The Quadratic f(x)=x^2-2x-15Using the functions of your graphing calculator calculate the coordinates of the following points (as shown in the calculator videos in this lesson). If the parabola doesn't intersect the x-axis then write "none." If necessary, round to the nearest hundredths place (2 decimal places).a. The vertex using the min/max calculate function.b. X-intercept(s) using the zero calculate function.c. Y-intercept using the value calculate function (w/ a value of x=0).d. Now, copy down the t-table generated by your calculator for integer input values from-3≤x≤3.
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Given: The function below
[tex]f(x)=x^2-2x-15[/tex]To Determine: The vertex, the x-intercept, the y-intercept, and the table for -3≤x≤3
Solution
The graph of the given function is as shown below
Hence:
The vertex is a minimum value at y = -16 and coordinate (1, -16)
(b) The X-intercepets is x = -3, x = 5, coordinates: (-3, 0) and (5, 0)
(c) The Y-intercept is at y = -15, coordinate: (0, - 15)
(d) The table showing the values of f(x) for -3≤x≤3 is as shown below
Related Questions
A researcher randomly purchases several different kits of a popular building toy. The following table shows the number of pieces in each kit in the sample. Find the standard deviation of the data. Round your answer to the nearest hundredth, if necessary.
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The Solution:
Given:
We are required to find the standard deviation of the given data.
Find the sample mean of the given data.
Find the standard deviation of the data.
Therefore, the correct answer is 68.07
Find the distance between the points (2,4) and (8,2) round to the nearest tenth if necessary
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6.3 units
Explanations
The formula for calculating the distance between two points is given as:
[tex]D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Given the following coordinate points
A(2,4) and B(8,2)
Substitute the given parameters into the formula to have:
[tex]\begin{gathered} D=\sqrt[]{(8-2)^2+(2-4)^2} \\ D=\sqrt[]{6^2+(-2_{})^2} \\ D=\sqrt[]{36+4} \\ D=\sqrt[]{40} \\ D\approx6.3\text{units} \end{gathered}[/tex]Hence the distance between the points (2,4) and (8,2) round to the nearest tenth is 6.3 units
Watch help videoKevin has a bag that contains orange chews, strawberry chews, and peach chews. Heperforms an experiment. Kevin randomly removes a chew from the bag, records theresult, and returns the chew to the bag. Kevin performs the experiment 32 times. Theresults are shown below:An orange chew was selected 5 times.A strawberry chew was selected 17 times.A peach chew was selected 10 times.Based on these results, express the probability that the next chew Kevin removesfrom the bag will be peach chew as a percent to the nearest whole number.Answer:Submit Answer
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Divide the amount of times that a peach chew was selected over the total number of times that the experiment was performed to find the probability that the next chew will also be a peach chew:
[tex]\frac{10}{32}=0.3125=31.25\text{ \%}[/tex]Then, as a percent to the nearest whole number, the probability that the next chew Kevin removes from the bag will be a peach chew, is:
[tex]31\text{ \%}[/tex]Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.tan(80°) – tan (20)1 + tan(80°)tan (20
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Okay, here we have this:
Considering the provided expression, we are going to use the tangent formula of a subtraction, and is the following:
[tex]\tan (A-B)=\frac{tan\mleft(A\mright)-tan\mleft(B\mright)}{1+tan\mleft(A\mright)tan\mleft(B\mright)}[/tex]We can see that the expression they provide us has the same form as that of the tangent of a subtraction, where A is equal to 80° and B is equal to 20°, so we obtain:
[tex]\begin{gathered} \frac{tan\left(80°\right)-tan\left(20°\right)}{1+tan\left(80°\right)tan\left(20°\right)} \\ =\tan (80\degree-20\degree) \\ =\tan (60\degree) \end{gathered}[/tex]Finally we obtain that the original expression is equal to tan(60°).
Which points are on the graph of a linear function? Select all that apply
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We will determine the points that belong to a linear function as follows:
*First set: We calculate the slope of the three points:
[tex]m_1=\frac{5-7}{0-(-1)}\Rightarrow m_1=-2[/tex][tex]m_2=\frac{3-7}{1-(-1)}\Rightarrow m_2=-2[/tex]So, the first set belongs to a linear function.
*second set:
[tex]m_1=\frac{0-1}{0-(-1)}\Rightarrow m_1=-1[/tex][tex]m_2=\frac{1-1}{1-(-1)}\Rightarrow m_2=0[/tex]So, the second set does not belong to a linear function.
*Third set:
[tex]m_1=\frac{5-5}{2-0}\Rightarrow m_1=0[/tex][tex]m_2=\frac{14-5}{3-0}\Rightarrow m_2=3[/tex]So, the third set does not belong to a linear function.
*Fourth set:
[tex]m_1=\frac{5-(-3)}{2-0}\Rightarrow m_1=4[/tex][tex]m_2=\frac{13-(-3)}{4-0}\Rightarrow m_2=4[/tex]So, the fourth set belongs to a linear function.
-What is the product of (a - 1) and (2a + 2)?A 2(a2 - 2)B 2(a2 - 1)C a2 + 4a - 2D2a2 - 4a - 2-
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The product of the sum and difference binomials is
[tex](x-y)(x+y)=x^2-y^2[/tex]We will use this rule to solve the question
We need to find the product of (a - 1) and (2a + 2)
At first, we will take 2 as a common factor from the second bracket
[tex]\begin{gathered} 2a+2=2(\frac{2a}{2}+\frac{2}{2}) \\ 2a+2=2(a+1) \end{gathered}[/tex]Now, we will multiply (a - 1) by 2(a + 1)
[tex](a-1)(2a-2)=2(a-1)(a+1)[/tex]By using the rule of the product of the sum and difference above, then
[tex]\begin{gathered} 2(a-1)(a+1)=2(a^2-1^2) \\ 2(a-1)(a+1)=2(a^2-1) \end{gathered}[/tex]The answer is B
.27 = as a percentage
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.27 = as a percentage
To find out the number as percentage , multiply by 100
so
0.27*100=27%
Determine whether the equation x + y2 = 5 is linear. If so, graph the function. If not, explain why.
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What is the value of x in the equation 7x+2y=48, when y=3?
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We have the following equation:
[tex]7x+2y=48[/tex]Which represents a line, and we need to determine the value of x when y = 3.
To achieve that, we can proceed as follows:
1. Substitute the value of y = 3 into the equation:
[tex][/tex]How are these functions related? How are their graphs related
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Notice that the difference between the two equations is the +5 on the right side of the second equation.
The graph of the following equations are as folllows:
For y=x:
For y=x+5:
Thus, the graph of y = x was shifted 5 units upward to obtain the graph of y=x+5.
Therefore, each value or output of y=x+5 is 5 more than the corresponding output of y=x. Consequently, the graph of y=x+5 is the graph of y=x translated up by 5 units.
Thus, the correct answer is option C.
can you please help me
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The slope intercept form is y = m x + b
We need to put the equation -x + 4y = -8 in this form
At first, add both sides by x
[tex]\begin{gathered} -x+x+4y=-8+x \\ 4y=-8+x \end{gathered}[/tex]Then divide both sides by 4 to make the coefficient of y = 1
[tex]\frac{4y}{4}=\frac{-8}{4}+\frac{x}{4}[/tex]-8/4 = -2
x/4 = 1/4 x
[tex]y=-2+\frac{1}{4}x[/tex]Now switch -2 and 1/4 x
[tex]y=\frac{1}{4}x-2[/tex]Let us find which choice is?
It is the first one for the equation
Let us choose the graph
For the graph, the line intersects the y-axis at (0, -2)
The slope is positive, then its direction to the right
The x-intercept is (8, 0)
Then it is the last graph you post with equation y = 1/4 x - 2
Do you see it
4. Pietro buys 24 candy bars for $6. He plans to sellall 24 candy bars in 1 day. He needs to make aprofit of $12 per day to meet his fundraising goal.How much must he charge for each candy bar?(Hint: He spent $6 on the candy bars so his startingprofit is $-6. How much does he need to make inorder to have a profit of $12?)He needs to charge $per candy bar.
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The cost of the 24 candy bars is $6.
If he is to make a profit of $12, that means that he must sell all the candy bars for:
[tex]\Rightarrow12+6=18\text{ dollars}[/tex]Since there are 24 candy bars, the cost of 1 candy bar can be calculated to be:
[tex]\Rightarrow\frac{18}{24}=0.75\text{ dollars}[/tex]He needs to charge $0.75 per candy bar.
Given the following exponential function, identify whether the change representsgrowth or decay, and determine the percentage rate of increase er decrease.y = 2500(1.04)
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The equation of a exponential function is of the form
[tex]y=a(b)^x[/tex]where
b is the base of the exponential function
If the value of b>1 -----> is a growth function
If the value of b<1 ----> is a decay function
In this problem
b=1.04
1.04 > 1
therefore
Is a growth functionPart b
Determine the percentage rate of increase
we have that
b=1+r
r=b-1
r=1.04-1
r=0.04
convert to percentage
r=0.04*100
r=4%Select the correct anawer Which of the following represents a function?
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A function relates input to output. Functions can be one to one or many to one. The x values represent the input while the y values represent the output. In the case of one to one, it means that the output has only one corresponding input. Many to one means that there are many input values for one output value. An input value cannot have more than 1 output value. If this happens, then it is not a function. Looking at the options given,
Option A is a function since no input value has more than one output value
Option B is not a function since the output values of 7 and 1 has the same input value of - 1
For option C, the values are (- 3, - 2)' (- 1, 1), (- 1, - 5), (1, 4). It is not a function since the output values of 1 and - 5 has the same input value of - 1
Option D is not a function since the output values of 7 and 1 has the same input value of - 1
The correct option is A
Cuanto es 123 x 200?
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Answer:
[tex]123\times200=24600[/tex]Explanation:
We want to find the product of 123 and 200;
Therefore, the product of 123 and 200 is;
El producto de 123 y 200 es;
[tex]123\times200=24600[/tex]Ray and Jon play a game of chance with two dice. If the sum of the dice is seven, Ray pays Jon $15. But if the sum is anything else, Jon pays Ray $10. What is the expected value of the game for Jon?Answer:
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Step 1
[tex]\text{Probability of any event = }\frac{\text{number of required outcomes}}{n\text{umber of possible outcomes}}[/tex]Step 2:
Draw the table of the possible outcomes.
Step 3:
Draw the table for the expected value
Number of the sum of seven = 6
Number of anything else = 30
Total possible outcomes = 36
[tex]\begin{gathered} \text{Expected value formula = Value }\times\text{ Probability of event} \\ \text{Expected value formula = xp(x)} \end{gathered}[/tex]Final answer
The expected value of the game for Jon
[tex]\begin{gathered} =\text{ }\frac{15}{6}\text{ + }\frac{50}{6} \\ =\text{ }\frac{65}{6}\text{ } \\ =\text{ 10.83} \end{gathered}[/tex]48, -24, 12, -6,... 50th term
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For the next series we will calculate its expression
[tex]a_n=(-1)^{n+1}3\cdot2^{^{5-n}}[/tex]For n = 1
an = 48
For n = 2
an = -24
For n = 50
an = 8.5265128e-14
the coordinates of the point shown in fig 23.16 are (3,5)
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Answer:
False
Explanation:
In the coordinate notation (x, y), the left entry represents the x-coordinate and the right entry the y-coordinate. Therefore, if we want to represent the point x = 5, y = 3, we would write
[tex](5,3)[/tex]Hence, the representation (3, 5) does not represent the point x =5, y = 3, rather, it represents x = 3, y = 5, and therefore, the statement given is false.
The dot plot shows how many customers purchased different numbers of shirts at a sale last weekend.
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The interquartile range IQR of a dataset is the difference between the upper and lower quartiles, Q3 and Q1
The median of the whole dataset is Q2 and corresponds to the value x=3.5
The value of Q1 is the median of the lower 3 values: Q1=2
The value of Q3 is the median of the upper 3 values: Q3=5
The IQR is: 5 - 2 = 3
Mailk earns 10 dollars per hour at his job. He wants to change to a job that will play 12 dollars per hour. What will be the porcent increase in Mailk's hourty pay if he makes this jobs change.:))))))))))))))))))))))))))))))))))))))
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5/6 = 83.33%
100 - 83.33 = 16.67%
16.67% increase
Points S and T are midpoints of the sides of triangle FGH.Triangle G H F is cut by line segment S T. Point S is the midpoint of side H G and point T is the midpoint of H F. The lengths of H T and T F are 6 centimeters. The lengths of H S and S G are 4 centimeters. The length of S T is 8 centimeters.What is GF?
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The measure of length of GF is 16 cm.
Given that point S is the midpoint of side HG and point T is the midpoint of HF of triangle FGH, the line segment ST is parallel to the side GF, and the triangles FGH and TSH are similar with proportional sides, then:
[tex]\frac{GF}{ST}=\frac{FH}{TH}=\frac{GH}{SH}[/tex]
We are given the following;
FH = HT + FT = 6 + 6 = 12 cm [HT = FT = 6 cm]
GH = HS + GS = 4 + 4 = 8 cm [HS = GS = 4 cm]
ST = 8 cm
Substitute the given values, we will get the following;
[tex]\frac{GF}{8} =\frac {12}{6} = \frac{8}{4}\\\frac{GF}{8} =\frac {12}{6}\\\frac{GF}{8} = 2[/tex]
GF = 2 * 8 = 16 cm
Thus, the measure of the length of GF is 16 cm.
To learn more about the midpoint theorem visit:
https://brainly.com/question/16958177
#SPJ9
29. How long will it take to double an investment at 3.7% compounded continuously? Round your answer to the nearest tenth of a year. years
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The formula for compounding continuously is :
[tex]A=Pe^{rt}[/tex]where A is the future amount
P is the principal amount
e is a constant
r is the rate of interest
and
t is the time in years.
The question stated that the investment will be doubled, so the future amount will be twice the principal amount.
A = 2P
The rate of interest is 3.7%
e is a constant approximately equal to 2.71828..
Subsitute the values to the formula and solve the value of t :
[tex]\begin{gathered} A=Pe^{rt} \\ 2P=Pe^{0.037t} \\ 2=e^{0.037t} \end{gathered}[/tex]Take the natural logarithm of both sides,
note that ln e = 1
[tex]\begin{gathered} \ln 2=\ln e^{0.037t} \\ \ln 2=0.037t\ln e \\ \ln 2=0.037t(1) \\ t=\frac{\ln 2}{0.037}=18.73 \end{gathered}[/tex]The answer is 18.73 years
Explain why this is true.6x1/9=3x2/9
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prove that
[tex]6\cdot(\frac{1}{9})=3\cdot(\frac{2}{9})[/tex]start on the left side
[tex]\frac{6}{1}\cdot\frac{1}{9}=\frac{6}{9}=\frac{2}{3}[/tex]continue with the right side
[tex]\frac{3}{1}\cdot\frac{2}{9}=\frac{6}{9}=\frac{2}{3}[/tex]we can conclude that both expressions are equal to 2/3.
Determine if the following equations are parallel, perpendicular, or neither. 7(x – 1) = 3y + 21 and 3.5x + 1.5y = 4.5
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Given the two equations
7(x - 1) = 3y + 21
3.5x + 1.5y = 4.5
To determine if the lines are visible or perpendicular
Step 1: Expand the equations and make y the subject of the formula
7(x - 1) = 3y + 21
=> 7x - 7 = 3y + 21
=> 3y = 7x - 7 - 21
=> 3y = 7x -28
Divide both sides by 3
y = 7/3x - 28/3 ------equation 1
3.5x + 1.5y = 4.5
1.5y = -3.5x + 4.5
Divide both sides by 1.5
y = -3.5/1.5 x + 4.5/1.5
y = -7/3x + 3--------equation 2
Step 2: compare the two equations to the equation of a line, y = mx + c
For equation 1
m = 7/3
For equation 2
m= -7/3
The slopes are not the same
Also, the product of the gradients did not give -1
It can be seen that the lines are neither perpendicular nor parallel
whats the rate of change in the equation 0.860(17) + 3.302.
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Given:
Let y= 0.860(17) + 3.302
The rate of change is the same as the slope of the equation
Comparing the given equation with the standard for of the equation y =mx + b
Work each problem according to the instructions given.a. Solve:2r +3=8=Previewb. Find r when y = 0:2x + 3y = - 8T =Previewc. Find y when I = 0;21 + 3y =- 8y =Previewd. Solve for y:2x + 3y8y =Preview
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a)
The given equationis expressed as
2x + 3 = - 8
To solve for x, the first step is to subtract 3 from both sides of the equation. We have
2x + 3 - 3 = - 8 - 3
2x = - 11
Finally, we would divide both sides of the equation by 2. We have
2x/2 = - 11/2
x = - 11/2
810 А 30° E Given: Circle C. What is the value of angle x? B 99° 69° 132 30°
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In this problem you can reflect the small triangle and you will see that the angle D is equal to the angle x, and the angle E is equal to the angle B so we can sum tyhe internal angles of the big triangle to find x so:
[tex]x+81+30=180[/tex]And we solve for x so:
[tex]\begin{gathered} x=180-81-30 \\ x=69 \end{gathered}[/tex]the angles x is equal to 69º
Identifies which property it belongs to1) 15^8/5^32) (8^2)^1
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Given the calculation
[tex]\frac{15^8}{5^3}[/tex]Second calculation
[tex](8^2)^1[/tex]which of the following expressions could be used to determine?
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We have the following:
They tell us that the capacity is 350, therefore that is the maximum value, it means that we must subtract the exchange rate from this value, that is, the number od tickets per hour that are sold, 23
thus
[tex]350-23h[/tex]The answer is the option B.
the heart of an elephant, at rest, will beat an average of 1560 beats in 60 minutes. what's the rate in beats per minute?