As the coefficient of x^2 is negative, we get that the parabola opens down. So the vertex is a maximum
Equation A matches graph __ because …….I need some help on this
Answer:
The function A is given below as
[tex]y=x^2-6x+8[/tex]Using a graphing tool, we will have the graph be
Hence,
Equation A matches graph 3 because the x-intercepts are on the positive x-axis and it has a y-intercept of 8(on the positive y-axis)
Step 2:
Equation B is given below as
[tex]y=(x-6)(x+8)[/tex]Using the graphing tool, we will have the graph as
Hence,
Equation B matches graph 4
The x-intercepts cuts at the negative x and positive x-axis and the y-intercepts is on the negative y-axis
Step 3:
Equation C is given below as
[tex]y=(x-6)^2+8[/tex]Hence,
Using a graphing calculator, we will have the graph as
Hence,
Equation C matches Graph 1, because its vertex is (6,8) and it has a y-intercept on the positive y-axis
The equation below describes a circle. What are the coordinates of the center
of the circle?
(x-4)² + (y+12)² = 17²
A. (-4,12)
B. (4,12)
C. (-4,-12)
D. (4.-12)
SUBMIT
Answer:
D. (4, -12)
Step-by-step explanation:
Given the equation of a circle is (x -4)² +(y +12)² = 17², you want to know the center.
CircleThe equation of a circle centered at (h, k) with radius r is ...
(x -h)² +(y -k)² = r²
Comparing this to the given equation, we can identify the values of the parameters as ...
(x -4)² +(y +12)² = 17²
h = 4, -k = 12, r = 17 . . . . . k = -12
This tells us the center is ...
(h, k) = (4, -12) . . . . . matches choice D
<95141404393>
6.75 +3/8x=13 1/4 solve please
To solve this equation, we can proceed as follows:
[tex]6.75+\frac{3}{8}x=13\frac{1}{4}[/tex]1. Subtract 6.75 to both sides of the equation:
[tex]6.75-6.75+\frac{3}{8}x=13\frac{1}{4}-6.75\Rightarrow\frac{3}{8}x=13\frac{1}{4}-6.75[/tex]We can solve the right part of the equation using fractions as follows:
[tex]6.75=6+\frac{3}{4}[/tex]We also know that
[tex]13\frac{1}{4}=13+\frac{1}{4}[/tex]Then, we have:
[tex]\frac{3}{8}x=13+\frac{1}{4}-(6-\frac{3}{4})=13-6+\frac{1}{4}-\frac{3}{4}=7+\frac{1-3}{4}_{}[/tex][tex]\frac{3}{8}x=7+(-\frac{3}{4})=7-\frac{3}{4}=\frac{7\cdot4-3}{4}=\frac{28-3}{4}_{}=\frac{25}{4}[/tex]Now, the equation is:
[tex]\frac{3}{8}x=\frac{25}{4}[/tex]We need to multiply by 8/3 to both sides to solve for x as follows:
[tex]\frac{8}{3}\cdot\frac{3}{8}x=\frac{8}{3}\cdot\frac{25}{4}\Rightarrow x=\frac{8}{4}\cdot\frac{25}{3}\Rightarrow x=2\cdot\frac{25}{3}\Rightarrow x=\frac{50}{3}=16.6666666\ldots=16\frac{2}{3}[/tex]Therefore, the value for x is equal to:
[tex]x=16\frac{2}{3}=\frac{50}{3}=16.6666666\ldots[/tex]Answer:
The exact form, decimal form, and the mixed number form are down
Step-by-step explanation:
exact form ; x = 208/3
decimal form ; 69.33333..
Mixed number form ; 69 1/3
6x2 = x + 2Write the quadratic equation in standard form:( a )x2 + ( b )x + ( c ) = 0Identify the values of a, b, and c.a =-b =C=Substitute these values into the quadratic formula and simplify:x = -(b)£/( b )2 –4()()2( a )
6x² = x + 2
Subtracting x and 2 at both sides:
6x² - x - 2 = x + 2 - x - 2
6x² - x - 2 = 0
where
a: 6
b: -1
c: -2
Substituting these values into the quadratic formula:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{1\pm\sqrt[]{(-1)^2-4(6)(-2)}}{2(6)} \\ x_{1,2}=\frac{1\pm\sqrt[]{49}}{12} \\ x_1=\frac{1+7}{12}=\frac{2}{3} \\ x_2=\frac{1-7}{12}=-\frac{1}{2} \end{gathered}[/tex]A computer is normally $500, but is discounted to $200. By what percentage did the computer decrease?
Answer:
60%
Step-by-step explanation:
If the measure of arc AB is 64 degrees, what is the measure of angle ADB?
Answer:
the answer is AB multi
Step-by-step explanation:
Is AB degrees
1 point The $140 repair bill included $42 for parts and the rest for labor. What percent of the bill was for labor?
we must first find the price of labor
then we subtract the value of the parts from the total
[tex]140-42=98[/tex]the price of the labor was 98$
now to calculate the percent, divide the price of the labor between the total and multiply by 100
[tex]\begin{gathered} \frac{98}{140}\times100 \\ \\ 0.7\times100 \\ =70 \end{gathered}[/tex]the percent was 70%
a.H1. Determine if the given points are collinear or not collinear.|points E, H, and J:b. points F, J, and E:points G, J, and E:points G, H, and J:C.d.J
Collinear means that the points all lie on a straight line
From the picture, we will see that:
I. points E, J & F all lie on a straight line (Line y)
II. points G, J & H all lie on a straight line (Line t)
a. Points E, H & J do no lie on a straight line; point E lies on line y while point H lies on line t
b. Points F, J & E all lie on the straight line y
c. Point G, H & J all lie on a straight line t
write in summation notation 13. 20 + 22 + 24 + ... + 36
Given the expression:
20 + 22 + 24 + ..... + 36
Let's write in summation notation.
Summation notation can be said to be the addition of a sequance of numbers.
From the sequence, we have:
Common difference = 22 - 20 = 2
Number of terms = 9
Apply the formula:
[tex]\sum ^n_{i\mathop=1}a+d(i-1)[/tex]Where:
n = upper limit (number of terms)
i = 1 ==> lower limit
Initial value, a = 20
d = common difference = 2
To write in summation notation, we have:
[tex]\sum ^9_{i\mathop=1}20+2(i-1)[/tex]ANSWER:
[tex]\sum ^9_{i\mathop{=}1}20+2(i-1)[/tex]A particular fruit's weights are normally distributed, with a mean of 598 grams and a standard deviation of 22 grams.
If you pick 9 fruits at random, then 16% of the time, their mean weight will be greater than how many grams?
Give your answer to the nearest gram.
If a particular fruit's weights are normally distributed, with a mean of 598 grams and a standard deviation of 22 grams and I pick 9 fruits at random, then their mean weight will be greater than 605.29263 grams 16% of the time.
As per the question statement, a particular fruit's weights are normally distributed, with a mean of 598 grams and a standard deviation of 22 grams and I pick 9 fruits at random.
We are required to calculate their mean weight will be greater than how many grams for 16% of the time.
Given (μ = 598), (σ = 22), and (n = 9)
Therefore, the standard deviation of the distribution of sample, otherwise know as the standard error, will be [s = (sdp)/√(ss)]
Where, "s" is the standard error, "sdp" is the standard deviation of the population and "ss" is the sample size.
Therefore, [s = (22/√9) = (22/3) = 7.33...
Now, we need to look up the z-score for an area to the right of it being equal to (0.16) since we are concerned about (16%) times among the random selection, and [16% = (16/100) = 0.16]
That is, we need to look up the z-score for an area of [(1 - 0.16) = 0.84] to the left of it.
Hence, a z-score with an area of 0.84 to the left of it will be equal to 0.99445.
Now to find the raw score associated with this, we will have to use the formula to calculate z-score which goes as [(x - m)/s].
Where, "z" is the z-score, "x" is the raw score, "m" is the mean and "s" is the standard error.
Therefore, with a mean of 598 and a standard error of 7.333 and a z-score of 0.99445, applied to the above mentioned formula to calculate z-score, we get:
[0.99445 = (x - 598)/7.33]
Or, (x - 598) = (0.99445 * 7.33)
Or, (x - 598) = 7.29263
Or, x = (598 + 7.29263)
Or, [x = 605.29263]
That is, if I pick a sample of 9 fruits at random, then their mean weight will be greater than 605.29263 grams 16% of the time.
Mean: In Mathematics and Statistics, the mean refers to the average of a set of values in a sample or observation.To learn more about Mean, click on the link below.
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Can you help and explain what to do with practice question below?
Solution:
Given the figure below:
To solve for the missing angles,
Step 1: Solve for c.
The sum of the interior angles of a triangle equals 180 degrees.
Thus,
[tex]\begin{gathered} 48+58+c=180(sum\text{ of interior angles in a triangle\rparen} \\ \Rightarrow106+c=180 \\ subtract\text{ 106 from both sides,} \\ 106-106+c=180-106 \\ \Rightarrow c=74\degree \end{gathered}[/tex]Step 2: Solve for d.
The sum of angles on a straight line gives 180 degrees.
[tex]\begin{gathered} 58+d=180\text{ \lparen sum of angles on a straight line\rparen} \\ subtract\text{ 58 from both sides,} \\ 58-58+d=180-58 \\ \Rightarrow d=122\degree \end{gathered}[/tex]Step 3: Solve for a.
From the figure,
[tex]a=58\degree\text{ \lparen alternate angles\rparen}[/tex]Step 4: Solve for b.
From the figure,
[tex]\begin{gathered} b+c=d\text{ \lparen alternate angles\rparen} \\ \Rightarrow b+74=122 \\ subtract\text{ 74 from both sides,} \\ b+74-74=122-74 \\ \Rightarrow b=48\degree \end{gathered}[/tex]Hence, we have
[tex]\begin{gathered} a=58\degree \\ b=48\degree \\ c=74\degree \\ d=122\degree \end{gathered}[/tex]Can anyone answer either of these questions with an explanation please I really need it thanks!
Answer:
6. 4
7. 8.25
Step-by-step explanation:
all the explanation for both questions is in the pics below please check it out also I am sorry if it's wrong I am only in middle school
Have a wonderful day:)
Find all angles 0 theta such that 0 degrees are less than or equal to 0 theta and less than or equal to 360 degrees for which the statement sin(-104) = sin 0 theta is true
Hello there. To solve this question, we'll have to remember some properties about angles and the unit circle.
First, remember the unit circle:
An angle is represented as the measure between the line joining the origin and any point of the circle with the x-axis, as follows
The full angle in this case, representing a cycle in the circle is
[tex]\theta=2\pi[/tex]So we want to determine all angles θ between 0 and 360º such that
[tex]\sin(-104^{\circ})=\sin(\theta)[/tex]For this, we have to remember about first positive determination of an angle.
Notice we can represent negative angles in the unit circle if, instead of following in the anti-clockwise orientation (we say positive orientation), we follow the other way around:
But notice that we can represent these angles with our first case if you consider:
[tex]2\pi-\alpha[/tex]Since you have the property that the full angles is 2pi, hence
Thefore you have that
[tex]360^{\circ}-104^{\circ}=256^{\circ}[/tex]In this case notice that we added 360º to the angle, since we fixed the point of which the angle was at and gave it a full rotation.
For smaller angles, for example, -1352º, you can add the biggest possible multiple of 360º, that represents the number of full rotations you have to have in order to find its first positive determination.
In this case, we found that
[tex]\theta=256^{\circ}[/tex]Satisfying the property that
[tex]0\leq\theta\leq360^{\circ}[/tex]prove why the function is even with the green highlighted formulathen show where the line of symmetry is at show all work
Here, the given function is f(x)=c.
Check whether the function is odd or even.
[tex]\begin{gathered} f(-x)=c \\ =f(x) \end{gathered}[/tex]Here, the out put of the function is constant whether it is +x or -x.
So, the function is even.
The graph of the function f(x)=c is shown below.
From, the graph, for any values of x there is a constant val;ue of y.
The function is symmetric with respect to y axis.
HELP ASAP PLEASE
Determine all real values of a.
a2 = 225
a = 112.5
a = ±112.5
a = 15
a = ±15
The real value of a is 15.
Given,
[tex]a^2 = 225[/tex]
Determine the real value of a
What is Perfect Square?
An integer that can be expressed as the square of another integer is called a perfect square. In other words, it is defined as the product of some integer with itself.
Here, find the square root of 225
Now,
[tex]a^2 = 225 \\\\a = \sqrt{225}[/tex]
a = 15 x 15 = 225
Hence, The real value of a is 15.
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Answer: the answer is the last option
Step-by-step explanation: I took the test and got it right
A coin is flipped 2,500 times. It lands on heads 1,223 times and tails 1,277 times. What is the empirical probability of getting tails on this coin
Answer:
The empirical probability of getting tails on this coin is 50.08%.
Step-by-step explanation:
The steps and answers please and thank you.
Answer:
Practical Domain: 0 ≤ g ≤ 22
Practical Range: 0 ≤ C(g) ≤ 78.32
Step-by-step explanation:
The domain is the input of the function, usually, x, but it is g in this problem.
The input here is the number of gallons you can get. The tank holds a maximum of 22 gallons, so if the tank is already full, you will get 0 gallons. If the tank is completely empty, you can get up to 22 gallons. The domain is the values of the input of the function. Since the input is from 0 gallons to 22 gallons, we get this for the domain:
Practical Domain: 0 ≤ g ≤ 22
The range is the output of the function. Usually it is f(x), but in this problem it is C(g). When you input the number of gallons into the function, the output is the cost of that number of gallons. The domain is from 0 to 22 gallons. Now we use the function to find the cost of 0 gallons and the cost of 22 gallons.
Here is the function:
C(g) = 3.56g
What is the cost of 0 gallons? In this case, g = 0.
C(0) = 3.56(0) = 3.56 × 0 = 0
0 gallons cot 0 dollars, which makes sense.
What is the cost of 22 gallons, the greatest amount of fuel you can fit in the tank?
C(g) = 3.56g
Here, g = 22.
C(22) = 3.56(22) = 3.56 × 22 = 78.32
22 gallons cost 78.32 dollars.
The range of the function is from 0 dollars to 78.32 dollars.
Practical Range: 0 ≤ C(g) ≤ 78.32
The distribution of sale prices (online) for four-year-old Harley Davidson touring motorcycles is approximately Normally distributed with a mean
of $14,000 and a standard deviation of $4,000.
8. What proportion of available motorcycles are priced at or below $9,000? Show your work.
9. What proportion of available motorcycles are priced at or below $12,000? Show your work.
10. Mr. Kawasaki plans to spend between $9,000 and $12,000 on a motorcycle. What proportion of the available motorcycles of this type can he
afford?
11. What is the approximate z-score for the 30th percentile in the standard Normal distribution?
12. Hence, what is the 30th percentile for the prices of motorcycles of this type? Show your work.
Answer:
$2000
Step-by-step explanation:
you subtract 4000-2000=2000
Which expression equals the expression 5x-3y?
Answer
Options A, C and D are all correct.
They simplify to give 5x - 3y
Explanation
We are asked to pick the expressions which simplify to give 5x - 3y
Taking the statements one at a time,
Option A
5x + -8y + 5y
= 5x - 8y + 5y
= 5x - 3y
This option is correct.
Option B
15xy ≠ (5x - 3y)
This option is not correct.
Option C
5 (x + y) + -8y
= 5x + 5y - 8y
= 5x - 3y
This option is correct.
Option D
-2 (2y - x) + x + x + x + y
= -4y + 2x + 3x + y
= 5x - 3y
This option is correct.
Hope this Helps!!!
Marian purchased a home valued at $465,000. She purchased homeowner insurance for 75% of the value of the home. If the annual premium on the policyhundred-dollar unit, how much did she pay to the nearest whole cent)?$2,875.50$2,695.00$2,580.75$3,050.74None of these choices are correct.
Ok, so
Marian purchased a home valued at $465,000. If She purchased homeowner insurance for 75% of the value of the home, she paid:
$(465,000)*(75) / (100)
$348,750.
Now, we know that the annual premium on the policy was $0.74 per hundred-dollar unit. Then, this is:
0.74/100 dollar unit.
And, if we multiply, we obtain:
$348,750 * (0.74/100) = $2,580.75
Therefore, she paid $2,580.75
8. Suppose that A, B, and C are sets. Prove or disprove that
(A − B) − C = (A − C) − B.
The equation be (A − B) − C = (A − C) − B. Then results exists different, so we contain disproven the hypothesis by counterexample.
Is (A − B) − C = (A − C) − B exists equivalent?Given: (A − B) − C = (A − C) − B.
First, we will attempt to show [tex]$A-(B-C) \subseteq(A-C)-C$[/tex]. Let [tex]$x \in A-(B-C)$[/tex]. Then [tex]$x \in A$[/tex] and [tex]$x \notin(B-C)$[/tex].
By De Morgan's law we have that
[tex]$$x \notin(B-C)=x \notin B \vee x \in C .$$[/tex]
We have that [tex]$x \in A \wedge(x \notin B \vee x \in C)$[/tex].
Then we have that [tex]$(x \in A \wedge x \notin B) \vee(x \in A \wedge x \in C)$[/tex].
So by definition of [tex]$\cup$[/tex] and [tex]$\cap$[/tex], we have [tex]$x \in(A-B) \cup(x \in(A \cap C))[/tex].
I can see a contradiction here in that LHS says x ∈ C but the RHS says x ∉ C.
For example, as longer as [tex]$C \neq 0$[/tex]. Let A = 4, B = 2, C = 1.
Then A - (B - C) = 4 - (2 - 1) = 4 - 1 = 3
On the other side (A - B) - C = (4 - 2) - 1 = 2 - 1 = 1.
The results exists different, so we contain disproven the hypothesis by counterexample.
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lynn is tracking the progress of her plants growth. today the plant is 5 cm high. the plant grows 1.5 cm per day. suppose Lynn's plant grewn to a height of 30.5 inches how many days will have passed
We have that the plant start with 5 cm high and it grows 1.5 cm per day, then the equation to model this situation is:
[tex]y=1.5x+5[/tex]where x represents the days that passes and y represents the height of the plant.
Now, let's convert 30.5 inches to cm:
[tex]\begin{gathered} 1in=2.54\operatorname{cm} \\ \Rightarrow(30.5)\cdot(2.54)=77.47\operatorname{cm} \end{gathered}[/tex]then, suppose that Lynn's plant grew to a height of 77.47 cm, then we have to make y = 77.47 and solve for x to get the following:
[tex]\begin{gathered} y=77.47 \\ \Rightarrow77.47=1.5x+5 \\ \Rightarrow77.47-5=1.5x \\ \Rightarrow72.47=1.5x \\ \Rightarrow x=\frac{72.47}{1.5}=48.3 \\ x=48.3 \end{gathered}[/tex]therefore, it will take approximately 48 days to the plant to grow to a height of 30.5 inches
Which formula should be used to find the circumference of a circle? C = pi dC = 2 pi dC = pi rC = StartFraction pi over d EndFraction
Solution
For this case the correct formula for the circumference of a circle is given by:
[tex]C=2\pi r=2\pi\cdot\frac{d}{2}=\pi d[/tex]Then the best option would be:
C = pi d
a Find the volume of the specified cone. Use 3.14 for x, and round your answer to the nearest whole number. Radius = 4 in., Height = 9 in. 301 cu. in. b. 226 cu. in. 75 cu. in. d. 151 cu. in. Please select the best answer from the choices provided ΟΑ OB с OD
volume of cone approximately is 151 cubic inch
help me please
thank you
Answer:
Domain: [tex](-\infty, \infty)[/tex]
Range: [tex][0, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Here is a graph of the function g.4-3-2-1Use the graph to find the following.If there is more than one answer, separate them with commas.(a) All local maximum values of g:(6) All values at which g has a local maximut:X
Graphically, the local maximum can be localized by spotting the "highest value" inside a range. A local maximum point on a function is a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).
We can see that in our g function at x= -2 and x = 3, with respective values y = 3 and y = -1.
The answer for item (a) is: -1, 3
For item (b): -2, 3
The first 19 terms of the arithmetic sequence 9, 2, -5, -12,...
9, 2, -5, -12,...
First let's find the common difference
Common difference= 2 - 9 = -7
So we will add - 7 to get the next term
9, 2, -5, -12, -19, -26, -33,-40, -47, -54, -61, -68, -75, -82, -89, -96, -103, -110, -117
a) A paralegal bills a law firm for 19.5 hours of work at a rate of £240 per hour.
much money has the paralegal earned from this job? Include units in your
answer.
b) The paralegal splits her earnings between utilities and savings in a ratio of 2:3.
How much money will be allocated to her savings?
1. The total earnings of the paralegal from this job was £4,680.
2. The amount of the earnings allocated to her savings, based on the allocation ratio, is £2,808.
What are the total earnings?The total earnings are a function of the unit hours worked and the hourly pay rate.
The total earnings are the product of the multiplication of the two variables.
What is a ratio?A ratio is a numerical relationship showing how much a value is contained in another value or variable.
Ratios are fractional values depicted in percentages, decimals, or fractions.
The total number of work hours = 19.5 hours
The work hour rate (per hour) = £240
The total earnings from the job = £4,680 (£240 x 19.5)
The ratio of utilities and savings = 2:3
The sum of the ratio = 5
The amount allocated to savings = 3/5 of £4,680 = £2,808.
The amount allocated to utilities = £1,872 or 2/5 (£4,680 - £2,808)
Thus, whereas, the paralegal earned £4,680 from the job, the amount allocated to her savings is £2,808, based on the subsisting allocation ratio.
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(02.04 MC) choose the equation that represents the line that passes through the point (2,6) and has a slope of -5
The slope intercept form of the equation that passes through the point (2,6) and has a slope of -5 is y = -5x +16
Slope intercept form:
Slope intercept form equation is used to calculate the equation of a straight line, for the given slope of the line and intercept.
The general form of slope intercept equation is,
y = mx +c
where
m represents the slope of the line
c represents the intercept.
Given
Here we have the the point (2,6) and has a slope of -5.
Now we need to find the equation of the line for this point and slope.
While we apply these value on the formula, in order to get the value of y intercept,
Then it can look like,
6 = (-5)2 + c
6 = -10 + c
c = 6 + 10
c = 16.
Therefore, the value of y intercept is 16.
Then the equation of the line is
y = -5x + 16
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What should be done to both sides of the equation in order to solve x = 4?Divide by 4.Multiply by 4.Divide by 1/3.Multiply by 1/3.
Given:
There are given that the equation:
[tex]\frac{1}{3}x=4[/tex]Explanation:
According to the question:
We need to find the value that orders to solve both sides of the equationn.
So,
From the equation:
[tex]\frac{1}{3}x=4[/tex]Then,
For the equation, divide by 1/3 on both sides of the equation:
So,
From the properties:
If,
[tex]\frac{a}{\frac{b}{\frac{c}{d}}}=\frac{a}{b}\times\frac{d}{c}[/tex][tex]\begin{gathered} \frac{1}{3}x=4 \\ \frac{\frac{1}{3}x}{\frac{1}{3}}=\frac{4}{\frac{1}{3}} \\ \frac{\frac{1}{3}x}{\frac{1}{3}}=4\times3 \\ \frac{1}{3}x\times3=12 \\ x=12 \end{gathered}[/tex]Final answer:
Hence, the correct option is C.
