The x and y values that makes the relation a function are x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8
How to determine the values of x and y?The ordered pairs are given as
(− 3, 7), (–2, 3), (0, 8), (1, − 1), (x,y)
For a list of ordered pairs to represent a function, the following must be true
The x values must have exactly one y value
Using the above as a guide, we can see that x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8 fits the above description
Hence, the values of x and y are x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8
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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
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
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
Help please asap asap
For this problem, we are given the dimensions of a right triangle, we need to apply the trigonometric relation to determine which one results in 3/5.
We have three possible options sin, cos, and tan. The sine is the division between the opposite cathetus and the hypothenuse, which for this case is equal to 3/5, therefore it is the correct option.
The answer is A. sin.
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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Need help for the questions need help with b and c
b) No, it is not
c) x + 1 is a factor
Explanation:[tex]b)\text{ }f(x)=x^3-7x^2+8x\text{ + 16}[/tex]To determine if 10 is a function, we substitute x with 10 in the function:
[tex]\begin{gathered} f(10)\text{ = 1}0^3-7(10)^2\text{ + 8(10) + 16} \\ f(10)\text{ = 1000-700+80+16} \\ f(10)\text{ = }396 \end{gathered}[/tex]No, it isn't a . This is because f(10) is not equal to zero, it is not a zero o. It has a remanider of 396.
c) Using synthetic division:
for x + 1: to be a factor, x = -1
+1 1 0
The last number is equal to zero. This indicates the remainder is zero.
Hence, x + 1 is a factor of the function f(x)
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.
HELPP
4,250/204 = y/528
Hello! So....
We are given the following:
[tex]\frac{4250}{204}= \frac{y}{528}[/tex]
_______________________
1. Switch sides.
[tex]\frac{y}{528} =\frac{4250}{204}[/tex]
_______________________
2. Cancel the common factor (34).
[tex]\frac{y}{528}= \frac{125}{6}[/tex]
_______________________
3. Multiply both sides by 528.
[tex]\frac{528y}{528} =\frac{125*528}{6}[/tex]
_______________________
4. Simplify.
[tex]y=11,000[/tex]
^Hence, our solution.
____________________________________
Hope this helps! If so, please lmk! Thanks and good luck!
4,250/204 = y/528
Multiply both sides of the equation by 8976, the lowest common denominator of 204,528.
44×4250 = 17y
Multiply 44 and 4,250 to get 187,000.
187000 = 17y
Swap the sides so that all the terms of the variables are on the left side.
17y = 187000
Divide both sides by 17.
y = 187000/17
Divide 187,000 by 17 to get 11,000.
y=11000
When you sold your shares, your account showed $4680.00 ($72.00 × 65 shares), for a total gain of $357.50 ($4680.00 – $4322.50). What percentage gain did you experience?
The percentage that 7.64% gain experienced you if sold your shares, your account showed $4680 for a total gain of $357.50.
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.
Given that when you sold your shares, your account showed $4680.00 ($72.00 × 65 shares)
For a total gain of $357.50 ($4680.00 – $4322.50).
Let the percentage gain you experienced be x %
As per the given data, the solution would be as:
⇒ x% of 357.50 = 4680.00
x% is expressed as x/100 in fractional form
⇒ (x/100)(357.50) = 4680.00
⇒ x = 357.50/4680.00 × 100
⇒ x = 7.64%
Therefore, the percentage that 7.64% gain experienced you.
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Algebraically determine whether the following function is Even, Odd, or Neither.
f(x)=x^3-2x
show all work please
The function is f(x) = [tex]x^3[/tex] + 2x is an odd function.
Given the function is :
f(x)=x^3-2x
To determine the function is Even , Odd , or Neither.
Let's Know :
What is an Odd function?
A function f is said to be an odd function if -f(x) = f(-x), for all value of x. In Mathematics, the functions even and odd are those that satisfy specific symmetry relations, with respect to considering additive inverses.
Now, Come to the question:
According to the question;
f(x) = [tex]x^{3}[/tex] - 2x
f(-x) = (-[tex]x^3[/tex]) - 2(-x)
f(-x) = -[tex]x^3[/tex] + 2x
Identify the relation between f(x) and f(-x)
f(x) ≠ f(-x)
Find -f(-x)
-f(-x) = -( -[tex]x^3[/tex] + 2x)
Remove the parentheses:
-f(-x) = [tex]x^3[/tex] + 2x
Identify the relation:
f(x) = -f(-x)
Hence, The function is f(x) = [tex]x^3[/tex] + 2x is an odd function.
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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
i have a derivative question about tangent lines, pic included
To find the horizontal tangent line, we have to conduct the first derivative test. The first derivative test sets the derivative of the function equal to 0.
Let's start out with finding the derivative of the function:
It seems like we will have to use Quotient Rule.
[tex]f^{\prime}(x)=\frac{(x^2-7x+1)(x+9)^{\prime}+(x^2-7x+1)^{\prime}(x+9)}{(x^2-7x+1)^2}[/tex]Now we can use basic derivative rules and properties to find the final derivative:
[tex]f^{\prime}(x)=\frac{(x^2-7x+1)+(2x-7)(x+9)}{(x^2-7x+1)^2}[/tex]Setting the derivative equal to 0, we can begin the first derivative test:
[tex]0=\frac{(x^{2}-7x+1)+(2x-7)(x+9)}{(x^{2}-7x+1)^{2}}[/tex]We can simplify the derivative before solving (expand and combine like terms):
[tex]0=\frac{-(x^2+18x-64)}{(x^2-7x+1)^2}[/tex]From here, we need to determine our values of x that will make the derivative equal to 0 or undefined. In this case, since we are not trying to find relative maxima or minima, we just need to find where the entire derivative is equal to 0. We can simply just graph the numerator and find its roots:
We can see that the values of x will be -21.0416 and 3.04159 will be the values that make the derivative equal to 0.
Also recall what the derivative is. The derivative is the slope of the tangent line. In order to find the horizontal tangent line, we know that horizontal tangent lines' slope is equal to 0.
Therefore, we can use either value of x to now find our equation.
Recall what the point-slope form of a line is:
[tex]y-y_1=m(x-x_1)[/tex]Since we know that the derivative slope must equal 0, then we know that m = 0. We now need to find a point (x, y). Substitute one of the x values into the original equation to find an actual point on the function (remember not to round intermediate values on your calculator!):
[tex]\begin{gathered} f(3.04159)=\frac{3.04159+9}{3.04159^2-7(3.04159)+1} \\ f(3.04159)=-1.09074 \end{gathered}[/tex]Now we have a point (x, y) (I will put it in the actual radical form here):
[tex]\bigg(\sqrt{145}-9,\frac{-2\sqrt{145}}{45}-\frac{5}{9}\bigg)[/tex]Substitute our variables into point-slope form:
[tex]y-\bigg(\frac{-2\sqrt{145}}{45}-\frac{5}{9}\bigg)=0\bigg(x-(\sqrt{145}-9)\bigg)[/tex]Simplify and rewrite to obtain our final answer:
[tex]y=\frac{2\sqrt{145}}{45}+\frac{5}{9}[/tex]The coldest recorded temperature in the United States is
–
80°F, in Alaska. The warmest recorded temperature in the United States is 134°F, in California.
How much higher is the warmest recorded temperature than the coldest recorded temperature?
The warmest recorded temperature is 214°F higher than the coldest temperature.
Since the sign of the two numbers are same, their final values will be added and the result will have the same signs as the two numbers (or the one with the greater absolute value). This is called the multiplicative property.
Expression for difference between the two temperatures is,
= 134−(−80)
By applying the multiplicative property of negative sign, we get
=134+80
= 214°F
Therefore, we conclude that the warmest recorded temperature is 214°F higher than the coldest temperature.
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A car leaves Albany, NY, and travels west toward Buffalo, NY. The equation D 280 59t can be used to represent the distance, D, from Buffalo after t hours. In this equation, the 59 represents the
1. Cars distance from Albany
2. speed of the car
3. distance between Buffalo and Albany
4. numbers of hours driving
Answer:
2. Speed of the car.
Step-by-step explanation:
Given equation:
[tex]D=280-59t[/tex]
where:
D = distance from Buffalo.t = time in hours.The car begins its journey at Albany.
Therefore, the car is at Albany when t = 0:
[tex]t=0 \implies D=280-59(0)=280[/tex]
Therefore, 280 represents the distance between Buffalo and Albany.
After 1 hour of driving:
[tex]t=1 \implies D=280-59(1)=221[/tex]
Therefore, after 1 hour of driving, the car is 59 miles closer to Buffalo and therefore 59 miles from Albany.
After 2 hours of driving:
[tex]t=2 \implies D=280-59(2)=162[/tex]
Therefore, after 2 hours of driving, the car is 158 miles closer to Buffalo and therefore 158 miles from Albany.
Therefore, the 59 represents the speed of the car as the car travels 59 miles per hour.
What helps the esophagus move food to the stomach?
A. Cardiac muscle contractions
B. Smooth muscle contractions
C. Skeletal and cardiac muscle contractions
D. Skeletal muscle contractions
answer asap for brainlist
[tex] \: \huge \tt{\pink{A}{\orange{N}S{\green{W}{\blue{E}{\purple{R}}}}}} : \\ \\ \: \: \rightarrow \tt \: \:B. \: Smooth \: \: muscle \: \: contractions[/tex]
Esophagus move food to the stomach with the help of Smooth muscle contractions. Thus, option B is correct.
What is esophagus?The esophagus is the tubular structure that transports food from your mouth to your stomach. Esophagitis can cause uncomfortable swallowing and chest discomfort. Esophagitis can be caused by a number of factors. Some typical causes comprise stomach acids backing up into the esophagus, illness, oral medications, and allergies.
As food enters the stomach, the esophagus contracts. The lower esophageal sphincter (LES) is a "valve" placed directly before the stomach entrance. This valve opens to allow food to travel from the esophagus into the stomach and closes to prevent food from moving back up into the esophagus from the stomach. Hence, option B is correct.
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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
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
Giving a test to a group of students, the grades and gender are summarized below A B C TotalMale 5 8 14 27Female 13 20 10 43Total18 28 24 70If one student was chosen at random, find the probability that the student got an A or a B on the test. Write your answer as a reduced fraction or whole number.P(A or B)=
Anime Girl, this is the solution:
We have a total of 70 students (male and female), in consequence:
• Students that got an A = 18
,• Students that got a B = 28
,• Stiudents that got a C = 24
• P(A or B) = A + B / Total students
• P(A or B) = 18 + 28/70
,• P(A or B )= 46/70
,• P(A or B) = 23/35 (Simplifying) or 0.66
3. For the number line shown, which
statement is NOT true?
Answer: A.
Step-by-step explanation:
D is not less than c because c is a negative number.
Correct answer answer now please for brainlist asap
Answer:
D. Organ systems
Step-by-step explanation:
Homeostasis is maintained by the nervous and endocrine systems.
Under a rotation about the origin, the point A ( 5 , − 1 ) is mapped to the point A ' ( 1 , 5 ) . What is the image of the point B ( − 4 , 6 ) under this rotation? Explain.
The image of the point B ( − 4 , 6 ) under 270° clockwise rotation is point (-6 , -4).
A transformation that revolves a figure around a point is called a rotation. The rotational center is where we refer to it. The shape and dimensions of a figure remain the same while facing in a different direction. You can rotate a figure either clockwise or counterclockwise.
Under a rotation about the origin, the point A ( 5 , − 1 ) is mapped to the point A ' ( 1 , 5 ) is a -
270° clockwise rotation: (x,y) becomes (-y,x)
The image of the point B ( − 4 , 6 ) under this rotation is
(x , y) = (-y , x)
i.e. (-6 , -4)
Assuming that the rotation's center is at (0, 0). Here are the guidelines for rotation:
90° clockwise rotation: (x,y) becomes (y,-x)90° counterclockwise rotation: (x,y) becomes (-y,x)180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)270° clockwise rotation: (x,y) becomes (-y,x)270° counterclockwise rotation: (x,y) becomes (y,-x)Therefore , The image of the point B ( 4, 6) when rotated 270 degrees clockwise is point (-6 , -4).
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will post a full pictures it did not fit
They will be parallel because the same transformations have been applied to it
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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The purchase price of a home is $150,000 what are the total closing cost if the following fees apply 5% purchase price title search $300 the buyer pays only half the fee low cost 4% recording $65 in taxes 1,235
It should be noted that the purchase price of the home will be $160865.
How to illustrate the information?Based on the information, the following can be illustrated:
Purchasing price = $150000
Purchase price fee = 5% × $150000 = $7500
Title search = $300
Love cost = 1/2 × 4% × $150000 = $3000
Taxes = $65
Total amount = $150000 + $7500 + $300 + $3000 + $65
= $160865
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10. An express train is travelling at 80 km/h. How far does it go in:
(a) 1 minute (b) 1 second?
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.
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]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]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
#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:
x(t) = -1 + 3t.y(t) = 5 - 2t.More can be learned about parametric equations at https://brainly.com/question/27247899
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