Answers
The equation to represent the function P is y=4x as per the given points in the table.
What is meant by slope-intercept form?It is easier to see the slope (m) and y-intercept (c) of a line in the slope-intercept form of a linear equation (y=mx+c).
18th-century Switzerland. The first person to present a line's equation in slope intercept format might have been Jakob Hermann.
Y = mx + c is the true slope intercept form. It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.
You can see the line's slope and y-intercept in Slope-Intercept form. One point the line travels through and the slope of the line are both clearly displayed in point-slope form.
We know that, the equation of the line is y=mx+c
If this line passes through (0,0) then,
0=m(0)+c
then, c=0
Now, substituting the point (1,4) in the above equation and c=0 then we get,
4=m(1)+0
m=4
Now substitute the point (2,8) then,
8=m(2)+0
m=4
Similarly, by substituting the points (3,12), (4,16), (5,20), (6,24) we get,
m=4
Now, by substituting c=0 and m=4 in the above equation we get,
y=4x+0
y=4x
Therefore, the equation to represent the function P is y=4x
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Related Questions
If point A is at (-2,-2) and point B is at (1,2), what is the distance between point A
and B?
Answers
The distance between point A and point B is 5 units.
According to the question,
We have the following information:
Point A = (-2,2)
Point B = (1,2)
Now, we know that the following formula is used to find the distance between two points:
Distance between two points = [tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} )}[/tex]
In this case, we have the values of x1 = -2, y1 = -2, x2 = 1 and y2 = 2.
Distance between two points = [tex]\sqrt{(2+2)^{2} +(1+2)^{2} )}[/tex]
(The sign has been changed from negative to positive because the multiplication of two negative integers is positive.)
Distance = [tex]\sqrt{(4)^{2} +(3)^{2} )}[/tex]
Distance = [tex]\sqrt{16+9}[/tex]
Distance = [tex]\sqrt{25}[/tex]
Distance = 5 units
Hence, the distance between point A and point B is 5 units.
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You take out a home loan for $162359. The interest on this loan is fixed at 9.6% compounded
monthly for 30 years.
How much is your required monthly mortgage payment?
Round your final answer to the nearest cent (2 decimal places)
4
Answers
Answer:
$1377.06
Step-by-step explanation:
You want the monthly payment on a 30 year loan of $162359 at 9.6% interest.
AmortizationThe payment value can be computed by any spreadsheet and most graphing calculators using built-in financial functions. Numerous apps and web sites are available for the same purpose.
The monthly payment is $1377.06 according to the attached calculator output.
FormulaThe formula used for the purpose is ...
A = P(r/12)/(1 -(1 +r/12)^(-12·t))
where P is the loan value, r is the annual interest rate, and t is the number of years. For P=162359, r=0.096, and t=30, you have ...
A = 162359(0.096/12)/(1 -(1 +0.096/12)^-360) ≈ 1377.06
__
Additional comment
The formula assumes the payment is made at the end of the month. Spreadsheet and calculator functions often need to be told that's when the payment is made.
12. Two functions are given below, one in equation form and the other in table form. Using these functions, give
the value of g (f (4)). Show how you arrived at your answer.
-2
f(x) -1
0
3
4
12
7
9
19
6
g(x)=3.25x+6
Answers
The composition of the fuctions g(x) and f(x) evaluated in x = 4 is equal to:
g( f(4)) = 45
How to find the value of the composition?Here we have two functions f(x) and g(x), such that:
g(x) = 3.25*x + 6
And f(x) is defined by the table:
x f(x)
-2 -1
0 3
4 12
7 9
19 6
And we want to find the composition of g(x) and f(x) evaluated in x = 4.
g( f(4))
By using the table of f(x), we can see that f(4) = 12
Then:
g( f(4)) = g(12)
Evaluating g(x) in x = 12 we get:
g(12) = 3.25*12 + 6 = 45
Then we conclude that g( f(4)) = 45
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Line g passes through points (2, 4) and (10, 1). Line h is parallel to line g. What is the slope of line h?
Answers
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line G
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 8 } \implies {\Large \begin{array}{llll} - \cfrac{3 }{ 8 } \end{array}}[/tex]
1. A cyclist estimates that he will bike 80 miles this week. He actually bikes 90 miles. What is the percent error of the cyclists estimate rounded to the nearest percent?
A 8%
B 9%
C 10%
D 11%
2. Jack borrows $3,000 at a rate of 4% per year. How much total will he pay if it takes 3 months to repay the loan?
$10
$20
$30
$40
Answers
Answer:
D 11%
$30
Step-by-step explanation:
1. A cyclist estimates that he will bike 80 miles this week. He actually bikes 90 miles. What is the percent error of the cyclists estimate rounded to the nearest percent?
A 8%
B 9%
C 10%
D 11%
Actual distance: 90 miles
Estimated distance: 80 miles
percent error = (estimate - real)/real × 100%
percent error = (80 - 90)/90 × 100%
percent error = -11%
His error is 11%. The negative sign just means his estimate is 11% less than the real distance.
Answer: 11%
2. Jack borrows $3,000 at a rate of 4% per year. How much total will he pay if it takes 3 months to repay the loan?
$10
$20
$30
$40
interest = Prt
where P = principal (the amount borrowed or deposited)
r = annual rate of interest
t = time
We have P = $3,000
r = 4% = 0.04
t = 3 months = (3 months)/(12 months) = 0.25 year
interest = $3,000 × 0.04 × 0.25
interest = $30
He pays a total interest of $30.
The CDC initially reported that the effectiveness of the Moderna Vaccine in preventing Covid-19 (after a second shot and two months time) could be given by the 95% confidence interval (.893, .967). Answer the following relating to this confidence interval.
Answers
a) The sample proportion would be of: 0.93.
b) The margin of error would be of: 0.037.
c) The critical value would be of: z = 1.96.
d) The standard error would be of: 0.0189.
e) The critical value for the 90% confidence interval would be of: z = 1.645.
f) The 90% confidence interval would be narrower.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.From the equation, the confidence interval can be described as follows:
The sample proportion plus/minus the margin of error.
For this problem, the interval is given as follows:
(.893, .967).
From the description, the sample proportion is the mean of the two bounds, hence:
Sample proportion = (0.893 + 0.967)/2 = 0.93.
The margin of error is the absolute value of the difference of each bound and the sample proportion, hence:
Margin of error = |0.967 - 0.93| = |0.893 - 0.93| = 0.037.
The critical values are found using the z-table, as follows:
95% confidence level -> p-value of 0.975 -> z = 1.96.90% confidence level -> p-value of 0.95 -> z = 1.645.The greater the critical value, the wider the interval, hence a 90% confidence interval would be narrower than the 95% confidence interval;
The standard error is the division of the margin of error by the critical value, hence:
Standard error = 0.037/1.96 = 0.0189 = 1.89%.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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Find the slope determined by the following pair of points.
(4,5), (1,3
Answers
Answer:
2/3
Step-by-step explanation:
we use y2-y1/x2-x1 to find slope
5-3/4-1
2/3
The slope is 2/3
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please check the image
Answers
The trigonometric measures in the context of this problem are given as follows:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3-\sqrt{3}}{6}}[/tex][tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3+\sqrt{3}}{6}}[/tex][tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]How to obtain the trigonometric measures?We are given the measure of the sine for the angle and we need to find the three measures, sine, cosine and tangent for half the angle.
To find the measure for half the angle, the cosine is needed to apply the identities, and the cosine is calculated by the following identity:
sin²(x) + cos²(x) = 1
[tex]\left(\frac{2}{3}\right)^2 + \cos^2{x} = 1[/tex]
[tex]\cos^2{x} = 1 - \frac{4}{9}[/tex]
[tex]\cos{x} = \pm \sqrt{\frac{5}{9}}[/tex]
The angle is in the first quadrant, in which the cosine is positive, hence:
[tex]\cos{x} = \sqrt{\frac{5}{9}}[/tex]
[tex]\cos{x} = \frac{\sqrt{3}}{3}[/tex]
Then, applying an identity, the sine for half the angle is given as follows:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \cos{x}}{2}}[/tex]
Considering the calculated value for the cosine:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \frac{\sqrt{3}}{3}}{2}}[/tex]
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3-\sqrt{3}}{6}}[/tex]
The identity for the cosine is:
[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 + \cos{x}}{2}}[/tex]
Hence:
[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3+\sqrt{3}}{6}}[/tex]
The tangent is obtained by the division of the sine and the cosine. The entire division can be placed into a single square root, and the common denominators of six are simplified, hence:
[tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]
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a triangle has a base of 1.5
Answers
Answer: bro You need To add more about the question
Step-by-step explanation:
1. Jasmine buys 4 bottles of water for $1.30 each. She buys a large bag of popcorn for $3.75. How much more money did Jasmine spend on water than pop
Answers
Answer:
Jasmine spent 1.45$ more on water than popcorn.
Step-by-step explanation:
Jasmine buys 4 bottles of water and spends 1.30$ for each one individually. To find out how much all of these 4 costs, we multiply 4 by 1.30$ which is 5.20$
To find out how much more money Jasmine spent on the water than popcorn, we subtract 5.20$ - 3.75$ = 1.45$
Elena Says x is a number that makes Equation A true but does not make Equation B true.
Equation A : 13 - 5x = 48
Equation B : 5x = 35
Write a convincing explanation as to why this is true
Answers
Answer:
See below
Step-by-step explanation:
13 - 5x = 48 Subtract 13 from both sides
-5x = 35
-5x = 35 is the not the same as 5x = 35
-5x = 35 Divide both sides by -5
x = -7
5x = 35 Divide both sides by 5
x = 7
7 and -7 are not the same solution. They are two different numbers.
What is the height of the cylinder? Round your answer to the nearest tenth, enter only the number, no label
Answers
To find the height, envision it as a third side to a right triangle. We have the first side, with a length of 7cm, and the hypotenuse, with a length of 15cm. When we have two sides of a right triangle with given lengths, we can employ the Pythagorean Theorem.
The Pythagorean Theorem states that the square of the hypotenuse, c, is equal to the sum of the squares of the other two sides, or:
[tex]a^2 + b^2 = c^2[/tex]
Well, we have a and c, so we can solve for b.
[tex]7^2 + b^2 = 15^2\\49+b^2 = 225\\49 - 49 + b^2 = 225 - 49\\b^2 = 176\\\sqrt{b^2}=\sqrt{176}\\b = 13.27[/tex]
b ≈ 13.27
The following angles are supplementary to each other.
m∠C = (2x + 18)° and m∠D = (3x − 18)°
Determine x.
Answers
Answer:
x = 36°
Step-by-step explanation:
Hello!
If angles are supplementary, that means that the sum of those angles is 180°.
Set up an equation and solve for x.
Solve for x2x + 18 + 3x - 18 = 1805x = 180x = 36The measure of x is 36°.
How much should be deposited in an account paying 4.5% interest, compounded semiannually, in order to have a balance of $ 5,000 after 19 years and 6 months?
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Principal ≈ $ ________
Answers
The amount that should be deposited in the account to earn a balance of $5, 000 after 19 years and 6 months is $2, 099.43
How to find the amount?First, find the periodic rate:
= 4.5% / 2 semi annual periods per year
= 2.25%
Find the number of periods:
= 19 years and 6 months = 19.5 years
= 19.5 years x 2 semi annual periods per year
= 39 periods
The amount to deposit in the account can be found by the future value formula:
Future value = Deposit x ( 1 + rate) ^ number of periods
5, 000 = Deposit x ( 1 + 2.25%)³⁹
Deposit = 5,000 / ( 1 + 2.25%)³⁹
= $2, 099.43
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The top of a 100 foot vertical tower is to be anchored by cables that make an angle of 60∘ with the ground. Please include units in your answers. All trig functions will be evaluated in degrees.
Answers
The horizontal distance which the cable is placed on is 57.74 feet
Trigonometric FunctionTrigonometric functions are the periodic functions which denote the relationship between angle and sides of a right-angled triangle. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Data;
Height = opposite = 100ftangle = 60 degreeshorizontal distance = adjacent = xUsing tangent ratio;
tanθ = opposite / adjacent
tan 60 = 100 / x
x = 100 / tan 60
x = 57.74 ft
The distance which the cable is anchored to the ground is 57.74ft.
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Find the value of x (desperately need help with this please! Due today!)
Answers
Answer:
x=48
Step-by-step explanation:
the 2 given angles if added together we know it’ll be 180 degrees
3x-12+x=180
4x-12=180
+12. +12
4x=192
x=48
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What is –11 + |-5|-|-15|?
-1
-11
-9
-26
-21
Answers
Answer:
-1
Step-by-step explanation:
you would do -11 + (-5) which will be -16. Then do -16 - (-15) which will get you -1.
SOMEONE PLS HELP ME!!!!!!Match the statements with their correct reason to complete the proof.
Given: AB = BC and AD = CD
Prove: Triangle ABD Triangle CBD
Answers
Proved that Triangle ABD ≅ Triangle CBD
Consider the triangle ABD and the triangle CBD
The length of the side AB = The length of the side BC
The length of the side AD = The length of the side cd
The third side is common
According to the SSS rule congruent . If the three side of the triangle is equal to the three sides of the another triangle then the both triangles are congruent
Then three sides of the triangle ABD is equal to the three sides of the triangle CBD, Therefore the triangle ABD and triangle CBD are congruent
Hence, proved that Triangle ABD ≅ Triangle CBD
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James is having a birthday party. It costs $350 to rent the hall plus $35 per person for food. Write an equation to show the total cost of the party (y) based on the number of guests (x) he invites.
Answers
y=35x+350 is the equation to show the total cost of the party (y) based on the number of guests (x) he invites.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
James is having a birthday party.
It costs $350 to rent the hall plus $35 per person for food
We need to write an equation to show the total cost of the party (y) based on the number of guests (x) he invites.
y=35x+350
Where x represents the number of guests.
350 is a constant value because it is the cost of the hall.
As 35 is the cost per person, 35x
Hence y=35x+350 is the equation to show the total cost of the party (y) based on the number of guests (x) he invites.
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Find the equation of the inverse of the following function: f (x) = 7x + 3. State the answer in slope-intercept form
Answers
The equation of the inverse function is f⁻¹(x) = x/7 - 3/7
How to determine the inverse functions?The function f(x) is given as
f(x) = 7x + 3
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = 7x + 3
The next step is to switch/swap the positions of x and y in the above equation y = x + 5
The equation becomes
x = 7y + 3
The next step is to make y the subject of the formula in the above equation
The equation becomes
y = x/7 - 3/7
Express as an inverse function
f⁻¹(x) = x/7 - 3/7
Hence, the inverse is f⁻¹(x) = x/7 - 3/7
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a pitcher of water is three-fourths full. six cups of water are served from the pitcher. then the pitcher is two-thirds full. how many cups of water can the pitcher hold?
Answers
The total cups of water the pitcher can hold is 72
What is a fraction?A fraction is the ratio of two integers.
It is divided into two parts by a division line and the part above the line is called the numerator and the part below the line is called the denominator.
Fraction are of three types: proper, improper and mixed fractions.
Let the total number of cups to fill the pitcher be x.
The pitcher is 3-fourths full of water, that is 3/4 of x = [tex]\frac{3x}{4}[/tex]
when 6 cups were taken away from the Pitcher it became 2/3 of x = [tex]\frac{2x}{3}[/tex]
So that,
[tex]\frac{3x}{4}[/tex] - [tex]\frac{2x}{3}[/tex] = 6
multiply [tex]\frac{2x}{3}[/tex] by 4/4 and [tex]\frac{3x}{4}[/tex] by 3/3
it becomes
[tex]\frac{9x}{12}[/tex] - [tex]\frac{8x}{12}[/tex] = 6
simplifying the numerator
x/12 = 6
cross multiplying
x = 12 x 6
x = 72
In conclusion, the total number of cups to fill the pitcher is 72
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18. If Allan swims at an average speed of 2
metres per second, how long will it take
him to complete a 200 metre race?
Answers
Answer:
100 seconds
Step-by-step explanation:
200/2 = 100s
How do I solve this problem step-by -step? 57x 2(4)+2
Answers
Answer:
=57×2of4+2
=57×8+2
=456+2
=458.
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The distance from -8 to 0 is the same as the distance from 8 to 0 on the number line true or false
Answers
Can you solve please
Answers
Answer:
Green x = 10
Purple x = 19
Step-by-step explanation:
Are we solve for x?
Green:
It is not staighted, but this looks like a straight angle. That would total 180
3x + 5 + 6x -5 +90 = 180 A right angle is 90 Combine like terms
9x + 90 = 180 Subtract each side by 90
9x = 90 Divide both sides by 9
x = 10
Purple:
5x - 19 + 2x + 5 = 119 Combine like terms
7x -14 = 119 Add 14 to both sides
7x = 133 Divide both sides by 7
x = 19
Find the exact value of tan195
Answers
The exact value of tan195° is 0.2679.
The given trigonometric ratio is tan195°.
What are trigonometric angles?Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.
Now, the value of trigonometric ratio is
tan195°=0.2679
Hence, the exact value of tan195° is 0.2679.
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Five hours and 20 minutes after a raft left a dock, a patrol boat left the dock and traveled in the same direction as the raft. The boat caught up to the raft 20 km away from their starting point. What was the speed of the raft if the speed of the patrol boat was 12 km/hr?
Answers
Answer:
20/7 km/hr
Step-by-step explanation:
To solve this problem, we use the formula of:
speed x time = distance
Both the raft and boat have their own speeds, times and distances, so we would write two equations based on the formula.
One for the raft: [tex](s_{r} )(t_{r} )=d_{r}[/tex]
And one for the boat: [tex](s_{b} )(t_{b} )=d_{b}[/tex]
Both vehicles travelled as total of 20 km, so both [tex]d_{r} =d_{b} =20[/tex]. We are also given that the boat goes 12 km/hr, so [tex]s_{b} = 12[/tex]. Lastly, the boat had been going for five hours and 20 minutes less than the raft. This is the same as 5 1/3 hrs. This can also be written as 16/3 hrs, so [tex]t_{r} = t_{b} +\frac{16}{3}[/tex]. We can now plug these in:
raft: [tex](s_{r} )(t_{b}+\frac{16}{3} )=20[/tex]
boat: [tex](12 )(t_{b} )=20[/tex]
We only have one variable in the boat equation, so we can solve for time:
[tex]t_{b} =\frac{20}{12} \\\\t_{b} = \frac{5}{3}[/tex]
Now, we can plug [tex]t_{b}[/tex] into the raft equation and solve for speed:
[tex](s_{r} )(t_{b}+\frac{16}{3} )=20\\\\(s_{r} )(\frac{5}{3} +\frac{16}{3} )=20\\\\(s_{r} )(\frac{21}{3} )=20\\\\(s_{r} )(7)=20\\\\s_{r}=\frac{20}{7}[/tex]
Therefore, the speed of the raft would be 20/7 km/hr
The speed of the raft if the speed of the patrol boat was 12 km/hr will be 20/7 km/hr.
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.
It is known that,
Speed = total distance / total time taken
The time is taken by petrol boat to reach the raft craft
Time = total distance/speed
Time = 20/12 = 5/3 hour.
The time taken the raft boat to reach 20 km = (5 hour + 20 minutes) + 5/3 hour
⇒ 5 + 1/3 + 5/3
⇒ 16/3 + 5/3 = 21/3 = 7
The speed of the raft will be as,
Speed of raft = 20/7 km/hr
Hence "The speed of the raft, if the speed of the patrol boat was 12 km/hr, will be 20/7 km/hr".
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please help please
show answer and question.
a crate is 24cm by 18cm by 15cm . it is to be packed with boxes that are 8cm by 6cm by 5cm . what is the largest number of boxes that can fit in the crate.
Answers
The largest number of boxes that can fit in the crate will be 27.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The dimension of the crate is 24cm by 18cm by 15cm.
And, it is to be packed with boxes that are 8cm by 6cm by 5cm.
Now,
By the given data;
Volume of the crate = 24 x 18 x 15
= 6480 cm³
And, The volume of the box = 8 x 6 x 5
= 240 cm³
Thus, The largest number of boxes that can fit in the crate = 6480 / 240
= 27
Therefore, The largest number of boxes that can fit in the crate will be 27.
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If the function f(x) is the absolute value of 3 more than the value of x. Select all the true statements. A. The x-intercept of the function is 3.
Answers
The true statement about the function is that (b) the y-intercept of the function is 3
How to determine the true statement?The mathematical statement of the representation of the function is given as
The function f(x) is the absolute value of 3 more than the value of x.
Mathematically, this can be represented as
f(x) = |x + 3|
To determine the y-intercept, we set the x value of the function to 0
This means that we calculate f(x) when x = 0
i.e. f(0)
Substitute the known values in the above equation, so, we have the following representation
f(0) = |0 + 3|
Evaluate the sum
This gives
f(0) = |3|
Remove the absolute bracket
f(0) = 3
Hence, the y-intercept is 3
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Possible question
If the function f(x) is the absolute value of 3 more than the value of x. Select all the true statements.
A. The x-intercept of the function is 3.
B. The y-intercept of the function is 3.
To find 50 x 20, I multiply
5 X 2 and then place the total number of
zeros in both factors at the end." Do you
agree? Explain.
Answers
Answer:
"i agree because.."
Step-by-step explanation:
50 x 20 = 1000
5 x 2 = 10
there are 2 zeros in both factors so placing the 2 zeros at the end of 10 (making 1000) would work since they are the same answer