graph f(x)= x if x < 2, 2 if x ≥ 2
Answers
The graph is shown below:
What is graph?A graph is a mathematical diagram which shows the relationship between two or more sets of numbers or measurements.
Given function: f(x) = x
We have to draw the graph for the function ,f(x) =x with two cases.
For x<2 and for x ≥ 2
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please i need it so badl please
The sum of the ages of Damien and Keyanna is 100 years. 10 years ago, Damien's age was 4 times Keyanna's age. How old is Damien now?
Answers
Answer:
Damien is 74 years old now
Step-by-step explanation:
Define the variables:
Let d = age of DamienLet k = age of KeyannaGiven information:
The sum of the ages of Damien and Keyanna is 100 years. 10 years ago, Damien's age was 4 times Keyanna's age.From the given information, create 2 equations:
Equation 1: d + k = 100
Equation 2: d - 10 = 4(k - 10)
Rewrite Equation 1 to make k the subject:
⇒ k = 100 - d
Substitute this into Equation 2 and solve for d:
⇒ d - 10 = 4(100 - d - 10)
⇒ d - 10 = 400 - 4d - 40
⇒ d - 10 = 360 - 4d
⇒ d - 10 + 10 = 360 - 4d + 10
⇒ d = 370 - 4d
⇒ d + 4d = 370 - 4d + 4d
⇒ 5d = 370
⇒ 5d ÷ 5 = 370 ÷ 5
⇒ d = 74
Therefore, Damien is 74 years old now.
1 (c)
Gavin goes to Joti's shop.
He is making a circular blanket.
The finished blanket will have a radius of 0.325 m
It will have ribbon all around the edge.
He thinks he will need 2.5 m of ribbon.
Gavin knows that is about 3.1416
Round to 1 decimal place and use this value to work out how much ribbon
Gavin will have left if he buys 2.5 m
[4 marks]
Answers
Answer: 0.5m
Hope this helps!
What are the approximate area and circumference, respectively, of a circle with a diameter of 30 inches?
Answers
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]
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.
Answers
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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Find the jacobian of the vector valued function F(v) = [3x*2y, 5xx, 9yy]
Answers
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
Brainliest to whoever answers :) Highly appreciated
Answers
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
40 points please Please help me
Answers
Answer:
19.51 units = x
Step-by-step explanation:
Here is one way :
Height = 18 cos 47 = 12.276
then cos 51 = 12.276 / x
x = 12.276 / cos 51 = 19.51
he area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.
Answers
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 is -36 degrees converted
to radians
Answers
Answer:
Answer: 0.628 radian
Step-by-step explanation:
how to convert from degrees to radians?
Answer:To convert the value of the angle in degree, to its equivalent radians, we need to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.
Answer:
See below
Step-by-step explanation:
- 36 * PI / 180 = -pi/5 radians = - .6283 R
What are your top 3 theorems in higher mathematics? Why do you like them the most?
Answers
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 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.
Answers
==========================================================
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
The Pythagorean Identity states that: (sin x)^2 + (cos x)2 = 1
Given sin 0 = 2/5, find cos 0.
cos 0 = ?/?
Answers
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]
What is the domain of the function y = StartRoot x + 6 EndRoot minus 7?
Answers
(x + 6) > = 0
x > = -6
Answer: B
Step-by-step explanation:
Edge 2023
Find the equation of a line containing the points (−2,−4) and (1,−3).
Answers
-4 = m(-2) + b
-3 = m(1) + b —> -3 = m + b —> -3 - m = b
Substitute (-3 - m) for b:
-4 = m(-2) + (-3 - m)
-4 = -2m -3 - m
-1 = -3m
1/3 = m
Plug in the solved m value to solve for b:
-4 = (1/3)(-2) + b
-4 = -2/3 + b
-3 1/3 = b
Write your final equation:
y = 1/3x - 10/3
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
Answers
Answer:
the answers are B and F since √8 x √8 = √64 which simplifies to 8.
a car corporation produced 1560 more cars this month than last. Write a signed number to represent this month's change in the production
Answers
Answer:
+1560
Step-by-step explanation:
Since the corporation produced 1560 more cars then the answer is simply +1560.
a random number is selected from a random set 2,3,4,10
Answers
The number is even or less than 12. Then the correct option is C.
The complete question is given below.
A number is selected at random from the set {2, 3, 4, … 10}. Which event, by definition, covers the entire sample space of this experiment?
a. The number is greater than 2.
b. The number is not divisible by 5.
c. The number is even or less than 12.
d. The number is neither prime nor composite.
e. The square root of the number is less than 3.
What are sets?A set is a group of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
A number is selected at random from the set {2, 3, 4, … 10}.
2, 4, 6, 8, 10 are even, but the rest are odd (BUT note the word “or”). The rest are less than 12. YES
Then the correct option is C.
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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.
Answers
∠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?
Answers
Answer:
150 ounces
Step-by-step explanation:
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]
Answers
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
Answers
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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how would i solve this problem
Answers
Answer:
30
Step-by-step explanation:
1500/50=30
X+(x^2+2)+y=4
Find 2 coordinates
(X,y) (x,y)
Answers
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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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?
Answers
Answer:
6.5 meters
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints.
(-3,-3) and (1, 2)
Answers
[tex]\left(\frac{-3+1}{2}, \frac{-3+2}{2} \right)=\boxed{\left(-1, -\frac{1}{2} \right)}[/tex]
Need help ASAP!! Will give Brainliest
Answers
Answer:
B
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?
Answers
Answer:
69 there hope it helps ;)
Step-by-step explanation:
420
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.
Answers
Answer:
$25
Step-by-step explanation:
3.75 is 15% of 25.
15% × 25 = 3.75
Square root of (-16)^2
Answers
Answer: [tex]\sqrt{(-16)^{2} } =16[/tex]
Step-by-step explanation:
I looked it up on my calculator. I hope this helps!! :)
Which statements about the location of the point are
true? Select three options.
The point is in the first octant.
The point lies behind the yz-plane.
The x-coordinate is -3.
The y-coordinate is positive.
The point lies to the left of the xz-plane.
Answers
Answer:
Step-by-step explanation:
