let's firstly find the equation of the parabola, bearing in mind that x-intercepts or solutions/zeros/roots means y = 0.
[tex]\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=1\\ k=-9 \end{cases}\implies y=a(x-1)^2-9 \\\\\\ \textit{we also know that } \begin{cases} x=0\\ y=-6 \end{cases}\implies -6=a(0-1)^2-9\implies 3=a(-1)^2[/tex]
[tex]\bf 3=a\qquad \qquad \textit{therefore}\qquad \qquad \boxed{y=3(x-1)^2-9} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{y}{0}=3(x-1)^2-9\implies 9=3(x-1)^2\implies \cfrac{9}{3}=(x-1)^2\implies 3=(x-1)^2 \\\\\\ \pm\sqrt{3}=x-1\implies \pm\sqrt{3}+1=x\implies x= \begin{cases} \sqrt{3}+1\\ -\sqrt{3}+1 \end{cases}\implies x\approx \begin{cases} 2.73\\ -0.73 \end{cases}[/tex]
A customer needs to seed an area 75 feet by 50 feet in size. Each bag of seed can cover 25 square feet of land. How many bags of seed do you need to cover the lot
Answer:
150 bags
Step-by-step explanation:
Given the total area:
The area will be:
=75*50
= 3750 square feet
As it is given that one bag covers 25 square feet. To find the total number of bags we have to find how many 25s will be in 3750 square feet.
So,
Total number of bags = 3750 / 25
= 150 bags
Hence, total number of bags that will be used are 150 ..
Simplify (11+19i)/ (8-5i)
Answer:
To simplify the expression let's multiply and divide by (8+5i) as follows:
[tex]\frac{(11+19i)(8+5i)}{(8-5i)(8+5i)}= \frac{207i-7}{89}= 2.32i - 0.08[/tex]'
Now, we have successfully removed the imaginary number from the denominator.
Which statement is true about the function f(x) = -√x?
A. It has the same domain and range as the function f(x) = √x.
B. It has the same range but not the same domain as the function f(x) = √x.
C. It has the same domain and range as the function f(x) = -√-x.
D. It has the same range but not the same domain as the function f(x) = -√-x.
Answer:
c
Step-by-step explanation:
Need help on number 20
Answer:
vertex: (-2, -1)axis of symmetry: x = -2graph: see belowStep-by-step explanation:
The equation is in vertex form ...
y = a(x -h)² +k . . . . . . . . vertex (h, k) and vertical scale factor "a"
y = (x +2)² -1
so, you can read the vertex coordinates directly from the equation:
(h, k) = (-2, -1)
__
The line of symmetry is the vertical line through the vertex, so has equation ...
x = h
x = -2 . . . . for this parabola
__
The vertex is always a point on the graph.
At x-values ±1 either side of the vertex, the vertical distance from the vertex is "a". Here, that is 1 unit, so the points (-3, 0) and (-1, 0) are on the graph.
At x-values ±2 either side of the vertex, the vertical distance from the vertex is a·2². Here that is 4 units, so the points (-4, 3) and (0, 3) are on the graph.
This is basically what the vertex form of the equation is telling you.
Between 2000 and 2014, the number of twin births in a certain country increased by 15%, to approximately 133975. About how many twin births were there in 2000?
Answer:
116500
Step-by-step explanation:
We are looking for the number of twin births in 2000.
Let the number of twin births in 2000 be x.
The number of twin births in 2000 is 100% of the number of births in 2000 since 100% of something is the entire thing.
The number of twin births went up 15% from 2000 to 2014, so in 2014, the number of twin births was 100% of the number of twin births plus another 15% of the number of twin births.
100% + 15% = 115%
The number of twin births in 2014 was 115% of x.
The number of twin births in 2014 was 133975.
115% of x = 133975
115% * x = 133975
1.15x = 133975
x = 133975/1.15
x = 116500
The number of twin births in 2000 was 116500.
An increase by 15% means 15 added to per cent (per = each; cent=100).
If the population was 100 in the year 2000 then it would be 115 in the year 2014. (adding 15 to 100)
The population was 116500 in the year 2000 and it increased to 133975 in the year 2014.
Let the population be x in the year 2000.
Using ratio and proportion
Year 2000 : Year 2014
100 : 115
x : 133975
Applying cross product rule
x × 115= 100× 133975
x= 100× 133975/115
x= 116500
The population was 116500 in the year 2000 and it increased to 133975 in the year 2014.
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If f(x)=3x - 15', thenNf^(-1)(x)=
Enter the correct answer.
Answer:
[tex]\large\boxed{f^{-1}(x)=\dfrac{1}{3}x+5}[/tex]
Step-by-step explanation:
[tex]f(x)=3x-15\to y=3x-15\\\\\text{exchange x to y and vice versa:}\ x=3y-15\\\\\text{solve for}\ y:\\\\3y-15=x\qquad\text{add 15 to both sides}\\\\3y=x+15\qquad\text{divide both sides by 3}\\\\y=\dfrac{x}{3}+5\\\\y=\dfrac{1}{3}x+5[/tex]
How many names does the angle have? What are those names?
A. 3 names: Z3, ZSTU, ZUTS
B. 3 names: ZT, ZSTU, ZUS
C. 4 names: Z3, ZT, ZSUT, ZUTS
D. 4 names: Z3, ZT, ZSTU, ZUTS
Answer:
4names: z3, zt, zstu, zuts
What is the inverse of the function below?
f(x)=(1/3)^x
The Inverse of the function f(x) = (1/3)^x is derived by swapping x and y and solving for y, resulting in f^-1(x) = log base (1/3) of x.
Explanation:To find the Inverse of a function in the form f(x) = (1/3)^x, you need to interchange x and y and solve for y.
So, the Inverse of the function f(x) = (1/3)^x is first represented as x = (1/3)^y. However, we need to isolate y. We can do this by taking a logarithmic function on both sides. It turns out that y = log base (1/3) of x.
In other words, the inverse of f(x) = (1/3)^x is f^-1(x) = log base (1/3) of x.
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Given a= 108 degree, b=9 and c = 15, use the law of cosines to solve the triangle for the value of A. Round answer two decimal places.
a. 19.13
b. 14.92
c. 19.73
d. 18.53
Answer:
c. 19.73
Step-by-step explanation:
The Cosine rule shows states that:
a²=b²+c²-2bcCos A, where a, b and c are the sides of the triangle and A is the angle at vertex A.
A=108°
b=9
c=15
Substituting with the values above gives:
a²=9²+15²-(2×9×15 Cos 108)
a²=389.4346
a=19.73
Zahra compares two wireless data plans Which equation gives the correct value of n
the number of GB for which Plans A and B cost the same
(G8 means 'gigabytes of data)
Wireless Plan A
No initiate fee and 8$ for each GB
Wireless Plan B
$20 for the
first 2 GB
$6 for each
additional GB
after the first 2
A) 8n = 20 + 60
B) 8n= 20(2n) + 6
C) 8n = 20 + 6(n-2)
D) 8n = 20 + 2n+6
Answer:
8n=20+6(n-2)
Step-by-step explanation:
n is the number of GB
Plan A has no initial fee and charges 8$ per each GB
So A has an equation that is y=0+8n or just y=8n.
Plan B has 20 for the first 2 GB and $6 for each addition GB after the first 2.
So B has an equation that is y=0+20+6(n-2) assuming n is 2 are greater.
So the two equations are y=8n and y=20+6(n-2).
We want Plan A to be the same as Plan B.
So we need to solve:
8n=20+6(n-2).
Let's check our equation:
Distribute:
8n=20+6n-12
Subtract 6n on both sides:
2n=20-12
2n=8
Divide both sides by 2:
n=4
Plan A charges 8 dollars ber GB, so plan A charges 4(8)=32 dollars.
Plan B charges 20 dollars for the first 2GB and 6 dollars for each GB after so we used 4 which means we are spending 20+6(2)=20+12=32 dollars.
They are the amount so n=4 is right.
I am very late to answer this, but I want to help others who struggle on this question! The answer and explanation is in the picture, thank me later! :)
I am confusion pls help me i am sad help
Answer:
A should be the answer
Step-by-step explanation:
ok so first find area of a circle the area of this circle
pi r sqared
the area of the circle is 3.14
since the raduis is diamter ÷ 2
the area of the small rectangle would be 2a sqared
so if i did it right the answer should be A
I could be wrong tho
hope this helped
Calculate the median and mode for the following data set: Data Set = 2, 9, 10, 4, 8, 4, 12
Answer:
The mode is 4 and the median is 8
Step-by-step explanation:
The mode is the number the occurs the most in the set, and as you can see 4 appears twice. The median is the number that lies in the middle of the set when put together from least to greatest. When you write it out it results in 2,4,4,8,9,10,12. As you can see the number 8 lies right in the middle, with three numbers on it's left and three numbers on it's right. Hope this helps :)
Final answer:
median: 8
mode: 4
Explanation:
Calculate the median and mode for a data set, including step-by-step instructions.
Median: To find the median, arrange the data set in numerical order first. As the data set has seven values, the median will be the fourth value, which is 8. Median represents the middle most value of the data
Mode: The mode is the value that appears most frequently in the data set. In this case, the mode is 4 as it occurs twice. Mode represents the maximum frequency.
Question
The nine numbers Jagger and his accomplices identified as occurring more frequently than the others were 7, 8, 9, 17, 18, 19, 22, 28, and 29. Are
these outcomes mutually exclusive if the wheel is spun once? Why or why not?
Answer:
Yes. These outcomes are mutually exclusive; they cannot occur simultaneously in one spin of the wheel.
Step-by-step explanation:
It's the answer trust
Given h(x) = |x-2| Find the following function values:
h(-4)
h(-x+2)
Answer:
6 and x
Step-by-step explanation:
h(-4)
=|-4-2|
=|-6|
=6
.
h(-x+2)
=|-x+2-2|
=|-x|
=x
In a nutshell and thorough explanation, what is MAD? (Mean absolute deviation) --Please do not give me a Khan Academy link. (The video did not help me)
Answer:
The average absolute deviation (or mean absolute deviation (MAD)) about any certain point (or 'avg. absolute deviation' only) of a data set is the average of the absolute deviations or the positive difference of the given data and that certain value (generally central values). It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be the mean, median, mode, or the result of any other measure of central tendency or any random data point related to the given data set. The absolute values of the difference, between the data points and their central tendency, are totaled and divided by the number of data points.
Measures of dispersion
Edit
Several measures of statistical dispersion are defined in terms of the absolute deviation. The term "average absolute deviation" does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well. Thus, to uniquely identify the absolute deviation it is necessary to specify both the measure of deviation and the measure of central tendency. Unfortunately, the statistical literature has not yet adopted a standard notation, as both the mean absolute deviation around the mean and the median absolute deviation around the median have been denoted by their initials "MAD" in the literature, which may lead to confusion, since in general, they may have values considerably different from each other.
Mean absolute deviation around a central point
Edit
For arbitrary differences (not around a central point), see Mean absolute difference.
The mean absolute deviation of a set {x1, x2, ..., xn} is
{\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}|x_{i}-m(X)|.} \frac{1}{n}\sum_{i=1}^n |x_i-m(X)|.
The choice of measure of central tendency, {\displaystyle m(X)} m(X), has a marked effect on the value of the mean deviation. For example, for the data set {2, 2, 3, 4, 14}:
Mean Absolute Deviation (MAD) is a measure of the average distance between each data point and the mean of the dataset. It is calculated by finding the absolute value of the difference between each data point and the mean, and then averaging those differences. MAD is a robust statistic, less sensitive to outliers compared to standard deviation.
Mean Absolute Deviation (MAD) is a statistical measure used to quantify the average deviation of data points from the mean or average of the dataset. To calculate MAD, you follow these steps:
Compute the mean (average) of the dataset by adding up all the data points and dividing by the number of points.Find the absolute differences between each data point and the mean. 'Absolute' means you consider only the magnitude of the differences, not whether they are above or below the mean.Calculate the average of these absolute differences which gives you the MAD.The mean is the sum of all data divided by the number of data points, while the median is the middle value of an ordered dataset. MAD is more robust than standard deviation as it is not affected as much by extreme values. For example, if we have a dataset of exam scores, the standard deviation tells us how scores are spread out from the mean, which could be influenced by extremely high or low scores. On the other hand, MAD gives us a measure of spread that is more resilient to outliers in the data.
Relative Average Deviation (RAD) is similar to MAD, but it expresses the deviation as a percentage of the mean and hence provides a relative measure of spread.
Austin made $168 for 8 hours of work.
At the same rate, how many hours would he have to work to make $252?
Answer:
12 hours
Step-by-step explanation:
If you divide 168 by 8, you get 21 which is the rate that Austin receives for every hour of work. Then divide 252 by 21 to find how many hours he worked and you get the answer, 12.
Which answers are equal to the expression below? Check all that apply PLEASE WILL GIVE BRAINLIEST
Answer:
B., D., E.
Step-by-step explanation:
[tex] \sqrt{9} \cdot \sqrt{100} = [/tex]
[tex] = \sqrt{9 \cdot 100} [/tex] This is choice B.
[tex] = \sqrt{900} [/tex] This is choice E.
[tex] = 30 [/tex] This is choice D.
Find the measure of the remote exterior angle.
Answer:
C.
Step-by-step explanation:
The remote exterior angles are angle x and y
The sum of two interior angles (x +y) is equal to the value of exterior angle (z)
m∠x=(5n-19)°
m∠y=(n+7)°
m∠z=(144-6n)°
Equate as
∠x+∠y=∠z
(5n-19)° +(n+7)°=(144-6n)°
5n-19+n+7=144-6n----------------------collect like terms
5n+n+6n=144+19-7
12n=156---------------------divide both sides by 12 to get value of n
n=156/12= 13°
substitute value of n is equations
∠x=(5n-19)° =(5×13)-19 =65-19=46°
∠y=(n+7)°= (13+7)=20°
Measure of remote exterior angle will be 20°+46°=66° (From the theorem of interior angles and exterior angles)
A 3.00" block is milled to 2.75".what percent is removed by milling.( round 2 places )
Answer:
[tex]8.33\%[/tex]
Step-by-step explanation:
we know that
The total removed by milling is equal to (3.00"-2.75")=0.25"
In this problem 3.00" represent the 100%
so
using proportion
Find out how much percentage represent the total removed by milling
[tex]\frac{3.00}{100}=\frac{0.25}{x}\\\\x=100*0.25/3.00\\\\x=8.33\%[/tex]
Final answer:
To find the percentage of the block removed by milling, subtract the final size from the original size, divide by the original size, and multiply by 100. A 0.25" reduction from a 3.00" block represents an 8.33% decrease.
Explanation:
The question asks us to calculate the percentage of material removed from a block through the milling process. To find the percentage reduction, we start by determining the difference in size before and after the milling, which is 3.00" - 2.75" = 0.25". The next step is to divide the amount removed by the original size and then multiply by 100 to get the percentage. The calculation is as follows:
Find the difference: 3.00" - 2.75" = 0.25" (amount removed)
Calculate the percentage: (0.25" / 3.00") × 100 = 8.33%
Therefore, 8.33% of the original block is removed by milling.
HURRY!!!!!
A carpenter cuts the corners of a rectangle to make the
trapezoid shown.
What is the value of x?
5.375
5.5
011
(7x + 4)
13
Answer:
[tex]x = 11[/tex]
Step-by-step explanation:
The bases of a trapezoid are parallel
The angles,
[tex](9x) \degree[/tex]
and
[tex](7x + 4) \degree[/tex]
are same side interior angles. These two angles are supplementary.
[tex](7x + 4) + 9x = 180 \degree[/tex]
[tex]7x + 9x = 180 - 4[/tex]
[tex]16x = 176[/tex]
Divide both sides by 16.
[tex]x = \frac{176}{16} [/tex]
[tex]x = 11[/tex]
Answer:
[tex]x=11[/tex]
Step-by-step explanation:
We have been given that a carpenter cuts the corners of a rectangle to make the trapezoid. We are asked to find the value of x.
Since trapezoid is made of rectangle, so both bases will be parallel to each other.
We know that two consecutive interior angle of parallel lines are supplementary. We can set an equation to solve for x as:
[tex]9x+7x+4=180[/tex]
[tex]16x+4=180[/tex]
[tex]16x+4-4=180-4[/tex]
[tex]16x=176[/tex]
[tex]\frac{16x}{16}=\frac{176}{16}[/tex]
[tex]x=11[/tex]
Therefore, the value of x is 11.
Which of these is least likely to be the average salary of another of the groups?
Answer:
$104,000
The probability that the average salary between two groups is the same, is actually low. It could be close, but it's quite difficult to get the same exact amount.
how would you solve this type of problem?
kMn
F= - ____
d^2
solve the equation for M
Answer:
[tex]M=-\frac{d^2F}{kn}[/tex]
Please look at what I assumed your equation was: [tex]F=-\frac{kMn}{d^2}[/tex].
Step-by-step explanation:
I'm going to pretend that says:
[tex]F=-\frac{kMn}{d^2}[/tex].
Please correct me if I'm wrong.
We want to solve for M.
The very first thing I'm going to do is multiply both sides by [tex]d^2[/tex].
[tex]d^2F=-kMn[/tex]
Now I'm going to divide both sides by -kn:
[tex]\frac{d^2F}{-kn}=\frac{-kMn}{-kn}[/tex]
Simplifying:
[tex]\frac{d^2F}{-kn}=M[/tex]
Sometimes people don't like the negative on bottom; just move it to the center:
[tex]-\frac{d^2F}{kn}=M[/tex]
[tex]M=-\frac{d^2F}{kn}[/tex]
Two points on a line are given by the ordered pairs (-3, 2) and (-3, -5). What type of line is this?
horizontal
vertical
slanted
none of these
[tex]\huge{\boxed{\text{vertical}}}[/tex]
Explanation:[tex]\text{A vertical line is a line where all of the x values are the same.}[/tex]
[tex]\text{In this case, both of the points have an x value of -3, so this is a vertical line.}[/tex]
the length of a lap is 15 meters. if lisa wants to swim 450 meters this week,how many laps must she swim
Lisa must swim 30 laps to cover the distance of 450 meters, by dividing the total distance she wants to swim by the length of one lap.
To calculate how many laps Lisa must swim to cover a distance of 450 meters, we divide the total distance she wants to swim by the length of one lap. Since the length of one lap is 15 meters, we perform the following calculation:
Divide the total distance (450 meters) by the length of one lap (15 meters).450 meters / 15 meters per lap = 30 laps.Therefore, Lisa needs to swim 30 laps to reach her goal of swimming 450 meters this week.
At a certain distance from a pole, the angle of elevation to the top of the pole is 28° . If the pole is 6.3 ft tall, what is the distance from the pole?
Answer:
11.84 feet
Step-by-step explanation:
The given scenario will form a right angled triangle where the distance and the point from where the angle of elevation is measured will be the base of the triangle.
We know
Angle of elevation = x = 28 °
Height of pole = p = 6.3 feet
Distance from pole = d= ?
So,
[tex]tan\ x = \frac{p}{b}\\ tan\ 28 = \frac{6.3}{b} \\0.5317 = \frac{6.3}{b}\\b = \frac{6.3}{0.5317}\\b=11.84\ feet[/tex]
Therefore, the distance from the pole is 11.84 feet ..
Find the approximate solution of this system of equations x+5y=10
3x+y=1
Answer:
x = -0.357, y = 2.071Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x+5y=10\\3x+y=1&\text{multiply both sides by (-5)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}x+5y=10\\-15x-5y=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-14x=5\qquad\text{divide both sides by (-14)}\\.\qquad x=-\dfrac{5}{14}\to x\approx-0.357\\\\\text{Put it to the equation}\ 3x+y=1:\\\\3(-0.357)+y=1\\-1.071+y=1\qquad\text{add 1.071 to both sides}\\y=2.071[/tex]
Translate the sentence into an equation.
Twice the difference of a number and 3 equals 7.
Answer:
2(x - 3) = 7
Step-by-step explanation:
Set up the difference part first.
x - 3
Now deal with the "Twice."
2(x - 3)
Next equals
2(x - 3) =
And finally what it equals
2(x - 3) = 7
Answer:
2(x-3)=7
Step-by-step explanation:
Dont take my word for it double check with someone else.
What is the standard form equation of the line shown below? Graph of a line going through negative 1, 5 and 2, 4
Answer:
x+3y=14
Step-by-step explanation:
Standard form for an equation of a line is ax+by=c . Some books have restrictions on a,b, and c.
So first thing I'm going to do is state the equation I'm going to use to get there.
I'm going to use the point-slope form because we are given a point (2 really) and we can find the slope using two points (we have).
Line up points and subtract. You will then put second difference over the first difference. This will give you the slope. You could just use (y2-y1)/(x2-x1).
( -1 , 5)
-( 2, 4)
-----------
-3 1
So the slope is 1/-3 or -1/3 .
So the equation in point-slope form, y-y1=m(x-x1), is y-4=-1/3 (x-2) .
y-4=-1/3 (x-2)
First step: I'm going to get rid of the fraction by multiplying both sides by 3.
3y-12=-1(x-2)
Second step: Distribute
3y-12=-x+2
Third step: add x on both sidfes
x+3y-12=2
Fourth step: add 12 on both sides
x+3y=14.
3. Which layer of the skin contains hair follicles?
Answer:
The second layer of skin is the dermis, located under the epidermis. It contains connective tissue, nerve endings, and hair follicles.
The dermis layer of the skin contains hair follicles.
Explanation:The layer of the skin that contains hair follicles is the dermis.
The dermis is the layer of skin directly under the epidermis, and it is made of tough connective tissue. It contains hair follicles, sweat glands, oil glands, and blood vessels.
For example, when you pluck a hair from your skin, you are pulling it out from the dermis.
Ashley is diving in the ocean. She wants to reach a coral reef that is 60 feet below sea level,that is , the reefs elevation is -60 feet. She decides to safely descend to the reef from the oceans surface in increments of 10 feet. Ashley dives in increments of 10 feet. What rational number represents diving 10 feet below sea level?
Answer:
-10 is the answer
Step-by-step explanation:
Diving 10 feet below sea level increases the pressure by 1 atmosphere (ATA), causing the body's air pockets to compress. Divers must equalize the pressure by adding air to these airspaces on the descent.
Explanation:When diving 10 feet below sea level, the pressure increases by 1 atmosphere (ATA). According to Boyle's law, the volume of gases decreases as pressure increases. The increase in pressure can compress the body's air pockets, such as those in the ears and lungs, which can cause discomfort or injury. Divers must equalize the pressure by adding air to these airspaces on the descent.
Learn more about Pressure and equalization in scuba diving here:https://brainly.com/question/30262529
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