Answer:
Step-by-step explanation:
Hello!
The box plot is a graph that shows the summary of a data set.
If for example the graphic is on the side:
Box
The left limit of the box is determined by the first quantile of the data set Q₁= 57
The right limit of the box is determined by the third quantile Q₃= 112
The vertical line inside the box represents the second quantile or median Me= 88
Depending on of the symmetry of the distribution you may find it in the middle of the box (symmetrical distribution), closer to the left limit (right skewed) or closer to the right limit of the box (left skewed)
Whiskers
The whiskers of the graphic are a line between the first quantile and the minimum value and the third quantile and the maximum value.
Left whisker goes from Q₁ to the minimum value min= 40
Right whisker goes from Q₃ to the maximum value max= 120
I hope this helps!
Answer:
for the people who don't understand, its A
Step-by-step explanation:
If I mix 5 gallons of p% boric acid with 5 gallons of water, what is the concentration of the mixture?
Answer: The concentration of the mixture is 0.5 p % .
Step-by-step explanation:
Given: 5 gallons of p% boric acid is mixed with 5 gallons of water.
Amount of boric acid = p% of 5 gallons
[tex]=\dfrac{p}{100}\times5\text{ gallons}= 0.05p\text{ gallons}[/tex]
Total solution : 5 +5 = 10 gallons
then, the concentration of the mixture = [tex]\dfrac{\text{Amount of boric acid in solution}}{\text{Total solution}}\times100[/tex]
[tex]=\dfrac{0.05p}{10}\times100\\\\=0.5p[/tex]
Hence, the concentration of the mixture is 0.5 p % .
Answer:
0.5p% is the answer
The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model Upper A equals 5 comma 500 e Superscript 0.065 t Baseline . How much did you initially invest in the account?
Answer:
initial investment in the account is 5500.
Step by step Explanation:
exponential growth model provide details of what happens when the same number is multiplied over and over again, it's applications can be found in economics and science generally.
Exponential models gives situations when the rate of change of a particular thing is directly proportional to how much of that thing is.
the given equation becomes A = 5500 * e^(0.065* T)
But an exponential growth equation can be expressed in this form F = P * e^(RT)
Where F = the future value
P = the present or initial value
R = interest rate per time period
T = number of time periods
From the given equation in the question, we can see that
F = A which is the future value
P = 5500 which is the present or initial value.
R = 0.065 which is interest rate per time period
Therefore, your initial investment in the account is 5500.
WILL MARK BRAINLEST
Drag each scenario to show whether the final result will be greater than the original
value, less than the original value, or the same as the original value.
Options:
An 80% increase followed by a 40% decrease
A 33 1/3% decrease followed by a 50% increase
A $25 increase followed by a $30 decrease
A 50% decrease followed by a 100% increase
A 20% increase followed by a 25% decrease
And they go into the categories that are...
Same as the original
Less than the original
And
Greater than original
Answer:
Let x be the original number. Also, please note that a percentage can be written as a decimal(54%=0.54), and that a percentage increase is the percent +1(A 54% increase is x*1.54), and that a percentage decrease is 1- the percent(A 54% decrease is 0.46)
1)1.8*0.6x= 1.08x (greater than the original)
2).6666*1.5x=0.9999x (same as original)(.999999 is essentially 1, because .3333 is not equal to 1/3)
3)x+25-30 = x-5 (less than original)
4)0.5*2x=x (same as original)
5)1.2*.75x=.9x (less than original)
Hope it helps <3
Greater than the original.
Same as the original.
Less than the original.
Same as the original.
Less than the original.
Step-by-step explanation:To check all the scenarios, let's say that the original value is 100.
An 80% increase followed by a 40% decrease:
100 * (1 + 0.8) = 100 * 1.8 = 180.
180 * (1 - 0.4) = 180 * 0.6 = 108.
It is greater than the original.
A 33 1/3% decrease followed by a 50% increase:
100 * (1 - 0.33333333) = 100 * 0.6666666667 = 66.666666667.
66.6666666667 * (1 + 0.5) = 66.666666667 * (3/2) = 100.
It is the same as the original.
A $25 increase followed by a $30 decrease:
100 + 25 = 125.
125 - 30 = 95.
It is less than the original.
A 50% decrease followed by a 100% increase:
100 * (1 - 0.5) = 100 * 0.5 = 50.
50 * (1 + 1) = 50 * 2 = 100.
It is the same as the original.
A 20% increase followed by a 25% decrease:
100 * (1 + 0.2) = 100 * 1.2 = 120.
120 * (1 - 0.25) = 120 * 0.75 = 90.
It is less than the original.
Hope this helps!Plot the points A(−2, − 2), B(4, −2), ( 8, 3) and D(−3, 3 ) on the Cartesian plane. Join them in order and identify the figure so formed. Join AC and BD. Also write the coordinates of the points of intersection of both the diagonals with the X-axis as well as the Y-axis.
Answer:
The shape formed is trapezium
Step-by-step explanation:
Diagonal BD point of intersection with the y-axis = (0, 9) ,
Point of intersection of diagonal BD with the x-axis = (1.2, 0)
Diagonal AC point of intersection with the y-axis = (2, 0),
Point of intersection of diagonal AC with the x-axis = (0, 1)
Length of segment DC = 10.99 ≈ 11
Length of segment AB = 6.04
Length of segment DA = 5.13
Length of segment CA = 6.38
The perimeter of the formed trapezium = 11 + 5.13 + 6.38 + 6.04 = 28.55
The area of the trapezium = 1/2*(sum of parallel sides)*distance between the parallel sides
The parallel sides are DC and AB
The area of the trapezium = 1/2*(6.04+11)*5 = 42.6 unit.
A box contains 6 red, 3 white, 2 green, and 1 black (total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting at least two white balls?
Answer:
10
Step-by-step explanation:
12 total and 3 whites
there is 10 11 and 12.
A section of a book fell out of it. The first page is numbered 35 and the last page is numbered 74. How many pages fell out?
Answer:
43
Step-by-step explanation:
Frieda worked 26 hours 13 minutes last week. She earns $18.75 per hour. What is Frieda's pay for this work period? Round your answer to the nearest hundredth.
Answer:
$491.56
Step-by-step explanation:
Total number of hours worked by Frieda = 26 hours 13 minutes
lets convert 13 minutes to hour
60 minutes = 1 hour\
1 minutes = 1/60 hours
13 minutes = 13/60 hours
Thus,
Total number of hours worked by Frieda = (26 + 13/60) hours
In 1 hours Freida earns = $18.75
in (26 + 13/60) hours Frieda earns = $18.75((26 + 13/60)) = 487.5 + 4.06
in (26 + 13/60) hours Frieda earns = $491.56 (Answer)
Please can someone help
Answer:
a) 0
b) 1
c) 0
Step-by-step explanation:
These are common values from the unit circle but you could also just check with your calculator. Just be sure to set it to degree mode and not radian mode.
Simplify the polynomial expressions by combining like terms, and then multiply the resulting
binomial expressions to find their product.
(6x - 9 - 2x)(8 + 5x - 5)
Answer:
The simplified expression is
20x^2 - 33x - 27
Step-by-step explanation:
(6x - 9 - 2x)(8 + 5x - 5)
We must first rewrite the expression as a product of two binomials.
This can be done by adding like terms
(6x - 9 - 2x)(8 + 5x - 5)
We have,
(4x-9)(5x+3)
Multiplying the resulting binomial expression
(4x-9)(5x+3)
(20x^2+12x-45x-27)
Add the like terms
20x^2-33x-27
The simplified expression is
20x^2 - 33x - 27
Twenty x squared minus thirty-three x minus twenty-seven
Answer:
20x^2 - 33x - 27
Step-by-step explanation:
I don't understand this question. Could someone please help me?
Answer:
its answer is a not b
As in Formula
A=3.14*r^2
A =144pift^2
Answer:
144π square feet
Step-by-step explanation:
The garden is shaped like a circle.
To find the area of it we can use the formula of area of a circle.
The formula for area of a circle is:
πr^2
Plug our values in.
π(12)^2
144π
The area of the garden is 144πft^2
Kelly is a waitress and her average tip rate is 18%. After taking a sample of her tips from a week, she thinks her tip rate is actually higher. The data below is the tip rate for 15 randomly chosen checks (the numbers represent percentage). Assume that tip rates are normally distributed.
18.5 18.2 20 21.3 17.9 17.9 18.1 17.5 20 18
a) Express the null and alternative hypotheses in symbolic form for this claim.
H0 : Select an answer
Ha: Select an answer
b) What is the test statistic. Round to 2 decimals.
c) What is the p-value. Round to 4 decimals p-value =
Answer:
Step-by-step explanation:
From the given information:
the null and alternative hypotheses in symbolic form for this claim can be computed as:
[tex]H_o:\mu = 18 \\ \\ H_a : \mu > 18[/tex]
Mean = [tex]\dfrac{18.5+18.2+20+21.3+17.9+17.9+18.1+17.5+20+18}{10}[/tex]
Mean = 18.74
Standard deviation [tex]\sigma = \sqrt{\dfrac{\sum(x_i - \mu)^2}{N}}[/tex]
Standard deviation [tex]\sigma = \sqrt{\dfrac{(18.5 - 18.74)^2+(18.2 - 18.74)^2+(20 - 18.74)^2+...+(18 - 18.74)^2}{10}}[/tex]
Standard deviation [tex]\sigma[/tex] = 1.18
The test statistics can be computed as follows:
[tex]Z= \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z= \dfrac{18.6- 18}{\dfrac{1.18}{\sqrt{10}}}[/tex]
[tex]Z= \dfrac{0.6}{\dfrac{1.18}{3.162}}[/tex]
Z = 1.6078
Z = 1.61
Degree of freedom = n -1
Degree of freedom = 10 -1
Degree of freedom = 9
Using t - calculator at Z = 1.6078 and df = 9
The P - value = 0.0712
Which of the following Functions is NOT Linear? A:f(x)=x+0.5 B:F(x)=-x+0.5 C: F(x)=x^2-0.5 D: f(x)=0.5x
Answer:
C: F(x)=x^2-0.5
Step-by-step explanation:
When the x is squared it's a parabola. A linear graph is shaped like a straight line, while a parabola is curved inward. I have included a graph of what that function would look like (tap/click on it to see the full graph.)
Answer:
C: f(x) = x² - 0.5Step-by-step explanation:
The grsaph of the linear function is a straight line.
The equation of a line in the slope-intercept fomr is:
y = mx + b
where
m - slope
b - y-intercept
We have:
A: f(x) = x + 0.5
it's a linear function: m = 1, b = 0.5
B: f(x) = -x + 0.5
it's a linear function: m = -1, b = 0.5
C: f(x) = x² - 0.5
it's not a linear function because in the equation is square of x (x²).
The graph of this function is a parabola.
D: f(x) = 0.5x
it's a linear function: m = 0.5, b = 0
F(x)=x^2 what is g(x)
Answer:
B
Step-by-step explanation:
Sorry this is late
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks
Dave and his cousin Emily are picking apples in their grandparents' orchard. Dave has filled 6
baskets with apples and is filling them at a rate of 5 baskets per hour. Emily has 9 full
baskets and will continue picking at 2 baskets per hour. Once the cousins get to the point
where they have filled the same number of baskets, they will carry them to the barn and then
eat lunch. How much fruit will they have picked by then? How long will that take?
Dave and Emily will each have filled
baskets in
hours.
Answer:
It will take 1 hour and they will have 11 baskets
Step-by-step explanation:
Dave
6 + 5h = b
Emily
9 + 2h=b
where h = hours and b = baskets
Setting the equations equal to each other
6+5h = 9+2h
Subtracting 2h from each side
6+3h = 9
Subtracting 6 from each side
3h = 3
Divide by 3
h =1
Then finding b
9+2h = b
9+2 =b
11=b
It will take 1 hour and they will have 11 baskets
Kate begins solving the equation (6x – 3) = (6x – 4). Her work is correct and is shown below. (6x – 3) = (6x – 4) 4x – 2 = 3x – 2 When she adds 2 to both sides, the equation 4x = 3x results. Which solution will best illustrate what happens to x ?
Answer:
x = 0.
Step-by-step explanation:
4x = 3x
4x - 3x = 0
x = 0
Hope this helps!
The best interpretation of the given equation is x = 0
What is the Equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Given that, Kate begins solving the (6x – 3) = (6x – 4). Her work is correct and is shown below. (6x – 3) = (6x – 4)
4x – 2 = 3x – 2 When she adds 2 to both sides, the equation becomes 4x = 3x
After performing the operations, we get,
4x = 3x
This is only possible when x = 0
Hence, the best interpretation of the given equation is x = 0
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The speed at which a bike travels can be determined by the formula s=d/t, where S represents speed, D represents distance, and T represents time. Select yes or no to indicate if the measurement unit given is an appropriate measurement unit for the speed at which a bike travels
Answer:
Yes, No, Yes
Step-by-step explanation:
Yes for m/s which is meters per second.
No for min/ft which is reversed and should be feet per minute.
Yes for km/h which is kilometers per hour.
The correct unit for speed is distance per time.
Answer:
MPH
Step-by-step explanation:
4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced? Answer: A= the cube with side length 6 cm, B= the cube with side length 8 cm, C= the cube with side length 10 cm, D= the cube with side length 12 cm. On one side of the scale : , on the other side of the scale : Which is the odd one out?
Answer:
Step-by-step explanation:
4 solids cubes A, B, C and D have been made with the same material.
Since material is same density of the material (grams per cm³) will be same.
It shows that the weight of the cubes will vary in the ratio of their volumes.
Volume of cube A = 6³ = 216 cm³
Volume of cube B = 8³ = 512 cm³
Volume of cube C = 10³ = 1000 cm³
Volume of cube D = 12³ = 1728 cm³
Therefore, weights of these cubes will be in the same proportion.
Since, Volume of D = Volume of (A + B + C)
1728 = (216 + 512 + 1000)
1728 = 1728
Therefore, weights of A, B, C, D will be arranged in the same way to balance the plates of a scale.
On one side of the scale cubes A, B, and C should be placed and on the the other side of the scale cube D should be placed to balance the scale.
Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us? 37 8 65 76 21 96 46 19 75 72 58 ti 84
Answer:
Mean = 52.09
The range is 88
Variance = 433. 44
Standard Deviation= s= 20.82
Step-by-step explanation:
The mean is obtained by adding all the values and dividing the number values .
Mean = 37+ 8 +65+ 76 +21 +96+ 46 +19 +75+ 72+ 58+ 84/12
Mean = 573/11 = 52.09
The mean gives the average value .
Range is the difference between the highest and smallest value. The highest value is 96 and lowest value is 8
96 - 8 = 88
The range is 88.
The range gives an idea of the spread of values between two points.
The variance can be calculated by
∑x²= 1369+ 64+ 4225+ 5776+ 441+ 9216+ 2116+ 361+ 5625+ 5184+ 3364= 37741
S²= ∑x²/n - ( ∑x/n)²
= ∑37741/ 11 - (52.09)²
= 3431 - 2997.56 = 433. 44
Standard deviation is the square root of the variance
s= √433. 44= 20.82
The large value of standard deviation implies that the observations are scattered widely about the mean. A smaller value indicates that the observations in data set are close to mean.
What is f(x) = 2x2 + 28x – 5 written in vertex form? f(x) = 2(x + 7)2 – 19 f(x) = 2(x + 7)2 – 103 f(x) = 2(x + 14)2 – 14 f(x) = 2(x + 14)2 – 98
Answer:
f(x)=2(x+7)^2-103
Step-by-step explanation:
[tex]f(x)=2x^{2} +28x-5\\=2(x^2+14x)-5\\=2(x^2+2(7)x+7^2-7^2)-5\\=2(x+7)^2-2(49)-5\\=2(x+7)^2-103[/tex]
Answer: B. f(x) = 2(x + 7)² - 103
Step-by-step explanation:
[tex]y=2x^2+28x-5\\\\\\y+5=2x^2+28x\\\\\\y+5=2(x^2+14x+\underline{\quad}\ )\\.\qquad \qquad \qquad \ \ \downarrow\\.\qquad \qquad \qquad \bigg(\dfrac{14}{2}\bigg)^2=7^2 \\\\\\y + 5 + 2(7)^2=2(x^2+14x+\underline{7^2} )\\\\\\y + 5 + 98 = 2(x + 7)^2\\\\\\y+103=2(x+7)^2\\\\\\y=2(x+7)^2-103[/tex]
how do i wright this as a expression? seven and the quotient of z and eight
8÷7=z and z is the answer you got when you divided,that's how I understand the question
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2,−3) B(4,−3) C(4,5) D(2,5) What is the perimeter of rectangle ABCD? please answer URGENT! :)
Answer:
21 unit square
Step-by-step explanation:
First you want to find the length and width of the rectangle using the distance formula:
d=√(x2-x1)²+(y2-y1)²
AB=√(6-3)²+ (-2 - -2)²
AB=√3² + 0
AB=√9
AB=3
BC=√(6-6)²+ (5 - -2)²
BC=√0 + 7²
BC=√49
BC=7
We can find the area by multiplying these two distances together:
A=(3)(7)
A=21 units square.
Hope it helped...... And plz mark BRAINLIEST
Tysm
Which of the following sets contains all roots of the polynomial f(x)=2x^3+3x^2-3x-2?
Answer:
C
Step-by-step explanation:
Given
f(x) = 2x³ + 3x² - 3x - 2
Note that
f(1) = 2 + 3 - 3 - 2 = 0 , thus
(x - 1) is a factor
Dividing f(x) by (x - 1) gives
f(x) = (x - 1)(2x² + 5x + 2) = (x - 1)(x + 2)(2x + 1)
To find the roots equate f(x) to zero, that is
(x - 1)(x + 2)(2x + 1) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x + 2 = 0 ⇒ x = - 2
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
The solution set is therefore
{ - 2, - [tex]\frac{1}{2}[/tex], 1 } → C
Susan has 3 lists, each with 10 numbers. If there are 4 numbers on all three lists and 5 numbers on exactly 2 lists, how many numbers belong to just one list?
Answer:
Susan has 8 numbers belonging to just one list.
Step-by-step explanation:
Susan's 3 lists have 10 numbers each = 10 x 3 = 30 numbers
4 numbers appear on all three lists = 4 x 3 = 12 numbers
The remaining numbers after these 12 = 18 (30 -12)
Then, there are 5 numbers on 2 lists only = 5 x 2 = 10 numbers
The numbers on just one list = 18 - 10 = 8 numbers
Or
List 1 List 2 List 3 Total
Numbers on each list 10 10 10 30
Numbers on 3 lists -4 -4 -4 12
Numbers on 2 lists -5 -5 -0 10
Numbers on 1 list only 1 1 6 8
Find the equation of a line with each of the following characteristics. A) Parallel to the line y = 3x + 5 and has a y-intercept of -1 B) Perpendicular to the line y = 5x - 1 and passes through the point (10, 8) C) Perpendicular to the line y = 1⁄3x + 4 and has an x-intercept of 2.
Answer:
A) y = 3x - 1.
B) y = -1/5x + 10.
C) y = -3x + 6.
Step-by-step explanation:
A) It is parallel, so it will have the same slope of 3. The y-intercept is -1.
So, we have y = 3x - 1.
B) It is perpendicular, so it will have the negative reciprocal slope of -1/5.
To find the y-intercept, put the points into the equation.
8 = -1/5(10) + b
8 = -2 + b
b - 2 = 8
b = 10
So, we have y = -1/5x + 10.
C) It is perpendicular, so the slope will have a negative reciprocal of -3. The x-intercept is 2, so it has a point at (2, 0). We put that into the equation.
0 = -3 * 2 + b
0 = -6 + b
b - 6 = 0
b = 6
So, we have y = -3x + 6.
Hope this helps!
Answer:
Equation of a line is y = mx + c
where m is the slope
c is the y intercept
A).y = 3x + 5
Comparing with the above formula
Slope / m = 3
y intercept = - 1
Since the lines are parallel their slope are also the same
Substituting the values into the formula
We have the final answer as
y = 3x - 1B).y = 5x - 1
Slope / m = 5
Since the lines are perpendicular the slope of the line is the negative inverse of the original line
That's
m = - 1/5
Equation of the line using point (10, 8) is
y - 8 = -1/5( x - 10)
y - 8 = -1/5x + 2
The final answer is
y = -1/5x + 10C).y = ⅓x + 4
Slope / m = ⅓
Since the lines are perpendicular the slope of the line is the negative inverse of the original line
That's
m = - 3
Equation of the line using point (2,0) is
y - 0 = -3( x - 2)
We have the final answer as
y = - 3x + 6Hope this helps you
find the center of the circle (x-2)^2+(y-8)^2=33
Answer:
The center is (2,8)
Step-by-step explanation:
The equation of a circle is written as
(x-h)^2+ (y-k)^2 = r^2
where ( h,k) is the center and r is the radius
(x-2)^2+(y-8)^2=33
The center is (2,8) and the radius is sqrt(33)
Which is the best description of the equivalency of the two expressions? Expression 1 Expression 2 5 x squared minus 2 x minus 4 + 6 x + 3 6 x squared minus 6 x + 6 minus x squared + 10 x minus 7 The two expressions are not equivalent because when x = 2, the two expressions do not have the same value. The two expressions are not equivalent because when they are simplified, they do not have the same coefficients for the x squared and x terms. They are equivalent because the sum of the constants is the same in both expressions. They are equivalent because when x = 2, the two expressions have the same value.
Answer:
The correct option is (D).
Step-by-step explanation:
The two expressions are:
[tex]\text{Exp}_{1}=5x^{2}-2x-4+6x+3\\\\\text{Exp}_{2}=6x^{2}-6x+6-x^{2}+10x-7[/tex]
On simplifying both the expressions we get:
[tex]\text{Exp}_{1}=5x^{2}+4x-1\\\\\text{Exp}_{2}=5x^{2}+4x-1[/tex]
Compute the value of both expressions for x = 2 as follows:
[tex]\text{Exp}_{1}=5(2)^{2}+4(2)-1=27\\\\\text{Exp}_{2}=5(2)^{2}+4(2)-1=27[/tex]
The value of both expressions are same for x = 2.
Thus, the correct option is:
"They are equivalent because when x = 2, the two expressions have the same value."
Answer:
d
Step-by-step explanation:
Lines $m_{1}$, $m_{2}$, $l_{1}$ and $l_{2}$ are coplanar, and they are drawn such that $l_{1}$ is parallel to $l_{2}$, and $m_{2}$ is perpendicular to $l_{2}$. If the measure of angle 1 is 50 degrees, what is the measure in degrees of angle 2 in the figure below?
Answer: 140 degrees
Step-by-step explanation:
Because m2 is perpendicular to l1, the bottom angle made from m2 and l1 is a right angle = 90 degrees. The angle vertical to 1 = 50 degrees. Thus, the angle made from both of these is equal to 140 degrees. Because l1 is parallel to l2, <2 is congruent to this angle, and thus equals 140 degrees.
Wow, that would be much easier if the angles were labeled.
Hope it helps <3
Answer:
angle = 140 degrees
Step-by-step explanation:
Given:
All lines coplannar.
L1 || L2
m2 perpendicular to L1
angle 1 = 50 degrees
Solution
Refer to attached diagram
angle 4 = 90 degrees ........... given
angle 3 = 180 - angle 4 - angle 1 = 180 - 90 - 50 = 40 degrees .... angles on a line
angle 2 + angle 3 = 180 degrees ............. sum interior angles between parallel lines L1 and L2
=>
angle 2 = 180 - angle 3 = 180 - 40 = 140 degrees.
How many pairs of points are reflections across the x-axis?
A)1
B)2
C)3
D)4
Answer:
C. 3
Step-by-step explanation:
C&D, A&F, K&J
The pairs of points are reflections across the x-axis will be 3. The correct option is C.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
In the given graph number of points is given in all four quadrants. The reflections of the points across the x-axis will be of the points C and D, A and F, K and J.
Therefore, the pairs of points that are reflections across the x-axis will be 3.
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find the value of x and y if the distance of the point (x,y) from (-2,0) and (2,0) are both 14 units.
Answer:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex] are both 14 units from points (-2, 0) and (2, 0).
Step-by-step explanation:
distance formula
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
We want the distance, d, from points (-2, 0) and (2, 0) to be 14.
Point (-2, 0):
[tex] 14 = \sqrt{(x - (-2))^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
Point (2, 0):
[tex] 14 = \sqrt{(x - 2)^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
We have a system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
Since the right sides of both equations are equal, we set the left sides equal.
[tex] \sqrt{(x + 2)^2 + y^2} = \sqrt{(x - 2)^2 + y^2} [/tex]
Square both sides:
[tex] (x + 2)^2 + y^2 = (x - 2)^2 + y^2 [/tex]
Square the binomials and combine like terms.
[tex] x^2 + 4x + 4 + y^2 = x^2 - 4x + 4 + y^2 [/tex]
[tex] 4x = -4x [/tex]
[tex] 8x = 0 [/tex]
[tex] x = 0 [/tex]
Now we substitute x = 0 in the first equation of the system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(0 + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{4 + y^2} = 14 [/tex]
Square both sides.
[tex] y^2 + 4 = 196 [/tex]
[tex] y^2 = 192 [/tex]
[tex] y = \pm \sqrt{192} [/tex]
[tex] y = \pm \sqrt{64 \times 3} [/tex]
[tex] y = \pm 8\sqrt{3} [/tex]
The points are:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex]
Select the statements that are true for the graph of y=−(x−0.5)^2 +9 . Choose all correct statements. The vertex is (−0.5,9) . The graph has a maximum. The graph has a minimum. The vertex is (0.5,9) .
Answer:
The second and fourth statements are correct.
Step-by-step explanation:
We are given the function for the graph of:
[tex]y=-(x-0.5)^2+9[/tex]
Note that this is a quadratic function in its vertex form, given by:
[tex]y=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
Rewriting our given equation yields:
[tex]\displaystyle y = (-1)(x-(0.5))^2 + (9)[/tex]
Therefore, a = -1, h = 0.5, and k = 9.
Therefore, the vertex of the graph is at (0.5 ,9).
Because the leading coefficient is negative, the parabola opens downwards.
Therefore, the parabola has a maximum value.
In conclusion, the second and fourth statements are correct.
1. the vertex is (0.5, 9)
2. it has a maximum.