The time taken for Eric to finish the book is 3 1/2 hours.
What is a fraction?A fraction simply means a part of a whole. It van also refer to any number of equal parts.
The information illustrated that Jessica finishes her book in 2 1 / 3 hours and that Eric takes 1 1 / 2
times longer than Jessica to finish his book.
In this case, the time that was used by Eric will be the multiplication of the fractions given. This will be illustrated as:
= 2 1/3 × 1 1/2
Change to improper fraction
= 7/3 × 3/2
= 7 / 2
= 3 1 / 2
Eric used 3 1/2 hours.
This illustrates the concept of multiplication of fractions.
The complete question is written below.
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Jessica finishes her book in 2 1/3.hours. Eric takes 1 1/2 times longer than Jessica to finish his book. How long did Eric take yo finish the book?
Hello! I think this works but I'm not 100% sure
Given:
1 counsellor for every 9 campers.
Lets' determine the type of variation and write the equation.
Here, we can see that for every 9 campers, there is one extra counsellor. This means that as the number of campers increase, the number of counsellors will also increase.
Since one variable as the other increases, this is a direct variation.
Hence, we have the equation which represents the direct variation below:
y = 9x
Where x represents the number of counsellors and y represents the number of campers.
ANSWER:
Direct variation.
y = 9x
how to solve 2x^2-3x-1=0
Explanation
[tex]2x^2-3x-1=0[/tex]Step 1
remember the quadratic formula.
if you have the equation
[tex]ax^2+bx+c=0[/tex]the value for x is
[tex]x=\frac{-b^2+\sqrt{b^2}-4ac}{2a}[/tex]Step 2
let
[tex]ax^2+bx+c=2x^2-3x-1[/tex]a=2
b=-3
c=-1
Step 3
replace
[tex]undefined[/tex]74. Noam wants to put a fence around his rectangular garden. His garden measures 35 feet by 50 feet. Thegarden has a path around it that is 3 feet wide. How much fencing material does Noam need to enclose thegarden and path?A. 97 ftB. 194 ftC. 182 ftD. 146 ft
Given:
The length of the rectangular garden, l=50 feet.
The breadth of the rectangular garden, b=35 feet.
The width of the path around the garden, w=3 feet.
The figure can be drawn as,
So, the length of the fence, L=l+2w.
The breadth of the fence, B=b+2w
The perimeter of the fence can be calculated as,
[tex]\begin{gathered} P=2(L+B) \\ =2(l+2w+b+2w) \\ =2(l+b+4w) \\ =2(50+35+4\times3) \\ =2(50+35+12) \\ =2\times97 \\ =194\text{ ft} \end{gathered}[/tex]Therefore, the perimeter of the fence is 194 ft.
Option B is correct.
A basic cellular package costs $20/month for 60 minutes of calling with an additional charge of $0.20/minute beyond that time. The cost function C(x) for using x minutes would beIf you used 60 minutes or less, i.e. if if x≤60, then C(x)=20 (the base charge). If you used more than 60 minutes, i.e. (x−60) minutes more than the plan came with, you would pay an additional $0.20 for each of those (x−60) minutes. Your total bill would be C(x)=20+0.20(x−60). If you want to keep your bill at $50 or lower for the month, what is the maximum number of calling minutes you can use?
The maximum number of calling minutes you can use for $50 is 210 minutes.
To solve this, we have the function cost C(x) that depends on the amount of acalling munutes (x)
We want this cost to be $50 or lower. This means:
[tex]\begin{gathered} CostFunction\colon C(x)=20+0.2(x-60) \\ Maximum\text{ value of 50:}C(x)\le50 \end{gathered}[/tex]Then we can create an inequality:
[tex]50\ge20+0.2(x-60)[/tex]And now we can solve for x:
[tex]\begin{gathered} 50\ge20+0.2(x-60) \\ \frac{50-20}{0.2}\ge x-60 \\ 150+60\ge x \\ x\le210\text{ minutes} \end{gathered}[/tex]Thus, with $50 we can talk up to 210 minutes.
To be sure of the result, let's plug x = 210 in the function and it should give us a cost of C(210) = 50:
[tex]\begin{gathered} x=210\Rightarrow C(210)=20+0.2(210-60) \\ C(210)=20+0.2\cdot150 \\ C(210)=20+30=50 \end{gathered}[/tex]This confirms the result.
3. x-intercept 4, y-intercept 2, passes through 5. Center on x = 3, radius 13, passes through Center on the y-axis, radius 5, x-intercept 3 cle having the given center and radius. (b) C (-2,-5), r = 4 (d) C(2, -3), r= 6 ving the given properties. (0,0) (6, 5)
Samantha, this is the solution to problem 5:
With the information given in the statement you can solve for k, where k is the center in y:
(x-h)^2 + (y-k)^2 = r^2
(6-3)^2 + (5-k)^2 = (√(13))^2
(3)^2 + (5-k)^2 = 13
9+(5-k)^2 = 13
(5-k)^2 = 4
√((5-k)^2) = √4
5-k = 2
-k = -3
k = 3
Then the equation of the circle will be
(x-3)^2 + (y-3)^2 = 13
Pic includes all informatin
Answer: 8squares
Step-by-step explanation:
find the measure of each of the other six angles
The measure of angle 1 is 71º, we can find this, because angle 1 and angle x form a straight line of 180º, so 180º - 109º = 71º
The measure of angle 2 is also 71º, we can use the vertical angles propierty, then m∠1 = m∠2
The measure of angle 3 is 109º, we can use again the vertical angles theorem to find that m∠x = m∠3
Themeasure of angle 7 is 109º. We need to use the alternating exterior angles theorem. Since angle x and angle 7 are not between the parallel lines they're exterior angles; and since they're on opposite sides of the transversal line, they're alternates. Then the theorem says that m∠x = m∠7
The measure of angle 6 is 71º, again we're using the fact that angle 7 and angle 6 forms a straight line, then m∠6 = 180º - 109º = 71º
Now we can find the lasts two measures using the vertical angles theorem.
The measure of angle 5 is 71º, because m∠6 = m∠5
The measure of angle 4 is 109º, because m∠7 = m∠4
Question 39.Find the inverse of the given function. Graph both functions on the some set of axes and show the line y=x as a dotted line in the graph.
First, to find the inverse of a function, call the original function "x" and call call "x" in the original function as the inverse function:
[tex]\begin{gathered} f(x)=5x+1 \\ x=5f^{-1}(x)+1 \end{gathered}[/tex]Now, we solve for the inverse function:
[tex]\begin{gathered} x=5f^{-1}(x)+1 \\ 5f^{-1}(x)+1=x \\ 5f^{-1}(x)=x-1 \\ f^{-1}(x)=\frac{x}{5}-\frac{1}{5} \end{gathered}[/tex]To graph lines, we can find two points in it and draw a line that passes through both.
Let's pick x = 0 and x = 1 for the first equation:
[tex]\begin{gathered} f(0)=5\cdot0+1=1 \\ f(1)=5\cdot1+1=6 \end{gathered}[/tex]So, we plot the points (0, 1) and (1, 6).
For the inverse, we can simply invet the coordinates, which is the same as picking x = 1 and x = 6:
[tex]\begin{gathered} f^{-1}(1)=\frac{1}{5}-\frac{1}{5}=0 \\ f^{-1}(6)=\frac{6}{5}-\frac{1}{5}=\frac{5}{5}=1 \end{gathered}[/tex]Thus, we have the points (1, 0) and (6, 1).
The line y = x is jus the diagonal that passes though point (0, 0) and (1, 1), for example.
Putting these points and drawing the lines, we get:
13. A co-ed soccer team has a boy to girl ratio of 3:2. There are 15 boys on the team. What is the total number of players on the team?
The ratio of boy to girl is 3:2. There are 15 boys on the team. The total number of players on the team can be calculated as follows.
[tex]\begin{gathered} \frac{3}{5}\times x=15 \\ \text{where} \\ x=\text{total number of players in the teams} \\ \frac{3x}{5}=15 \\ \text{cross multiply} \\ 3x=15\times5 \\ 3x=75 \\ x=\frac{75}{3} \\ x=25 \end{gathered}[/tex]Total players = 25
I will give brainliest. By the way, two people need to answer for someone to give brainliest.
For the direct variation equation y=223x, what is the constant of proportionality?
A: 2
B: 2 2/3
C: 2/3
D: 3
The equation y=7x gives the relationship between the number of road projects, x, and the number of weeks it takes a crew of workers to complete all the projects, y. What is the constant of proportionality? What does it mean in this context?
A: The constant of proportionality is 7. It takes the crew of workers 7 weeks to complete 1 road project.
B: The constant of proportionality is 7. It takes the crew of workers 7 days to complete all of their road projects.
C: The constant of proportionality is 7. It takes the crew of workers 7 days to complete 1 road project.
D: The constant of proportionality is 7. It takes the crew of workers 7 weeks to complete all of their road projects.
Write a direct variation equation to find the number of miles a jet travels in 3 hours if it is flying at a rate of 600 mph.
A: 600 = 3x
B: 3 = 600x
C: y = 600/3
D: y = 600 x 3
Jamal earns $125,000 a year as a systems analyst. He wants to know how much he will earn if he continues at the same rate of pay for 7 years. Which equation will help him find this amount?
A: x = 125,000/5
B:125,000 = 7x
C:125,000 = 7/x
D: y = 125,000 x 7
Answer: I think B and for the second one I think C
Step-by-step explanation: The constant of proportionality is 7. It takes the crew of workers 7 days to complete 1 road project. That means they have to take at least 7 days which is correct.
What is the value of the expression shown? 5 – a(3² + (ab + 2)² – 7) when a = 2 and b = –3
The expression has a value of -31 when a = 2 and b = –3
How to evaluate the expression?From the question, the expression is given as
5 – a(3² + (ab + 2)² – 7)
Also, we have the values of the variables to be
a = 2 and b = –3
Substitute a = 2 and b = –3 in the expression 5 – a(3² + (ab + 2)² – 7)
So, we have the following equation
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (2 * -3 + 2)² – 7)
Evaluate the expressions in the bracket
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (-4)² – 7)
Evaluate the exponents
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (9 + 16 – 7)
So, we have
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * 18
This gives
5 – a(3² + (ab + 2)² – 7) = 5 – 36
Evaluate the difference
5 – a(3² + (ab + 2)² – 7) = -31
Hence, the value of the expression is -31
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Juan and María López wish to invest in a no-risk saving account. they currently hace $30,000 in an account bearing 5.25% annual interest, compounded continuously. the following choices are available to them.A. Keep the Money in The account they currently have B. invest the Money in an account earning 5.875% interest compounded annually c. invest the Money in an account earning 5.75% compounded semi annually d. invest Money in an account earning 5.5% annual interést compounded quarterly
The general formula for the amount in savings account compounded annually is given as;
[tex]\begin{gathered} A=P(1+\frac{r}{100n})^{nt} \\ \text{Where A=Amount} \\ P=\text{Initial deposit} \\ r=\text{rate} \\ n=n\text{ umber of times it is compounded annually} \\ t=\text{time} \end{gathered}[/tex]A. The equation for the value of the investment as a function of t in the current account they have is;
[tex]A(t)=\text{ \$30000(1+}\frac{5.25}{100})^t[/tex]B. The equation for the value of the investment in an account earning 5.875% interest compounded annually is;
[tex]A(t)=\text{ \$30000(1+}\frac{5.875}{100})^{t^{}}[/tex]C. The equation for the value of the investment in an account earning 5.75% compounded semi-annually; that is twice in a year is;
[tex]\begin{gathered} A(t)=\text{ \$30000(1+}\frac{5.75}{100(2)})^{2t} \\ A(t)=\text{ \$30000(1+}\frac{5.75}{200})^{2t} \end{gathered}[/tex]D. The solution for the value of the investment in an account earning 5.5% annual interest compounded quarterly; that is four times in a year;
[tex]\begin{gathered} A(t)=\text{ \$30000(1+}\frac{5.5}{100(4)})^{4t} \\ A(t)=\text{ \$30000(1+}\frac{5.5}{400})^{4t} \end{gathered}[/tex]i need help, i already did the first part but i don’t understand the second part.
a) To convert to radical form, we follow this:
[tex]m^{\frac{a}{b}}=\sqrt[b]{m^{a}}[/tex]So:
[tex]R=73.3m^{\frac{3}{4}}=73.3\sqrt[4]{m^{3}}[/tex]b) The formula we have is for mass in Kilograms, so the first step is to convert the mass stated from lbs to kg.
1 lb -- 0.454 kg
160 lb -- m
[tex]m=0.454\cdot160=72.64\operatorname{kg}[/tex]Now, we can use this value in the formula:
[tex]R=73.3m^{\frac{3}{4}}=73.3\cdot(72.64)^{\frac{3}{4}}=1823.84[/tex]a) To convert to radical form, we follow this:
[tex]m^{\frac{a}{b}}=\sqrt[b]{m^{a}}[/tex]So:
[tex]R=73.3m^{\frac{3}{4}}=73.3\sqrt[4]{m^{3}}[/tex]b) The formula we have is for mass in Kilograms, so the first step is to convert the mass stated from lbs to kg.
1 lb -- 0.454 kg
160 lb -- m
[tex]m=0.454\cdot160=72.64\operatorname{kg}[/tex]Now, we can use this value in the formula:
[tex]R=73.3m^{\frac{3}{4}}=73.3\cdot(72.64)^{\frac{3}{4}}=1823.84[/tex]give the coordinates of the image of each point under a reflection across to given line.(0,8); y=x
Answer:
(8, 0)
Explanation:
Whenever a point (x,y) is reflected across the line y=x, the transformation rule is given below:
[tex](x,y)\to(y,x)[/tex]That is, the x-coordinate and y-coordinate change places.
Therefore, the image of the point (0,8) when reflected across the line y=x is:
[tex](8,0)[/tex]The correct answer is (8,0).
ratios 1 to 32 spoonful of 32 sprinkles
If for each sundae the shop uses 4 spoonfuls of sprinkles, if we want to know how many sundaes the shop did with 32 spoonfuls we must divide 32 by 4, if we do it we get
[tex]32\div4=8[/tex]Therefore, the shop did 8 sundaes! we can count it to make sure:
4 spoonfuls - 1 sundae
8 spoonfuls - 2 sundaes
12 spoonfuls - 3 sundaes
16 spoonfuls - 4 sundaes
20 spoonfuls - 5 sundaes
24 spoonfuls - 6 sundaes
28 spoonfuls - 7 sundaes
32 spoonfuls - 8 sundaes
Given the base band height of a triangle, calculate the area A using the formula for the area of a triangle: A ) bh
Solution
For this case the area is given by:
[tex]A=\frac{1}{2}bh[/tex]Then we can replace b = 5ft and h = 20 ft and we got:
[tex]A=\frac{1}{2}(5ft)(20ft)=50ft^2[/tex]Consumption and savings if real domestic output is $370 billion and planned investment is $15 billion
The consumption is 355 billion .
Given,
In the question:
Consumption and savings if real domestic output is $370 billion and planned investment is $15 billion.
Now, According to the question:
Based on the given condition,
Formulate;
Aggregate expenditure (consumption)= Output - Savings= Investment
370 - 15
Calculate the sum or difference
= 355billion
Hence, The consumption is 355 billion .
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Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P,P, in terms of x,x, representing Madeline's total pay on a day on which she sells xx computers.
I need equation
The equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x.
Given, At an electronics store, Madeline sells computers as a salesperson. She receives a $80-per-day base salary in addition to a $20 commission for each computer she sells.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We can model the equation for Madeline's total pay as follows -
P = base pay + (number of sold computer) × (cost of 1 computer)
P = 80 + 20x
Therefore, the equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x
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Roberts Company has the following sales budget for the first four months and the year:
January February March April
Budgeted units to sell
200
400
800
950
Total - 2,350
Sales price per unit
$25
$25
$25
$25
Total-$25
Total sales
$5,000
$10,000
$20,000
$23,750
Total - $58,750
What is the new amount of budgeted total sales for March if the budgeted number of units is expected to be 1,100 units instead of 800 units?
A. $27,500
B. $10,000
C. $47,500
D. $66,250
Using some simple mathematical operations we can conclude that the new amount of budgeted total sales is (D) $66,250.
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers. A mathematical action is called an operation. Mathematical operations include addition, subtraction, multiplication, division, and finding the root.So, new amount of budgeted total sales for March:
So, we know that:
2350 × 25 = $58,750And 2350 is further:
2350 = 200 + 400 + 800 + 950.Let's replace 800 with 1100.
Now, solve as follows:
200 + 400 + 1100 + 950 = 2,6502,650 × 25 = $66,250Therefore, using some simple mathematical operations we can conclude that the new amount of budgeted total sales is (D) $66,250.
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Find the coordinates of the vertex of the graph of y=4-x^2 indentify the vertex as a maximum or minimum point A.(2,9);maximumB.(0,4);minimumC.(0,4);maximum D.(2,0);minimum
Let's begin by identifying key information given to us:
[tex]\begin{gathered} y=4-x^2 \\ y=-x^2+4 \\ a=-1,b=0,c=4 \\ x_v=-\frac{b}{2a}=-\frac{0}{2(-1)}=0 \\ y_v=-\frac{b^2-4ac}{4a}=-\frac{0^2-4(-1)(4)}{4(-1)} \\ y_v=-\frac{0+16}{-4}=\frac{-16}{-4}=4 \\ y_v=4 \\ \\ \therefore The\text{ vertex of the equation is }(0,4) \end{gathered}[/tex]To know if the vertex is the maximum or minimum point, we will follow this below:
[tex]\begin{gathered} y_v=4 \\ \Rightarrow This\text{ is a minimum point} \end{gathered}[/tex]Hence, the answer is B.(0,4); minimum
at a sale a desk is being sold for 24% of the regular price. the sale price is $182.40 what is the regular price
at a sale a desk is being sold for 24% of the regular price. the sale price is $182.40 what is the regular price
we have that
24% ------> represent $182.40
so
Applying proportion
Find out the 100%
Let
x ----> the regular price
182.40/24=x/100
solve for x
x=(182.40)*(100)/24
x=$760
therefore
The regular price is $760Solve for the missing side of the triangle. Round to the hundredths place if needed.
The Pythagoras theorem gives the relation for the right-angle triangle between the perpendicular, base, and hypotenuse thus the perpendicular x will be 14.70.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Triangle is a very common figure to deal with in our daily life.
In a triangle, the sum of all three angles is 180°
As per the given right-angle triangle,
Pythagoras' theorem states that in a right-angle triangle →
Hyp² = Perp² + Base²
In the given triangle Hyp = 21 , Base = 15 and Perp = x
So,
21² = x² + 15²
x² = 21² - 15²
x = √216 = 14.6993 ≈ 14.70
Hence "The value of x for the given right-angle triangle is 14.70 units".
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Several friends go to a casino and do some gambling. The following are the profits each of these friends make: $120, -$230, $670, -$1020, $250, -$430, and -$60. What is the average profit of this group? A. $100 B. -$100 C. -$1020 D. $397
The average profit of this group is B. -$100.
The average represents the total profits and losses generated by the group of friends, divided by the number in the group.
The average is the data set's mean after performing the mathematical operations of addition and division on the data values.
Friends Profits
A $120
B -$230
C $670
D -$1020
E $250
F -$430
G -$60
Total -$700
Average profit = -$100 (-$700/7)
Thus, we can conclude that the friends generated an average profit of B. -$100 from gambling or a total loss of $700.
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The length of a new rectangular playing field is 7 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 454 yards, what are its dimensions?
The dimensions of new rectangular playing field are 183 yards and 44 yards, by the concept of perimeter of rectangle.
What is perimeter of rectangle?The whole distance that the sides or limits of a rectangle cover is known as its perimeter. Since a rectangle has four sides, its perimeter will be equal to the sum of those four sides. Given that the perimeter is a linear measurement, the rectangle's perimeter will be expressed in meters, centimeters, inches, feet, etc.
Formula, perimeter of rectangle =2× (length +width)
Given, perimeter of rectangular playing field = 454 yards (equation 1)
Let us assume, width =x
According to question length = 4x+7 (quadruple=4times)
By the above equations,
Perimeter=2×(4x+7+x)
2×(5x+7) =454 (by equation 1)
Dividing the above equation by 2 both the sides
(5x+7) =227
Subtracting the above equation by 7 both the sides
5x=220
Dividing the above equation by 5 both the sides
x=44
Therefore, the required width of new rectangular playing field is 44 yards and length of new rectangular playing field is 183 yards
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Li’s family is saving money for their summer vacation. Their vacation savings account currently has a balance of $2,764. The family would like to have at least $5,000.Which inequality can be used to determine the amount of money the family still needs to save?
EXPLANATION
Savings account balance = $2,764
Desired amount = $5,000
Let's call x to the amount of money the family needs.
The inequality that could be used to determine the amount of money the family needs is the following:
2,764 + x ≥ 5,000
A jar of marbles contains the following: two red marbles, three white marbles, five blue marbles, and seven green marbles.What is the probability of selecting a red marble from a jar of marbles?
ANSWER
[tex]\frac{2}{17}[/tex]EXPLANATION
Given;
[tex]\begin{gathered} n(Red)=2 \\ n(white)=3 \\ n(blue)=5 \\ n(green)=7 \end{gathered}[/tex]The total number of marble is;
[tex]n(Total)=2+3+5+7=17[/tex]Recall, the probability of an event can be calculated by simply dividing the favorable number of outcomes by the total number of the possible outcome
Hence, the probability of selecting a red marble is;
[tex]\begin{gathered} Prob(Red)=\frac{n(Red)}{n(Total)} \\ =\frac{2}{17} \end{gathered}[/tex]I need some help with this! I know about the trig identitys and stuff like that, but I just get a little confused on how to apply sometimes.
we have that
Let
x ------> the distance in miles from a point on the ground (the red line)
In the right triangle of the figure
sin(6.5)=7,000/x
solve for x
x=7,000/sin(6.5)
using a calculator
x=61,835.70 ft
Convert to miles
Remember that
1 mile=5,280 ft
so
61,835.7 ft=61,835.7/5,280=11.71 miles
therefore
the answer is 11.71 milesDerek has $20 to spend on used books, but he can not spend all $20.Hardcover books cost $5 each and paperbacks cost $2 each. Create aninequality which determines the number (x) of hardcover books and the number(y) of paperback books he can buy.
Given:
The amount to spend on books, T=$20.
The cost of a handcoverbook, m=$5.
The cost of a paperback, n=$2.
Let x be the number of handcover books and y be the number of paperback books.
It is said that the complete amount of $20 cannot be spend.
So, the inequality to determine x and y can be written as,
[tex]\begin{gathered} T>mx+ny \\ 20>5x+2y \end{gathered}[/tex]So, the inequality is 20>5x+2y.
convert 7 ounces to grams. Round to the nearest whole number
Answer:
[tex]198\text{ g}[/tex]Explanation:
Here, we want to convert from ounces to grams
Mathematically,we have it that:
[tex]1\text{ ounce = 28.3}495\text{ g}[/tex]7 ounces will be the product of 7 and this
Mathematically,we have this as;
[tex]7\text{ }\times\text{ 28.3495 = }198.4465[/tex]To the nearest whole number, this is 198 g
Hello, I need assistance with this question within the image posted below.
A(-4, 0) and B(4, 0)
Explanation:A parabola is symmetrical about the y-axis, if the vertex is of the form (0, y). The y-axis is the line of symmetry. That is, the point x = 0.
If the parabola is symmetric about the y-axis, points A and B should fall on opposite sides of the y-axis.
For the parabola to be symmetric about the y-axis, the possible points to move A and B to are A(-4, 0) and B(4, 0)