Five less than twelve times a number is represented by 12n - 5
Expressing word problems as EquationsLet the unknown nmber be represented as n Such that twelve times the number will be represented as 12 nThere fore Five less than twelve times the number becomes 12n - 5
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Rick bought a fan for his living room he was looking at it while he was installing it wondered to himself what the angle between each blade measured. The fan has 3 blades evenly spaced. What is the angle between each blade and what type of angle are they?
Answer:
The angle between the two blades is 120 degree.
Step-by-step explanation:
number of blades = 3
The blades are equally spaced.
The total angle around a circle is 360 degree.
So, the angle between the two blades is given by
[tex]\theta =\frac{360}{n}\\\theta =\frac{360}{3} = 120^{o}[/tex]
Find the area of a circle with a diameter of 31.
Answer:
hope this helps
Step-by-step explanation:
31 divided by 2 = 15.5 then do 15.5 x 15.5= 240.25 then you do 240.25 x 3.14 = 754.385
The equation of a parabola is y=x2–8x+14. Write the equation in vertex form.
Answer:
Step-by-step explanation:
y=x^2-8x+14
To write in vertex form, group the two x-terms to make a complete square, adjust the constant term accordingly
y = x^2-8x+16 -2
factor the first three terms on the right hand side
y = (x-4)^2 -2
This means that the vertex is at x-4 = 0, or x=4, and y=2.
Shane can run the length of a football field (100 yards) in 12 seconds what's shanes speed?
Answer:
8 1/3 or 8.33 yards per second
Step-by-step explanation:
100/12 = 8 1/3
Write out the five number summary for each data set.
I'll do problem 1 to get you started
First sort the values from smallest to largest and you should end up with this set
{1, 6, 7, 11, 13, 16, 18, 21, 22, 23}
The smallest value is 1 and the largest value is 23, so the min and max are 1 and 23 in that order.
We have ten values in this set. The middle-most number is going to be between the 10/2 = 5th slot and the 6th slot. The numbers 13 and 16 are in the fifth and sixth slots respectively. Average those values to get (13+16)/2 = 29/2 = 14.5
The median is 14.5 which is another name for the second quartile (Q2).
Now split the data set into two halves
L = lower half of values smaller than the median
U = upper half of values larger than the median
In this case,
L = {1, 6, 7, 11, 13}
U = {16, 18, 21, 22, 23}
sets L and U have five items each
Find the median of set L and U to get 7 and 21 respectively. These medians of L and U represent the values of Q1 and Q3 in that order.
Q1 = first quartile = 7
Q3 = third quartile = 21
===================================================
Answer:
The five number summary for problem 1 is
Minimum = 1Q1 = 7Q2 = 14.5 (this is the median)Q3 = 21Maximum = 23Find the value of y. 108 degrees 40 degrees. x, y, z, w
Answer:
[tex] \frac{108}{2 } = 54[/tex]
The value of y for the given circle will be 54°.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The diameter is the longest line that can be drawn inside a circle.
In our daily life, we always see circle objects for example our bike wheel.
Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.
In the given question by the circle theorem that if a curve makes a 2x angle then the extreme point will make the angle on circle as x.
So angle y = half of angle 108°
∠Y = 108°/2 = 54°
Angle w will also same as 54° because it also satisfies the theorem of the circle.
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i need help
5times 10 +25-9+2times2
Answer:
put it on the calculator
Answer:
its 136
Step-by-step explanation:
Work backward to solve.
What is the starting position (x, y)?
Which graph shows the line y = 4x - 2?
Answer:
Hi, there the answer is Graph A because the y-intercept and I did rise over run
Step-by-step explanation:
Hope this helps :)
A bus departed from New York at 11 pm with 44 passengers. An hour later, a few passengers got off at New Jersey. The number of passengers who boarded the bus at New Jersey were twice the number of passengers who got off the bus. If the bus has 50 passengers now, how many passengers got off at New Jersey?
Answer:
6 passengers got off at New Jersey
Step-by-step explanation:
let the number of passengers who got off be x and let the number of passengers who boarded the bus be y
y=2x
44 - x + y=50
y=50-44+x
y=6+x
subst y=2x
2x=6+x
2x-x=6
x=6
please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
∠ G ≈ 8.3°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan G = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{HI}{GI}[/tex] = [tex]\frac{1.1}{7.5}[/tex] , then
∠ G = [tex]tan^{-1}[/tex] ([tex]\frac{1.1}{7.5}[/tex] ) ≈ 8.3° ( to the nearest tenth )
Evaluate 1/3m-1-1/2n when m=21 and n=12
Answer:
12
Step-by-step explanation:
The length of a rectangular piece of
construction paper is 8 inches and the width
is 17 inches. Vincent folded the piece of
paper along its diagonal. Which
measurement is closest to the length of the
diagonal in inches?
A. 5 in.
B. 18.79 in
C. 15 in
D. 25 in.
Answer:
B 18.79
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Given two points P(sinθ+2, tanθ-2) and Q(4sin²θ+4sinθcosθ+2acosθ, 3sinθ-2cosθ+a). Find constant "a" and the corresponding value of θ when these two points coincide. (0 ≤ θ < 2π)
Show your work, thanks!
Answer:
[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]
[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1, \frac{\sqrt{3}}{2} - 1[/tex]
Step-by-step explanation:
we are given two coincident points
[tex] \displaystyle P( \sin(θ)+2, \tan(θ)-2) \: \text{and } \\ \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]
since they are coincident points
[tex] \rm \displaystyle P( \sin(θ)+2, \tan(θ)-2) = \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ )\cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]
By order pair we obtain:
[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ) = \sin( \theta) + 2 \\ \\ \displaystyle 3 \sin( \theta) - 2 \cos( \theta) + a = \tan( \theta) - 2\end{cases}[/tex]
now we end up with a simultaneous equation as we have two variables
to figure out the simultaneous equation we can consider using substitution method
to do so, make a the subject of the equation.therefore from the second equation we acquire:
[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sinθ \cos(θ)+2a \cos(θ )= \sin( \theta) + 2 \\ \\ \boxed{\displaystyle a = \tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) } \end{cases}[/tex]
now substitute:
[tex] \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2 \cos(θ) \{\tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) \}= \sin( \theta) + 2 [/tex]
distribute:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ)+4 \sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) - 6 \sin( \theta) \cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]
collect like terms:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]
rearrange:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) + 4 \cos ^{2} ( \theta) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + = \sin( \theta) + 2 [/tex]
by Pythagorean theorem we obtain:
[tex]\rm\displaystyle \displaystyle 4 - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) + 2 [/tex]
cancel 4 from both sides:
[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) - 2[/tex]
move right hand side expression to left hand side and change its sign:
[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+\sin(θ ) - 4\cos( \theta) + 2 = 0[/tex]
factor out sin:
[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) - 4\cos( \theta) + 2 = 0[/tex]
factor out 2:
[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) + 2(- 2\cos( \theta) + 1 ) = 0[/tex]
group:
[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(- 2 \cos(θ)+1) = 0[/tex]
factor out -1:
[tex]\rm\displaystyle \displaystyle - ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]
divide both sides by -1:
[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]
by Zero product property we acquire:
[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) + 2 = 0 \\ \displaystyle2 \cos(θ) - 1= 0 \end{cases}[/tex]
cancel 2 from the first equation and add 1 to the second equation since -1≤sinθ≤1 the first equation is false for any value of theta
[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) \neq - 2 \\ \displaystyle2 \cos(θ) = 1\end{cases}[/tex]
divide both sides by 2:
[tex] \rm\displaystyle \displaystyle \displaystyle \cos(θ) = \frac{1}{2}[/tex]
by unit circle we get:
[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]
so when θ is 60° a is:
[tex] \rm \displaystyle a = \tan( {60}^{ \circ} ) - 2 - 3 \sin( {60}^{ \circ} ) + 2 \cos( {60}^{ \circ} ) [/tex]
recall unit circle:
[tex] \rm \displaystyle a = \sqrt{3} - 2 - \frac{ 3\sqrt{3} }{2} + 2 \cdot \frac{1}{2} [/tex]
simplify which yields:
[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1[/tex]
when θ is 300°
[tex] \rm \displaystyle a = \tan( {300}^{ \circ} ) - 2 - 3 \sin( {300}^{ \circ} ) + 2 \cos( {300}^{ \circ} ) [/tex]
remember unit circle:
[tex] \rm \displaystyle a = - \sqrt{3} - 2 + \frac{3\sqrt{ 3} }{2} + 2 \cdot \frac{1}{2} [/tex]
simplify which yields:
[tex] \rm \displaystyle a = \frac{ \sqrt{3} }{2} - 1[/tex]
and we are done!
disclaimer: also refer the attachment I did it first before answering the question
Renting video games from Store S costs $2.50 per game plus a monthly fee of $5.00. Renting video games from Store T costs $5.00 per game with no monthly fee. The monthly cost to rent video games depends on the number of video games, v, rented. ?
Answer:answer is 2.5v+5<5v A.k.a:A
Step-by-step explanation:
Question 4
1 pts
3. Aracelli has a class of kindergardeners. Each student gets a six oz cup of milk at
snack time. How many gallons of milk will she need to buy for a class of 23 students?
O 1.08 gallons
1.1 gallons
O 2 gallons
1 gallon
1 pts
Question 5
Answer:
There is a little over 1 gallon
Step-by-step explanation:
Escribe en lenguaje simbólico las siguientes expresiones, teniendo en cuenta que llamamos x a la edad de María. La edad que tenía María hace 3 años. El doble de la edad que tendrá María dentro de 10 años. La tercera parte de la edad que tenía María hace 1 año.
Answer:
i don't know that language sorry
Step-by-step explanation:
plss help me answer this
Answer:
c≈5.2
Step-by-step explanation:
c=a2+b2=1.412+52≈5.19501
The lengths of three sides of a triangle are given. Classify each triangle as acute, right, or obtuse. 6,9,7
Joe tried to prove that the sum of a triangle's interior angle measures is 180°
Answer: Angles ∠4 and∠2 are not alternate interior angles and neither are ∠1 and ∠5
Step-by-step explanation: Khan Academy
Joe made the mistake by guessing Angles ∠4 and∠2 are not alternate interior angles and neither are ∠1 and ∠5.
The correct option is (b).
What is Parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
WE have to prove that the sum of a triangle's interior angle measures is 180°
According to the figure <1 and <4 are the alternate interior angle and <2 and <5 are alternate interior angle.
So, Joe made the mistake by guessing Angles ∠4 and∠2 and ∠1 and ∠5 are alternate interior angles.
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Square ABCD is translated 9 units to the right, followed by a translation 6 units down
Square ABCD is reflected across the y-axis, followed by a translation 6 units down
Square ABCD is translated 6 units down, followed by a translation 9 units to the right
Answer:
71
Step-by-step explanation:
ndndnrbrjen3n3nn3b2n2b2b
need help ASAP plz
hiii can someone help me please it’s really greatly appreciated!!THANK YOUUU
Answer:
Step-by-step explanation:
so we know that a triangle degrees have to add up to 180 in the inside right? So we know c is 90 and so you need to find A and B. The left over degrees you have is 90 so the sum of B and A would have to be 90, thats all i can help you with sorry.
Please help me!! How do I do this?
Answer:
Taking 45 degree as reference angle
Then using sine rule
sin 45=
p/h
replacing the value of sin 45 degree by 1/root 2.so
1/root 2=9/c
doing cross multiplication
9*root 2=1*c
9 root 2 =c
therefore the value of c is 9 root 2
Step-by-step explanation:
help mehhhhhhh pleaseeeeeeeee
Answer:
1/2
Step-by-step explanation:
Because there are 2 numbrs that are greater than 3.
Hope this helped!
Stay Safe!
Calculate the theoretical probability of each of the following events:
You spin a spinner with 3 equal sections labeled blue, red, and purple, and it lands on purple.
Answer:
There is a 1/3 chance it lands on each section
Step-by-step explanation:
Can someone please help me
With Geometry
Answer:
4.2
Step-by-step explanation:
By intersecting chords theorem:
[tex]x \times 10 = 6 \times 7 \\ \\ 10x = 42 \\ \\ x = \frac{42}{10} \\ \\ x = 4.2[/tex]
The average mass of a certain type of microorganism is 2.4x10^-6 grams. What is the approximate total mass, in grams, of 5x10^3 of these microorganisms?
a. 1.2X10^-4
b. 1.2X10^-3
c. 1.2X10^-2
d. 1.2X10^-1
The total mass of 5 x 10³ microorganisms is 1.2 x [tex]10^{-2}[/tex].
Option C is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Mass of an organism = 2.4 x [tex]10^{-6}[/tex] grams
The total mass of 5 x 10³ microorganism.
= 5 x 10³ x 2.4 x [tex]10^{-6}[/tex]
= 12.0 x [tex]10^{3 - 6}[/tex]
= 12 x [tex]10^{-3}[/tex]
= 1.2 x [tex]10^{-2}[/tex]
Thus,
The total mass is 1.2 x [tex]10^{-2}[/tex]
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After solving the system of equations, what is the value of y?
6x+2y=-4
x-2y=4
Answer:
x=0, y=-2
Step-by-step explanation:
6x0=0
2(-2)=-4
so, -4=-4 so it is determined true
Then 0-2(-2), -2(-2)=4
subtract 0 from 4 which is 4
so, 4=4, so it is determined true
2. Which equation describes a line that has
a slope of and a y-intercept of ?
A) 5y + 4x = 2
C) Sy - 4x = 2
B) 4x5y = 2
D) -5y - 4x = 2
Answer:
What?
Step-by-step explanation:
G8ve me more info and Ill answer again