The x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10 are (-2.6,5.2).
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction. A ray has only one endpoint and an endlessly long another end, as opposed to a line segment that has two ends.
If a point (x,y) divides the line segment joining the points A(x1,y1) and B (x2,y2) is in the ratio m:n, then
[tex]x=\frac{mx2+nx1}{m+n} \\y=\frac{my2+ny1}{m+n} \\[/tex]
Here,
m:n = 3:10
The endpoint of line AB are at: A(-4,8) and B(2,-4)
We substitute the given values to obtain:
x= 3*2+10*(-4)/3+10
x= -34/13
x= -2.6
and
y= 3*(-4)+10*(8)/3+10
y= 68/13
y= 5.2
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pls solve before friday
The result of the given mathematical expression is 8459.46
What is Mathematical expression and decimal
Mathematical expression consist of combination of numbers along with addition, subtraction, multiplication and division.
Decimal numbers are those numbers which have an integer part and a fractional part.
Decimal can be terminating as well as non terminating.
Terminating decimals are those numbers which have finite number of digits after decimal point.
Non terminating decimals are those numbers which have infinite number of digits after decimal point.
Mathematical expression to be solved
[tex]31520 \times 0.029 \times \frac{(1+0.029)^4}{(1+0.029)^4-1}[/tex]
Decimal number is present in the above expression.
The given expression is to be simplified to get a solution
Now,
[tex]31520 \times 0.029 \times \frac{(1+0.029)^4}{(1+0.029)^4-1}\\\\31520 \times 0.029 \times \frac{(1.029)^4}{(1.029)^4-1}\\\\31520 \times 0.029 \times \frac{1.1211442633}{0.1211442633}[/tex]
8459.46
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A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 456 in³, what were the original dimensions of the piece of metal?
The width of the piece of metal will be 21 inches while the length will be 26 inches.
What is a rectangle?
A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Main body:
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the width of metal w then the length will be w + 5
Now if we cut 1 inch square from the corner of the metal and then fold then the resultant cuboid will have;
Length = w+5 - 2 -= w + 3
Width = w - 2
Height = 1
So,
Volume = (w+3)(w-2)1
456 = w² - 2w + 3w - 6
w² + w - 462 = 0
By solving this
w = 21 so width will be 21 and length will be 21 + 5 = 26.
Hence "The width of the piece of metal will be 21 inches while the length will be 26 inches".
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1. Calculate the expected value of the number of cups of coffee Alex drinks each day. 00.200 cups 00.163 cups 00.976 cups 01.881 cups
The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.
the mean/ average is gotten by dividing the sum of the values in the set by their number.
The concept of mean/average is used in this ques to calculate the expected value of the number of cups of coffee Alex drinks each day.
Mean/ Average= sum of values
number of values
Substituting the values into the equation we have:Mean/ Average= 00.200 cups +00.163 cups+ 00.976 cups+ 01.881 cups
4
Mean/ Average= 00.805 cups
Hence, The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.
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A variable needs to be eliminated to solve the system of equations below. Choose the correct first step
X-7y=-45
-x+8y=51
Step-by-step explanation:
x - 7y = -45
-x +8y = 51
the X's cancel out
-7y + 8y = -45 + 51
y = 6
what is the area of the convince store
Answer:
please add screenshots of the question and/or illustrations
Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.
You need a $160,000 loan.
Option 1: a 30-year loan at an APR of 10%
Option 2: a 15-year loan at an APR of 9.5%
Find the monthly payment for each option.
The monthly payment for option 1 is $___
The monthly payment for option 2 is $___
Monthly payment option 1 = $300,000 / 166.79161 = $1,798.65 and the monthly payment option 2 = $300,000 / 130.7201 = $2,294.98.
How to calculate the monthly payment?The numbers are missing, so I looked for similar questions to fill in the blanks:
You need a $300,000 loan. Option 1: a 30-year loan at an APR of 6%. Option 2: a 15-year loan at an APR of 4.5%.
We can use the present value of an annuity formula to calculate monthly payments.
Present value = monthly payment x PV annuity factor
Monthly payment = present value / PV annuity factor
Present value = $300,000
Option 1: PV annuity factor, 0.5%, 360 periods = 166.79161
Option 2: PV annuity factor, 0.375%, 180 periods = 130.7201
Monthly payment option 1 = $300,000 / 166.79161 = $1,798.65
Monthly payment option 2 = $300,000 / 130.7201 = $2,294.98
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HELP ASAP!
Find the volume of a cone with a radius of 6.5 inches and a height of 12 inches.
A) 670.2 in ³
B) 530.9 in³
C) 414.7 in ³
D) 513.1 in³
Select the two values of x that are roots or this equation x^2-5x+2=0
The roots of the given quadratic equation are 4.56 and 0.439.
What are the roots of an equation?The roots of an equation are the solution of that equation, since an equation consists of hidden values of the variable so to determine them by different processes and then the resultant is called roots.
As per the given quadratic equation,
x² - 5x + 2 = 0
The roots will be as,
x = [+5 ± √(5² - 4 × 1 × 2)]/(2 × 1)
x = [5 ± 4.1232]/2
x = 4.56,0.439
Hence "The roots of the given quadratic equation are 4.56 and 0.439".
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Kyle buys last years best selling hardcover for $19.50 . This is with a 25% discount from the original price. What was the original price of the novel ,
Use variable x to set up an equation to solve the given problem. DONT TAKE STEPS TO SOLVE
Answer:
original price is 26 dollars
Step-by-step explanation:
19.50/0.75=26
PLS HURRY A recipe calls for 6 ounces of raisins. How many milligrams of raisins is this? (1 ounce = 28.35 grams and 1 gram = 1,000 milligrams)
170.1 milligrams
1,701 milligrams
17,010 milligrams
170,100 milligrams
Answer:
170,100 milligrams
Step-by-step explanation:
1 ounce = 28.35 grams
6 ounces = ?
6*28.35 = 171.10 grams
1 gram - 1000 milligrams
171.10 grams = ?
171.10*1000 =
171,100 milligrams
Answer:
A recipe calls for 170,100 milligrams of raisins.
Step-by-step explanation:
I took the exam and got it right
A high - powered model rocket is traveling at 150 mph What is the rockets speed in feet per second ?
Speed of rocket travelling at 150 m/h into feet per second is 0.1367 feet per second
How to covert meter to feet ?3.28084 feet is about equal to one meter. Multiply 3.28084 feet to the given meter value to convert
According to the given information
Speed of rocket in meter per hour is 150 m/h
To know the speed of rocket in feet per second
1 meter = 3.280 feet
15o meter = 150 × 3.280
= 492 feet
1 hour = 60 × 60
= 3600 second
So,
speed of rocket in feet per second = [tex]\frac{492}{3600}[/tex]
= 0.1367 feet per second
Speed of rocket travelling at 150 m/h into feet per second is 0.1367 feet per second
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Need help please:
show that the two quadrilaterals are congruent
The two quadrilaterals JKLQ and LMNP are congruent.
What is congruent quadrilaterals?
You will always have two opposite pairs of parallel sides if the two pairs of opposite sides in a quadrilateral are congruent. They must measure similarly to be considered congruent. Consider this: two congruent sides must always maintain the same separation between the opposing lines to maintain the other pair of opposite sides.
To prove that all corresponding pairs of sides and angles are congruent, you must put the interior angles and sides of one quadrilateral in correspondence with those of another.
For the given quadrilaterals JKLQ and LMNP it is given that,
JK ≅ MN, JQ ≅ NP, QL ≅ PL and KL ≅ ML
Also,
∠J ≅ ∠N, ∠Q ≅ ∠P, ∠K ≅ ∠M, and ∠L is the common for both quadrilaterals.
Here the corresponding sides and angles of the quadrilaterals are congruent.
Hence, the two quadrilaterals JKLQ and LMNP are congruent.
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Solve the equation -128 = 4x for x
-124
132
-32
32
x= -32.
Step-by-step explanation:1. Write the expresion.[tex]-128 = 4x[/tex]
2. Divide both sides by 4.[tex]\frac{-128}{4} = \frac{4x}{4} \\\\-32=x\\ \\x=-32[/tex]
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
h(p) =
p − 4 /
p^2 + 5
The critical points of the given function are p = 2 ± √13.
What are functions?A relation between a collection of inputs and outputs is known as a function.
A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Each function has a range, codomain, and domain.
Critical function:
The key points are locations inside the function's domain where the function's nature changes.
The function stops increasing or decreasing at these places.
The function is: [tex]h(p)=\frac{p-2}{p^2+9}[/tex]
The derivative test will be applied here:
[tex]\begin{aligned}& \therefore h^{\prime}(p)=0 \\& \Rightarrow \frac{d}{d p}\left(\frac{p-2}{p^2+9}\right)=0 \\& \Rightarrow \frac{\frac{d}{d p}(p-2)\left(p^2+9\right)-\frac{d}{d p}\left(p^2+9\right)(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{1 \cdot\left(p^2+9\right)-2 p(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{-p^2+4 p+9}{\left(p^2+9\right)^2}=0 \\& \Rightarrow-p^2+4 p+9=0\end{aligned}[/tex]
Then,
[tex]\begin{aligned}& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{4^2-4(-1) 9}}{2(-1)} \\& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{52}}{-2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm \sqrt{52}}{2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm 2 \sqrt{13}}{2} \\& \Rightarrow p_{1,2}=2 \pm \sqrt{13}\end{aligned}[/tex]
Therefore, the critical points of the given function are p = 2 ± √13.
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4. Classify the system as independent, dependent, or inconsistent.
-3x + y = 4
x-1/3y = 1
The system of equation is dependent because both equation has same slope.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
An equation is an expression that shows the relationship between two or more numbers and variables.
We are given a system of equation as;
-3x + y = 4
x-1/3y = 1
Therefore, we need to write as straight line equation.
-3x + y = 4
y = 3x + 4
Thus, the slope is 3 and the y intercept is 4
Now x-1/3y = 1
x= 1 + 1/3y
y = 3x - 3
Thus, the slope is 3 and the y intercept is -3
The system of equation is dependent.
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A school hockey team was given a budget at the start of
the year. The team used 60% of the money for uniforms,
10% for equipment, and 30% for travel. Which circle
graph shows this information?
The circle which shows the distribution of the money has been attached.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circular objects for example our bike wheel.
As per the given,
The team used 60% of the money for uniforms,10% for equipment, and 30% for travel.
60% of the area of the circle is used for uniforms.
10% of the area of the circle is used for equipment.
30% of the area of the circle is used for travel.
Hence "The attached circle depicts how the funds were distributed.".
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You are offered a job in sales where you can choose to
either make a salary $500 (constant) every week or
commission of $20 per sale. Write 2 equations that
represent this scenario and solve the system (find two equations)
The linear equation for the first scenario is y = 500 while for the second scenario is y = 20x
The equation of a straight line is given by:
y = mx + b;
where y,x are variables, m is the slope of the line and b is the y intercept.
let x represent the number of sales and y represent the total salary for a weeks.
For scenario 1, there is a constant salary of $500. The linear equation becomes:
y = 500
For scenario 2, there is a commission of $20 per sale. The linear equation becomes:
y = 20x
(g) (4 5)(2 -1)
(h) (2 6)(-3 -4)
(i) (1 2)(4 6 5 7)
(j) (0 5)(3 6 4 1)
Travelling at 24 km/h on a snowmobile makes an air temperature of 4°C feel like -6°C because of the wind chill. What is the difference in these temperatures?
The difference in temperature is currently six degrees Celsius. Therefore, the appropriate reaction is six degrees Celsius.
What is the difference in temperatures?When two independent temperature readings are subtracted, or when calculating the amount of temperature rise or fall, the result is a temperature difference, also referred to as a delta temperature (T).
Simply subtract the smaller amount from the larger one to determine the difference in temperature, in this case 19 degrees Celsius from 25 degrees Celsius. We now have a six-degree Celsius temperature difference as a result. Therefore, six degrees Celsius, is the appropriate response.
Due to the varied amounts of radiation the Earth receives from the Sun at various periods of the year, there are variations in climate all over the world. The equator receives more heat from the Sun than the north and south poles, where the angle of the Sun's beams is lower.
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Which expression is equivalent to √80
4√2·√5
√2⁴.√5
√2.√2.√5
√2².√2².√5²
As we can solve the square root 80 or [tex]\sqrt{80\\}[/tex] = [tex]\sqrt{2^4}.\sqrt{5}[/tex]
so [tex]\sqrt{2^4}.\sqrt{5}[/tex] is the correct answer for square root 80
What is Square root?
The component of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots. Think about the number 9. When the number 3 is multiplied by itself, the result is 9. This can be expressed as either 32 or 3 3. We refer to this as a square since there is a 2 exponent. When the exponent is now 1/2, the square root of the integer is being discussed. For instance, when n is a positive integer, n = n1/2
The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way. It is symbolised by the character "." The number behind the square root sign is referred to as the radicand, whereas the square root symbol itself is known as a radical.
1)
[tex]\sqrt[4]{2} .\sqrt{5}[/tex] =[tex]2^{\frac{1}{4} } .\sqrt{5}[/tex]
which is not equal to [tex]\sqrt{80\\}[/tex]
2)
[tex]\sqrt{2^4}.\sqrt{5}[/tex] = [tex]2^{4.\frac{1}{2} } .\sqrt{5}[/tex]
=[tex]4\sqrt{5}[/tex] or[tex]\sqrt{16 * 5} =\sqrt{80}[/tex]
3)
[tex]\sqrt{2}. \sqrt{2}. \sqrt{5} =2\sqrt{5}[/tex]
which is not equal to [tex]\sqrt{80\\}[/tex]
4)
[tex]\sqrt{2^{2} } .\sqrt{2^{2} } .\sqrt{5^{2} } = 2.2.5 \\\\\4.5 = 20[/tex]
which is not equal to [tex]\sqrt{80\\}[/tex]
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Write an equation of the line that passes through the given points.
(−7,0),(−7,5)
The given points form an equation for a line that has a value of 14.
How do you determine the equation of a line that goes through two points?Utilize the slope formula to determine the slope. To determine the y-intercept, use the slope and one of the points (b). Once you are aware of the values for m and b, you can enter these values into the slope-intercept form of a line (y = mx + b) to obtain the equation for the line.The equation that depicts the line that crosses the coordinates (-7 , 0) and (-7, 5).A line's equation is y=mx+c. Since you have two points, you may use the formula m=y2y1x2x1 to determine the slope.Explanation:
m =( -5 - -7)(0 - -7)
= 2*7
= 14.
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There are 32 teams in the first round of a basketball tournament. One half of the teams that play in each round of the tournament move on to play in the next round.
a. Explain why the expression 32 x 1/2^3 represents the number of teams that play in the fourth round?
b. How many teams play in the fourth round? Show your work.
Answer:
So there are 32/4= 8 such groups. In each group, every team plays once against every other team
Step-by-step explanation:
please help me on math very easy graphing! thank you!! due soon
The graph that shows the proportional relationship between the number of liters of water (y) supplied after some time (x), is shown below.
What is a Proportional Relationship?A proportional relationship can be defined as a relationship between two variables, say x and y, in such a way that the equation, y = kx, models their relationship, where k is the constant of proportionality.
Given that the faucet supplies 12 liters of water after 3 minutes, where:
y = liters of water
x = number of minutes
Constant of proportionality, k = y/x = 12/3 = 4
The equation that describes the relationship would therefore be written by substituting the value of k = 4 into y = kx:
y = 4x
Thus, the graph that shows this proportional relationship is attached below.
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The average person burns approximately 221 calories per half-hour while bicycling. If a person
does 2 hours of bicycling per day then how many calories will they burn in a week if they work
out 5 days a week?
A small box measures 6in by 11in by 13 in high. Find the volume of the box.
The volume of the box is 858 cube inches.
What is a cuboid?A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height
length of box = 13 inches
Width of box = 11 inches
height of box = 6 inches
Volume of cuboid = length x width x height
volume of cuboid = 13 x 11 x 6 which is 858 cube inches
In conclusion the volume of the box is 858 cube inches
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At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 21 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots
Firstly we need to an equation to represent both ships and the distance between each. A is moving [tex]$25 \mathrm{knots}$[/tex] west and [tex]$B$[/tex] is moving [tex]$17 \mathrm{knot}$[/tex] north. [tex]$D$[/tex]will be the distance between the two. Drawing it, you'll notice that it creates a right triangle.
So we use the Pythagorean Theorem:
[tex]$$D^{\wedge} 2=A^{\wedge} 2+B^{\wedge} 2$$[/tex]
Differentiate in relation to time:
[tex]$$2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt})$$[/tex]
Now we must find all of our variables.
[tex]& A=\text { time(speed })+\text { original distance }=5(25)+10=135 \\[/tex]
[tex]& B=5(17)+0=85 \\[/tex]
[tex]& D=V\left(A^{\wedge} 2+B^{\wedge} 2\right)=159.53 \\[/tex]
[tex]& d A / d t=25 \\[/tex]
[tex]& d B / d t=17[/tex]
Plug in all your variables and solve for
[tex]$(\mathrm{dD} / \mathrm{dt})$ :[/tex]
[tex]& 2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt}) \\[/tex]
[tex]& 2(159.53)(\mathrm{dD} / \mathrm{dt})=2(135)(25)+2(85)(17) \\[/tex]
[tex]& 319.061(\mathrm{dD} / \mathrm{dt})=9640 \\[/tex]
[tex]& \mathrm{dD} / \mathrm{dt}=9640 / 319.061 \\[/tex]
[tex]& \mathrm{dD} / \mathrm{dt}=30.21 \text { knots }\end{aligned}[/tex]
At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots
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if sinθ 1÷2 and θ is in quadrant , evaluate each expression. a) sin 2θ b) cos 2θ c) tan 2θ
The values of sin 2θ, cos 2θ, and tan 2θ are:
a) sin 2θ = √(3)/2
b) cos 2θ = 1/2
c) tan 2θ = √(3)
What is a quadrant?Generally, If sin θ = 1/2 and θ is in quadrant I, then θ is equal to 30 degrees.
To evaluate each expression, we can use the trigonometric identities:
a) sin 2θ = 2 * sin θ * cos θ
= 2 * (1/2) * (√(3)/2)
= √(3)/2
b) cos 2θ = cos^2 θ - sin^2 θ
= (√(3)/2)^2 - (1/2)^2
= (3-1)/4 = 1/2
c) tan 2θ = (2 * tan θ) / (1 - tan^2 θ)
= (2 * (√(3)/3)) / (1 - (√(3)/3)^2)
= 2 * √(3) / (4 - 3)
= √(3)
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Determine a series of transformations that would map figure G onto Figure H
The series of transformation that would map the quadrilateral in figure G to the quadrilateral in figure H are;
A reflection about the y-axisA translation of three units leftWhat is a transformation in geometry?A geometric transformation involves either a change in location, size, or orientation or a combination of changes of a geometric figure.
The possible polygon with vertices in the question obtained from a similar question online and drawn using MS Excel is attached;
The vertices of the polygon are;
The coordinates of the vertices of Figure G; (-2, 7), (-6, 3), (-1, 5), (-1, 1)
The coordinates of the corresponding vertices of Figure H; (5, 7), (9, 3), (4, 5), (4, 1)
The y-values of figure G and figure H are the same, while the x-values changes both value and sign.
The coordinates of the point (x, y), following a reflection about the y-axis is the point (-x, y)
Therefore, the possible transformation that maps figure G unto figure H includes a reflection across the y-axis;
The coordinates of the vertices of figure G following a reflection about the y-axis are;
Image of figure G following a reflection about the y-axis; (2, 7), (6, 3), (1, 5), and (1, 1)
The transformation that maps the image produced by the reflection and figure H are;
Transformation (5 - 3, 7 - 7) = (3, 0)
(9 - 6, 3 - 3) = (3, 0)
(4 - 1, 5 - 5) = (3, 0)
(4 - 1, 1 - 1) = (3, 0)
The transformation that maps the image of figure G to figure H is therefore T₍₃, ₀₎, which is a translation of 3 units to the right.
The series of transformation that maps figure G to figure H are therefore;
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A large container holds 4.7 gallon of water. Use the following information to convert this amount of water to liters.1 gallon =4 quarts 1L =1.057 quarts
Answer:
Step-by-step explanation:
To convert the amount of water in gallons to liters, we need to first convert the number of gallons to quarts and then convert the number of quarts to liters.We know that 1 gallon is equal to 4 quarts, so 4.7 gallons is equal to 4.7 gallons * 4 quarts/gallon = 4.7*4=18.8 quarts.We also know that 1 liter is equal to 1.057 quarts, so to convert the number of quarts to liters, we can divide the number of quarts by 1.057 quarts/liter: 18.8 quarts / 1.057 quarts/liter = 18.8/1.057=17.8 liters.Therefore, 4.7 gallons is equal to 17.8 liters.
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 18 miles per hour slower than the westbound train. If the two trains are 320 miles apart after 2 hours, what is the rate of the eastbound train?
Answer:
71 mph
Step-by-step explanation:
Lets call the speed of the eastbound train E and the speed of the westbound train W.
E = W - 18
distance travelled = speed * time
thus
Wt + Et = 320
Wt + (W - 18)t = 320
factor out t
t * (2W - 18) = 320
t = 2 hours
2 * (2W - 18) = 320
2W - 18 = 160
2W = 178
W = 89
Then, E = (89) - 18 = 71 mph