The first number is 8.33 percent more than the second number.
Let m be the first number, n be the second number and p be the third number.
Two numbers are respectively twenty percent and ten percent more than a third number.
m = (100 + 20)% of p
m = 120 percent of p
m = 120 % of p
m = (120 / 100) × p
m = 1.2 p
And the second number would be,
n = (100 + 10)% of p
n = 110 percent of p
n = (110 / 100) × p
n = 1.1 p
We need to find by how much number the first number more than the second.
Consider the difference,
1.2 p - 1.1p = 0.1 p
So the required percentage noting but the difference is what percent of the first number.
(0.1 p / 1.2 p) × 100 = 8.33%
Therefore, the first number is 8.33 percent more than the second number.
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Question 1 (1 point)
write an equation (slope-intercept form) of the line
passing through the point (-20, 4)
that is perpendicular to the line
2x + 5y = 10.
y =
Blank 1:
The an equation (slope-intercept form) of the line is 2y = 5x + 108.
What is described as the slope-intercept form?A line's equation can be written in a variety of ways, each of which is valid. The slope-intercept form of such a line is a way of writing a line's equation so that the slope and y-intercept are easily recognizable. The slope of the line is its steepness, and the y-intercept is the point where line intersects the y-axis.For the given question;
The equation of the perpendicular line is given as 2x + 5y = 10.
The passing points of the line (-20, 4)
(x₁, y₁) = (-20, 4)
The equation of line in slope-intercept form is given as; y = mx + c.
Where, c is the y intercept and m is the slope.
The relation of the slope of two perpendicular lines are-
m₁ x m₂ = -1
The equation of line is-
2x + 5y = 10; find m₁
5y = -2x + 10
y = (-2/5)x + 10
Comparing with standard form.
m₁ = (-2/5)
Then, m₁ x m₂ = -1
(-2/5) x m₂ = -1
m₂ = 5/2
Put in the equation of line;
y - y₁ = m(x - x₁)
Put the values;
y - 4 = (5/2) (x + 20)
Solving;
2y - 8 = 5x + 100
2y = 5x + 108
Thus, the an equation (slope-intercept form) of the line is 2y = 5x + 108.
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PLS HELP I NEED IT IM GOING TO GET AGRDE ON THIS PLE HELP
Answer: The answer is 6 presents
Step-by-step explanation: Here is the math: He used 25 cm of tape to wrap 5 presents, so that is 25/5= 5 cm of tape per present. Now you take 30 cm of tape and divide it by 5 = 6 presents wrapped with 30 cm of tape.
What is the reason for each step in the solution of the equation?
4x−1=−2(x+1)
11 of 25 students in class own a dog.What is the ratio of students who own a dog to students in the class?What is the ratio of students who own a dog to students who DON'T own a dog?
Answer:
(a)11:25
(b)11:14
Explanation:
he total number of students in the class = 25
The number of students that own a dog = 11
do not 25-11=14
(a)The ratio of students who own a dog to students in the class will be:
[tex]=11\colon25[/tex](b)The ratio of students who own a dog to students who DON'T own a dog will be:
[tex]=11\colon14[/tex]I WILL GIVE YOU BRAINLIEST PLEASE HELPPPP
What’s the correct answer answer now for brainlist
the answer to this would be D
I need help because i can’t seem to understand it
sinA = 0.37
cosA = 0.93
tanA = 0.40
secA = 1.08
cscA = 2.69
cot A = 2.50
Explanation:Given that a = 4, b = 10. To obtain c, we use the Pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ =4^2+10^2 \\ =116 \\ c=\sqrt{116}=10.77 \end{gathered}[/tex]Now
[tex]\begin{gathered} \sin A=\frac{Opposite}{hypotenuse}=\frac{a}{c} \\ \\ =\frac{4}{10.77}=0.37 \end{gathered}[/tex][tex]\begin{gathered} \cos A=\frac{adj}{hyp}=\frac{b}{c} \\ \\ =\frac{10}{10.77}=0.93 \end{gathered}[/tex][tex]\begin{gathered} \tan A=\frac{opp}{adj}=\frac{a}{b} \\ \\ =\frac{4}{10}=0.40 \end{gathered}[/tex][tex]secA=\frac{1}{cosA}=\frac{10.77}{10}=1.08[/tex][tex]cscA=\frac{1}{sinA}=\frac{10.77}{4}=2.69[/tex][tex]cotA=\frac{1}{tanA}=\frac{10}{4}=2.50[/tex]Find the LCD for:
2/x²-x-12, 1/x² - 16
The LCD for the expressions is (x + 3)(x² - 16)
How to calculate the LCD for the expressions?The expressions are given as
2/x² - x - 12 and 1/x² - 16
Write out the denominator of the expressions
This is represented as
x² - x - 12 and x² - 16
Factorize the above denominators
This gives
x² - x - 12 = (x+3)(x-4)
x² - 16 = (x-4)(x+4)
Multiply the common factors without repetition
LCD = (x+3)(x-4)(x+4)
Evaluate the products
LCD = (x + 3)(x² - 16)
Hence, the LCD in this case is (x + 3)(x² - 16)
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What is the rate of return when 10 shares of Stock
A, purchased for $30/share, are sold for $380? The
commission on the sale is $6.
Rate of Return = [?] %
Give your answer as a percent rounded to the
nearest tenth.
Answer:
24.7%
Step-by-step explanation:
You want to know the rate of return if 10 shares of stock purchased at $30 per share are sold for $380 with a commission on the sale of $6.
ReturnThe net proceeds from the sale will be ...
$380 -6 = $374
Rate of returnThe percentage change in stock value is ...
% change = (proceeds/cost -1) × 100%
% change = (374/300 -1) × 100% ≈ 24.7%
The rate of return on the stock is about 24.7%.
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heyyyyyyyyyyyyyyyyyyy
The statement says that Kristen read a total of 18 books over 3 months.
And then ask us to calculate the numbers of books that he will read in a period of 5 months.
In order to calculate that, we must determine first how many books Kristen read in a month.
# of books that Kristen read in a month = 18 books / 3 months = 6 books / month
So, in order to calculate the number of books that Kristen read in 5 month, we just multiply:
5 months * 6 books/month = 30 books (answer)
The parent function f(x)=3√x is transformed to g(x)=f(x+2)-4 which is the graph of g
This graph shows a proportional relationship.500450400350300Words2502001501005023455670010Time (minutes)What is the unit rate shown by the graph?75 minutes per word1.25 minutes per word1.25 words per minute75 words per minute
In the graph we can see that the person wrote 300 words after 4 minutes. so the rate is:
[tex]\frac{300}{4}=75[/tex]75 words per minute
If 37% of high school students said that they exercise regularly, find the probability that 5 randomly selected high school students will say that they exercise regularly. Would you consider this event likely or unlikely to occur?
Very unlikely to occur
1) In this problem, let's find the binomial probability of that event to take place.
[tex]\begin{gathered} P(X=5)=\binom{5}{5}(0.37)^5(1-0.37)^{5-5}= \\ P(X=5)=1\cdot(0.37)^5(1-0.37)^{5-5}= \\ P(X=5)=0.37^5\mleft(0.63\mright)^{5-5} \\ P(X=5)=0.0069343957 \end{gathered}[/tex]2) Note the binomial probability of that event happening is very very low.
3) So we can state that this event is very unlikely to occur
Which statement is true regarding the graphed functions?
On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 6, 0) and the y-axis at (0, 6). A straight blue line with a negative slope, labeled f of x, crosses the x-axis at (negative 0.75, 0) and the y-axis at (0, negative 2).
The following statement is true about the functions f(x) and g(x):
f(–2) = g(–2)
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the true statement about the functions?A system of linear equations is a collection of at least two linear equations.
In this case, the system of functions is given as
Functions f(x) and g(x)
From the attached graph, we can see that:
The values of the function f(x) at f(2), or f(4) do not have a match to the function g(x) at g(2) or g(4).
However, the functions intersect at x = -2
This means that f(-2) = g(-2)
Hence, the true statement about the functions is f(–2) = g(–2)
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Complete question
Which statement is true regarding the graphed functions?
See attachment
f(4) = g(4) f(4) = g(–2) f(2) = g(–2) f(–2) = g(–2)
−5x≤−15 or 7x−17≥32 please help me!!! This is due tonight and I need to get my grade up because I have under 60% in math class!! :(
Answer:1. x≥3 2. x≥7
Step-by-step explanation:
the waiters at a restaurant have agreed to give one third of their tips to the kitchen staff if a waiter collects 72$ how much does he end up keeping
Answer:
48
Since they are giving one third of it to the staff, they are keeping 2 thirds of it for themselves. Two thirds of 72 is 48.
Answer:
He keeps $48.
Step-by-step explanation:
If he gives away 1/3, he keeps 2/3 so that's what we need to calculate.
First find 1/3 of 72 by dividing by 3: 72/3=24
Now to find 2/3, multiply by 2: 24*2=48
(72/3)*2= $48
provide the correct reason for the statement in line 3. (please help)
The property that completes the proof is the segment addition postulate
How to determine the statement that represents the reason in the proof?The given parameters in the question are:
The point C is the midpoint of AE
BC = CD
The above implies that
AC = CE
And it also means that:
The line segment BC and the line segment CD have equal lengths
Using the above as a guide, we have the following equations
AB + BC = AC
CD + DE = CE
The above equations are true because of the segment addition postulate
This postulate states that:
For any two points (A and C) located on a line segment and a third point (b) between the initial points. The lengths between the points can be represented as AB + BC = AC
Hence, the statement that represents the reason 3 in the proof is (b) segment addition postulate
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Which equation represents this graph?
In the picture there is a graph with one line. The equation of the line is x+2y=1.
Given that,
In the picture there is a graph with one line.
We have to find the equation of the line in the graph.
The points on line are (2,1) and (0,3).
The slope of the line formula is
m=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m=(3-2)/(0-2)
m=1/(-2)
m=-1/2
The equation of the line formula is y=mx+b
Take point (2,1) as (x,y).
2=(-1/2)1+b
1=-1/2+b
b=1-1/2
b=2-1/2
b=1/2
The equation of the line is y=-1/2x+1/2
2y=-x+1
x+2y=1
Therefore, the equation of the line is x+2y=1.
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Which expression represents the distance between 14.6 and −5.2 on the number line?
A. |-5.2 + 14.6|
B. |5.2 - 14.6|
C. |14.6 - {-5.2}
Answer:
The correct expression is
C. |14.6 - (-5.2)|
Question
Two sides of a right triangle have lengths of 5 inches and 12 inches. Which of the following could be the
length, in inches, of the third side of the triangle?
A 3
B 8
C 13
D 17
Solve F(x) for the given domain. Include all of your work in your final answer. Submit your solution.
F(x) = x2 + 2
F(x - h) =
Based on the domain, the equation of the function f(x) is F(x - h) = x^2 - 2xh + h^2 + 2
What is the domain of a function?The domain of the function is the set of input values of the graph
How to determine the solution of the function f(x)?The equation of the function is given as
F(x) = x^2 + 2
The required function is given as
F(x - h)
The above means that the value of x in the function F(x) = x^2 + 2 is x - h
i.e.
x = x - h
So, we substitute x - h for x in the equation F(x) = x^2 + 2
This gives
F(x - h) = (x - h)^2 + 2
Evaluate the exponent
So, we have
F(x - h) = x^2 - 2xh + h^2 + 2
The above equation cannot be further simplified
Hence, the solution of the function f(x) at the given domain is F(x - h) = x^2 - 2xh + h^2 + 2
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If 2 tan x 1- tan2 x 1 V3 then x can equal: + MT B. X= A. x=112 x- 7 C. X = ST D. X=
Solve for x
[tex]\frac{2\tan (x)}{1-tan^2(x)}=\frac{1}{\sqrt[]{3}}[/tex]Step 1: Let tan(x) represent y
[tex]\begin{gathered} \frac{2y}{1-y^2}=\frac{1}{\sqrt[]{3}} \\ \text{cross multiply} \\ 1-y^2=2\sqrt[]{3}y \\ y^2+2\sqrt[]{3}y-1=0 \end{gathered}[/tex]Step 2: Using quadratic equation solve for y
[tex]\begin{gathered} y^2+2\sqrt[]{3}y-1=0 \\ y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=1,b=2\sqrt[]{3},c=-1 \\ y=\frac{-2\sqrt[]{3}\pm\sqrt[]{(2\sqrt[]{3})^2-4(1)(-1)}}{2(1)} \\ y=\frac{-2\sqrt[]{3}\pm\sqrt[]{12+4}}{2} \\ y=\frac{-2\sqrt[]{3}\pm\sqrt[]{16}}{2} \\ y=\frac{2(-\sqrt[]{3}\pm2)}{2} \\ y=-\sqrt[]{3}\pm2 \end{gathered}[/tex]Since the y represents tan x
[tex]\begin{gathered} \tan \mleft(x\mright)=-\sqrt{3}-2,\: \tan \mleft(x\mright)=2-\sqrt{3} \\ x=\arctan \mleft(-\sqrt{3}-2\mright)+\pi n,\: x=\arctan \mleft(2-\sqrt{3}\mright)+\pi n \\ x\text{ in degrees} \\ \: x=-75^{\circ\: }+180^{\circ\: }n,\: x=15^{\circ\: }+180^{\circ\: }n \\ \: x=15^{\circ\: }+180^{\circ\: }n \end{gathered}[/tex]Therefore the correct answer is
[tex]x=\frac{\pi}{12}+n\pi[/tex]Hence the correct answer is Option B
What is the value of x?
Answer: Value of x is 16
Step-by-step explanation:
Triangle ABC and ADE are Similar Triangles using Angle-Angle-Angle similarity,
therefore,
[tex]\frac{AB}{BC}=\frac{AD}{DE}[/tex]
AB=x
BC=8
AD=x+6
DE=11
on substituting value,
[tex]\frac{x}{8}=\frac{x+6}{11}[/tex]
on cross multiplying,
11x = 8x+48,
subtracting 8x on both sides,
3x = 48,
dividing both sides by 3,
x=16
Therefore, value of x is 16
(2-√3)²=7-4√3
How we solve this question ?
Hurry answer please
Answer the question.
A juice drink contains 24% real fruit juice. Find the amount of real fruit juice in 8 ounces of the drink. (Include units in your answer. More information.)
Answer:
i think it is 24.76% of real jucie
Step-by-step explanation:
because the rest is not real jucie
Lin drew the following dilation of triangle AED and she made triangle ABC
What is The center of dilation is ?
The Scale factor for triangle AED to triangle ABC is?
1. A, as A is the shared vertex of both triangles. and 2. The original is ABC, and the dilated version is AED. as triangle ABC's half is represented by triangle AED.
How do you calculate a triangle's dilation?The following is a basic formula to determine a dilated figure's scale factor: Scale factor is equal to the difference between the dimensions of the old and new shapes.
What is the triangle's center of dilation?A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.
The center, which may be found within, outside, or on a figure, is the only invariant (constant) point under a dilation (k 1).
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if RS equals 59 and ST equals 10x - 31 find x
The chord RS and chord ST subtends equal angles the center. So length of chord ST is equal to length of chord RS.
Determine the value of x.
[tex]\begin{gathered} RS=ST \\ 59=10x-31 \\ 10x=59+31 \\ x=\frac{90}{10} \\ =9 \end{gathered}[/tex]So value of x is 9.
Deluxe coffee is to be mixed with regular coffee to make at
least 43 pounds of a blended coffee. The mixture must
contain at least 12 pounds of deluxe coffee. Deluxe coffee
costs $6 per pound and regular coffee $5 per pound. How
many pounds of each kind of coffee should be used to
minimize costs?
Answer:
12 pounds of deluxe and 31 pounds of regular.
Step-by-step explanation:
$227 is the minimum cost.
Answer:
We have to minimize the cost of 51 pounds of blended coffee.
The mixture must contain 13 pounds of deluxe coffee.
Deluxe coffee costs $4 per pound while regular coffee costs $3 for the same amount.
So, we need to maximize the concentration of regular coffee in the blended coffee to minimize our costs, but we must mix 13 pounds of deluxe coffee in order to make the blended coffee as it is the condition given to us in the problem.
Hence, apart from this 13 pounds, all the rest weight in blended coffee should come from the regular one.
Hence, the amount of regular coffee we have to use = (51 - 13) = 38 pounds.
Now, the cost of the 51 pounds of blended coffee
38×3+13×4 = ₹166.
How do u determine the value of the ratio?
Answer:
Step-by-step explanation:
Divide data A by data B to find your ratio. In the example above, 5/10 = 0.5. Multiply by 100 if you want a percentage. If you want your ratio as a percentage, multiply the answer by 100.
What is the area, in square inches, of a square whose perimeter is 44 inches?
The area is 121 square inches
Explanation:The perimeter of a square is given as:
P = 4l
where l is the length of its sides
Given that the perimeter is 44 inches, we have:
44 = 4l
l = 44/4 = 11
The length of it's sides is 11 inches.
The area is given as:
[tex]\begin{gathered} A=l^2 \\ \\ =11^2 \\ =121 \end{gathered}[/tex]The area is 121 square inches.
Answer:121 square inches.
Step-by-step explanation: