Answer:
Slower trains: 123 km/h
Faster train: 134 km/h
Step-by-step explanation:
In order to solve this problem, one must know the following formula:
[tex]speed*time=distance[/tex]
The problem gives one the following information:
There are two trains heading towards each other, one is (11 km/h) faster than the other.There are (1542 km) between the two trains.It takes 6 hours for the two trains to meet each other.Let ([tex]speed_1[/tex]) represent the speed of the slower train and ([tex]speed_2[/tex]) represent the speed of the faster train.
One can form an equation, let (x) represent the speed of the slower train. Using the distance equation, one can state that the speed of each train times the travel time equals the distance. Since the trains met each other in (6) hours, and the combined distance traveled between the two trains is (1542 km); one can use this information to form an equation.
[tex](travel\ time)(speed_1)+(travel\ time)(speed_2)=distance[/tex]
Substitute,
[tex]6(x)+6(x+11)=1542[/tex]
Simplify, distribute, multiply every term inside of the parenthesis by the term outside of it. Then combine like terms,
[tex]6x+6x+66=1542[/tex]
[tex]12x+66=1542[/tex]
Inverse operations,
[tex]12x+66=1542[/tex]
[tex]12x=1476[/tex]
[tex]x=123[/tex]
Solve for the speed of the faster train. It is given that it is (11 km/h) faster than the slower train.
[tex]speed_1+11=speed_2\\123+11=speed_2\\134=speed_2[/tex]
Graph the exponential function.
f(x)=3/2(2)^x
Plot five points on the graph of the function. Then click on the graph-a-function button.
[tex] \bf \: f(x) = \frac{3}{2} \times {2}^{x} \\ \\ = > \bf \: f(0) = \frac{3}{2} \times {2}^{0} = \frac{3}{2} \times 1 = \frac{3}{2} = 1.5 \\ \\ = > \bf \: f(1) = \frac{3}{2} \times {2}^{1} = 3 \\ \\ = > \bf \: f(2) = \frac{3}{2} \times {2}^{2} = 6 \\ \\ = > \bf \: f( - 1) = \frac{3}{2} \times {2}^{ - 1} = \frac{3}{2} \times \frac{1}{2} = \frac{3}{4} = 0.75 \\ \\ = > \bf \: f( - 2) = \frac{3}{2} \times {2}^{ - 2} = \frac{3}{2} \times \frac{1}{4} = \frac{3}{8} = 0.375[/tex]
A restaurant has two appetizer specials. Tomato bread costs $5.50, and stuffed mushrooms cost $6.75. The total amount in sales from the two appetizers on a Friday night was $186.75. Which equation can be used to represent x, the number of stuffed mushroom orders and y, the number of tomato bread orders?
Answer:
6.75x + 5.50y = 186.75
Step-by-step explanation:
The stuffed mushrooms cost 6.75 dollars and the tomato bread costs 5.50 dollars.
Answer:
186.75
Step-by-step explanation:
6.75x+5.50y=186.75
The Volume of a sphare is 28/3 times the surface area calculate The surface area and the Volume of the sphere, correct to the nearest whole number.
Given:
Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.
To find:
The surface area and the volume of the sphere.
Solution:
Volume of a sphere:
[tex]V=\dfrac{4}{3}\pi r^3[/tex] ...(i)
Surface area of a sphere:
[tex]A=4\pi r^2[/tex] ...(ii)
Where, r is the radius of the sphere.
Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.
[tex]V=\dfrac{28}{3}\times A[/tex]
[tex]\dfrac{4}{3}\pi r^3=\dfrac{28}{3}\times 4\pi r^2[/tex]
Multiply both sides by 3.
[tex]4\pi r^3=112\pi r^2[/tex]
[tex]\dfrac{\pi r^3}{\pi r^2}=\dfrac{112}{4}[/tex]
[tex]r=28[/tex]
Using (i), the volume of the sphere is:
[tex]V=\dfrac{4}{3}\times \dfrac{22}{7}\times (28)^3[/tex]
[tex]V\approx 91989[/tex]
Using (ii), the surface area of the sphere is:
[tex]A=4\times \dfrac{22}{7}\times (28)^2[/tex]
[tex]A=9856[/tex]
Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.
Nissa is going to plant 485trees this year. If Nissa plants 5 orchards of trees, how many trees will be in each orchard?
Answer:
"97" is the appropriate answer.
Step-by-step explanation:
Given:
Number of trees,
= 485
Orchards of trees,
= 5
The number of trees in each orchard will be:
= [tex]\frac{Number \ of \ trees}{Orchards \ of \ trees}[/tex]
= [tex]\frac{485}{5}[/tex]
= [tex]97[/tex]
Find the value of a. A. 57 B. 104 C. 26 D. 52
Answer:
Option D, 52
Answered by GAUTHMATH
URGENT+Brainliest. Convert r=2sin(2theta) into rectangular cords.
Answer:
try 14n
Step-by-step explanation:
Answer:
[tex]r \: = 2sin2 \theta \\ = > r = 2.2sin\theta.cos\theta \\ = > r = 4sin\theta.cos\theta \: \\ \\ \sf \: we \: know \: that \: \\ x = r \: cos\theta \: \therefore \: cos\theta = \frac{x}{r} \\ \\ y = r \: sin\theta \: \therefore \: sin\theta = \frac{y}{r} \\ \\ \sf \: now \\ \\ r = 4 \times \frac{y}{r} \times \frac{x}{r} \\ = > {r}^{3 } = 4xy \\ \\ \sf \: again \: \: r = \sqrt{ {x}^{2} + {y}^{2} } \\ \\ = > {( \sqrt{ {x}^{2} + {y}^{2} } })^{3} = 4xy \\ = > {( {x}^{2} + {y}^{2} })^{ \frac{3}{2} } = 4xy \\ = > {( {x}^{2} + {y}^{2} })^{3} = 16 {x}^{2} {y}^{2} [/tex]
Please mark me as Brainliest
Help please please help me please
Answer:
[tex]\sqrt[2]{8}[/tex]
Step-by-step explanation:
Remember the basic format of a fraction raised to a fractional exponent:
[tex]a^\frac{b}{c}=\sqrt[b]{a^c}[/tex]
Some terms to keep in mind are the following:
(a) is the base
(c) is the exponent
(b) is the index
Apply this information to the given problem:
[tex]2^\frac{3}{2}[/tex]
In this case, (2) is the base, and the index; (3) is the exponent. Apply the general format of the fraction exponent to change the expression from an exponent to a radical.
[tex]2^\frac{3}{2}=\sqrt[2]{2^3}[/tex]
Simplify the term under the radical:
[tex]\sqrt[2]{2^3}=\sqrt[2]{8}[/tex]
1. when the expression x^3+ 2kx+2 is divided by x+2, the remainder is less than the remainder when the expression is divided by x+1 find the value of k. help plz
Answer:
let the polynomial be
f(x)=x³+2kx+2
is divided by
g(x)=x+2
hence
(x+2) is a factor of f(x)
so comparing with x-a we get a=-2
so
f(a)=0
f(-2)=(-2)³+2*-2*k+2
0=-8-4K+2
4k=-6
K=-6/4
k=-3/2
again
when divided by x+1
g(x)=x+1
hence
x+1 is a factor
so a=-1
f(-1)=-(1)³+2*-1*k+2
0=-1-2k+2
0=1-2k
k=1/2
The value of k is 1/2 when divided by x+1
and
K =-3/2 when divided by x+2
how do i know when an equation has 1 solution
Answer:
you can plug it back into the original equation to see if it fits the solution. if not then you have another solution you need to solve for.
Answer:
if we're talking on linear equations, then the two equations would intersect at one point. or when you solve it, it'll be only 1 number that can fit that equation.
p.s.: sub to #gauthmath# sub reddit if ya can ^^
what must be subtracted from 61 to get 5
Answer: 56
Step-by-step explanation:
Let x be the number that is supposed to be subtracted from 61.
Given
61 - x = 5
Add both sides by x
61 - x + x = 5 + x
61 = 5 + x
Subtract 5 on both sides
61 - 5 = 5 + x - 5
x = 56
Hope this helps!! :)
Please let me know if you have any questions
The sum of two integers equals twelve, while their product equals thirty-five. Which two numbers are they?
Answer: 5 and 7
Step-by-step explanation:
Given
Sum of the integers is 12
Product of the integers is 35
Suppose the integers are [tex]x[/tex] and [tex]y[/tex]
[tex]\Rightarrow x+y=12\\\\\Rightarrow y=12-x\\\Rightarrow xy=35\\\text{Substitute y}\\\Rightarrow x(12-x)=35\\\Rightarrow 12x-x^2=35\\\Rightarrow x^2-12x+35=0\\\Rightarrow x^2-7x-5x+35=0\\\Rightarrow (x-7)(x-5)=0\\\Rightarrow x=5\ or\ 7[/tex]
[tex]\therefore \text{y can be }7\ or\ 5[/tex]
Hence, the numbers are 5 and 7.
Can someone help with this please
Step-by-step explanation:
5.
[tex]3\cdot 10^{8} : 1000 = 3\cdot 10^{8} : 10^{3} =3 \cdot 10^{8-3} =3 \cdot 10^{5}[/tex]
Answer: [tex]3 \cdot 10^{5}[/tex]
6.
[tex]\dfrac{0.0046}{0.000000000513} =\dfrac{46 \cdot 10^{-4} }{5.13 \cdot 10^{-10} } =\dfrac{46 \cdot 10^{-4-(-10)}}{5.13} =\dfrac{46 \cdot 10^{6}}{5.13} \approx 9 \cdot 10^{6}[/tex]
Answer: [tex]9 \cdot 10^{6}[/tex]
Horace is running a race. He wonders how fast he is running.
Which unit rates would be reasonable for Horace to use to describe how fast he is running?
Select each correct answer.
a miles per hour
b millimeters per minute
c kilometers per hour
d inches per hour
Answer:
C. Kiometers per hour. I think
Rewrite this equation in the form y = ax + b.
2y = 4x - 8
Enter the correct answer.
OOÐ
DONE
Clear all
ĐOO
?
Answer:
y = 2x -4
Step-by-step explanation:
2y = 4x - 8
Divide each side by 2
2y/2 = 4x/2 - 8/2
y = 2x -4
$10 bet between you and me. At any time during the game, I can ask to double it. If you accept we both put in another $10 and if you win, you win the $20 and if you lose, you lose it all. If you reject, you lose the initial $10. What is the minimum probability you would take to accept the double
Answer:
66%
Step-by-step explanation:
[tex]-10x\:+\:\left(20\cdot \left(1-x\right)\right)=\:0[/tex]
x = [tex]\frac{2}{3}[/tex] = .666 = 66%
In one college, 67 students made the dean's list. If this was 33.5% of the student body, what was the total number of students in the college?
Answer:
Total number of students in the college = 200 student
Step-by-step explanation:
Given:
Number of student make dean's list = 67 student
Percentage of student make dean's list = 33.5% of all student
Find:
Total number of students in the college
Computation:
Total number of students in the college = Number of student make dean's list / Percentage of student make dean's list
Total number of students in the college = 67 / 33.5%
Total number of students in the college = 67 / 0.335
Total number of students in the college = 200 student
(x^2+1)(x-1)=0 help me pls
Answer:
x = ±i , x=1
Step-by-step explanation:
(x^2+1)(x-1)=0
Using the zero product property
x^2 +1 = 0 x-1= 0
x^2 = -1 x=1
Taking the square root of the equation on the left
sqrt(x^2) = sqrt(-1)
x = ±i where i is the imaginary number
We still have x=1 from the equation on the right
help please ITS OF TRIGONOMETRY
PROVE
Answer:
The equation is true.
Step-by-step explanation:
In order to solve this problem, one must envision a right triangle. A diagram used to represent the imagined right triangle is included at the bottom of this explanation. Please note that each side is named with respect to the angle is it across from.
Right angle trigonometry is composed of a sequence of ratios that relate the sides and angles of a right triangle. These ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
One is given the following equation,
[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]
As per the attached reference image, one can state the following, using the right angle trigonometric ratios,
[tex]sin(A)=\frac{a}{c}\\\\sin(B)=\frac{b}{c}\\\\cos(A)=\frac{b}{c}\\\\cos(B)=\frac{a}{c}[/tex]
Substitute these values into the given equation. Then simplify the equation to prove the idenity,
[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]
[tex]\frac{\frac{a}{c}+\frac{b}{c}}{\frac{b}{c}+\frac{a}{c}}+\frac{\frac{b}{c}-\frac{a}{c}}{\frac{a}{c}-\frac{b}{c}}=0[/tex]
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]
Remember, any number over itself equals one, this holds true even for fractions with fractions in the numerator (value on top of the fraction bar) and denominator (value under the fraction bar).
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{-(a-b)}{c}}{\frac{a-b}{c}}[/tex]
[tex]1+(-1)=0[/tex]
[tex]1-1=0[/tex]
[tex]0=0[/tex]
Help please fast geometry surface area!
Answer:
SA=2πrh+2πr2=2·π·12·3+2·π·122≈282.7cm2
18. DEFG is a rectangle. Find the
length of each side.
Answer:
DE=27
EF=13
DG=13
GF=27
Step-by-step explanation:
12x+3=5x+17
12x-5x=17-3
u'll get 14 then simply it by the numbe of X u'll get 2 then replace the X with the number
what is the area of the figure below?
Answer:
15x^9
Step-by-step explanation:
A=l x w
5x^4 times 3x^5 is basically 3*5*x^4*x^5
when you multiply exponents with the same base, you add the exponents, so it becomes 15x^9
A 20kg patient requires a 500 mg dose of a particular drug solution contains 100 mg/tsp. How many milliliters of the solution should be given to the patient to deliver the required dose?
Answer:
The answer is "25 ml".
Step-by-step explanation:
Dose[tex]= 500 \ mg\\\\[/tex]
Solution [tex]= 100\ \frac{mg}{teaspoonful}\\\\[/tex]
Calculating the Conversions:
Teaspoonful [tex]= 5 \ ml \ \text{(Ounce = 30 ml = 6 Tablespoonsful)}[/tex]
[tex]\therefore\\\\Solution = \frac{100\ mg}{ 5\ ml} = 20\ \frac{mg}{ml}\\\\Dose \ volume = \frac{500\ mg}{ 20\ \frac{mg}{ml}} = 25\ ml[/tex]
[3x - 4 × 5] bằng bao nhiêu
Answer:
-60
Step-by-step explanation:
The diameter of a cylindrical construction pipe is 4ft. If the pipe is 22ft long, what is its volume?
Use the value 3.14 for pi
Answer:
V = 276.32 ft^3
Step-by-step explanation:
Volume of a cylinder is
V = pi r^2 h
The diameter is 4 so the radius is d/2 = 4/2 = 2
V = (3.14) ( 2)^2 * 22
V = 276.32 ft^3
find a volume of a cube whose base radius is 5 cm and height 28 cm
Answer:
The volume of the cube is 21952.
Step-by-step explanation:
V = L x W x H
because a cube's sides are all the same, the length, width, and height are also the same. So we use the formula:
V= S^3
(S standing for side)
we know the height is 28 and as all sides measure the same we use the equation:
V= 28^3
28^3 = 21952
So, V= 21952
Explain the relationship between an inda vidual and a society
Answer:
The relation between individual and society is very close. Essentially, “society” is the regularities, customs and ground rules of antihuman behavior. ... Man is biologically and psychologically equipped to live in groups, in society. Society has become an essential condition for human life to arise and to continue.
Name three collinear points.
Answer: l,j,k
Step-by-step explanation:
Find the surface areas of each figure. Round your answers to the nearest tenth, if necessary
Answer:
678
Step-by-step explanation:
12*11=132
11*9=99
12*9=108
132+99+108=339
339*2=678
Can someone answer any of these with working out?
Answer:
sorry I don't know
sorry I Don't know
17. Find an equation of the straight line that is perpendicular to x - y = 5 and passes through the point (8, -1).
18. Find the equation of the line in slope-intercept form that passes through the points (12, 4) and (4, 6)
Answer:
17.y=-x+12
18.y=-1/4x+7
Step-by-step explanation:
17.a Solve for y (y=-5+x)
17. b Reciprocal (y=-1x-5)
17. c Subsitute equation into (8,-1) (-1=-13=y=x+12)
18.a Subtract y values and x values= (6-4)/(4-12)=2/-8=-1/4, this will be your slope
18. b Plug in -1/4 into either of the two ordered pairs to find y value=(12,4)=(4=-3)=y value=7.
18. c=y=-1/4x+7
