The simplified form of the given expression is 2015
Simplifying expressionsThe given expression is (x-2)(x+2)(x²+4)-(x²+3)(x²-3)+2022
The expression can be simplified as shown below
(x-2)(x+2)(x²+4) - (x²+3)(x²-3) + 2022
x(x+2)-2(x+2)(x²+4) - x²(x²-3) +3(x²-3) + 2022
(x²+2x-2x-4)(x²+4) - (x⁴-3x²+3x²-9) + 2022
(x²-4)(x²+4) - (x⁴-9) + 2022
x²(x²+4) -4(x²+4) - (x⁴-9) + 2022
(x⁴+4x²-4x²-16) - (x⁴-9) + 2022
(x⁴-16) - (x⁴-9) + 2022
x⁴ -16 -x⁴ +9 + 2022
x⁴ -x⁴ -16 +9 +2022
= 2015
Hence, the simplified expression is 2015
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What is the smallest possible length of the hypotenuse for a non-degenerate
right triangle with integer side lengths given that it has at least 1 leg of length
84.
The smallest possible length of the hypotenuse is 118
How to determine the hypotenuse?The given parameters are:
Triangle type: non-degenerate right triangleLegs: Length = 84 (at least 1)The non-degenerate implies that the right triangle has a positive area.
Since at least one length is 84, then both lengths can also be 84.
The hypotenuse is then calculated using the following Pythagoras theorem.
h^2 = 84^2 + 84^2
Evaluate the sum
h^2 = 14112
Take the square root of both sides
h = 118.8
Round down
h = 118
Hence, the smallest possible length of the hypotenuse is 118
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A newspaper sold 46453 copies today.
Yesterday it sold 42979 copies.
How many more copies were sold today
Answer:
3474
Step-by-step explanation:
To determine the difference in the amount sold, take the amount sold today and subtract the amount sold yesterday
46453-42979
3474
Geometry question I need help
Answer:
Step-by-step explanation:
help me please i need help
Answer:
The answer is 74.
Step-by-step explanation:
To find the area, you have to divide the shape into rectangles. To solve, I divided it like the image above. (Sorry if the lines are squiggly I'm trying to do this fast)
So first, now that we've divided it into smaller rectangles, we find the area of the smaller ones. Remember, the area of a rectangle is length * height.
Since the two smaller rectangles are the same, we just need to find one and multiply it by 2.
[tex]3 \times 5=15 \\15\times 2=30[/tex]
So the area of the two smaller ones is 30. Now we need to find the big rectangle and add it together. We know that the length is 11, but we don't know the height. The height of the small rectangles was 5, so the height is 4 since 9 - 5 = 4. So to finish up, we do this:
[tex]11\times4=44 \\ 44 + 30=74[/tex]
So our final answer is 74.
I dont understand how to work it out
Answer:
If you ever see a big word like greatest,biggest,largest,etc,that stands for Greatest Common Divisor(GCD) and therefore,you have to find prime numbers that can divide the two numbers each equally.
the greatest number of trees Abe can have in each row would be 9
3| 54|27
3 | 18| 9
3|. 6|3
you take the prime factors and multiply which would give you 9
Please help me
Pleaseee hellllppppp asap
Answer:
a: -13º
b: 83º
Step-by-step explanation:
- a: [tex]-27 + 14 = -13[/tex]º
- b: [tex]68 + 15 = 83[/tex]º
- the equation would originally be written as 68 - -15 but 2 negatives make a positive so -- becomes +
hope this helps :)
Line segment pq is a directed line segment beginning at p(6,-5) and ending at q(-2,4). find point r on the line segment pr that partitions it into the segments pr and pq in the ratio 3:2.
Using proportions, the coordinates of point R are given as follows: R(1.2, 0.4).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Segments pr and pq are partitioned in the ratio 3:2, hence:
[tex]PR = \frac{3}{5}PQ[/tex]
[tex]R - P = \frac{3}{5}(Q - P)[/tex]
The points are:
R(x,y).P(6,-5).Q(-2,4).For the x-coordinate, we have that:
[tex]R - P = \frac{3}{5}(Q - P)[/tex]
[tex]x - 6 = \frac{3}{5}(-2 - 6)[/tex]
x - 6 = -4.8
x = 1.2.
For the y-coordinate, we have that:
[tex]R - P = \frac{3}{5}(Q - P)[/tex]
[tex]y + 5 = \frac{3}{5}(4 + 5)[/tex]
y + 5 = 5.4.
y = 0.4.
The coordinates are: R(1.2, 0.4).
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im so confused can anyone help
Answer:
45
Step-by-step explanation:
the number of ones expected is
probability × number of rolls
= 0.3 × 150
= 45
A voice grade modem has a maximum data rate of 14,400 bps. What would be the maximum data rate of that modem if the number of points in its constellation were doubled
The maximum data rate of that modem is doubled if the number of points in its constellation were doubled
According to statement
Modem has a data rate is 14,400 bps
we know that the data rate can be calculated by T=A/S
If a is Doubled then the data rate is also doubled.
Because A is directly proportional to the T and S is inversely proportional to T.
So, The maximum data rate of that modem is doubled if the number of points in its constellation were doubled
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An appliance repair person charges $60 for a service call and a labor charge of $30 per hour. What is the rate of change represented in this situation? (PLEASE INCLUDE HOW TO SOLVE IT TYSM)
Answer:
30$ (the labor charge per hour)
Step-by-step explanation:
The rate of change can be described as the slope, or how much the y-value is going to change as the x-value increases by 1. So the first step would be to understand what is x and what is y in this context. Well usually y is the dependent variable and x is the independent variable, so as x changes y changes as a result. In this case the y would represent the price the repair person charges and the x would represent the amount of hours, since as the amount of hours changes, the price changes. And since the person charges 30$ per hour, that means the rate of change is 30, since as the amount of hours increases by 1, the price or amount charged increases by 30$
Answer: $30
Step-by-step explanation:
The appliance repair person charges $30 per hour, meaning the rate of change is 30
the question is on the image.
Answer:
18+[tex]6\sqrt{5}[/tex]
Step-by-step explanation:
Since the helicopter flies east for six miles and north for 12 miles, it flies 18 miles. Then on the way back, it flies an unknown amount of miles. the path the helicopter takes is in the form of a triangle, and the path back is the hypotenuse of the triangle. To find the hypotenuse, we can do [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse. We do
[tex]6^2+12^2=c^2\\36+144=c^2\\180=c^2\\\sqrt{180}=c\\ 6\sqrt{5}=c[/tex]Therefore, the total distance flown by the helicopter is 18+[tex]6\sqrt{5}[/tex].
In a flower shop, if 5929 plants are to be set in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
Answer:
77
Step-by-step explanation:
Based on the question, we can deduce the arrangement of the plants is in a form of a square. (Number of rows = Number of Columns).
In that case, the answer is very straightforward, just square root the number of plants to be planted:
[tex]\sqrt{5,929} \\= 77[/tex]
This means there would be 77 rows of 77 plants per row.
Calcula de dos maneras diferentes
1) (-12).8
2) 14.(-5).(-11)
Porfa
The value of (-12) . 8 is -96 and the value of 14.(-5).(-11) is 770
How to solve the expressions?The question implies that we calculate the expressions in two different ways.
1) (-12).8
Way 1:
We have:
(-12).8
This means
(-12) . 8 = -12 * 8
Evaluate
(-12) . 8 = -96
Way 2
We have:
(-12).8
This means
(-12) . 8 = -12 * 8
Express 8 as 4 + 4
(-12) . 8 = -12 * (4 + 4)
Expand
(-12) . 8 = -12 * 4 -12 * 4
Evaluate the products
(-12) . 8 = -48 - 48
Evaluate the sum
(-12) . 8 = -96
Hence, the value of (-12) . 8 is -96
2) 14.(-5).(-11)
Way 1:
We have:
14.(-5).(-11)
This means
14.(-5).(-11) = 14 * -5 * -11
Evaluate
14.(-5).(-11) = 770
Way 2
We have:
14.(-5).(-11)
This means
14.(-5).(-11) = 14 * -5 * -11
Multiply -5 and -11
14.(-5).(-11) = 14 * 55
Multiply 14 and 55
14.(-5).(-11) = 770
Hence, the value of 14.(-5).(-11) is 770
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Polygons ABDC and A′B′D′C′ are shown on the following coordinate grid:
A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A polygon ABDC is shown with vertex A on ordered pair 2, negative 2, vertex B on ordered pair 4, negative 2, vertex D on ordered pair 5, negative 3 and vertex C on ordered pair 1, negative 3. A polygon A prime B prime D prime C prime is shown with vertex A prime on ordered pair 1, 2 , vertex B prime on ordered pair 1, 4, vertex D prime on ordered pair 2, 5 and vertex C prime on ordered pair 2, 1.
What set of transformations is performed on ABDC to form A′B′D′C′?
A: A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
B: A translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin
C: A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
D: A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin
(Sorry if its hard to understand)
Answer: A
Step-by-step explanation:
Let's first review how turning about the origin changes a point's coordinates:
After rotating and translating some points, one can see the following pattern:
180° Rotation: (x,y) -> (-x,-y)90° Clockwise Rotation: (x,y) -> (y, -x)90° Counter-clockwise Rotation: (x,y) -> (-y, x)Translation a units to the left: (x, y) -> (x-a, y)Using these patterns will make it much easier to find the correct series of transformations than graphing each one.
A: A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
Using the patterns found above, this set of transformations would make (x,y) move first to (-y, x), then (-y-1, x).
A(2,-2) -> A'(1,2)B(4,-2) -> B'(1,4)D(5,-3) -> D'(2,5)C(1,-3) -> C'(2,1)B: A translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin
This would make (x,y) move first to (x-1,y), then to (-y, x-1)
A(2,-2) -> A'(2, 1)B(4,-2) -> B'(2,3)D(5,-3) -> D'(3,4)C(1,-3) -> C'(3,0)C: A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
This would make (x,y) move first to (y, -x), then (y-1, -x)
A(2,-2) -> A'(-3, -2)B(4,-2) -> B'(-3,-4)D(5,-3) -> D'(-4, -5)C(1,-3) -> C'(-4, -1)D: A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin
This would make (x,y) move first to (x-1,y), then (y, -x+1)
A(2,-2) -> A'(-2, -1)B(4,-2) -> B'(-2, -3)D(5,-3) -> D'(-3, -4)C(1,-3) -> C'(-3, 0)Therefore, the answer is A, as only it correctly matches to polygon A'B'D'C'.
Which side measures would create an acute triangle?
O2,4,5
O 3,4,5
O 3,6,7
O 6,8,9
39. For the following exercises, sketch a line with the given features.
39. An x-intercept of (-2,0) and y-intercept of (0,4)
Answer: the attachment i put with this file
Step-by-step explanation:
to graph this linear function, you can use the mantra "rise and run" to plot the points on the graph, and draw a line through the points.
help ASAP!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
ATTACHED IS THE SOLUTIONTodd and his brother robert are going to use 512 square feet of their backyard for skateboard ramps. the shape of the backyard is rectangular, with the length twice as long as the width. what are the dimensions of the backyard? which quadratic equation would be used to solve for the unknown dimensions? 0 = 2w2 512 = w2 512 = 2w2 512 = 2l 2w
The dimensions are 16 ft by 32 ft
The quadratic equation is w^2-256=0
We have given that,
Todd and his brother Robert are going to use 512 square feet of their backyard for skateboard ramps. the shape of the backyard is rectangular, with the length twice as long as the width.
What is the area of the rectangle?
The area of a rectangle is equal to
A=WL
Where L is the long side of the rectangle
W is the width side of the rectangle
in this problem we have
A=512ft^2
S0,512=LW -----> equation A
L=2W ------> equation B
substitute equation B in equation A
512=2W(W)
512=2w^2
2w^2-512=0
W^2=512/2
W=\sqrt(256)
W=16
Find the value of L
L=2W
L=2(16)
L=32ft
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Answer:
C)512 = 2w2
Step-by-step explanation:
trust
5
Select the correct answer.
A basket weaver is making a square basket. A sketch of the top shows the its diagonal will measure 6 inches. What is the perimeter of the top of
the basket to the nearest inch?
6 in
A.48 in
B. 24 in
C. 34 in
D. 20 in
The perimeter of the top of the basket is 20 in.
What is perimeter of square?Perimeter of square is defined as addition the lengths of the square's four sides.
Diagonal = 6
Let, side of square = a
a²+a² = 6²
2a² = 36
a² = 18
a = 3√2
Perimeter of the square = 4 × side of square
Perimeter of the square = 4 × 3√2
Perimeter of the square = 12√2 ≈ 20 in
Hence, the perimeter of the top of the basket is 20 in.
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what is the chance to get 4 items with 10% chance of each occurring, while there 8 items in total with other 4 items having a 90% chance of each occurring
Step-by-step explanation:
Simple events in probability have a certain chance of happening. For example, a 10% chance of rain today. When two or more probabilities are possible, they are added together to get the total probability. A 10% chance of snow and a 15% chance of hail would mean a 10% + 15% = 25% chance of bad weather. This article will show you how to find the probability of a simple event happening.
A system with the same line has an infinite number of solutions.
True or False
Three rectangular-shaped holes have been drilled passing all the way through a solid 3 × 4 x 5 cuboid. The diagrams show the front, side and top views of the resulting block. What fraction of the original cuboid remains?
The volume of a cuboid implies the product of its length, width, and height. So that the fraction of the original cuboid that would remain is [tex]\frac{7}{15}[/tex].
A cuboid is a solid derived from a rectangle, thus it has rectangular faces. Its volume can be determined by;
volume of a cuboid = length x width x height
In the given question, the volume of the original cuboid can be determined as;
volume = 3 x 4 x 5
= 60 Cubic units
Since holes can not be drilled at the intersection of the holes, then the volume of the hole has to be determined.
To determine the volume of the hole drilled, we have:
(6 x 3) + (3 x 2) + (2 x 2) = 28 Cubic units
So that the fraction of the original cuboid that would remain = [tex]\frac{28 cubic units}{60 cubic units}[/tex]
= [tex]\frac{7}{15}[/tex]
Therefore, [tex]\frac{7}{15}[/tex] of the original cuboid would remain.
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Write an algebraic expression for each statement:
a. The value of a three digit number if the tens digit is c, the hundreds digit is three less than the tens and the ones digit is 0?
b. The tens digit of a number is b and the units digit is twice as big. What is the value of the number in terms of b if the digits are reversed?
I hope you can help me with these questions!!
For the given sentences, the algebraic expressions are:
a) N = 110*c - 300
b) N = 12*b
How to get the algebraic expressions?
For the first statement:
A 3-digit number, where the tens digit is c, can be written as:
N = 100*a + 10*c + b
Then the hundreds digit is a, and here we know that is 3 less than the tens digit, then:
a = c - 3
The ones digit is b, here we know that it is 0, then b = 0.
Replacing that in our number we get:
N = 100*(c - 3) + 10*c = 110*c - 300
N = 110*c - 300
That is the algebraic expression.
b) A two-digit number can be written as:
N = b*10 + a
Where b is the tens digit and a is the ones digit.
Here we know that the units digit is twice as bit as the tens digit, then:
a = 2b
Replacing that we get:
N = b*10 + a = b*10 + 2b = 12*b
N = 12*b
That is the algebraic expression.
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Trigonometry Problem, please help and explain
The bottom triangle is a 30°-60°-90° triangle that has the special property that its hypotenuse is twice the length of the shortest leg, 20√3.
The upper triangle is a 45°-45°-90° triangle, in which the hypotenuse is longer than one of its legs by a factor of √2.
All this to say x = √2 × 20√3 = 20√6 (A).
the stem plot shows the number of swimming laps completed by swim team members at a single practice
Which of the following is a correct statement about the distribution?
The correct statement is the distribution is unimodal.
What is the correct statement?A Stem plot is a table where each data value is split into a stem which is the first digit or digits and a leaf which is the last digit.
Mode refers to a value that appears most frequently in a data set. A unimodal data set is a distribution with one clear most frequent values. There are only one set of modes in the data. They are 76.
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Or dylan, an nfl running back, rushed for an average of 88 yards per game this season, which is 20% lower than his average was last season. what was his average then?
Question 8
Which equation best represents the set-up for solving the following.
A
9 + 16 = x
B
x + 9 = 16
C
x2 + 162 = 92
D
92 + x2 = 162
The equation that best represents the set-up is (d) 9^2 + x^2 = 16^2
How to determine the equation?The complete question is in the image
The value of x is calculated using the following Pythagoras theorem
16^2 = x^2 + 9^2
Rewrite as:
9^2 + x^2 = 16^2
Hence, the equation that best represents the set-up is (d) 9^2 + x^2 = 16^2
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Average Allowance
Amount Frequency
$20
$15
$10
$5
||
MH
NHM
|||
What is the
range of
allowance
amounts?
Answer:
$15
Step-by-step explanation:
Range is the difference of the highest and lowest data.
Based on the given $20 is the highest and $5 is the lowest.
$20 - $5 = $15
Answer:
15
Step-by-step explanation:
you can think of this table as a data set--and you could even write it out
5, 5, 5, 10, ......... 20, 20 {I did not write it out in full of course}
so, when thinking about the range, we can think of it as a range of our data set.
We find the range of a data set by finding the difference between the highest and lowest values
So, we know that our highest data value (amount) is 20, and the lowest is 5:
20 - 5 = 15
meaning that there is a range of $15 in this data set of allowance amounts
hope this helps!! have a lovely day! :)
Consider a standard 52-card deck of cards with 13 card values (Ace, King, Queen, Jack, and 2-10) in each of the four suits (clubs, diamonds, hearts, spades). Answer each of the below. Note that "or" in this question refers to inclusive, not exclusive, or. If a card is drawn at random, what is the probability that it is a heart?
The probability that it is a heart = 1/4 or 0.25.
Total standard cards = 52
The probability of choosing a heart from a deck of cards with 13 card values (Ace, King, Queen, Jack, and 2-10) in each of the four suits (clubs, diamonds, hearts, spades) is given by =
P(Heart) = number of hearts / total number of cards
= 13 / 52
= 1/4 or 0.25
Hence, The probability that it is a heart = 1/4 or 0.25.
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Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
6 is added to the product of 7 and a number.
Answer:
6 +7x
Step-by-step explanation:
To write an English expression as an algebraic one, you must first understand what the English is telling you. Then the translation is straightforward.
Algebraic representationA plus sign (+) signifies addition. Multiplication is signified several different ways. The simplest is writing the factors next to each other.
Parsing the EnglishThe objects involved in the addition are 6 and a product:
6 + product
The product is said to consist of two factors: 7 and "a number". The instructions say to use "x" for "a number", so the product can be written ...
7x
Algebraic expressionThen the complete algebraic expression is ...
6 +7x