If p =(3x+1) and q = ( 3x-1),show that : pq+1 =x2
Answer:
See explanation
Step-by-step explanation:
It should be 9x² not x²
p = (3x + 1) and q = (3x - 1)
pq + 1 = (3x + 1)(3x - 1) + 1
= (9x² - 3x + 3x - 1) + 1
= (9x² - 1) + 1
= 9x² - 1 + 1
= 9x²
Therefore,
pq + 1 = 9x²
Can someone pls help me with this answer?
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if
Needed.
Answer:
Step-by-step explanation:
Kylie baked 40 cookies. She brought 90% of the cookies to work. How many cookies did Kylie bring to work?
Percentage plz help
Explain why 51 is not a prime number
Step-by-step explanation:
51 is not a prime number because it is divisible by 1,3 and 17
and we know prime number are only those number who arenot divisible by any other number except 1
Answer:
57 is divisible by 1,3,19 and 57
Step-by-step explanation:
A prime number is a number that is divisible only by 1 and itself; and 57 is not among the numbers like 2,3,5,7,11 etc
PLZZZ HELPPP, IF NOT 100% SURE PLZ DONT ANSWER…BRAINLIEST TO FIRST AND CORRECT ANSWER, THX TO SECOND AND CORRECT ANSWER
Answer:
2 batches
Step-by-step explanation:
We can divide 7 1/2 by 3 3/4 to get 2, so the factory made 2 batches of granola bars yesterday.
Fine FG , given that line HF is perpendicular bisector or EG
Answer:
FG = 7
Step-by-step explanation:
We'll begin by calculating HF. This can be obtained by using the pythagoras theory as illustrated below:
EF = 7
EH = 3
HF =?
EF² = EH² + HF²
7² = 3² + HF²
49 = 9 + HF²
Collect like terms
49 – 9 = HF²
40 = HF²
Take the square root of both side
HF = √40
Finally, we shall determine FG. This can be obtained as follow:
GH = 3
HF = √40
FG =.?
FG² = GH² + HF²
FG² = 3² + (√40)²
FG² = 9 + 40
FG² = 49
Take the square root of both side
FG = √49
FG = 7
Can someone please help, I'll give out 20 points !
Question - Where is the blue point on the number line?
Answer:
-6
Step-by-step explanation:
The number line is created by skip counting of 2.
So, -2 , then -4 and then -6.
So, blue dotted point is (-6)
Expand the following:
a) 2(x+3)
b) 512x-4)
C) 4(2x + 1)
d) 6 x - 4y
Answer:
A.2x+6
B.60x-20
C.8x+4
D.6x-24y
what is the solution to this equation?
5x-4+3x=36
A. x=16
B. x=5
C. x=20
D. x=4
B. x = 5
tip : if in a rush just plug in the number and see if its true
8x - 4 = 36
x = 5
When a boy stands on the bank of a river and looks across to the other bank, the angle of depression is 12°. If he climbs to the top of a 10 ft tree and looks across to other bank, the angle of depression is 15°. What is the distance from the first position of the boy to the other bank of the river? How wide is the river? Give your answers to the nearest foot.
Please look at the scanned picture.
You own 7 pairs of jeans and are taking 4 on vacation. In how many ways can you choose 4 pairs of jeans form the 7?
Answer:
35 ways
Step-by-step explanation:
The selection process in the given question can be referred to as combination, since 4 pairs of jeans are to be selected from the 7 pairs. There is no specific pattern of selecting the 4 pairs.
Thus, the selection can be done in 7[tex]C_{4}[/tex] ways.
7[tex]C_{4}[/tex] = [tex]\frac{7!}{(7-4)!4!}[/tex]
= [tex]\frac{7!}{3!4!}[/tex]
= [tex]\frac{7*6*5*4!}{3*2!4!}[/tex]
= 7 x 5
= 35
Therefore, 4 pairs of jeans can be selected from 7 pairs in 35 ways.
Applying Probability Concepts
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Did you know that all 50 states in the United States have some sort of state fair? Fairs and carnivals
include a variety of games of chance that aren't typically "fair." What does it mean for a game to be fair? In
this task, you'll analyze different scenarios to determine fairness. You will use probability and expected
value to make these determinations. You will also use these concepts to make decisions.
As you complete the assignment, keep this question in mind:
Tanya should play The second game to win more.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, Tanya is considering playing a game at the fair. There are three different ones to choose from, and it costs $2 to play a game. The probabilities associated with the games are given in the table.
From the general formula of weighted possibility :
Total weighted possibility = Sum of the weighted probability of desired outcomes - the weighted possibility of undesired outcomes
In our case,
For first game
The sum of the weighted possibility of desired outcomes = 0.20*1 + 0.25 *4
The sum of the weighted possibility of desired outcomes = 1.20
the weighted possibility of undesired outcomes = 0.55 * 2 = 1.10
Thus,
Total weighted desired possibility = 1.20 - 1.10
Total weighted desired possibility = 0.10
For second game
The sum of the weighted possibility of desired outcomes =0.35*1 + 0.50 *4
The sum of the weighted possibility of desired outcomes = 2.35
the weighted possibility of undesired outcomes = 0.15 * 2 = 0.30
Thus,
Total weighted desired possibility = 2.35 - 0.30
Total weighted desired possibility = 2.05
For third game
The sum of the weighted possibility of desired outcomes = 0.60*1 + 0.20*4
The sum of the weighted possibility of desired outcomes = 1.40
the weighted possibility of undesired outcomes = 0.20 * 2 = 0.40
Thus,
Total weighted desired possibility =1.40 - 0.40
Total weighted desired possibility = 1
Therefore, Tanya should play The second game to win more.
Learn more about probability here:
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Complete question:
A bag contains 10 marbles,7 of which are black and 3 are red.three marbles are drawn at one after the other.find the probability of choosing at most two black marbles.
==========================================================
Explanation:
We have these four cases or possible outcomes
Case 1) We select 0 black marbles and 3 red marbles.Case 2) We select 1 black marble and 2 red marbles.Case 3) We select 2 black marbles and 1 red marble.Case 4) We select 3 black marbles and 0 red marbles.Let's calculate the probability for case 4.
There are 7 black marbles out of 10 total. The probability of picking black is 7/10. If no replacement is made, then 6/9 is the probability of picking black again (subtract 1 from the numerator and denominator separately). Finally, 5/8 is the probability of getting black a third time.
The probability of getting 3 black marbles in a row is
(7/10)*(6/9)*(5/8) = (7*6*5)/(10*9*8) = 210/720 = 7/24.
That fraction 7/24 means that if you had 24 chances, then you expect about 7 of them will lead to getting three black marbles in a row (aka case 4). Therefore, 24-7 = 17 occurrences are expected where we get cases 1 through 3 occur in some fashion (pick one case only).
Notice how cases 1 through 3 encapsulate the phrasing "at most 2 black marbles" which is another way of saying "2 black marbles is the highest we can go".
So that's why the answer is 17/24.
What is the effect of k on f(x)=g(5x) where g(x) is a piecewise function? Explain.
Answer:
g(x) will be dilated horizontally to get f(x)
Step-by-step explanation:
Given
f(x) = g(kx) --> the correct equation
Required
The effect of k
The given equation is an illustration of horizontal dilation.
If |k| is greater than 0, then the function will be compressed.
However, if |k| is between 0 and 1 (exclusive), then the function will be stretched.
Take for instance:
f(x) = g(x/5)
In the above function, g(x) will be stretched by 5 units
Another instance is:
f(x) = g(x/0.5)
In the above function, g(x) will be stretched by 0.5 units
i will brainliest
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Express each of the following percentages as a fraction and simplify it.
(i) 25% (ii) 40% (iii) 16% (iv) 150%
(v) 120% (vi) 58% (vii) 32% (viii) 175%
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
[tex]\sf{25\%=\dfrac{25}{100}=\dfrac{1}{4} }[/tex] [tex]\sf{ 40\%=\dfrac{40}{100}=\dfrac{2}{5} }[/tex] [tex]\sf{16\%=\dfrac{16}{100}=\dfrac{4}{25} }[/tex][tex]\sf{150\%=\dfrac{150}{100}=\dfrac{3}{2} }[/tex][tex]\sf{120\%=\dfrac{120}{100}=\dfrac{6}{5} }[/tex][tex]\sf{58\%=\dfrac{58}{100}=\dfrac{29}{50} }[/tex][tex]\sf{32\%=\dfrac{32}{100}=\dfrac{8}{25} }[/tex][tex]\sf{175\%=\dfrac{175}{100}=\dfrac{7}{4} }[/tex][tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\hookrightarrow\sf{ 25\% =\dfrac{25}{100}=\boxed{\bf \dfrac{1}{4} }} \\\hookrightarrow\sf{ 40\% =\dfrac{40}{100}=\boxed{\bf \dfrac{2}{5} }} \\\hookrightarrow \sf{16\%=\dfrac{16}{100}=\boxed{\bf\dfrac{4}{25}} } \\ \hookrightarrow\sf{150\%=\dfrac{150}{100}=\boxed{\bf\dfrac{3}{2} }} \\ \hookrightarrow\sf{120\%=\dfrac{120}{100}=\boxed{\bf\dfrac{6}{5} }} \\\hookrightarrow \sf{58\%=\dfrac{58}{100}=\boxed{\bf\dfrac{29}{50}} } \\\hookrightarrow \sf{32\%=\dfrac{32}{100}=\boxed{\bf\dfrac{8}{25} }} \\ \hookrightarrow\sf{175\%=\dfrac{175}{100}=\boxed{\bf\dfrac{7}{4}} } \\ [/tex]
how do i find upper and lower quartile
please help will give brainliest
Answer:
Step-by-step explanation:
Arrange the data set in ascending order. then find the median.
Data in ascending order:
2, 5 , 6 , 7 , 8 , 11 , 15
Median = 7
Lower quartile:
Then again find the median of the numbers from the first to the number before the median. This is the lower quartile.
2 , 5, 6
Median = 5 ----> this is the lower quartile.
Upper quartile:
Then again find the median of the numbers that comes after the median to the end of the data set. This is the upper quartile.
8 , 11 , 15
Median = 11 ------> is the upper quatile
Car A covers 100 miles in 120 minutes, while car B covers 300 miles in 5 hours. How do car A and car B speeds compare (Hint: 60 minutes = 1 hour)
A. Car A is faster than car B.
B. Car B is faster than car A.
C. Car B is slower than car A.
D. Car A has the same speed as car B.
Answer:
option D. Car A has the same speed as car B.
The dimensions of a screen are 21 ft by 20 ft. Find the length of the diagonal .
Answer:
29 ft
Step-by-step explanation:
the screens have 90 degree angles so they form right triangles with the diagonal, so use Pythagorean theorem to solve for the diagonal
diagonal² = 21² +20² , square and square root both sides of the equation
diagonal = √441+400, add
diagonal = √841, square root
diagonal = 29ft
Jack can build 1/5 of a shed in the same time Kyle build 5/8 of a shed. How much of a shed will jack have built when Kyle has finished building 1 shed.
Answer:
Step-by-step explanation:
If Kyle can get 5/8 of a shed built in x amount of time, he can get 62.5% done; if Jack can get 1/5 of the shed built in the same time, he can 20% of it done. As a ratio:
[tex]\frac{Kyle}{Jack}:\frac{62.5}{20}[/tex] Kyle gets the whole thing done, 100% of the way, leaving Jack lagging behind at a somewhat lower percentage of the work being done.
[tex]\frac{Kyle}{Jack}:\frac{62.5}{20}=\frac{100}{x}[/tex] and cross multiply to solve for the percentage of the shed built by Jack by the time Kyle gets it completed:
62.5x = 2000 so
x = 32%
When Kyle will complete the work the amount of the work done by Jack will be 32%.
What is an expression?Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
If Kyle can get 5/8 of a shed built in x amount of time, he can get 62.5% done; if Jack can get 1/5 of the shed built in the same time, he can 20% of it done. As a ratio:
Jack falls behind Kyle, completing only a small portion of the work, while Kyle completes the entire task and cross multiplies to solve for the percentage of the shed built by Jack by the time Kyle gets it completed:
Kyle / Jack ÷ 62.5 / 20 = 100 / x
62.5x = 2000 so
x = 32%
Therefore, when Kyle will complete the work the amount of the work done by Jack will be 32%.
To know more about an expression follow
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The blue dot is at what value on the number line?
Answer:
[tex]8[/tex]
Step-by-step explanation:
Hope it helps you:D
*copied*
Answer:
"8"
4,6,8
Step-by-step explanation:
In circle G with m<FJH=31° , Find the angle measure of minor arc FH
Answer:
62°
Step-by-step explanation:
Inscribed Angle Theorem
Inscribed angles measures are 1/2 of the arc they create.
m∠FJH x 2 = arc FH
Just take the 31° and double it.
Give your answer in standard form.
You and a friend decide to take a road trip. You drive an average speed of 70 mph and your friend drives an average of 75 mph. You want to drive at least 500 miles per day. You also plan to spend no more than 10 hours driving each day. Which of the following is a system of linear inequalities that represents this situation? Let x = number of hours you drive and let y represent the number of hours your friend will drive.
Given:
your speed = 70 mph
Your friend's speed = 75 mph
You want to drive at least 500 miles per day.
You also plan to spend no more than 10 hours driving each day.
To find:
The system of linear inequalities that represents this situation.
Solution:
Let x be the number of hours you drive and let y represents the number of hours your friend will drive.
You also plan to spend no more than 10 hours driving each day.
[tex]x+y\leq 10[/tex]
Your speed is 70 mph and your friend's speed is 75 mph. So, the distance covered in x and y hours are 70x miles and 75y miles respectively.
You want to drive at least 500 miles per day. So, the total distance must be greater than or equal to 500.
[tex]70x+75y\geq 500[/tex]
[tex]5(14x+15y)\geq 500[/tex]
Divide both sides by 5.
[tex]14x+15y\geq 100[/tex]
Therefore, the required system of inequalities has two inequalities [tex]x+y\leq 10[/tex] and [tex]14x+15y\geq 100[/tex].
Help Please Now!!!
Find The Volume Of This Cylinder
Answer:
V ≈ 4021 mm³
General Formulas and Concepts:
Symbols
π (pi) ≈ 3.14Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Cylinder Formula: V = πr²h
r is radiush is heightStep-by-step explanation:
Step 1: Define
Identify variables
r = 8 mm
h = 20 mm
Step 2: Find Volume
Substitute in variables [Volume of a Cylinder Formula]: V = π(8 mm)²(20 mm)Evaluate exponents: V = π(64 mm²)(20 mm)Multiply: V = 1280π mm³Round: V ≈ 4021 mm³What are the coordinates of the midpoint between the points (-4, -9) and (-8, -5)?
Select the best answer from the choices provided.
A.
(-4, -4)
B.
(-6, -7)
C.
(-6, -4)
D.
(-4, -7)
Solve for x. = x/2 = -7
Answer:
x = -14
Step-by-step explanation:
x/2 = -7
~Multiply 2 to both sides
x = -14
Best of Luck!
use a double angle or half angle identity to find the exact value of each expression
θ is given to be in the fourth quadrant (270° < θ < 360°) for which sin(θ) < 0 and cos(θ) > 0. This means
cos²(θ) + sin²(θ) = 1 ==> sin(θ) = -√[1 - cos²(θ)] = -3/5
Now recall the double angle identity for sine:
sin(2θ) = 2 sin(θ) cos(θ)
==> sin(2θ) = 2 (-3/5) (4/5) = -24/25
Which of the integers shown is the greatest?
Answer:
-3
Step-by-step explanation:
because as you vo more to the negative side the less.it gets and more to the positive side it gets moe
A colony of 150 bacteria doubles in size every 36 hours. What will the population be 72 hours from now?
