Answer:
- Inverse Variation
- Equation: [tex]XY = 12[/tex]
Step-by-step explanation:
Given
X-> 2 | 4 | 8 | 12
Y-> 6 | 3 | 3/2 | 1
Required
- State the type of variation the table represents
- Determine the equation to model the data
To check for type of variation; we'll make use of trial by error method.
To start with; We'll check for direct variation.
This is done using the following expression;
[tex]Y = kX[/tex]where k is the constant of variation
Make k the subject of formula
[tex]k = \frac{Y}{X}[/tex]
When Y = 6, X= 2
[tex]K = \frac{6}{2} = 3[/tex]
When Y = 3, X = 4
[tex]K = \frac{3}{4}[/tex]
There's no need to check further as both values of k are not equal
To check for inverse variation;
[tex]Y = \frac{k}{X}[/tex]
Make k the subject of formula
[tex]k = YX[/tex]
When Y = 6, X= 2
[tex]K = 6 * 2 = 12[/tex]
When Y = 3, X = 4
[tex]K = 3 * 4 = 12[/tex]
When Y = 3/2; X = 8
[tex]K = \frac{3}{2} * 8 = \frac{24}{2} = 12[/tex]
When Y = 1, X = 12
[tex]K = !2 * 1 = 12[/tex]
Note that for all values of X and Y, K remains constant;
Hence, the table represents an inverse direction
To determine the equation;
We make use of [tex]k = YX[/tex]
Substitute 12 for k
So, the equation becomes
[tex]12 = XY[/tex]
Reorder
[tex]XY = 12[/tex]
Hence, the equation is [tex]XY = 12[/tex]
Imagine you have a very long belt. Well, extremely long, really … in fact, it’s just long enough that it can wrap snugly around the circumference of our entire planet. (For the sake of simplicity, let’s suppose Earth is perfectly round, with no mountains, oceans, or other barriers in the way of the belt.) Naturally, you’re very proud of your belt. But then your brother, Peter, shows up—and to your disgruntlement, he produces a belt that’s just a bit longer than yours. He brags his belt is longer by exactly his height: 6 feet. If Peter were also to wrap his belt around the circumference of Earth, how far above the surface could he suspend the belt if he pulled it tautly and uniformly?
Answer:
H = 0.95 feet
Step-by-step explanation:
The circumference of Earth = 2πR
My belt = 2πR (Where R is the radius of the Earth)
Peter's belt = 2πR+6
We have to find the Height "h" so the radius of the circle for Peter's belt becomes R+h So the expression becomes 2π(R+h)
But we already know,
Peter's belt = 2πR+6
So,
2πR+6 = 2π(R+H)
2πR + 6 = 2πR + 2πH
Subtracting 2πR to both sides
=> 6 = 2πH
OR
=> H = 6/2π
=> H = 3/π
Where π = 3.14
=> H = 0.95 feet
Answer: 0.00016 miles
Step-by-step explanation:
According to Google, the circumference of the Earth is 24,901.461 miles. Using the formula 2*pi*r = circumference, the radius of your belt is around 3963.19061 miles. Now, 6 feet is 0.001 miles. So his belt is 24,901.461+0.001 = 24,901.462 miles. Use 2*pi*r to get 3963.19077 miles, a full 0.00016 miles above the surface!
In the diagram, which pair of angles are corresponding angles?
Answer:
You shoulda showed us the diagram but corresponding angles are the 2 angles on the diagram which are the same, look closely and you could tell which 2 are the same, they also have to be on THE SAME SIDE, right or left
Hope that helps!
Step-by-step explanation:
Answer:
C, Angle 3 and Angle 7
Step-by-step explanation:
heres the full question
In the diagram, which pair of angles are corresponding angles?
Angle 1 and Angle 8
Angle 4 and Angle 6
Angle 3 and Angle 7
Angle 2 and Angle 4
Based on the graph below, what is a reasonable estimate for the у value when x is 4?
PLEASE HELP!!!! I'M STUCK The graph shows two lines, A and B. A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 6, 2. Another straight line labeled B joins the ordered pair 0, 3 with the ordered pair 4.5, 6. Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer. (5 points) Part B: What is the solution to the equations of lines A and B? Explain your answer. (5 points)
Answer:
A: There is only one solution since the two lines meet up. If it was parallel or the two lines where on top of each other there would be either an infinite amount of solutions or zero.
B:(3,5)
Step-by-step explanation:
What is the height of the cone below?
Find the value of the letter in each of the following. Give your answers to 1 d.p.
Answer:
a) z = 70.5°
b) s = 83.6°
c) x = 0.7cm
Step-by-step explanation:
We would solve for the above questions using Trigonometric functions of either Sine, Cosine or Tangent.
a) We are given the following values
Hypotenuse = 21 inches
The triangle is divided into two to give us a right angle triangle
The adjacent side = 14inches/2 = 7 inches
We are to find Angle z
The Trigonometric function we are using is Cosine
cos z = Adjacent / Hypotenuse
cos z = 7/21
cos z = 1/3
z = arc cos(1/3)
z = 70.528779366°
To 1 decimal place
z = 70.5°
b) We are given the following values
Hypotenuse = 12 cm
The triangle is divided into two to give us a right angle triangle
The opposite side = 16cm/2 = 8 cm
We are to find Angle s, but it is split into 2
So we represent the half as x
The Trigonometric function we are using is Sine
sin x = Opposite/ Hypotenuse
sin x = 8/12
sin x = 2/3
x = arc sin(2/3)
x = 41.810314896°
Remember in the question, we are to find s.
s = x° × 2
s = 41.810314896 × 2
s = 83.620629792
To 1 decimal place
s = 83.6°
c) From the above diagram, we are to find the Opposite side represented by x
Our triangle is split into two equal halves
Adjacent side = 2cm
Angle θ = 36°/2 = 18°
We are using Trigonometric function tan to solve for question c
tan θ = Opposite/ Adjacent
tan 18° = Opposite/ 2
Cross Multiply = tan 18° × 2
0.3249196962 × 2
= 0.726542528cm
To one decimal place,
x = 0.7cm
Find the y-intercept for the parabola defined by
this equation:
y=7x2 + 5x – 2
Separate the values with a comma.
Answer:
(0, -2)
Step-by-step explanation:
The y-int is where the graph crosses the y-axis when x = 0. The easiest and fastest way to do this problem is to graph the equation using a graphing calc and tracing the graph to find your value.
Answer:
Step-by-step explanation:
for y intercept x=0
thus y= -2
the point is (0,-2)
Parallel lines r and s are cut by two transversals, parallel lines t and u. Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of u and r, 13, 14, 15, 16. Which angles are alternate exterior angles with angle 11? Angle5 and Angle13 Angle7 and Angle15 Angle6 and Angle16 Angle8 and Angle14
Answer:
5 to13
Step-by-step explanation:
hope it help
Answer:5
5 and 13
Step-by-step explanation:
All of the pairs of corresponding angles and sides in ΔCAT and ΔDOG are congruent. Based on this information, which of the following is a true statement? Question 20 options: A) There isn’t enough information to make a statement about ΔDOG and ΔCAT. B) ΔDOG has been dilated to form ΔCAT. C) ΔCAT is congruent to ΔDOG. D) ΔDOG has half the area of ΔCAT.
Answer: C) ΔCAT is congruent to ΔDOG
Step-by-step explanation:
If all the sides of two triangles are congruent, then the triangles are congruent.
Answer:
c. ΔCAT is congruent to ΔDOG
Step-by-step explanation:
Due to each the AAA (angle-angle-angle) and SSS (side-side-side) theorems, if all of the facets and/or angles of triangles are congruent, then the triangles are congruent.
please mark me brainliest!
*PLEASE ANSWER TY* What is the area of minor sector DFE?
Answer:
x ≈ 34.88 square cm
Step-by-step explanation:
Solve by proportional formula:
Area of a sector/area of circle* = sector central arc measure/360
*area of a circle = πr²
x/(53.29π) = 75/360
x/53.29π = 0.2083
x = 11.1020833π
x = 34.8782233
x ≈ 34.88 square cm
Answer:
Other guy is right also i had it on my test x ≈ 34.88 square cm
Step-by-step explanation:
HELP PLEASE !!!2. Solve for x in the figure below. Show your work.
Answer:
×=19
Step-by-step explanation:
90-22=68
3x+11=68
68-11=57
3x=57
57÷3=19
x=19
Help me find area guys please!!!!
Answer:
you would multiply length times width witch would be 12in by 30in 360
Billy has three times as many llamas as lambs.
Milly has twice as many lambs as llamas.
They have 17 animals in total.
How many of the animals are llamas?
Answer:
There are 9 llamas.
Step-by-step explanation:
For Billy, we have to find a number that is divisible by four, because he has one group of lambs, and 3 times as many llamas, which gives us 4 groups altogether. The number must be below 10 in order to not go above 17 when Milly's number of animals are included, but above 4 itself in order to reach the target of 17 in the first place.
As you can guess, the only number that fits all the criteria is 8. It's divisible by 4 and below 10, but above 4 itself.
If Billy has three times as many llamas as lambs, then he must have 2 lambs, and 6 llamas, as 2 × 3 = 6.
If we know that Billy has 8 animals, then we also know that Milly must have 9 animals, as 17 - 8 = 9.
We also know that Milly has 3 groups of animals; one group of llamas, and two groups of lambs, meaning we divide the number of animals she has by 3.
9 ÷ 3 = 3.
This tells us Milly has just 3 llamas, because 3 is one group of 9, and 3 × 2 = 6, because she has twice the amount of lambs.
Billy has 2 lambs and 6 llamas.
Milly has 6 lambs and 3 llamas.
The amount of lambs is irrelevant to our final answer, so we can disregard them and do a final sum of 6 + 3 = 9, which gives us our answer.
Answer:
Billy: Has 4 lots of animals
Milly: Has 3 lots of animals
17 animals in total means that Billy must have 4 lots of 2 (8 animals) and Milly must have 3 lots of 3 (9 animals) So Billy has 6 llamas and Milly has 3, giving 9 llamas in total
What is the equation of the line that passes through the point (-2,14) and is perpendicular to the line with the following equation?
y = -x-1
OA
y =
OB
y =
- + 9
o + 16
1 - 12
Oc.
y =
OD.
y =
+ 19
Answer:
y = x + 16
Step-by-step explanation:
Step 1: Find slope of perpendicular line
Take the negative reciprocal of the 1st line
m = 1
Step 2: Find b
y = x + b
14 = -2 + b
b = 16
Step 3: Write equation
y = x + 16
Answer:
y = x + 16
Step-by-step explanation:
Given the equation y = -x - 1, we see that the slope (the coefficient of the x term) is -1. A line perpendicular to this one has a slope which is the negative reciprocal of the given equation: +1.
Using the point-slope formula for the equation of a straight line, we get:
y - 14 = +1(x + 2), or y - 14 = x + 2, or y = x + 16
Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7,2), and is parallel to the graph of x + 3y = -5. Pls help ASAP btw, the answer isn't -12/19 or 12/19
Answer:
The found values are:
A = 1/3
B = -8/3
Step-by-step explanation:
We know that general equation is given by:
y = mx + c
where m is the slope and c is a constant.
x + 3y = -5
y = -(1/3)x - 1/3(5)
Slop of the equation is -(1/3). As parallel line have same slope substitute it in the first equation:
Ax + By = 3
By = -Ax - 3
By = (1/3)x - 3
Hence, A = 1/3
Substitute point (-7,2) into the equation:
B(2) = (1/3)(-7) -3
B(2) = -7/3 - 3
B(2) = -16/3
B = -16/6
B = -8/3
Help plz with this question. Needed fast. I will mark brainliest.
Answer:
≈ 68.2°
Step-by-step explanation:
tan X= 20/8
tan X= 2.5
x= tan ⁻¹ 2.5
x ≈ 68.2°
Answer:
Step-by-step explanation:
To find the size of YXZ we should use some trigonometry but first let's find the length of YZ
The Pythagorian theorem :(XZ)²+(ZY)²=(YX)²
YX=[tex]\sqrt{20^{2}+8^{2} }[/tex]
=4[tex]\sqrt{29}[/tex]
We khow that sin(YXZ)=(YZ)/(YX) = 20/(4[tex]\sqrt{29}[/tex]) = 5/[tex]\sqrt{29}[/tex]using a calculator we get (YXZ)= 68°
Factorise
(a + c)2- 62
AWARDING BRANLIEST FOR FIRST CORRECT ANSWER
10a - 41=19 pls help!!!!!
Answer:
a = 6
Step-by-step explanation:
10a - 41 = 19
10a = 19 + 41
10a = 60
a = 60/10
a = 6
Answer:
a= 6
Step-by-step explanation:
10a - 41=19
+41 +41
10a = 60
÷10 ÷10
a= 6
the skateboard Rita would like to buy cost $6 less than three times the amount she has saved the skateboard cost $69 how much does Rita have to save?
Choose the steps that show how to solve this problem using arithmetic.
Answer: Rita has $25 saved.
Step-by-step explanation:
You could think about it this way: $69 is $6 less than 3 times the amount of money that she has. So, let's solve this:
1) First you would add $6 to the $69 that the skateboard costs because you need to know what her savings would be if she multiplied it by 3.
$69+$6=$75
2) Now that we know that if we tripled her savings, we would have $75. We can now find out how much she actually has saved up by dividing the total of $75 by 3.
$75÷3=$25
I hope this helped you with your question!
Answer:
she saved $25
Step-by-step explanation:
Why is the slope of line segment AC the same as the slope of line segment DF in the figure below?
A.because AB/EF=BC/DE? ...................................
B.because AB/DE=BC/DF ?...............................
C.because AB=EF ?...............................
D.because BC=DE?............................
Answer:
The answer would be A. because AB/EF=BC/DE
Step-by-step explanation:
AB = 2
EF = 5
BC = 1
DE = 2.5
2/5 = 0.4
1/2.5 = 0.4
The equation AB/EF=BC/DE is correct. All of the others are not.
The slope of line segment AC the same as the slope of line segment DF in the figure below because AB/EF = BC/DE.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
We need to find the proportionality statement for the ratio of the sides of the triangles.
If two triangles are similar, then the corresponding sides are proportional.
ABC ≈ DEF,
Here AB, BC, and AC are corresponding sides of DE, EF, and DF respectively.
Using the definition of similarity we ge
AB = 2
EF = 5
BC = 1
DE = 2.5
2/5 = 0.4
1/2.5 = 0.4
The equation AB/EF = BC/DE is correct. All of the others are not.
Learn more about a triangle;
https://brainly.com/question/7116550
#SPJ2
Find the area of the shaded polygons: all of them not one
Answer:
6 sq units, 4 sq units, 6 sq units
Step-by-step explanation:
Method:
count dots inside ...(a)
the ones on the border of the polygon and divide by two ...(b)
(a)+(b)-1 = area
use this method for the red, green, and yellow polygons.
Red:
(a): 2
(b): 10/2 = 5
2+5-1 = 6 sq units
Green:
(a): 0
(b): 10/2 = 5
0+5-1 = 4 sq units
Yellow:
(a): 3
(b): 8/2 = 4
3+4-1 = 6 sq units
I hope this helps, and plz mark me brainliest!!!!
HURRY PLZZ!!! THIS IS 90 POINTS!!! I WILL MARK BRANLYEST!!!! 2. A ladder is leaning against the outside wall of a building. The ladder is exactly 10 feet long and makes an angle of 60° with the ground. Let’s find the height the ladder reaches along the building. Label this height as x in your diagram. e. Use your calculator to find the value of sin 60°. In your equation, replace sin 60° with this number, and solve your equation to find the height up the wall. f. Now let’s figure out how far the base of the ladder is from the building. Label this distance as z in your diagram. i. Which trig ratio (sin 60°, cos 60°, or tan 60°) would be most helpful for finding z? _________ Explain. ii. Write and solve a trig equation to help you find z (Use #1d as a guide.)
Answer & Step-by-step explanation:
Answer:
answer is above in the attachment.Step-by-step explanation:
I hope this helps u toohave a nice day ✌please help me and hurry
Answer:
median: 90
mode: 91
mean: 84.2 or round it to 84
Step-by-step explanation:
Let me know if this helps! have a great day! :)
Answer:
a) Median = 91
b) mode = 91
c)Mean 84.2
Step-by-step explanation:
a) Median is the middle term. So, 6th term
Median = 91
b) Mode is the score which occurs more number of times
91 occurs 3 times
Mode = 91
c) Mean= sum of all data's/Number of data's
= 85 + 91 + 48 +98 + 99 /5
= 421/5
Mean = 84.2
* PLEASE ANSWER TY! *
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Circles.
thus the, Equation of circle with centres as (h, k) is given as,
(y-k)^2 + (x-h) ^2 = r^2
where, r is the radius if the circle.
so here, we can see that,
[tex] {r}^{2} = 100 \\ r = 10 \\ [/tex]
thus , we can say that, 2r = d
thus diameter = 20 units
1 Point
Which of the following best describes a random event?
A. The number of doctor visits a person makes in a year
B. The winner of an election
C. The age at which a baby will get her first tooth
D. The age at which a person is legally allowed to drive in the state of
California
SEBNI
Answer: B
Step-by-step explanation:
Makes the most sense out of all the options because it’s the most random or unpredictable
five sixths of a number equals 4,375. What is the number
Answer:
The number is 5250
Step-by-step explanation:
5/6 * x = 4375
Multiply each side by 6/5 to isolate x
6/5 * 5/6 x = 4375 * 6/5
x =5250
Answer:
5250
Step-by-step explanation:
5/6x= 4375
x= 4375*6/5
x= 5250
Select the cube number out of the following numbers: 10,100,1000,10000 A=10 B=100 C=1000 D=10000
Answer:
C. 1000
Step-by-step explanation:
10 is not a perfect cube.
100 is not a perfect cube, it is a perfect square.
1000 is a perfect cube.
10 × 10 × 10 = 1000
10000 is not a perfect cube.
Answer:
it says 10
Step-by-step explanation:
A decade is 10 years.
apparently
Find the area ratio of a cube with volume 125m3 to a cube with volume 64m3.
Answer:
25:16
Step-by-step explanation:
i think its right
I need help on these questions pls answer asap 1.) A 1 km long train is travelling at 30km/h. If the train enters a tunnel that is 1 km long, how much time will it take for the train to clear the tunnel? 2.)The two top NBA players played a basketball game against the RSM team. Together the NBA players made 85 baskets, scoring one point for free throws and two or three points for field goals. They scored a total of 184 points during the game. If they made 22 free throws, how many three-point field goals did they make?
Answer:
1. The train is will cross the tunnel in 2 minutes.
The train is traveling at 30 km every hour or 60 minutes, so it will move 1 km every 60/30 minutes, or every 2 minutes.
2. Explanation here first: 22 free throws means 22 points and 22 field goals.
184-22=162 points they still needed to get, and
85-22=63 goals they still needed to score
We can now use a system of equations, (where x is 3-point goals, and y is 2-point goals) to solve the problem:
3x+2y=162
x+y=63 (-2)
-------------------------------------------------------------
3x+2y=162
-2x-2y= -126
-------------------------------------------------------------
x=36, and y=27 so the NBA players got 36 3-point goals, and 27 2-point goals
We can check this:
(36*3) + (27*2) + 22 = 108+54+22 = 184 total points
Step-by-step explanation:
Hope this helps!
use the explicit formula an = a1 + (n - 1) * d to find the 500th term of the sequence below. 24,30,36,42,48,... A. 3018 B. 3042 C. 2994 D. 3024
Answer:
Option A.
Step-by-step explanation:
The given sequence is
24, 30, 36, 42, 48, ...
It is an AP. Here,
First term = 24
Common difference = 30-24 = 6
The given explicit formula for nth term is
[tex]a_n=a_1+(n-1)d[/tex]
where, [tex]a_1[/tex] is first term, d is common difference.
Substitute [tex]a_1=24, d=6 \text{ and }n=500[/tex] in the above formula.
[tex]a_{500}=24+(500-1)(6)[/tex]
[tex]a_{500}=24+(499)(6)[/tex]
[tex]a_{500}=24+2994[/tex]
[tex]a_{500}=3018[/tex]
The 500th term of the sequence is 3018.
Therefore, the correct option is A.
Answer:
A is correct
Step-by-step explanation: