Answer:
Step-by-step explanation:
Solution
I'm assuming you want this simplified. If not leave a note.
a(x + 1) - b(x + 1) - x - 1 remove the brackets
ax + a - bx - b - x - 1 gather like terms
ax - bx - x + a - b - 1
x(a - b - 1) + (a - b - 1) Use the distributive property to simplify
Answer
(x + 1)(a - b - 1)
The common factor is (a - b - 1). That can be pulled out on either side of the isolated + sign
A rectangle has sides measuring (4x 5) units and (3x 10) units. part a: what is the expression that represents the area of the rectangle? show your work. (4 points) part b: what are the degree and classification of the expression obtained in part a? (3 points) part c: how does part a demonstrate the closure property for polynomials? (3 points)
(4x + 5)(3x + 10) or 12x² + 55x +50
b: The degree of the computed expression is 2 and it is classified as a quadratic expression.c: The polynomial expression written in part a is closed under addition multiplication.Forming the Expression for the Area of Rectangle
The formula for the area of a rectangle is given as,
Area, A = length × breadth
Here, the dimensions of the rectangle are given as,
length = (4x + 5)
breadth = (3x + 10)
∴ The equation for the area of the rectangle is,
A = (4x + 5)(3x + 10)
A = 12x² + 55x +50
Hence, 12x² + 55x +50 is the required expression.
Degree and Classification of the Expression
The highest power of a variable that is present in an expression is known as its degree.
Since the degree of the expression formed in part a is 2, it is classified to be a quadratic expression.
Closure Property For Polynomials
When the output is the same kind of object as the inputs, an expression is said to be closed. The expression obtained for the area of the rectangle is a combination of constants and variables closed under multiplication and addition.
Hence the expression formed in part a indicates at the closure property for polynomials.
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find the HCF of a²b²-2a+1
Answer:
1
Step-by-step explanation:
Just '1'
The point-slope form of the equation of line that passes through points (8, 4) and (0, 2) is y - 4 = 1/4(x -8). What is
the slope-intercept form of the equation for this line?
y=1/4 x-12
y= 1/4x-4
y= 1/4x+2
y=1/4 x + 6
Answer:
y = 1/4x +2
Step-by-step explanation:
The slope-intercept form of the equation for a line can be found by solving the given equation for y. It can be written directly from the slope and the y-intercept.
Solve for yIt is helpful to simplify the equation first, then isolate the y-variable by eliminating non-y terms from that side of the equation.
y -4 = (1/4)(x -8) . . . . . . . given
y -4 = (1/4)x -2 . . . . . . . . eliminate parentheses
y = 1/4x +2 . . . . . . . . . . add 4. This is the desired form
Use given informationAlternatively, you can use the given information to write the slope-intercept equation directly. The slope in the point-slope form is the multiplier outside parentheses. In y-4 = 1/4(x -8), the slope is 1/4.
The y-intercept is the point where the line crosses the y-axis. Its coordinates always have an x-coordinate of 0. That is, the given point (0, 2) tells you the y-intercept is 2.
Using the slope and intercept in the slope-intercept form, you get the equation you're looking for:
y = mx +b . . . . . line with slope m and y-intercept b
y = 1/4x +2 . . . . . line with slope 1/4 and y-intercept 2
In the figure, ∠ABD = 50° and ∠BCD = 60°.
Calculate ∠ADC and ∠ADO.
Answ
Step-by-step explanation:
25 POINTS FOR INMEDIATE RESPONSE PLEASE
What is the algebraic expression for fifteen more than n is at least 48
n+15 ≥ 48n; n≥33
15n ≥ 48; n≥33
n+15 ≥ 48; n≥33
n-15 ≥ 48; n≥33
Inequalities help us to compare two unequal expressions. The algebraic expression for fifteen more than n is at least 48 is n+15 ≥ 48; n≥33. Thus, the correct option is C.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given statement "fifteen more than n is at least 48" can be written in the form of an algebraic expression as,
n+15 ≥ 48
Solving the inequality,
n ≥ 48 - 15
n ≥ 33
Hence, the algebraic expression for fifteen more than n is at least 48 is n+15 ≥ 48; n≥33. Thus, the correct option is C.
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which pair of statements describes the end behavior of the graphed function
HELP PLEASE DUE NOW
The statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial function:
[tex]\rm f(x) = x^{3}+2x^{2}-5x-6[/tex]
The function is a cubic function and the graph of the cubic function will be a curve.
As we can see in the graph, f(x) grows larger as x approaches negative infinity. f(x) also becomes closer to infinity as x does.
Thus, the statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.
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Which statement about the following graph is correct?
O
The graph is symmetric about the line x = -1.
The graph is symmetric about the line y = -1.
The graph is not symmetric.
The graph is symmetric about the line x-1.
Answer:
the graph is symmetric about the line y=-1
Step-by-step explanation:
A function is symmetric about y=a when the following is true for all points: f(a-x) = f(a+x). By just looking at the graph, it appears to be symmetric about y=-1, and it can be further proven, by finding the difference of two points, that have the same y-value. So for example if you look at (0, 1) and (-2, 1). The difference between 0 and -1 is 1, and the difference between -2 and -1, is also 1. And this appears to be true for all the other values as well. So the graph is symmetric about the line y=-1
Answer:
The graph is symmetric about the line x=-1
Step-by-step explanation:
Given: AC and BD bisect each other.
Prove: AB | CD and BC || AD.
2) [tex]\overline{AE} \cong \overline{EC}[/tex] (a segment bisector splits a segment into two congruent parts)
3) [tex]\overline{BE} \cong \overline{ED}[/tex] (a segment bisector splits a segment into two congruent parts)
4) [tex]\angle AEB \cong \angle CED[/tex] (vertical angles are congruent)
5) [tex]\triangle BEA \cong \triangle DEC[/tex] (SAS)
6) [tex]\angle EBA \cong \angle EDC[/tex] (CPCTC)
7) [tex]\overline{AB} \parallel \overline{CD}[/tex] (converse of alternate interior angles theorem)
8) [tex]\angle BEC \cong \angle AED[/tex] (vertical angles are congruent)
9) [tex]\triangle BEC \cong \triangle DEA[/tex] (SAS)
10) [tex]\angle ECB \cong \angle EAD[/tex] (CPCTC)
11) [tex]\overline{BC} \parallel \overline{AD}[/tex] (converse of alternate interior angles theorem)
Evaluate: −5−(x+y)2, where x=3 and y=6
Answer: -23
Step-by-step explanation:
-5-2x-2y
-5-2(3)-2(6)
-5-6-12 = -23
write an equivalent expression.
4 + m
Triangle J K L is shown. Point N is the midpoint of side J L and point M is the midpoint of side K L. The length of J K is 19.6 meters. The lengths of J N and N L are 7.4 meters. The lengths of K M and M L are 10.7 meters.
What is the distance between points M and N?
meters
The distance between points M and N according to the task content is; 9.8 meters.
What is the distance between points M and N?From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints KL and JL respectively.
Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;
NM/19.6 = 7.4/(2×7.4)
NM = 19.6/2 = 9.8 meters.
This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.
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Answer: 9.8 meters
Step-by-step explanation: Trust Me!! I got the answer correct on Edge.
Q: What is the distance between points M and N?
A: 9.8 meters
QT=
Help me please thanks:)
The length of QJ is 4√20 units if the QJ = 4×PQ after using the intersecting chords theorem.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
By intersecting chords theorem:
QM×QL = QJ×PQ
10×8 = QJ(QJ/4)
4×80 = QJ²
QJ = 4√20 units
Thus, the length of QJ is 4√20 units if the QJ = 4×PQ after using the intersecting chords theorem.
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In the following diagrams calculate the
sides marked with letters x and y.
All dimensions are in cm.
Answer:
x ≈ 6.5 , y ≈ 12.1
Step-by-step explanation:
(2x)² + (10.2)² = (16.5)²
4x² = 272.25 - 104.04
x² = 168.21 ÷ 4
x = √(42.0525) ≈ 6.5
y² = 42.0525 + 104.04 = 146.0925
y = √(146.0925) ≈ 12.1
What is the inevitable result of running statistical inference on a random sample rather than on an entire population
Your question is incomplete. Please read below to find the complete questin.
B. Sampling error is the inevitable result of running statistical inference on a random sample rather than on an entire population.
A sampling mistake is a statistical blunder that occurs when an analyst does now not pick out a sample that represents the entire population of records. As a result, the outcomes found in the pattern no longer constitute the outcomes that would be received from the entire population.
Sampling error takes place when a sample is chosen from the incorrect populace statistics. Non-reaction errors occur when a user reaction is not received from the surveys. it can happen because of the incapacity to contact capability respondents or their refusal to respond.
The maximum generally used measure of sampling errors is referred to as the same old errors (SE). the standard error is a measure of the spread of estimates across the "true fee". In exercise, only one estimate is available, so the same old blunders can not be calculated at once.
What is the inevitable result of running statistical inference on a random sample rather than on an entire population?
A. Standard deviation
B. Sampling error
C. Sampling distribution
D. Stratified sampling
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Lines DE and AB intersect at point C.
D
A
C
B
(2x+2) E
(5x + 3)*
E
What is the value of x?
O12
25
38
52
Answer:
25
Step-by-step explanation:
2x+2+5x+3=180
7x=175
x=24
Polygon abcd has the following vertics: a( -3, 3) b (5, 5) c (5, -4 ), d (-3 -4). caculate the area of the polygon
Mark the point on the coordinate system and draw the polygon (attachment).
This is the trapezoid.
The formula of an area of a trapezoid:
[tex]A=\dfrac{a+b}{2}\cdot h[/tex]
a, b - the lengths of the parallel sides
h - the height
Substitute:
[tex]a=9,\ b=7,\ h=8\\\\A=\dfrac{9+7}{2}\cdot8=\dfrac{16}{2}\cdot8=8\cdot8=64[u^2][/tex]
[tex]\huge\boxed{A=64u^2}[/tex]
A rectangle has integer side lengths. One pair of opposite sides is increased by $30\%$ and the other pair of sides is decreased by $20\%$. The new side lengths are also integers. What is the smallest possible area, in square units, of the new rectangle
The smallest possible area of the new rectangle is 52 square units.
In the question, we are given that a rectangle has side lengths of integral value.
We assume the lengths to be x and y units respectively, such that x and y are integers.
In the new arrangement, one pair is increased by 30%, and the other pair is decreased by 20%, such that the new sides are also integers.
We assume a 30% increase in x.
New side = x + 30% of x = x + 30/100 of x = x + 3x/10 = 13x/10.
For this to be an integer, x needs to be a multiple of 10.
Since we are considering the smallest area, we will consider the smallest multiple of 10, that is, 10 itself.
Hence, side 1 = 13 units.
We assume a 20% decrease in y.
New side = y - 20% of y = y - 20/100 of y = y - y/5 = 4x/5.
For this to be an integer, y needs to be a multiple of 5.
Since we are considering the smallest area, we will consider the smallest multiple of 5, that is, 5 itself.
Hence, side 2 = 4 units.
Now, the area of this rectangle is the product of its sides = 13*4 sq. units = 52 sq. units.
Therefore, the smallest possible area of the new rectangle is 52 square units.
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Expand. (y^2 + 6)(-2y^2 + 7) =
[tex] \: \: \: \: \: \: \: \: \: \: \: \large\underline{\bf{ANSWER}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: [/tex]
[tex] \tt↠(y^2+6)(−2y^2+7)[/tex]
[tex]\tt↠(-2y^2+7)y^2+6(-2y^2+7)[/tex]
[tex]\tt↠-2y^4+7y^2+6(−2y^2+7)[/tex]
[tex]\tt↠-2y^4+7y^2-12y^2+42[/tex]
[tex]\tt↠-2y^4-5y²+42[/tex]
Answer:
-2y⁴ - 5y² + 42
Step-by-step explanation:
[tex](y^2 + 6)(-2y^2 + 7)[/tex]
[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
Here First terms are
[tex]y^2 \textrm{ and } -2y^2\\(y^2)(-2y^2) = -2y^4[/tex]
Outer terms are y² and 7 ==> (y²)(7) = 7y²
Inner terms are 6 and -2y² ==> 6(-2y²) = -12y²
Last terms are 6 and 7 ==> 6.7 = 42
So result is obtained by adding all these terms
-2y⁴ + 7y² - 12² + 42 ==> -2y⁴ - 5y² + 42
6. The difference between 2 number is 36.
The larger number is 4 times as great as the
smaller. What are the 2 numbers?
Answer: 48 and 12.
Step-by-step explanation:
Let the smaller number is x. Hence, the larger number is 4*x.
The difference between 2 number is 36.
So,
4*x-x=36
3*x=36\ |:3
x=12.
4*x=12*4
4*x=48.
Good luck an' have a nice day!
evaluate
3x³ 2x² + 7y for x = -3 and y = -7.
-
Answer:
2511
Step-by-step explanation:
Geometry!!! Find the lengths of the 45°-45°-90° Triangle
Answer:
Step-by-step explanation:
Please help me with this geometry question, Im pretty sure you need to use Sas congruence rule
The information about SAS Congruence is illustrated below.
How to illustrate the information?The complete information wasn't found. Therefore, an overview will be given. SAS congruence simply means that two triangles are congruent.
This implies that the sides of the triangles are equal. The rule states that if two sides and the angles if one triangle are equal to two sides and included in another triangle, then the triangles are congruent.
For example, given AC = PQ, BC = RQ and angle C = angle P. Then according to SAS, ABC = QRP.
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Question 5 of 10
If f(x)=3x-2 and g(x)=x+1, find (f+g)(x).
OA. 4x²-1
OB. +3x+1
OC. +3x-1
OD. 2x+3
Answer: 4x-1
Step-by-step explanation:
[tex](f+g)(x)\\\\=f(x)+g(x)\\\\=3x-2+x+1\\\\=\boxed{4x-1}[/tex]
The table represents the cost of flowers at the Tigerlily Flower Shop.
Cost of Flowers
Quantity
Price
1
$2.00
2
$3.50
3
$5.00
4
$6.50
5
$8.00
6
$9.00
Which graph is the best interpretation of this table?
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. Points are at (1, 2), (2, 3.5), (3, 5), (4, 6.5), (5, 8), (6, 9).
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. Points are at (1, 2), (2, 4), (3, 6), (4, 8), (5, 10), (6, 12).
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. A line with positive slope goes through points (2, 4) and (4, 8).
On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. A curved line with positive slope is on the graph.
The graph which is the best interpretation of the table given is; On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. Points are at (1, 2), (2, 3.5), (3, 5), (4, 6.5), (5, 8), (6, 9).
Which graph is the best interpretation of the table?The table given in the task content is a tabular representation of the quantity and the corresponding prices. On this note, plotting the quantity on the x-axis and the price on the y-intercept with the point descriptions above best represents the graph of the table.
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Answer:
The short answer to my well taught friend, is A
Please help me asap!!!!!!!
Identify the range of the function shown in the graph.
Answer:
D. 0≤y≤5
Step-by-step explanation:
The range refers to how far on the y axis a function exists on a graph. This function starts at y=0 and ends at y=5, meaning you can find a point on the function for any y-level between 0 and 5. So y is greater than or equal to 0, and is less than or equal to 5.
A: A function with a range of all real numbers goes both up and down infinitely, however this function does not go up and down infinitely so we can rule out A.
B: If y>0, the function would start above y-level 0 and go up infinitely, however this graph does not display that so we can rule out B as well.
C: C is the domain of the graph, which is how far left and right the function exists.
On a coordinate plane, solid circles appear at the following points: (negative 5, negative 3), (negative 4, negative 4), (negative 2, 2), (1, 3), (1, negative 2), (2, 1), (5, negative 4).
Which ordered pair can be removed so that the resulting graph represents a function?
The ordered pair that can be removed so that the resulting graph represents a function is (1, 3) or (1, -2)
How to determine the points?The ordered pairs are given as:
(-5, -3), (-4, -4), (-2, 2), (1, 3), (1, -2), (2, 1), (5, -4)
For a set of ordered pairs to represent a function, each x value must point to exactly one y value
From the above ordered pairs, we have:
(1, 3) and (1, -2)
The x value 1 has y values 3 and -2
When one of these pairs is removed, the graph becomes a function
Hence, the ordered pair that can be removed so that the resulting graph represents a function is (1, 3) or (1, -2)
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Convert 8125 g into kilograms (kg) and grams (g).
Answer:
8125 x 10^-3
= 8.125
8125 g
= 8.125 kg
Step-by-step explanation:
First, note that g is the same as grams and kg is the same as kilograms. Thus, when you are asking to convert 8125 g to kg, you are asking to convert 8125 grams to kilograms.
A gram is smaller than a kilogram. Simply put, g is smaller than kg. In fact, a gram is "10 to the power of -3" smaller than a kilogram.
Since a gram is 10^-3 smaller than a kilogram, it means that the conversion factor for g to kg is 10^-3. Therefore, you can multiply 8125 g by 10^-3 to get 8125 g converted to kg.
Here is the answer with the math showing you how to convert 8125 g to kg by multiplying 8125 by the conversion factor of 10^-3.
Answer:
8.125kg and 8125g
Step-by-step explanation:
1kg=1000g
From the diagram below, we can tell that < ADB is congruent to ____.
Select one:
a.
< CBA
b.
< DBC
c.
< C
d.
< A
Answer:
<CBA
Step-by-step explanation:
<CBA = 90 degrees (given)
<ADB = 90 degrees (given)
Hence They are congruent, so choose A
From the diagram below, we can tell that < ADB is congruent to <CBA.
Here, we have,
given that,
from, the given diagram, we get,
both the triangles ABD and BCA are right angle triangle.
here, we have,
angle D = 90
and angle B = 90
so, we have,
<CBA = 90 degrees (given)
<ADB = 90 degrees (given)
Hence They are congruent, so choose A.
From the diagram below, we can tell that < ADB is congruent to <CBA.
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The graph plots four equations, A, B, C, and D: Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7. Which pair of equations has (0, 8) as its solution? (1 point) Equation A and Equation C Equation B and Equation C Equation C and Equation D Equation B and Equation D
The pair of equations that has (0, 8) as its solution is: A. equation A and equation C.
What is the Solution to a System of equations?The solution to a system of linear equations that are graphed is the pair of x and y coordinates of the points where two lines intersect.
In the graph given, the lines representing equations A and C intersect at point (0, 8). Therefore, the pair of equation that has a solution of (0, 8) is: A. equation A and equation C.
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