Fabio is driving west away from Albany and towards Buffalo along Interstate 90 at a constant rate of speed
of 62 miles per hour. After driving for 1.5 hours, Fabio is 221 miles from Albany.
Answers
Answer:
a) ( D - 128 ) = m ( 1,5 - 0)
b) D = 62*h + 128
Step-by-step explanation:
Fabio drives at a constant speed of 62 miles per hour therefore:
62 * 1,5 = 93 miles
But he is 221 miles away from Albany, then he started
221 - 93 = 128 miles from Albany
In a coordinates system D (distance in the y-axis ), and h ( hours in x-axis), we have two points
h₁ = 0 (h) D (y intercept) = 128 miles and h = 1,5 (h) D = 221 miles
P₁ ( 0 , 128 ) P₂ ( 1,5 , 221 )
Then the equation for straight-line passing through two points is:
m = ( D - D₁ ) / ( h - h₁ )
( D - D₁ ) = m ( h - h₁ )
a) ( D - 128 ) = m ( 1,5 - 0)
And
b) m = 93/ 1,5
m = 62
And
b) D = mh + b
D = mh + D₁
D = 62*h + 128
a)
The equation is:
\(D - 221 = 62(h - 1.5)\)
b) Initially, he was 128 miles away from Albany.
Item a:
Fabio is traveling from Albany to Buffalo, and his distance D from Albany after h hours is modeled by a linear function in the following format:
\(D - D_1 = m(h - h_1)\)
We have that:
Velocity of 62 miles per hour, thus the slope is \(m = 62\).After 1.5 hours, he is 221 miles away from Albany, thus the point is \(h_1 = 1.5, D_1 = 221\).The equation is:
\(D - D_1 = m(h - h_1)\)
\(D - 221 = 62(h - 1.5)\)
Item b:
The initial distance is D when h = 0, so:\(D - 221 = 62(0 - 1.5)\)
\(D = -1.5(62) + 221\)
\(D = 128\)
Initially, he was 128 miles away from Albany.
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Related Questions
The 13-year $1,000 par bonds of Vail Inc. pay 13 percent interest. The market's required yield to maturity on a comparable-risk bond is 14 percent. The current market price for the bond is $870.
a. Determine the yield to maturity.
Answers
The current market price for the bond is $870 the yield to maturity is 14.13%
How is yield to maturity calculated?The approximate yield to maturity of this bond is 11.25%, which is above the annual coupon rate of 10% by 1.25%. You can then use this value as the rate (r) in the following formula: C = future cash flows/coupon payments. r = discount rate (the yield to maturity)
knowing that:
Face value (par value) of the bond (F) = $1,000Annual coupon rate (C) = 13% of the face value = 0.13 * $1,000 = $130Years to maturity (n) = 13 yearsCurrent market price of the bond (P) = $870the formula is:
\(P = (C / (1 + r))^1 + (C / (1 + r))^2 + ... + (C + F) / (1 + r)^n\)
Putting the values:
\($870 = (130 / (1 + r))^1 + (130 / (1 + r))^2 + ... + (130 + 1,000) / (1 + r)^13\)
Using the math we find that the percentage is approximately 14.13%;
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Q:
To which axis is the line passing through A(4,3) and B(4,-2) parallel to?
Answers
Answer:
y-axis.
Step-by-step explanation:
The x coordinate of both points is 4, so it is parallel to they-axis.
CGiven: ABCD is a parallelogram.Prove: ABCD and BC - DAAngles Segments Triangles Statements ReasonsERREAB11ACBCCDVXDAСBStatementsReasonsADDemo) Intro
Answers
Given the parallelogram ABCD, draq diagonal AC
From the parallelogram above, it can observed that line BCis parallel to line AD. Also, the line AB is parallel to line DC
The diagonal AC is a transversal to the two parallel lines BC and line AD
In the triangles ABC and triangle CDA,
\(\begin{gathered} \angle BAC=\angle DCA(\text{alternate angles of parallel line AB and line DC)} \\ \angle BCA=DAC(alternate\text{ angles of parallel line BC and line AD)} \end{gathered}\)From the two triangles ABC and CDA, line AC and line CA are common to them
\(i\mathrm{}e\text{. AC=CA (Common length)}\)It can be deduced that triangle ABC is congruent to triangle CDA
\(ie\text{. }\Delta ABC\cong\Delta CDA(A\text{ AS)}\)Hence, AB≅CD and BC≅DA (Matching sides of congruent triangles ABC and triangles CDA)
pi, 2 square root 7, square root of 7, and square root 2 (a) Approximate the square root terms using the perfect squares approximation method. Your answer should be a mixed fraction. Make sure to show your work.(b) order the numbers from least to greatest please use the original symbols and radicals provided for your final answer you may use decimals or fraction as part of your work for figuring it out
Answers
A figure is shown, where lines CE and FD intersect at point B.
.
A figure is shown, where lines CE and FD intersect at point B.
.
Angle ABC is complementary to angle DBC.
What is the measure, in degrees of ?
Answers
Answer:
Step-by-step explanation:
Its 4.51
A rectangle has a length that is three foet more than twice its width what would be the perimeter of this rectangle if the width was 10 feet
Answers
Answer:
The length is 3 feet more than twice the width (L=3+2w).
The formula for perimeter is 2L + 2W.
Step-by-step explanation:
I HOPE THIS HELPS , AMRK AS BRAINLIST
Help!!!!!!!!!!!!!!!!!
Answers
Answer:
7.5 i got
Step-by-step explanation:
60%8= 7.5
Answer: the shaded area is 1/6 of the circle and is 60 degrees thats all i know sorry if not right
Step-by-step explanation: HAVE A GREAT DAY
When the sun is at a certain angle in the sky, a 100-foot building will cast a 25-foot shadow. How tall is a person if he casts a 1. 5-foot shadow at the same time? enter only the number.
Answers
A person's height if he casts a 1. 5-foot shadow at the same time is 6 feet.
What is a scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Given:
When the sun is at a certain angle in the sky,
a 100-foot building will cast a 25-foot shadow.
That means the ratio of shadow to the actual height,
= 25/100
= 1/4
So, a person's height if he casts a 1. 5-foot shadow at the same time is,
= 1.5 x 4
= 6 feet.
Therefore, the height is 6 feet.
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Please help me i really need help please i really need help please please really need help please or i'm not gonna pass please
identify a personality trait that best characterizes Oya. Explain how she demonstrates this trait. Provide specific textual evidence to illustrate it. And explain how a specific character from A Raisin in the Sun is similar to Oya.
Answers
3. An investor plans to invest $500/year and expects to get a 10.5% return. If the investor makes these contributions at the end of the next 20 years, what is the present value (PV) of this investment today?
Answers
The present value (PV) of the investment today is approximately $2,965.05.
To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.
The formula for the present value of an annuity is given by:
PV = C * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value
C = Cash flow per period
r = Interest rate per period
n = Number of periods
In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.
Let's plug in these values into the formula and calculate the present value (PV):
PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]
Using a calculator, we can evaluate the expression inside the brackets:
PV = $500 * [(1 - 0.376889) / 0.105]
Simplifying further:
PV = $500 * [0.623111 / 0.105]
PV = $500 * 5.930105
PV = $2,965.05
Therefore, the present value (PV) of the investment today is approximately $2,965.05.
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Sally had 52 more stickers than Joe after Joe gave 1/5 of his stickers to her. if they both had a total of 260 stickers, how many stickers did Sally have to start?
Answers
There are 125 stickers did Sally have to start.
We have to given that,
Sally had 52 more stickers than Joe after Joe gave 1/5 of his stickers to her.
Let us assume that,
Joe had x stickers to start with.
Since, After Joe gave 1/5 of his stickers to her.
He have 4/5 of his original amount left.
That is, 4/5x
Since, Sally had 52 more stickers than Joe
Hence, We get;
4/5x + 52 = 1/5x + y .. (i)
where y is the number of stickers Sally had to start with.
Here, they both had a total of 260 stickers,
Hence,
x + y =260 .. (ii)
From (i) and (ii);
y = 125
Thus, There are 125 stickers did Sally have to start.
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Bob packs 13 pounds of nuts in bags. Each bag has 1/4 pound of nuts. Which equation shows the number of bags Bob packed with all the nuts?
13 × 1/4 = 52
13 ÷ 1/4 = 52
13 ÷ 1/4 = 14/4
13 × 1/4 = 13/4
Answers
The equation for the bag with all nuts is 13 / ( 1/4 ) = 52 bags
Given data ,
Bob packs 13 pounds of nuts in bags.
Each bag has 1/4 pound of nuts
Now , the number of bags = pounds of nuts / pounds of nuts in each bag
A = 13 / 1/4
On simplifying the equation , we get
A = 52 bags
Hence , the number of bags is 52 bags
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Which pair of expressions represents inverse functions?
4x-3x/4x-2 and x+2/x-2
4x+2/x-3 and 5x+3/4x-2
2x+5 and 2+5x
x+3/4x-2 and 2x+3/4x-1
Answers
Answer:2 hope this helps it was right on my test
Step-by-step explanation: it was right on the test i took
Solve the inequality and enter your solution as an inequality comparing the
variable to a number.
x-30 > 30
Answers
Answer:
\(x > 60\)
Step-by-step explanation:
\(x-30 > 30\)
\(x > 60\) (add 30 onto both sides of the inequality)
angles A and B together make up a straight line the measure of angle a is 5x-1 The measure of angle B is 6+2x find the value of X
PLEASE HELP SOON
Answers
Answer
16x-2 hope this helps love thx
Area of a triangleFind the area of the triangle below.Be sure to include the correct unit in your answer.ftft?ft24H18 ft12 ftX 5?
Answers
Given:
Base b= 18ft
Height h = 4 ft
The area of the triangle = 1/2 bh
\(\begin{gathered} A=\frac{1}{2}\times18\times4 \\ =9\times4 \\ =36ft^2 \end{gathered}\)Hence, the required answer is 36 ft^2.
What percent of
950 is 36?
Answers
Chandler decided to go cliff jumping into the lake at his cottage. He started on the cliff at 32 ft above sea level. He jumped for 40 feet! How far below sea level did Chandler end up?
Answers
Chandler ended up 8 feet below sea level. The negative sign indicates that his final position is below sea level. This means that he has descended further into the lake compared to the starting point on the cliff.
Chandler started on the cliff at 32 feet above sea level. When he jumped for 40 feet, we need to determine the final position in relation to sea level.
Since Chandler jumped down, the distance below sea level will be calculated as a negative value. To find how far below sea level Chandler ended up, we subtract the jump distance (40 feet) from the starting height (32 feet above sea level):
32 feet - 40 feet = -8 feet
It's important to note that negative values are used here to represent the direction and magnitude of Chandler's descent relative to sea level
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Answer:
-8 feet
Step-by-step explanation:
Which of the following pairs show(s) triangles that are similar but not congruent?
Answers
Answer:
simelier means the same except diffrent size the only one that doesn't fit that is
b B only
Hope This Helps!!!
solve ~
\(2x + 1 - 4x = 7x + 5\)
don't spam .-.
thankyou ~
Answers
Answer:
\(x=-\frac{4}{9}\)
Step-by-step explanation:
2x + 1 - 4x = 7x +5
First, take 7x to the left side.
2x + 1 - 4x - 7x = 5
Now take 1 to the right side.
2x - 4x - 7x = 5 - 1
Now combine like terms.
-2x - 7x = 4
-9x = 4
Now divide both sides by -9.
x = - 4/9
Answer:
2x+1-4x=7x+5
-->2x-4x-7x=5-1
-->-2x-12x=4
-->-9x=4
-->x=-4/9
-->x=-4/9
What is the volume of the right rectangular prism?
5 m
10 m
5 m
75 m 3
125 m
3
200 m 3
3
250 m
Answers
Answer: 250m 3
Step-by-step explanation:
The base multiplied is 50m and the height is 5m, so, 50 x 5 = 250.
The whole question though, is just multiplication.
10m x 5m = 50m
50m x 5m = 250m
Also, since there are 3 different numbers in this problem, the metric unit would be typed as "m 3"
Your answer would be 250m 3
Jollys scores for the first 3 quarters of the school year were 82, 94, and 88. ahe wants to get an average of 90 for this year. What must her 4th quarter score be?
Answers
Answer:
96
Step-by-step explanation:
You add the scores, add 96, divide by 4 and you get 90.
At the store the ratio of books sold to movies sold was 4:5.For every_books sold there were _ movies sold.
Answers
Answer:
At the store the ratio of books sold to movies sold was 4:5.For every 4 books sold there were 5 movies sold.
Step-by-step explanation:
Write 3^7/2 in surd form.
Answers
Answer:
\(\sqrt[2]{3^7}\)
Step-by-step explanation:
\(\sqrt[2]{3^7}\)
The top number is the power and the bottom of the fraction is the root
Does someone know this please respond ASAPPP thank you.
Answers
Answer:
It would be 6 times the old area
Step-by-step explanation:
To find the area you do 6×9=54 then you do 6 doubled and 9 tripled to get 12 and 27. So 12×27=324 then you do 323÷54=6
convert the following ratios in to percentage 35:16
Answers
Which graph shows the solution to the system of linear inequalities? y ≥ 2x + 1 y ≤ 2x – 2
Answers
The graph which shows the solution to the system of inequalities is attached in the picture below :
Given the inequalities :
y ≥ 2x + 1
y ≤ 2x - 2
From y ≥ 2x + 1 ;
Since the inequality sign is ≥, a solid line is used to draw the straight line graph of y ≥ 2x + 1
From :
y = mx + c
Where, m = slope ; c = intercept
Hence, a straight line graph with ;
Intercept, c = 1 (where the line crosses the y-intercept)
Slope, m = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality :
0 ≥ 2(0) + 1
0 ≥ 0 + 1
0 ≥ 1
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
From : y ≤ 2x - 2
Since the inequality sign is ≤, a solid line is used to draw the straight line graph of y ≤ 2x - 2
Graph the line y ≤ 2x - 2, with ;
Intercept, c = - 2
Slope = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality y ≤ 2x - 2:
0 ≤ 2(0) - 2
0 ≤ 0 - 2
0 ≤ - 2
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
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Answer:
Its graph B on edge 2022
Step-by-step explanation:
\(-5(4-1/2n) + 1/16(-32+8)\)
Answers
Answer:
2.5n - 21.5
Step-by-step explanation:
\(-5(4 - \frac n2) + \frac1{16}(-32 + 8) \\ \\\to -5 \times 4 + 5 \times \frac n2 - \frac1{16} \times 32 + \frac1{16} \times 8 \\ \\\to -20 + \frac{5n}2 - \frac{32}{16} + \frac{8}{16} \\ \\\to -20 + 2.5n -2 + 0.5 \\ \\\to 2.5n - 21.5\)
Simplify your answer as much as possible.
Answers
By using the substitution method, we will see that the value of y is 23.
How to solve the system of equations?Here we have a system of linear equations, the system is:
y - x = 11
x = 12
The second equation is trivial, it just gives the value of x. Then we can use the substitution method and replace it in the first equation, then we will get:
y - 12 = 11
Now we can solve this for y, we will get:
y = 11 + 12
y = 23
That is the value of y.
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Find the perioa
equation.
llowing
y = 2 cos(5x + 3) - 6
77
Period = [2]T
Give your answer in simplest form.
![Find the perioaequation.llowingy = 2 cos(5x + 3) - 677Period = [2]TGive your answer in simplest form.](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/LQPTncYwbgWAlBk9oUI1EamQ5J0oFRZg.png)
Answers
Answer:
In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.
The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.
The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.
So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:
T = 2π / 5
This is the simplest form for the period of the given function.