Sally buys a hand bag. there was a discount of 23%. If sally paid $20.02, what was the original price?
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The segment image is drawn from F(2, 9) to H(10, 1) with point G on the segment. What coordinates for point G will divide image so that is imageis 3:5?
What is the graph of y = x - 3 (shown below) translated up 2 units?
Answer:
The graph is that one which corresponds to the equation y = x-1. The graph is shown in the image below.
Step-by-step explanation:
Translate a linear curve means to move the whole curve up or down, where the final line will be in parallel to the original curve.
For translate the graph up to 2 unit, it must to be summed 2 unit in the right member of the original equation:
[tex] y = (x-3) + 2 [/tex]
[tex] y = x-3 + 2 [/tex]
[tex] y = x-1 [/tex]
Explain how to tell 100/105 is not in simplest form without finding all the factors
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1. The population of Linton is 12 times as great as the population of Ellmore. The combined population of both towns is 9,646 people. What us the population of Linton?
2. Jessie bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jessie bought?
For which data representation is the median the better measure of center
Answer with explanation:
Mean is sum of all the observation divided by total number of observation, where as median is middlemost observation of the data set, while mode is most occurring variate or data value in the data set.
1. Variate or Data set which is represented in Histogram is
3,8,4,8,3
Arranging it in ascending order, we get
3,3,4,8,8
Data is skewed right.So, Mean >Median>Mode
Mean =5.2
Number of observation is 5. So,Median will be Middle term,that is third term equal to 4.
Mode =3 or ,8 which will be equal to 3,as data is skewed right.
→Mean gives better representation of data set,because, 5.2-3=2.2 and, 8-5.2=2.8
2. Variate or Data set which is represented through dots is
2, 2, 3,5,5
Arranging it in ascending order, we get
2,2,3,5,5
Data is skewed right.So, Mean >Median>Mode
Mean=3.4
Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.
Mode =2 or 5 which will be equal to 2,as data is skewed right.
→Mean gives better representation of data set,because, 3.4-2=1.4 and, 5-3.4=1.6
3. Variate or Data set which is represented in Histogram is
6,2,6,2,6
Arranging it in ascending order, we get
2,2,6,6,6
Data is skewed left.So, Mean <Median<Mode
Mean=4.4
Number of observation is 5. So,Median will be Middle term,that is third term equal to 6.
Mode =6
→Mode gives better representation of data set.
4.Variate or Data set which is represented through dots is
1,3,4,3,1
Arranging it in ascending order, we get
1,1,3,3,4
Data is skewed left.So, Mean <Median<Mode
Mean=2.4
Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.
Mode =1 or 3,data is skewed left,so mode =3
Here, in this data set, both mode and median are better measure of center than Mean,as there are two modes in the data set, so choosing median as measure of center,because data is skewed left,
For ,Option 4: Median is the better measure of center.
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Using the transformation T: (x, y) (x + 2, y + 1). Find the distance named.
Find the distance CA (the answer must be in the square root form)
Find the equatio of the line tht contains the point (5,6) and is perpendicualr to the line 4x+2y=2
Final answer:
The equation of the line that passes through the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.
Explanation:
The question asks us to find the equation of a line that passes through a given point and is perpendicular to a given line. To solve this, we first need to determine the slope of the given line, then find the perpendicular slope, and finally, use the point-slope form of a line to write the equation for our new line.
Here are the steps:
Find the slope of the given line. For the equation 4x + 2y = 2, we rearrange it to slope-intercept form (y=mx+b), which gives us y = -2x + 1. The slope is -2.
Since we want a line that is perpendicular to the given line, we need the negative reciprocal of -2, which is 1/2.
Now we use the point-slope form of a line, y-y1 = m(x-x1), with point (5,6) and slope 1/2. This gives us y - 6 = 1/2(x - 5).
Solving for y to get the slope-intercept form, we multiply both sides by 2 to get rid of the fraction: 2y - 12 = x - 5, and then solve for y: y = 1/2x + 7/2.
The equation of the line that contains the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.
The graph below shows a line segment MN: Which of the following equations best represents the line segment MN?
y = −3x + 2
y = −2x + 1
y = −3x − 2
y = −2x − 1
Answer:
D. [tex]y=-2x-1[/tex]
Step-by-step explanation:
We have been given a line on coordinate plane. We are asked to find the equation of our given line.
First of all, we will find slope of our given line using points [tex](-2,3)[/tex] and [tex](0,-1)[/tex] in slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where,
[tex]y_2-y_1[/tex] = Difference between two y-coordinates,
[tex]x_2-x_1[/tex] = Difference between two x-coordinates of same y-coordinates.
Upon substituting our given values in slope formula, we will get:
[tex]m=\frac{-1-3}{0--2}[/tex]
[tex]m=\frac{-4}{0+2}[/tex]
[tex]m=\frac{-4}{2}[/tex]
[tex]m=-2[/tex]
Now, we will use slope-intercept form of equation [tex]y=mx+b[/tex], where,
m = Slope of line,
b = The y-intercept.
Upon looking at our given graph, we can see that y-intercept is [tex]-1[/tex].
Therefore our required equation would be [tex]y=-2x-1[/tex] and option D is the correct choice.
Next school year 4 out of every 9 students plan to take an elective computer course if there are 2664 students at the high school how many computer students should the school plan for
1200 calories in 3 liters. Write a unite rate.
1)
What is the area of a sector with a central angle of 5π/7 radians and a diameter of 5.6 in.?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
2)
What is the area of a sector with a central angle of 4π/5 radians and a radius of 11 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
The area of the given sectors of circles is required.
The area of the sector is [tex]8.79\ \text{in}^2[/tex]
The area of the sector is [tex]151.98\ \text{cm}^2[/tex]
Area of sector[tex]\theta[/tex] = Central angle = [tex]\dfrac{5\pi}{7}\ \text{rad}[/tex]
d = Diameter = 5.6 in
r = Radius = 2.8 in
Area of a sector is given by
[tex]A=\dfrac{\theta}{2}r^2\\\Rightarrow A=\dfrac{\dfrac{5\times 3.14}{7}}{2}\times 2.8^2\\\Rightarrow A=8.79\ \text{in}^2[/tex]
[tex]\theta=\dfrac{4\pi}{5}\ \text{rad}[/tex]
r = 11 cm
[tex]A=\dfrac{\dfrac{4\times 3.14}{5}}{2}\times 11^2\\\Rightarrow A=151.98\ \text{cm}^2[/tex]
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A rectangle basin is being filled with water. The basin is 7 feet long, 12 feet wide, and 4 feet high. How much water is going to be needed to fill the basin.
A rectangular piece of sheet metal has a length that is 6 in. less than twice the width. a square piece 3 in. on a side is cut from each corner. the sides are then turned up to form an uncovered box of volume 1014 in. cubed find the length and width of the original piece of metal.
Determine the dimensions of the metal sheet by setting up and solving equations based on the given volume of the box and the relationship between its length and width.
Explanation:This problem can be tackled by using a bit of algebra and understanding volume calculations. We can use the equation for the volume of a box which is V=length*width*height. The problem gave us the volume of 1014 cu in. When a 3 in. square is cut from each corner of the rectangular piece of metal, the sides fold up to form the box, the height of the box becomes 3 in. This means we're missing the length and width of the box to solve for volume.
Since the length equals to twice the width minus 6 in., we can express the length as 2W - 6. Substituting these into the volume equation we get: 1014 = (2W - 6)(W)(3) which when simplified gives W, the width of the metal piece. Then substitute W into the length formula 2W - 6 to solve for the length.
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The sum of 555 consecutive integers is 505505505. What is the third number in this sequence?
Answer: The answer is 101!
Step-by-step explanation:
Call the first number in the sequence x
The next integer in the sequence is x + 1
The sum of the 5 consecutive integers is:
x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4) = 505
5x + 10= 505
5x = 495
x = 99
Since x is the first number, x + 2 is the third integer.
Thus, the third number in the sequence is 101
What is the value of h when the function is converted to vertex form?
Note: Vertex form is p(x)=a(x−h)^2+k .
p(x)=x^2−14x+29
H = ___
Which ordered pair (a, b) is a solution to the given system of linear equations?
A (1, 7)
B (3, 1)
C (11, –23)
D (23, –11)
Answer:
C. (11,-23)
Step-by-step explanation:
The given equations are
[tex]3a+b=10[/tex].....................equation 1
[tex]-4a-2b=2[/tex]...................equation 2
Multiply first equation by 2
[tex]6a+2b=20[/tex]
Now add this new equation to 2nd equation
[tex]6a-4a +2b-2b = 20+2[/tex]
[tex]2a = 22[/tex]
Divide both sides by 2
[tex]a=11[/tex]
We got a=11 , plug this value in anyone equation
3(11)+b=10[tex][/tex]
[tex]33+b=10[/tex]
Subtract 33 from both sides
[tex]b=-23[/tex]
So solution is (a,b) = ( 11,-23)
A= 48 degrees what is C
What is the approximate volume of a cone with a height of 9 ft and radius of 3 ft?
Use 3.14 to approximate pi, and express your final answer to the nearest tenth.
@phi,
John wants to buy a new bike that cost 337 and he already has saved 103. Estimate to find about how much more John needs to save to buy the bike
The value of x must be greater than _____.
What is the area of this figure?
Enter your answer in the box.
Answer:
[tex]\text {Area of figure is }44 units^2[/tex]
Step-by-step explanation:
Given the figure and we have to find the area of given figure.
Area of figure=ar(ABC)+ar(CDE)+ar(AEFH)+ar(GHF)
From the figure, dimensions according to square boxes can be written as
AE=HF=8 units, EF=3 units, BI=3 units, GH=2 units, AC=CE=4 units.
[tex]ar(ABC)=ar(CDE)=\frac{1}{2}\timesAC\times BI=\frac{1}{2}\times4\times3=6 units^2[/tex]
[tex]ar(AEFH)=HF\times EF=8\times 3=24 units^2[/tex]
[tex]ar(GHF)=\frac{1}{2}\timesHF\timesGH=\frac{1}{2}\times8\times 2=8units^2[/tex]
∴ [tex]\text {Area of figure is }44 units^2[/tex]
What is the following quotient? 2- sqrt 8 / 4 + sqrt 12
we have
[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}[/tex]
Multiply the numerator and denominator by the conjugate of the denominator
so
[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}*\frac{4-\sqrt{12}}{4-\sqrt{12}}=\frac{(2-\sqrt{8})(4-\sqrt{12)}}{4^{2}-(\sqrt{12})^{2}}\\ \\= \frac{2*4-2*\sqrt{12}-4*\sqrt{8}+\sqrt{12}*\sqrt{8}}{16-12}\\ \\=\frac{8-4\sqrt{3}-8\sqrt{2}+4\sqrt{6}}{4} \\ \\=2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]
therefore
the answer is
[tex]2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]
Use synthetic division to find the quotient and the remainder for the problem: (12x^4 + 5^3 + 3x^2 - 5)/(x+1)?,
To use synthetic division to divide a polynomial by a linear expression, follow the steps: arrange the terms, change the sign of the linear expression, bring down the coefficient, multiply and add, write the result, and determine the quotient and remainder.
Explanation:To use synthetic division to divide a polynomial by a linear expression, follow these steps:
Arrange the terms of the polynomial in descending order of their degrees.Change the sign of the linear expression you're dividing by.Write down the coefficient of the term with the highest degree of the polynomial and bring it down.Multiply this coefficient by the changed sign of the linear expression and write the result under the next coefficient.Add these two values together and write the result under the next coefficient. Repeat this process until you've reached the constant term.Write the final result as the quotient and the last value as the remainder.In this case, the quotient is[tex]9x^3 + 4x^2 + 5x + 2[/tex].
easy math problem 5pts
What is the slope of a line perpendicular to the line with equation y = 4x + 5?
The slope of a line perpendicular to the line with equation y = 4x + 5 will be, [tex]-\frac{1}{4}[/tex].
What is a slope of a straight line?A straight line is a combination of endless points joined on both sides of the point.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope 'm' of any straight line is given by:
The given equation in the problem is;
y = 4x + 5
The slope of the given equation is found from the standard equation of the straight line as;
y=mx+c
On comparing, we get, m = 4.
The perpendicular line slopes are reciprocals with the negative sign of each other.
Hence, the slope of a line perpendicular to the line with equation y = 4x + 5 will be, [tex]-\frac{1}{4}[/tex]
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How Many Toys Will Remain?
A small combination lock on a suitcase has 6 wheels, each labeled with the 10 digits 0 to 9.
How many digit combinations are possible if no digit is repeated? If digits can be repeated? If successive digits must be different?,
There will be, 590490 possible combinations.
What is combination?The number of different groups which can be formed from the available things can be calculated using combinations.
Given that, A small combination lock on a suitcase has 6 wheels, each labelled with the 10 digits 0 to 9.
We have 10 for the first wheel, but second wheel only has 9 options because 2nd number can't be the same as first. The third and fourth wheels also has 9 options for the same reason.
10x9x9x9x9x9 = 590490 combinations
Hence, There will be, 590490 possible combinations.
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Find the solution of this system of equations
-5x=-21+6y
-5x+y=-84