and J (1,1), M(3,5), N(7,1). Draw DJKL and DJMN.
Answer and Step-by-step explanation: The triangles are plotted and shown in the attachment.
SAS Similarity Theorem is by definition: if two sides in one triangle are proportional to two sides of another triangle and the angles formed by those sides in each triangle is congruent, the triangles are similar.
For the triangles on the grid, we know that ΔJKL and ΔJMN have a congruent angle in J as shown in the image. To prove they are similar, we find the slope of sides KL and MN:
Slope of KL:
slope = [tex]\frac{y_{K} - y_{L} }{x_{K} - x_{L} }[/tex]
slope = [tex]\frac{3-1}{2-4}[/tex]
slope = -1
Slope of MN:
slope = [tex]\frac{y_{N} - y_{M} }{x_{N} - x_{M} }[/tex]
slope = [tex]\frac{1-5}{7-3}[/tex]
slope = -1
Since the slopes of KL and MN are the same and the angle is congruent, we can conclude that ΔJKL~ΔJMN.
Construct a histogram to display for each given data set.
The data for the circumferences of the pumpkins in the Jeffiers' family pumpkin crop are 22.1, 35.6, 15.8, 36.9, 40.0, 28.5, 38.4, 20.4, 25.8, 34.1, 39.9, 42.2, 24.3, 22.7, 19.8, 27.9, 22.2, 34.3, 40.4, 20.6, 38.2, and 18.1. Use 10 sx < 20 as the first interval.
Answer:
See attachement
Step-by-step explanation:
The interval 0-20 on vertical axis will be skipped on paper graph and graph will start from 20.
Write a word problem that represents this equation 5s+6=46
Answer:
max buys 5 packs of 8 stickers for his class. Then he buys 6 additional stickers. How many stickers did he buy in total?
Step-by-step explanation:
A circle has a center at (4, -7) and a radius of 4 units.
Write the equation of the circle.
Which one is the right answer below-
Answer:
The third one
Step-by-step explanation:
The equation for a circle is [tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
(h, k) is the center
A sample space consists of 80 separate events that are equally likely. What is the probability of each? A sample space consists of 80 separate events that are equally likely. What is the probability of each?
Answer:
1/80
Step-by-step explanation:
The probability of selecting each of the event in the sample space is; 1/80
How to Find the Probability?We are given;
Sample Space = 80 separate events
Now, we are told that each event is equally likely to be selected.
Thus;
Probability of selecting each event = 1/80
Read more about Probability at; https://brainly.com/question/251701
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Isaiah was given a gift card for a coffee shop. Each morning, Isaiah uses the card to buy one cup of coffee. Each cup of coffee costs $2.50 and after buying 16 cups of coffee, the card had a $5 remaining balance. Write an equation for A(x),A(x), representing the amount money remaining on the card after buying xx cups of coffee.
Answer:
$45-$2.50xx
Step-by-step explanation:
Let first of all determine the original amount on the gift card as follows
amount utilized=$2.50*16=$40
balance left after utilizing $40=$5
original amount on the gift card=amount utilized+balance left=$40+$5=$45
if xx cups of coffee is purchased ,the amount utilized would be xx*$2.50
i.e $2.50xx
The equation for the amount left would total amount on the gift card minus the $2.50xx
equation for amount remaining =$45-$2.50xx
If the questioner has duplicated x,which means he or she meant just x
equation of the amount remaining would=$45-$2.50x
You start with a penny which doubles each day for 30 days. How much money would you have after 30 days?
Answer:
$5,368,709.12
Step-by-step explanation:
Kono Dio Da!!
Answer:
5368709.12
Step-by-step explanation:
i just did this earlier
if anyone know probability stuff pls help w this!!
Answer:
A - 9/34
B - 7/34
Step-by-step explanation:
A girl grabs a lollipop - 9/34 (Event A)
A boy grabs a fruit chew - 7/34 (Event B)
Because there are 34 possibilities in total....
Thanks!
i need the missing blanks .
Answer:
K, (-3.5,-5), E, (3.5, 3)
Step-by-step explanation:
2x² - x-6=0 resuelve
Answer:
x = -3/2 x=2
Step-by-step explanation:
2x² - x-6=0
Factor
(2x ) (x ) =0
6 = 2*3
2*-2 +3 = -1
(2x +3 ) (x -2 ) =0
2x+3 =0 x-2 =0
2x = -3 x=2
x = -3/2 x=2
not good with these someone should help me:( picture included
Answer:
Volume=2/6cu.ft
Step-by-step explanation:
.........................
option B
two integers that multiply to 18 and add to -11
Answer:
-9 and 2
Step-by-step explanation:
Find the hypotenuse of a right triangle with the side length of 7 and an angle of 64 degrees.
Answer:
16.0 (to 3 s.f.)
Step-by-step explanation:
Please see the attached picture for full solution.
3x-2y=2 in slope intercept form
Answer:
y= - 3/2x + 1
Which reason best describes why you can divide any number by 10 by moving the decimal point one place to the left?
1.Dividing a number by 10 is the same as subtracting the number ten times.
2. Dividing by 10 is the same as removing a zero.
3. Moving the decimal point left makes the number smaller.
4. Moving the decimal point one place to the left makes the number 1/10 of its original value.
4 is the answer
The next best is 3
Which is the correct way to model the equation-+8 = 7x+(-8) using algebra tiles?
1 positive x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 positive unit tiles on the right side
8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side
1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side
8 positive x-tiles and 1 negative unit tile on the left side; 8 negative X-tiles and 7 positive unit tiles on the right side
VX
Answer:
Step-by-step explanation:
1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side
Answer:
the answer is c
Step-by-step explanation:
Reduce the following mixed number 2 2/8
Answer:
2 1/4
Step-by-step explanation:
2 2/8
The top and bottom of the fraction can be divided by 2
2 1/4
Can y'all help my little sister i am workin right now so i can't answer but pleaseee.
What is the length of arc S shown below?
units
S
0.4
5
Answer:
Length of arc S:
L = radius x angle (in rad) = 5 x 0.4 = 2
Hope this helps!
:)
Pls help I am stuck on this question
Answer:
153.94 cm
Step-by-step explanation:
a = r^pi squared
r = d/2
7^pi = 21.98
21.98 squared = 153.94 cm
Answer:
see below
Step-by-step explanation:
The diameter is 14 cm
The radius is 1/2 of the diameter
r = d/2 = 7cm
We want to find the area
A = pi r^2 where r is the radius
If pi = 3.142
A = 3.142 ( 7)^2
A =153.958 cm^2
If pi = 3.14
A = 3.14 ( 7)^2
A =153.86 cm^2
Depends on the value of pi
What is 13 - 4 x = 1 - x?
Answer:
x=4
Step-by-step explanation
Answer:
x = 4
Explanation:
Find the surface area of a right cone that has a diameter of 11.2 feet and a height of 9.2 feet. Round your answer to the nearest hundredth.
Answer:
S=288ft^2
Step-by-step explanation:
d=11.2ft, h=9.2ft
r=d/2=11.2/2=5.6
e=√r^2+h^2=√5.6^2+9.2^2
e=10.77ft
s=πr^2+πre
s=π(5.6)^2+π(5.6) (10.77)
s=91.67π
s≈288ft^2
If the slant height of the cone is 10.77 feet and the radius of the base circle is 5.6 feet. Then the surface area of the cone is 189.48 square feet.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The height of the cone is 9.2 feet and the diameter is 11.2 feet. Then the radius will be
r = d/2
r = 11.2/2
r = 5.6
Then the slant height of the cone will be
[tex]l = \sqrt{5.6^2 + 9.2}\\\\l = 10.77 \ \rm ft[/tex]
Then the surface area of the cone will be
[tex]\rm Surface \ area = \pi rl\\\\Surface \ area = \pi \times 5.6 \times 10.77\\\\Surface \ area = 189.48 \ ft^2[/tex]
More about the geometry link is given below.
https://brainly.com/question/7558603
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write the equation of a line through the points (2,3) and (-1,-9)
Answer:
with the points (2,3) and (-1,-9) the answer is y=4x+10
Step-by-step explanation:
you have to do (x1,y1) (x2,y2) thats for each point
the equation to get the slope is y2-y1 divided by x2,x1
to get the y-intercept to plug in one of the points to the slope-intercept equation
y=4x+5
I picked the points (2,3) but you should get the same answer with the other points
3=4(2)=5
3=8+5
3=13
-3+-3
=10 thats your y intercept.
100 POINTS!!!!!! the following stem and leaf plot shows the number of hours that mrs. dixon's students spent on their pre calc work last week. what is the mean absolute deviation for the data
Answer:
11.2467
Step-by-step explanation:
First we need to find the mean
Add up all the data and divide by number of points)
(6+7+8+10+12+13+14+17+17+17+18+19+21+23+24+24+25+27+31+31+32+36+36+39+41+45+45+46+49+50)/30
261/10
26.1
Then to find the mean absolute deviation take each value and find the absolute value from the mean and sum it and then divide by the number of points
((26.1 -6)+(26.1-7)+(26.1-8)+(26.1-10)+(26.1-12)+(26.1-13)+(26.1-14)+(26.1-17)+(26.1-17)+(26.1-17)+(26.1-18)+(26.1-19)+(26.1-21)+(26.1-23)+(26.1-24)+(26.1-24)+(26.1-25)+(27-26.1)+(31-26.1)+(31-26.1)+(32-26.1)+(36-26.1)+(36-26.1)+(39-26.1)+(41-26.1)+(45-26.1)+(45-26.1)+(46-26.1)+(49-26.1)+(50-26.1))/30
11.2467
Answer:
11 16/75
Step-by-step explanation:
Find the mean: sum/n
783/30
26.1
Find individual |x - 26.1| and add them:
|6-26.1| + |7-26.1| + ...... + |50-26.1|
= 20.1 + 19.1 + .... + 23.9
= 336.4
M.A.D = 336.4/30
11 16/75
what is the answer to 10% of 90?
Answer:
9
Step-by-step explanation:
Answer:
10% of 90 is 9
Step-by-step explanation:
10% of a number is like taking 1/10 of the original number.
Jerry has a CD case that contains 4
country music CDs, 1 rock and roll CD,
2 rap CDs, and
3 Tejano CDs.
What is the probability of Jerry
randomly selecting a Tejano CD and the
without replacing it, randomly selecting
a rap CD from his case?
Answer:[tex]\frac{1}{15}[/tex]
Step-by-step explanation:
Given
There are
4 country music CD
1 rock and roll CD
2 rap CD
3 Tejano CD
[tex]\text{Probability that Jerry randomly select a Tejano CD and then a rap CD from his case}=\text{Probability of selecting a Tejano CD}\times \text{Probability of selecting a rap CD}[/tex]
[tex]P=\frac{3}{10}\times \frac{2}{9}[/tex]
[tex]P=\frac{2}{30}[/tex]
[tex]P=\frac{1}{15}[/tex]
The function f(x)=200/x + 10 models the cost per student of a field trip when x students go on the trip. How is the parent function f(x)=1/x transformed to create the function f(x)=200/x + 10
Answer:
Step-by-step explanation:
We need to explain the transformations applied to 1/x to get f(x). We get f by following the following steps.
1. Multiply 1/x by 200 to get the function 200/x. This represents taking the graph of 1/x and expanding it vertically by a factor of 200.
2. Sum 10 units to 200/x. This represents a vertical shift of 10 units to the graph of 200/x.
The probability that Shruti succeeds at any given free-throw is 80%, percent. She was curious how many free-throws she can expect to succeed in a sample of 12 free-throws.
She simulated 25 samples of 12 free-throws where each free-throw had a 0.8, point, 8 probability of being a success.
Shruti counted how many free-throws were successes in each simulated sample. Here are her results:
Use her results to estimate the probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.
Give your answer as either a fraction or a decimal.
Answer:
0.5584 probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.
Step-by-step explanation:
For each free throw, there are only two possible outcomes. Either she makes it, or she does not. The probability of making a free throw is independent of other free throws. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability that Shruti succeeds at any given free-throw is 80%, percent.
This means that [tex]p = 0.8[/tex]
Sample of 12 free throws:
This means that [tex]n = 12[/tex]
Use her results to estimate the probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.
[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{12,10}.(0.8)^{10}.(0.2)^{2} = 0.2835[/tex]
[tex]P(X = 11) = C_{12,11}.(0.8)^{11}.(0.2)^{1} = 0.2062[/tex]
[tex]P(X = 12) = C_{12,12}.(0.8)^{12}.(0.2)^{0} = 0.0687[/tex]
[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) = 0.2835 + 0.2062 + 0.0687 = 0.5584[/tex]
0.5584 probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.
Answer:0.8
Step-by-step explanation:in 5 of the 25 stimulated trials, scrutiny continued federal than 10 successes
What is the mean and median of 25,50,58,54,55
Answer:
median = 58
mean= 48.4
Step-by-step explanation:
to find the mean you add all of the numbers and divide it by 5 in this case
