Answer:Let x km/hr be the speed of train
Let y be the time taken by the train
Distance = speed x time
= x y
To form the first equation let us consider the given information from the question that is If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time.
it clearly says that speed is increased by 6 and time is reduced by 4
So , (x + 6) (y - 4) = x y
x y - 4 x + 6 y - 24 = x y
x y - x y - 4 x + 6 y = 24
- 4 x + 6 y = 24
divided by (-2) => 2 x - 3 y = -12 ----- (1)
To form the second equation let us consider the given information from the question that is If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time.
it clearly says that speed is reduced by 6 and time is increased by 6
So , (x - 6) (y + 6) = x y
x y + 6 x - 6 y - 36 = x y
x y - x y + 6 x - 6 y = 36
6 x - 6 y = 36
divided by (6) => x - y = 6 ----- (2)
2 x - 3 y = -12
(2) x 2 => 2 x - 2 y = 12
(-) (+) (-)
---------------
- y = -24
y = 24
Now we have to apply the value of y in the first equation to get value of x
Substitute y = 24 in the first equation we get
2 x - 3 (24) = -12
2 x - 72 = -12
2 x = -12 + 72
2 x = 60
x = 60/2
x = 30
Speed of the train = 30 km/hr
Time taken by the train = 24 hours
Distance covered by the train = x y = 30 x 24 = 720 km
Verification:
2 x – 3 y = -12
2(30) - 3(24) = -12
60 - 72 = -12
-12 = -12
given the mapping f:x-7x-2, determine f(2)
Answer:
Value of F(2) = 12
Step-by-step explanation:
Given:
F(x) = 7x - 2
Find:
Value of F(2)
Computation:
F(x) = 7x - 2
putting x = 2
f(2) = 7(2) -2
f(2) = 14 - 2
f(2) = 12
So, Value of F(2) = 12
what is the equation, in factored form, of the quadratic functions shown in the graph?
Answer:
(x+3)(x-2)
Step-by-step explanation:
We can immediately see that there are roots at x = -3, and x = 2.
Because the website gives us that this in the form of (x + _) (x - _), our anwser is (x+3)(x-2)
oops I just saw your comment. Too late i guess...
Answer:
f(x)=1(x+3)(x-2)
Step-by-step explanation:
How do I solve this question 5x - [7 - (2x - 1)] = 3(x - 5) + 4(x + 3)
Answer:
x = 6/4, or x = 3/2, OR x = 1 1/2
Step-by-step explanation:
5x - [7 - (2x-1)] = 3(x-5) + 4(x+3)
Pick one side to work on first, I will chose the right side,
Distribute on the right side.
5x - [7 - (2x-1)] = 3x - 15 + 4x + 3
Now, add like terms on the right side.
5x - [7 - (2x-1)] = 7x - 12
Now, to isolate 7 - (2x -1), subtract 5x from both sides.
so now,
-7 - (2x-1) = 2x - 12
Now, we can add 7 to both sides of the equation to isolate -(2x-1)
we add instead of subtract because the seven is a negative.
-(2x-1) = 2x - 5
Now, there is still a negative sign in front of the (2x-1), so we distribute the - to the equation.
-2x + 1 = 2x - 5
Now, we can isolate the variable and numbers bu adding five to both sides, and adding 2 to both sides. This is to make the equation easier by removing any negative terms.
6 = 4x
Divide both sides by 4
x = 6/4, or x = 3/2, OR x = 1 1/2
The common difference of an ap is -2 find its sum of first term is hundred and last term is minus 10
Answer:
The sum of the arithmetic progression is 2520
Step-by-step explanation:
The sum, Sₙ, of an arithmetic progression, AP, is given as follows;
[tex]S_{n}=\dfrac{n}{2}\cdot \left (2\cdot a+\left (n-1 \right )\cdot d \right )[/tex]
Where;
n = The nth term of the progression
a = The first term = 100
d = The common difference = -2
Given that the last term = -10, we have;
-10 = 100 + (n - 1) ×(-2)
n = (-10 - 100)/(-2) + 1 = 56
Therefore, the sum of the 56 terms of the arithmetic progression is [tex]S_{56}=\dfrac{56}{2}\cdot \left (2\cdot 100+\left (56-1 \right )\cdot (-2) \right )[/tex]
Which gives;
[tex]S_{56}={28}\cdot \left (200-\left 110 \right ) = 2520[/tex]
select all options that represents the side lengths of a 30 60 90 triangle.
Answer:
Options (B) and (D)
Step-by-step explanation:
If a triangle is a 30° - 60° - 90° triangle, measure of the angle between the leg and hypotenuse will be either 60° or 90°.
Therefore, by applying Cosine rule in the given options.
c² = a² + b² - 2abCosC
All the given options are the right triangles.
[Since they follow the Pythagoras theorem]
Option (A),
Angle between the sides having measures 3 and 5 units,
4² = 3² + 5² - 2(3)(5)CosC
16 = 9 + 25 - 30.CosC
30.CosC = 18
[tex]C=\text{Cos}^{-1}(\frac{5}{6} )[/tex]
C = 33.56°
Therefore, this triangle is not a 30-60-90 triangle.
Option (B),
Angle between the sides measuring 5 and 10 units,
[tex](5\sqrt{3})^2=5^2+10^2-2(5)(10)\text{CosC}[/tex]
75 = 125 - 100(CosC)
Cos(C) = 0.5
C = 60°
Therefore, other angles of the triangle will be 30° and 90°.
And it's a 30°-60°-90° triangle.
Option (C),
10, 10, 10√2
It's a right triangle and the measure of legs are equal.
Since legs of this sides are equal, angles opposite to these equal sides will be equal.
Sum of all interior angles = 180°
m∠A + m∠B + m∠C = 180°
If m∠B = 90°
m∠A + 90° + m∠C = 180°
2(m∠A) = 90°
m∠A = 45°
Therefore, the given sides make a 45°- 45°- 90° triangle.
Option (D).
Angle between the sides 3 and 6,
(3√3)² = 3² + 6² -2(3)(6)CosC
27 = 9 + 36 - 36.(CosC)
CosC = [tex]\frac{18}{36}[/tex]
C = [tex]\text{Cos}^{-1}(\frac{1}{2})[/tex]
C = 60°
Therefore,
These sides make a 30°- 60°- 90° triangle.
Options (B) and (D) are the 30°- 60°- 90° triangle.
Simplify the following leave the answer in radical notation:
Please explain!!
1. Square root of (125x^2y^7)
2. Cubed root of (24x^3y8)
Answer:
1- 5xy³√5y
2- 2xy²∛3y²
Step-by-step explanation:
√125x²y^7=
√25*5x²y^6y
5xy³√5y
2) ∛24x³y^8=
∛2³*3x³y^8=
2xy²∛3y²
A student decided to research primate psychology for their science project. They measured how long it took gorillas to adapt to their new habitat when moved from one zoo to another. They measured how long it took the new gorilla to interact regularly (more than 3 times per day) with the gorillas that already live there. Seven different cases were examined and the data collected. What can be said about the data?
The question is not complete, so i have attached it.
Answer:
Option A - The data may not be reliable because there is an outlier.
Step-by-step explanation:
Looking at the question attached and the number of the gorrila vis - a - vis the time to interact, we can see that majority of the time to interact falls between 2.5 and 3.4.
However, we have a time of 8.3 days which is for gorrila 3.
This 8.3 is far higher than the range of the other values. Thus, we have an outlier because an outlier is a value is much more smaller or larger than most of the other values in a set of given data.
Thus, the data may not be reliable because there is an outlier.
Find the approximate volume of this prism (Image down below)
Answer:
about 62m^3
Step-by-step explanation:
PQRS is a parallelogram. Find the values of a and b. Solve for the value of c, if c=a+b.
Answer:
i. a = 7
ii. b = 7
iii. c = 14
Step-by-step explanation:
1. In a parallelogram, the pair of opposite sides are equal, thus;
6a + 10 = 8a -4
4 + 10 = 8a - 6a
14 = 2a
Divide both sides by 2,
a = 7
2. <SPQ + <PSR = [tex]180^{0}[/tex]
(18b - 11) + (9b + 2) = [tex]180^{0}[/tex]
18b + 9b + 2 -11 = [tex]180^{0}[/tex]
27b -9 = [tex]180^{0}[/tex]
27b = [tex]180^{0}[/tex] + [tex]9^{0}[/tex]
27b = [tex]189^{0}[/tex]
Divide both sides by 27,
b = 7
Therefore,
c = a + b
= 7 + 7
= 14
c = 14
Clarissa and Shawna, working together, can paint the exterior of a house in 6 days. Clarissa by herself can complete this in 5 days less than Shawna. how long will it take Clarissa to complete the job by herself?
Answer:
Clarissa will take 10 hours by herself
Step-by-step explanation:
Let s = time for shawna
s-5 = time for clarissa
The formula for determining the time is
1/a + 1/b = 1/c where a and b are the times alone and c is the time together
1/s + 1/(s-5) = 1/6
Multiply each side by 6s(s-5) to clear the fractions
6s(s-5) ( 1/s + 1/(s-5)) = 1/6 *6s(s-5)
Distribute
6(s-5) + 6s = s(s-5)
Distribute
6s -30 +6s = s^2 -5s
Combine like terms
12s -30 = s^2 -5s
Move everything to the right
0 = s^2 -5s -12s +30
0 = s^2 -17s +30
Factor
0 = ( s-15) (s-2)
Using the zero product property
s-15 =0 s-2 =0
s =15 s=2 ( This is not a reasonable answer since it is less than the time together)
s=15
s-5 = 10
Clarissa will take 10 hours by herself
Find all complex numbers $z$ such that $z^4 = -4.$
Note: All solutions should be expressed in the form $a+bi$, where $a$ and $b$ are real numbers.
Converting -4 to polar form gives [tex]-4=4\exp(i\pi)[/tex].
Then the 4th roots of -4 would be the numbers
[tex]4^{1/4}\exp\left(i\dfrac{\pi+2k\pi}4\right)[/tex]
where k is taken from {0, 1, 2, 3}.
So we have
[tex]z_1=4^{1/4}\exp\left(\dfrac{i\pi}4\right)=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)=1+i[/tex]
[tex]z_2=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4\right)=-1+i[/tex]
[tex]z_3=\sqrt2\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=-1-i[/tex]
[tex]z_4=\sqrt2\left(\cos\dfrac{7\pi}4+i\sin\dfrac{7\pi}4\right)=1-i[/tex]
what is the area of the shaded region?
Answer:
330.00cm²
Step-by-step explanation:
find the area of both circles and subtract the smaller one from the bigger one.
area of a circle= πr²
π wasn't given so I will use 22/7
so area of the bigger circle = 22/7 × 11²
=22/7 × 121
=380.28cm²
area of the small circle=22/7 × 4²
= 22/7 × 16
= 50.28cm²
Area of the shaded portion = 380.28 - 50.28
= 330.00cm²
An isosceles triangle has a side that measures 12 inches. What is the length of the hypotenuse
Answer:
[tex] \boxed{12 \sqrt{2} }[/tex]
Step-by-step explanation:
Isosceles triangle are those triangle which have two equal sides.
Perpendicular ( p ) = 12 inches
Base ( b ) = 12 inches
Hypotenuse ( h ) = ?
Now,Using Pythagoras theorem,
[tex] \mathsf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
Plug the values
[tex] \mathsf{ {h}^{2} = {12}^{2} + {12}^{2} }[/tex]
Evaluate the power
[tex] \mathsf{ {h}^{2} = 144 + 144}[/tex]
Calculate the sum
[tex] \mathsf{ {h}^{2} = 288}[/tex]
Squaring on both sides
[tex] \mathsf{h = 12 \sqrt{2} }[/tex]
Hope I helped!
Best regards!
Help please, I would really appreciate it. :)
Answer:
9, 13, 17, 21
Step-by-step explanation:
If x=2,
y=1+4(2)
y=9
This goes on, like a pattern. If x increases by 1, y inreases by 4. So, if y=3, x=13. If x=4, y=17, and so on.
Which graph has a slope of 4/5?
Answer:
[tex]\boxed{ Graph. B}[/tex]
Step-by-step explanation:
Hey there!
Well slope is aka rise/run,
so starting at the red dot and rising 4 units an ruing to the right 5 units,
graph b is the correct answer.
Hope this helps :)
Graph B has a slope of 4/5.
How is a slope calculated?Slope is calculated with the aid of finding the ratio of the "vertical change" to the "horizontal alternate" among (any) distinct factors on a line.
What is a slope in a straight line?Typically, the slope of a line offers the measure of its steepness and path. The slope of an instant line among two factors says (x1,y1) and (x2,y2) may be without problems decided by finding the difference between the coordinates of the points. The slope is commonly represented by using the letter 'm'.
Learn more about slope here https://brainly.com/question/1884491
#SPJ2
high reward low risk claim ur prize and help with math
the two lines are parallel, the angle they make should be equal and one angle is common so the triangles are similar by AAA.
Now the ratio of sides are [tex] \frac{20+8}{20}=\frac{x+18}{x}[/tex]
use divideno, [tex]\frac8{20}=\frac{18}x[/tex]
and then inverse the whole equation to get [tex]x=20\times\frac{18}{8} \implies x= 45[/tex]
Answer:
[tex]\Large \boxed{\mathrm{B) \ 45}}[/tex]
Step-by-step explanation:
We can solve the problem using ratios.
[tex]\displaystyle \frac{x}{20} =\frac{x+18}{20+8}[/tex]
Cross multiply.
[tex]20(x+18)=x(20+8)[/tex]
Expand brackets.
[tex]20x+360=28x[/tex]
Subtract 20x from both sides.
[tex]360=8x[/tex]
Divide both sides by 8.
[tex]45=x[/tex]
Look at the figure below: Triangles ABC and BDC have a common base BC. E is the point of intersection of BD and AC. AE = EC and ED = BE Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? HELPPPPP MEEEEEE WILL GIVE BRAIN POINTS
Answer:
AEB and CED
Step-by-step explanation:
Given the two pairs of congruent sides, you now use the vertical angles as the pair of congruent included angles, <AEB and <DEC.
The congruent triangles are:
AEB and CED
Answer:
B- Triangle AEB and triangle CED
Step-by-step explanation:
I took the test and it was correct
What is the perimeter (in centimeters) of a rectangle with length 4.5 cm and width 8.2 cm
Answer:
25.4 cm
Step-by-step explanation:
will make it simple and short
2*b + 2*h
2*4.5 + 2*8.2 = 25.4 cm
Hey there! I'm happy to help!
The perimeter is the distance around the rectangle.
In a rectangle, there are two pairs of opposite sides, and those opposite sides are equal. They are known as the length and the width.
In a rectangle, you have two sides that have the same length and two that have the same width. If you add these all up, you get the perimeter.
If our length is L and our width is W, we can write this equation.
P=2L+2W
So, we can plug in our lengths and widths to find the perimeter!
P=2(4.5)+2(8.2)
P=9+16.4
P=25.4
Therefore, our perimeter is 25.4 cm.
Have a wonderful day! Feel free to message me if you have any questions! :D
Simplify 3 x times the fraction 1 over x to the power of negative 4 times x to the power of negative 3.
Answer:
3x^2
Step-by-step explanation:
Given:
(3x) * {(1/x)^-4 }* (x^-3)
=(3x) * {1 ÷ (1/x)^4} * {1/x^3}
=(3x) * {1(x/1)^4} * (1/x^3)
=(3x) * (x^4) * (1/x^3)
=(3x) (x^4) (1) / x^3
Multiply the denominators
=3x^5 / x^3
Can also be written as
=3*x*x*x*x*x / x*x*x
Divide the x
= 3*x*x / 1
=3x^2
Simplify the following: a) [ -6 +22 – 6 + 8 ] ÷ ( -9 ) b) 400 ÷ { 40 – (-2) -3 – ( -1)} c) 40 x -23 + 40 x -17 d) 1673 x 99 – (-1673) e) 490 x 98
Step-by-step explanation:
a) [ -6 +22 – 6 + 8 ] ÷ ( -9 )[ -6 +22 – 6 + 8 ] = 18
18 ÷ (-9) = -2
b) 400 ÷ { 40 – (-2) -3 – ( -1)}{40 – (-2) -3 – ( -1)} = { 40 + 2 -3 + 1} = 40
400 ÷ 40 = 10
c) 40 x -23 + 40 x -17(40 x 23) + (40 x -17)
920 + (-680)
= 240
d) 1673 x 99 – (-1673)(1673 x 99) + 1673
1673 x 100
= 167300
e) 490 x 98 = 48020Hope this helps ^-^
___H2 + ___Br2 → ___HBr
Answer:
H2+Br2 HBrH2+Br2. 2HBrwhat is an equivalent expression for 3a + 5 ?
Answer:
Equivalent expression:
6a + 10
or
9a + 15
the cylindrical part of an architectural column has a height of 305 cm and a diameter of 30 cm find the volume of the cylindrical part of the column.use 3.14 for pi and round youre answer to the nearest cubic centimete if needed.
Answer:
215483 cm³
Step-by-step explanation:
Formula for volume of a cylinder = πr² · h
radius = 1/2diameter
1. Set up the equation
(3.14)(15²)(305)
2. Solve
215482.5
rounded to the nearest cubic centimeter = 215483 cm³
Answer:
215483 cm³
Step-by-step explanation:
credit goes to person up top
3. A ship sails 35 km on a bearing of 042º.
a) How far north has it travelled?
b) How far east has it travelled?
4 A ship sails 200 km on a bearing of 243.7°
a) How far south has it travelled?
b) How far west has it travelled?
3 and 4 please
Answer:
3(a). The ship travelled in north is 26.0 km.
(b). The ship travelled in east is 23.4 km.
4(a). The ship travelled in south is -88.61 km.
(b). The ship travelled in west is -179.29 km.
Step-by-step explanation:
Given that,
(3). Distance = 35 km
Angle = 42°
Let distance in north is y km.
We need to calculate the distance
Using vertical component
[tex]y = d\cos\theta[/tex]
Put the value into the formula
[tex]y = 35\cos42[/tex]
[tex]y=26.0\ km[/tex]
Let distance in east is x km
We need to calculate the distance
Using horizontal component
[tex]x =d\sin\theta[/tex]
Put the value into the formula
[tex]x = 35\sin42[/tex]
[tex]x=23.4\ km[/tex]
(4). A ship sails 200 km on a bearing of 243.7°
Let distance in south is y km.
We need to calculate the distance
Using vertical component
[tex]y = d\cos\theta[/tex]
Put the value into the formula
[tex]y = 200\cos243.7[/tex]
[tex]y=-88.61\ km[/tex]
Let distance in west is x km
We need to calculate the distance
Using horizontal component
[tex]x =d\sin\theta[/tex]
Put the value into the formula
[tex]x = 200\sin243.7[/tex]
[tex]x=-179.29\ km[/tex]
Hence, 3(a). The ship travelled in north is 26.0 km.
(b). The ship travelled in east is 23.4 km.
4(a). The ship travelled in south is -88.61 km.
(b). The ship travelled in west is -179.29 km.
It fractional equation should be solve in quadric equation
x+ 7/x =9
Answer:
0.86, 8.14
Step-by-step explanation:
x+ 7/x =9, where x≠0x^2+7= 9x multiply each term by x to get rid of fractionx^2 - 9x + 7= 0 solving as normal quadratic equationx= (9 ± √ (9^2 - 4*7)) / 2x= (9 ± √53) /2 x≈ 0.86x≈ 8.14If the initial amount of iodine-131 is 537 grams , how much is left after 10 days?
Answer:
225.78 grams
Step-by-step explanation:
To solve this question, we would be using the formula
P(t) = Po × 2^t/n
Where P(t) = Remaining amount after r hours
Po = Initial amount
t = Time
In the question,
Where P(t) = Remaining amount after r hours = unknown
Po = Initial amount = 537
t = Time = 10 days
P(t) = 537 × 2^(10/)
P(t) = 225.78 grams
Therefore, the amount of iodine-131 left after 10 days = 225.78 grams
Find the equation of a line given the point and slope below. Arrange your answer in the form y = mx + b, where b is the constant. (1, 3) m = 2
Answer:
y = 2x + 1
Step-by-step explanation:
Given a point and the slope, we can plug in these values into the equation to find the value of b:
y = mx + b
3 = 2(1) + b
3 = 2 + b
1 = b
Plug b into the equation:
y = 2x + 1
Answer:
y = 2x + 1
Step-by-step explanation:
What is the equation for the line of symmetry in this figure?
Answer:
y=3
Step-by-step explanation:
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 9 cubic feet and the volume of each large box is 24 cubic feet. A total of 24 boxes of paper were shipped with a combined volume of 441 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
Answer:
9 small boxes and 15 large boxes
Step-by-step explanation:
x = small box
y = large box
x + y = 24
9x + 24y = 441
-9x - 9y = -216
15y = 225
y = 15
x + 15 = 24
x = 9
Answer:
Let x be the small boxes
Let y be the large boxes
x+y=24
9x+24y=441
Step-by-step explanation:
The phone company offers to long-distance plans the first charges a flat value of five dollars per month plus $.99 each minute used and the second charge is $10 a month plus $.79 for each minute used if X represents the number of minutes use each month which system each of equations represent the amount of money why are you spin
Answer:
The systems of equation for the amount spent are as follows
[tex]Y= 0.99x+5[/tex]
[tex]Y= 0.79x+10[/tex]
Step-by-step explanation:
In this problem we are expect to give a model or an equation that represents the amount of money spent per month given a fix subscription amount and a variable fee which is based on extra minutes spent.
let Y represent the amount of money spent in total for the month
The first case:
Subscription =$5
charges per minutes = $0.99
therefore the amount spent can be modeled as
[tex]Y= 0.99x+5[/tex]
The second case:
Subscription =$10
charges per minutes = $0.79
therefore the amount spent can be modeled as
[tex]Y= 0.79x+10[/tex]
