The equation of direct proportion is y = 62x
Direct variation
Two quantities are said to vary directly proportional to each other when an increase in one leads to an increase in the other or a decrease in one leads to a decrease in the other.
Direct variation is given by:
y = kx
where y, x are the variables and k is the constant of proportionality.
The equation of direct proportion is y = 62x
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When constructing inscribed polygons and parallel lines, how are the steps similar?
A) A protractor and ruler are used to take accurate measurements.
B) A compass is used to draw arcs.
C) Four right angles are created.
D) There are no similarities.
Answer:
A compass is used to draw arcs is the answer.
Answer: Intersecting arcs are created and connected.
Step-by-step explanation:
Intersecting arcs are created and connected.
which subsets of the real numbers does the number 70 belong
a
rational numbers only
b
integers, rational numbers, natural numbers, and whole numbers
c
whole numbers, natural numbers, and integers only
d
whole numbers, integers, and rational numbers only
Answer:
B.
Step-by-step explanation:
Integers are any whole numbers that can be positive or negative.
Rational numbers are any numbers that can be expressed as a fraction such as an integer, whole number, or decimals.
Natural numbers include 1, 2, 3 etc.
(Extra fact: 0 is not a natural number :0)
Whole numbers are are numbers without fractions or decimals.
I hope this helps :)
Evelyn watches airplanes take off at an airport. She is 200 meters away from where the planes take off from the runway. The initial angle at takeoff of a plane is 12°. A triangle is shown. The triangle is made up of the initial takeoff of the plane, where the plane currently is in the sky, and where Evelyn is watching the plane. The angle of takeoff is 12 degrees. The distance from the initial takeoff to Evelyn is 200 meters and the distance from the initial takeoff to the plane apostrophe s current position is 100 meters. What is true when the plane is 100 meters away from takeoff? Check all that apply. The given information is the SSS case. The given information is the SAS case. The given information is the SSA case. Evelyn is approximately 104 meters from the plane. The angle of elevation of the plane is 12°.
Two triangle are congruent when the shape and size of both the triangle are same.
The given information is the SAS case. Thus the option B is the correct option.
What is triangle congruence theorem?Two triangle are congruent when the shape and size of both the triangle are same.
Triangle congruence theorem are-
Angle-Side-Angle theorem (AAS)- This theorem states that two triangle is congruent when two angle and one side of the triangle are respectively equal to the two angles and same side of the other triangle.Side-Side-Side theorem (SSS)- When the three sides of the one triangle is equal to the three sides of the other triangle respectively, then the triangle are congruent. Side-Angle-Side theorem (SAS)- Two sides and the included angle of are equal to the two sides and one angle of other triangle respectively.Given information-
The distance of the Evelyn from the airplane is 200 meters.
The initial angle at takeoff of the plane is 12 degrees.
Evelyn is approximately 104 meters from the plane.
The angle of elevation of the plane is 12°.
The triangle made for this situation is attached below.
As in the shown triangle below this question. The distance of Evelyn from the initial takeoff of the plane is shown.
This distance is equal to the base of the triangle. Therefore we get the one side of the tingle.
Now the plane is flied 100 meters, which gives the value of another side of the triangle as shown in the image below attached.
Angle of elevation of the plane is 12 degrees, which gives the one angle of the triangle.
Thus we have one side equal to the 100 meters, one angle equal to the 12 degrees and another side with equal to the 200 meters.
Thus it is the case of side angle side.
Hence, the given information is the SAS case. Thus the option B is the correct option.
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Answer:
The correct answer would be Options B. D. and E.
Step-by-step explanation:
Just got this question correct on Edge. - hope this helps!
Brainliest would be greatly appreciated :)
For art class, Mrs. Stone asked her 6th grade student's to draw a zoo. She wanted the class to draw a zoo with a ratio of 5 trees for every 8 birds.
Answer:
lucy
Step-by-step explanation:
(5:8) *2
10:16
im almost done with math
Answer:
X=16
Step-by-step explanation:
52/13=4
4 = how much the shape was dialated
And so you would multiply 4 by 4 to get the corresponding side which is X
The diagram shows a regular octagon ABCDEFGH. Each side of the octagon has length 10cm. Find the area of the shaded region ACDEH.
The area of the shaded region /ACDEH/ is 325.64cm²
Step 1 - Collect all the facts
First, let's examine all that we know.
We know that the octagon is regular which means all sides are equal.since all sides are equal, then all sides are equal 10cm.if all sides are equal then all angles within it are equal.since the total angle in an octagon is 1080°, the sum of each angle within the octagon is 135°.Please note that the shaded region comprises a rectangle /ADEH/ and a scalene triangle /ACD/.
So to get the area of the entire region, we have to solve for the area of the Scalene Triangle /ACD/ and add that to the area of the rectangle /ADEH/
Step 2 - Solving for /ACD/
The formula for the area of a Scalene Triangle is given as:
A = [tex]\sqrt{S(S-a)(S-b)(S-c) square units}[/tex]
This formula assumes that we have all the sides. But we don't yet.
However, we know the side /CD/ is 10cm. Recall that side /CD/ is one of the sides of the octagon ABCDEFGH.
This is not enough. To get sides /AC/ and /AD/ of Δ ACD, we have to turn to another triangle - Triangle ABC. Fortunately, ΔABC is an Isosceles triangle.
Step 3 - Solving for side AC.
Since all the angles in the octagon are equal, ∠ABC = 135°.
Recall that the total angle in a triangle is 180°. Since Δ ABC is an Isosceles triangle, sides /AB/ and /BC/ are equal.
Recall that the Base angles of an isosceles triangle is always equal. That is ∠BCA and ∠BAC are equal. To get that we say:
180° - 135° = 45° [This is the sum total of ∠BCA and ∠BAC. Each angle therefore equals
45°/2 = 22.5°
Now that we know all the angles of Δ ABC and two sides /AB/ and /BC/, let's try to solve for /AC/ which is one of the sides of Δ ACD.
According to the Sine rule,
[tex]\frac{Sin 135}{/AC/}[/tex] = [tex]\frac{Sin 22.5}{/AB/}[/tex] = [tex]\frac{Sin 22.5}{/BC/}[/tex]
Since we know side /BC/, let's go with the first two parts of the equation.
That gives us [tex]\frac{0.7071}{/AC/} = \frac{0.3827}{10}[/tex]
Cross multiplying the above, we get
/AC/ = [tex]\frac{7.0711}{0.3827}[/tex]
Side /AC/ = 18.48cm.
Returning to our Scalene Triangle, we now have /AC/ and /CD/.
To get /AD/ we can also use the Sine rule since we can now derive the angles in Δ ABC.
From the Octagon the total angle inside /HAB/ is 135°. We know that ∠HAB comprises ∠CAB which is 22.5°, ∠HAD which is 90°. Therefore, ∠DAC = 135° - (22.5+90)
∠DAC = 22.5°
Using the same deductive principle, we can obtain all the other angles within Δ ACD, with ∠CDA = 45° and ∠112.5°.
Now that we have two sides of ΔACD and all its angles, let's solve for side /AD/ using the Sine rule.
[tex]\frac{Sin 112.5}{/AD/}[/tex] = [tex]\frac{Sin 45}{18.48}[/tex]
Cross multiplying we have:
/AD/ = [tex]\frac{17.0733}{0.7071}[/tex]
Therefore, /AD/ = 24.15cm.
Step 4 - Solving for Area of ΔACD
Now that we have all the sides of ΔACD, let's solve for its area.
Recall that the area of a Scalene Triangle using Heron's formula is given as
A = [tex]\sqrt{S(S-a)(S-b)(S-c) square units}[/tex]
Where S is the semi-perimeter given as
S= (/AC/ + /CD/ + /DA/)/2
We are using this formula because we don't have the height for ΔACD but we have all the sides.
Step 5 - Solving for Semi Perimeter
S = (18.48 + 10 + 24.15)/2
S = 26.32
Therefore, Area = [tex]\sqrt{26.32(26.32-18.48)(26.32-10)(26.32-24.15)}[/tex]
A = [tex]\sqrt{26.32 * 7.84*16.32 * 2.17)}[/tex]
A = [tex]\sqrt{7,307.72}[/tex] Square cm.
A of ΔACD = 85.49cm²
Recall that the shape consists of the rectangle /ADEH/.
The A of a rectangle is L x B
A of /ADEH/ = 240.15cm²
Step 6 - Solving for total Area of the shaded region of the Octagon
The total area of the Shaded region /ACDEH/, therefore, is 240.15 + 85.49
= 325.64cm²
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A $\textit{palindrome}$ is a positive integer which reads the same forward and backward, like $12321$ or $4884$. How many $4$-digit palindromes are there
There are 90 4-digit palindromes
What are palindromes?Palindromes are numbers whose reverse is the same as the original number
How to determine the count of 4-digit palindromesSince the digit is 4, then
The first digit of the palindrome can be any of 1 to 9 (i.e. 9 digits)The second digit can be any of 0 - 9 (i.e. 10 digits)The third digit must be the second digit (i.e. 1 digit)The last digit must be the first digit (i.e. 1 digit)So, the total number of digits is:
[tex]n =9 * 10 * 1 * 1[/tex]
Evaluate the product
[tex]n =90[/tex]
Hence, there are 90 4-digit palindromes.
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How to find the standard deviation of a discrete random variable.
Answer:
Step-by-step explanation:
by summing the product of the square of the difference between the value of the random variable and the expected value, and the associated probability of the value of the random variable, taken over all of the values of the random variable
write the equation of the line in point slope form that passes through the given point with the given slope 6. (-4, 3); m = 2
Analyze the problem
ignoring the "6."
using point slope form,
y-3=2(x+4)
multiplication
y-3=2x+8
move the three and add
y=2x+11
What is the area of the
composite figure?
Answer:
111 meters, break each area into a rectangle, find the areas, then add.
In AWXY, mW
Find mZX
(2x – 12), m_X = (2x + 17), and m_Y = (9x-7)
Find m
Answer:
45
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180
2x - 12 + 2x + 17 + 9x - 7 = 180 add like terms
13x - 2 = 180 add 2 to both sides
13x = 182 divide both side by 13
x = 14
m<X = 2x + 17 replace x with 14
2*14 + 17 = 45
sloving systems of equations by elimination
Answer:
First you have to get the y by itself to make it into y=mx+b form. so it goes to
6y= 2x+18 then simplify and get y=2x+3. for the bottom one y=5
Help me please someone…..
Answer:
24
Step-by-step explanation:
1. First, let's find the common ratio between the sides we know.
[tex]\frac{XY}{AB} = \frac{XZ}{AC}[/tex] [tex]\frac{8}{2} = \frac{12}{3}[/tex] [tex]4[/tex]2. The number 4 is the scale factor, so we multiply 6 by 4 to get the missing side length.
[tex]6 * 4[/tex] [tex]24[/tex]Therefore, the missing side length is 24.
2) The wind blew away 16 of your muffins. That was 4/7 of all of them! How many are left?
A) 28
B) 31
C) 12
D) 9.14286
Answer: Option C, 12 muffins are left
28 is the value of all the muffins, since 1/7 of the muffins would be 4. subtract 16 from 28, and you get 12.
Identify the unit rate of the graph
Answer:
1.5
Step-by-step explanation:
just choose a point and divide the Y by Z :o
plssssssssssssssssssssssss help
Answer:
D
Step-by-step explanation:
The slope is -100/3 and the y intercept is 450
Answer:
letter D
Step-by-step explanation:
hope it helps alot
Owners of a recreation area are adding water to a pond. The graph below shows the amount of water in the pond ( in liters) versus the amount of time that water is added (in hours)
The amount of water in the pond per hour is 300 liters per hour
How to determine the amount of water in the pond per hour?From the graph, we have the following points:
(x,y) = (0,100) and (1,400)
This means that:
There are 100 liters of water in the pond at 0 hoursThere are 400 liters of water in the pond at 1 hourThe amount of water per hour is the calculated using:
Rate = (y2 - y1)/(x2 - x1)
Substitute known values
Rate = (400 - 100)/(1 - 0)
Evaluate the quotient
Rate = 300
Hence, the amount of water in the pond per hour is 300 liters per hour
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Which subshell (for example, 1������1s ) is designated by each set of quantum numbers?.
Subshells are designated using orbital quantum numbers.
What are quantum numbers?
Quantum numbers are values that describe an electron's position within the atom. There are four sets of quantum numbers which are;
Principal quantum numberMagnetic quantum numberSpin quantum numberOrbital quantum numberSubshells are designated using orbital quantum numbers. The question is incomplete hence the quantum numbers were not shown.
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8(x − 5) + 38 = 8x − 2 what is the solution please help me
anwer 2(4x-1)
Distribuye
Distribuye 8 ( − 5 ) + 3 8 {\color{#c92786}{8(x-5)}}+38 8 − 4 0 + 3 8 Suma los números 8 − 4 0 + 38 − 2Factoriza por agrupamiento Factoriza por agrupamiento 8 ( − 5 ) + 3 8 8(x-5)+38 2 ( 4 − 1 )
Answer:
Infinitely many solutions!
Step-by-step explanation:
Using PEMDAS rules, let's distribute the 8 to (x - 5)
Now the equation looks like: 8x - 40 + 38 = 8x - 2
We combine like terms, so -40 + 38 would be -2
Now the equation would look like 8x - 2 = 8x - 2
Let's add 2 on the other side to try and get x by itself
8x = 8x - 2 (+2) Which brings the equation to 8x = 8x
Technically speaking, you can stop here because the statement is true. No matter what x equals, the statement would be true. Therefore infinitely many solutions would be your answer. You can plug in any number for x and the equation would still be correct.
If θ is an angle in standard position and its terminal side passes through the point (1,-8), find the exact value of csc θ in simplest radical form.
Check the picture below.
well, we know the angle's cosine and sine or namely adjacent and opposite sides, let's get the hypotenuse.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{1}\\ b=\stackrel{opposite}{-8}\\ \end{cases} c=\sqrt{1^2+(-8)^2}\implies c=\sqrt{65} \\\\[-0.35em] ~\dotfill\\\\ csc(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{65}}}{\underset{opposite}{-8}}\implies csc(\theta )=-\cfrac{\sqrt{65}}{8}[/tex]
which is more, 1 pound or 32 ounces?
Answer:
32 ounces is more than 1 pound
Step-by-step explanation:
1 pound equals 16 ounces because 1x16=16. 2 pounds equals 32 ounces because 2x16=32. 3 pounds equals 48 ounces because 3x16=48
thank you, like us
find the rate of 250mm to 75cm
what is the area of the circle if the circumference is 150
Answer:
Area≈1790.49311
Using the formulas
A=πr2
C=2πr
Solving forA
A=C2
4π=1502
4·π≈1790.49311
If 60% of a car company's sales are from SUVs, and they sell a total of 360 cars that are not SUVs, how many SUVs did they sell?
Answer:
540 SUV's
Step-by-step explanation:
Sales percentage of non SUV's = 100 - 60 = 40%
Let total cars be x
40% of x = 360
[tex]\dfrac{40}{100}*x=360\\\\\\x=360*\dfrac{100}{40}\\\\\\x = 900[/tex]
Number of SUV's = Total cars - number of non SUV's
= 900 - 360
= 540
lana has a collection of 59 crayons. She has 6 boxes of crayons, each with the same number of crayons. Ilana also has 17 loose crayons. How many crayons are in each of the boxes?
Answer: There are 7 crayons in each box.
Step-by-step explanation: First, the most difficult part is coming up with the equation. You know that she has a total of 59 since it mentioned “a collection of 59 crayons”. Then you also know there are 17 crayons on the side, so you can subtract 17 from 59, the total (which is now 42). Then you have 6x. 6 is for the number of boxes and x is for the unknown number of crayons found in each box. Then you can just simply solve after identifying each factor of the equation.
Explain the steps to find the difference of the question below
Step-by-step explanation:
1 -5/8
lcm=8
8-5=3
3/8
mark me brainliest or else I will report this question.
Which expression is equivalent to c+0.61c−0.59c
Answer:
1.02c
Step-by-step explanation:
A salesperson earns a commission of 418 for selling 2200 in merchandise.
Find the commission rate. Write your answer as a percentage.
Answer:
19%
Step-by-step explanation:
percent = part/whole × 100%
percent = 418/2200 × 100%
percent = 19%
Which expression is equivalent to – 8( – 5k+4)+6k
Answer:
46k - 32Step-by-step explanation:
–8(–5k + 4) + 6k=> (40k - 32) + 6k=> 40k - 32 + 6k=> 46k - 32Hence, the expression is 46k - 32.
Hi!
First, let's distribute -8:
-8(-5k+4)+6k
[tex]\rm{40k-32+6k[/tex]
Combine Like Terms:
[tex]\rm{46k-32[/tex] (Answer)
Hope it helps!
~Misty~
Help asap
3. To break the school's record, the girls' time had to be faster than 12 2/5 minutes.
Did the girls break the record? If so, how much faster were
they? If not, how much slower were they?
Using improper fractions, it is found that they broke the record and were 0.8 minutes faster.
How to convert improper fractions to standard fractions?The conversion is made according to the following formula:
[tex]a\frac{b}{c} = a + \frac{b}{c} = \frac{ac + b}{c}[/tex]
In this problem, the time had to be faster than [tex]12\frac{2}{5}[/tex] minutes, which is a time in minutes of:
[tex]12\frac{2}{5} = 12 + \frac{2}{5} = 12 + 0.4 = 12.4[/tex]
Researching the problem on the internet, it is found that their time was of [tex]11\frac{3}{5}[/tex] minutes, hence:
[tex]11 + \frac{3}{5} = 11 + \frac{3}{5} = 11 + 0.6 = 11.6[/tex]
11.6 < 12.4, hence they broke the record.
12.4 - 11.6 = 0.8, hence they were 0.8 minutes faster.
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