The equation of a parabola in standard form is
[tex]y\text{ }=ax^2\text{ + bx + c}[/tex]So, we have the following equations,
For ( 2, -20) , -20 = a(2)^2 + b (2) + c,
For (-2, -4), -4 = a( -2)^2 + b (-2) + c,
For (0.-8), -8 = a (0) + b (0) + c
Then solving,
4a + 2b + c = -20 .............. equ 1
4a - 2b + c = -4 ................... equ 2
c= -8
put c= -8 in equ 1,
we have
4a + 2b -8 = -20 = 4a + 2b = -12 ------equ 3
put c= -8 in equ 2,
4a - 2b -8 = -4 = 4a - 2b = 4................... equ 4
Solving equ 3 and equ 4, a= -1 , b= -4
so a =-1, b= -4, c= -8
Then substituting the values in
[tex]y=ax^2\text{ + bx + c}[/tex][tex]y=-1(x^2)\text{ + -4(x) + }(-8)[/tex]
So, y= -x^2 -4x-8
Harriet found the number of At-Bats (AB) using the formula below
Here, we want to get what should have been written as step 1
As we can see from what is presented, she went directly to step 2 without writing out the individual product and summing them
So, we have the step 1 correctly written as;
[tex]0.520\text{ = }\frac{(28)\text{ + (94) +(3) + 240}}{AB}[/tex]Which is the image of vertex K after the parallelogram is rotated 180degrees about the origin?
Answer:
The image of vertex K is (3,-2)
Step-by-step explanation:
Rotated 180 degrees about the origin means that the value of x will not change, while y will have the same distance from the origin, but in a different direction.
Vertex K:
Value of x: x = 3
Value of y: y = 2
Distance from the origin: 2 - 0 = 2
Rotated, new coordinate: 0 - 2 = -2
The image of vertex K is (3,-2)
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers
Explanation
Let's remember some properties ofthe fractions ans exponents,
[tex]\begin{gathered} a^{-n}=\frac{1}{a^n} \\ (\frac{a}{b})^n=\frac{a^n}{b^n} \\ (ab)^n=a^nb^n \\ (a^n)^m=a^{m\cdot n} \end{gathered}[/tex]so
Step 1
[tex]\lbrack\frac{4p^{-2}q}{3^{-1}m^3}\rbrack^2[/tex]reduce by using the properties
[tex]\begin{gathered} \lbrack\frac{4p^{-2}q}{3^{-1}m^3}\rbrack^2 \\ \lbrack\frac{4q}{3^{-1}m^3p^2}\rbrack^2 \\ \lbrack\frac{3^1\cdot4q}{m^3p^2}\rbrack^2 \\ \lbrack\frac{12q}{m^3p^2}\rbrack^2 \\ \lbrack\frac{144q^2}{m^{3\cdot2}p^{2\cdot2}}\rbrack^{} \\ \lbrack\frac{144q^2}{m^6p^4}\rbrack^{} \end{gathered}[/tex]therefore, the answer is
[tex]\lbrack\frac{144q^2}{m^6p^4}\rbrack^{}[/tex]I hope this helps you
Determine the value of k for which f(x) is continuous.
These are the conditions of the continuity in a function:
First, the value of x must have an image.
Second, the lateral limits must be equal:
[tex]\lim_{x\to a^+}f(x)=\lim_{x\to a^-}f(x)[/tex]Finally, the value of the limit must be equal to the image of x. This means that:
[tex]f(a)=\lim_{x\to a^}f(x)[/tex]In this case, we must find a value of k that can make the two lateral limits equal in x =3:
[tex]\lim_{x\to3^+}x^2+k=\lim_{x\to3^-}kx+5[/tex]We can solve these two limits easily by replacing the x with the value of 3
[tex]3^2+k=3k+5[/tex][tex]\begin{gathered} 9+k=3k+5 \\ 4=2k \\ k=2 \end{gathered}[/tex]Finally, we can see that the answer is k=2.
(x+?)(x+3)=x squared+5x+6
The given expression is :
(x + ) (x + 3) = x² + 5x + 6
The polynomial is factorize and then written in the form of (x + ) (x + 3)
Let the missing number is "b" substitute in the equation and simplify :
(x + b ) (x + 3) = x² + 5x + 6
x² +bx + 3x + 3b = x² + 5x + 6
x² +x(b +3) + 3b = x² + 5x + 6
Comparing the constant term together :
3b = 6
Divide both side by 3
3b/3 = 6/3
b = 2
Since b is the missing term so, Missing term is 2
(x + 2 ) (x + 3) = x² + 5x + 6
Answer :(x + 2 ) (x + 3) = x² + 5x + 6
given which of the following describes the boundary line and shading for the second inequality in the system
Answer:
Solid Line, Shade Above
Explanation:
Given:
[tex]\left\{\begin{array}{l} y<-2 x+3 \\ y \geq x-4 \end{array}\right.[/tex]The second inequality in the system is:
[tex]y\geq x-4[/tex]The intercepts of the boundary line (y=x-4) are (0, -4) and (4,0).
Since the inequality has an equal to sign attached, we use a solid line.
At (0,0)
[tex]\begin{gathered} y\geq x-4 \\ 0\geq-4 \end{gathered}[/tex]Since the inequality 0≥-4 is true, shade the side that contains (0, 0) as shown in the graph below:
So, we use a solid line and shade above the boundary line.
Mr. Edmonds is packing school lunches for a field trip for the 6th graders of Apollo Middle school. He has 50 apples and 40 bananas chips. Each group of students will be given one bag containing all of their lunches for the day. Mr. Edmonds wants to put the same number of apples and the same number of bananas in each bag of lunches. What is the greatest number of bags of lunches Mr.Edmonds can make? How many apples and bananas will be in each bag?
There is a bag with 7 red buttons, 4 green buttons, 2 blue buttons, and 5 orange buttons. You are drawing thebuttons one at a time. Each time you draw a button, you keep it.P(red then green) =Show Your Work
7 red buttons, 4 green buttons, 2 blue buttons, and 5 orange buttons
In total there are
= 7 + 4 + 2 + 5
= 18 buttons
P (red) = 7/18
P(green) = 4/18
P(red then green) = 7/18 * 4/18
=7/81
Retest: ProbabilityFor problems 1-3: Johnny Awesome has three red marbles, two blue marbles, five green marbles, and 7 yellowmarbles in a bag. What is the probability that'Johnny.....3) draws a blue marble, does not replace it, and then draws a green marble?
Answer
5/136
Step-by-step explanation
Events
• A: a blue marble is drawn
,• B: without replacing the first marble, a green marble is drawn
There are 17 (= 3 + 2 + 5 + 7) marbles in total in the bag. Two of them are blue, then the probability of drawing a blue marble is:
[tex]P(A)=\frac{2}{17}[/tex]After a blue marble is drawn, 16 marbles are left in the bag. Five of them are green, then the probability of drawing a green marble is:
[tex]P(B)=\frac{5}{16}[/tex]Finally, the probability of drawing a blue marble and then a green marble without replacement is:
[tex]\begin{gathered} P(A\text{ and }B)=P(A)\cdot P(B) \\ P(A\text{ and }B)=\frac{2}{17}\cdot\frac{5}{16} \\ P(A\text{ and }B)=\frac{5}{136} \end{gathered}[/tex]The bases of the prism below are rectangles. If the prism's height measures 3 units and its volume is 198 units^3. solve for x
The volume of a rectangular prism is given by
V=L*W*H
where
V=198 units3
L=6 units
W=x units
H=3 units
substitute given values
198=(6)*(x)*(3)
solve for x
198=18x
x=198/18
x=11 unitsBob buys a vase for $15 and spends $2 per flower.
4) Write an equation to represent the cost of buying flowers.
If Bob buys a vase for $15 and spends $2 per flower, then the equation to represent the cost of buying flowers is 15+2x
The cost of flower vase = $15
The cost of each flower = $2
Consider the number of flowers as x
Then the linear equation that represents the cost of buying flowers = The cost of flower vase + The cost of each flower × x
Substitute the values in the equation
The equation that represents the cost of buying flowers = 15+2x
Hence, If Bob buys a vase for $15 and spends $2 per flower, then the equation to represent the cost of buying flowers is 15+2x
Learn more about linear equation here
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I need help with this and it is delivered at 3:30 pm and sadly I did not understand almost anything and I am confused.Problem 1
Reflection across the y-axis transforms the point (x,y) into (-x, y)
Applying this rule to points A, B, and C, we get:
A(-5, 6) → A'(5, 6)
B(3, 6) → B'(-3, 6)
C(-3, 2) → C'(3, 2)
Given that figure ABC was reflected, then figure A'B'C' is congruent with figure ABC
Witch phrase best describes the position of the opposite of +4
To find the position that is opposite to +4, we need to consider 0 as a "mirror point", then we check which point has the same distance to 0 as the distance from +4 to 0:
The position which is opposite to +4 is the position -4.
This position is 4 units to the left of 0 and 8 units to the left of +4.
Looking at the options, the correct option is the second one.
The rat population in major metropolitan city is given by the formula n(t)=40e^0.015t where t is measured in years since 1991 and n(t) is measured in millions. What does the model predict the rat population was in the year 2008?
To use the model we need to find the value of t. To do this we substract the year we want to know from the year the model began, then:
[tex]t=2008-1991=17[/tex]Now that we have t we plug it in the function:
[tex]n(17)=40e^{0.015\cdot17}=51.618[/tex]Therefore the model predict that there were 51.618 millions of rats in 2008.
Kimberly has an empty cardboard box that weighs 0.5 pounds. She puts 10 loaves of bread and a 4-pound jar of peanut butter in the box. The total weight of the box and its contents is 19.5 pounds. One way to represent this situation is with the equation 0.5 - 106 + 4 = 19.5 In this situation, what does the solution to the equation represent? In other words, if you solved for b. what would the value of b tell you? You do not have to find the solution to answer the question
The equation is represented by:
0.5 + 10b + 4 = 19.5
In which 19.5 is the total weight of the box and it's contents.
0.5 is the weight of the cardboard box.
4 is the weight of the jar of peanut butter.
10b is the weight of all loaves of bread.
And b is the weight of a single loaf of bread
The answer is:
The solution of the equation, which is the value of b, represents the weight of a single loaf of bread.
What is the y intercept of this equation10x+5y=30Write answer in (x,y)
The y intercept of a straight line is the point on the y axis where the line cuts the y axis.
Given equation of lineis
[tex]10x+5y=30[/tex]Putting x=0 in the above equation, we have,
[tex]\begin{gathered} 5y=30 \\ y=6 \end{gathered}[/tex]So, the y intercept is
[tex](0,6)[/tex]If mZABD = 70°, what are mZABC and mZDBC?
mZABC=
mZDBC=
(6x+3) D
B
(9x-8)
Please help me
Answer:
Step-by-step explanation:
ABD = ABC + DBC
Eqivalent to:
78 = (5x + 3) + (5x - 5)
78 = 5x + 5x + 3 - 5
78 = 10x - 2
80 = 10x (move -2 to the left side and get 78 + 2 = 80)
8 = x (80/10 = 8)
With x = 8,
ABC = 5x - 5 = 8*5 - 5 = 40 - 5 = 35
DBC = 5x +3 = 8*5 + 3 = 40 + 3 = 43
HELP ASAP
What is the size of the smallest angle in Triangle A? Give your answer correct to one
decimal place. Show your calculations.
Answer:
A is an included angle between 3 and 5
Use (60° - 45°) = 15° to find the exact value of cos 15º.vaV2 + V6V-V6(b)(c)4(d)4+ V62
Answer;
[tex]B\text{. }\frac{\sqrt[]{2}+\sqrt[]{6}}{4}[/tex]Explanation;
Given that;
[tex](60^0-45^0)=15^0[/tex]Hence;
[tex]\text{Cos 15}^0=Cos(60^0-45^0)[/tex]According to trigonometry identity;
[tex]\begin{gathered} Cos(60^0-45^0\text{) = Cos60 Cos45 + Sin60Sin45} \\ Cos(60^0-45^0\text{) }=\frac{1}{2}(\frac{1}{\sqrt[]{2}})+\frac{\sqrt[]{3}}{2}(\frac{1}{\sqrt[]{2}}) \end{gathered}[/tex]Evaluate the result by finding the LCM
[tex]Cos(60^0-45^0\text{) }=\frac{1+\sqrt[]{3}}{2\sqrt[]{2}}[/tex]Rationalize;
[tex]\begin{gathered} Cos(60^0-45^0\text{) }=\frac{1+\sqrt[]{3}}{2\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ Cos(60^0-45^0\text{) }=\frac{\sqrt[]{2}(1+\sqrt[]{3})}{2\cdot2} \\ Cos(60^0-45^0\text{) }=\frac{\sqrt[]{2}+\sqrt[]{6}}{4} \end{gathered}[/tex]Hence the required reusult is;
[tex]\frac{\sqrt[]{2}+\sqrt[]{6}}{4}[/tex]How do you know when an equation has infinite many solution?A. The coefficients are differentB. The coefficients are the same and the constants are differentC. The coefficients are the same and the constants are same
Solution:
An equation has infinitely many solutions when the coefficients are the same and the constants are the same.
This is illustrated as shown below:
[tex]\begin{gathered} 2a+5+a=\text{ 5+3a,} \\ thus,\text{ we have infinitely many solution} \end{gathered}[/tex]Hence, the correct option is C.
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges to rent trucks plus an additional fee of for each ton of sugar. The second company charges to rent trucks plus an additional fee of for each ton of sugar.For what amount of sugar do the two companies charge the same? What is the cost when the two companies charge the same?
step 1
Find the equation of the line First Company
y=100.25x+6,500
where
y is the total charge
x is the number of ton of sugar
Second Company
y=225.75x+4,492
Part a)
Equate both equations
100.25x+6.500=225.75x+4,492
solve for x
225.75x-100.25x=6,500-4,492
125.50x=2,008
x=16
answer part a is 16 tonPart b) For x=16 ton
substitute the value of x in any of the two equations (the result is the same)
y=100.25(16)+6,500
y=$8,104
answer Part b is $8,104What is the slope of the line in the graph?A. 2/3B. -2/3C. 3/2D. -3/2
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph
Step 02:
slope of the line:
we must analyze the graph to find the solution.
point 01 (0, 8)
point 02 (12, 0)
slope:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{0-8}{12-0}=\frac{-8}{12}=\frac{-2}{3}[/tex]The answer is:
m = - 2/3
The graph shows the proportional relationship between the number of gems collected and the number of levels that have been completed in a video game.
Graph with x axis labeled game levels and y axis labeled gems collected. A line begins at 0 comma 0 and goes through points 6 comma 420 and 8 comma 560.
Determine the constant of proportionality for the relationship.
p = 70
p = 140
p equals 2 over 140
p = 0.0143
Answer: P = 70
Step-by-step explanation:
p = 70 because on the graph everytime the y number is the x number multiplied by 70.
70 x 2 = 140
70 x 4 = 280
70 x 6 = 420
70 x 8 = 560
70 x 10 = 700.
Heres the chart for proof
The constant of proportionality (p) for this proportional relationship is equal to: A. p = 70.
How to determine the constant of proportionality?In Mathematics, the graph of any proportional relationship is characterized by a straight line because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously.
Mathematically, a proportional relationship can be represented by the following equation:
y = px
Where:
p is the constant of proportionality.y represents the gems collected.x represents the game levels.Next, we would determine the constant of proportionality (p) for the data points on this graph as follows:
p = y/x
p = 420/6 = 560/8
p = 70.
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Write an equation or inequality and solve:32 is at most the quotient of a number g and 8
The quotient of a number g and 8 can be written as:
[tex]\frac{g}{8}[/tex]Since it is given that 32 is at most( this quotient, then it follows that:
[tex]32\le\frac{g}{8}[/tex]Next, solve the resulting inequality:
[tex]\begin{gathered} 32\le\frac{g}{8} \\ \text{Swap the sides of the inequality and change the sign:} \\ \frac{g}{8}\ge32 \end{gathered}[/tex]Multiply both sides of the inequality by 8. Note that the sign will not change since you are multiplying a positive number:
[tex]\begin{gathered} \Rightarrow8\times\frac{g}{8}\ge8\times32 \\ \Rightarrow g\ge256 \end{gathered}[/tex]Hence, the inequality is:
[tex]32\le\frac{g}{8}[/tex]The solution is:
[tex]g\ge256[/tex]Show all five steps of the hypothesis test. You can either type them in here, or write them out on paper and send me a scan/picture of your work.The average movie ticket in 2010 cost $7.89. A random sample of 15 movie tickets from the suburbs of a large U.S. city indicated that the mean cost was $11.09 with a standard deviation of $4.86. At the 0.01 level of significance, can it be concluded that the mean in this area is higher than the national average?
Step 1
State the null and alternative hypothesis
[tex]\begin{gathered} H_o=7.89 \\ H_a>7.89 \end{gathered}[/tex]Step 2
State the p-value of the significance level.
[tex]\begin{gathered} \alpha=0.01 \\ p=\frac{\alpha}{2}=\frac{0.01}{2}=0.005 \end{gathered}[/tex]Step 3
Calculate the statistical test
[tex]\begin{gathered} n=15 \\ \mu(\operatorname{mean})=11.09 \\ \sigma(s\tan dard\text{ deviation)=4.86} \end{gathered}[/tex]The t-test formula is given as
[tex]t=\text{ }\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]Where
[tex]\begin{gathered} \bar{x}=\operatorname{mean} \\ \mu=theoretical\text{ }value \\ \end{gathered}[/tex][tex]\begin{gathered} t=\frac{7.89-11.09}{\frac{4.86}{\sqrt[]{15}}} \\ t=\frac{7.89-11.09}{1.254846604} \\ t=\frac{-3.2}{1.254846604} \\ t=-2.550112492 \end{gathered}[/tex]Step 4
Find the p-value from the t-test.
[tex]\text{The p-value from the t-test is 0.01}209[/tex]Step 5
Conclusion
The result is not significant at p<0.01. Therefore, the null hypothesis is rejected. It cannot be concluded that the mean in this area is higher than the national average because the p-value is greater than 0.01t
Each parking spot is 8 feet wide. A parking lot has 24 parking spots side by side. What is the width (measured in yards) of the parking lot? The shorter tree is
The width would be: 8ft*24 = 192 ft
Then, we have to convert the unit from ft to yards. Doing so,we have:
[tex]192ft\cdot\frac{1\text{ yard}}{3\text{ ft}}=64\text{ yards (Multiplying and dividing)}[/tex]The answer is 64 yards
Solve the right triangle. Write your answers in simplified, rationalized form. DO NOT ROUND!
base = FG = root 30
perpendicular HG = x
angle = 45 degrees,
we know that
[tex]\text{tan}\theta=\frac{perpendicualr}{base}[/tex][tex]\tan 45=\frac{HG}{\sqrt[]{3}}[/tex][tex]\begin{gathered} 1=\frac{HG}{\sqrt[]{3}} \\ HG=\sqrt[]{3} \end{gathered}[/tex]so, the value of HG = root 3
Find the area of a triangle with vertices at N(-4,2), A(3,2)and P(-1,-4).
The distance between points N and A is 7, and we can take that as the base of the tringle (up side down)
The distance between the base (NA) and the point P is 6, and we can take that as the height of the triangle
Area of a triangle = (Base x Height)/2
Area = (7 x 6)/2 = 42/2 = 21
Answer:
Area = 21
answer yes or no and explain why or why not.if a/5 = 8 + 9, does a/5 + 9 = 8 + 9?
Equations
We are given the following equation:
a/5 = 8+ 9
Adding 9 to both sides of the equation we have:
a/5 + 9 = 8 + 9 + 9
It's evident that a/5 + 9 is not equal to 8 + 9, but to 8+9+9 instead.
Answer: No
What is the slope: (-2, 1) (5,-2)
Answer: slope = -3/7
Step-by-step explanation:
m(slope) = (y2-y1)/(x2-x1)
m = (-2+-1)/(5--2)
m = (-2-1)/5+2)
m = -3/7