Answer:
x = 20.
Step-by-step explanation:
First, you should remember the relation:
Distance = Speed*Time.
First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.
We can write this as:
20km = (x km/h)*T
We know that the time is shortened by 12 minutes if the speed is increased by 5km/h
Rewriting these 12 minutes in hours (remember that 60min = 1 hour)
12 min = (12/60) hours = 0.2 hours
Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h
We can write this as:
20km = (x + 5 km/h)*(T - 0.2 h)
Then we have a system of two equations, and we want to find the value of x:
20km = (x km/h)*T
20km = (x + 5 km/h)*(T - 0.2 h)
First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:
20km/(x km/h) = T
Replacing that in the other equation we get:
20km = (x + 5 km/h)*(T - 0.2 h)
20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)
Now we can solve this for x.
Removing the units (that we know that are correct) so the math is easier to read, we get:
20 = (x + 5)*(20/x - 0.2)
We only want to solve this for x.
20 = x*20/x - x*0.2 + 5*20/x - 5*0.2
20 = 20 - 0.2*x + 100/x - 1
subtracting 20 in both sides we get:
20 - 20 = 20 - 0.2*x + 100/x - 1 - 20
0 = -0.2*x + 100/x - 1
If we multiply both sides by x we get:
0 = -0.2*x^2 + 100 - x
-0.2*x^2 - x + 100 = 0
This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:
[tex]x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2} = \frac{1 \pm 9 }{-0.4}[/tex]
Then the two solutions are:
x = (1 + 9)/-0.4 = -25
x = (1 - 9)/-0.4 = 20
As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.
x = 20
then the average speed initially is 20 km/h
What is the sum of the measures of the interior angles of an octagon?
Answer:
1080
Step-by-step explanation:
(n-2) × 180
(8-2) × 180= 1080
Find the lateral area of a cone with a diameter of 10 centimeters and a slant height of 9 centimeters round to the nearest tenth
Answer:
The lateral area of a cone is 141.4 square centimeters
Step-by-step explanation:
Mathematically, we have the formula for the lateral area of a cone as;
A = pi * r * l
where r is the radius of the cone and l
is the slant height of the cone
Mathematically, the radius is simply half the measure of the diameter
we have that as 10/2 = 5 cm
So substituting these values;
A = 22/7 * 9 * 5
A = 141.4 square centimeters
the numerator of a fraction is 2 less than the denominator . If one is added to its denominator ,it becomes 1/2 ,find the fraction.
tell me with full explanation
Answer:
numerator = 2 and denominator is 4
Step-by-step explanation:
let the denominator be x
numerator = x-2
according to the question
[tex]\frac{x-2}{x} = \frac{1}{2}[/tex]
do cross multiplication
x*1 = 2(x-2)
x = 2x -4
4 = 2x - x
4 = x
therefore denominator is 4
numerator = x-2
=4-2
=2
100 POINTS HELP! THIS IS A PROJECT. BUT AN ANSWER TOMORROW OR TODAY IS OKAY!
Describe how to find the terms mean, median, mode, and range of a group of numbers then, give examples. Make sure you include the data set (the group of numbers) you will be working with.
Answer: We will be working with the numbers 1-4, you can change the numbers to anything, just change the math.
The mean is the "average" of a set of numbers. Add up ALL the numbers, and then divide by how many numbers there are.
Ex. 1+2+3+4 then, 10/4 =2.5
The mode is the number that occurs most frequently in a set of numbers.
Ex. 1, 2, 2, 2, 3, 4, 2, 2, 4, : The mode would be 2.
The range is the difference between the smallest and highest numbers.
Ex. 1, 2, 3, 4, ,3, 2, 3, 4, : Put all the numbers in order, then subtract highest from lowest.
1,2,2,3,3,3,4,4
4-3=1 The range would be 1.
Answer:
The median is the middle. You add and divide for the mean. The mode is the one that appears the most. And the range is the difference in between. For example, the median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above. The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count. The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode! The difference between the highest and the lowest values in a set. Interval, also called range, a set of real numbers that includes all numbers between any two numbers in the set.
Allison measured her rectangular deck and found that it has dimensions of 512 yards by 8 yards. Both the length and the width may have a measurement error of up to 15%. What is the maximum possible area of Allison’s deck, rounded to the nearest thousandth of a square yard?
Answer:
5416.96 square yards
Step-by-step explanation:
To find the maximum possible area, increase the dimensions by 15%, since the measurement error may be up to 15%.
512(1.15) = 588.8
8(1.15) = 9.2
Find the area using the area formula, A = lw
Plug in the length and width:
A = lw
A = (588.8)(9.2)
A = 5416.96
So, the maximum possible area is 5416.96 square yards
can someone please help me with this?? please please please help me
Step-by-step explanation:
base is 12, hypotenuse is 20
so X² is h²-b²
so X=16
A carpenter needs three pieces of wood to complete a furniture. The longest piece must be twice the length of the middle-sized piece. The shortest piece must be 2 in. Shorter than the middle-sized piece. If a board 70 in. Long is to be used, then find the length of each piece.
Answer: Shortest piece = 16 in.
Middle piece = 18 in.
Longest pice = 36 in.
Step-by-step explanation:
Let x be the length of the shortest piece.
as per given, length of the middle piece = x+2
Length of the longest piece=2(x+2)
Total length = 70 in.
i.e. [tex]x+(x+2)+2(x+2)=70[/tex]
[tex]2x+2+2x+4=70\\\\4x+6=70\\\\4x=70-6\\\\4x=64\\\\ x=\dfrac{64}{4}\\\\ x=16[/tex]
Shortest piece = 16 in.
Middle piece = 18 in.
Longest pice = 2(18) in.
= 36 in.
What is the value of s?
Answer:
s = 53.3
Step-by-step explanation:
The square shows that the angle is 90 degrees, and is a shared angle. Therefore, the angles together make 90.
So, to get the unknown angle, you subtract the other angle by 90.
36.7 - 36.7 = 53.3
Brainliest for help please
Answer:
B
Step-by-step explanation:
Given
5 [tex]\frac{11}{40}[/tex]
= [tex]\frac{5(40)+11}{40}[/tex]
= [tex]\frac{200+11}{40}[/tex]
= [tex]\frac{211}{40}[/tex] → B
may I have help?! Thanks
Answer:
Hello! answer: A
Step-by-step explanation:
9 × 3 × 12 = 324 cm3
Answer:
324 cm cubed
Step-by-step explanation:
length×width×height. hope this helps!
Help me please it’s urgent
Answer:
(y-7) = 2(x-1)
Step-by-step explanation:
The point slope form of a line with slope m passing through (a,b) is
(y-b) = m(x-a)
here slope m = (7-3)/(1- -1) = 4/2 = 2
The point used was (1,7)
So the equation is
(y-7) = 2(x-1)
Note:
#11 is correct
Find the value of x.
Answer:
Step-by-step explanation:
The equation for this is
12(x + 1) = 10(10 - x) and
12x + 12 = 100 - 10x and
22x = 88 so
x = 44
Find each product. (30 Points!)
just need an answer
Find m∠E.
m∠E= ___∘
HELP 20 points
Answer:
55
Step-by-step explanation:
Angle C = Angle D (Corresponding Angles)
Therefore, BD//AC
Angle A = Angle B (Corresponding Angles)
=>6x-15=5x-1
=>6x-5x=-1+15
=>x=14
Angle B=5x-1
=5(14)-1
=70-1
=69
Angle D=4x
=4(14)
=56
Angle E=180-(Angle D+ Angle B) [Angle Sum Property]
=180-(69+56)
=180-125
=55
The distance to your cousin's house is 156 miles, and the distance to Dallas is 936 miles. If it took 3 hours to drive to your cousin's house, how long would it take to drive to Dallas?
Answer:
18 hours
Step-by-step explanation:
Calculation to determine how long would it take to drive to Dallas
First step is to calculate the Miles per hour, mph
Using this formula
Miles per hour, mph = Miles/hour
Let plug in the formula
Miles per hour=156 miles/3 hours
Miles per hour= 52 mph
Now let determine how long would it take to drive to Dallas
Using this formula
Distance overtime=Distance per miles/Miles per hour
Let plug in the formula
Distance overtime=936 miles/52 mph
Distance overtime= 18 hours
Therefore how long would it take to drive to Dallas will be 18 hours
The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2.50 each and bottles of water sell for $1.25 each. The club needs to raise at least $600 to cover the cost of renting costumes. The students can accept a maximum of 460 cans and bottles.
Write a system of inequalities that can be used to represent this situation.
The club sells 144 cans of lemonade. What is the least number of bottles of water that must be sold to cover the cost of renting costumes? Justify your answer.
Answer:
Step-by-step explanation:
The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2.50 each and bottles of water sell for $1.25 each. The club needs to raise at least $600 to cover the cost of renting costumes. The students can accept a maximum of 460 cans and bottles.
Write a system of inequalities that can be used to represent this situation.
The club sells 144 cans of lemonade. What is the least number of bottles of water that must be sold to cover the cost of renting costumes? Justify your answer
The value of ( - 2 / 3 ) will be ……
a) Will be negative but more than -1
b) Will be greater than 0
c) Will be a positive but less than 1
d) Will be positive but between 0.5 and 1
Answer:
will be -0.667 so the answer will be greater than 0
If f(x) = x2 – 3, then f(-1) is equivalent
to
Answer:
negative 5. or -5
Step-by-step explanation:
f(-1)= (-1)2-3
2 times -1= -2
-2-3= -5
f= -5
The vertices of quadrilateral DEFG are D(-2, 6), E(-4, 6), F(-6, 9), and G(-1, 9). Find the coordinates of the image of quadrilateral DEFG after a translation using the rule (x, y) → (x + 1, y - 6), a reflection over the x-axis, and a reflection over the y-axis
Answer:
the coordinates from all of the transformations are (1,0) (3,0) (5,-3) (0,-3)
Step-by-step explanation:
after using the first rule the coordinates were (-1,0)(-3,0)(-5,3)(0,3)
after reflectiong it over the x-axis (-1,0)(-3,0)(-5,-3)(0,-3)
after reflecting it over the y-axis it gave the final answer of (1,0) (3,0) (5,-3) (0,-3)
Darryl was shopping for a new camera. He found one with an original price of $125.00 and is marked 45% off. Sales tax for the item is 5.2%. What is the final price of the camera, including tax?
Answer:
$75.25
Step-by-step explanation:
Given data
Original price =$125
Discount =45%
Tax=5.2%
Let us find the discount
45/100*125
0.45*125
56.25
Let us find the tax
5.2/100*125
0.052*125
6.5
Hence the amount is
125-56.25+6.5
=$75.25
SOMEONE PLEASE HELP ME
Brainliest goes to whoever answers correctly
Answer:
The answer is C.
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Please help, will give BRAINLIEST
47 cm
Find the surface area of the triangular prism. The base of the
prism is an isosceles triangle.
37 cm
35 cm
24 cm
The surface area is cm².
Answer:
I'll setup the problem. But I have a question about the car the equal sides of the isosceles triangle. We'll go with 37 cm
Step-by-step explanation:
you will have to find the areas of the 2 isosceles triangles at either end and the 3 rectangles around the triangles.
Area for the triangles
[tex]A = \frac{1}{2} bh[/tex]
b = base of triangle, I'll guess it's 24cm
h = height (draw a line between the vertex of the equal sdes to the base at a right angle, then use Pythagoras to
find the height)
[tex]
h = \sqrt{ {37}^{2} - {( \frac{1}{2}b) }^{2}}[/tex]
area for rectangles
37x47 + 24x47 + 37x47
sorry it's a little sloppy (I'm on a cellphone)
comment if you have questions
Which line is the correct graph for y = -3/4x
A/ blue line
B/ purple line
C/ green line
D/ red line
Answer:D
Step-by-step explanation:
PLS ANSWER ASAP PLS DUE AT 9:35
Answer:
your answer is option B
Answer:
Your answer came out to be B.
Which is the correct data set for the box-and-whisker plot shown above?
Answer:
b
Step-by-step explanation:
10.5 rounded to 14.25 =15 so that is called natural number
Pls help me with this question
Answer:
its 6
Step-by-step explanation:
Answer:
Option D, 5 ounces
Hope this helps!
Solve the inequality, then identify the graph of the
solution.
2x – 1 > x + 2
N
X
-20
-10
0
10
20
r
-20
-10
0
10
20
-20
-10
0
10
20
-20
-10
0
10
20
Hope this is straightforward.
