The systems of equations which correctly models the situation as described is;
s = 5c ands + c = 48Which systems of equations correctly models the situation as described in the task content?It follows from the task content that the system of equations which models the production process of caffe mocha be determined.
As given in the task content;
Let c represent the number of ounces of coffee.Let s represent the number of ounces of chocolate syrup.Hence, since For each ounce of chocolate syrup, she uses 5 ounces of coffee, the situation can be represented algebraically as;
s = 5c.Also, since she wants to make 48 ounces of caffe mocha; we have;
s + c = 48.Therefore, the required system of equations is;
s = 5c ands + c = 48.Read more on system of equations;
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I need help figuring out if what I got is rigjt
The figure in the picture shows 3 squares that form a right triangle. Each side of the triangle is determined by one side of the squares.
The only information we know is the area of two of the squares. The area of a square is calculated as the square of one of its sides
[tex]A=a^2[/tex]So to determine the side lengths of the squares, we can calculate the square root of the given areas:
[tex]\begin{gathered} A=a^2 \\ a=\sqrt[]{A} \end{gathered}[/tex]For one of the squares, the area is 64m², you can determine the side length as follows:
[tex]\begin{gathered} a=\sqrt[]{64} \\ a=8 \end{gathered}[/tex]For the square with an area 225m², the side length can be calculated as follows:
[tex]\begin{gathered} a=\sqrt[]{225} \\ a=15 \end{gathered}[/tex]Now, to determine the third side of the triangle, we have to apply the Pythagorean theorem. This theorem states that the square of the hypothenuse (c) of a right triangle is equal to the sum of the squares of its sides (a and b), it can be expressed as follows:
[tex]c^2=a^2+b^2[/tex]If we know two sides of the triangle, we can determine the length of the third one. In this case, the missing side is the hypothenuse (c), to calculate it you have to add the squares of the sides and then apply the square root:
[tex]\begin{gathered} c^2=225+64 \\ c=\sqrt[]{225+64} \\ c=\sqrt[]{289} \\ c=17 \end{gathered}[/tex]So the triangle's sides have the following lengths: 8, 15 and, 17
Now that we know the side lengths we can calculate the perimeter of the triangle. The perimeter of any shape is calculated by adding its sides:
[tex]\begin{gathered} P=8+15+17 \\ P=40m \end{gathered}[/tex]Find the volume of a cone with a height of 8 m and a base diameter of 12 mUse the value 3.14 for it, and do not do any rounding.Be sure to include the correct unit in your answer.
The volume V of a cone with radius r and height h is:
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]And the radius is half the diameter. Since this cone has a diameter of 12 m, the radius is:
[tex]r=\frac{12m}{2}=6m[/tex]And the height is 8m. Thus, the volume V is:
[tex]\begin{gathered} V=\frac{1}{3}\pi(6m)^28m \\ \\ V=\frac{\pi}{3}(36m^2)8m \\ \\ V=\frac{\pi}{3}(288)(m^2\cdot m) \\ \\ V=\pi\cdot\frac{288}{3}m^3 \\ \\ V=96\pi m^{3} \end{gathered}[/tex]Now, using 3.14 for π, we obtain:
[tex]\begin{gathered} V=96\cdot3.14m^3 \\ \\ V=301.44m^{3} \end{gathered}[/tex]Therefore, the volume of that cone is 301.44m³.
20. Write the slope-intercept form of the line described in the followingPerpendicular to -2+3y=-15and passing through (2, -8)
The equation of a line in Slope-Intercept form is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
Solve for "y" from the equation given in the exercise in order to write it in Slope-Intercept form:
[tex]\begin{gathered} -2+3y=-15 \\ 3y=-15+2 \\ y=-\frac{13}{2} \end{gathered}[/tex]You can notice that the equation has this form:
[tex]y=b[/tex]Where "b" is the y-intercept.
Then, it's a horizontal line, which means that its slope is:
[tex]m=0[/tex]Since it is a horizontal line, the lines perpendicular to that line is a vertical line, whose slope is undefined and whose equation is:
[tex]x=k[/tex]Where "k" is the x-intercept.
Knowing that the x-coordinate of any point on a vertical line is always the same, and knowing that this line passes through this point:
[tex]\mleft(2,-8\mright)[/tex]You can determine that the equation of the line is:
[tex]x=2[/tex]F(x) = -3x,x<0 4,x=0 x^2, x>0 given the piece wide functions shown below select all of the statements that are true
The correct statements regarding the numeric values of the piece-wise function are given as follows:
B. f(3) = 9.
D. f(2) = 4.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
A piece-wise function means that the definition of the input is different based on the input of the function. In this problem, all the numeric values we are calculating are for positive numbers, hence the definition of the function is given by:
f(x) = x².
Then the numeric values of the function are given as follows:
f(1) = 1² = 1.f(2) = 2² = 4.f(3) = 3² = 9.f(4) = 4² = 16.Meaning that options B and D are correct.
Missing informationThe options are given by the image at the end of the answer.
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Find the length of the segment indicated. Round to the nearest tenth if necessary. Note: One segment of each triangle is a tangent line
Given
A circle with a tangent drawn to it forming one side of a triangle
Required
we need to find the diameter of the circle
Explanation
clearly it is a right angled triangle as radius through point of contact is perpendicular to the tangent. let the lenght of missing side be d
Therefore
[tex]d^2+12^2=20^2[/tex]or
[tex]d^2=400-144[/tex]or
[tex]d^2=256[/tex]or d=16
The table below shows the average annual cost of health insurance for a single individual, from 1999 to 2019, according to the Kaiser Family Foundation.YearCost1999$2,1962000$2,4712001$2,6892002$3,0832003$3,3832004$3,6952005$4,0242006$4,2422007$4,4792008$4,7042009$4,8242010$5,0492011 $5,4292012$5,6152013$5,8842014$6,0252015$6,2512016$6,1962017$6,4352017$6,8962019$7,186(a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).Pt = (b) Using this linear model, predict the cost of insurance in 2030.$ (c) = According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020)..
The given data plot will look thus:
a) Building a model using just the 1999 and 2019 years:
[tex]\begin{gathered} 1999\rightarrow0\rightarrow2196 \\ 2019\rightarrow20\rightarrow7186 \\ \text{Havng} \\ x_1=0,y_1=2196 \\ x_2=20,y_2=7186 \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}_{} \\ \text{The model will be:} \\ P_t=249.5t+2196 \end{gathered}[/tex]b) The cost of insurance in 2030
[tex]\begin{gathered} P_t=249.5t+2196 \\ t=2030-1999=31 \\ \text{The cost of insurance in 2030 therefore will be:} \\ =249.5(31)+2196 \\ =7734.5+2196 \\ =\text{ \$9930.5} \end{gathered}[/tex]c) When do we expect the cost to reach $12,000
[tex]\begin{gathered} P_t=249.5t+2196 \\ 12,000=249.5t+2196 \\ 12000-2196=249.5t \\ 9804=249.5t \\ \frac{9804}{249.5}=\frac{249.5t}{249.5} \\ 39.2946=t \\ Since\text{ t = year -1999} \\ 39.2946+1999=\text{year} \\ 2038.2946=\text{year} \\ Since\text{ we are to give our answer as an exact year} \\ \text{The year will be }2039. \end{gathered}[/tex]What is 9207 /10 equivalent to?
Answer:
9207/10 is equivalent to 920.7
find x..in a right triangle ️ with a height of 10 and hypotenuse of 19
Since it is a right triangle we can apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c= hypotenuse (the longest side) = 19
a & b = the other 2 legs of the triangle
Replacing:
19^2 = 10^2 + x^2
Solve for x
361 = 100 + x^2
361 - 100 = x^2
261 = x^2
√261 =x
x= 16.16
Write an equation of a circle with diameter AB.A(1,1), B(11,11)Choose the correct answer below.A. (X-6)2 + (y-6)2 = 11C. (x-6)2 – (y+6)2 = 50E. (X+6)2 + (y-6)2 = 50G. (X+6)2 – (y + 6)2 = 50
The question asks us to find the equation of a circle with diameter AB with coordinates:
A = (1, 1), B = (11, 11)
In order to solve this, we need to know the general form of the equation of a circle.
The general form of the equation of a circle is given by:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where,} \\ (a,b)=\text{ coordinates of the center of the circle} \\ r=\text{radius of the circle} \end{gathered}[/tex]We have been given the coordinates of the diameter. This means that finding the midpoint of the diameter
will give us the center coordinates of the circle, which is (a, b).
The formula for finding the midpoint of a line is given below:
[tex]\begin{gathered} (x,y)=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ \text{where,} \\ x_2,y_2=\text{ second coordinate} \\ x_1,y_1=\text{first coordinate} \end{gathered}[/tex]For better understanding, a sketch is made below:
Therefore, let us find the coordinates of the center of the circle using the midpoint formula given above:
[tex]\begin{gathered} a,b=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ x_2=11,y_2=11 \\ x_1=1,y_1=1 \\ \\ \therefore(a,b)=\frac{11+1}{2},\frac{11+1}{2} \\ \\ (a,b)=6,6 \\ Thus, \\ a=6,b=6 \end{gathered}[/tex]Now that we have the coordinates of the center, we now need to find the value of the radius of the circle.
This is done by finding the length from the center of the circle to any side of the diameter.
Let us use from point (6,6) which is the center to the point (11, 11) which is one side of the diameter.
The formula for finding the distance between two points is given by:
[tex]\begin{gathered} |\text{distance}|^2=(y_2-y^{}_1)^2+(x_2-x_1)^2_{} \\ \text{where,} \\ x_2,y_2=\text{second point} \\ x_1,y_1=\text{first point} \end{gathered}[/tex]hence, we can now find the square of the radius as:
[tex]\begin{gathered} r^2=(y_2-y^{}_1)^2+(x_2-x_1)^2_{} \\ x_2,y_2=11,11_{} \\ x_1,y_1=6,6 \\ \\ \therefore r^2=(11-6)^2+(11-6)^2 \\ r^2=5^2+5^2 \\ r^2=25+25 \\ \therefore r^2=50 \end{gathered}[/tex]Now that we have the radius, we can now compute the equation of the circle as:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ a=6,b=6,r^2=50 \\ \\ \therefore(x-6)^2+(y-6)^2=50\text{ (Option B)} \end{gathered}[/tex]A graph of the circle is given below:
points E,D and H are the midpoints of the sides of TUV, UV=100,TV=126,and HD=100, find HE.
Since the triangles are similar there exists correspondance in the angles, so in order to solve this you just have to clear the function:
[tex]\begin{gathered} \frac{VD}{VU}=\frac{HD}{TU} \\ \end{gathered}[/tex]Since D is the midpoint of VU, VD=50
[tex]\begin{gathered} \frac{50}{100}=\frac{100}{TU} \\ 50\times TU=100\times100 \\ TU=200 \end{gathered}[/tex]then
[tex]\begin{gathered} \frac{HE}{UV}=\frac{HD}{TU} \\ \frac{HE}{100}=\frac{100}{200} \\ HE=\frac{100}{200}\times100 \\ HE=50 \end{gathered}[/tex]Maya bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $400 less than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was 7.5 % per year and for the laptop it was 8% per year. The total finance charges for one year were $371. How much did each computer cost before finance charges? Desktop: $Laptop: $
1. Let D be price of desktop
let L be price of a Laptop
• we know that the laptop cost $400 less than the desktop
L = D -400
• for desktop D, Maya paid interest of 7.5% per year: 7.5/100 = 0.075
,• For Laptop L , Maya paid interest of 8 % per year : 8/100 = 0.08
,• We know that total charges for finance was $ 371,
therefore :
0.075 D + 0.08L = 371, (remember from the above , L = D-400 , lets substitute this value for L)
0.075 D + 0.08( D-400) = 371
0.075D + 0.08 D -32 = 371
0.155D = (371 +32)=403
D = 403/0.0155
D = $26 000
and L = D-400
= 26000-400
= $25600
• This means that Desktopcost $26000 and Laptop cost $25600,
Lucky's Market purchased a new freezer for the store.When the freezer door stays open, the temperatureinside rises. The table shows how much thetemperature rises every 15 minutes. Find the unit rate.temperature (°F) =10number of minutes =15(answer) °F per minute
Notice that the information in the table can be modeled using a linear function. To find the slope (rate of change) given two points, use the formula below
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow slope=m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (15,10),(30,20) \\ \Rightarrow slope=\frac{20-10}{30-15}=\frac{10}{15}=\frac{2}{3} \end{gathered}[/tex]Simplify the following equations in ax^2+bx+c=0 or ay^2+c=0 2x+y=6 4x^2+5y+y+1=0
Given the equation;
[tex]4x^2+5y^2+y+1=0[/tex]We shall begin by Subtracting 5y^2 + y from both sides;
[tex]\begin{gathered} 4x^2+5y^2+y+1-5y^2-y=0-5y^2-y \\ 4x^2+1=-5y^2-y \\ \text{Factor out -1 from the right hand side;} \\ 4x^2+1=-1(5y^2+y) \end{gathered}[/tex]Next step we subtract 1 from both sides;
[tex]\begin{gathered} 4x^2+1-1=-1(5y^2+y)-1 \\ 4x^2=-(5y^2+y)-1 \\ \end{gathered}[/tex]Next step we take the square root of both sides;
[tex]\begin{gathered} \sqrt[]{4x^2}=\pm\sqrt[]{-(5y^2+y)-1} \\ 2x=\pm\sqrt[]{-(5y^2+y)-1} \end{gathered}[/tex]We can now open the parenthesis on the right hand side;
[tex]\begin{gathered} 2x=\pm\sqrt[]{-5y^2-y-1} \\ \text{Divide both sides by 2;} \\ x=\frac{\pm\sqrt[]{-5y^2-y-1}}{2} \end{gathered}[/tex][tex]undefined[/tex]Which of the following expressions is equivalent to 2^4x − 5? the quantity 8 to the power of x end quantity over 10 the quantity 4 to the power of x end quantity over 5 the quantity 16 to the power of x end quantity over 32 the quantity 1 to the power of x end quantity over 32
The equivalent expression for the given exponent equation is 16^x/32
Given,
The exponent equation; 2^4x - 5
We have to find the expressions which is equivalent to 2^4x - 5
Exponential equations are inverse of logarithmic equations.
This can also be expressed as;
2^(4x-5) = 2^4x/2^5
2^4x-5 =16^x/2^5
2^4x-4 = 16^x/32
Hence the equivalent expression is 16^x/32
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Answer:it's not 4^x/5
Step-by-step explanation:
Mrs. Williams estimates that she will spend $65 onschool supplies. She actually spends $73. What is thepercent error? Round to the nearest tenth ifnecessary.
We can calculate the percent error as the absolute difference between the predicted value ($65) and the actual value ($73) divided by the actual value and multiplied by 100%.
This can be written as:
[tex]e=\frac{|p-a|}{a}\cdot100\%=\frac{|65-73|}{73}\cdot100\%=\frac{8}{73}\cdot100\%\approx11.0\%[/tex]Answer: the percent error is approximately 11.0%
Find the slope of every line that is parallel to the graph of the equation
Select the correct choice below and, if necessary, fill in the answer box within your choice
x² - 20x + 100
Find two numbers, such that its sum gives -20 and its product gives 100
If such numbers exist, this implies that the polynomial is NOT prime
The two numbers are: -10 and -10
Replace the coefficient of x with the two numbers
x² - 10x -10x + 100
x(x-10) - 10(x - 10)
(x-10)(x-10)
(x-10)²
Therefore, the correct option is A.
x² - 20x + 100 = (x-10)²
Identify the key features of the graph, including the x - intercepts. Y-intercept, axis of symmetry, and vertex. (3)
The graph of the given finction is:
Here, the x-intercept is at -1 and -6
The y-intercept is at 6
The axis of symmetry is x=-3.5
The vertex is (-3.5,-6.2)
Which sequence of transformations will map AABC onto AA' B'C'?A- reflection and translationB- rotation and reflectionC- translation and dilation D- dilation and rotation
For the given problem, we can observe that the image is bigger than the original diagram.
We can also observe that the image is rotated counterclockwise.
Hence, the sequence of transformation that maps triangle ABC onto triangle A'B'C' is a dilation and a rotation.
Answer: Option D
Writing a equation of a circle centers at the origin
ANSWER
[tex]x^2+y^2=100[/tex]EXPLANATION
The general equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) = the center of the circle
r = radius of the circle (i.e. distance from any point on its circumference to the center of the circle)
The center of the circle is the origin, that is:
[tex](h,k)=(0,0)[/tex]To find the radius, apply the formula for distance between two points:
[tex]r=\sqrt[]{(x_1-h)^2+(y_1-k)^2_{}}[/tex]where (x1, y1) is the point the circle passes through
Hence, the radius is:
[tex]\begin{gathered} r=\sqrt[]{(0-0)^2+(-10-0)^2}=\sqrt[]{0+(-10)^2} \\ r=\sqrt[]{100} \\ r=10 \end{gathered}[/tex]Hence, the equation of the circle is:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=(10)^2 \\ \Rightarrow x^2+y^2=100 \end{gathered}[/tex]What is 120 percent of 118?
120 percent of 118 is expressed mathematically as;
120% of 118
120/100 * 118
= 12/10 * 118
= 6/5 * 118
= 708/5
= 141.6%
Hence 120 percent of 118 is 141.6%
This is Calculus 1 Problem! MUST SHOW ALL THE JUSTIFICATION!!!
Given: A surveyor standing 50 feet from the base of a large tree measures the angle of elevation to the top of the tree as 75.8 degrees.
Required: To determine how accurately the angle must be measured if the percent error in estimating the tree's height is less than 5%.
Explanation: To estimate the angle, we will use the trigonometric ratio
[tex]tanx=\frac{h}{50}\text{ ...\lparen1\rparen}[/tex]where h is the tree's height, and x is the angle of elevation to the top of the tree.
Hence we get
[tex]\begin{gathered} h=50\cdot(tan75.8\degree) \\ h=197.59\text{ feet} \end{gathered}[/tex]Now differentiating equation 1, we get
[tex]sec^2xdx=\frac{1}{50}dh[/tex]We can write the above equation as:
[tex]sec^2x\cdot\frac{xdx}{x}=\frac{h}{50}\cdot\frac{dh}{h}\text{ ...\lparen2\rparen}[/tex]Also, it is given that the error in estimating the tree's height is less than 5%.
So
[tex]\frac{dh}{h}=0.05[/tex]Also, we need to convert the angle x in radians:
[tex]x=1.32296\text{ rad}[/tex]Putting these values in equation (2) gives:
[tex]\frac{dx}{x}=\frac{197.59}{50}\cdot\frac{cos^2(1.32296)}{1.32296}\cdot0.05[/tex]Solving the above equation gives:
[tex]\begin{gathered} \frac{dx}{x}=3.9518\cdot0.04548551012\cdot0.05 \\ =0.008987\text{ radians} \end{gathered}[/tex]Let
[tex]d\theta\text{ be the error in estimating the angle.}[/tex]Then,
[tex]\lvert{d\theta}\rvert\leq0.008987\text{ radians}[/tex]Final Answer:
[tex]\lvert{d\theta}\rvert\leq0.008987\text{ radians}[/tex]1. Which of the following is NOT a linear function? (1 point ) Oy=* -2 x x Оy - 5 ya 0 2. 3*- y = 4 3.
hello
to solve this question we need to know or understand the standard form of a linear equation
the standard form of a linear equation is given as
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}[/tex]from the options given in the question, only option D does not corresponds with the standard form of a linear equation
[tex]undefined[/tex]quien me puede ayudar a resolver estos ejercicios porfa de ecuaciones
3x^2 -5x +1 =0
Aplica la formula cuadrática:
[tex]\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]Donde:
a = 3
b= -5
c= 1
Reemplazando:
[tex]\frac{-(-5)\pm\sqrt[]{(-5)^2-4\cdot3\cdot1}}{2\cdot3}[/tex][tex]\frac{5\pm\sqrt[]{25-12}}{6}[/tex][tex]\frac{5\pm\sqrt[]{13}}{6}[/tex]Positivo:
(5+√13) /6 = 1.43
NEgativo:
(5-√13) /6 = 0.23
In the picture below, angle 2 = 130 degrees, what is the measurement of angle 8?
Answer:
130°
Step-by-step explanation:
Alternate interior angles are equal in measure.
A music club charges an initial joining fee of $24.00. The cost per CD is $8.50. The graph shows the cost of belonging to the club as a function of CDs purchased. How will the graph change if the cost per CD goes up by $1.00.? (The new function is shown by the dotted line.)
Given the function with a graph that shows the cost of belonging to the club as a function of CDs purchased
linear function with the form
[tex]y=x[/tex]since the new graph has a new cd cost up by $1.00
then the new line is
Correct answer
Option C
hello, while doing the question please don't put A decimal Answer ( ex: 1.5) because my teacher told me that's incorrect, you can add or subtract depending on the question, or check if you need to simplify! Thank you:)
Notice that the unit segment is divided in 8 parts. Then, each mark is equal to 1/8.
The kitten that weighs the most is placed over the 5ft mark. Then, its weight is:
[tex]\frac{5}{8}[/tex]The kitten that weighs the least is placed over the third mark. Then, its weight is:
[tex]\frac{3}{8}[/tex]Substract 3/8 from 5/8 to find the difference on their weights:
[tex]\frac{5}{8}-\frac{3}{8}[/tex]Since both fractions have the same denominator, we can substract their numerators:
[tex]\frac{5}{8}-\frac{3}{8}=\frac{5-3}{8}=\frac{2}{8}=\frac{2/2}{8/2}=\frac{1}{4}[/tex]Therefore, the difference in pounds between the heaviest and the lightest kittens, is:
[tex]\frac{1}{4}[/tex]Question 10 of 11 Step 1 of 1CorrectThcorrectOne group (A) contains 390 people. Three fifths of the people in group A will be selected to win $100 fuel cards. There is another group (B) in a nearby town that willreceive the same number of fuel cards, but there are 553 people in that group. What will be the ratio of nonwinners in group Ato nonwinners in group B after theselections are made? Express your ratio as a fraction or with a colon.AnswerkeypadRestore Your Guth2019 Hawkes Learning
Given : Two groups
Group A: contains 390 people.
Three fifths of the people in group A will be selected to win $100 fuel cards.
So, the number of people who will win = 3/5 * 390 = 234
Group B : contains 553 people
the group will receive the same number of fuel cards
so, the group will receive 234 cards
The non-winners of group A = 390 - 234 = 156
The non-winners of group B = 553 - 234 = 319
The ratio between them = 156 : 319
the table below shows the attendance and revenue at theme parks in the us
Let
y ------> the year
x ----> revenue
so
Plot the given ordered pairs
see the attached figure
(please wait a minute to plot the points)
In the graph the x-coordinate 0 represent year 1990
Find out the equation of the line
take two points
(1990, 5.7) and (2006, 11.5)
Find the slope m
m=(11.5-5.7)/(2006-1990)
m=5.8/16
m=0.3625
Find the equation of the line in slope intercept form
y=mx+b
we have
m=0.3625
point (1990, 5.7)
substitute and solve for b
5.7=(0.3625)(1990)+b
b=-715.675
therefore
y=0.3625x-715.675A diesel train left Abuja and traveled west. One hour later a freight train left traveling 50 mph faster in an effort to catch up to it. After three hours of freight train finally caught up. Find the diesel train’s average speed.
The speed at which diesel train was moving is = 150mph
In the above question, it is given that,
Let the speed of the diesel train which left Abuja be x mph
then, speed of freight train which is moving 50 mph faster than diesel train = (50 + x)mph
Further, the freight train finally caught up the diesel train after three hours
So time taken by freight train = 3 hours
While time taken by diesel train would 1 hour more than freight train as its moving slower = 3 + 1 = 4 hours
Now, it is given that both the trains finally catch up, it means the distance travelled by both the trains would be equal
We know that,
Speed = [tex]\frac{Distance}{Time}[/tex]
Distance = Speed x Time
Distance travelled by Diesel train = distance travelled by Freight train
4x = 3(50 + x)
4x = 150 + 3x
x = 150 mph
Hence, the speed at which diesel train was moving is = 150mph
While, the speed at which freight train was moving is = (150 + x)mph = (150 + 50)= 200mph
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