Answer: Slope between two points equation is y2-y1/x2-x1
Step-by-step explanation:
Angles P and Q are supplementary. If mZP is
32°, what is the mZQ?
Step-by-step explanation:
Supplementary angles add up to 180°
[tex]\therefore m\angle P + m\angle Q = 180° \\ \therefore 32 \degree+ m\angle Q = 180° \\ \therefore m\angle Q = 180° - 32° \\ \huge \purple{ \boxed{\therefore m\angle Q = 148°}}[/tex]
. What is a Golden Rectangle? Why is it important in architecture and art? Look around you right now. Do you see anything that looks like a Golden Rectangle in your classroom?
Answer:
see below
Step-by-step explanation:
A golden rectangle is one that has an aspect ratio of the "golden ratio". That ratio is an irrational number:
Φ = (1+√5)/2 ≈ 1.618034
This number is the positive solution to the equation ...
x = 1/(x -1)
__
Books have been written about the properties of the Golden Ratio and all the ways it shows up in Nature and in mathematics. For example, the ratios of sequential numbers in the Fibonacci sequence approach the Golden Ratio in the limit.
__
The proportion is often called the "divine proportion" because of the ways it shows up in nature. Some say a rectangle with this proportion is most pleasing to the eye. Hence, it may show up in architecture and art for that reason. A 5×8 photo is approximately this shape.
(The 1.6:1 aspect ratio is one that used for some video screens. It isn't quite as wide as the 16:9 aspect ratio seen more commonly. It is somewhat longer and narrower than the aspect ratio of common paper sizes.)
_____
The attached graph shows rectangles with the proportion of Φ.
A Golden Rectangle is a rectangle with side lengths in the golden ratio (approximately 1:1.618), known for its aesthetically pleasing proportions. Its importance in architecture and art stems from its use to create harmonious and balanced designs. Students often study golden rectangles to improve their understanding of symmetry and composition in art and architecture.
A Golden Rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1 : 1.618. This ratio is also known as Phi. The significance of the golden rectangle in architecture and art lies in its aesthetically pleasing proportions which have been utilised since antiquity. It is believed that the human eye finds shapes and proportions based on the golden ratio to be naturally beautiful.
In architecture and art, the golden rectangle has been used to structure designs with a sense of harmony and balance. Modern artists such as Georges Seurat and Piet Mondrian have integrated the golden rectangle into their works to create compositions that are pleasing to the eye.
When constructing a golden rectangle, students may use a computer drawing program, maintaining its proportions even when resizing it. They can use this golden rectangle as a template over scanned images of Renaissance paintings or their own compositions, incorporating elements such as doorways or windows that conform to its proportions.
By understanding and using the golden rectangle, students can explore symmetry and visually satisfying geometrical forms, enhancing their artistic or architectural work.
-53 + n = -28 solve for n
Answer:
n will be equal 25
Step-by-step explanation:
-53 + n = -28
collect like terms, and we will have
n = -28 + 53
n = 25
Answer: n = -25
Since, -23 + -25 = -53
2 prime numbers with the sum of 34
Answer:
The two numbers are 15 and 19
Sure, the two prime numbers that add up to 34 are 17 and 17.
The terms in a sequence are given by 3 + 2x. what are the first 6 terms in the sequence?
First 6 terms are 5, 7, 9, 11, 13 and 15
Step-by-step explanation:
Step 1: Given terms in the sequence = 3 + 2x. Find the first 6 terms.a(1) = 3 + 2 × 1 = 3 + 2 = 5
a(2) = 3 + 2 × 2 = 3 + 4 = 7
a(3) = 3 + 2 × 3 = 3 + 6 = 9
a(4) = 3 + 2 × 4 = 3 + 8 = 11
a(5) = 3 + 2 × 5 = 3 + 10 = 13
a(6) = 3 + 2 × 6 = 3 + 12 = 15
Use the distributive property to write the following expression in expanded form. 3(2x+11y)
Answer:
6x + 33y
Step-by-step explanation:
3(2x+11y) Distribute the 3 to the 2x and the 11y separately
6x + 33y This is the expression in expanded form.
If this answer is correct, please make me Brainliest!
Answer: 6x+33y
Step-by-step explanation:
What are the zeros of f(x) = x2 + 2x - 80?
-20 and 4
®
-4 and 20
-10 and 8
-8 and 10
Answer:
The zeros are 8 and -10, all u have to do is substitute x for those values, factor it, or graph it.
The zeros of f(x) = x2 + 2x - 80 are -10, 8
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.
In other words the function represents the graph between x and y that is for each value of x there exist one value of y but here there is no restriction in values of y that is y can have infinity values.
zero's are nothing but the roots of the equation which by putting in the equation gives zero value.
Given equation is f(x) = x^2 + 2x - 80 solving it to find the zero's by factorization :
f(x) = x^2 + 2x - 80
f(x) = x^2 + 10x-8x - 80
f(x) = x(x+10)-8 (x + 10)
f(x) = (x+10)(x-8)
Now equating it to zero we get
x= -10, 8
Therefore, the zeros of f(x) = x2 + 2x - 80 are -10, 8
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The two-way table shows data for a florist’s inventory by flower and color. A 5-column table has 3 rows. The first column has entries roses, tulips, total. The second column is labeled red with entries 25, 11, 36. The third column is labeled Pink with entries 8, 14, 22. The fourth column is labeled white with entries 16, 12, 28. The fourth column is labeled total with entries 49, 37, 86. What is the probability that the florist randomly selects a tulip for a bouquet? P(tulip) = StartFraction 11 Over 37 EndFraction P(tulip) = StartFraction 37 Over 86 EndFraction P(tulip) = StartFraction 37 Over 49 EndFraction P(tulip) = StartFraction 49 Over 86 EndFraction
Answer:
37/86
Step-by-step explanation:
eh
The probability that the florist randomly selects a tulip for a bouquet using the given table is; 37/86
How to find probability from tables?From the given table we see that;
Total number roses = 49
Total number of tulips = 37
Now, we want to find the probability that the florist randomly selects a tulip for a bouquet. Thus;
P(selecting tulip for a bouquet) = total number of tulips/total number of bouquets
Thus;
P(selecting tulip for a bouquet) = 37/(49 + 37)
P(selecting tulip for a bouquet) = 37/86
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what is 6 and 2 thirds minus 2 and 4 fifths?
Answer:
58/15
Step-by-step explanation:
Step 1: Convert words into an expression
6 and 2 thirds minus 2 and 4 fifths
6 2/3 - 2 4/5
Step 2: Make common denominator aka 15
6 2/3 = 6*3/3 + 2/3 = 18/3 + 2/3 = 20/3
20*5 / 3*5 = 100/15
2 4/5 = 2*5/5 + 4/5 = 10/5 + 4/5 = 14/5
14*3 / 5*3 = 42/15
Step 3: Subtract
100/15 - 42/15
58/15
Answer: 58/15
What value does the red dot represent on the number line?
I think it's 6/7, but i'm not sure
Answer:
The answer is 5/6
Step-by-step explanation:
There are five sections in between 0 and 1; since the dot is five sections away from zero out of six sections, it is 5/6.
A soccer goal is 24 feet wide. Point A is 40 feet in front of the center of the goal. Point B is 40
feet in front of the right goal post.
a) find the measure of ∠A and ∠B
b) which angle is larger, ∠A or ∠B?
c) from which point would you have a better chance of kicking the ball into the goal? Why?
Answer:
a) Angles A and B are 90 degree.
b) The 2 angles are equal
c) From point A having a better chance to kicking the ball in to goal
Step-by-step explanation:
a, b) 2 points are in front of the center and right post of goal. Because there is no detail, we can assume that point A, point B, center of goal, right goal post make up a rectangle. Therefore, the 2 angles are measured equally as 90 degree.
c) Because it's a rectangle, the distance between point A and center of goal is shorter than that between point B and center of goal.
To determine the measures of ∠A and ∠B and identify which is larger, trigonometry is used based on the geometry of the soccer goal and the distances given. ∠A is associated with a larger shooting angle and a better chance of scoring compared to ∠B.
Explanation:The situation presents a geometry problem involving a soccer goal and positions A and B. To find the measure of ∠A and ∠B, we can visualize the scenario as two triangles with a common side, the 24-foot width of the goal. The distance from the center of the goal to both points A and B is 40 feet. We can use trigonometry to solve for the angles.
For ∠A, we have a right triangle where the width of the goal forms one leg (half is 12 feet, as it is from the center), and 40 feet is the hypotenuse. Applying the cosine function:
cos(∠A) = adjacent / hypotenusecos(∠A) = 12 / 40
Calculating this gives ∠A.
For ∠B, the full width of the goal (24 feet) is the adjacent side of the right triangle, and 40 feet again is the hypotenuse. Therefore:
cos(∠B) = adjacent / hypotenusecos(∠B) = 24 / 40
Calculating this gives ∠B.
Comparing the cosine values will indicate which angle is larger, since a smaller cosine correlates with a larger angle.
From which point would you have a better chance of scoring a goal? Since ∠A is larger, it represents a wider view of the goal, suggesting that kicking the ball from Point A provides a better chance of scoring because you see more of the goal, giving you a larger target area to aim at. This is an application of the concept of shooting angles in soccer.
Change this radical to an algebraic expression with fractional exponents.
[tex]5\sqrt{x^3}[/tex]
Rational exponents
[tex]a^\frac{m}{n}[/tex]
work like this: the numerator is the actual exponent of the base, while the denominator is the index of the root.
In other words, we have
[tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex]
So, in you case, we have
[tex]\sqrt[5]{x^3}=x^\frac{3}{5}[/tex]
Assuming that the question contanis a typo. If you actually mean [tex]5\sqrt{x^3}[/tex],
then you can write it as [tex]5x^\frac{1}{3}[/tex]
a farmers land is separated into sections of size 2 1/7 acres. Suppose there are 2 2/3 such sections. how many acres of land does the farmer own
Answer:
5 5/7 acres
Step-by-step explanation:
The product is ...
(2 1/7 acres/section)(2 2/3 sections) = (15/7)(8/3) acres = 40/7 acres
= 5 5/7 acres
The farmer owns 5 5/7 acres of land.
The farmer's land amounts to approximately 5.71 acres. The problem involves conversion of mixed numbers to improper fractions and multiplication.
Explanation:The problem involves the concepts of multiplication and fractional numbers in mathematics. If one section is 2 1/7 acres and there are 2 2/3 such sections, you multiply these two amounts to find the total acreage. First, convert the mixed numbers to improper fractions: 2 1/7 becomes 15/7, and 2 2/3 becomes 8/3. Multiply the numerators together (15*8=120) and the denominators together (7*3=21) to get 120/21, which simplifies to about 5.71 acres.
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which two beverages have a sum of 5/8 of the students votes favorite beverages iced tea 3/8 fruit juice 2/8 water 1/8 soda 2/8 _fraction of student votes
Answer:
The two beverages can be (iced tea,fruit juice) or (iced tea,soda).
Step-by-step explanation:
Given : Beverages iced tea [tex]\frac{3}{8}[/tex], fruit juice [tex]\frac{2}{8}[/tex], water [tex]\frac{1}{8}[/tex], soda [tex]\frac{2}{8}[/tex].
To find : Which two beverages have a sum of [tex]\frac{5}{8}[/tex] of the students votes ?
Solution :
We have to get the two beverages whose sum became [tex]\frac{5}{8}[/tex] .
The possible ways are
1) Iced tea + Fruit juice = [tex]\frac{3}{8}+\frac{2}{8}[/tex]
Iced tea + Fruit juice = [tex]\frac{5}{8}[/tex]
2) Iced tea + Soda = [tex]\frac{3}{8}+\frac{2}{8}[/tex]
Iced tea + Soda = [tex]\frac{5}{8}[/tex]
Therefore, the two beverages can be (iced tea,fruit juice) or (iced tea,soda).
A satellite is 6,000 miles from the horizon of Earth. Earth’s radius is about 4,000 miles. Find the approximate distance the satellite is from the point directly below it on Earth’s surface. The diagram is not to scale.
Answer:
3211 miles
Step-by-step explanation:
A right triangle can be used to model the geometry of the problem. One leg of it is the radius of the Earth. The leg at right angles to that is the satellite-to-horizon distance of 6000 miles. The hypotenuse of the triangle is the distance from the satellite to the center of the Earth, so the question will be answered by subtracting the Earth radius from that.
The Pythagorean theorem relates the various distances. Refer to the attachment.
AB² = AD² +BD²
(BC +4000)² = 4000² +6000² . . . . . . . . . . . . use given values
BC +4000 = 1000√(4² +6²) = 2000√13 . . . . take the square root
BC = 2000(√13 -2) . . . . . subtract 4000
BC ≈ 3211.1
The satellite is about 3211 miles from the point directly below it.
Simplify.
3+ (-2) • 6
Step-by-step explanation:
[tex]3 + ( - 2) \ast6 \\ = 3 + ( - 2 \times 6) \\ = 3 + ( - 12) \\ = 3 - 12 = - 9[/tex]
Mr. Duncan mixed 0.00055 pounds of sulfur and 0.00104 pounds of iron powder in a test tube before heating it. What is the total weight of the mixture in the test tube?
Answer:
1.59 × 10-3 pounds
Step-by-step explanation:
Add the weights of the sulfur and iron powder to find the total weight of the mixture.
First, write both numbers in scientific notation.
Now that both numbers are written in scientific notation, compare the exponents. Since both exponents are not the same, rewrite 5.5 × 10-4 as 0.55 × 10-3. Now the numbers multiplied by the powers of 10 can be added while keeping the power of 10 the same.
So, the total weight of the mixture in the test tube is 1.59 × 10-3 pounds.
I need help with this problem
Yo sup??
net population of Mexico and Canada is= 110.65+33.89
=144.54 million
net population of US=317.64 million
difference=317.64-144.54
=173.1 million
Hope this helps
Hello Red, Need help training your charizard?
Anyways
if you add 110.65million and 33.89million, you would get
144.54
now the united states has a population of 317.64 million
317.64- 144.54= 173.1
so the U.S has 173.1 million more than Canada And Mexico Combined
(−3x − 6)(3x2 − 6x + 3)
From Sim’s house to the lake is 30 kilometers. If he completed the round trip on his bike in 2 hours and 30 minutes, what was his average speed in kilometers per hour?
Solution:
Given that,
Distance = 30 km
Time = 2 hours 30 minutes
We know that,
[tex]1\ minute = \frac{1}{60}\ hour\\\\Therefore\\\\30\ minute = \frac{30}{60} = 0.5\ hour[/tex]
Thus,
Time = 2 hour + 0.5 hour = 2.5 hour
The average speed is given as:
[tex]Average\ speed = \frac{ total\ distance}{total\ time\ taken }[/tex]
Therefore,
[tex]Average\ speed = \frac{60}{2.5} = 24[/tex]
Thus average speed is 24 km/hr
Solve the equation.
x2 − 6x − 7 = 0
Answer:
x = 7 and x = -1
Step-by-step explanation:
Step 1: Factor
x^2 - 6x - 7 = 0
(x - 7)(x + 1) = 0
Step 2: Solve for x
(x - 7)(x + 1) = 0
x - 7 = 0 and x + 1 = 0
x - 7 + 7 = 0 + 7 and x + 1 - 1 = 0 - 1
x = 7 and x = -1
Answer: x = 7 and x = -1
What is the solution to the equation x + 14 = 63?
Pleas help
Answer:
x = 49
Step-by-step explanation:
x + 14 = 63
x = 63 - 14
x = 49
Answer:
49
Step-by-step explanation:
Subtract 14 for both sides
–2(g − 13) + 15 = 1
how do you do this
Answer:g=20
Step-by-step explanation:
-2g+26+15=1
-2g+41=1
-2g=1-41
-2g=-40
-40/-2= 20
Answer:
20=g
Step-by-step explanation:
-2g--26+15=1
-2g+26+15=1
-15 -15
-2g+26= -14
-26 -26
-2g= -40
-40/-2
g=20
For what number A does the equation 3Ax - 24 = 5x - 9 + x$ have no solutions for x?
HELLLLPPPP
Answer:
A=2
Step-by-step explanation:
3Ax - 24 = 5x - 9 + x (simplifying the right side)
3Ax - 24 = 6x - 9
Equating the term x,
It will have no solution when 3A = 6 ⇒ A = 2
To see why:
3(2)x - 24 = 6x - 24
and this can never equate to 6x - 9 and have no solutions for x.
Steve os three times as old as Thresa. in four years he will be twice as old as she will be. How old is each one?
Answer:
Theresa is 4 years old while Steve is 12
The length of a ribbon is 7/ 8 meter. Sun Yi needs pieces measuring 1/ 7 meter for an art project. What is the greatest number of pieces measuring 1 /7 meter that can be cut from the ribbon? How much ribbon will be left after Sun Yi cuts the ribbon?
To find the greatest number of pieces measuring 1/7 meter that can be cut from a ribbon of length 7/8 meter, divide the length of the ribbon by the length of each piece. The greatest number of pieces that can be cut is 6. Subtract the total length of the 6 pieces from the original length of the ribbon to find how much ribbon will be left.
Explanation:To find the greatest number of pieces measuring 1/7 meter that can be cut from a ribbon of length 7/8 meter, we need to divide the length of the ribbon by the length of each piece. So, 7/8 divided by 1/7 is equal to (7/8) x (7/1) = 49/8 = 6.125. Since we can't have a fraction of a piece, the greatest number of pieces that can be cut is 6. This means 6 pieces measuring 1/7 meter can be cut from the ribbon.
To find out how much ribbon will be left after cutting the 6 pieces, we need to subtract the total length of the 6 pieces from the original length of the ribbon. Each piece measures 1/7 meter, so the total length of the 6 pieces is (1/7) x 6 = 6/7 meter. Subtracting this from the original length, we get 7/8 - 6/7 = 49/56 - 48/56 = 1/56 meter. Therefore, there will be 1/56 meter of ribbon left after Sun Yi cuts the ribbon.
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Find the volume of the prism.
22 m
26 m
The volume of the prism is
The volume of the triangular prism is 2,002 m³.
Step-by-step explanation:
Step 1:
The volume of a triangular prism can be determined by multiplying its area of the triangular base with the height of the prism.
The base triangle has a base length of 26m and a height of 7m.
The area of a triangle is given by; [tex]A = \frac{1}{2} (b)(h)= \frac{1}{2} (26)(7) = 91[/tex].
So the area of the triangle is 91 m².
Step 2:
The volume of the prism is determined by multiplying the area with the height.
The area is 91 m² and the height is 22m.
The volume = (area)(height) [tex]= (91)(22) = 2,002.[/tex]
The volume of the given prism is 2,002 m³.
What is the slope between (-4,4) and (-6,6)
[tex]\textsf{Let's calculate the slope of the line passing thought the points (-4, 4) and (-6, 6) } \\ \textsf{using the following formula: }\mathsf{m = \frac{\Delta y}{\Delta x}} \textsf{ where m is the slope of the line.}[/tex][tex]\textsf{So:}[/tex]
[tex]\mathsf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{4 - 6}{-4 - (-6)} = \dfrac{-2}{2} = -1}[/tex]
[tex]\textsf{Hence the slope is -1.}[/tex]
The coordinates of triangle BCD are B(8.2), C(11, 13) and D(2,6). Which equality proves that triangle BCD is isosceles? (d =
V(x2-x} + ()2 + y)2)
BC = CD
BC = BD
CD = BD
DB = CB
Answer:
BC=BD
Step-by-step explanation:
This is the correct answer for Usatestprep
Answer:
BC=CD
Step-by-step explanation:
Calculate mean, median, and mode for each set of data. IQ’s: 78, 79, 87, 88, 101, 120, 132
Answer:The median is 88,The mode is none because they all repeat the same. The mean is 97.9
Step-by-step explanation:
Answer
The median is 88. The mode is none because they all repeat the same. The mean is 97.9
Step-by-step explanation: