To add or subtract mixed numbers, first add or subtract the integer (whole number) portions of the mixed numbers, then add or subtract the fractional portions of the mixed numbers. Reduce the fractional portion of the answer to its lowest terms and combine it with the integer portion of the answer to get the final answer.
1. To add mixed numbers, first add the integer (whole number) portions of the two mixed numbers together. The result is the integer portion of your answer.
2. Next, add the fractional portions of the two mixed numbers together. If the fractional parts of the two mixed numbers have different denominators, you'll need to convert them to have the same denominator.
3. Reduce the fractional portion of your answer to its lowest terms. This is the fractional portion of your answer.
4. Combine the integer portion of your answer with the fractional portion of your answer to get the final answer.
5. To subtract mixed numbers, first convert the fractional portion of the subtrahend (the number being subtracted) to an equivalent fraction with the same denominator as the minuend (the number being subtracted from).
6. Subtract the integer portions of the two mixed numbers. The result is the integer portion of your answer.
7. Subtract the fractional portions of the two mixed numbers. Reduce the fractional portion of your answer to its lowest terms. This is the fractional portion of your answer.
8. Combine the integer portion of your answer with the fractional portion of your answer to get the final answer.
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Find a unit vector that has the same direction as the given vector. -3i + 7j
The unit vector that has the same direction as the given vector is[tex]& (3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].
The given vector(v) is -3i+7j
The unit vector is found by dividing the vector by its magnitude
Unit vector of [tex]$v=\frac{v}{\|v\|}$[/tex]
A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector.The formula of unit vector in the direction of a given vector is:
Unit Vector = Vector/Vector's magnitudeWe have to find the magnitude first
So,
[tex]& \|v\|[/tex] =[tex]\sqrt{(3)^{2}+(-7)^{2} } =\sqrt{9+49} =\sqrt{58}[/tex]
[tex]& \|v\|=\sqrt{58}[/tex]
The unit vector is:
The i, j, and k are the unit vectors in the directions of the x-axis, y-axis, and z-axis respectively in a 3-dimensional plane. i.e.,
|i| = 1|j| = 1|k| = 1[tex]$$\begin{aligned}& =(1 / \sqrt{58})(3 \mathrm{i}-7 \mathrm{j}) \\& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}\end{aligned}$$[/tex]
Therefore, the unit vector is [tex]& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].
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16/1 x 3/8 in simplest form
Answer: 6
Step-by-step explanation:
1. 16/1 × 3/8= 48/8
2. 48/8= 6
Please Help. I'll give Brainliest
Answer: Number 2
Step-by-step explanation:
Angle 1 + Angle 2 + Angle 3 = 180 degrees because its a straight line, so we immediately eliminate number 1 and 4 (Because it says the angles add up to 270). Next, we look at 2 and 3. 3 is incorrect because with just 1 right angle, QRST might be a rectangle. Therefore, number 2 is correct. :>
The monthly rents for five apartments advertised in a newspaper were $670, $670, $790, $1550, and $810. Use the mean, median, mode, and range of the rents to answer the following question: Which measure of central tendency best described the advertised rents? Calculate the four measures of central tendency and provide two to four sentences supporting the answer. (I already calculate the four, I just need help with picking out the best one. Range: 880. Mode: 670. Mean: 898. Median: 790)
The MEAN best describes the monthly rents.
The best one is Mean : 898
Now, According to the question:
The monthly rents for five apartments advertised in a newspaper were $670, $670, $790, $1550, and $810.
We are required to use the mean, median and mode to explain which measure of central tendency best describes the monthly rent.
The mean, median and mode (as calculated) are the measures of central tendency for the data set given.
This measures which value is closest to the center such that it can conveniently represent every other data. Observe carefully that the least value is 670 while the highest is 1550.
Also, observe that the value which is "more central" to both extremes is the mean.
The median is closer to the lowest value and much farther from the highest value.
The mode is actually at the lowest end of the data set.
However, the mean is safely between both ends. Its farther away from the least value than the median which means its moving closer to the "center" unlike the other two measures.
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THE AREA OF A SECTOR IS A = 384 in².
A. IF THE RADIUS IS 24 IN. , WHAT IS THE MEASURE OF THE CENTRAL ANGLE, IN RADIANS?
B. IF THE CENTRAL ANGLE MEASURES RADIANS, WHAT IS THE RADIUS OF THE CIRCLE? ROUND TO THE NEAREST HUNDREDTH.
A) The measure of the central angle is [tex]\frac{4}{3} \pi[/tex] .
B) The radius of the circle is 55.43 in.
A) We know,
The area of a sector is [tex]\frac{n}{2\pi } \pi R^{2}[/tex]
where n = the degree of the central angle of the sector
R = radius of the circle
Suppose, the measure of the central angle is x.
[tex]\frac{x}{2\pi } .\pi .24^{2} = 384\pi[/tex]
⇒ [tex]\frac{x}{2\pi } = \frac{384\pi }{576\pi }[/tex]
⇒ [tex]x = \frac{384\pi }{576\pi } * 2\pi[/tex]
⇒ [tex]x = \frac{4}{3} \pi[/tex]
So, the measure of the central angle is [tex]\frac{4}{3} \pi[/tex].
B) Suppose the radius of the circle is r in.
[tex]\frac{\pi /4}{2\pi } .\pi .r^{2} =384\pi[/tex]
⇒[tex]\frac{1}{8} .\pi .r^{2} =384\pi[/tex]
⇒ [tex]r^{2} = 384\pi / \frac{1}{8} \pi[/tex]
⇒ [tex]r^{2} = 3072[/tex]
As r > 0
So, r = 55.43
Hence, The radius of the circle is 55.43 in.
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In parallelogram ABCD, AB = 6x-4, CD = 5x + 1, and BC = 2x.
What is the perimeter of ABCD?
D
Perimeter =
A
units
C
B
Answer:
15x-3
Step-by-step explanation:
Recall that parallelograms, as the name implies, have two pairs of parallel sides. In this case, line segments AB and CD are parallel to each other, and then BC and DA are parallel to each other:
Perimeter = AB + BC + CD + DA = (6x-4) + (2x) + (5x+1) + (2x) = 15x - 3
From the observation deck of a skyscraper, Morgan measures a 67
∘ angle of depression to a ship in the harbor below. If the observation deck is 955 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
Angle of depression and elevation:The angle of depression refers to the angle above the hill.The ship is 349.8 feet away from the skyscraper's base horizontally.
How far does the ship extend horizontally from the skyscraper's base?You could calculate the angle of elevation, for instance, if you were standing on the ground and were looking up at a mountain's summit.
The angle between a line of sight's horizontal axis and its downward axis is known as the angle of depression.
The ship is 349.8 feet away from the skyscraper's base horizontally.
Angle of depression and elevation:The angle of depression refers to the angle above the hill.
given the aforementioned variables
The harbor is 824 feet tall.
Depression angle is 67 degrees.
SOH CAH TOA identification claims that:
Tan = opp/adj Tan = 824 Tan = 67
d = 824.8/tan67 d = 349.8 feet
Therefore, the vertical distance from the skyscraper's base to the ship is 349.8 feet.
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What is the expanded form for 72 cubed?
Answer:373248
Step-by-step explanation:
72^3 = 373248
How do you solve it WITHOUT using graph paper?
Line A passes through the points (-4, 3) and (-2, -1).
Line B passes through the points (-4, 4) and (-5, 7).
At what point do the lines intersect?
A step by step explanation please!
Answer: To find the point of intersection of two lines without using graph paper, we can use the method of solving a system of equations.
First, we need to find the slope-intercept form of each line. The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of Line A, we can use the slope formula: m = (y2 - y1)/(x2 - x1). Plugging in the given points, we get: m = (-1 - 3)/(-2 - (-4)) = -4/2 = -2.
Therefore, Line A can be written as y = -2x + b. To find the y-intercept, b, we can plug in one of the points, such as (-4,3) and solve for b: 3 = -2(-4) + b, so b = 11.
So, the slope-intercept form of Line A is y = -2x + 11
We can use the same process to find the slope-intercept form of Line B: m = (7 - 4)/(-5 - (-4)) = 3/1 = 3. So Line B can be written as y = 3x + b. Plugging in one of the points, (-4,4), we get 4 = 3(-4) + b, so b = 16.
So, the slope-intercept form of Line B is y = 3x + 16
Now we have two equations: y = -2x + 11 and y = 3x + 16. To find the point of intersection, we need to find the values of x and y that make both equations true. To do this, we can set the two equations equal to each other:
-2x + 11 = 3x + 16
Subtracting 3x from both sides:
-5x = 5
Dividing both sides by -5:
x = -1
Now we can substitute this value of x back into either equation to find the corresponding value of y. Using y = -2x + 11:
y = -2(-1) + 11 = -2 + 11 = 9
So the point of intersection of Line A and Line
Step-by-step explanation:
A painter is making a mural on the side of a building. In planning this project, he first creates the same painting on a normal sized sheet of paper at a scale of 2 in. to 5 ft. If the width of the paper drawing is 4.9 inches, what will be the width of the mural (in feet) when it is finished?
The width of the mural (in feet) when it is finished is equal to 12.25 feet.
What is scale factor?In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
Scale factor = 2/5
For the width of the mural (in feet), we have:
2/5 = 4.9/x
x = (5 × 4.9)/2
x = 24.5/2
x = 12.25 feet.
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give three points that lie on a line with a slope of -2/5
The three points that lie on a line y = -2/5x with a slope -2/5 will be:
(0, 0)
(5, -2)
(10, -4)
How to illustrate the slope?Given slope = m = -2/5. We suppose the line passes through the origin, so b = 0
substituting m = -2/5 and b = 0 in the slope-intercept form
y = -2/5x + 0
y = -2/5x
Thus, the equation of line with the slope m = -2/5 and passes through the origin (0, 0) will be:
y = -2/5x
As the equation of line passes through (0, 0), thus the point (0, 0) lies on the line.
Putting x = 0 in the equation y = -2/5x
y = -2/5 × (0)
y = 0
Thus, (0, 0) is the point which also passes through the line
Putting x = 5 in the equation y = -2/5x
y = -2/5 × 5
y = -2
Thus, (5, -2) is the point which also passes through the line.
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Does someone mind helping me with this problem? Thank you!
Answer:
0.01 goes in the first box
0.10 goes in the second box
Therefore, the first equation is 0.01p + 0.10d = 1.50
===========================================================
Reason:
The last part mentions "A penny is 0.01" which means $0.01 or 1 cent. The 0.01 is the coefficient of the variable p.
1 penny = $0.01
p number of pennies = 0.01p dollars
A similar situation happens with the dimes.
Create a table from y=5x. You can just do numbers like
Y 7. 9. 6
X 4. 7. 4 or sum I just need the table
When y = 5x the possible outcome of table is 2.8 when x = 4 , 3.88 when x= 7 and 3.33 when x= 4 .
Function range :A function's range can refer to one of two closely related ideas: The function's image is its codomain. Given two sets, X and Y, a function is a binary relation between X and Y if, for every x in X, there is exactly one y in Y that corresponds to f. Take a look at the function y = f(x). The range of the function is the spread of all the y values from the lowest to the highest. Substitute all of x's values into the given expression for y to determine whether it is positive, negative, or equal to other values.
if y=5 x
y= 7 and X = 4 , then
7= 5(4)
7 = 20
= 20/7
= 2.8
when Y =9 and X = 7 then,
9 = 5(7)
9 = 35
35/9
= 3.88
when Y = 6 and X = 4 then,
6= 5(4)
6= 20
20/6
= 3. 33
Missing function of table are 2.88 , 3.88,3.33
What is the range of the function?
The range is (0;+∞). The values are all positive (if a positive number is raised to a power, the result cannot be negative), and the value cannot be zero, so the range is (0;+∞).
Incomplete question :
Create a table from y=5x. You can just do numbers like
Y 7. 9. 6
X 4. 7. 4 or sum I just need the table
Complete the table for the given rule.
Rule:y=5x
x, y
5,4,2
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• The dimensions of a rectangle are 3x by 4x-9. Find x if the perimeter is 52.
Draw a picture if you need a visual
Answer:
x = 6, length of the rectangle is 18cm, and width is 21cm
Step-by-step explanation:
To solve this problem, we can use the perimeter of a rectangle formula: P = 2l + 2w.
Here, l = 3x and w = 4x - 9, so the perimeter is P = 2(3x) + 2(4x - 9) = 52.
Solving for x, we get x = 6.
Therefore, the length of the rectangle is 3x = 18 cm, and the width is 4x - 9 = 21 cm.
Systems of Linear Inequalities
PLEASE HELP
Th systems of Linear Inequalities are:
x>=-7,
y<6-2x/3,
y<=-1,
y>3/5x-5,
y<6+5x
How to solve the linear inequalities?Step1:
x>=-7,y<6-2x/3,y<=-1,y> 3/5x-5,y<6+5x: [x>=-7]
[y<6-2x/3]
[y<=-1]
[ y>3/5x-5]
[y<6+5x]
x>=-7
[tex]3y+2x < 6\sy < =-1\sy > \frac{3}{5}[/tex]
x-5\sy-5x<6
Separate y for 3y+2x6 as follows: y6-2x/3 3y+2x6
Step2:
shuffle twice to the right side
Divide both sides by 3 using the formula 3y/6/3-2x/3.
simplify
3y/3<6/32x/3
Simplify 3y/3 by dividing it by y.
3/3=1
simplify 6/3-2x/3: 6-2x/3
6/3-2x/3
Apply the formula a/c + b/c = a+-b/c = 6-2x/3 y 6-2x/3
Identify y for y-5x6: y6+5x y-5x6.
Y=6+5x move the right side by 5x.
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hi help pls n thanks
The required domain is x ≥ -4.So option(4) is correct.
What is domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
According to question:From the graph, we can see that curve is starting from -4 to infinity in x direction.
By baby curve method
x ≥ -4
Thus, required domain is x ≥ -4.So option(4) is correct.
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R
102°
o
S
What is the measure of arc RT?
102 degrees
156 degrees
204 degrees
88 degrees
Previous
E
Please help
The measure of arc RT is: C. 204 degree.
How to find the measure of arc RT?arc ORT = 102° - 90°
arc = 12°
arc ROT = 180° - 2×12°
arc ROT = 180° - 24°
arc ROT = 156°
Hence:
Measure of arc RT
arc RT= 360° - 156°
arc RT = 204°
Therefore the correct option is C.
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Find the values of the variables for the parallelogram.
Answer:
which parallelogram?
Step-by-step explanation:
repost it and add a pic
y=x^2+6x+8
solve by using completing the square.
what are the roots/zeros/x-intercepts of your parabola?
The roots of the parabola are given as follows:
x = -2 and x = -4.
How to obtain the roots of the quadratic function?The quadratic function for this problem is defined as follows:
y = x² + 6x + 8.
Completing the squares, the quadratic function can be factored as follows:
y = (x + 4)(x + 2).
As:
The sum of the roots is of 6.The product of the roots is of 8.Then the roots are obtained as follows:
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The ratio of the volumes of the bags of dog food is [ Select ] which means the scale factor of the dimensions of the two bags is [ Select ] . Therefore the scale factor of the surface area of the two bags is [ Select ] .
Answer:
Step-by-step explanation:
Answer:
20, 2.7, 7.4
Step-by-step explanation:
I completed the assingment and got it 100
The equation y =7400x represents the number of miles, y, that the satellite Space Explorer flies in x hours. Find the rate of change.
If the equation "y = 7400x" represents the number of miles(y) , that satellite space explorer files in x hours , then the rate of change is 7400 miles per hour.
The Rate Of Change is also known as "Slope" ,
The rate of change can be found by taking the derivative of the equation ⇒ y = 7400x with respect to x.
The derivative of the equation "y = 7400x" with respect to x is ;
⇒ dy/dx = d/dx(7400x) = 7400 .
Therefore , rate of change of the equation "y = 7400x" is 7400 miles per hour , that means the satellite explorer files will cover 7400 miles in 1 hour .
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heellllpp guys i will give brainlist
Quadrilateral ABCD'is a reflection of quadrilateral ABCD over the x-axis.
What is the length of A'D' ?
A. 3 units
B. 7 units
C. 4 units
D. 6 units
option D is correct- The length of quadrilateral of A’D’ is 6. When it is reflected ,the lengths don’t change.
image is attached below,
Quadrilateral
A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.
Reflection
A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
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D. Ray saved $4 on a shirt that was was originally
$32. What percent was the discount?
Answer: The percent was 12.5%
t
he points that are on the graph of the function defined by y=2x+3
.
The point that lies on the function defined by the equation is (2, 7)
How to determine the point that lies on the graph of the equationFrom the question, we have the following parameters that can be used in our computation:
y = 2x + 3
The point in the ordered pair that lies on the graph of the equation is the solution set
Take for instance, we set x = 2
So, we have the following representation
y = 2 * 2 + 3
Evaluate the product and the sum
This gives
y = 7
When repesented as an ordered pair, we have
(2, 7)
Hence, the point is (2, 7)
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Divide the following: MUST SHOW WORK. (30 points)
On dividing the expression [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)], the value obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The expression is given as - [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)]
Apply the fraction rule, (a/b)/(c/d) = a·d/b·c
= [(x²-9) × (x²-2x-15)]/[(x²-4x-5) × (x²+5x+4)]
= [(x²-9) × (x+3)]/[(x²-4x-5) × (x+1)]
Expand the expression -
= [(x²-9) × (x+3)]/(x³-3x²-9x-5)
= (x³+3x²-9x-27)/(x³-3x²-9x-5)
= 1 + [(6x²-22)/(x³-3x²-9x-5)]
Therefore, the expression obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].
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A local hamburger hop old a combined total of 491 hamburger and cheeeburger on Friday. There were 59 fewer cheeeburger old than hamburger. How many hamburger were old on Friday?
The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.
432 hamburgers.
We can write an equation to represent the information given.
Hamburgers + Cheeseburgers = 491
Cheeseburgers = Hamburgers - 59
Substitute the second equation into the first equation:
Hamburgers + (Hamburgers - 59) = 491
Solve for 'Hamburgers':
2Hamburgers - 59 = 491
2Hamburgers = 550
Hamburgers = 275
Since the question asks for the number of hamburgers, the answer is 275 hamburgers.
The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.
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Find the measures of the numbered angles.
Answer: ∠1= 75°, ∠2= 105°, ∠3=105°, ∠4=75°, ∠6=105°, ∠7= 105°, ∠8=75°
Step-by-step explanation:
∠1 is corresponding to angle 75° which make them equal.
∠2 is supplementary to ∠1 which means they add up to 180°. Since ∠1 is 75° you would subtract 75° from 180° to get 105°.
∠3 is vertical to ∠2 which makes them equal.
∠4 is vertical to ∠1 which makes them equal.
∠6 is corresponding to ∠2 which makes them equal.
∠7 is vertical to ∠6 which makes them equal.
∠8 is vertical to 75° which makes them equal.
Solve the system by substitution. Check your solution. 0.5 x + 0.25 y = 36. y + 18 = 16 x. a. (36, 72) c. (49, 81) b. (9, 126) d. (21, 9) Please select the best answer from the choices provided A B C D
Answer:
Answer is in attached photo. (B)
Step-by-step explanation:
SolutionThe solution is in the attached photo , do note the question might specify the method to use to solve the equations, just like this the question:
1) Substitution Method
2) Elimination Method
What is the equation of the following graph? Use equation y = mx + b (picture included)