The symmetry of a quadratic equation is given by the line that passes through its vertex, so in order to find the axis of symmetry we need to find the coordinate of the vertex, which is done below.
[tex]x_{\text{vertex}}=\frac{-b}{2a}[/tex]Where "a" is the number multiplying the square factor and "b" is the number multiplying the factor that isn't squared. To find these two constants we need to expand the equation given.
[tex]\begin{gathered} (x-3)\cdot(x+7) \\ x^2+7x-3x-21 \\ x^2+4x-21 \end{gathered}[/tex]We have that a = 1 and b = 4, therefore:
[tex]x_{\text{vertex}}=\frac{-4}{2\cdot1}=-2[/tex]The axis of symmetry for this quadratic equation is x=-2.
There are 360° in a circle graph. If 50° of the graph represents rent and 7" of the graph represents savings, what fractional portion of the whole graph is not represented by rent and savings?
The fractional portion of the whole graph is not represented by rent and savings? is 101/120.
How to illustrate the information?From the information, there are 360° in a circle graph and 50° of the graph represents rent and 7" of the graph represents savings.
The part that isn't savings or rent will be:
= 360° - (7° + 50°)
= 360° - 57°
= 303°
Therefore, the fractional part will be:
= Part that isn't savings or rent / Entire degree
= 303/360
= 101 / 120
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Find the domain of the graphed function.A. -4sxs 8B. X2-4C. x is all real numbers.D. -4sxs 9
The domain of a function is the set of values over the x-axis where it is defined on a coordinate plane.
From the image, notice that the given graph is defined whenever x is between -4 and 9. Therefore, the domain of the function is:
[tex]-4\le x\le9[/tex]Write the decimal for each word. Then round the answer to the nearest tenthc) nine hundred forty-two ten-thousandths
nine hundred forty-two ten-thousandths:
1. Write the first part as a number: nine hundred forty-two
nine hundred: 900
forty-two: 42
900+42= 942
2. Identify the position of number above in the decimal knowing that ten-thousandths ends in 4 disgits after the decimal point (the last digit of number above needs to be in the ten-thousandths position):
The given number is: 0.0942Rounded the answer to the nearest tenth: 0.1find the value of. abe, bec, and the minor arc ec
Answer
Angle ABE = 64°
Angle BEC = 48°
Minor arc EC = 134°
Explanation
The key to solving this is to take a look at this image below
According to the tangent-chord theorem, we know that
Tangent Chord angle ABE = (Intercepted arc BE)/2
Angle ABE = (128°/2)
Angle ABE = 64°
Tangent chord angle CED = (Intercepted arc EC)/2
68° = (Minor arc EC/2)
Multiply both sides by 2
136° = Minor arc EC
To find the Angle BEC, we need to first obtain the arc BC
The total angle around a circle is 360°
Arc BE + Arc BC + Arc EC = 360°
128° + Arc BC + 136° = 360°
Arc BC = 360° - 128° - 136°
Arc BC = 96°
Then to find the Angle BEC, the image attached below guides us
So, we can easily say that
Angle BEC = ½ (Arc BC)
Angle BEC = ½ (96°)
Angle BEC = 48°
Hope this Helps!!!
Give the slope and y - intercept for each of the following equations, then sketch the graph. Give the slope ofany line perpendicular to the given line.y =22 +5Slope =y - intercept = (0,_ ) Slope of a Line Perpendicular =
The slope is 2.
The y-intercept is 5 or (0, 5)
See graph below
Explanation:Given:
y = 2x + 5
To find:
the slope, y-intercept, and plot a graph
To determine the slope and y-intercept, we will use the equation of line formula:
y = mx + b
m = slope
b = y-intercept
Comparing both equations:
y = y
2x = mx
m = 2
The slope = 2
5 = b
The y-intercept = 5
To plot the graph, we will assign values to x in order to get values to y that will be plotted:
let x = -4, 0, 4
when x = -4
y = 2(-4) + 5 = -3
when x = 0
y = 2(0) + 5 = 5
when x = 4
y = 2(4) + 5 = 13
Plotting the points:
Each line on the graph represents 1 unit
1. Write the equation of a line perpendicular to thex 5and that passes through thepoint (6,-4).line y
The line we want has a slope that is the negative reciprocal of the slope of the line
y = -(1/2)x - 5
The slope of this line is -1/2. So, the slope of its perpendicular lines is 2. Therefore, their equations have the form:
y = 2x + b
Now, to find b, we use the values of the coordinates of the point (6, -4) in that equation:
-4 = 2*6 + b
-4 = 12 + b
b = -4 - 12 = -16
Therefore, the equation is y = 2x - 16.
–2(1 – 5x) = 4 – 4(-2x)
-2(1 - 5x) = 4 - 4(-2x)
First, we eliminate the parentheses and solve the multiplications
-2*1 - 2*(-5x) = 4 + 8x
-2 + 10x = 4 + 8x
Now, we subtract 8x from both sides and add 2 to both sides
-2 + 10x - 8x + 2 = 4 + 8x - 8x + 2
2x = 6
Then, we divide both sides by 2
2x/2 = 6/2
x = 6/2
x = 3
Use the given sets to find A∩B.A={2,4,6,8,10,12}B={7,9,11,13,14,15,16}
Recall that
[tex]A\cap B[/tex]is a set that consists of all the elements that are in both A and B.
From the given sets we get that the elements that are in both A and B are:
[tex]\text{None.}[/tex]Therefore, the intersection of the sets is the empty set.
Answer:
[tex]A\cap B=\emptyset.[/tex]May I please get help with this. I need help with finding the original and final points on the figure and also finding out where I should put my reflection?
Answer:
Step-by-step explanation:
The rule for a reflection over the y-axis is represented by the following equation:
[tex](x,y)\rightarrow(-x,y)_{}[/tex]Therefore, for the given figure and given point:
Hello I need help with this . Thanks ok ok
Answer:
The given graph is not a graph of a function because a vertical line can be drawn that will intersect this graph more than once.
Explanation:
A vertical line test is generally used to determine if a relation is a function or not by drawing a vertical line across the graph of the relation.
If the vertical line intersects the graph of the relation more than once, it means that the relation is not a function because one x-value will have more than one y-value.
If the vertical line intersects the graph just once, then we can say that the relation is a function since one x-value will be associated with only one y-value.
Looking at the given graph, we can see that a vertical line can be drawn across the graph that will intersect the graph more than once, therefore the given graph is not a graph of a function because a vertical line can be drawn that will intersect the graph more than once.
I need a math wiz to explain this to me, are you a math wiz?
SOLUTION
The questions is outside scope
Find the volume of the cylinder and round to the nearest hundreth. Use 3.14 for pi
Volume of a cylinder: pi * r^2 * h
Where:
pi = 3.14
r= radius = 8km
h= heigth = 7km
Replacing:
V = 3.14 * (8)^2 * 7 = 1,406.72 km3
Find the solution of the system by graphing.-x - 4y=4y=1/4x-3Part B: The solution to the system,as an ordered pair,is
Solution
-x -4y = 4
y= 1/4 x -3
Replacing the second equation in the first one we got:
-x -4(1/4x -3) =4
-x -x +12= 4
-2x = 4-12
-2x = -8
x= 4
And the value of y would be:
y= 1/4* 4 -3= 1 -3= - 2
And the solution would be ( 4,-2)
The derivative of tan(ln(t)) is?
Answer: The derivative of tan(t) with respect to t is sec2(t) sec 2 ( t ) .
Step-by-step explanation:
hope this helps
For the function f(x)5x – 2, what does the x represent?
The given function is
f(x) = 5x - 2
If we are given a function f(x), the x is called argument of the function.
You just have to pass argument x to get the value of f(x).
solve the equation for x. x/16=10
To solve further cross multiply both sides
so that
[tex]x\text{ }\times1\text{ = 16 }\times10[/tex]x = 160
PLS HELP ASAP WILL GIVE BRAINLIST
Answer:
65
Step-by-step explanation:
[tex]-4a + 65 = 2a + 5\\60 = 6a\\a = 10\\[/tex]
KJN = 25 degrees
MJN = 25 degrees
KJM = KJN + MJN = 25 + 25 = 50 degrees
total angles = 360 degrees
JKL = (360 - 50 - 50 )/2 = 130 degrees
LKN is half of JKL = 130/2 = 65
I’m confused on this question. I just have to choose which one
SOLUTION:
Case: Circle theorems
Method:
From the given circle
Theorem: The angle at the center of the circle is twice the angle at the circumference formed by the same segment.
The implication to the circle in the question is:
[tex]\begin{gathered} \hat{mST}=2m\angle2 \\ OR \\ m\angle2=\frac{1}{2}(\hat{mST}) \end{gathered}[/tex]Final answer
[tex]m\operatorname{\angle}2=\frac{1}{2}(\hat{mST})[/tex]You have 4/5 of a pizza left over from your pool party. If you sent 4/9 of the leftover pizza home with your friends how much of the pizza do you have left in the box
If I sent 4/9 of the leftover pizza home with your friends the pizza do I have left in the box is 16/45.
What is pizza?
Pizza is an Italian food consisting of a typically flat, spherical foundation composed of leavened wheat dough that is topped with cheese, tomatoes, and frequently a number of additional toppings. Following that, the pizza is baked at a high temperature, typically in a wood-fired oven. A small pizza is also known as a pizzetta. A pizza maker is referred to as a pizzaiolo.
To get the quantity of the leftover pizza, we need to subtract the pizza sent by me to home from the total pizza I had in my lunch box.
So,
Pizza I have left = Pizza in lunch box - Pizza I have sent
Pizza I have left = 4/5 - 4/9
Pizza I have left = (4(9) - 4(5))/45
Therefore, Pizza I have left is 16/45.
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I need help with this quadratic function… I thought I knew the answer, but obviously I don’t
Let us start with the following quadratic function:
[tex]f(x)=x^2-x-12[/tex]the X-intercepts are the collection of values to X which makes f(x) = 0, and it can be calculated by the Bhaskara formula:
[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where the values a, b, and c are given by:
[tex]f(x)=ax^2+bx+c[/tex]Substituting the values from the proposed equation, we have:
[tex]\begin{gathered} x_{1,2}=\frac{1\pm\sqrt{1^2-4*1*(-12)}}{2*1} \\ x_{1,2}=\frac{1\pm\sqrt{1+48}}{2}=\frac{1\pm\sqrt{49}}{2} \\ x_{1,2}=\frac{1\pm7}{2} \\ \\ x_1=\frac{1+7}{2}=\frac{8}{2}=4 \\ x_2=\frac{1-7}{2}=-\frac{6}{2}=-3 \end{gathered}[/tex]From the above-developed solution, we are able to conclude that the solution for the first box is:
(-3,0) ,(4,0)Now, the y-intercept, is just the value of y when x = 0, which can be calculated as follows:
[tex]\begin{gathered} f(0)=0^2-0-12=-12 \\ f(0)=-12 \end{gathered}[/tex]From this, we are able to conclude that the solution for the second box is:
(0, -12)Now, the vertex is the value of minimum, or maximum, in the quadratic equation, and use to be calculated as follows:
[tex]\begin{gathered} Vertex \\ x=-\frac{b}{2a} \\ y=\frac{4ac-b^2}{2a} \end{gathered}[/tex]substituting the values, we have:
[tex]\begin{gathered} x=-\frac{-1}{2*1}=\frac{1}{2} \\ y=\frac{4*1*(-12)-(-1)^2}{4*1}=\frac{-48-1}{4}=\frac{-49}{4} \end{gathered}[/tex]which means that the solution for the thirst box is:
(1/2, -49/4) (just as in the photo)Now, the line of symmetry equation of a quadratic function is a vertical line that passes through the vertex, which was calculated to be in the point: (1/2, -49,4).
Because this is a vertical line, it is represented as follows:
[tex]x=\frac{1}{2}[/tex]A spinner has eight = sections, five of which are gray and red with your blue. The Spinners spun twice. What is the probability that the first spin lands on blue and the second spin lands on gray.
The probability that the first spin lands on blue and the second spin lands on gray is 15 / 56.
What is probability?Probability is the likelihood that an event will happen or take place.
The spinner has eight = sections, five of which are gray and red with your blue.
Probability that the first spin lands on blue = 8
(8 - 5)/8 = 3/8
The probability of landing of gray is 5/7 for the second time.
Therefore, the probability will be:
= 3/8 × 5/7
= 15 / 56
This illustrates the concept of probability.
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I have the answers for the first two but now I'm just confused
Paula will make fruit punch for a party she will mix 1 1/2 gallons of orange juice with 5/8 of a gallon of pineapple juice how many 1/8 gallon servings will Paula have
First let's find the total number of gallons of the fruit punch. To do so, we just need to sum the gallons of orange juice (1 1/2) ith the gallons of pineapple juice (5/8):
[tex]1\frac{1}{2}+\frac{5}{8}=\frac{3}{2}+\frac{5}{8}=\frac{12}{8}+\frac{5}{8}=\frac{17}{8}[/tex]Now, in order to find how many 1/8 servings can be made, we need to divide the total number of gallons of the fruit punch by the number of gallons of a serving:
[tex]\frac{\frac{17}{8}}{\frac{1}{8}}=\frac{17}{8}\cdot\frac{8}{1}=17[/tex]So Paula can have 17 servings.
Answer:
17
Step-by-step explanation:
5/8 - 5
1 1/2 - 12
The House of Pizza say that their pizzas are 14 inches wide, but when you measured it, the pizza was 12 inches. What is your percent error? Make sure to include your percent sign! (Round to 2 decimals)
The percent error of the house of the pizza would be 2.
The difference between the estimated and actual values in comparison to the actual value is expressed as a percentage. In other words, the relative error multiplied by 100 equals the percent error.
How to calculate the percent error?Percent errors indicate the magnitude of our errors when measuring something in an analysis process. Lower percentage errors indicate that we are getting close to the accepted or original value.
Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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The equation of a curve is y=f(x)
The vertex of the curve is at (2,-3)
Write down the coordinates of the vertex of the curve with the equation
a) f(x)+5
b) -f(x)
The rigid transformations of the vertex of the curve are listed below:
(i) (2, 2).
(ii) (2, 3).
How to determine the coordinates of the vertex
In this problem we find the value of a point of a curve f(x), this point (the vertex) must be transformed by using rigid transformations. There are two cases: (i) Vertical translation, (ii) Reflection about the x-axis. The formulas for each case are described below:
Vertical translation
P'(x, y) = P(x, y) + (0, k)
Reflection about the x-axis
P'(x, y) = P(x, y) + (0, - 2 · p)
Where p is the y-coordinate of point P.
If we know that P(x, y) = (2, - 3), then the coordinates for each case are, respectively:
Vertical translation
P'(x, y) = (2, - 3) + (0, 5)
P'(x, y) = (2, 2)
Reflection about the x-axis
P'(x, y) = (2, - 3) + (0, 6)
P'(x, y) = (2, 3)
The transformations of the vertex of the curve are (i) (2, 2) and (ii) (2, 3).
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(x^2+9)(x^2-9) degree and number of terms
ANSWER
Degree: 4
Number of terms: 2
EXPLANATION
Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows.
Given the table that shows the number of movies and the corresponding frequency, you can determine that the total frequency is:
[tex]Total\text{ }Frequency=25[/tex]By definition:
[tex]Relative\text{ }Frequency=\frac{Frequency}{Total\text{ }Frequency}[/tex]By definition, the Cumulative Frequency can be obtained by adding the corresponding frequency with the previous frequencies and dividing the sum by the Total Frequency.
Therefore, you can determine that:
- For:
[tex]Frequency=3[/tex]You know:
[tex]Relative\text{ }Frequency=\frac{3}{25}[/tex]And:
[tex]Cummulative\text{ }Relative\text{ }Frequency=\frac{3}{25}[/tex]- Given:
[tex]Frequency=8[/tex]You get:
[tex]Relative\text{ }Frequency=\frac{8}{25}[/tex]And:
[tex]Cummulative\text{ }Relative\text{ }Frequency=\frac{3+8}{25}=\frac{11}{25}[/tex]- Given:
[tex]Frequency=9[/tex]You get:
[tex]Relative\text{ }Frequency=\frac{9}{25}[/tex]And:
[tex]Cummulative\text{ }Relative\text{ }Frequency=\frac{3+8+9}{25}=\frac{4}{5}[/tex]- Given:
[tex]Frequency=4[/tex]You get:
[tex]Relative\text{ }Frequency=\frac{4}{25}[/tex]And:
[tex]Cummulative\text{ }Relative\text{ }Frequency=\frac{3+8+9+4}{25}=\frac{24}{25}[/tex]- Given:
[tex]Frequency=1[/tex]You get:
[tex]Relative\text{ }Frequency=\frac{1}{25}[/tex]And:
[tex]Cummulative\text{ }Relative\text{ }Frequency=\frac{3+8+9+4+1}{25}=\frac{25}{25}=1[/tex]Hence, the answer is:
-3x + 14y =7 -2x + 13y = -1Should this be solved by elimination or substitution?
ANSWER
Elimination
EXPLANATION
We want to decide what method will be easier to solve the system of simultaneous equations.
From the equation, we see that attempting substitution will be quite difficult because there will be fractions involved thereby making simplification difficult.
On the other hand, elimination will involve multiplying the two equations by certain factors and solving.
Therefore, elimination will be more convenient.
Solve the inequality
And how do I graph Graph the solution below:
Answer:
Step-by-step explanation:
to solve, divide both sides by -3/2 to isolate x
you'll get x>1.5
to graph, make a ray pointing right from 1.5 with an open dot
In how many ways can the letters in the word PAYMENT be arranged using 4 letters?A. 42B. 840C. 2520D. 1260
The word PAYMENT has 7 letters. They can be arranged in groups of 4 like shown below:
PYNT, TA
