Answer:
[tex]\frac{-100(100+x)}{(x-100)}[/tex]
Step-by-step explanation:
Let the original price of the item = p
Let there was q% of increase on the original value, so
the printed price of the item, [tex]C= p+p \frac{q}{100}=p(1+\frac{q}{100})[/tex]
After a price reduction of x%, the has its price increased to its original value, so,
[tex]C-C\times \frac {x}{100} =[/tex] original price + increased price
[tex]p(1+\frac{q}{100})-p(1+\frac{q}{100})\times \frac {x}{100} = p+p[/tex]
[tex](1+\frac{q}{100})-(1+\frac{q}{100})\times \frac{x}{100} =2[/tex]
[tex]-(1+\frac{q}{100})\times \frac{x}{100} =2-1-\frac{q}{100}[/tex]
[tex]-(1+\frac{q}{100})\times \frac{x}{100} =1-\frac{q}{100}[/tex]
[tex](1+\frac{q}{100})\times \frac{x}{100} =\frac{q}{100}-1[/tex]
[tex]\frac{x}{100}+\frac{q}{100}\times\frac{x}{100}-\frac{q}{100}=-1[/tex]
[tex]x+x \times \frac{q}{100}-q=-100[/tex]
[tex]q(\frac{x}{100}-1)=-100-x[/tex]
[tex]q=\frac{-100(100+x)}{(x-100)}[/tex]
Hence, the percent of the increase is [tex]\frac{-100(100+x)}{(x-100)}[/tex]
1. A small college requires its students to take at least one Mathematics course and at least one Science course. A survey of 140 of its students shows that:
60 completed their Mathematics requirement, 45 completed their Science requirement and 20 completed both Mathematics and Science requirements. Use a Venn diagram to find the number of students who had completed:
a. exactly one of the two requirements;
b. at least one of the requirements;
c. neither requirement.
Answer:
65
85
Step-by-step explanation:
Exactly one of the two requirement
Maths only = 45 - 20 = 25
Science only = 60 - 20 = 40
Exactly one = (25 + 40) = 65
B.) Atleast one :
(25 + 40 + 20) = 85
C) Neither :
140 - 85 = 55
Solve the system by substitution
Answer:
(x,y) = (-36,6)
Step-by-step explanation:
-6y=x
x+y=-30
x=-6y,
so -6y+y=-30
-5y=-30
y=6
x=-36
Hope this helps pls hit the crown :D
factor 64x² + 114x + 81
um idk how to do these and I'm not gonna learn please help. also I'm gonna have a lot more like this so if you can go through my questions and answer them if you know how... that would be great :)
3(1−9a)+22a=2(2a−9)−15
i need a step by step explanation please
Answer:a=4
Step-by-step explanation:
Expand the brackets. Collect like terms. Get the same values on each side so it’s easier to isolate a. Divide 9 from 9a so that u get a by itself and this gives u the answer if 36/9 or 4.
Answer:
a = 4
Step-by-step explanation:
first distrubute the 3 and then 2 in the equations to whatever is inside the parantheses:
3 ( 1-9a) + 22a = 2(2a-9) -15
3 - 27a + 22a = 4a - 18 - 15
then combine the terms:
3 - 5a = 4a -33
then isolate the variables and constants to one side, for example move the 5a to the right side of the equation and move the 33 to the left side of the equaiton and then simplfy
36 = 9a
divide both sides by 9
a = 4
As part of summer camp, Henry goes on a treasure hunt. He starts at the base of a tree and walks 180 feet due north. He then turns and walks 80 feet due east. (Hint: Draw a picture.)
How far is Henry from the tree? Round your answer to the nearest foot.
Answer:
hmmmmmmmmmmmmmmm
62
Step-by-step explanation:
find the values of x in [0,360) which satisfy 2cot^2x=-3cscx
Answer:
The values of x is -30 degrees and undefined
None of these values fall within the given range
Thus, no value within the given range is the solution to the equation
Step-by-step explanation:
Here, we want to find the value of x that works for the equation in the selected range
2cot^2x = -3csc x
Mathematically, from trigonometry;
cot^2x = csc^2x - 1
Substitute this above
2(csc^2x - 1)= -3csc x
let csc x = b
2(b^2-1) = -3b
2b^2 - 2 + 3b = 0
2b^2 + 3b - 2 = 0
2b^2 + 4b - b - 2 = 0
2b(b+ 2) - 1( b + 2) = 0
(2b-1)(b + 2) = 0
2b = 1
b = -2
b = 1/2 = 0.5
or b = -2
Recall;
csc x = b
x = csc^-1 b
x = csc^-1 0.5
x = undefined
Secondly;
b = -2
x = csc^-1 (-2)
x = -30 degrees
As we can see , between the points
0 ≤ x < 360
None of our answers fall in these range
nothing sorry.......
Answer:
ok
Step-by-step explanation:
well thats good
Bill wanted to try out different water craft he went 62 mikes downstream in a motor boat and 27 mikes down stream on a jest ski his speed on the jet ski was 10 mph faster than the motor boat bill spent a total of 4 hours on the water what was his speed in the motor boat
Answer:
The speed on motorboat is 20 mph
Step-by-step explanation:
here, we want to find the speed on the motorboat
if he has a speed of x mph on the motor boat, his speed on the ski will be (x + 10) mph
The total hours is 4 hours
Mathematically; speed = distance/time
Time on ski is 27/x+ 10
Time on motor boat is 62/x
The addition of both is 4
Thus;
27/(x + 10) + 62/x = 4
27(x) + 62(x + 10) = 4(x)(x + 10)
27x + 62x + 620 = 4(x^2 + 10x)
89x + 620 = 4x^2 + 40x
4x^2 -49x-620 = 0
using the quadratic formula;
{-b ± √(b^2-4ac)}/2a
where a = 4, b = -49 and c = -620
= 49 ± √(-49)^2-4(4)(-620)/8
So we have
49+ 111/8 or 49-111/8
Speed cannot be negative
(49 + 111)/8
= 20 mph
Find the value of k so that the binomial (x – 3) is a factor of the function f(x) = 3x + 2x + kr - 3.
A. 32
B. -32
C. 13
D. -13
E. -22
!PLEASE HELP ME!
Tim thinks that the following expression will only yield values that are positive. x^2
Is Tim correct? Explain why or why not and provide three examples that prove whether Tim’s statement is correct.
Answer:
We conclude that Tim is correct when he says that the expression x² only yields values that are positive.
Step-by-step explanation:
Given the expression
x²
Plug in and checking x = 1 and x = -1 in the expressionPutting x = 1 in the expression
x²= (1)² = 1
Putting x = -1 in the expression
x²= (-1)² = 1
Thus, the expression yields the same output '1' when we enter x = 1, and x=-1.
Plug in and checking x = 2 and x = -2 in the expression
Putting x = 2 in the expression
x²= (2)² = 4
Putting x = -1 in the expression
x²= (-2)² = 4
Thus, the expression yields the same output '4' when we enter x = 2, and x=-2.
Plug in and checking x = 3 and x = -3 in the expressionPutting x = 3 in the expression
x²= (3)² = 9
Putting x = -1 in the expression
x²= (-3)² = 9
Thus, the expression yields the same output '9' when we enter x = 3, and x=-3.
The reason why the expression x² only yields positive values because the expression is in the square form, and the square of any number will always yield a positive value, no matter whether the input number is negative or positive.
Therefore, we conclude that Tim is correct when he says that the expression x² only yields values that are positive.
What is the equation of the line through the points (1, 1), (5, 4), (9, 7) and (13, 10)? y=3/4x+1/4
y=4/3x+1/3
y=3/4x−1/4
y=4/3x−1/3
Please help
Answer:
y = 3/4 x + 1/4
Step-by-step explanation:
line through the points (1, 1), (5, 4)
slope (m) = (4 - 1) / (5 - 1) = 3/4
y = mx + b b = y - mx ... for point (1 , 1)
b = 1 - 3/4 = 1/4
Line: y = 3/4 x + 1/4
check for point (9 , 7): 3/4 * 9 + 1/4 = 28/4 = 7
Classify the triangle. Check all that apply
Acute
Obtuse
Right
Scalene
Isoceles
Equilateral
Equiangular
None of the above
Answer:
The answer is Right because of the tiny square in the right corner and scalene because none of the three sides are equal in length.
Step-by-step explanation:
I hope this helps!
What is the length of segment V? Help please asap
Answer:
11
Step-by-step explanation:
8+6=14
14-3=11
please help look at the picture to see the question.
Answer: oo I did this in one quiz i thnk is c I put thaha
Step-by-step explanation:
Can someone tell me if these equations are parallel, perpendicular, intersect but not perpendicular, or coincide??
3x = 4y - 6
-4x = 3y - 6
When solving 7.6 ÷ 10, how is the decimal point moved?
1 place to the right
1 place to the left
2 places to the right
2 places to the left
Answer:
1 place to the left
Step-by-step explanation:
im pretty sure
please help this is due in 10 mins. 1
Can you please help me!? Explain and show work, please!
Answer:
no solution
Step-by-step explanation:
State if the following graph is discrete or continuous.
Please help me
Answer:
the graph is continuous
On a two-week job, a repairman works a total of 70 hours,He charges 75$ plus 40$ per hour. An equation shows this relationship, where x is the number of hours and y is the total fee. 3.Which number is the slope of the line shown by the equation? A .14 C .70 B. 40 D.75 4.Which number is the y-intercept A. 14 C. 70 B.40 D.75
Answer:
Which number is the slope of the line shown by the equation?
B. 40
Which number is the y-intercept
D.75
Step-by-step explanation:
The formula for the Equation of a line =
y = mx+b
where:
m is the slope and b is the y-intercept.
Hence, interpreting the above question:
On a two-week job, a repairman works a total of 70 hours,He charges 75$ plus 40$ per hour.
x is the number of hours and y is the total fee.
Hence, the Equation we have is:
y = $40 × x + 75
y = 40x + 75
Comparing with the Equation of a line formula
= y = mx+b
Therefore:
The slope of the line = 40
The y intercept = 75
Which value is equivalent to 7 multiplied by 3 multiplied by 2 whole over 7 multiplied by 5, the whole raised to the power of 2 multiplied by 7 to the power of 0 over 5 to the power of negative 3, whole to the power of 3 multiplied by 5 to the power of negative 9? (1 point)
Answer:
36/25
Step-by-step explanation:
7 multiplied by 3 multiplied by 2 whole over 7 multiplied by 5, the whole raised to the power of 2 multiplied by 7 to the power of 0 over 5 to the power of negative 3, whole to the power of 3 multiplied by 5 to the power of negative 9
((7 * 3 * 2)/(7 * 5))^2 * (7^0/5^-3)^3 * 5^-9 =
= (42/35)^2 * (1 * 5^3)^3 * 5^-9
= (6/5)^2 * 5^9* 5^-9
= 36/25 * 5^0
= 36/25
Q8
The table below shows the masses of 6 stick insects.
Name of Insect
Mass (m)
Arthur
7.825 9
Bethan
7.265 9
Clarry
8.15 9
Deena
7.455 9
Ethan
8.945 9
Freya
7.0159
(a) Write the name of the stick insect with m > 8.85 g
Answer:
(b) Write the name of the stick insect with m s 7.155 g
Answer:
(1
Score:
out of 16
Answer:
Ethan
Question b is incomplete
Step-by-step explanation:
Given the masses of the 6 insects below :
Name of Insect ______ Mass (m)
Arthur _____________ 7.8259
Bethan ____________ 7.2659
Clarry ______________8.159
Deena _____________ 7.4559
Ethan ______________ 8.9459
Freya ______________ 7.0159
Write the name of the stick insect with m > 8.85g
Mass (m) greater than 8.55 g
From the table :
8.945 > 8.55 ;
Hence, Ethan
(b) Write the name of the stick insect with m s 7.155 g
Question b isn't complete
josh sketched on a paper tree one-fifth of a foot tall. Then he drew the same tree on the wall two-thirds of a foot tall to decorate his room. how much larger than the sketch is the drawing.
Answer:
Step-by-step explanation:
Subtraction
Equation
2/3 - 1/5
Solution
20/30 - 6/30
14/30
7/15
The tree on the wall is 7/15 of a foot larger than the tree on paper.
Division
2/3 // 1/5 = 2/3 * 5/1 = 10/3 = 3 1/3
The tree on the wall is 3 1/3 times the tree in the drawing.
someone please help
Answer:
6
Step-by-step explanation:
PLS HELP FIRST ONE RIGHT GETS BRAINLEST |||| A produce stand is packing blueberries into 2/5 pound containers. How many containers can be filled with 60 pounds of blueberries? 1/150 1/24 24 150
Answer:
The answer is 24
Step-by-step explanation:
24
Answer:
24
Step-by-step explanation:
24
Sandra rollerbladed ALL DAY. When she got home, she realized that she had
traveled 93.5 miles in 8 hours. What is her unit rate?
her unit rate was about 11.7 miles per hour.
divide 93.5 by 8 to get answer.
hope this helps.
i could also be wrong.
Find the perimeter of the triangle
Answer:
60 ft
Step-by-step explanation:
(x+13) = (3x-1) = (6x-22) since the triangle is equaililateral
(x+13) = (3x-1) (we only need to chose 2)
-2x=-14
x=7
after this, we just need to plug in the number for x
3(7)-1= 20--->since the triangle has 3 congruent sides, they all have the distance, so 20x3=60
60FT
A bowl contains blueberries and strawberries. There are a total of 16 berries in the bowl. The ratio of blueberries to strawberries is 3 : 1. How many of each berry are in the bowl?
Answer:
12 blueberries and 4 strawberries
Step-by-step explanation:
We can try the guess method.
3:1 3 + 1 = 4 4 is too low. We need a sum of 16.
Multiply both numbers in the ratio by 2.
6:2 6 + 2 = 8 8 is still too low
Multiply both numbers in the ratio by 4.
12:4 12 + 4 = 16 16 is correct.
Answer: 12 blueberries and 4 strawberries
the order of the surd 7√8
Hello,
[tex]7 \sqrt{8} = \sqrt{7.7.8} = \sqrt{392} [/tex]
Býe býe.
please help! i need this done now<3
Answer:
25
Step-by-step explanation: