Car A is traveling east at a steady speed of 50 miles per hour. After 2 hours, it is 140 miles east of Johnstown.
Car B is traveling east on the same road. its distance east of Johnstown is represented by the graph.
Where were the two cars in relation to each other when they began traveling?
Answers
The two cars in relation to each other when they began travelling will be car B was 20 miles east of car A. Then the correct option is A.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Car A is travelling east at a steady speed of 50 miles per hour.
Then the equation of car A is given as
y = 50x + C
where x be the number of miles and x be the number of hours.
Then we have
After 2 hours, it is 140 miles east of Johns town.
Then we have
y = 50x ..1
Car B is travelling east on the same road. its distance east of Johns town is represented by the graph.
Then the equation of car B will be
y = [(120 - 20) / (2 - 0)]x + 20
y = 50x + 20 ...2
Then the two cars in relation to each other when they began travelling will be car B was 20 miles east of car A.
Then the correct option is A.
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Answer:
Car A was 20 miles east of car B.
Step-by-step explanation:
Related Questions
On Thursday, the amount of snowfall was 1/8 cm. On Wednesday, the amount of snowfall was 4 1/4 cm. What was the amount of snowfall on the two days combined?
Answers
The total amount of snowfall on the two days combined is 4 3/8 cm
Addition of fractionsFrom the question, we are to determine the amount of snowfall on the two days combined
From the given information,
the amount of snowfall was 1/8 cm on Thursday
The amount of snowfall was 4 1/4 cm on Wednesday
Then,
The total amount of snowfall on the two days combined will be
[tex]\frac{1}{8}+4\frac{1}{4}[/tex] cm
= [tex]\frac{1}{8}+\frac{17}{4}[/tex]
= [tex]\frac{1+34}{8}[/tex]
= [tex]\frac{35}{8}[/tex]
= [tex]4\frac{3}{8} \ cm[/tex]
Hence, the total amount of snowfall on the two days combined is 4 3/8 cm
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if the exterior angles of a pentagon are x° 2x° (x+30)°,(x-10)° and (x+40)° find x
a) 30
b) 50
c) 60
d) 80
Answers
Answer:
[tex]\fbox {b) 50}[/tex]
Step-by-step explanation:
The sum of the exterior angles of any polygon (including a pentagon) is equal to 360 degrees.
Then :
⇒ x + 2x + x + 30 + x - 10 + x + 40 = 360
⇒ 6x + 60 = 360
⇒ 6x = 300
⇒ x = 50
Answer:
[tex]\huge\boxed{\sf x = 50}[/tex]
Step-by-step explanation:
Statement:The exterior angles of a pentagon add up 360 degrees.Given angles:x°2x°(x+30)°(x-10)°(x+40)°Solution:x + 2x + x + 30 + x - 10 + x + 40 = 360
6x + 60 = 360
Subtract 60 to both sides
6x = 360 - 60
6x = 300
Divide 6 to both sides
x = 300/6
x = 50
[tex]\rule[225]{225}{2}[/tex]
Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C?
How far would Pete walk if he went from A to B to C? yards
The direct distance from A to C is more than yards.
The inequality w < represents the distance, w, that Pete might save by taking the direct path.
Answers
The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.
Total distance if Pete walks from A to B to C:
= 15 + 25 = 40 yards
As we know in the triangle the sum of the two sides is greater than the third side.
25 + 15 > AC
40 > AC
or
AC < 40
The direct distance from A to C is more than 10(25-15) yards.
The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.
Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30
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Answer:
40, 10, 30
see picture
Step-by-step explanation:
The average time between accidents in a factory is 5 weeks.
Find the probability that more than 7 weeks pass between accidents.
Answers
Answer:
The probability that more than 7 weeks pass between accidents is 4.0551 .
Step-by-step explanation:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes
A Poisson distribution is a probability distribution that is used to show how many times an event is likely to occur over a specified period.
mean = 5 weeks
rate = 1/5 = 0.2
x = average time
P(x > 7) = e^(0.2×7) = 4.0551
The probability that more than 7 weeks pass between accidents is 4.0551 .
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How do I solve the following system of inequalities graphically on the set of axes below?
y> x-3 y≥− 6/1 x+4
Answers
Thank you!!
if the unit rate is 30 miles per hour , then how much miles is traveled in 9 hours
Answers
Answer:
270 miles
Step-by-step explanation:
Since the unit rate is 30 miles per hour, the miles on 9 hours will be:
= 30 × 9
= 270 miles.
X Y
-2 6
0 3.5
2 1
4 -1.5
Which equations represent the data in the table?
Check all that apply.
y-6= =5 (x+2)
y-2=-(x-1)
y + 2 = S(x-6)
y-1=-(x-2)
y-3.5 = -1.25.x
Answers
Using the point-slope equation, the equations that represent the data are:
y - 6 = -1.25(x + 2)
y -3.5 = -1.25x
What is the Point-Slope Equation?Given a point (a, b) and slope (m), the point-slope equation is expressed as, y - b = m(x - a).
Find the slope (m) using two pairs from the table of values say, (-2, 6) and (2, 1):
Slope (m) = change in y / change in x = (6 - 1)/(-2 - 2) = 5/-4 = -1.25
Using the point, (a, b) = (-2, 6) and m = -1.25, plug the values into y - b = m(x - a):
y - 6 = -1.25(x - (-2))
y - 6 = -1.25(x + 2)
This cam be rewritten as:
y - 6 = -1.25x - 2.5
y - 6 + 2.5 = -1.25x
y -3.5 = -1.25x
The equations that represent the data in the table are:
y - 6 = -1.25(x + 2)
y -3.5 = -1.25x
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Complete the steps to factor the polynomial by grouping. p(x) = x3 5x2 – x – 5 p(x) = x2 (x ) – (x 5) p(x) = (x2 – )(x 5) p(x) = (x – )(x 1)(x )
Answers
The polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).
The given polynomial to us is p(x) = x³ + 5x² - x - 5.
We are asked to factor the polynomial by grouping.
We can do this by following these steps:
p(x) = x³ + 5x² - x - 5.We group the first two terms and the next two terms to get p(x) = (x³ + 5x²) + (-x -5).Now, we take x² common from the first group and -1 common from the second group to get p(x) = x²(x + 5) -1(x + 5)Now, we take (x + 5) common from both the terms to get, p(x) = (x + 5)(x² - 1).Now, we right (x² - 1) as (x + 1)(x - 1). to get the polynomial as, p(x) = (x + 5)(x + 1)(x - 1).Therefore, the polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).
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a tissue box has a lentgh of 11 inches a width of 5 inches and a height of 4 inches
Answers
or 180cm3
What are the solutions of the equation x4 - 5x2 - 14 = 0? Use factoring
to solve.
Answers
Answer:
x = ±√7, ±i√2
Step-by-step explanation:
[tex]x^4-5x^2-14=0\\(x^2-7)(x^2+2)=0\\[/tex]
[tex]x^2 - 7 = 0[/tex] or [tex]x^2 + 2 = 0\\[/tex]
x^2 - 7 = 0
x^2 = 7
x = ±√7
or x^2 + 2 = 0
x^2 = -2
x = ±i√2
I need help lol xoxoxo
Answers
In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks. If at year’s end an auditor
checks your accounting records and randomly selects one week to check the company’s payroll, what is the probability that the auditor will select a week in which you paid overtime wages and hired
temporary help?
Answers
The probability that the auditor will select a week in which you paid overtime wages and hired is 0.28
In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks.
What is probablitity?
Probability, can be define as the ratio of favorable outcomes to the n number of total events.
Here, p(a) = Overtime was paid for 26 weeks = 26/32= 0.81
p(b) = temporary help was hired for 15 weeks = 0.46
Required probability = P(a) + P(b) - 1
= 0.81 + 0.46 -1
= 0.28
The the required probability that the auditor will select a week in which you paid overtime wages and hired is 0.28
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Im in math 2 and I just need help with this to pass please
Answers
Answer:
.7 I your answer to your question hope it's help
Answer:
[tex]\frac{7}{10}[/tex]
Step-by-step explanation:
35/50 --> [tex]\frac{7}{10}[/tex]
divide 35 by 5 = 7
divide 50 by 5 = 10
The graph of f(x)=x2 is shown. Use the parabola tool to graph the function g(x)=(12x)2. To graph a parabola, first plot the vertex then plot another point on the parabola.
Answers
Answer:
Pease check my assumptions.
Step-by-step explanation:
I will assume that f(x)=x2 is actually f(x) = x^2.
Same for g(x)=(12x)^2 [Is it g(x)=12x^2 ???]
See the attached image.
Note that (12x)^2 results in a narrower, steeper graph. That's because (12x)^2 can be rewritten as 144x^2, so every value is multiplied by 144, compared to just x^2.
I want to know the answer quick
Answers
Answer:
[tex]\fbox {B. Exponential Decay}[/tex]
Step-by-step explanation:
As the exponent is applied to a number less than 1, the future values of the function f(x) will become smaller and smaller. Hence, it represents exponential decay.
Triangle is reflected across the y-axis and then dilated by a factor of centered at the origin. Which statement correctly describes the resulting image, triangle ? Image of right triangle ABC in a graph with vertices A (minus 4, minus 2), B (4, minus 2), and C (4, 4) A. Both the reflection and dilation preserve the side lengths and angles of triangle . B. The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths. C. The dilation preserves the side lengths and angles of triangle . The reflection does not preserve side lengths and angles. D. Neither the reflection nor the dilation preserves the side lengths and angles of triangle .
Answers
Answer: B. The reflection preserves the side lengths and angles of the triangle. The dilation preserves angles but not side lengths.
Step-by-step explanation:
Reflections are congruency transformations, but dilations are similarity transformations.
Y W P 8 cm E R WERP is a square. Find.
1. m2WER=
2. measure of PE =_______
3. measure of WA =
4. Value of y=
Answers
1) All interior angles of a square are right angles, so angle WER measures 90°
2) All squares are parallelograms, and diagonals of a parallelogram bisect each other, meaning PA=AE=8 cm. Thus, PE=16 cm
3) All squares are rectangles, and diagonals of a rectangle are congruent, meaning WR=16 cm. Then, using the fact that the diagonals bisect each other, we get that WA=8 cm
4) If we consider right triangle WPR, we know it is isoceles because all sides of a square are congruent. So, the length of WP is:
[tex] \frac{16}{ \sqrt{2} } = 8 \sqrt{2} [/tex]
To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? first equation: 4x − 3y = 34 second equation: 3x 2y = 17
Answers
To eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.
Elimination is a process of solving a system of equations to eliminate one variable and solve for the other.
To eliminate the y terms from the equations,
first equation: 4x - 3y = 34, and
second equation: 3x + 2y = 17,
we take the L.C.M. of the coefficients of y, that is 3 and 2, which is 6, and multiply the equation by the value = (LCM of the coefficients/respective coefficient of y).
That is, for :
the first equation, we multiply the equation by (LCM of the coefficients/respective coefficient of y) = 6/3 = 2.
the second equation, we multiply by (LCM of the coefficients/respective coefficient of y) = 6/2 = 3.
Thus, to eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.
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Which expression is equivalent to 3^0x3^-3?
Answers
Step-by-step explanation:
[tex] = {3}^{0} \times {3}^{ - 3} [/tex]
[tex] = 1 \times \frac{1}{ {3}^{3} } [/tex]
[tex] = \frac{1}{3 \times 3 \times 3} [/tex]
[tex] = \frac{1}{27} [/tex]
A book seller a book for Rs 70 at a gain of 40 percent find the profit
Answers
Answer:
Rs 20
Step-by-step explanation:
140%=Rs 70
100%
(100%×Rs 70)÷140%=50
Rs 70-Rs 50=Rs 20
If * >0 and y > 0, which expression is equivalent to √768x1937?
A. 8r4y6/12r4y
B. 16r4y6√3x¹y
C. 8r9y18/12xy
D. 16r9y18√3xy
Answers
;)
whats 10 + 4? i need to know if you answer you get 25 points
Answers
The table below shows the results of a survey that asked 1052 adults from a certain country if they favored or opposed a tax to fund education. A person is selected at
random. Complete parts (a) through (c).
(a) Find the probability that the person opposed the tax or is female.
P(opposed the tax or is female) =
(Round to the nearest thousandth as needed.)
(b) Find the probability that the person supports the tax or is male.
P(supports the tax or is male) =
(Round to the nearest thousandth as needed.)
(c) Find the probability that the person is not unsure or is female.
P(is not unsure or is female)=
(Round to the nearest thousandth as needed.)
Answers
The complete options are P(opposed the tax or is female) = 0.28, b. P(supports the tax or is male) = 0.15, c. P(is not unsure or is female) 0.025.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
(a) The probability that the person opposed the tax or is female.
P(opposed the tax or is female) = 298 / 1052 = 0.28
(b) The probability that the person supports the tax or is male.
P(supports the tax or is male) = 168/1052 = 0.15
(c) The probability that the person is not unsure or is female.
P(is not unsure or is female) = 27 / 1052 = 0.025
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Prove: 45= m/ZXY
Complete the proof. Number your reasons in the textbox below.
Answers
Step-by-step explanation:
since the two angles from a straight line, they make a linear pair and linear pairs are supplementery. by the angle addition postulate, you can determine that the two angles sum to 180. substituting the one angle mearsure that you are guven and using a bit of simple arithmetic and the subtraction property of equality, you can determine that the other angle,angle YXZ, is 45 degrees. I hope this is helpful
Ethan is using 30 cupcakes . he spreads mint icing on 1/5 of the cupcakes and chocolate on 1/2 of the reimagining cupcakes . the rest will get vanilla frosting. how many will have vanilla frosting
Answers
Answer:
12 Vanilla Frosted Cupcakes
Step-by-step explanation:
30 Cupcakes.
1/5 Of 30 is 6.
30 - 6 = 24.
24/2 = 12.
Write the equation of the line that passes through (5, 6) and (8, 4) in slope-intercept form.
Answers
Answer:
Step-by-step explanation:
Equation of the line in slope- intercept form:[tex]\sf \boxed{\bf y = mx +b}[/tex]
Here, m is the slope and b is the y-intercept
Find the slope with the given two points.
[tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{4-6}{8-5}\\\\=\dfrac{-2}{3}[/tex]
Slope = -2/3 and choose any one the given points.
Substitute m = -2/3 and (5,6) in the above equation and find 'b'
[tex]\sf 6 =\dfrac{-2}{3}*5+b\\\\6 =\dfrac{-10}{3}+b\\\\6+\dfrac{10}{3}=b\\\\\dfrac{6*3}{1*3}+\dfrac{10}{3}=b\\\\\dfrac{18}{3}+\dfrac{10}{3}=b\\\\\boxed{b=\dfrac{28}{3}}[/tex]
Equation of the line:
[tex]y = \dfrac{-2}{3}x + \dfrac{28}{3}[/tex]
Question 3 of 32
Which of the following could be the equation for a parabola that opens to the
left with vertex (-17, 2)?
A. x=-3(y-2)² - 17
OB. x-3(y +17)² +2
OC. y-3(x-2)² - 17
D. y=3(x+17)² +2
Answers
Answer:
A
Step-by-step explanation:
The parabola opens to the left, so this eliminates C and D.
Also, the vertex is at (-17, 2), and out of A and B, the only parabola with this vertex is A.
True or False? A circle could be circumscribed about the
quadrilateral below.
• A. True
• B. False
Answers
Answer:
False
Step-by-step explanation:
m∆A+m∆C=180°
110°+110°=180°
220°(/=) 180°
A circle can be circumscribed about the given quadrilateral, the answer is true.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
To circumscribe a circle about a quadrilateral means to place the quadrilateral inside the circle, such that the four vertices of the quadrilateral touches the the circumference of the circle.
Opposite angles of a circumscribed polygon are supplementary.
Therefore, a circle can be circumscribed about the given quadrilateral is true
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find x if 2+x = -2/3
Answers
First you want to isolate x by subtracting 2 from -2/3. To do this make sure there is a common denominator of 3 so our equation is now x=-6/3 -2/3 which with regular subtraction is -8/3.
Hope this helps:)
\frac { 6 ^ { n + 2 } - 6 ^ { n } } { 6 ^ { n + 1 } + 6 ^ { n } }
Solve this ...
this is the question of laws of indices(exponent)
Answers
Work Shown:
[tex]m = \frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}\\\\m = \frac{6^{n}*6^2-6^{n}}{6^{n}*6^1+6^{n}}\\\\m = \frac{6^{n}*36-6^{n}}{6^{n}*6+6^{n}}\\\\m = \frac{6^{n}(36-1)}{6^{n}(6+1)}\\\\m = \frac{6^{n}(35)}{6^{n}(7)}\\\\m = \frac{35}{7}\\\\m = 5\\\\[/tex]
Therefore,
[tex]\frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}=5\\\\[/tex]
