Answer:
C
Step-by-step explanation:
d / rate = time
d / 90 + d/60 = 6 hours
(2d+ 3d)/180 = 6
5d = 1080
d = 216 miles
The distance from NYC to Boston is 216 miles.
We have a guy named Steve travels from NYC to Boston at 90 mph and returns to NYC at 60 mph taking 6 hours total for the round-trip without stopping.
We have to determine distance between NYC and Boston.
What is the formula to calculate the distance travelled by the body moving with speed ' v mph ' for ' t hours '.The distance covered by the body will be -
d = v x t
According to question, we have -
Assume that the distance travelled by Steve from NYC to Boston be x.
Then, total distance covered for the round trip = 2x.
From NYC to Boston -
Suppose that in going from NYC to Boston, Steve takes t hours. Then
x = 90 x t (1)
From Boston to NYC -
Steve will take (6 - t) hours to travel the distance. Then -
x = 60 x (6 - t) (2)
Now, Equating the equations (1) and (2), we get -
90 x t = 60 x (6 - t)
1.5t = 6 - t
1.5t + t = 6
2.5 t = 6
t = [tex]\frac{12}{5}[/tex] = 2.4 hours
Therefore -
x = 90 x 2.4 = 216 miles
Hence, the distance from NYC to Boston is 216 miles.
To solve more questions on Speed, time and Distance visit the link below -
https://brainly.com/question/24999473
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Determine the equation of the circle with center (-7,7)(−7,7) containing the point (-2,-5)(−2,−5)
Circular equations are often organized in the following form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](h,k)[/tex] is where the circle is centered[tex]r[/tex] is the radiusTo find the equation of a circle given its center and a point:
Plug the center into the general equation as (h,k)Plug the given point into the general equation as (x,y)Solve for r²Plug (h,k) and r back into the original equationSolving the QuestionWe're given:
Center: (-7,7)Point: (-2,-5)Plug the center into the general equation:
[tex](x-(-7))^2+(y-7)^2=r^2\\(x+7)^2+(y-7)^2=r^2[/tex]
Plug in the given point (-2,-5) and find r²:
[tex]((-2)+7)^2+((-5)-7)^2=r^2\\(5)^2+(-12)^2=r^2\\25+144=r^2\\r^2=169[/tex]
Plug the center and radius back into the original equation:
[tex](x-h)^2+(y-k)^2=169\\(x+7)^2+(y-7)^2=169[/tex]
Answer[tex](x+7)^2+(y-7)^2=169[/tex]
How many solutions can be found for the equation 5x + 3(x − 1) = 10x − 2x − 3? (4 points) None
One
Two
Infinitely many
Answer:
infinitely many
Step-by-step explanation:
5x+3(x-1)=10x-2x-3
5x+3x-3=10x-2x-3
8x-3=8x-3
A rectangular prism has a length of 11ft, a height of 4ft, and a width of 3ft. What is its volume, in cubic ft?
Need some help with a math problem. The problem is: The figure is made by attaching semicircles to each side of an 11 ft-by-11-ft square. Find the area, in square feet, enclosed by the figure. Use 3.14 for pi. Round to the nearest whole number.
I dont understand this to save my life, Please help !
The entire rectangle below has an area of 36 ft2. Find the area of the shaded triangle. Be sure to include the correct unit in your answer.
Which angles are corresponding angles
Answer:
second option is correct onee
Step-by-step explanation:
mark me brainliest
To be a member at sal's gym, there is a one-time sign-up fee plus a monthly fee for each month of membership. the table shows the total cost to be a member of the gym for different numbers of months.
Let f be the function defined by 1 2 1 1 4 3 2 f x( ) = x − x + x − x 4 3 2 2 . For how many values of x in the open interval (0, 1.565) is the instantaneous rate of change of f equal to the average rate of change of f on the closed interval [0, 1.565] ?
There are three values of x where the instantaneous rate of change of f(x) are equal in the open and closed intervals
How to determine the number of x values?The function is given as:
[tex]f(x) = \frac 14x^4 - \frac 23x^3 + \frac 12x^2 - \frac 12x[/tex]
Calculate f(0)
[tex]f(0) = \frac 14 * 0^4 - \frac 23 * 0^3 + \frac 12 *0^2 - \frac 12 * 0[/tex]
[tex]f(0) = 0[/tex]
Calculate f(1.565)
[tex]f(1.565) = \frac 14 * 1.565^4 - \frac 23 * 1.565^3 + \frac 12 *1.565^2 - \frac 12 * 1.565[/tex]
[tex]f(1.565) = -0.613[/tex]
The average rate of change is then calculated using:
[tex]m = \frac{f(1.565) - f(0)}{1.565 - 0}[/tex]
This gives
[tex]m = \frac{-0.613 - 0}{1.565 - 0}[/tex]
[tex]m = -0.392[/tex]
Differentiate the function f(x)
[tex]f'(x) = x^3 - 2x^2 + x - \frac 12[/tex]
Set f'(x) to [tex]m = -0.392[/tex]
[tex]x^3 - 2x^2 + x - \frac 12 = -0.392[/tex]
From the graph of the above equation (see attachment), we have three values of x at:
x = 0.1492, x = 0.5614 and x = 1.2894
Hence, there are three values of x in the open interval (0,1.565)
Read more about instantaneous rate at:
https://brainly.com/question/24592593
A car normally sells for $20,000 is on sale for $16,000. The sales tax is 7.5%.
What percent of the original price of the car is the final price?
Answer:
86% of original (with tax included)
Step-by-step explanation:
(16 000 x 1.075) / 20 000 x 100% = 86 %
Harvey the wonder Hamster can run 3 1/6 km in 1/4 hour. Harvey runs at a constant rate find his average speed in kilometers per hour
let's firstly convert the mixed fractio to improper fraction.
[tex]\stackrel{mixed}{3\frac{1}{6}}\implies \cfrac{3\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{19}{6}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{ccll} Km s&Hour\\ \cline{1-2} \frac{19}{6}&\frac{1}{4}\\[1em] x&1 \end{array}\implies \cfrac{~~ \frac{19}{6}~~}{x}~~ = ~~\cfrac{~~ \frac{1}{4}~~}{1}\implies \cfrac{~~ \frac{19}{6}~~}{\frac{x}{1}}=\cfrac{1}{4}\implies \cfrac{19}{6}\cdot \cfrac{1}{x}=\cfrac{1}{4} \\\\\\ \cfrac{19}{6x}=\cfrac{1}{4}\implies 76=6x\implies \cfrac{76}{6}=x\implies \cfrac{38}{3}=x\implies 12\frac{2}{3}=x[/tex]
Which set of side lengths forms a right triangle?
A. 6,8,10
B. 2,4,6
C.1,2,3
D. 2,3,4
Answer:
A. 6,8,10
Step-by-step explanation:
For a right triangle the the values for the three sides we pick must satisfy the Pythagorean theorem:
a(2 + b(2= c(2
A. 6,8,10
6(2 + 8(2 = 10(2
36 + 64 = 100
100 = 100
Bingo!
(For example lets solve the rest)
B. 2,4,6
2(2 + 4(2 = 6(2
4 + 16 = 36
20 ≠ 36
Nope.
C. 1,2,3
1(2 + 2(2 = 3(2
2 + 4 = 9
6 ≠ 9
No again!
D. 2,3,4
2(2 + 3(2 = 4(2
4 + 9 = 16
13 ≠ 16
Not this one.
Therefore our answer is A.
i dont really kno what to do.
Answer:
Step-by-step explanation:
rearrange the equation to the letter on the left side until you find an equation equal to one of the answers
Evaluate (8+t)^3 - 6 minutes when T=2
Answer:
994
Step-by-step explanation:
Answer:
994
Step-by-step explanation:
Given the expression
[tex](8+t)^{3}-6[/tex]
Also given
[tex]t=2[/tex]
We can substitute 2 for t.
[tex](8+2)^{3}-6[/tex]
Do the parenthesis first.
[tex]8+2=10[/tex]
Therefore
[tex]10^{3}-6[/tex]
Evaluate [tex]10^{3}[/tex]
[tex]10^{3}=1000[/tex]
[tex]1000-6=994[/tex]
Find the area of the parallelogram. 24 cm 9cm 8 cm
How do you find the surface area of a cube if one side measures 10cm? show your solution.
Answer:
600 cm squared :)
Step-by-step explanation:
Surface area of cube: 6 x s^2
Now lets solve!!
6 x 10^2
6 x 100
600
Have an amazing day!!
Please rate and mark brainliest!!
Please help me and tysm!
Answer:
200
Step-by-step explanation:
156.7
since the number before the hundred is more than 4
it becomes 200
Which expressions are equivalent to 3(6+b)-(2b + 1)?
Select two answers.
Step 1 - Use the distributive property and pick your first answer
Step 2 - Combine like terms and pick your second answer.
Answer:
18+3b-2b-1
b+17
Step-by-step explanation:
[tex]\mathrm{Using\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b[/tex]
[tex]-\left(2b+1\right)=-2b-1[/tex]
[tex]=3\left(6+b\right)-2b-1[/tex]
[tex]=18+3b-2b-1[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=3b-2b+18-1[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:18-1=17[/tex]
[tex]=3b-2b+17[/tex]
[tex]\mathrm{Add\:similar\:terms:}\:3b-2b=b[/tex]
[tex]=b+17[/tex]
[RevyBreeze]
help me pls (2x+3) (x+5)
Answer: C
Step-by-step explanation:
[tex]\left(2x+3\right)\left(x+5\right)[/tex]
[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
[tex]=2xx+2x\cdot \:5+3x+3\cdot \:5[/tex]
[tex]$$Simplify[/tex]
[tex]=2x^2+13x+15[/tex]
Which ordered pair is the solution to the system of linear equations y=-7x+2 and y = 9x-14?
(-5.1)
(1.-5)
(5.-1)
(-1,5)
what is the mean of this data set
56,87,90,42,36,77
Answer:
64.7 when rounded up to one decimal place
Step-by-step explanation:
Bryan is trying to catch up with his friends during a road trip they are 100 miles ahead of him and driving 50 mph Bryan is driving 75 mph to try and catch up
65 brainleiest! Can someone help?!
Answer:
m∡EFG = 139°, and m∡ IFH = 49°
Step-by-step explanation:
We know that vertical angles are congruent so we can say that
∡EFG ≅∡DFH and that ∡EFD≅∡GFH
Congruent angles have the same measure therefore
∡EFG = ∡DFH = 6x+25 and
∡EFD = ∡GFH = 2x+3
Use that all those angles add up to 360° to find x
∡EFG +∡GFH +∡DFH + ∡EFD = 360°, substitute the given measures
6x+25 +2x+3 + 6x+25 +2x+ 3 = 360 , combine like terms
16x + 56 = 360, subtract 56 from both sides
16x = 304, divide both sides by 16
x = 19
m∡EFG = 6x +25 , substitute x with 19 and calculate
m∡EFG = 6·19 +25
m∡EFG = 139°
m∡ IFH = 90°- m∡GFH, substitute m∡GFH with 2x+3
m∡ IFH = 90°- (2x +3), substitute x with 19
m∡ IFH = 90°- (2·19 +3)
m∡ IFH = 90°- 41
m∡ IFH = 49°
find p if t=6 years , r=12% and I=$240
Answer:
the future value would be 473.72 if p is referring to future value
if p is referring to present value it is 121.59
if p is referring to payment it is 58.37
Step-by-step explanation:
you can use spreadsheets to solve this equation using =pmt/=fv/=pv
Step-by-step explanation:
[tex]s .i = \frac{prt}{100} [/tex]
[tex]240 = p \times \frac{12}{100} \times 6[/tex]
[tex]240 = \frac{18}{25} p[/tex]
[tex]240 \div \frac{18}{25} = p[/tex]
[tex]p = 333.3333[/tex]
What is the solution for the following equation 2(y+3) squared
Answer:
2y² + 12y + 18
Step-by-step explanation:
2(y + 3)²
First use formula (a + b)² = a² + 2ab + b² to expand (y + 3)²:
(a + b)²
(y + 3)²
y² + 2*y*3 + 3²
y² + 6y + 9
Dont forget the 2:
2(y² + 6y + 9) <== distribute and multiply
2y² + 12y + 18
Hope this helps!
Determine the simplified expression for (5^2)(5^1/4)(5^-1)
A: 125^5/4
B: 5^-1/2
C: 5^5/4
D: 15^-1/2
Answer:
C is the answer please
C. 5^5/4
Using positive and negative integers, find four pairs of integers with a sum of 5.
Answer:
-8, 13
-3, 8
6, -1
10, - 5
Step-by-step explanation:
what is 8(4 - x) = 7x + 2
Answer: x = 2
Step-by-step explanation:
8(4 - x) = 7x + 2= 8(-x + 4) = 7x + 2= -8x + 32 = 7x + 2= -8x + 32 - 32 = 7x + 2 - 32= -8x = 7x + 2 - 32 = -8x = 7x = 30= -8x - 7x = 7x + 30 - 7x= -15x = 7x - 30 - 7x= -15x = 30 -15x/-15 = -30/-15 = x = -30/-15= x = 2And thats how you get the answer!
what is 13 x 350?
My calculator does not work
Which two expressions are equivalent?
29
А
x + x + x and x3
B
14x + 10 - 2x and 16x + 10
C
12x + 16x and 4(3x + 4x)
D
12x2 + 5x + 10 and 17x2 + 10
Answer:
[tex]12x+16x~ \text{and}~ 4(3x+4x)[/tex]
Step-by-step explanation:
[tex]4(3x+4x) =4\cdot 3x +4\cdot 4x= 12x + 16x[/tex]
