I’m gonna ask this question again can someone help me solve this and leave in terms of pi
Answers
The equation of the circumference of a circle in terms of [tex]\pi[/tex] is [tex]2\pi r[/tex] or [tex]\pi d[/tex].
The circumference for a circle with diameter 10 is [tex]10\pi[/tex].
The circumference for a circle with diameter 19 is [tex]19\pi[/tex].
The circumference for a circle with diameter 30 is [tex]30\pi[/tex].
The circumference for a circle with diameter 16 is [tex]16\pi[/tex].
Relatively easy, right?
The equation of the area of a circle in terms of [tex]\pi[/tex] is [tex]\pi r^2[/tex].
The area of a circle with radius 5 is [tex]25\pi[/tex].
The area of a circle with radius 9.5 is [tex]90.25\pi[/tex].
The area of a circle with radius 15 is [tex]225\pi[/tex].
The area of a circle with radius 8 is [tex]64\pi[/tex].
Hope this helped!
(By the way, I don't know why you're using hard formulas for trying to find the radius or diameter. The diameter is simply twice the radius, and the radius is simply half the diameter.)
Answer:
Circumference = 10[tex]\pi[/tex], 19[tex]\pi[/tex], 30[tex]\pi[/tex], 16[tex]\pi[/tex]
Area = 25[tex]\pi[/tex], 90.25[tex]\pi[/tex], 225[tex]\pi[/tex], 64[tex]\pi[/tex]
Step-by-step explanation:
For the first row we have the radius which is 5, the diameter is 10. The formula for circumference is 2[tex]\pi[/tex]r. So for this one its gonna be 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]
radius = 5
diameter = 10
circumference = 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]5^{2}[/tex] or 25[tex]\pi[/tex]
for the second row
radius = 9.5
diameter = 19
circumference = 2[tex]\pi[/tex]9.5 or 19[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]9.5^{2}[/tex] or 90.25[tex]\pi[/tex]
for the third row
radius = 15
diameter = 30
circumference = 2[tex]\pi[/tex]15 or 30[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]15^{2}[/tex] or 225[tex]\pi[/tex]
for the fourth row
radius = 8
diameter = 16
circumference = 2[tex]\pi[/tex]8 or 16[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]8^{2}[/tex] or 64[tex]\pi[/tex]
Related Questions
My car uses 8.5L of petrol per 100km travelled. If petrol costs $2.05 per litre, how much will the petrol cost for my trip?
Answers
Answer:
$0.17425/Km
Step-by-step explanation:
8.5L/100Km*$2.05/L
= $0.17425/Km
Question 1: The population of Ohio's three largest cities are: Cleveland, 479,459; Columbus, 715,230; and Cincinnati, 367,000. The average population of Ohio's three largest cities is:
a. 520,563
b. 620,563
c. 502,563
d. 602,563
Q2: Mr. Gorski bases each student's grade on 4 tests. On the first 3 tests, Horace scored 84, 93, and 88. What must he score on the final test to make his average 90?
a. 85
b. 88
c. 92
d. 95
Answers
A. 520,563
The answer to question 2:
D. 95
To solve question one, we need to find the average of these three numbers. To do so, we add all three first:
479,459 + 715,230 + 367,000 = 1,561,689
Then, after adding, we can divide our result by three because that is how many numbers were used.
1,561,689 divided by 3 = 520,563
Therefore, the average population of Ohio’s three largest cities is 520,563.
To find the answer to question two, we can start by adding the three numbers we have:
84 + 93 + 88 = 265
Because Horace had two tests where he scored in the eighties, we know that in order to average at least a 90, Horace will need to score either a 92 or a 95. When calculating, we will find that if Horace scores a 92, he will be at an average of 89.25. That means that our only reasonable answer is 95 because we can calculate that:
84 + 93 + 88 + 95 = 360
360 divided by 4 equals 90.
Therefore, scoring a 95 on Horace’s final test will put him right on the dot for an average of 90.
Your final answer is D, or 95. Horace will need to score a 95 on his final test to average out to a 90. If you need any extra help, let me know and I will gladly assist you.
Pls help I’ll brainlest
Asap
Answers
Answer:
C. slope
Greetings !
The symbol for slope is "m". Slope can be calculated by taking any two locations along a line and calculating the ratio of the RISE to the RUN (the ratio of the difference between vertical positions of the locations to the difference between horizontal positions of the locations).
Answer: slope.
Step-by-step explanation:
Hypotenuse: The ________ side of a right triangle; side ________ from the right angle.
Answers
The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.
According to the statement
we have given that the property of the hypotenuse of the triangle and we have to complete it.
So, For this purpose, we know that the
A hypotenuse is the longest side of a right-angled triangle, and The length of the hypotenuse can be found using the Pythagorean theorem.
Now we discuss about the properties of the hypotenuse;
The hypotenuse is the longest side in a right angled triangle. The hypotenuse is opposite the right angle. The midpoint of the hypotenuse is the circumference.And from these properties we have to complete the given property.
So, The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.
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Get every whole number from 0-10 using exactly five 3's, and any arithmetic operations and parentheses
Answers
See below for the combination of the arithmetic operations and exactly five 3's
How to determine the operations?The conditions are given as:
Exactly five 3'sAny arithmetic operation or combination of operationsThere are no direct rules to this, except by trial and error.
After several trials, we have the following operations:
(3 * 3 - 3 * 3)/3 = 0
3 - 3/3 - 3/3 = 1
(3 + 3 - 3 / 3)-3 = 2
(3 * 3 - 3 + 3)/3 = 3
3 *3/3 + 3/3 = 4
3 +3/3 + 3/3= 5
3 + 3 + (3 - 3)/3 = 6
(3^3 - 3 - 3)/3 = 7
3 + 3 + (3 + 3)/3 = 8
3 + 3 + 3+ 3 -3 =9
3 + 3 + 3 + 3/3 = 10
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Which term is not possible in the domain of a sequence?
Answers
The term that is not possible in the domain of a sequence is:
-5.
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexes of the terms, starting at 0 and going until the nth term.
For example, suppose we have the following sequence: 3, 5, 7, ...
The term with index 0 is 3.The term with index 1 is 5.The term with index 2 is 7.From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:
-5.
Which is the only negative number of the options.
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Find the value of x.
OA. 66
OB. 122
OC. 98
O D. 76
SUBMIT
Answers
Answer:
C) 98
Step-by-step explanation:
Hope this helps! sry if I'm wrong
The value of x in the given equation 15x + 120 = 5x + 1100 is 98. Option C is correct.
An equation is a combination of numbers, variables, mathematical operations, and functions. It is basically a statement emphasising that the two or more expressions are equal to each other.
The given equation is
15x + 120 = 5x + 1100
Take the like terms together,
15x - 5x = 1100 - 120
10x = 980
x = [tex]\frac{980}{10}[/tex]
x = 98.
Thus, the option C is correct stating that the value of x in the given equation is 98.
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The complete question is as follows:
Find the value of x in the equation:
15x + 120 = 5x + 1100.
A. 66
B. 122
C. 98
D. 76
SUBMIT.
THE FIRST PERSON TO ANSWER GETS BRAINLIEST!!! A student traveled to a foreign country on an airplane. It took 18 hours to arrive at his destination, and the plane was traveling 900 kilometers per hour. When returning home, the same trip took only 15 hours going at a speed of 1,080 kilometers per hour. If t represents time and s represents the speed of the plane, which statement is true about this relationship?
(answer choices are below)
Answers
Answer:
4
Step-by-step explanation:
the time it takes for a plane to travel a distance varies directly as the speed of the plane because ts=16,200
A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. if a marble is randomly selected from the bag, what is the probability that it is blue?
Answers
3/12, or 1/4 is the probability that it is blue.
What is probability?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .Probability = number of successes / total number of outcomes
Total marbels in bag = 4+ 3 + 5 = 12
A total of 12 marbles are in the bag.
3 blue marbles are in the bag.
Therefore, the probability of picking a blue is 3/12, or 1/4.
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In △ABC, AB = 13, AC = 20, BC = 21. Find the length of the altitude AD
Answers
The length of the altitude AD is 12 units.
How to find the height of a triangle?The height of the triangle can be found as follows:
We have to find an angle using cosine law before we can find the height.
Therefore,
20² = 13² + 21² - 2 × 21 × 13 cos B
400 = 169 + 441 - 546 cos B
400 - 610 = - 546 cos B
-210 = - 546 cos B
cos B = -210 / -546
cos B = 0.38461538461
B = cos⁻¹ 0.38461538461
B = 67.3810899783
B = 67.38°
Hence,
sin 67.38° = opposite / hypotenuse
sin 67.38° = AD / 13
cross multiply
AD = 13 sin 67.38°
AD = 11.9999882145
AD = 12 units
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Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $48 and costs an additional $0.15 per mile driven.
The second plan has an initial fee of $53 and costs an additional $0.10 per mile driven. For what amount of driving do the two plans cost the same?What is the cost when the two plans cost the same?
Answers
Answer:
100 miles
Cost = $63
Step-by-step explanation:
Let us assume that the distance driven for both plans when they both equal in cost is X miles
Plan 1
Cost = 48 + 0.15X
Plan2
Cost = 53 + 0.1X
If they are both equal then
48 + 0.15X = 53 + 0.10X
Collecting like terms
0.15X - 0.10X = 53 - 48
0.05X = 5
X 5/0.05 = 100 miles
Plan 1 Cost = 48 + 0.15(100) = 48 + 15 = $63
Plan 2 Cost = 53 + 0.1(100) = 53 + 20 = $63
neeed help more more please uwu
Answers
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Let's calculate its discriminant ~
[tex]\qquad \sf \dashrightarrow \: {t}^{2} + \cfrac{17}{2} t - 5 = 0[/tex]
[ Multiply both sides by 2 ]
[tex]\qquad \sf \dashrightarrow \: 2 {t}^{2} + 17t - 10[/tex]
a = 2b = 17 c = 10[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (17) {}^{2} - (4 \times 2 \times - 10)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 289 - ( - 80)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 369[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d }= 3 \sqrt{41} \approx19.209 [/tex]
So, by quadratic formula :
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {17}^{} \pm \sqrt{369} }{2 \times 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 17 - 19.209}{4} \: \: and \: \: t = \dfrac{-17+19.209}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 36.209}{4} \: \: and \: \: t = \dfrac{2.209}{4} [/tex]
[tex]\qquad \sf \therefore \: t = - 9.052 \: \: \: or \: \: \: t = 0.552[/tex]
Find a power series for the function, centered at c. g(x) = 4x x2 2x − 3 , c = 0
Answers
The power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]
For given question,
We have been given a function g(x) = 4x / (x² + 2x - 3)
We need to find a power series for the function, centered at c, for c = 0.
First we factorize the denominator of function g(x), we have:
[tex]\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}[/tex]
We can write g(x) as,
[tex]\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\[/tex]
We know that, [tex]\frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n}[/tex] if |x| < 1
and [tex]\frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n[/tex] if [tex]|\frac{x}{6}| < 1[/tex]
[tex]\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\[/tex] if |x| < 1 and if [tex]|\frac{x}{6}| < 1[/tex]
[tex]\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex] if |x| < 1
Therefore, the power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]
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What is the value of y¹ when y = 5 and x - 10?
Answers
Answer:
5
Step-by-step explanation:
y^1 = 5^1 (y = 5)
Anything raised to the power of 1 is just itself.
So, 5^1 = 5
Use the diagram to answer each part of the question. The image is not drawn to scale.
will mark brainiest if corrects. try ur best!
In the afternoon, the person (who is 1.6 m tall) casts a shadow that is 8 m. The distance along the ground from the person (H) to the tree (G) is 30 m, and the distance from the tree (G) to the building (F) is 105 m. Calculate the height of the tree and the building. Round answers to the nearest tenth of a meter and show all your work.
Answers
The height of the tree and the building are 7.6 m and 28.6 m respectively.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Two triangles are similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.
Triangle BGD, CHD and AFD are similar triangles.
CH = 1.6, DH = 8, GH = 30, GF = 105
FH = GF + GH = 105 + 30 = 135
FD = FH + DH = 135 + 8 = 143; GD = 30 + 8 = 38
Hence, using similar triangles:
BG/CH = GD / DH
BG / 1.6 = 38/8
BG = 7.6 m
Also:
building/CH = DF / DH
building / 1.6 = 143/8
building = 28.6 m
The height of the tree and the building are 7.6 m and 28.6 m respectively.
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HElp meee mwa mwa mwa
Answers
Answer:
[tex]a = 1, \ - 3[/tex]
Explanation:
[tex](a-6)(a+8) = -45[/tex]
distribute
[tex]a^2 + 8a - 6a - 48 = -45[/tex]
collect terms
[tex]a^2 + 8a - 6a - 48 + 45=0[/tex]
simplify
[tex]a^2 + 2a - 3=0[/tex]
factor
[tex](a - 1)(a + 3)= 0[/tex]
set to zero
[tex]a = 1, \ - 3[/tex]
Answer:
a = 1, -3
Step-by-step explanation:
Given equation:
[tex](a-6)(a+8)=-45[/tex]
Expand the brackets:
[tex]\implies a^2+8a-6a-48=-45[/tex]
[tex]\implies a^2+2a-48=-45[/tex]
Add 45 to both sides:
[tex]\implies a^2+2a-48+45=-45+45[/tex]
[tex]\implies a^2+2a-3=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
Two numbers that multiply to -3 and sum to 2 are: 3 and -1.
Rewrite the middle term as the sum of these two numbers:
[tex]\implies a^2+3a-a-3=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies a(a+3)-1(a+3)=0[/tex]
Factor out the common term (a + 3):
[tex]\implies (a-1)(a+3)=0[/tex]
Apply the zero product property:
[tex]\implies (a-1)=0 \implies a=1[/tex]
[tex]\implies (a+3)=0 \implies a=-3[/tex]
Verify the solutions by inputting the found values of a into the original equation:
[tex]a=1 \implies (1-6)(1+8) & =-5 \cdot 9 = -45[/tex]
[tex]a=-3 \implies (-3-6)(-3+8) & =-9 \cdot 5 = -45[/tex]
Hence both found values of a are solutions of the given equation.
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suppose sin(A) = 2/5. use the trig identity sin^2(A)+cos^2(A)=1 to find cos(A) in quadrant I. show all steps and round to ten-thousandth
Answers
In quadrant I, [tex]\cos(A)[/tex] is positive. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} = \dfrac{\sqrt{21}}5 \approx \boxed{0.9165}[/tex]
Hurry show your work
24- 4 to rhe power of 2 x 3+15
Answers
the expression is simplified to give - 39
How to simply the expression
Given the expression;
= 24- 4 to the power of 2 x 3+15
= 24 - (4^2 × 3 ) + 15
First, expand the bracket
= 24 - ( 16 × 3) + 15
Find the product of the bracket
= 24 - 48 + 15
From our knowledge of BODMAS, we add before we subtract
Now, let's add first
= 24 - 63
The, subtract
= - 39
The expression is simplified to - 39
Thus, the expression is simplified to give - 39
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3. What is the greatest common factor for the two expressions? Use ^ to mean an exponent (use Shift +6 key). For example, 3x2 would be written as 3x^2. 15v³ and 12v² Write your response on the line below. Do not use any spaces or words.
Answers
The greatest common factor of the two expressions given as in the task content is; 3v².
What is the greatest common factor of the two expressions given?It follows from the task content that the terms whose greatest common factor are to be determined are: 15v³ and 12 v².
15v³ and 12v²
= 3v²(5v) and 3v²(4)
= 3v²(5v) and (4)
Consequently, in a bid to factorise the two expressions by means of their greatest Common factor, the greatest common factor can be determined as; 3v².
The correct answer choice which therefore represents the greatest common factor as required in the task content is; 3v².
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A toy store retailer charges $26.88 for a board game. He marks up his goods by 25% before selling them. What was the cost of the game before the markup?
Answers
The price of the board game before the markup is $21.50.
What is the cost before the markup?
Percentage can be described as a fraction an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.
When the price of an item is marked up, it means that the price of the item has been increased by a predetermined percentage. In this question, the price of the board game is increased by 25%.
Price of the item before the mark up = price the retailer sells / ( 1 + percentage)
$26.88 / 1.25 = $21.50
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find the total surface area and volume, then multiply by 0.0004
Answers
The Total surface area of the rectangular prism = 168 in.²
The Volume of the rectangular prism = 108 in.³
What is the Total Surface Area of a Rectangular Prism?The total surface area of a rectangular prism is given as: SA = 2(wl + hl + hw), where:
w = width of the rectangular prism
h = height of the rectangular prism
l = length of the rectangular prism
What is the Volume of a Rectangular Prism?The volume of a rectangular prism = l × w × h
Find the Total surface area of the rectangular prism:
Length (l) = 9 in.
Width (w) = 2 in.
Height (h) = 6 in.
Total surface area of the rectangular prism = 2(wl+hl+hw) = 2·(2·9+6·9+6·2) = 168 in.²
Find the volume of the rectangular prism:
Length (l) = 9 in.
Width (w) = 2 in.
Height (h) = 6 in.
Volume of the rectangular prism = l × w × h = 9 × 2 × 6
Volume of the rectangular prism = 108 in.³
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4. Joe has five times as much money as Bill. However, Joe pays Bill $5 he owes him, after which Joe has just twice the amount Bill now has. How much money did each have in the beginning?
Answers
Answer:
Bill starts with $5 and Joe starts with $25Step-by-step explanation:Let Ji and Bi represent the initial amounts that Joe and Bill have at the start. Number after J and B will be used to indicate subsequent steps in the problem.
We are told that "Joe has five times as much money as Bill," which we can write as:
1) Ji = 5Bi
We learn that "Joe pays Bill $5," which we can represent as:
2) J1 = Ji - 5
This would mean that Bill has added $5:
3) B1 = Bi + 5
We are then told that "Joe has just twice the amount Bill now has," which we can write as:
4) J1 = 2B1
===
We can rearrnage and substitute the above relationships to eliminate one of the two variables (B1 or J1)
J1 = Ji - 5 [from 2]
2B1 = Ji - 5 [Substitute 4 to eliminate J1]
Ji = 5Bi [from 1]
2B1 = 5Bi - 5 [Substitute 1 to eliminate Ji]
B1 = Bi + 5 [Rearrange]
2(Bi + 5) = 5Bi - 5 [Use the above expression in the previous equation to eliminate B1]
2Bi + 10 = 5Bi - 5 [Simplify]
-3Bi = -15 [Simplify]
Bi = $5 [Solve]
Ji = 5Bi [from 1]
Ji = 5*(5) [Since Bi = $5]
Ji = $25 [Solve]
Bi = $5 and Ji = $25===
CHECK:
Does Joe has five times as much money as Bill?
Ji = $25 and Bi = $5 YES
When Joe pays Bill $5 he owes him, does Joe has just twice the amount Bill now has?
J1 = $25 - $5 = $20
B1 = $5 + $5 = $10 YES
Is there any number in base 10 (positive or negative) that can be written in multiple
ways in base −4? Can you prove it? If yes, provide the number and the base −4
representations, and if no, show why.
Answers
The true statement is that no number in base 10 can be written in multiple ways in base 4
How to determine the true statement?The base of the numbers are given as:
Base 10 and base 4
Base 10 numbers are also referred to as decimal numbers, while base 4 numbers are quaternary numbers
There is only one equivalent of each number in each base.
This means that (for instance)
357 in base 10 is 11211 in base 4
The above number does not have any other representation in base 4 and it can not be written in another way.
This is the same for other numbers in base 10
Hence, the true statement is that no number in base 10 can be written in multiple ways in base 4
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PLEASE HELP IM STUCK
Answers
Answer:
23
Step-by-step explanation:
The question gives the first equation:
0.05N + 0.10D = 2.20
It can be rewritten as:
0.05$ times the number of nickels plus 0.10$ times the number of dimes is equivalent to $2.20.
Notice that 0.05$ or 5 cents is equivalent to one nickel and 0.10$ or 10 cents is equivalent to one dime.
The question asks for N+D. We know that N stands for the number of nickels Daniel has and D stands for the number of dimes Daniel has. We also know that Daniel only has dimes and nickels in his pocket. Therefore N+D most be equivalent to the total number of coins, which is given in the question to be equal to 23 coins.
Therefore...
N+D = 23
The points A(-3, 4), B(3, 2), C(1,4), and D(-5, -2) form quadrilateral ABCDin the coordinate plane. What condition verifies that the
diagonals are perpendicular?
PLEASED HELP
Answers
The diagonals of the qudrilateral will not be perpendicular to each other.
What is a quadrilateral?A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.
Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. If two segments are perpendicular, the multiplication of their slopes is -1.
The slope of a coordinate pair is given by the change in y divided by the change in x, that is:
For the diagonal AD the slope will be:-
Slope = ( -5 + 3 ) / ( -2 - 4) = ( 1 / 3 )
For the diagonal BC, the slope will be:-
Slope= ( 1 - 3) / ( 4 - 2 ) = ( -2 / 2) = -1
The multiplication of the two slopes will be,
M = ( 1 / 3 ) x -1 = ( - 1 / 3 )
Therefore, the diagonals of the quadrilateral will not be perpendicular to each other. Because the product of the slope is not equal to -1.
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Answer:
The product of the slopes of the diagonals is -1.
Step-by-step explanation:
I had the question and got it right.
A cube shaped box has a side length of 15 inches and contains 27 identical cube shaped blocks. what is the surface area of all 27 blocks compared to the surface area of the box?
Answers
The surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.
What is a cube?A cube is a three-dimensional solid object with six square faces, facets, or sides, three of which meet at each vertex.To find the total surface area of the 27 blocks:
A cube's surface area
SA = 6s² (where s is the side length)Given that the box's side length is 15 inches:
SA of box = 6152 = 1350 in2Surface Area of 3-inch side length blocks:
⇒ SA = 6 · 3² = 54 in²27 blocks SA = 27 54 = 1458 in2Surface Area of 4-inch side length blocks:
⇒ SA = 6 · 4² = 96 in²27 96 = 2592 in2 SA of 27 blocksSurface Area of 5-inch side length blocks:
⇒ SA = 6 · 5² = 150 in²27 blocks SA = 27 150 = 4050 in2Therefore, from the given answer options for the total surface area of the 27 blocks, the side length of the blocks must be 5 inches.
To calculate how many times the total surface area of the 27 blocks is to the surface area of the box:
So,
The side length of the blocks is 5 inches.
The total surface area of the 27 blocks is 4050 square inches.
This is 3 times the surface area of the box.
Therefore, the surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.
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FIND the smallest number by which 576 mus be divided to make it perfect cube
Answers
Answer:
9
Step-by-step explanation:
when you divide 576 by 9 you get 64 which is a perfect cube
cbrt(64) = 4
so your answer is 9
30. You want to simulate an experiment to draw cards out of a deck. You
plan to draw 35 cards (with replacement), and list which card you drew. How
many times would you expect to draw a face card?
6
8
12
10
Answers
Using the binomial distribution, we have that you would expected to draw a face card 8 times.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
For this problem, the parameters are given as follows:
n = 35, as the experiment will be repeated 35 times.p = 0.2308, as of the 52 cards, there are 12 faces, hence 12/52 = 0.2308.Then the expected value is found as follows:
E(X) = np = 35 x 0.2308 = 8
You would expected to draw a face card 8 times.
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Solve the following systems of equations algebraically:
[tex]\left \{ {{y=\frac{1}{2}*2^x } \atop {y=5x+2}} \right.[/tex]
Answers
The value of x in the system of equation is 6
How to solve the system of equations?The system of equations is given as:
y = 1/2 * 2^x
y = 5x + 2
Substitute y = 1/2 * 2^x in y = 5x + 2
1/2 * 2^x = 5x + 2
Multiply through by 2
2^x = 10x + 4
Next, we use the trial by error.
Set x = 6
This gives
2^6 = 10 * 6 + 4
Evaluate the product and the exponent
64 = 60 + 4
Evaluate the sum
64 = 64
Hence, the value of x in the system of equation is 6
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(a+b)^2-2(a+b)
Factorise (please explain)
Answers
Answer:
(a + b)(a + b - 2)
Step-by-step explanation:
(a + b)² - 2(a + b) ← factor out (a + b) from each term
= (a + b)(a + b - 2)