I need help on #13 please !!! Also with the (circle the vertex on the graph and draw the axis of symmetry) !
Answers
Given the quadratic equation
[tex]2x^2-16x+24=0[/tex]we want to solve for the vertex and its axis of symmetry.
To easily identify these properties of quadratic equation, we must put the equation first into its vertex form. The first step to write it in its vertex form is to move the constant on the right-hand side of the equation
[tex]\begin{gathered} 2x^2-16x=-24 \\ x^2-8x=-12 \end{gathered}[/tex]After that, we add the square of b/2 on the equation above. The value of b on the quadratic equation is -16. We have
[tex]x^2-8x+(\frac{-8}{2})^2=-12+(\frac{-8}{2})^2[/tex]Simplify the equation above
[tex]\begin{gathered} x^2-8x+16=-12+16 \\ x^2-8x+16=4 \end{gathered}[/tex]We write the expression on the left-hand side as perfect square, which is (x-4)^2.
[tex](x-4)^2=4[/tex]Transfer 4 to left-hand side to write the vertex form of the quadratic equation
[tex](x-4)^2-4=0_{}[/tex]The vertex form has the general equation
[tex]y=a(x-h)^2+k[/tex]where (h,k) is the vertex of the parabola.
Based on the vertex form of the quadratic formula, the vertex exists at (4,-4). Also, the axis of symmetry is equal to h, which is in this case, equal to 4.
The representation of a vertex and axis of symmetry in a quadratic plot will be
Answer: Vertex = (4,-4)
Axis of symmetry = 4
Related Questions
Question 1 (1 point)
What integer represents a rise in temperature of 19°?
O a -|-191
Ob
-19
Oc
19
Od
-|19|
Answers
The integer which represents the rise in temperature of 19° is -|19|
Positive, negative, and zero numbers all fall under the category of integers. The word "integer" is a Latin word that signifies "whole" or "intact." Therefore, fractions and decimals are not considered to be integers.
A number without a decimal or fractional element is known as an integer, which encompasses both positive and negative numbers, including zero. The following are some examples of integers: -5, 0, 1, 5, 8, 97, and 3,043. Z denotes a collection of integers,
hence the correct form is answered.
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(A) How many ways can a 2-person subcommittee be selected from a committee of 8 people?
Answers
To solve this problem, we have to use the combination formula
[tex]C^r_n=\frac{n!}{r!(n-r)!}[/tex]Where r represents the number of people for the subcommittee (2), and n represents the total committee (8). Replacing this information, we have
[tex]C^2_8=\frac{8!}{2!(8-2)!}=\frac{8!}{2!(6)!}[/tex]Remember that factorials are solved by multiplying the number in a reversal way, as follows
[tex]C^2_8=\frac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(2\cdot1)(6\cdot5\cdot4\cdot3\cdot2\cdot1)}=\frac{40,320}{2(720)}=\frac{40,320}{1,440}=28[/tex]Therefore, there are 28 ways to form a 2-person subcommittee from a committee of 8.-3x plus 12y equivalent expressions
Answers
The equivalent expression for -3x + 12y is 3 (-x + 4y).
What are expressions?Expressions include a statement, at least one arithmetic operation, and at least two numbers or variables.
Given equation:
-3x + 12y
Take 3 as common from both the term, and we get,
= 3 (-x + 4y) so the equivalent expression will be 3(-x + 4y).
Therefore, the equivalent expression for -3x + 12y is 3 (-x + 4y).
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Joe borrowed $9,000 from the bank at a rate of 7% simple interest pa year. How much interest did he pay in 5 years? In 5 years, Joe pays ? In Interest
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Principal = 9000
Interest rate = 7% = 0.07
Time = 5 years
Simple interest formula:
A = P(1 + rt)
In this case:
A = 9000(1 + 0.07*5) = 9000(1 + 0.35) = 9000(1.35) = 12150
Interest = A - P = 12150 - 9000 = 3
Onions are on sale at four different grocery stores. Which store offers thelowest unit rate for onions, in dollars per pound?$3.20• Farm Fresh:4 pounds• Mother Nature:1 pound$1.70• Hobson's:2 pounds• Veggie Delight: $0.70/poundO A. Farm FreshOB, Veggie DelightOC. Mother NatureD. Hobson's
Answers
T determine which store offers the lowest unit rate for onions ($/pound) you have to express calculate the price per pound for each grocery store and then compere the results.
To calculate the price per pound you can use corss multiplication
Farm Fresh
4pounds _____$3.20
1pound____$x
[tex]\begin{gathered} \frac{3.20}{4}=\frac{x}{1} \\ x=\frac{3.20}{4} \\ x=0.80 \end{gathered}[/tex]The onions cost $0.80 per pound
Mother nature
1/3pound ____$1/4
1pound____$x
[tex]\begin{gathered} \frac{\frac{1}{3}}{\frac{1}{4}}=\frac{x}{1} \\ x=\frac{1}{3}\cdot\frac{4}{1} \\ x=\frac{4}{3}\cong1.33 \end{gathered}[/tex]The onions cost $1.33 per pound
Hobson's
2pounds_____$1.70
1pound____$x
[tex]\begin{gathered} \frac{1.70}{2}=\frac{x}{1} \\ x=\frac{1.70}{2} \\ x=0.82 \end{gathered}[/tex]The onions cost $0.82 per pound
Veggie Delight
$0.70 per pound
calculate the average speed of a lion that runs 45 m in 5 seconds
Answers
Answer:
9 m /s
Step-by-step explanation:
To find the speed, take the distance and divide by the time
45 m/ 5 s
9 m /s
Answer:
[tex] \sf9ms ^{ - 1} [/tex]
Step-by-step explanation:
[tex] \sf \: Average \: speed = \frac{ Total \: distance }{Total \: Time}[/tex]
Let us find the average speed now.
[tex] \sf \: Average \: speed = \frac{ Total \: distance }{Total \: Time} \\ \sf \: Average \: speed = \frac{ 45m }{5s} \\ \sf \: Average \: speed = 9ms ^{ - 1} [/tex]
Can somebody help me with 2.) C? Thx, this is Algebra 2.
Answers
SOLUTION
Step 1 :
We need to list the transformation for the equation,
[tex]y\text{ = -}\frac{1}{5}x^2\text{ -3}[/tex]compared to the parabola parent function,
[tex]y=x^2[/tex]Step 2 :
We need to graph the function,
[tex]\begin{gathered} y\text{ = -}\frac{1}{5}x^2\text{ - 3} \\ \text{compared to the parabola parent function, y =x}^2 \end{gathered}[/tex]Step 3 :
The graph is as shown below:
Step 4 :
Based on the two graphs, we can see that:
The transformations are Reflection, Vertical Shift and Vertical Compression.
The value of 41 squared is between which two whole numbers?
Answers
The image shows the square root of 41
The root of 41 in decimal is 6.403.
As such the integers before and after 6.403 are 6 and 7
Another way to solve this is to consider the perfect square before 41 which is 36.
The square root of 36 is 6. Since 41 is higher than 36, the number before root 41 would be 6 and the next number after 6 is 7.
Hence the two numbers before and after √41 are 6 and 7
I NEED HELP WITH THIS
Answers
Answer:
see explanation
Step-by-step explanation:
given that W varies jointly with l and d² then the equation relating them is
W = kld² ← k is the constant of variation
(a)
to find k use the condition W = 6 when l = 6 and d = 3 , then
6 = k × 6 × 3² = 6k × 9 = 54k ( divide both sides by 54 )
[tex]\frac{6}{54}[/tex] = k , then
k = [tex]\frac{1}{9}[/tex]
W = [tex]\frac{1}{9}[/tex]ld² ← equation of variation
(b)
when W = 10 and d = 2 , then
10 = [tex]\frac{1}{9}[/tex] × l × 2² ( multiply both sides by 9 to clear the fraction )
90 = 4l ( divide both sides by 4 )
22.5 = l
(c)
when d = 6 and l = 1.4 , then
W = [tex]\frac{1}{9}[/tex] × 1.4 × 6² = [tex]\frac{1}{9}[/tex] × 1.4 × 36 = 1.4 × 4 = 5.6
Chang drove 871 miles in 13 hours. At the same rate how long would it take him to drive 536 miles?
Answers
Answer:
8 hours
Step-by-step explanation:
You need to find time per every mile.
So you do 13/871 which is 0.0149253731 miles for every hour.
You multiply that number by 536 which gets you 7.99999998 hours which allows you to round to 8 hours.
Given (x – 7)2 = 36, select the values of x.
Answers
Answer:
x = 1 , x = 13
Step-by-step explanation:
(x - 7)² = 36 ( take square root of both sides )
x - 7 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 7 to both sides )
x = 7 ± 6
then
x = 7 - 6 = 1
x = 7 + 6 = 13
GG is considering two websites for downloading music. The costs are detailed here.
Website 1: a yearly fee of $15 and $5 for each download
Website 2: $7 for each download
Select the equation for Website 1.
Responses
y=15x+5
y=5x+15
y=−7x
y=7x
Answers
The equation for Website 1 is y = 15 + 5x option (A) is correct if yearly fee of $15 and $5 for each download
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
GG is considering two websites for downloading music.
Website 1: a yearly fee of $15 and $5 for each download
Let x be the number of downloads
Equation for the website 1:
Total cost is y
y = 15 + 5x
Thus, the equation for Website 1 is y = 15 + 5x option (A) is correct if yearly fee of $15 and $5 for each download
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I need guidance on finding the correct answers because I am confused
Answers
The Solution:
The correct answer is [option 4]
Given:
Required to select the correct statements.
[tex]\Delta ABC\cong\Delta DCB\text{ \lparen Reason: Side-Angle-Side Triangle Congruence Theorem}[/tex]Thus, the correct answer is [option 4]
The table below gives the dimensions of a statue and a scale drawing of the statue.Find the scale factor of the drawing to the real statue.Write your answer as a fraction in simplest form.Height (inches)Length (inches)Scale factor:Drawing8006Statue6448 I need help with this math problem.
Answers
Given:
Find-:
The scale factor
Explanation-:
The scale factor is:
[tex]S.F.=\frac{\text{ Status}}{\text{ Drawing}}[/tex][tex]S.F.=\frac{64}{8}\text{ or }\frac{48}{6}[/tex]So, the scale factor is:
[tex]\begin{gathered} S.F.=\frac{64}{8}\text{ or }\frac{48}{6} \\ \\ S.F.=8\text{ or }8 \\ \\ S.F.=8 \end{gathered}[/tex]The scale factor is 8.
two cards are drawn without replacement from a standard deck of 52 playing cards what is the probability of choosing a club and then without replacement a spade
Answers
occurringGiven a total of 52 playing cards, comprising of Club, Spade, Heart, and Spade.
[tex]\begin{gathered} n(\text{club) = 13} \\ n(\text{spade) =13} \\ n(\text{Heart) = 13} \\ n(Diamond)=\text{ 13} \\ \text{Total = 52} \end{gathered}[/tex]Probability of an event is given as
[tex]Pr=\frac{Number\text{ of }desirable\text{ outcome}}{Number\text{ of total outcome}}[/tex]Probability of choosing a club is evaluated as
[tex]\begin{gathered} Pr(\text{club) = }\frac{Number\text{ of club cards}}{Total\text{ number of playing cards}} \\ Pr(\text{club)}=\frac{13}{52}=\frac{1}{4} \\ \Rightarrow Pr(\text{club) = }\frac{1}{4} \end{gathered}[/tex]Probability of choosing a spade, without replacement
[tex]\begin{gathered} Pr(\text{spade without replacement})\text{ = }\frac{Number\text{ of spade cards}}{Total\text{ number of playing cards - 1}} \\ =\frac{13}{51} \\ \Rightarrow Pr(\text{spade without replacement})=\frac{13}{51} \end{gathered}[/tex]Thus, the probability of both events occuring (choosing a club, and then without replacement a spade) is given as
[tex]\begin{gathered} Pr(\text{club) }\times\text{ }Pr(\text{spade without replacement}) \\ =\frac{1}{4}\text{ }\times\text{ }\frac{13}{51} \\ =\frac{13}{204} \end{gathered}[/tex]Hence, the probability of choosing a club, and then without replacement a spade is
[tex]\frac{13}{204}[/tex]Kyle can wash the car in 30 minutes. Michael can wash the car in 40 minutes. Working together, can they wash the car in less than 16 minutes?
Answers
Step-by-step explanation:
Kyle can do in 1 minute 1/30 of the work.
Michael can do in 1 minute 1/40 of the work.
the whole work is 1.
how much can they do together in 16 minutes ?
16×1/30 + 16×1/40 = 8/15 + 2/5 = 8/15 + 3/3 × 2/5 =
= 8/15 + 6/15 = 14/15
which is less than 1 = 15/15.
so, as they cannot even do the whole work in 16 minutes, they cannot do it in less than 16 minutes either.
can someone help and explain how to do this. Ive been stuck in this lesson for days. This is so confusing and hard.
Answers
when x = 0:
y = 0/2 = 0
when x = 2:
y = 2/2 = 1
when x = 4:
y = 4/2 = 2
when x = 6:
y = 6/2 = 3
Divide f(x) = x^3 - x^2 - 2x + 8 by (x-1) then find f(1)
Answers
Division of f(x) = x³ - x² - 2x + 8 by (x-1) will have a quotient of x² - 2 and a remainder of 6.
What is the remainder theoremThe remainder theorem states that if f(x) is divides by x - a, the remainder is f(a).
We shall divide the f(x) = x³ - x² - 2x + 8 by x - 1 as follows;
x³ divided by x equals x²
x - 1 multiplied by x² equals x³ - x²
subtract x³ - x² from x³ - x² - 2x + 8 will result to -2x + 8.
-2x² divided by x equals -2
x - 1 multiplied by -2 equals -2x + 2
subtract -2x + 2 from -2x + 8 will result to a remainder of 6, and a quotient of x² - 2.
f(1) = (1)³ - (1)² - 2(1) + 8
f(1) = 1 - 1 - 2 + 8
f(1) = 6
Therefore, f(1) is a remainder of as x - 1 divides f(x) = x³ - x² - 2x + 8 resulting to a quotient of x² - 2 and a remainder of 6
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a tree standing vertically on level ground casts a 118 foot long shadow. the angle of elevation from the end of the shadow to the top of the tree is 22.3 degrees. find the height of the tree to the nearest tenth of foot.
Answers
Since the situation forms a right triangle, we can apply trigonometric functions:
Tan a = opposite side/ adjacent side
Where:
a= angle = 22.3°
opposite side = x
adjacent side = 118
Replacing:
Tan 22.3° = x / 118
Solve for x
Tan 22.3 * 118 = x
x = 48.4 ft
There is a population of 205 tigers in a national park. They are being illegally poached at the rate of 7tigers per year.Assume the population is otherwise unchanging, write a linear model using "P" for population and "t" fortime.What does the t-intercept signify?NOTE: This answer will NOT be automatically graded and will appear as a 0 until the instructor hasgraded it.Question Help: Message instructorSubmit Question
Answers
Solution.
Initial population = 205
After 1 year, population = 205 - 7 = 198
After 2 years , population = 198 - 7 = 191
After 3 years , population = 191 - 7 = 184
We can generate a table of value for the changes
[tex]\begin{gathered} Slope\text{ of the line, m = }\frac{198-205}{1-0} \\ m=-\frac{7}{1} \\ m=-7 \end{gathered}[/tex]One point on the line = (0, 205)
[tex]\begin{gathered} The\text{ equation of the linear model can be gotten using the formula} \\ y-y_1=m(x-x_1) \\ y-205=-7(x-0) \\ y-205=-7x \\ y=-7x+205 \\ Replacing\text{ y with P and x with t} \\ The\text{ linear model is P = -7t + 205} \end{gathered}[/tex]The t-intercept signifies the time when the population of the tiger will be zero. That is the time when there will be no more tigers in the park
Answer:
Step-by-step explanation:
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i inserted a picture of the question, i can give you the answer to the previous question if it helps. C(t) = -0.30(t-12)^2 + 40
Answers
Answer:
F(t) = -0.54(t - 12)² + 104
Explanation:
We know that C(t) = -0.30(t - 12)² + 40 and F(t) = 9/5C(t) + 32
Then, we can replace C(t) on the equation of F(t) to get
[tex]\begin{gathered} F(t)=\frac{9}{5}C(t)+32 \\ F(t)=\frac{9}{5}(-0.30(t-12)^2+40)+32 \\ F(t)=\frac{9}{5}(-0.30)(t-12)^2+\frac{9}{5}(40)+32 \\ F(t)=-0.54(t-12)^2+72+32 \\ F(t)=-0.54(t-12)^2+104 \end{gathered}[/tex]Therefore, the new function F(t) is
F(t) = -0.54(t - 12)² + 104
Nate's age is six years more than twice Connor's age. If the sum of their ages is 24 find each age
Answers
Answer:
12
Step-by-step explanation:
nate's age=6
connor's age =6+6=12
Nate's age +connor's age =24
Nate's age=24÷3=8
connor's age=8+8=16
the sum of thier ages =24
2.1 Simplify without using a calculator. 2.1.1 √√125 -√√
[tex] \sqrt{125 - \\ \sqrt{ \frac{1 \\ }{?} } } [/tex]
-
Answers
Logarithm 6) If log 5 = A and log 3 = B, find the following in terms of A and B:
Answers
Given the following parameters:
log 5 = A
log 3 = B
According to the law of product and quotient of logarithm as shown:
[tex]\begin{gathered} \log AB=\log A+\log B \\ \log (\frac{A}{B})=\log A-\log B \\ \log A^b=b\log A \end{gathered}[/tex]Applying the laws of logarithm in solving the given logarithm
[tex]\begin{gathered} a)\log 15 \\ =\log (5\times3) \\ =\log 5+\log 3 \\ =A+B \end{gathered}[/tex]For the expression log(25/3)
[tex]\begin{gathered} b)\log (\frac{25}{3}) \\ =\log (\frac{5^2}{3}) \\ =\log 5^2-\log 3 \\ =2\log 5-\log 3 \\ =2A-B \end{gathered}[/tex]For the expression log135
[tex]\begin{gathered} \log (135) \\ =\log (5\times27) \\ =\log (5^{}\times3^3) \\ =\log 5^{}+\log 3^3 \\ =\log 5+3\log 3 \\ =A+3B \end{gathered}[/tex]For the expression log₅27
[tex]\begin{gathered} \log _527 \\ =\frac{\log 27}{\log 5} \\ =\frac{\log 3^3}{\log 5} \\ =\frac{3\log 3}{\log 5} \\ =\frac{3B}{A} \end{gathered}[/tex]For the expression log₉625
[tex]\begin{gathered} \log _9625 \\ =\frac{\log 625}{\log 9} \\ =\frac{\log 5^4}{\log 3^2} \\ =\frac{4\log 5}{2\log 3} \\ =\frac{\cancel{4}^2A}{\cancel{2}B} \\ =\frac{2A}{B} \end{gathered}[/tex]For the value of 15, this can be expressed as shown. Since:
[tex]\begin{gathered} \log 5=A;10^A=5 \\ \log 3=B;10^B=3^{} \end{gathered}[/tex]Since 15 = 5 × 3, writing it in terms of A and B will be expressed as:
[tex]\begin{gathered} 15=5\times3 \\ 15=10^A\times10^B \\ 15=10^{A+B} \end{gathered}[/tex]Select the correct difference.-325 - (-725)4 z4 25-10 25-45
Answers
Given:
-325 - (-725)
We know that negative negative equals positive
(- -) = +
Therefore, we have:
-325 - (-725)
= -325 - -725
= -325 + 725 = 400
ANSWER:
400
what is a probability of surveying a student that is in math Spanish and chemistry round to the three decimal places
Answers
From the figure, the total number of students is
[tex]\begin{gathered} N=70+3+17+15+5+60+85+5 \\ N=260 \end{gathered}[/tex]The number 15 is common in spanish, chemistry and math.
Hence, the number of students studying spanish, chemistry and math, n=15.
Therefore, the probability of surveying a student that is in math Spanish and chemistry is,
[tex]\begin{gathered} P=\frac{n}{N} \\ P=\frac{15}{260} \\ P=0.058 \end{gathered}[/tex]Therefore, the
Triangle OPQ is similar to triangle RST. find the neasure of side ST. Round to the nearest tenth if necessary
Answers
By definition, when two figures are similar, their corresponding angles are congruent (this means that they have equal measure) and the ratios of the lengths of their corresponding sides are the same.
In this case you know that the triangles shown in the picture are similar, therefore, you can set up the following proportion:
[tex]\frac{OP}{RS}=\frac{PQ}{ST}[/tex]You can identify that:
[tex]\begin{gathered} OP=37 \\ RS=7 \\ PQ=48 \end{gathered}[/tex]Therefore, you can substitute values into the proportion:
[tex]\frac{37}{7}=\frac{48}{ST}[/tex]Now you have to solve for ST:
[tex]\begin{gathered} (ST)(\frac{37}{7})=48 \\ \\ ST=(48)(\frac{7}{37}) \\ \\ ST\approx9.1 \end{gathered}[/tex]The answer is:
[tex]ST\approx9.1[/tex]Please help quickly
Answers
The equation of the function in standard form is y = 3x -12.
How to write the equation of a function in a standard form when two points are given?
1. First find the slope using the slope formula, m = (y₂ - y₁) / (x₂ - x₁)
2. Find the y-intercept by substituting the slope and the coordinates of 1 point into the slope-intercept formula, y = mx + b.
3. Write the equation using the slope and y-intercept.
Here, we have
Points (2,-6) and (5, 3)
First we find the slope using the slope formula, m = (y₂ - y₁) / (x₂ - x₁), we get
m = (3 + 6) / (5 - 2)
m = 3
then, we find the y-intercept by substituting the slope and the coordinates of 1 point into the slope-intercept formula, y = mx + b.
we get,
-6 = 3*2 + b
-6 - 6 = b
b = 12
Now, we write the equation using the slope and y-intercept
we get,
y = mx + b
y = 3x - 12
Hence, the equation of the function in standard form is y = 3x -12.
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Find an equation of the line that satisfies the conditionPasses through (-1,-3) and (4,2)
Answers
The points given are:
(-1, -3) and (4, 2)
Coordinates are:
x₁ =-1 y₁=-3 x₂ = 4 y₂ = 2
First, let's find the slope(m) of the equation using the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]=\frac{2+3}{4+1}=\frac{5}{5}=1[/tex]Next, find the inetercept of the equation by substituting x =-1 y=-3 m = 1 into y=mx+ b
-3 = 1(-1) + b
-4 = -1 + b
Add 1 to bothside
-4+1 = b
-3 = b
b = -3
We can now form the equation of the line by simply substituting the value of m and b into y=mx+ b
y = x - 3
Therefore, the equation of the line that satisfies the condition is y = x - 3
Pls, answer in a minute. PLS
Answers
Answer: The square will fit.
Step-by-step explanation:
the diameter of the circle is large enough that since the square is 7cm across, (each side is the same length, therefore the diameter is the same,) The square will fit on the inside of the circle.