The distance between the cars after a hour is 14 meters.
How to calculate the distance of the cars?Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.
In this case, the cars leave town at the same time. One travels west at 56 mph, and the other travels south at 42 mph.
With the speed, the total distance after an hour will be:
= 56 - 42
= 14 meters
The cars are 14 meters apart.
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Simplifying 6(x+4)2/3x(x+4)
Answer:
[tex]\dfrac{2(x+4)}{x}[/tex] or [tex]2 + \dfrac{8}{x}[/tex]
Step-by-step explanation:
Rewrite the problem as a fraction.
[tex]\dfrac{6(x+4)^2}{3x(x+4)}[/tex]
Then, represent the squared term on the top as two values to make it easier to cancel.
[tex]\dfrac{6(x+4)(x+4)}{3x(x+4)}[/tex]
Now, cancel an x+4 from the top and bottom.
[tex]\dfrac{6(x+4)}{3x}[/tex]
Finally, divide the numerator and denominator by 3.
[tex]\dfrac{2(x+4)}{x}[/tex] or [tex]2 + \dfrac{8}{x}[/tex]
[tex]\bf{\dfrac{6(x+4)2}{3x(x+4)} \iff \ Eliminate \ (x+4).}\\ \\ \bf{That\:is, isolating\:the \ common \ factor \ \dfrac{\not{6}\times2 }{\not{3}x} \ \--\to\dfrac{2\times2}{x}=\dfrac{4}{x} } \\ \\ \boldsymbol{\sf{\dfrac{4}{x} }}\bf{\iff}\boxed{\boxed{\bf{Answer}}}[/tex]
The Miller family is taking a road trip to visit some relatives. With a full gas tank, the car has a range of 456 miles. Mr. Miller wants to stop to fill up when the range reaches 57 miles remaining. If the car averages 28.5 miles per gallon, then the equation 456 - 28.5g represents how many gallons of gas they will use before they need to fill up. How many gallons of gas will they use before they need to fill up? 57
Answer:
14 gallons
Step-by-step explanation:
456 - 28.5g = 5
28.5g =399
G=14
I NEEED HELP IM FAILING THIS CLASS WITH A (F) someone pls I’ll give brainliest and tons of points
Answer:
A reflection over the x axis
Step-by-step explanation:
x is the horizontal line we are reflecting one across it to get the other
(-14)+(-7) irrational
For the given expression -21 is not a irrational number.
What is irrational number?
In mathematics, all real numbers that are not rational are referred to as irrational numbers. Irrational numbers can't be expressed as the ratio of two integers, in other words.
Any real number that cannot be expressed as the ratio of two integers—that is, as p/q, where p and q are both integers—is an irrational number. For instance, there is no integer or fraction that equals the square root of 2.
Consider the given expression,
(-14) + (-7)
Solving this, we get
(-14) + (-7) = -14 - 7 = -21
Here 21 can be written in the form p/q.
⇒ -21 = -21/1
So, -21 is a rational number.
Hence, -21 is not a irrational number.
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Interesting Slopes- Definitions
the slope of the line is zero, as change in y cordintae is 0.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
In the given line in the graph, the change in y coordinate is 0.
We know that slope = change in y / change in x
As the change in y coordinate is 0.
The slope of the line will be zero.
Hence, the slope of the line is zero.
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What’s 0.4 divided by 2.56 i need help
Answer:
Step-by-step explanation:
0.15625
Does anyone know this?
Answer: i think it's 942,480
Step-by-step explanation:
i just multiplied all of the numbers but i'm probably wrong srry
Answer:
7986m^2
Step-by-step explanation:
140-102=38
area of triangle:
(38*66)/2=1254m^2
area of rectangle:
66*102=6732m^2
total area:
1254+6732=7986m^2
Data were recorded for a car's fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour
(mph). Given the least-squares regression line, In(Fuel Efficiency) = 1.437 +0.541 In(Speed), what is the fuel efficiency
for a speed of 60 mph?
A)3.65 mpg
B)33.90 mpg
C)36.52 mpg
D)38.55 mpg
The fuel efficiency for the speed of 60 mph is (d) 38.55 mpg
How to determine the fuel efficiency for the speed?From the question, we have the following least-squares regression line equation that can be used in our computation:
ln(Fuel Efficiency) = 1.437 +0.541 In(Speed)
Also from the question, we have the following parameters:
Speed = 60 mph
This means that we substitute 60 mph for speed in the given equation
ln(Fuel Efficiency) = 1.437 + 0.541 In(Speed)
So, we have the following representation
ln(Fuel Efficiency) = 1.437 + 0.541 In(60)
Take the natural logarithm of 60
This gives
ln(Fuel Efficiency) = 1.437 + 0.541 * 4.09434456222
Evaluate the products
So, we have the following representation
ln(Fuel Efficiency) = 1.437 + 2.21504040816
Evaluate the sum
So, we have the following representation
ln(Fuel Efficiency) = 3.65204040816
Take the exponent of both sides
Fuel Efficiency = e^(3.65204040816)
Evaluate
Fuel Efficiency = 38.5532502162
Approximate
Fuel Efficiency = 38.55 mpg
Hence, the fuel efficiency is (d) 38.55 mpg
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Jack spends 15 % of his pocket money on sweets and 35 % on magazines. He saves the rest.
Work out how much he spends and saves each week.
Sweets ____p
Magazines £___
Savings £____
Jack spend $15 on sweets
Jack spend $35 on magazines
Jack saves $50
Given,
Jack spends 15 % of his pocket money on sweets and 35 % on magazines.
Jack save the rest ; 100 - (15 + 35) = 100 - 50 = 50%
Here,
If Jack has a pocket money of $100
The money he spends on sweets = 15% of 100 = $15
The money he spends on magazines = 35% of 100 = $35
Then,
The money he saves = 50% of 100 = $50
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Using the functions s = 13.5h, which statement is true?
The domain of s = 13.5h is (0, 1, 2, 3, 4).
The range of s = 13.5h is (0, 13.5, 27, 40.5, 54).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
s = 13.5h
For h = 0,
s = 0
For h = 1,
s = 13.5
For h = 2,
s = 27
For h = 3,
s = 40.5
For h = 4,
s = 54
Thus,
The domain is (0, 1, 2, 3, 4).
The range is (0, 13.5, 27, 40.5, 54).
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4. Find s if the line through the points (7,3)
and (s, -7) has a slope of -5.
Answer:
s = 9
Step-by-step explanation:
calculate the slope m through the 2 points using the slope formula and equate to - 5
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (7, 3 ) and (x₂, y₂ ) = (s, - 7 )
m = [tex]\frac{-7-3}{s-7}[/tex] = [tex]\frac{-10}{s-7}[/tex]
equate m to slope of - 5
[tex]\frac{-10}{s-7}[/tex] = - 5 ← multiply both sides by s - 7
- 10 = - 5(s - 7) ← divide both sides by - 5
2 = s - 7 ( add 7 to both sides )
9 = s
On a coordinate plane, the points (3,4) (8,4) (5,0) and (0,0) form a parallelogram. What is the perimeter of the parallelogram?
Question 15 options:
25
20
30
15
Answer:
20
Step-by-step explanation:
A parallelogram has 4 sides.
Each pair of opposite sides is congruent.
To find the perimeter, find the length of 2 adjacent sides and multiply by 2.
Length of side (0, 0) to (5, 0) is 5.
Length of side (5, 0) to (8, 4) is the hypotenuse of a right triangle with legs of lengths 3 and 4.
a² + b² = c²
3² + 4² = c²
c² = 9 + 16
c² = 25
c = √25
c = 5
The hypotenuse measures 5 units.
perimeter = 2(5 + 5)
perimeter = 2(10)
perimeter = 20
Given that cosO =8/17 and sinO=-15/17 what is the value of tanO
.
Answer:
15/8
Step-by-step explanation:
Function p represents the number of people in the library on a Monday as a function of hours since the library opened. Here is the graph of function p.
Based on the graph and the situation, which domain and range make sense for function p?
A.
Domain: all numbers from 0 to 85. Range: all numbers from 0 to 14.
B.
Domain: whole numbers only from 0 to 14. Range: whole numbers only from 0 to 85.
C.
Domain: all numbers from 0 to 14. Range: whole numbers only from 0 to 85.
D.
Domain: whole numbers only from 0 to 14. Range: all numbers from 0 to 85.
Answer: the correct anserw is A.!
Step-by-step explanation:
Select all the equations that represent a line passing through the point (–2, 5) with a slope of 4. Multiple select question. cross out A) y − 5=4(x+2) cross out B) 4x – y= –13 cross out C) y+5=4(x – 2) cross out D) 4x – y=13 cross out E) y+2=4(x – 5) cross out F) 2x – 5y=4
The equations that represent a line passing through the point (–2, 5) with a slope of 4 are:
A) y − 5=4(x+2) B) 4x – y= –13How to find the equation of a line passing through point (–2, 5) with a slope of 4Equation of the line of slope = 4 passing through point (-2, 5) is calculated using the point slope formula which is
(y - y') = m(x - x')
y' = 5
slope, m = 4
x' = -2
substituting the known variables and solving
(y - 5) = 4(x - ( -2 ) )
y -5 = 4( x + 2)
y - 5 = 4x + 8
y = 4x + 8 + 5
y = 4x + 13
the equation of the line with a slope of 4 and passing through point (-2, 5) is y = 4x + 13
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A tower on the bank of a river is of 20 m high and the angle of elevation of the top of the tower from the opposite bank is 30 degree. find the breadth of the river
the breadth of the river is [tex]20\sqrt{3} m[/tex] or 34.614 m
as per given in the question ,
the length of the tower (l) = 20m
the angle of elevation of the top of the tower from the opposite bank
[tex]\theta[/tex] = [tex]30^{0}[/tex]
the breadth of the river should be found
let the breadth of the river be x,
to find breadth,
[tex]tan\theta=\frac{opposite\ side}{adjacent\ side}[/tex] ----(1)
the opposite side will be the length of the pole i.e, 20m
the adjacent side will be the breadth of the river i.e, x
now substitute all the values in equation (1)
[tex]tan\theta=\frac{20}{x}[/tex]
=> [tex]tan 30^0= \frac{20}{x}[/tex] ( the value of [tex]tan30^0 =\frac{1}{\sqrt{3} }[/tex] )
=> [tex]\frac{1}{\sqrt{3} } =\frac{20}{x}[/tex]
=> [tex]x=20\sqrt{3}m[/tex]
so,
the breadth of the river is [tex]20\sqrt{3} m[/tex] or we can write 34.614m
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Once i give you brainliest It will be 25 Points!
Answer:
Step-by-step explanation:
First question. Answer is
are the following required to file a federal income tax return? MFJ HUSBAND AGE 66 WIFE AGED 60 GROSS INCOME OF $25200
The answer to the Question based on Federal Income Tax return is Yes
What is Federal Income Tax Returm?
It is a kind of tax that people have to pay to government.
Federal Income tax has some of its special conditions also and so is suggested by its name
Solution:
As MJF husband is aged 66 and his Gross income is 25200$ and this amount of money is not very less but infact very high hence there is fixed percentage of tax decided by government per fixed amount of money and MJF husband has to pay that amount of tax to government
Hence answer to the Question is Yes
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there are 72 players on 9 teams. How many players are on one team
Answer:
8
Step-by-step explanation:
72 ÷ 9 = 8
Answer:
8
Step-by-step explanation:
72 divided by 9 is 8
Which is an equivalent expression for {(5/7)²· (1/3)⁻³}⁻¹ ?
(5/7)² .(1/3)⁻³
(5/7). (1/3)⁻⁴
(7/5)⁻² . (1/3)⁻³
(7/5)² .(1/3)³
Equivalent expression to the given expression [ ( 5/7)² ( 1/3)⁻³]⁻¹ is equal to
Option d. ( 7 /5)² ( 1/3)³.
As given in the question,
Given expression is equal to :
[ ( 5/7)² ( 1/3)⁻³]⁻¹
Apply law of exponent power to power we get,
( mᵃ nᵇ )ˣ = (m)ᵃˣ × (n )ᵇˣ
( x /y)⁻ᵃ = ( y /x)ᵃ
Here m = 5/ 7, n = 1/3 , a = 2 , b = -3 and x = -1
Equivalent expression of the given expression is:
[ ( 5/7)² ( 1/3)⁻³]⁻¹
= ( 5 / 7 )^(2 × -1) ( 1 / 3)^(-3 × -1)
= ( 5 / 7 )⁻² ( 1 / 3)³
= ( 7 / 5 )²× ( 1 / 3)³
Therefore , equivalent expression of [ ( 5/7)² ( 1/3)⁻³]⁻¹ is equal to the
option d.( 7 /5)² ( 1/3)³.
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What is a simplified expression for the perimeter of the polygon?
Perimeter of the polygon is [tex]5x^{2} +y^{2}+3x+4y[/tex]
What do you mean by perimeter of polygon?
A polygon is a closed, straight-sided two-dimensional plane shape in geometry. There are no curves on the polygon's surface.
The total of a polygon's sides is referred to as the polygon's perimeter. A regular polygon's perimeter is provided by if it is one.
Regular polygon perimeter equals (number of sides) x (length of polygon's sides) units.
Given sides of the polygon are 4y , [tex]y^{2} , 4x^{2} -y^{2},3x,x^{2} +y^{2}[/tex]
Perimeter of the polygon is the sum of all sides of the polygon
Perimeter of the polygon = [tex]4y+4x^{2} -y^{2}+3x+x^{2} +y^{2} +y^{2}[/tex]
= [tex]5x^{2} +y^{2}+3x+4y[/tex]
Therefore, perimeter of the polygon is [tex]5x^{2} +y^{2}+3x+4y[/tex]
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3 out of 4 cats are orange
Answer:
3 cats are orange and The other 1 is not
Because
The sum of Lance's and Chad's ages is 27 years. Chad is 6 years younger than twice Lance's age. Let l represent Lance's age, and let c represent Chad's age. This situation can be represented by the system l+c=27 and c=2l−6 . Find the age of each person.
The age of Lance and Chad are 7 years and 20 years respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let age of Lance's is = L
Age of Chad's = C
Given that The sum of Lance's and Chad's ages is 27 years. Chad is 6 years younger than twice Lance's age.
The system of equations that represents this situation is;
L + c = 27
C - 6 = 2L
2L - c = -6------ (1)
Therefore,
⇒ ( 2L - c ) + (L + c) = 21
⇒ 3L = 21------- (2)
L = 7
C = 20
Therefore the age of each person;
7 years and 20 years
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The James family purchased a home for $180,000 five years ago and obtained an 80% LTV loan. Now the property has appreciated 25%. In addition, the loan has been paid down $11,000. What is the James’s current equity in the home?
$92000 is the James’s current equity in the home.
What is equity?Equity, also known as shareholders' equity or owners' equity for privately held businesses, is the sum of money that, in the event of a company's liquidation, would be distributed to its shareholders after all of the company's assets have been sold and its debt has been fully repaid.
In an acquisition scenario, it is equal to the sum of the company's sales less any liabilities that were not transferred to the new owner.
A company's book value can also be represented by shareholder equity. A payment-in-kind arrangement may occasionally include equity. Furthermore, it represents the proportionate ownership of a company's shares.
James’s current equity = (180000 × 1.25) - ((180000 × 0.8) -11000)
= 92000
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ILL GIVE BRAINLY PLEASE HURRY State the area of the given parallelogram.
Responses
A 35 units squared35 units squared
B 28 units squared28 units squared
C 70 units squared70 units squared
D 11 units squared11 units squared
Answer:
35
Step-by-step explanation:
The area of the parallelogram will be equal to 28 units squared. Hence, option B is correct.
What is Parallelogram?The phrase "parallelogram" is a translation of the Greek phrase "parallelogrammon," which means "bound by the contract by parallel lines." As a consequence, a quadrilateral that is bordered by parallel lines is called a parallelogram. It has parallel and equal opposite sides on all sides.
As per the data obtained from the given values,
Length of base (b) of parallelogram = 7
Length of height (h) of parallelogram = 4
Use the formula of area (A) of a parallelogram,
[tex]Area = Base*Height[/tex]
A = 7 × 4
A = 28 units squared.
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How to divid mix numbers
First correct answer gets brainliest
Given a line with slope = -4 and y-int= (0, 5), write the equation of the line.
Writing the equation algebraically.
Answer:
[tex]y=-4x+5[/tex]
Step-by-step explanation:
The equation of a line with slope [tex]m[/tex] and [tex]y[/tex]-intercept [tex](0,b)[/tex] is [tex]y=mx+b[/tex].
1.)The half-life of Radium-228 is 5.75 years. What is the annual decay rate? Express the result to four decimal places.
Answer:
Express the annual decay rate as a percentage to two decimal places.
2.) The equation N(t) = 600/ 1 + 59e^−0.7t models the number of people N in a town who have heard a rumor after t days.
How many people started the rumor?
3.) The equation N(t) = 700/1 + 69e−0.8t models the number of people N in a town who have heard a rumor after t days.
To the nearest whole number, how many people will have heard the rumor after 3 days?
1) The annual decay rate of the exponential function is given as follows: 12.94%.
2) The number of people who started the rumor is of 10.
3) The number of people who will have heard the rumor after 3 days is given as follows: 96 people.
How to obtain the measures?For item 1, the format of the exponential function is given as follows:
A(t) = A(0)(1 - r)^t.
In which r represents the annual decay rate.
The half-life of Radium-228 is 5.75 years, hence:
A(5.75) = 0.5A(0).
Thus the annual decay rate of the exponential function is given as follows:
0.5A(0) = A(0)(1 - r)^5.
(1 - r)^5 = 0.5
Applying the fifth root to both sides:
1 - r = (0.5)^(1/5)
1 - r = 0.8706
r = 1 - 0.8706
r = 0.1294 = 12.94%.
Then for items 2 and 3 we just obtain the numeric values.
The number of people who started the rumor is N(0), hence:
N(0) = 600/(1 + 59e^(-0.7 x 0)) = 600/60 = 10 people.
The number of people who heart the rumor after three days is N(3), hence:
N(3) = 700/(1 + 69e^(-0.8 x 3)) = 96 people.
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How do I integrate this problem?
[tex]\int\limits\frac{4}{x^2+2} \, dx[/tex] = [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex] + C where C is the integrating constant.
What do you mean by integration?
The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a collection of little data that cannot be measured separately, the integral is calculated.
The idea of integration has evolved to address the following issues:
once the derivatives of the problem function have been determined.
to determine the region enclosed by a function's graph under specific restrictions.
Given function f(x) = [tex]\frac{4}{x^2+2}[/tex]
[tex]\int\limits\frac{4}{x^2+2} \, dx[/tex]
Substitute u = [tex]\frac{x}{\sqrt{2} }[/tex]
⇒ [tex]\frac{du}{dx} =\frac{1}{\sqrt{2} }[/tex]
⇒ dx = [tex]\sqrt{2}[/tex] du
= [tex]\frac{2^{\frac{5}{2}} }{2u^2+2}du[/tex]
On simplifying
= [tex]2^{\frac{3}{2} }[/tex][tex]\int\limits\frac{1}{u^2+1} \, du[/tex] .........(1)
Now [tex]\int\limits\frac{1}{u^2+1} \, du[/tex] = [tex]tan^{-1} (u)[/tex]
Substitute this value in equation (1)
= [tex]2^{\frac{3}{2} }tan^{-1}(u)[/tex]
Substitute the value of u here
= [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex]
Therefore, [tex]\int\limits\frac{4}{x^2+2} \, dx[/tex] = [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex] + C where C is the integrating constant.
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What is the slope of the lines
Answer: the slope of the line is 2 or 2/1
Step-by-step explanation: