Answer:
already in standard form
Step-by-step explanation:
the equation of a quadratic in standard form is
y = ax² + bx + c ( a ≠ 0 )
y = x² + 4x + 3 ← is in standard form
with a = 1 , b = 4 , c = 3
The Pythagorean Identity states that: (sin x)^2 + (cos x)2 = 1
Given sin 0 = 2/5, find cos 0.
cos 0 = ?/?
Answer:
[tex]\cos \theta =\dfrac{\sqrt{21}}{5}[/tex]
Step-by-step explanation:
Given:
[tex]\sin \theta=\dfrac{2}{5}[/tex][tex](\sin x)^2+(\cos x)^2=1[/tex]Substitute the given value of sin θ into the given identity and solve for cos θ:
[tex]\begin{aligned}(\sin x)^2+(\cos x)^2 & =1\\\implies (\sin \theta)^2+(\cos \theta)^2 & =1\\\left(\dfrac{2}{5}\right)^2+(\cos \theta)^2 & =1\\\left(\dfrac{2^2}{5^2}\right)+(\cos \theta)^2 & =1\\\dfrac{4}{25}+(\cos \theta)^2 & =1\\(\cos \theta)^2 & =1-\dfrac{4}{25}\\(\cos \theta)^2 & =\dfrac{21}{25}\\\cos \theta & =\sqrt{\dfrac{21}{25}}\\\cos \theta & =\dfrac{\sqrt{21}}{\sqrt{25}}\\\cos \theta & =\dfrac{\sqrt{21}}{5}\end{aligned}[/tex]
The number of employees working for Sprockets R Us in 2005 was 8110, with an expected decrease of 0.5% per year. At the rate of decrease given, what is the expected number of employees working at Sprockets R Us in 2006? Round your answer to the nearest integer.
The expected number of employees working at Sprockets R Us in 2006 will be 8069.45.
What are percentages?The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
The number of employees working for Sprockets R Us in 2005 was 8110, with an expected decrease of 0.5% per year. At the rate of decrease given, what is the expected number of employees working at Sprockets R Us in 2006?
The number of the employees in 2006 will be calculated as:-
Number of employees decreased = 0.5% x 8110
Number of employees decreased = (0.5/100) x 8110
Number of employees decreased = 40.55
The number of the employees in 2006 will be
N = 8110 - 40.55 = 8069.45
Therefore the expected number of employees working at Sprockets R Us in 2006 will be 8069.45.
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he area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.
Answer:
14m
Step-by-step explanation:
Area = πr²
A = 153.86m²
153.86 = 3.14 *r²
r² = 153.86/3.14
r = √49
r = 7
d = 2r
d = 2*7
d = 14
What are the approximate area and circumference, respectively, of a circle with a diameter of 30 inches?
Solution:
[tex]\searrow[/tex]
Detailed explanation:
Here we need to find both the circumference and the area of a circle whose diameter is 30 in.
///\\\///\\\///\\\///\\\///\\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\////\\\\////\\\\///\\\///\\\///\\\///
⚜ Circumference ⚜
This is the formula that we use for the circumference. [tex]\large\texttt{$C=\pi d$}[/tex].
Here, C is the circumference,
[tex]\pi[/tex] is pi, *
d is the diameter
_____________
* The number pi is an irrational number. This means that no matter how hard we try, we cannot write this number as a fraction. The reason for that is: The number pi has never-ending digits after its decimal point.
To avoid getting never-ending numbers, we will use 3.14 for pi.
_____________
Alright, so now we just stick in the values.
[tex]\boldsymbol{C=3.14\cdot30}[/tex]
[tex]\boldsymbol{C=94.2\:inches}[/tex]
The circumference is successfully calculated.
///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\\///\\\///\\\///\\\//\\//\/\/\/\//\///\\//
⚜ Area ⚜
This is the formula we will use to work out the area.
[tex]---\mapsto\boldsymbol{A=\pi r^2}[/tex]
Here,
A denotes the area
[tex]\pi[/tex] denotes pi
r denotes the radius (30/2=15, because the diameter is always two times the radius)
[tex]\large\boldsymbol{\therefore,\;the\;radius\;is\;15}[/tex]
Once again, it's just a matter of sticking in the values.
[tex]---\mapsto\boldsymbol{A=3.14\cdot15^2}[/tex]
NB:Remember the Order of Operations!
P.E.M.D.A.S.
P=Parentheses
This operation tells us to evaluate all expressions in the parentheses first, if any are present.
E=Exponents
This one tells us to evaluate all expressions with exponents, if any are present.
M=Multiplication | D=Division
Unlike the two operations above, these two are completely interchangeable.
A=Addition | S=Subtraction
Like M and D, A and S are interchangeable.
_________________
Now let's simplify... According to P.E.M.D.A.S., we should square 15 first.
[tex]---\mapsto\boldsymbol{A=3.14\cdot225}[/tex]
Now, we need to multiply.
[tex]---\mapsto\boldsymbol{A=706.5\;square\;inches}[/tex]
how would i solve this problem
Answer:
30
Step-by-step explanation:
1500/50=30
Find the midpoint of the segment with the following endpoints.
(-3,-3) and (1, 2)
[tex]\left(\frac{-3+1}{2}, \frac{-3+2}{2} \right)=\boxed{\left(-1, -\frac{1}{2} \right)}[/tex]
Write 4 1/7 as an improper fraction?
Answer:
29/7
Step-by-step explanation:
4 1/7 = 4 + 1/7
4 = 28/7
then:
4 1/7 = 28/7 + 1/7 = (28+1) / 7
= 29/7
X+(x^2+2)+y=4
Find 2 coordinates
(X,y) (x,y)
Answer: (-2,0) and (1,0)
Step-by-step explanation:
If y=0, then:
[tex]x+x^2 + 2=4\\\\x^2 + x-2=0\\\\(x+2)(x-1)=0\\\\x=-2, 1[/tex]
So, the points (-2,0) and (1,0) lie on the curve.
The points (-2,0) and (1,0) lie on the curve.
If y=0, then:
[tex]x+(x^2+2)+0=4\\x^2+x+2=4\\[/tex]
What is the coordinate of the axis?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
[tex]x^2+x-2=0[/tex]
[tex]=\left(x^2-x\right)+\left(2x-2\right)[/tex]
[tex]=x\left(x-1\right)+2\left(x-1\right)[/tex]
[tex]=\left(x-1\right)\left(x+2\right)[/tex]
[tex]x=-2,x=1[/tex]
So, the points (-2,0) and (1,0) lie on the curve.
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A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses. A roll of green pays $2.00. A roll of blue pays $5.00. The charge to play the game is $2.00. What is the expected value of the game?
The expected value of the game is $2.00.
To Find: The fair price to pay to play the game of rolling a colored die with three red sides, two green sides, and one blue side
Now the question arises how to find the Fair Price
We are told that in the game of rolling the colored die;
A roll of a red loses.
A roll of blue pays 5.00 and A roll of green pays 2.00.
Now, the best game to get the fairest price is to play; RRRGGB i.e (RED, RED, RED, GREEN, GREEN,BLUE)
Fair price = 2(3/6) + 6(1/6) + 0(2/6)
Fair price = $2
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a car corporation produced 1560 more cars this month than last. Write a signed number to represent this month's change in the production
Answer:
+1560
Step-by-step explanation:
Since the corporation produced 1560 more cars then the answer is simply +1560.
The following data represent the high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts (a) through (c
Temperature Lower Limit Upper Limit Days
50-59 50 59 4
60-69 60 69 316
70-79 70 79 1426
80-89 80 89 1532
90-99 90 99 345
100-109 100 109 7
Answer:
The Mean and Standard deviation for the given data would be as follows:
μ =79.7
б =7.81
Step-by-step explanation:
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values.
Frequency Distribution
Given that,
Temperature Lower Limit Upper Limit Days([tex]f_{i}[/tex])
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Average([tex]x_{i\\}[/tex])
[tex]\frac{50+59}{2} = 54.5\\ \\\frac{60+69}{2} = 64.5\\ \\\frac{70+79}{2} = 74.5\\\\\frac{80+89}{2} = 84.5\\ \\\frac{90+99}{2} = 94.5\\ \\\frac{100+109}{2} = 104.5[/tex]
As we know,
Mean (μ) =∑ [tex](x_{i}f_{i})[/tex]/∑[tex]f_{i}[/tex]
= { (54.5 * 2) + (64.5 * 313) +(74.5 * 1419)+(84.5*1503)+(94.5*319) + (104.5*9)/ (2+313+1419+1503+319)
∵ μ = 79.7
As we know,
Standard Deviation:-
[tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]
by putting the values, we get
∵ б = 7.81
Hence, μ = 79.7 and б=7.81 are the correct answers.
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Which choices are equivalent to the expression below? Check all that apply. √8 × √8
A. √ 8
B. 8
C. 64
D. 8
E. 16
F. √64
Answer:
the answers are B and F since √8 x √8 = √64 which simplifies to 8.
Need help ASAP!! Will give Brainliest
Answer:
B
Step-by-step explanation:
Square root of (-16)^2
Answer: [tex]\sqrt{(-16)^{2} } =16[/tex]
Step-by-step explanation:
I looked it up on my calculator. I hope this helps!! :)
The figure below shows parallel lines cut by a transversal:
A pair of parallel lines is shown with arrowheads on each end. A transversal cuts through these two lines. An angle formed between the top parallel line and the transversal on the inner left side is marked 1. Another angle formed between the bottom parallel line and the transversal on the inner right side is marked 2.
Which statement is true about ∠1 and ∠2?
∠1 and ∠2 are congruent because they are a pair of adjacent angles.
∠1 and ∠2 are complementary because they are a pair of adjacent angles.
∠1 and ∠2 are congruent because they are a pair of alternate interior angles.
∠1 and ∠2 are complementary because they are a pair of alternate interior angles.
∠1 and ∠2 are congruent because they are a pair of alternate interior angles , Option C is the right answer.
What are Parallel Lines ?When two lines do not meet at any point and the distance between them remains constant , then the two lines are called parallel to each other .
It is given that the parallel lines are cut by a transversal and the angles are marked
The angle 1 and angle 2 are congruent because they are pair of alternate interior angles .
Therefore Option C is the right answer.
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What is 9 lbs 6 oz converted to ounces?
Answer:
150 ounces
Step-by-step explanation:
A flower garden is shaped like a circle. Its diameter is 24yd . A ring-shaped path goes around the garden. Its outer edge is a circle with diameter 30yd.
==========================================================
Explanation:
We have two concentric circles. Think of a bulls-eye on a dart board. The inner circle is the garden itself. The outer circle is the garden plus the surrounding pathway. What we're interested in is the area of the outer ring, which is the area of the garden path only.
To find this ring area, we'll need to find the area of each circle.
A = area of the smaller circle
A = pi*r^2
A = pi*12^2
A = 144pi
Notice how I took half of the 24 yard diameter to get the radius of 12 yards.
B = area of the larger circle
B = pi*r^2
B = pi*15^2
B = 225pi
Subtract the two results
C = area of the outer ring, aka the garden path only
C = B - A
C = 225pi - 144pi
C = (225-144)pi
C = 81pi
We're told to use 3.14 in place of pi
C = 81*pi
C = 81*3.14
C = 254.34
The garden path has an area of roughly 254.34 square yards.
1 bag of sand covers 8 square yards.
So we'll need (254.34)/(8) = 31.7925 = 32 bags of sand
To estimate the height of a totem pole, Jorge uses a small square of plastic. He holds the square up to his eyes and walks backward from the pole. He stops when the bottom of the pole lines up with the bottom edge of the square and the top of the pole lines up with the top edge of the square. Jorge's eye level is about 2 m from the ground. He is about 3 m from the pole. Which of the following is the best estimate of the height of the totem pole?
Answer:
6.5 meters
Step-by-step explanation:
FAST!
A right rectangular prism has a square base and a height of 2.5 meters. If the length of a side of the square base is 4 meters, what is the volume of the prism?
Answer:
69 there hope it helps ;)
Step-by-step explanation:
420
A rectangular bedroom has an area of 117 ft. the length of the bedroom is 4ft more than the width. find the length and the width of the bedroom
Answer: Length = 13 ft. , Width = 9 ft.
Step-by-step explanation:
Rectangle area = Length x width
Area = 117 ft.
Length = x + 4
Width = x
To solve
(x)(x + 4) = 117
x^2 + 4x = 117
x^2 + 4x - 117 = 0
(x - 9)(x + 13)
x = 9, -13
x = 9 (measurement cannot be negative)
Length
x + 4
9 + 4 = 13
What are your top 3 theorems in higher mathematics? Why do you like them the most?
My theorems include the Pythagoras theorem, midpoint theorem, and angle bisector theorem.
How to illustrate the theorem?The Pythagoras theorem is used to find the length in a right angle.
The midpoint theorem states that the line segment in a triangle is parallel to the third side and is half the length.
The angle bisector theorem is concerned with the lengths of the two segments that the triangle side is divided into by a line which bisects the opposite angle.
I like them because they're important when solving triangle related problems.
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A clothing store is having a 15% off sale on t-shirts. If you will save $3.75 on a shirt, what was the original price before the sale? Show your work.
Answer:
$25
Step-by-step explanation:
3.75 is 15% of 25.
15% × 25 = 3.75
Brainliest to whoever answers :) Highly appreciated
Answer:
the answer is L
Step-by-step explanation:
rounding up to any number/decimal requires the digit before the specified digit to be 5 or greater.
rounding down requires the digit to be 4 or less.
if the estimated time to the nearest 0.01 of a second is 35.20 then the actual race time could be from 35.195 to 35.205 since any number between could be rounded to 35.20
Find the jacobian of the vector valued function F(v) = [3x*2y, 5xx, 9yy]
Answer:
F(v)=0
Step-by-step explanation:
F(v) = [3x*2y, 5xx, 9yy]
Calculate the product
F(v) =[tex]\frac{d}{dv\\}[/tex] [3x*2y, 5x*x, 9y*y]
The derivative of a constant is always 0
F(v) =[tex]\frac{d}{dv\\}[/tex]((6xy,5[tex]x^{2}[/tex],9[tex]y^{2}[/tex]))
f(v)=0
What is the domain of the function y = StartRoot x + 6 EndRoot minus 7?
Answer: B
Step-by-step explanation:
Edge 2023
Each year the Royal London company gives
its employees a gift box containing 6 bags of
coffee, 4 boxes of tea, and 2 boxes of biscuits.
If in the first three years, the number of
employees grew from 2 to 12 to 18, what was
the total quantity of coffee, tea, & biscuits
distributed by the company in those years?
The total number of tea received in three years is 192.
The total number of coffee received in three years is 128.
The total number of biscuits received in three years is 64.
What is the total quantity of tea, coffee and biscuits distributed in the three years?The total quantity of tea, coffee and biscuits received in the first year = (6 x 2) , (4 x 2) , (2 x 2) = 12, 8, 4 respectively
The total quantity of tea, coffee and biscuits distributed in the second year = (6 x 12) , (4 x 12) , (2 x 12) = 72, 48, 24 respectively
The total quantity of tea, coffee and biscuits distributed in the third year = (6 x 18) , (4 x 18) , (2 x 18) = 108, 72, 36 respectively
Total number of tea received in three years = 108 + 72 + 12 = 192
Total number of coffee received in three years = 8 + 48 + 72 = 128
Total number of biscuits received in three years = 4 + 24 + 36 = 64
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A cooler contains five colas, seven root beers, and four ginger ales. Three people grab a drink at random, one at a time. a) What is the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs b) What is the probability that the third person grabs a root beer given that the first two grabbed colas?
The probabilities are:
a) P = 0.024
b) P = 0.5
How to get the probabilities?
a) The probability that the first person grabs a cola is given by the quotient between the number of colas and the total number of drinks.
There are 5 colas, and 16 drinks in total, so the probability is:
P = 5/16
The second person needs to grab a ginger ale, now there are 15 drinks on the cooler (because one cola was taken) so this time the probability is:
Q = 4/15
Finally, the third person grabs (this is incomplete, I will assume that is another cola), this probability is:
Z = 4/14
The joint probability is:
prob = P*Q*Z = (5/16)*(4/15)*(4/14) = 0.024
b) If the two first persons grabed colas, then in the cooler we have:
3 colas, 7 root beers, and 4 ginger ales, for a total of 14 drinks.
Then the probability of grabbing a root beer is:
p = 7/14 = 1/2 = 0.5
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Multiply and remove all perfect squares from inside the square roots. Assume a is positive.
3[tex]3\sqrt{5a}*8\sqrt{35a^{2} }[/tex]
The multiplication is 120*[tex]a^{3/2}[/tex].
What is exponents and powers?
Power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.
Given:
3√(5a) * 8 √(35a²)
= 3√(5a)* 8* a *√7* √5
= 3*8*5*a *√(7a)
= 120 [tex]a^{1/2+1}[/tex]
=120*[tex]a^{3/2}[/tex]
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Answer:
[tex]120a\sqrt{7a}[/tex]
Step-by-step explanation:
It's right on khan academy
In the diagram, DG = 15, GF = 5, EH = 12, and DE = 8.
Triangle D F E is shown. Line segment G H is drawn from side D F to side E F to form triangle G F H. The length of D G is 15, the length of G F is 5, the length of E H is 12, and the length of D E is 8.
To prove that △DFE ~ △GFH by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that
To prove that △DFE ~ △GFH by the SSS similarity theorem, the correct answer is; Option C: HF is 4 units and GH is 2 units
How to prove the similarity theorem?The SSS Similarity theorem states that two triangles are similar If all the three sides of one of the triangles are in same proportion to the three sides of the other triangle.
Since triangle DFE is similar to triangle GHF as seen in the attached diagram, then we can say that;
DF/GF = DE/GH
20/5 = 8/GH
GH = 2 units
Also:
EF/HF = DF/GF
(12 + HF)/HF = 20/5
HF = 4 units
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Find the equation of a line containing the points (−2,−4) and (1,−3).
