Answer:
Step-b 4.55 g/cmy-step explanation:
What is the answer to this question
Answer:
m1 = 33 degrees ; m3 = 33 degrees
Step-by-step explanation:
m8 = m4 = 147 degrees
m4 + m1 = 180
147 + m1 = 180
m1 = 180 - 147
m1 = 33 degrees
m1 = m3 (vertical angles)
PLEASE HELP ME I NEED ANSWER RIGHT NOS
1 Triangle ABC is similar to triangle DEF with the side lengths of triangle ABC being 5 times the side lengths of triangle DEF. What characteristic of the two triangles is the same? the side lengths the areas the angles the perimeters
Answer:
Only the angles of each corner will be the same.
Step-by-step explanation:
Examine the system of equations.
2x − 4y = 6,
x − 2y = 3
How many solutions does this system of equations have?
Answer:
infinitely many solutions
Step-by-step explanation:
When you put the equations in desmos, the lines are the same therefore it has infinitely many solutions.
Answer:
✔️ c) infinitely many
Step-by-step explanation:
1. Y= 3x + 5
+0
2
Increasing
Decreasing
Positive
Negative
Answer:
The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.
Step-by-step explanation:
A sphere has a volume of 90m3 at room temperature. When heated to a certain temperature
its volume increases to 93m3, what is the percent of increase in volume?
Answer:
33.33%.
Step-by-step explanation:
93-90 = 3 m3 is the increase in Volume.
Percent increase = (3/90) * 100
= (1/30)*100
= 33.33%.
=
Find the most general antiderivative of the function (Check your answee by differentiation. Use C for the constant of the antiderivative.
f(x) = ^4√2 + ^4√x
To find the most general antiderivative of the function f(x) = 4√2 + 4√x, follow these steps:
1. Rewrite the function in terms of powers: f(x) = 2^(1/4) + x^(1/4)
2. Apply the power rule for antiderivatives: ∫(x^n)dx = (x^(n+1))/(n+1) + C
3. Find the antiderivative for each term:
For the constant term, 2^(1/4):
∫(2^(1/4))dx = (2^(1/4))x + C₁
For the variable term, x^(1/4):
∫(x^(1/4))dx = (x^(1/4 + 1))/(1/4 + 1) + C₂
∫(x^(1/4))dx = (x^(5/4))/(5/4) + C₂
∫(x^(1/4))dx = (4/5)x^(5/4) + C₂
4. Add both antiderivatives together and combine constants:
F(x) = (2^(1/4))x + (4/5)x^(5/4) + C
where F(x) is the most general antiderivative and C = C₁ + C₂.
Now, check your answer by differentiation:
F'(x) = d/dx[(2^(1/4))x] + d/dx[(4/5)x^(5/4)] + d/dx[C]
F'(x) = 2^(1/4) + (4/5)(5/4)x^(-3/4) + 0
F'(x) = 2^(1/4) + x^(1/4)
This matches the original function f(x), so the most general antiderivative is correct:
F(x) = (2^(1/4))x + (4/5)x^(5/4) + C
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At Ashley Furniture Store, there is a marble table that you want to
purchase for your mother. The length of the table is (-8x+2) and the width
of your rug is (3x-4). What is the total area of the table? Solve the
problem using the best method. Write the answer as a trinomial.
Step-by-step explanation:
in my opinion
total area = the width × the length
= (3x-4)(-8x+2)
= -24x²+6x+32x -8
= -24x² + 38x -8
The lengths of two sides of a triangle are shown.
Side 1: 8x2 − 5x − 2
Side 2: 7x − x2 + 3
The perimeter of the triangle is 4x3 − 3x2 + 2x − 6.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (4 points)
Part B: What is the length of the third side of the triangle? Show your work. (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)
Answer:
To find the total length of the two sides, we simply add them together:
Total length = Side 1 + Side 2
Total length = (8x^2 - 5x - 2) + (7x - x^2 + 3)
Total length = -x^2 + 8x^2 - 5x + 7x - 2 + 3
Total length = 7x^2 + 2x + 1
Therefore, the total length of the two sides of the triangle is 7x^2 + 2x + 1.
Step-by-step explanation:
To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle:
Perimeter = Side 1 + Side 2 + Side 3
We are given the perimeter of the triangle as 4x^3 - 3x^2 + 2x - 6 and we know the lengths of Side 1 and Side 2. Therefore, we can rewrite the formula as:
4x^3 - 3x^2 + 2x - 6 = (8x^2 - 5x - 2) + (7x - x^2 + 3) + Side 3
Simplifying the right-hand side:
4x^3 - 3x^2 + 2x - 6 = 7x^2 + 2x + 1 + Side 3
Side 3 = 4x^3 - 3x^2 + 2x - 6 - 7x^2 - 2x - 1
Simplifying further:
Side 3 = 4x^3 - 7x^2 - x - 7
Therefore, the length of the third side of the triangle is 4x^3 - 7x^2 - x - 7.
Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction.
Closure under addition means that when two polynomials are added, the result is also a polynomial. In Part A, we added the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 to get the total length of the two sides of the triangle, which is 7x^2 + 2x + 1. Since the total length is also a polynomial, this shows that the polynomials are closed under addition.
Closure under subtraction means that when one polynomial is subtracted from another polynomial, the result is also a polynomial. In Part B, we subtracted the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 from the given perimeter of the triangle, 4x^3 - 3x^2 + 2x - 6, to get the length of the third side of the triangle, which is 4x^3 - 7x^2 - x - 7. Since the length of the third side is also a polynomial, this shows that the polynomials are closed under subtraction.
Therefore, the answers for Part A and Part B demonstrate that the polynomials are closed under addition and subtraction.
Consider the least-squares estimated fitted line: Y
i
=b 0
+b 1
X i
. Prove the following properties: (a) ∑ i=1
n
e i
=0, where e i
are residuals defined as e i
=Y i
− Y
i
. (b) Show that b 0
,b 1
are critical points of the objective function ∑ i=1
n
e i
2
, where b 1
= ∑ j
(X j
− X
ˉ
) 2
∑ i
(X i
− X
ˉ
)(Y i
− Y
ˉ
)
,b 0
= Y
ˉ
−b 1
X
ˉ
. (c) ∑ i=1
n
Y i
=∑ i=1
n
Y
^
i
. (d) ∑ i=1
n
X i
e i
=0. (e) ∑ i=1
n
Y
i
e i
=0. (f) The regression line always passes through ( X
ˉ
, Y
ˉ
).
The least-squares estimated fitted line is a straight line that minimizes the sum of the squared errors (vertical distances between the observed data and the line).
For every x, the value of Y is calculated using the least squares estimated fitted line:Yi^=b0+b1XiHere, we have to prove the following properties:
a) ∑ i=1nei=0,
b) Show that b0,b1 are critical points of the objective function ∑ i=1nei^2, where b1=∑j(Xj−X¯)2∑i(Xi−X¯)(Yi−Y¯),b0=Y¯−b1X¯.c) ∑ i=1nYi=∑ i=1nY^i,d) ∑ i=1nXi ei=0,e) ∑ i=1nYiei=0,f)
The regression line always passes through (X¯,Y¯).
(a) Let's suppose we calculate the residuals ei=Yi−Y^i and add them up. From the equation above, we get∑i=1nei=Yi−∑i=1n(Yi−b0−b1Xi)=Yi−Y¯+Y¯−b0−b1(Xi−X¯).
The first and third terms in the equation cancel out, as a result, ∑i=1nei=0.
(b) Let us consider the objective function ∑i=1nei^2=∑i=1n(Yi−b0−b1Xi)2, which is a quadratic equation in b0 and b1. Critical points of this function, b0 and b1, can be obtained by setting the partial derivatives to 0.
Differentiating this equation with respect to b0 and b1 and equating them to zero, we obtainb1=∑j(Xj−X¯)2∑i(Xi−X¯)(Yi−Y¯),b0=Y¯−b1X¯.∑i=1nYi=∑i=1nY^i, because the slope and intercept of the least-squares fitted line are calculated in such a way that the vertical distances between the observed data and the line are minimized.
(d) We can write Yi−b0−b1Xi as ei.
If we multiply both sides of the equation by Xi, we obtainXi ei=Xi(Yi−Y^i)=XiYi−(b0Xi+b1Xi^2). Since Y^i=b0+b1Xi, this becomes Xi ei=XiYi−b0Xi−b1Xi^2.
We can rewrite this equation as ∑i=1nXi ei=XiYi−b0∑i=1nXi−b1∑i=1nXi^2. But b0=Y¯−b1X¯, and therefore, we can simplify the equation as ∑i=1nXi ei=0.
(e) Similarly, if we multiply both sides of the equation ei=Yi−Y^i by Yi, we get Yi ei=Yi(Yi−Y^i)=Yi^2−Yi(b0+b1Xi).
Since Y^i=b0+b1Xi, this becomes Yi ei=Yi^2−Yi(b0+b1Xi).
We can rewrite this equation as ∑i=1nYi ei=Yi^2−b0∑i=1nYi−b1∑i=1nXiYi.
But b0=Y¯−b1X¯ and ∑i=1n(Yi−Y¯)Xi=0, which we obtained in (d), so we can simplify the equation as ∑i=1nYi ei=0.(f) The equation for the least squares estimated fitted line is Yi^=b0+b1Xi, where b0=Y¯−b1X¯.
Therefore, this line passes through (X¯,Y¯).
We have shown that the properties given above hold for the least squares estimated fitted line.
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easy math problem !,!!,!
A- 9B- 87C- -2D -9
Step-by-step explanation:
Find two consecutive integers such 4 that times the smaller integer is 50 less than 6
times the larger integer.
The consecutive integers such 4 that times the smaller integer is 50 less than 6 times the larger integer are 22 and 23.
How to calculate the value?Let the consecutive integers be x and x + 1.
In this case, the integers are such 4 that times the smaller integer is 50 less than 6 times the larger integer.
This will be:
4(x) = 6(x + 1) - 50
4x = 6x + 6 - 50
Collect like terms
4x - 6x = -44
-2x = -44
Divide
x = 44/2
x = 22
Also, x + 1 = 22 + 1 = 23
The numbers are 22 and 23.
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Tony spent a total of 140 minutes studying for his algebra test this total was 5 more than 3 minutes the amount of minutes he spent studying for his biology test how many minutes did Tony spend studying for his biology test
Proportionately, if Tony spent a total of 140 minutes studying for his algebra test, and this total was 5 more than 3 minutes the amount of minutes he spent studying for his biology test, the time Tony spent studying for his biology test was 132 minutes.
What is proportion?Proportion refers to the equation of two or more ratios.
Ratios show the relative size of a value compared to another.
Proportions are fractional values like ratios.
The total minutes Tony spent studying for his algebra test = 140
5 more than 3minutes = 8 minutes
140 > 132 by 8 minutes (140 - 8)
The time spent studying biology = 132
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Can someone please help me? 3t + 7 = -8
Answer:
Step-by-step explanation:
Look at 3%2At%2B7=%28+-8+%29.
Moved these terms to the left %28 +8+ %29
It becomes 3%2At%2B7%2B _green%28+8+%29=0.
Look at 3%2At%2B_red%28+7+%29%2_red%28+8+%29=0.
Added fractions or integers together
It becomes 3%2At% 2B % 28+15+%29=0.
Look at highlight_red%28+3%2At%2B15+%29=0.
Solved linear equation %28+3%2At%2B15=0+%29 equivalent to 3*t+15 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: t=-5.
Answer: t= -1/3
Step-by-step explanation:
3t+7=-8
subtract 7 from 7 and 8 (this cancels out the 7)
left with 3t = -1
divide 3 into 3t and -1
the 3 in 3t is canceled out, leaving us with t, therefore t= -1/3
Which of the following expressions is equivalent to 4(2x+y) ?
Answer:
what expressions
Step-by-step explanation:
Answer:
Step-by-step explanation:
First expand the expression so you know the coefficients of x and y.
4(2x+y+2y) = 4(2x+3y) = 8x+12y
8x+12y = 8x+12y
6x+7y ≠ 6x+12y
8x+y+2y = 8x + 3y ≠ 8x+12y
8x+4y+8y = 8x+12y = 8x+12y
hope this help
I need to know what point has the coordinates of 3,3 please help :(
Answer:
B: N
Step-by-step explanation:
Down Below: Question
Please help (50 BRAINLIST!!!!!!!!!!!)
The inequalities that represent the constraints in this situation are r+c≥80 and 1.45R +0.75c≤200 respectively
How to determine the inequalities?The amount with victor = $200
Let the number of roses purchased by Victor be R,
Also, Rose cost $1.45 each
Therefore cost of rose = 1.45R
A;so, let the number of carby Victor be C at a cost of $0.65 each nation purchased by victor be $0.65 each
Therefore, cost of carnation = $0.65c
1) The inequality to represent the constraint that every person takes home at least one rose is r+c≥80 and
2) the inequality to represent the cost constraint is 1.45R + 0.65≤200
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The population of a city is increasing at a steady rate of 2.4% per annum.
The current population is 528 000.
What is the expected population in 4 years?
Give your answer to the nearest thousand.
The expected population of a city in 4 years is 581,000.
What is defined as the rate of population growth?The average annual rate of change in population size for a specific ethnicity, country, or region over a given time period. It expresses the proportion, usually multiplied by 100, between the annual growth in population size and also the total population in that year.Current population (P) = 528 000.
Rate of growth (r) = 2.4%
Time t = 4 years
Expected population (A) = ?
The formula used is-
A = P(1 + r/100)∧t
Put the values.
A = 528 000(1 + 2.4/100)∧4
A = 528 000 x (1.042)∧4
A = 581,000
Thus, the expected population of a city in 4 years is 581,000.
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WILL MARK AS BRAINLIEST PLEASE HURRY
Asha found that a vertical line intersects the graph of x = {y} at two points. What can Asha conclude about x = {y} ?
1. It is a function of x but not a relation.
2. It is a relation but not a function of x.
3. It is both a function of x and a relation.
4. It is neither a function of x nor a relation.
Answer:
3. It is both a function of x and a relation i think
Step-by-step explanation:
Victoria buys 5 scarves for a total of 36.25. If each scarf costs the same amount of money, how much did one scarf cost?
Answer:
7.25
Step-by-step explanation:
36.25/5=7.25 simple
Step-by-step explanation:
cost of 5 scarf = 36.25
cost of one scarf = 36.25/5
= 725/100
= 7.25 $
so one scarf cost = 7.25$
plz mark my answer as brainlist plzzzz vote me also and hope this helps you ...
Mr. Howard and Ms. Egan enjoy running on the weekends. They both usually run at a steady pace and try to meet in the middle. They are 14 miles apart. Mr. Howard can run 3 miles in 30 minutes. Ms. Egan can run 4 miles in 30 minutes.
Given :
Distance between them, D = 14 miles .
Mr. Howard can run 3 miles in 30 minutes.
Ms. Egan can run 4 miles in 30 minutes.
To Find :
Time taken by them to meet.
Solution :
Mr Howard speed, \(v_H=\dfrac{3}{0.5}=6\ mph\) .
Mr Egan speed, \(v_e=\dfrac{4}{0.5}=- 8\ mph\) . [ Since they run in opposite direction ]
Their relative speed :
\(v=v_E-v_H\\\\v = 8-(-6) \ mph \\\\v = 14 \ mph\)
Time taken by them to meet :
\(T = \dfrac{14}{14}\ hours\\\\T = 1 \ hours\)
Hence, this is the required solution.
Consider the following. Tis the reflection through the origin in R2: T(X,Y) = (-X, -y), v = (4, 2). (a) Find the standard matrix A for the linear transformation T. A =____ (b) Use A to find the image of the vector v. T(v)= _____
The standard matrix A for the linear transformation T, which represents the reflection through the origin in R2, can be obtained by applying T to the standard basis vectors.
Applying T to the first standard basis vector (1, 0) gives T(1, 0) = (-1, 0).
Applying T to the second standard basis vector (0, 1) gives T(0, 1) = (0, -1).
The standard matrix A is constructed by placing the images of the standard basis vectors as columns:
A = [(-1, 0), (0, -1)].
(b) To find the image of the vector v = (4, 2) under the transformation T, we can multiply the standard matrix A by v:
A * v = [(-1, 0), (0, -1)] * (4, 2) = (-14 + 02, 0*4 + (-1)*2) = (-4, -2).
Therefore, T(v) = (-4, -2) is the image of the vector v under the reflection transformation T.
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write the equation and graph the line with a slope of -3 and passes though point (4, -5)
Answer:
y = - 3x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute (4, - 5 ) into the partial equation
- 5 = - 3(4) + c = - 12 + c ( add 12 to both sides )
7 = c
y = - 3x + 7 ← equation of line
suppose a finite model for an incidence geometry satisfies the additional axiom: every line has exactly three points lying on it. what is the minimum number of points needed for such a geometry? why?
In an incidence geometry with the additional axiom that every line has exactly three points lying on it, the minimum number of points required is 4.
This is because a line must have at least two-points to exist, and if it has only two points, it is not possible to have another point lying on it (since every line must have exactly three points).
Hence, there must be at least 4-points to create two lines such that each line contains exactly three points.
Also, with 4 points, it is possible to create 6 lines such that each line contains exactly 3 points, forming a configuration known as the Fano-plane, which is the smallest example of an incidence geometry that satisfies the given axiom.
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Suppose a survey of 580 women in the United States found that more than 64% are the primary investor in their household. Which part of the survey represents the descriptive branch of statistics? Make an inference based on the results of the survey.64% of women in the sample are the primary investor in their household.
There is an association between U.S. women and being the primary investor in their household.
The sentence "64% of women in the sample are the principal investor in their household" serves as an example of descriptive statistics.
What will the inference be?This sentence provides a summary of the survey's data and a descriptive statistic (percentage) that characterizes the sample's characteristics.
According to the survey's findings, "there is a correlation between American women and being the principal investor in their household." The sample data are used to draw this conclusion about the population. Despite the fact that the sample is not representative of all American women, the findings indicate that a sizable number of the women in the sample are the principal investors in their households.
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Please help 60 points for a rapid answer-In the figure below which of the following is true in circle E?
Answer:
all 3 options are true : A, B, C
Step-by-step explanation:
warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.
they say that A and C are correct.
but I am going to show you that if A and C are correct, then also B must be correct.
therefore, my given answer above is the actual correct answer (no matter what the test systems say).
originally the information about the alignment of the point F in relation to point E was missing.
therefore, I considered both options :
1. F is on the same vertical line as E.
2. F is not on the same vertical line as E.
because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :
the vertical line of EF is like a mirror between the left and the right half of the picture.
A is mirrored across the vertical line resulting in B. and vice versa.
the same for C and D.
this leads to the effect that all 3 given congruence relationships are true.
if we consider assumption 2, none of the 3 answer options could be true.
but if the assumptions are true, then all 3 options have to be true.
now, for the "why" :
remember what congruence means :
both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.
for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.
so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.
therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.
but do you notice something ?
both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.
now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.
therefore, AC must be equal to BD.
and that means that AC is congruent to BD.
because lines have no other congruent criteria - only the lengths must be identical.
PLEASE HELP, DUE SOON, TY!!:)
Solve for MN.
A)21
B)9
C)6
D)4
C) 6
Solution: 6.
Because the segments in the triangle are parallel, we can set up a proportion to solve for MN.
\(\frac{4}{10}=\frac{x}{15}\)
Find the circumferences of both circles to the nearest tenth.
The circumference of the blue circle is about cm.
The circumference of the orange circle is about cm.
Answer:
Step-by-step explanation:
The answer would be 10 because you are adding the circumference of the orange and blue, so therefore, it would be 10. Also the 10 is the nearest tenth.
What is the image of the point ( 0 , 1 ) after a rotation of 270 ∘ counterclockwise about the origin?
The image of the point (0,1) after a rotation of 270 degrees counterclockwise about the origin is the point (1,0).
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
A rotation of 270 degrees counterclockwise about the origin corresponds to a transformation in which every point in the plane is rotated 270 degrees counterclockwise about the origin.
To find the image of the point (0,1) under this transformation, we can use the following formula for a counterclockwise rotation of a point (x,y) about the origin by an angle of θ:
x' = x cos(θ) - y sin(θ)
y' = x sin(θ) + y cos(θ)
Plugging in the values x = 0, y = 1, and θ = 270 degrees, we get:
x' = 0 cos(270°) - 1 sin(270°) = 0 - (-1) = 1
y' = 0 sin(270°) + 1 cos(270°) = 0 + 0 = 0
Therefore, the image of the point (0,1) after a rotation of 270 degrees counterclockwise about the origin is the point (1,0).
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The table below shows the number of homes in a certain city which have computers, C(x), as a function of x, the number of years since 1990.
Which function best models this set of data?
A.
C(x) = 29,800x + 745,000
B.
C(x) = 745,000(1.04)x
C.
C(x) = 1.04(745,000)x
D.
C(x) = 30,992x + 743,808
The best function that models this set of data is option B. C(x) = 745000 * \((1.04)^2\)
What is exponential?Exponential refers to a mathematical operation or function involving a constant called the base, raised to a power that is a variable, which is usually represented by the letter x.
According to question:The best function that models this set of data is option B.
C(x) = 745000 \(* (1.04) ^ x\)
This is an exponential function that models the growth of the number of homes with computers over time. The base of the exponential function is 1.04, which indicates that the number of homes with computers is growing at a rate of 4% per year.
We can verify this by checking the values in the table.
When x = 1,
C(1) = 745000 * \((1.04) ^ 1\)
C(1) = 774800
When x = 2,
C(2) = 745000 * \((1.04) ^ 2\)
C(2) = 805792
We can see that the function closely matches the given data points. Therefore, option B is the best function that models this set of data.
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