The two column proof for the given angle addition has been carried out below.
How to Carry out two column proof?
1) m∠CZE = m∠1 + m∠2
Reason: Angle Addition Property
2) m∠FXH = m∠3 + m∠4
Reason: Angle Addition Property
3) m∠CZE = m∠FXH
Reason: Given
4) m∠1 + m∠2 = m∠3 + m∠4
Reason: Substitution Property
5) m∠1 = m∠3
Reason: Subtraction Property
6) m∠3 + m∠2 = m∠3 + m∠4
Reason: Substitution Property
7) m∠2 = m∠4
Reason: Subtraction Property
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50% if £80 pls helppp
Answer:
50%×€80
50/100×80
€40
Step-by-step explanation:
please mark me as brainlest
Answer:
£40
Step-by-step explanation:
▪︎ Method I:
£80 - 100%
£x - 50%
x = (£80 * 50%) / 100% = £40
▪︎ Method II:
50% is one half
Therefore, 50% of £80 is £80 / 2 = £40
This table represents the proportional relationship between the number of boxes and the number of magnetic cubes held by the boxes. cubes boxes number of cubes 1 n 5 625 8 1,000 what is the unknown value representing the unit rate? 8 125 140 156
The unknown value representing the unit rate is 125.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
This table represents the proportional relationship between the number of boxes and the number of magnetic cubes held by the boxes.
Cubes boxes number of cubes
1 5
n 625
8 1,000
If the unit cube box has 5 number of cubes.
then,
n cubes boxes = 625/5
= 125
The unknown value representing the unit rate is 125.
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Answer:
125
Step-by-step explanation:
Nick wants to write a 1,260 page science-fiction novel.
How many pages will Nick need to write each month to finish his novel in 1 year?
1 year = 12 months
Pages to write in 12 months = 1260
Pages to write in 1 month = 1260/12
= 105 pages per month
A parabola opens upward. The parabola goes through the point (3, -1), and the vertex is at (2, -2). write the equation of the parabola
The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)
What is a Parabola ?A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.
(x-h)² = 4a(y-k)
It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).
Therefore
(x -2)² = 4a(y +2)
The parabola passes through the point (3,-1)
(3-2)² = 4*a(-1+2)
1 = 4 a
a = 1/4
The equation of the parabola is
(x-2)² = (y+2)
Therefore The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)
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What is the difference between the highest and lowest points in a data set?the mean the median the mode the range
Answer:
Range
Step-by-step explanation:
Range is found by subtracting the highest and lowest point in the dataset
Mode is the number that occurs most frequently in the set
Median is the central number in the dataset when arranged from lowest to highest
Mean is the sum of all the numbers in the dataset divided by how many numbers there are.
For example, take this list of numbers: 10, 10, 20, 40, 70.
The mean (also known as average) is found by: 10 + 10 + 20 + 40 + 70 / 5 = 30.
The median is found by ordering the set from lowest to highest and finding the exact middle. The median is just the middle number: 20.
Parallel to y=−3/4x, through (4, -1)
Write the slope intercept form of each equation of the line. Use a fraction for slope if needed.
y = ___x + ___
Answer:
[tex]y=-\frac{3}{4}x+2[/tex]
Step-by-step explanation:
The slope-intercept form is given by y=mx+c, where m is the slope and c is the y-intercept.
Slope of given line= [tex]-\frac{3}{4}[/tex]
Parallel lines have the same slope. Thus, the slope of the line would also be [tex]-\frac{3}{4}[/tex].
[tex]y=-\frac{3}{4}x +c[/tex]
The value of c can be found by substituting a pair of coordinates.
When x= 4, y= -1,
[tex]-1=-\frac{3}{4} (4)+c[/tex]
-1= -3 +c
Add 3 to both sides:
c= -1 +3
c= 2
Thus, the equation of the line is [tex]\bf{y=-\frac{3}{4}x+2[/tex].
Additional:
Do check out the following for a similar question on slope-intercept form!
https://brainly.com/question/25549430Which are applications of mathematics in music? Select all that apply.
identifying measurements
calculating beats per minute
calculating the time signature
finding ratios of note frequencies
mapping marching band performances
Answer:
calculating beats per minute
((-7,1). (-3,2). (0, -2). (5, -5)}What are the domain and range of the function represented by the set of ordered pairs?
Answer:
Domain:{-7,-3,0,5}
Range:{1,2,-2,-5}
Step-by-step explanation:
i know because it works for me.
6. What is the measure of angle A rounded to two decimal places? 15 A) 25.02° B)27.82° C) 62.18° D)64.98°
sin A=Perpendicular/ Hypotenuse
sin A = 7/15
A= arcsin(7/15)
= 27,82 degree
Answer is option (B)
What is the solution for x in the equation?
-2x+14+ 10x=34
OA. x = 6
OB. x = 5/2
OC. x = 1/8
OD. x = 2/5
Answer:
B. x = 5/2
Step-by-step explanation:
-2x+14+ 10x=34
-2x+10x=34-14
8x=20
x=20/8 =5/2
HELP MEE ,20 POINTS !!!!
Celina says that each of the following expressions is actually a binomial in disguise:
5abc-2a^2+6abc
5x^3∙2x^2-10x^4+3x^5+3x∙(-2) x^4
(t+2)^2-4t
5(a-1)-10(a-1)+100(a-1)
(2πr-πr^2 )r-(2πr-πr^2)∙2r
Celina says true that each of the following expressions is actually a binomial expression.
What is binomial?The binomial is a polynomial of two-term only. For example, x + 5 where x and 5 are the two separate terms.
Celina says that each of the following expressions is actually a binomial in disguise:
a. 5abc - 2a² + 6abc = 11abc - 2a²
The is a binomial expression.
b. 5x³∙2x² - 10x⁴ + 3x⁵ + 3x∙(-2) x⁴ = 7x⁵ - 10x⁴
The is a binomial expression.
c. (t+2)² - 4t = t² + 4
The is a binomial expression.
d. 5(a - 1) - 10(a - 1) + 100(a - 1) = 95a - 95
The is a binomial expression.
e. (2πr - πr² )r - (2πr - πr²)∙2r = -2πr² + πr³
The is a binomial expression.
Celina says true that each of the following expressions is actually a binomial expression.
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MATH!!! 15 points;))) find the surface area of the composite figure
please answer correctly and check over your work...
The area of a 2D form is the amount of space within its perimeter. The surface area of the composite figure is 76.8 ft².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The surface area of the composite figure,
Surface area = 2(3.6×2) + (4×2) + 3(3.6×4) + 2(5.6)
= 14.4 + 8 + 43.2 + 11.2
= 76.8
Hence, the surface area of the composite figure is 76.8 ft².
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Through aregular hexagonal prism whose base edge is 8cm whose height 12 cm ahole in the shape of aright prism with its end being arhombus with diagonals 6cm and 8cm is drilled find total surface area of remaining solid and the volume
Answer:
96 cm2, 48 cm2
Step-by-step explanation:
Basically you times the first two questions and then the other 2, that leads you with the answer
A ride ticket usually costs
$1.50, but if you buy 10 tickets, you get
a 5% discount. Find the sale price of 10 tickets
Answer: Hope this helps if this is what you want.
$14.25
Step-by-step explanation:
$1.50 = 1 ticket
1.50 * 10 = 15
$15 = 10 tickets
100% - 5% = 95% (0.95)
15 * 0.95 = 14.25
$14.25
Justin did push-ups for the past 555 days.The following data points are the number of push-ups he did each day.
21,24,24,27,29
Find the standard deviation of the data set.
Round your answer to the nearest hundredth.
push-ups
Answer: σ: 2.76
Step-by-step explanation:
Count, N: 5
Sum, Σx: 125
Mean, μ: 25
Variance, σ2: 7.6
Steps
look at attached pic for formula
σ^2 = [tex]\frac{Σ(xi - μ)^{2} }{N}[/tex]
[tex]\frac{(21 - 25)2 + ... + (29 - 25)2}{5}[/tex]
⇒ [tex]\frac{38}{5}[/tex]
⇒ 7.6
σ = [tex]\sqrt{7.6}[/tex]
⇒ 2.756809750418
⇒ or 2.76
Kamaria opens a bank account with $300. Five weeks later, her account balance is $500. What was the average rate of change of her account balance in dollars per week?
Answer:
$40 average
Step-by-step explanation:
500-300=200
200/5=40
hello people, can anybody solve it
[tex]\\ \rm\Rrightarrow \left(\dfrac{x^a}{x^{-b}}\right)^{a^2-ab+b^2}\times \left(\dfrac{x^b}{x^{-c}}\right)^{b^2-bc+c^2}\times \left(\dfrac{x^c}{x^{-a}}\right)^{c^2-ca+a^2}=1[/tex]
[tex]\\ \rm\Rrightarrow (x^{a+b})^{a^2-ab+b^2}\times (x^{b+c})^{b^2-bc+c^2}\times (x^{c+a})^{c^2-ac+a^2}=1[/tex]
[tex]\\ \rm\Rrightarrow x^{(a+b)(a^2-ab+b^2)}\times x^{(b+c)(b^2-bc+c^2)}\times x^{(c+a)(c^2-ca+a^2)}=1[/tex]
a³+b³=(a+b)(a²-ab+b²)[tex]\\ \rm\Rrightarrow x^{a^3+b^3}\times x^{b^3+c^3}\times x^{c^3+a^3}=1[/tex]
[tex]\\ \rm\Rrightarrow x^{a^3+b^3+b^3+c^3+c^3+a^3}=1[/tex]
[tex]\\ \rm\Rrightarrow x^{2a^3+2b^3+2c^3}=x^0[/tex]
[tex]\\ \rm\Rrightarrow 2(a^3+b^3+c^3)=0[/tex]
[tex]\\ \rm\Rrightarrow a^3+b^3+c^3=0[/tex]
URGENT PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!
The attached graph represent the points in the domain -6 < x ≤ -2
How to graph the points?The function is given as:
[tex]f(x) = \left[\begin{array}{ccc}-2&-6 < x \le -1\\1&-1 < x \le 2 & \\5 & 2 < x \le 4\end{array}\right[/tex]
The question says that we plot two points in the domain -6 < x ≤ -2
The domain -6 < x ≤ -2 means that the values of x are greater than -6, but they do not exceed -1
The function at this interval means that all values of x have an output value of -2
So, the two points to plot could be (-5,-2) and (-1,-2)
See attachment for the graph of the points
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The oblique prism below has an isosceles right triangle
base.
x
(x+2)
(x+3)
Mark this and return
53:21
What expression represents the volume of the prism, in
cubic units?
01/2+2²
028+22²
02 +2
O²+37²2²
Save and Exit
Submit
Next
The volume of the prism, in cubic units is V = 1/2*x³ + x²
The figure and options are in the figure attached
What is an Oblique Prism ?An oblique prism is a polyhedron figure , with a rectangular base and triangular side faces .
It is given that
The oblique prism below has an isosceles right triangle base.
In the figure attached, the oblique prism is shown.
The volume of the prism is given by
V = b*h
h is the height and b is the Area of the base
It is given that the base is an isosceles right triangle, its area is:
Area of a Triangle = (1/2) base * height
here the base and height is x
b = 1/2*x²
The height of the prism is (x + 2).
Then, the volume is:
V = 1/2*x²*(x + 2)
V = 1/2*x³ + x² cu. units
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Which measurements could create more than one triangle?
A. Angles measuring 85°, 45°, and 60°
B. Angles measuring 95°, 35°, and 50⁰
C. Sides measuring 8 cm and 15 cm and an included angle measuring 60°
D. Sides measuring 5 inches, 7 inches, and 13 inches
Answer:
A.
Step-by-step explanation:
The sum of angles of a triangle is 180. if you add 85+45+60 you get 190. That is more than 180.
For the complex number z = (5sqrt(3))/4 - 5/4 * i what is the polar form
Answer: 3
Step-by-step explanation:
The required polar form of the equation is [tex]Z = 5/2cos30 - 5/2sin30i.[/tex]
For the complex number z = (5sqrt(3))/4 - 5/4 * i the polar form is to be determined.
The number that constitutes real and imaginary numbers are called complex numbers. The standard form of complex number = a + bi
[tex]z = 5\sqrt{3}/4 - 5/4i[/tex]
the polar form complex numbner can be given as
[tex]z = rcos\theta +rsin\theta i[/tex] - - - - - -(1)
where r = [tex]\sqrt{a^2+b^2}[/tex]
and [tex]\theta=tan^-\frac{b}{a}[/tex]
Since a = 5√3/4 and b = -5/4
[tex]r = \sqrt{(5\sqrt{3}/4)^2+(5/4)^2}[/tex]
r = 10/4
r = 5/2
Now,
[tex]\theta=tan^-\frac{b}{a}[/tex]
[tex]\theta=tan^-\frac{-5/4}{5\sqrt{3}/4 }\\\theta=tan^-\frac{1}{\sqrt{3} }\\\theta=tan^-(-tan30)\\\theta=-30[/tex]
Now the polar form is given by substituting the values of r and [tex]\theta[/tex] in equation 1
Here,
[tex]z = 5/2cos30 +5/2sin(-30)i\\z = 5/2cos30-5/2sin30 i[/tex]
Thus, the required polar form of the equation is [tex]Z = 5/2cos30 - 5/2sin30i.[/tex]
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. Here is a table that shows the ratio of flour to water in an art paste. Complete the table with values in equivalent ratios.
K is an example of.
O an equation
O a formula
O a constant
O a variable
Answer:
a variable.
Step-by-step explanation:
I know this because I had a test today that I studied for but I of course failed it…
It was for math.
The following table shows how the average constituency changes for two regional governing boards, joshua and salinas, when a new representative is added to each board.
joshua's
average
constituency salinas's
average
constituency
joshua receives
new board
member 1232 1520
salinas receives
new board
member 1448 1333
(a) determine the relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas. round to the nearest thousandth.
(b) determine the relative unfairness of an apportionment that gives a new board member to salinas rather than to joshua. round to the nearest thousandth.
(c) using the apportionment principle, determine which regional governing board should receive the new board member.
joshua
salinas
The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be
How to calculate the values?The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be:
= (1520 - 1232)/1232
= 288/1232
= 0.234
The relative unfairness of an apportionment that gives a new board member to salinas rather than to Joshua will be:
= (1448 - 1333)/1333
= 115/1333
= 0.086
The regional governing board that should receive the new board member is Salinas.
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If lines Joined each given point on the graph to the origin, which points would be on lines that represent a unit rate greater than the one
represented in the table?
x y
5 11
10 22
15 33
10
9
3
022 Edmentum. All rights reserved.
The points (2, 8), (3, 9) and (4, 10) have a greater slope than the table
How to determine the points?The table and the graph that complete the question are added as an attachment
Start by calculating the slope of the table using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (22 - 11)/(10 - 5)
m = 2.2
Next, we calculate the slope of each point on the graph when connected to the origin using:
m = y/x
So, we have:
(2,8) ⇒ m = 8/2 = 4
(3,9) ⇒ m = 9/2 = 3
(4,10) ⇒ m = 10/4 = 2.5
(5,8) ⇒ m = 8/5 = 1.6
(6,7) ⇒ m = 7/6 = 1.2
(7,6) ⇒ m = 6/7 = 0.9
By comparing the slopes with 2.2, we can see that only points (2, 8), (3, 9) and (4, 10) have a greater slope than the table
Hence, the points are (2, 8), (3, 9) and (4, 10).
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Answer: The points: (5,8) (6,7) (7,6)
Step-by-step explanation: I took the test and the points going ↘️ (down) are correct but the points ↖️ (up) are incorrect
Sid has a water dispenser in his refrigerator as shown in the figure.
PLS HELP!
A prism has a length of 4 inches, height of 14 inches, and width of 8 inches.
Sid would like to have three water dispensers in his refrigerator. How much cubic space will all three dispensers take up in Sid’s refrigerator?
448 in.3
896 in.3
1,200 in.3
1,344 in.3
Answer:
c. I'm sorry if I'm wrong
Step-by-step explanation:
The original price of a hat is $35. The sale price is $19.95. What is the percent of discount?
Answer:
43%
Step-by-step explanation:
19.95 ÷ 35 = .57 or 57%
100 - 57 = 43
Which expression is equivalent to -6(-2+2x)?
O −4-12%
O −4+2%
O 4-12%
O 4+12%
Use distributive law
a(b+c)=ab+ac
-6(-2)-6(2x)12-12x12(1-x)four students are trying to determine what number must replace the question (x^2)^7=x^4*x^8 in order to make it true
Joe said the answer is 6. Sam said it is impossible to answer.
Peter said the answer is 32. Alex said the answer is 16.
Who is correct? Explain why.
Let's solve ourselves instead of believing anyone
[tex]\\ \rm\Rrightarrow (x^2)^7=x^4x^8[/tex]
a^m+a^n=a^m+n[tex]\\ \rm\Rrightarrow x^{14}=x^{4+8}[/tex]
[tex]\\ \rm\Rrightarrow x^{14}=x^{12}[/tex]
[tex]\\ \rm\Rrightarrow x^{14}-x^{12}=0[/tex]
[tex]\\ \rm\Rrightarrow x^{12}(x^2-1)=0[/tex]
[tex]\\ \rm\Rrightarrow x^2-1=0[/tex]
[tex]\\ \rm\Rrightarrow x^2=1[/tex]
[tex]\\ \rm\Rrightarrow x=\pm 1[/tex]
0 is also a solutionAnswer:
Joe is correct
Step-by-step explanation:
Given equation:
[tex](x^2)^?=x^4 \cdot x^8[/tex]
The exponent outside the bracket is a question mark and the students are trying to determine the value of the question mark.
For ease of answering, let y be the unknown number (question mark):
[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]
First, simplify the equation by applying exponent rules to either side of the equation:
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}\quad\textsf{to the left side}:[/tex]
[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]
[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c} \quad \textsf{to the right side}:[/tex]
[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]
[tex]\implies x^{2y}=x^{4+8}[/tex]
[tex]\implies x^{2y}=x^{12}[/tex]
Now, apply the exponent rule:
[tex]x^{f(x)}=x^{g(x)} \implies f(x)=g(x)[/tex]
Therefore,
[tex]x^{2y}=x^{12}\implies 2y=12[/tex]
Finally, solve for y:
[tex]\implies 2y=12[/tex]
[tex]\implies 2y \div 2 = 12 \div 2[/tex]
[tex]\implies y=6[/tex]
Therefore, Joe is correct as the unknown number is 6.
I saw this in a newspaper – it was a puzzle for adults, fully grown humans, but I think you will find it easy.
All the digits from 1 to 9 are used in this grid, but only once. Can you work out their positions in the grid so that each of the six different sums work?
Two of the numbers have been inserted in order to get you started. Just identify the other seven numbers.
(NOTE: perform operations in the order they appear, e.g., 3+4×5=35 (not 23))
a=
b=
c=
d=
e=
f=
Answer:
d=9
Step-by-step explanation:
any other idea
helpp plss