Tyler was making a meal for his family. For every 3/4 pound of beef, the recipe calls for 9/8 cups of broccoli. How many cups of broccoli would be needed for a pound of beef?
a1/2 cup of broccoli per beef
b2/3 pound of broccoli per beef
c1 and ½ cup of broccoli per beef
d5/4 cup of broccoli per beef
The number of cups of broccoli that would be needed for a pound of beef is C. 1 1/2 cup of broccoli per beef.
How to calculate the value?From the information, it was stated that Tyler was making a meal for his family and that for every 3/4 pound of beef, the recipe calls for 9/8 cups of broccoli.
Therefore, the cups of broccoli that would be needed for a pound of beef will be:
3/4/1 = 9/8/x.
where x = cups of broccoli
Cross multiply
3/4x = 9/8
x = 9/8 ÷ 3/4
x = 9/8 × 4/3
x = 3/2
x = 1 1/2cups
Therefore, the correct option is C.
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Answer:
[tex]\textsf{c) \quad $1 \frac{1}{2}$ cups of broccoli per 1 lb of beef}.[/tex]
Step-by-step explanation:
Given information:
For every ³/₄ lb of beef, the recipe calls for ⁹/₈ cups of broccoli.Create a ratio of pounds of beef to cups of broccoli, where x is the number of cups of broccoli to one pound of beef:
[tex]\implies \dfrac{3}{4}: \dfrac{9}{8}=1:x[/tex]
[tex]\implies \dfrac{\frac{3}{4}}{\frac{9}{8}}=\dfrac{1}{x}[/tex]
Cross multiply:
[tex]\implies \dfrac{3}{4}x=\dfrac{9}{8}[/tex]
[tex]\implies x=\dfrac{9}{8} \div \dfrac{3}{4}[/tex]
To divide fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:
[tex]\implies x=\dfrac{9}{8} \times \dfrac{4}{3}[/tex]
[tex]\implies x=\dfrac{9 \times 4}{8 \times 3}[/tex]
[tex]\implies x=\dfrac{36}{24}[/tex]
[tex]\implies x=\dfrac{3 \cdot \diagup\!\!\!\!\!\!12}{2 \cdot \diagup\!\!\!\!\!\!12}[/tex]
[tex]\implies x=\dfrac{3}{2}[/tex]
[tex]\implies x=1 \frac{1}{2}[/tex]
Therefore, 1¹/₂ cups of broccoli would be needed to one pound of beef.
Your local library holds a penny drive in which people in the community are asked to donate their spare pennies to the library. When you stop by to donate some pennies, you hear someone announce that she plans to donate pennies for one month in the following manner: she will donate 1 penny today, 2 pennies tomorrow, 4 pennies the next day, and will continue to double the number of pennies that she donates each day thereafter.
The amount donated by the person follows a geometric progression, which is given by an exponential function.
First part:
The relationship between the amount donated and the day of the month is not a constant rate relationshipSecond part;
Please find attached the graph of the Amount Donated to the Days which is shaped as the graph of an exponential equationWhat is an exponential function?An exponential function is one in which the input variable is an index of a constant
A constant rate relationship is one in which at all points of the function, the ratio of the output to input stays the same or is a constant.
The given parameters are;
The Pennies a person plans to donate to the library on each day of the month, is given by the following table;
Day. Amount Donated
1. 1
2 2
3 4
4 8
First part
Required;
If the relationship between the day and the amount donated is a constant rate relationship
Solution;
Given that we have;
1/1 = 2/2 ≠ 4/3 ≠ 8/4, the relationship between the day of the month and the amount donated is not a constant rate relationship
Second part;
The shape of the graph of Day to the Amount Donated
Solution;
The sequence of the day has a constant difference of one day, which is given by the equation;
U = 1 × n
Where;
U = The day of the month
n = The number of days
The sequence for the amount donated is given by the exponential function;
S = a•r^n
Where;
a = The first term = 1
r = The common ratio = 2
U = The number of days
The graph of Amount Donated to the Days is therefore the graph of an exponential function, please see the attached graph of Amount Donated to the Day of the month
The possible questions obtained from a similar question are;
First part; If the amount donated and the days have a constant rate relationship
Second part; The shape of the graph of the Amount Donated to the Day of the month
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Addison has x pennies and y nickels. She has a minimum of 16 coins worth no more
than $0.40 combined. Solve this system of inequalities graphically and determine
one possible solution.
Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita reports that 48% of its customers order their food to go. If this proportion is correct, what is the probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go?
The probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go is 0.3240
Probability:
The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes.
Given,
Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita reports that 48% of its customers order their food to go.
Here we need to find the probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go.
Let us consider this as,
Binomial Problem with
n = 5 and
By converting the percentage into decimal value,
=> 48/100 = 0.48
p(to go) = 0.48
Then the value is,
P(x=3) = 5C3(0.52)^3*(0.48)2
P(x=3) = 0.3240
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For the following situation make an input- output table
The nearby amusement park charges $15 for admission, which includes 5 rides.
After 5 rides, each extra ride costs $1.50. The input, r, is the number of rides you
take. The output, c, is the total cost for the day at the amusement park. Let r = 0, r
3, 5, 6, 10, and 15 rides.
The input- output table for the total cost of the amusement park charges is made.
What is defined as the linear equation?A linear equation is just an algebraic expression of a form y=mx+b, according to Wolfram MathWorld involving just a constant and a first-order (linear) term, for which m represents the slope and b represents the y-intercept. The above is sometimes referred to as a "linear equation of two variables," in which y and x are the variables.For the given question;
The admission charge of the amusement park = $15 (including 5 rides).
For extra rides $1.50 per ride.
Let r be the total rides.
Let n be the extra rides above 5 rides.
Let C be the total cost of the ride.
Then, the liner equation forming the condition is;
C = 1.5n + 15.
For n = 1, 2 , 3...
The value of C will be determined.
Thus, the input- output table for the total cost of the amusement park charges is made.
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Roxy created a table listing some of her fixed expenses for the first three months of the year. Expense Jan Feb Mar emergency fund $50 $50 $50 cell phone $89 $89 $89 internet $55 $55 $55 rent payment $986 $986 $986 transportation $30 $30 $30 insurance $15 $15 $15 gym membership $24 $24 $24 entertainment $35 $35 $35 Which pie chart accurately represents the data in the table? PLATO
The amount in Roxy's table listing of expenses gives the ratio of the items in the pie chart as follows;
Emergency fund; 3.89%
Cell phone; 6.93%
Internet; 4.28%
Rent payment; 76.79%
Transportation; 2.34%
Insurance; 1.17%
Gym membership; 1.97%
Entertainment; 2.73%
The pie chart can then be constructed using those percentage as a proportion of 100
Please see the attached pie chart of the expenses created with Sheets
What is a pie chart?A pie chart illustrates the numerical proportion of items in a dataset by using a circular graphic that is divided into sector slices
The given values in the question are;
Emergency fund = $50
Cell phone = $89
Internet = $55
Rent payment = $986
Transportation = $30
Insurance = $15
Gym membership = $24
Entertainment = $35
The total cost of the fixed expense is therefore;
$50+$89+$55+$986+$30+$15+$24+$35 = $1284
The proportion of each component in the pie chart is found as follows;
[tex] \displaystyle{Emergency \: fund = \frac{50}{1284} \times 100 \approx 3.89 \%}[/tex]
[tex] \displaystyle{Cell \: phone = \frac{89}{1284} \times 100 \approx 6.93 \%}[/tex]
[tex] \displaystyle{Internet = \frac{89}{1284} \times 100 \approx 4.28 \%}[/tex]
[tex] \displaystyle{Rent \: payment = \frac{986}{1284} \times 100 \approx 76.79 \%}[/tex]
[tex] \displaystyle{Transportation = \frac{30}{1284} \times 100 \approx 2.34 \%}[/tex]
[tex] \displaystyle{Insurance = \frac{15}{1284} \times 100 \approx 1.17 \%}[/tex]
[tex] \displaystyle{Gym \: membership = \frac{24}{1284} \times 100 \approx 1.87 \%}[/tex]
[tex] \displaystyle{Entertainment = \frac{35}{1284} \times 100 \approx 2.73 \%}[/tex]
Using the above percentages, the pie chart can be constructed
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Valentina knits 16 centimeter of scarf each night.How manynightswillValentinahavetospendknittinginordertoknitatotalof48centimetersofscarf?
You have the following information:
- Valentina knits 16 cm of scarf each night.
To determine how many night does Valentina need to knit 48 cm of scarf, you simply calculate the quotient between 48 cm and 16 cm, just as follow:
48/16 = 3
Hence, Valentina needs 3 days to knit 48 cm of scarf
Before art class starts, Gordon makes sure that each table has a full bowl of paint. He has 1/2 of a gallon of paint and is able to fill the bowls for all 7 tables. How many gallons of paint does each table have?
Answer:0.07142857142
Step-by-step explanation:
0.07142857142 because 1/2/7= or .5/7=0.07142857142
.5= how much paint
7= how many tables that are needed to be filled
0.07142857142= how much paint
each table will receive
Write an equation of the parabola that has the same shape as the graph of f(x) = 4x², but with the point (10,4) as the vertex.
An equation of the parabola that has the same shape as the graph of f(x) = 4x², but with the point (10,4) as the vertex is y = 4x² - 80x + 404.
What is the vertex form of the parabola?The standard vertex form of the parabola is given by,y = a(x - h)² + k where (h, k) is the vertex.
Real numbers, a, h, and k are included here, where a ≠ 0. A point on the parabola is represented by the variables x and y, respectively.Given:
f(x) = 4x²
Vertex = (10,4)
a = 4
The value of a in the vertex form of the equation is taken to be 4 since the coefficients of x² must match for the parabola to have the same shape as the given parabola.
The equation can be written as,
y = a(x - h)² + k where (h, k) is the vertex.
Replacing the value of the vertex, we get
y = 4(x - 10)² + 4
y = 4(x² - 20x + 100) + 4
y = 4x² - 80x + 400 + 4
y = 4x² - 80x + 404
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Throughout the 2016 Presidential election primaries, Millennials (those aged 20 t 36 years)
consistently supported Senator Bernie Sanders over Secretary Hillary Clinton. According to the
2016 Gallup poll of 1,754 Millenials, 55% had a favorable opinion of Sanders than Hillary Clinton
(38%). Calculate the 90% confidence interval for for Hillary Clinton.
*round to two decimals
The 90% confidence interval for Hillary Clinton is
to
Answer:
favorable opinion of Sanders than Hillary Clinton
(38%). Calculate the 90% confidence interval for for Hillary
4m
Kelsey earned some Money doing odd jobs last summer and put it in a savings account that earns 5% interest compounded quarterly after 7 years there is 400.00 in the account how much did Kelsey earn doing odd jobs
The final amount is
[tex]\begin{gathered} A=P(1+\frac{R}{n\times100})^{nT} \\ Here,\text{ A is the final amount, P is the principal or the money earned by Kelsey, T is time in years, n is the number of tnes the comound interest is taken.} \end{gathered}[/tex]Here,A=400, R=5%, N=4,T=7. We have to find the principal.Substituting the values,
[tex]\begin{gathered} 400=P(1+\frac{5}{4\times100})^{4\times7} \\ \text{ 400=P(1+}\frac{5}{400})^{28} \\ \text{ P=}\frac{400}{\text{(1+}\frac{5}{400})^{28}} \\ \text{ =282.48} \end{gathered}[/tex]Therefore, the money earned by Kelsey doing odd jobs is 282.48.
What is the slope of the line that passes through the points (9,1) and (10,−1)? Write your answer in simplest form.
The slope of the linear equation that passes through the points (9,1) and (10,−1) is -2.
How to get the slope of the line?For a linear equation that goes through two points (x₁, y₁) and (x₂, y₂), the slope is given by the formula:
slope = (y₂ - y₁)/(x₂ - x₁)
In this case, we know that our line goes through the points (9,1) and (10, −1), so we can use these two values in the equation for the line, we will get:
slope = (-1 - 1)/(10 - 9) = -2/1 = -2
So the slope of the linear equation is -2.
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9. Please help. Thank you
By definition, a one-to-one function is a function that maps distinct elements of its domain to distinct elements of its codomain.
Graph 1
From this graph, we see that for distinct elements of x, we have the same value of y. For example:So this function is NO a one-to-one function.
• f(2) = f(-2) = 4.
T
Graph 2
From this graph, we see that for distinct elements of x, we have the same value of y. For example:is function is NO a one-to-one function
• f(2) = f(4) = 4.
Th.
Graph 3
From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.
Graph 4
From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.
Graph 5
From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.
Graph 6
From this graph, we see that for distinct elements of x, we have the same value of y.This function is NO a one-to-one function.
Answer• Graph 1: No
,• Graph 2: No
,• Graph 3: Yes
,• Graph 4: Yes
,• Graph 5: Yes
,• Graph 6: No
will post a full pictures it did not fit
They will be parallel because the same transformations have been applied to it
Aisha paid $33.15 for the pizza for her and her two friends. How much did it cost each of them for the pizza?
Answer:$11.05
Step-by-step explanation:
Answer:
$11.05 each
Step-by-step explanation:
To find x, the cost between Aisha and her two friends you must divide the total amount by the number of people.
There are three people, her and two friends and the total cost for the pizza is $33.15
$33.15 ÷ 3 = $11.05
Dina goes to a carnival. Some rides at the carnival have a height requirement, but others do not. Dina is tall enough to go on all rides.
What is a mathematical question you can ask about this situation? What information would you need to know to answer your question?
The mathematical question that can be asked in a situation when Dina goes to a carnival and some rides have a height requirement is how many extra centimeters of height Diana has? The information required to solve this question is the required height for the ride and the height of Diana.
According to the question,
We need to ask a mathematical question. Let's solve a mathematical question in the given situation by taking one example.
If the required height to ride is 150 cm and the height of Diana is 165 cm, how many extra centimeters of height Diana has than the required height?
Solution:
Required height = 150 cm
Dian's height = 165 cm
Extra height = Diana's height - required height of the ride
Extra height = 165 cm - 150 cm
Extra height = 15 cm
Hence, in this supposed situation, Diana's height is 15 cm extra than the required height of the ride.
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fcbdxfhbdxfnxfgmndfgxhbnxf
ANSWER:
A. The midline of the function is y = 2
STEP-BY-STEP EXPLANATION:
we can determine the answer from the graph, just like this:
Therefore, the only correct option is A. The midline of the function is y = 2
You are multiplying as many 5s and 2s as you want but you must have at least one of each. What could the last digit of the product be?
The last digits of multiplying 5s and 2s with at least one of each will be zero (0)
Multiplication of numbersFrom the question, we are to determine what the last digit of the product could be
From the given information,
We are multiplying as many 5s and 2s as we want but we must have at least one of each
Since we must have at least one of each of 5 and 2, we will always have a 5 × 2
But, 5 × 2 = 10
NOTE: 10 multiplied by any number will always result in a number with a last digit of zero (0)
Example
2 × 5 × 2 × 2 × 2 × 2 = 160
5 × 2 × 5 × 5 × 5 × 5 = 6250
Thus, the last the digit of the product will be 0
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There are 4 triangles and 2 circles. What is the simplest ratio of circles to total shapes?
Answer:
1:3
Step-by-step explanation:
circles:total
2:4+2
=2:6
=1:3
Reason
There are 2 circles and 4+2 = 6 shapes total.
The ratio of circles to total shapes is 2:6 which reduces to 1:3
The order is important since 3:1 is different from 1:3.
Please help me find the horizontal asymptote.
Answer:
[tex]y=3/2[/tex]
Step-by-step explanation:
[tex]f(t)=\frac{3t^{1/3}}{(64t^2 +4)^{1/6}} \\ \\ =\frac{3}{(64+4t^{-2})^{1/6}} \\ \\ \\ \lim_{t \to \infty} f(t)=\frac{3}{64^{1/6}}=3/2 \\ \\ \\ \lim_{t \to -\infty} f(t)=\frac{3}{64^{1/6}}=3/2 \\ \\ \therefore y=3/2[/tex]
Giana has started collecting sea shells. Every month she adds 66 new shells to her collection. After 66 months of collecting, she has 3838 shells in her collection. Using this information, create an equation written in point-slope form that models the amount of shells y in Giana’s collection after x months
She has 3838 shells in her collection after 66 months of gathering. The equation using this data is 33x+33y=1919.
Given that,
Giana has begun to gather seashells. She grows her collection by 66 new shells each month. She has 3838 shells in her collection after 66 months of gathering.
We have to create an equation using this data that models the number of shells y Giana's collection will include after x months in point-slope form.
We can write as
The total number of shells she collected =(The amount of shells she collect each month)×y+(The month of collecting the shells)×x
3838=66y+66x
66x+66y=3838
33x+33y=1919
Therefore, the equation using this data that models the number of shells Giana's collection will include after x months in point-slope form is 33x+33y=1919.
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Answer: give correct answers only or people on here will do the same thing u did to them bozo
Step-by-step explanation:EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Write an equation in slope-intercept form of the lime that passes through the point(6,2) and is perpendicular to y=-2x+5
Consider that the slope-intercept of a line is given by,
[tex]y=mx+c[/tex]Here, 'm' is the slope and 'c' is the y-intercept of the line.
The equation of the given line is,
[tex]y=-2x+5[/tex]Comparing the coefficients, it can be observed that the slope of the given line is -2,
[tex]m=-2[/tex]It is asked to determine the equation of line perpendicular line to this given line.
Let the slope of this perpendicular line be 'k'. Then, the equation of this perpendicular line will take the form,
[tex]y=kx+c^{\prime}[/tex]Theorem: The product of slopes of perpendicular lines is -1.
[tex]\begin{gathered} k\cdot m=-1 \\ k\cdot(-2)=-1 \\ k=\frac{-1}{-2} \\ k=\frac{1}{2} \end{gathered}[/tex]Now, the equation becomes,
[tex]y=\frac{1}{2}x+c^{\prime}[/tex]Consider that any point lying on the line must satisfy the equation of that line.
So the point (6,2) must also satisfy the equation of the perpendicular line,
[tex]\begin{gathered} 2=\frac{1}{2}(6)+c^{\prime} \\ 2=3+c^{\prime} \\ c^{\prime}=2-3 \\ c^{\prime}=-1 \end{gathered}[/tex]Substitute the values of 'k' and c' in the equation,
[tex]\begin{gathered} y=\frac{1}{2}x+(-1) \\ y=\frac{1}{2}x-1 \end{gathered}[/tex]Thus, the required equation of the line is obtained as,
[tex]y=\frac{1}{2}x-1[/tex]Rick's car gets 29.7 miles per gallon on the highway. If his fuel tank holds 10.45 gallons, then how far can he travel on one full tank of gas?
We will investigate how to use the mileage meter of a car to determine the amount of distance a car can travel per given fuel.
Mileage is a economic performance parameter of a car that gives the fuel economy. It is usually expressed as a ratio of:
[tex]\text{Mileage = }\frac{Total\text{ Distance Travelled}}{Total\text{ Fuel consumed}}[/tex]The mileage of a car is given as follows:
[tex]\text{Mileage = 29.7 }\frac{miles}{gallon}[/tex]We can say that this car can travel 29.7 miles per gallon on highway.
We now stop at the petrol station for re-fueling. We fuel up the car to:
[tex]\text{Fuel = 10.45 gallons}[/tex]We need to determine the distance that this car can travel for the amount of re-fueling. This is where we can use the mileage to determine the distance the car can travel as follows:
[tex]\begin{gathered} \text{Distance = Mileage}\cdot Fuel \\ \end{gathered}[/tex]Plug in the respective quantitites and solve for the distance that the car can travel as follows:
[tex]\begin{gathered} \text{Distance = 29.7}\frac{miles}{gallon}\cdot10.45\text{ gallons} \\ \\ \textcolor{#FF7968}{Dis\tan ce}\text{\textcolor{#FF7968}{ = 310.365 miles}} \end{gathered}[/tex]For the amount of re-fueling the distance travelled is 310.365 miles
number 7 please help mequestions: find the sum of each infinite geometric serie
The sum to infnity of the series is;
[tex]S\infty\text{ = 1,066}\frac{2}{3}[/tex]Here, we want to find the sum to infinity of the given geometric series
We have this as follows;
[tex]S_{\infty}\text{ =}\frac{a}{1-r}[/tex]a is the first term which is 800
The common ratio is r and it is the second term divided over the first or the third over the second
We have this as;
[tex]\frac{200}{800}\text{ = }\frac{50}{200}\text{ = }\frac{1}{4}\text{ =0.25}[/tex]Substituting these values, we have it that;
[tex]S_{\infty}\text{ = }\frac{800}{1-0.25}\text{ = }\frac{800}{0.75}\text{ = 1,066 }\frac{2}{3}[/tex]Mary multiplied a number by-3.When she added the result to 6,she got 12. What is her number?
Explanation
Step 1
set the equation
a) let x represents the number
[tex]number=x[/tex]b) now , translate
[tex]i)Mary\text{ multiplied a number by 3}\Rightarrow x*3=3x[/tex]then
[tex]\begin{gathered} ii)shed\text{ added the result to 6} \\ 3x+6 \end{gathered}[/tex]finally
[tex]\begin{gathered} iii)\text{ she got 12, hence} \\ 3x+6=12 \end{gathered}[/tex]therefore, the equation is
3x+6=12
Step 2
now, solve the equation
[tex]3x+6=12[/tex]The subtraction property of equality states that if the same number is subtracted from both sides of an equation, then the equality still holds, so we can subtract 6 in both sides in order to isolate the term where x is, hence
[tex]\begin{gathered} 3x+6=12 \\ 3x+6-6=12-6 \\ 3x=6 \end{gathered}[/tex]finally, apply the division property of equality and divide both sides by 3
[tex]\begin{gathered} 3x=6 \\ \frac{3x}{3}=\frac{6}{3} \\ x=2 \end{gathered}[/tex]so, the number is 2
I hope this helps you
#31 and 35 please show work THANK YOU!!
The parametric equations for this problem are given as follows:
31. [tex]x = t, y = \sqrt[3]{t} + 1[/tex].
35. x(t) = -1 + 3t, y(t) = 5 - 2t.
Item 31
For item 31, the parent function is the cube root function, defined as follows:
[tex]y = \sqrt[3]{x}[/tex]
From the graph of the function, it was translated two units up, hence it is defined as follows:
[tex]y = \sqrt[3]{x} + 2[/tex]
We want to parametrize the equation as a function of t, hence:
x = t.[tex]y = \sqrt[3]{t} + 2[/tex].Item 35
A linear function is parameterized as follows:
x(t) = x(0) + at.y(t) = y(0) + at.The initial point of the function, at t = 0, is (-1, 5), hence:
x(0) = -1, y(0) = 5.
After 1 second, they moved to point (2,3), hence the coefficients are given as follows:
a = 2 - (-1) = 3.b = 3 - 5 = -2.Thus the parameterized equations are given as follows:
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Which function is shown in the graph? A. f(x) = x2 – 3x – 10 B. f(x) = x2 + 3x – 10 C. f(x) = x2 + x - 12 D. f(x) = x2 – 5x – 8
The graph shown have roots of x = -2 and x = 5
We could solve for x in each of the quadratic equations or we could plot the graphs of each of the quadratic equation.Then we pick the one with the roots of -2 and 5.
Plotting the graphs:
The roots of quadratic functionis the value of x when y is equal to zero.
From the graph attached above, f(x) = x² + 3x – 10 representing the blue parabola has roots of (-5, 0) and (2, 0).
This means the roots are -5 and 2.
Hence, the function in the graph is f(x) = x² + 3x – 10
In his music class, Mr. Thompson played short samples of 80 classical pieces of music. The students were able to identify 16 of the pieces.
What percent of the classical pieces did the students identify?
The students were able to identify 16 of the pieces out of 80 which is 20 % in the percentage form.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.
The students were able to identify 16 of the pieces out of 80.
We have to determine the percentage of the classical pieces the students identify.
As per the given information, the required solution would be as:
⇒ (16/80) × 100
⇒ (0.20) × 100
⇒ 20 %
Therefore, the percentage of the classical pieces the students identify would be 20 %.
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Combine the like terms in this expression: -x3 + 2xy + 4y - xy + 2x - 11y
A. -7xy
B. 2xy + 15
C. 23X + y
D. - X + XY -7y
Answer:
[tex]{ \rm{ {x}^{3} + 2xy + 4y - xy + 2x - 11y}} \\ \\ = { \rm{ {x}^{3} + (2xy - xy) + 2x + (4y - 11y)}} \\ \\ = { \rm{ {x}^{3} + 2x + xy - 7y}}[/tex]
What is the equation of the parabola with focus at (1, 1) and directrix y = -1?
The equation of the parabola having focus (1,1) and directix y = -1 is
y = x²/4 - x/2 + 1/4
The focus of the parabola (h , k + p) = (1,1)
The directrix of the parabola is y = -1
From, the focus
k + p = 1
k = 1 - p
The formula of directrix is
y = k - p (1)
Substituting the value of directrix and k
-1 = 1 -p -p
-1-1 = -2p
-2 = -2p
p = 1
Substituting the value p in equation (1)
k = 0
Now, we have got the vertex of the parabola (h ,k) is (1,0)
The equation of the parabola is
(x-h)² = 4p (y - k)
(x - 1)² = 4 (1) (y - 0)
( x -1 )² = 4(y )
x² - 2x + 1 = 4y
x²/4 - 2x/4 + 1/4 = y
y = x²/4 - x/2 + 1/4
which is the equation of the parabola.
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