Answer:
Part A = 36z² - 9z + 8
Part B = 5z³ + 4z² + 16z - 23
Part c = Yes.
Step-by-step explanation:
Polynomials : Polynomials are algebraic expressions that consist of variables and coefficients.
Trapezium: A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.
Given the length of sides :
Side 1: 11z² - 4z + 2
Side 2: -2z + 3 + 12z²
Side 3: 3 - 3z + 13z²
and The perimeter of the trapezoid is 5z³ + 40z² + 7z - 15.
PART A:
The total length of sides 1, 2, and 3 of the trapezoid is obtained by the sum of the trapezoid :
11z² - 4z + 2 + (-2z + 3 + 12z²) + 3 - 3z + 13z²
11z² - 4z + 2 - 2z + 3 + 12z² + 3 - 3z + 13z²
36z² - 9z + 8
PART B:
The length of the fourth side of the trapezoid is given by the difference between the perimeter of the trapezoid and the sum of length of sides 1, 2, and 3.
5z³ + 40z² + 7z - 15 - 36z² + 9z - 8
5z³ + 4z² + 16z - 23
PART C:
From part A, we can see that the addition of polynomials results in a polynomial.
Likewise, the subtraction of polynomials results in a polynomial.
Therefore, we can say that the polynomials are closed under addition and subtraction.
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Complete the steps in solving the quadratic function 7x – 9 = 7x2 – 49x by completing the square.
answer below:
–9 = 7x2 –
⇒ 56 x
–9 +
⇒ 112 = 7(x2 – 8x +
⇒ 16 )
56, 112, 16 in that order
Answer:
it's actually 28+/-√721/7
Step-by-step explanation:
1. Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Choosing 5 people (without replacement) from a group of 58 people, of which 15 are women, keeping track of the number of men chosen.
A) Not binomial: there are too many trials.
B) Procedure results in a binomial distribution.
C) Not binomial: there are more than two outcomes for each trial.
D) Not binomial: the trials are not independent.
The 15 are women, keeping track of the number of men chosen is Not binomial the trials are not independent.
We have given that,
The given procedure results in a binomial distribution. If not, state the reason why. Choosing 5 people (without replacement) from a group of 58 people, of which 15 are women, keeping track of the number of men chosen.
What is the Binomial distribution?In samples with replacement, the probability has to be the same for each trial, that is, they are independent.
Hypergeometric distribution
Samples without replacement, as the probabilities depend on the previous outcomes, that is, they are not independent.
In this question
Marbles are chosen without replacement, which means that for each trial the probabilities of choosing a red marble are different, which means that the trials are not independent. So the answer is:
Not binomial the trials are not independent.
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What is the effect on the graph of the function f(x) = x2 when f(x) is changed to f( 1 3 x) + 6? A) stretched horizontally and shifted up B) stretched vertically and shifted right C) compressed vertically and shifted left Eliminate D) compressed horizontally and shifted down
Answer:
A
Step-by-step explanation:
f(x) = x²
f(x) becomes f(13x) + 6
the "+ 6" at the end tells us already everything, because there is only one aber option listed that contains a shift up. and that is exactly what that "+ 6" did. it adds 6 to every possible y value of the function. so, the whole function moves up by 6 units.
and yes, the 13x of f(13x) stretches the function horizontally (along the x axis).
simply said, whenever the x value for the original function increased by 1, it increases for the new function by 13.
3x + 2(x − 1) − 4? pleeeessssssssssssssssssssssssssss
Answer:
5x - 6Step-by-step explanation:
3x + 2(x − 1) − 4 =
3x + 2x - 2 - 4 =
5x - 6
Answer:
[tex]\boxed{\bf 5x - 6}[/tex]Step-by-step explanation:
[tex]\bf 3x + 2(x - 1) - 4?[/tex]
Distribute.
[tex]\bf 3x + 2x - 2 - 4[/tex]Subtract the numbers.
[tex]\bf 3x + 2x - 2 - 4[/tex][tex]\bf 3x + 2x - 6[/tex]Combine like terms.
[tex]\bf 5x - 6[/tex]_____________________ANSWER FAST PLEASE!!!
Which of the following systems of inequalities would produce the region
indicated on the graph below?
+11
10
Jadosak
-1
2 3
15
6
7
8 9
A. v2x+1; y210; x ≥ 0
B. v2x+1; y<10; x ≥ 0
O c. v
OD. V > x+1; y≤ 10; x ≥ 0
Answer: D
Step-by-step explanation:
We know that the line [tex]y=10[/tex] is shaded below, so it represents [tex]y \leq 10[/tex].
Similarly, the line [tex]y=x+1[/tex] is shaded above, so it represents [tex]y > x+1[/tex].
If angle 2 is 5x plus 5 degrees and angle 6 is 30 degrees then what is x
The value of x is 5.
What is Adjacent angle?Two angles that have the same vertex and a side in common.
Here, m∠2 = m∠6
5x + 5 = 30
5x = 25
x = 25/5
x = 5
Thus, The value of x is 5.
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(c) (i) A new truck costs $15 000 and loses 23% of its value each year. Calculate the value of the truck after three years. ( c ) ( i ) A new truck costs $ 15 000 and loses 23 % of its value each year . Calculate the value of the truck after three years .
Answer:
$6847.955
Explanation:
Use the compound interest formula, but the value decreases over time.
[tex]\sf A = P(1 - \dfrac{r}{100} )^t[/tex]
where 'A' is final amount, r is rate, t is time
Inserting P = $15,000, r = 23, t = 3 years
[tex]\sf A = 15000(1- \dfrac{23}{100} )^3[/tex]
[tex]\sf A = 6847.995[/tex]
Hence the value of truck after three years will be $6847.955.
What else would need to be congruent to show that ABC = XYZ by ASA
Answer:
Option d
Step-by-step explanation:
BC = YZ
AC cannot be equal to XZ else it will be SAA congruency
are these right tell me yes or no
Answer:
Question 4: letter c
Question 3: letter c
Step-by-step explanation:
Help please.. z zzz z Z z z z z z z z z z z z z zz
Answer:
B
Step-by-step explanation:
look at the graph, it is really easy with such basic numbers involved :
the red dotted line is
y = 2
since the line is dotted (= the points on the line are not included in the solution), the colored area is below the line is
y < 2
the blue line is clearly just a 45° basic line through the origin (0,0), and that means for every point in that line x is equal to y.
y = x
and the line is solid, so the points are included in the solution. the shaded area is above the line, so, we need to use the ">" relation :
y >= x
the required solution is the combination of both, and therefore, B is correct.
What is the slope of a line that is parallel to the line y 3/4x+2
Answer:
-4/3
Step-by-step explanation:
mtan × mline = -1
mtan× 3/4 = -1
mtan =-4/3
What is the value of f(1)?
0
1
2
4
Answer:
Solution*-1
Step-by-step explanation:
because 1 is the value of (1)
Select the correct answer.
In the given figure, m AD = 79° and m
Answer:
2 or 3
Step-by-step explanation:
write it down dummy
Which expression is equivalent to 4 √10 ?
(૧/x
0 x ²
022
○ +³² (+ √/x)
0 +5
A shop increases all their prices by 6%
A picture frame increases by £294
Find the new price of the picture frame.
Answer:
0riginal price = 4900
Step-by-step explanation:
294 = 6%
294/6 = 49 49 = 1%
49 x 100 = 4900
0riginal price = 4900
please help fast grade 5 math extra points to those who explain and giving brainliest
Answer:
[tex]\frac{45}{7}[/tex]
Step-by-step explanation:
9 is the same as [tex]\frac{9}{1}[/tex]
∴ 9 ˣ [tex]\frac{5}{7}[/tex]
= [tex]\frac{9}{1}[/tex] ˣ [tex]\frac{5}{7}[/tex]
To multiply two fractions, just multiply their numerators together and their denominators together.
9 x 5 = 45
1 x 7 = 7
∴ [tex]\frac{9}{1}[/tex] ˣ [tex]\frac{5}{7}[/tex]
= [tex]\frac{45}{7}[/tex]
How does the graph of g(x)=
X-5
+2 compare to the graph of the parent function f(x) = ?
g(x) is shifted 5 units left and 2 units up from f(x).
g(x) is shifted 5 units right and 2 units up from f(x).
Og(x) is shifted 5 units left and 2 units down from f(x).
Og(x) is shifted 5 units right and 2 units down from f(x).
Answer:
B. g(x) is shifted 5 units right and 2 units up from f(x).
g(x) = [tex]\frac{1}{x-5}[/tex] + 2 is compared to the parent function, f(x) = [tex]\frac{1}{x}[/tex] by g(x) is shifted 5 units right and 2 units up from f(x).
What is Translation of Functions?Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.
There are horizontal translation and vertical translation of functions.
Given parent function is,
f(x) = [tex]\frac{1}{x}[/tex]
And the translated function is,
g(x) = [tex]\frac{1}{x-5}[/tex] + 2
When f(x) becomes g(x), the first change occurred is [tex]\frac{1}{x}[/tex] changes to [tex]\frac{1}{x-5}[/tex].
That is f(x) changes to f(x-5).
This translation occurs when the function undergoes horizontal translation towards right.
Then [tex]\frac{1}{x-5}[/tex] is translated to [tex]\frac{1}{x-5}[/tex] + 2.
That is, f(x-5) is changed to f(x-5) + 2.
This occurs for the vertical translation towards up.
Hence the translation occurred is g(x) is shifted 5 units right and 2 units up from f(x).
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Rewrite in simplest terms: (4x+5)+(−5x−1) pls help
Answer:
-x + 4
Step-by-step explanation:
(4x+5)+(−5x−1)
4x+5−5x−1 [Remove the parentheses]
-x + 4 [Combine Like Terms]
Answer:
-x+4
Step-by-step explanation:
Given:
(4x+5)+(−5x−1)
Solution:
To re-write this in it's simplest terms:
4x+5-5x−1Combine like terms:
4x-5x+5-1-x+4Hence the simplest form is -x+4.
Done.
can someone help me here pls thanks!
Using proportions, it is found that the measure of the inscribed angle B is of 30º.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In a circle, the inscribed angle is half the measure of the outside angle. Hence, in this problem, the measure of angle B is of 50% of 60º, hence:
m<B = 0.5 x 60º = 30º.
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Answer:
Using proportions, it is found that the measure of the inscribed angle B is of 30º.
Step-by-step explanation:
Need help with this question (pic included)
Answer:
answer= 3
hope this helps if not I'll try to do it again
0.39 recurring as a fraction please [ 3 and 9 are both recurring]
Answer:
[tex]\frac{13}{33}[/tex]
Step-by-step explanation:
we require 2 equations with the repeating digits placed after the decimal point.
let x = 0.3939.... (1) ← multiply both sides by 100
100x = 39.3939... (2)
subtract (1) from (2) thus eliminating the repeating digits
99x = 39 ( divide both sides by 99 )
x = [tex]\frac{39}{99}[/tex] = [tex]\frac{13}{33}[/tex] ← in simplest form
Step-by-step explanation:
0.39 repeating as a fraction
= 13/33
What function does this graph represent?
whats the y-inter of the line? interpet the y-inter in the context of the problem
Answer:
How do you interpret the y-intercept in the context of the problem?
The y-intercept of a line is the value of y where the line crosses the y-axis. In other words, it is the value of y when the value of x is equal to 0. Sometimes this has true meaning for the model that the line provides, but other times it is meaningless.
Step-by-step explanation:
please I need step by step solution of this question
The value of the expression will be 2. Then the correct option is B.
The complete question is given below.
What is the limit?The value that approaches the output for the given input value. Limits are a very important tool in calculus.
The expression is given below.
[tex]\rightarrow \displaystyle \lim_{x \to 0}\dfrac{\cos x \ \tan 2x}{x}[/tex]
Then the value of the expression will be
Applying L'hospital rule, then we have
[tex]\rightarrow \displaystyle \lim_{x \to 0}\dfrac{\dfrac{d}{dx} \cos x \ \tan 2x}{\dfrac{d}{dx}x}\\\\\\\\\rightarrow \displaystyle \lim_{x \to 0}\dfrac{2 \cos x \sec^2 2x - \sin x \ \tan 2x}{1}\\[/tex]
Put the limit, then we have
⇒ 2 × cos 0 × sec² (2 × 0) – sin 0 × tan (2 × 0)
⇒ 2 × 1 × 1 – 0
⇒ 2
Then the correct option is B.
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what is the domain of the following function: y=x^-5 + (x-1)
Answer:
Step-by-step explanation:
AandBhave coordinates (-1,1.5) and (3,2).
Tangents to the curve have been drawn at A and B.
Calculate the gradient of the curve at A and at B.
What are the vertex, focus, and
directrix of the parabola with
equation y-6=2(x-4)²?
Answer:
vertex (2,6)focus(49/8,2)directrix y=47/846. Geometry The volume of a cube is a function of the length of a side of the cube. Write a function for the volume of a cube. Find the volume of a cube with a side 13.5 cm long.
Answer:
1/3×22/7×r^2h
Step-by-step explanation:
the volume =1/3 ×22/7×r^2×13.5
A circle is defined by the equation given below.
The centre of the circle is (1/2, 1) and the radius of the circle is 2 if the circle equation is x² + y² − x − 2y − 11/4 = 0
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 centre of a circle)
The question is incomplete.
The complete question is:
A circle is defined by the equation given below.
x² + y² − x − 2y − 11/4 = 0
What are the coordinates for the centre of the circle and the length of the radius?
We know the standard form of a circle:
(x - h)² + (y - k)² = r²
Here (h, k) is the centre of the circle and r is the radius of the circle
[tex]\rm x^2 - x + \dfrac{1}{4} + y^2 - 2y + 1= \dfrac{11}{4} +\dfrac{1}{4} + 1\\\\[/tex]
[tex]\rm (x - \dfrac{1}{2})^2+(y-1)^2 = 2^2[/tex]
Thus, the centre of the circle is (1/2, 1) and the radius of the circle is 2 if the circle equation is x² + y² − x − 2y − 11/4 = 0
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Which table represents a proportional relationship? A 2-column table with 3 rows. Column 1 is labeled x with entries 4, 8, 18. Column 2 is labeled y with entries 6, 12, 26. A 2-column table with 3 rows. Column 1 is labeled x with entries 5, 20, 60. Column 2 is labeled y with entries 7, 28, 84. A 2-column table with 3 rows. Column 1 is labeled x with entries 12, 18, 26. Column 2 is labeled y with entries 5, 7, 9. A 2-column table with 3 rows. Column 1 is labeled x with entries 3, 9, 15. Column 2 is labeled y with entries 2, 8, 14.
Answer:
X Y
5 7
20 28
60 84
This table shows the proportional relationship.
Step-by-step explanation:
The equivalent ratios of two variables known as proportional relationship.
Table 1: X Y Table 3: X Y
4 6 12 5
8 12 18 7
18 26 26 9
Ratio = 4:6 = 8:12 ≠ 18:26 Ratio = 12:5 ≠ 18:7 ≠ 26:9
Table 2: X Y Table 4: X Y
5 7 3 2
20 28 9 8
60 84 15 14
Ratio = 5:7 =20:28=60:84 Ratio = 3:2 ≠ 9:8 ≠ 15:14
Here we see table 2 shows the proportional relationship.
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