The linear measure of arc vw as described in the task content is; 46.89in.
What is the linear measure of the arc vw?It follows from the task content that the radius of the circle with center p is given as pv = 32in. and the angle subtended by the arc is; 84.
On this note, the measure of arc vw is;
= (84/360) × 2 × 3.14 × 32
= 46.89 inches.
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The length of a rectangle is units greater than twice its width. If its width is w, which expression gives the perimeter of the rectangle in terms of w?
A.
2(w) + w
B.
w + w
C.
3w +
D.
6w + 5
The expression that gives the perimeter of the rectangle in terms of w is 6w+5 units.
Given that, the length of the rectangle is [tex]\frac{5}{2}[/tex] units greater than twice its width.
We need to determine the expression that gives the perimeter of the rectangle in terms of w.
Given, width = w units, then length= 2w + [tex]\frac{5}{2}[/tex] units.
What is the perimeter of the rectangle?The perimeter of the rectangle is the sum of all the sides of the rectangle.
That is, perimeter of a rectangle = 2 (length+width).
Now, perimeter of a rectangle = 2 (2w + [tex]\frac{5}{2}[/tex]+w)=6w+5 units.
Hence, the expression that gives the perimeter of the rectangle in terms of w is 6w+5 units.
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HI PLEASE ANSWER THIS QUESTION THANK YOU!
(NO TROLLS PLEASE!)
Suppose ∠A and ∠B are complements, while ∠B and ∠C are supplements. If m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1), then m∠A=44, m∠B=46, and m∠C=134. TRUE OR FALSE? Please show your work.
Answer:
TRUE
Step-by-step explanation:
Angle <A and angle <B are complementary, which means their sum must be = 90
Angle <B and angle <C are supplementary which means their sum must be = 180
Now let's see
m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1)
first find the sum of A and B
3x + 17 + 55 - x = 90 add like terms
2x + 72 = 90 subtract 72 from both sides
2x = 18 divide both sides by 2
x = 9
TRUE OR FALSE is asked for
m∠A=44, m∠B=46, and m∠C=134
to find that we just replace c with 9 with every expression given for angles
m<A = 3x + 17
m<A = 3*9 + 17 = 44
m<B = 55 - x
m<B = 55 - 9 = 46
m<C = 134, we don't really need to calculate one by one since the angle are complementary and supplementary.
The answer is TRUE
The statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have:
∠A and ∠B are complements, while ∠B and ∠C are supplements.
∠A + ∠B = 90 degree
3x + 17 + 55 - x = 90
2x = 18
x = 9
Angle ∠B and angle ∠C are supplementary:
∠B + ∠C = 180
55 -x + 67(x/3 - 1) = 180
x = 9
Put the value of x and find angles A, B, and C.
m∠A = 44
m∠B = 46
m∠C = 134
∠A + ∠B = 90
∠B + ∠C = 180
The above statement is true.
Thus, the statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.
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The driving distance between Manchester and London is 195 miles. Farid intends to travel from Manchester to London by coach. The coach will leave Manchester at 3.30pm.
Farid assumes that the coach will travel at an average speed of 50mph
A)Using his assumption, work out Faris's arrival time at London.
It actually turns out that the coach has a lower average speed.
B)Describe how this affects the arrival time
Answer:
7:24pm
Step-by-step explanation:
At 50 mph, it will take 195/50 = 3.9 hours to reach London
3.9 hours = 3 .9 * 60 = 3 hours and 54 minutes(54 = 0.9 * 60 )
3:30 + 3:34 ==> 7:24
(one way to do this is to add up the hours and minutes separately so we get 6:84) Since 84 minutes = 1 hour and 24 minutes, just add 1:24 to 6 to get 7:24
Another way to do this is to see that if the distance was 200 miles, then it would take exactly 4 hours (200/50) to reach at 7:30pm But it is short by 5 miles. At the speed of 50mph, the time taken to travel 5 miles = 60/50 * 5 = 6 minutes so deduct 6 minutes from 7:30pm to get 7:24pm
If the train is slower average speed, then the arrival time is delayed beyond 7:24pm
SOS help please ignore the answers I put they are wrong
The conversion to logarithm function will be that log3 27 = 3.
How to calculate the log?From the information given, we are to convert the exponential equation to logarithm function. This will be:
log 3 27
This will be log 3 3³
= 3 × log 3^3
= 3 × 1
= 3
Therefore, x = 3.
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I already worked on most of my question, although, I am just curious about how you would go about finding the fourth power of the square root of 50. Can someone please explain this in detail?
Answer:
(50^1/2)^4
Step-by-step explanation:
basically if I am comprehending your question correctly, the square root of 50 can also be written as 50^1/2
If you put 50^1/2 to the 4th power, it basically becomes (50^1/2)^4
(49p2–490p) ÷(p–10)
please help!!
Answer:
(49p2–490p) ÷(p–10)
Step-by-step explanation:
Population 422 increasing by 10 people per year. Write an equation to determine the population (y) after any number of years (x).
Answer:
y = 10x + 422
Step-by-step explanation:
(-2/3)^3 (Evaluate)
A: 8/9
B: 6/9
C: -8/27
D: 8/27
Answer:
C
Step-by-step explanation:
using the rule of exponents
[tex](\frac{a}{b}) ^{m}[/tex] = [tex]\frac{a^{m} }{b^{m} }[/tex] , then
[tex](\frac{-2}{3}) ^{3}[/tex]
= [tex]\frac{(-2)^{3} }{3^3}[/tex]
= [tex]\frac{-8}{27}[/tex]
= - [tex]\frac{8}{27}[/tex]
Definition:
[tex]a^2=a\cdot a\\\\a^3=a\cdot a\cdot a\\\\a^4=a\cdot a\cdot a\cdot a\\\vdots\\a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}[/tex]
also
[tex]a^1=a\\\\a^0=1[/tex]
We have
[tex]\left(-\dfrac{2}{3}\right)^3=\left(-\dfrac{2}{3}\right)\cdot\left(-\dfrac{2}{3}\right)\cdot\left(-\dfrac{2}{3}\right)=-\dfrac{2\cdot2\cdot2}{3\cdot3\cdot3}=-\dfrac{8}{27}[/tex]
[tex]\huge\boxed{C:\ -\dfrac{8}{27}}[/tex]
Logarithm of x to the root 2 + logarithm (x-1) to the root 2 = 1
By the application of algebraic procedures and logarithm properties, the roots of the logarithmic equation [tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex] are x = 2 and x = -1.
How to solve a logarithmic functions
In this question we need to solve a logarithmic equation by means of algebraic procedures and logarithm properties:
[tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex]
[tex]\log \sqrt{x\cdot (x-1)} = 1[/tex]
[tex]\log \sqrt{x^{2}-x} = 1[/tex]
[tex]\frac{1}{2}\cdot \log (x^{2}-x) = 1[/tex]
[tex]\log (x^{2}-x) = 2[/tex]
[tex]x^{2}-x = 2[/tex]
[tex]x \cdot (x-1) = 2[/tex]
[tex]x - 1 = \frac{2}{x}[/tex]
[tex]x - \frac{2}{x} = 1[/tex]
[tex]\frac{x^{2}-2}{x} = 1[/tex]
[tex]x^{2} - 2 = x[/tex]
[tex]x^{2}-x-2 = 0[/tex]
[tex](x-2)\cdot (x + 1) = 0[/tex]
[tex]x = 2 \,\lor \,x= -1[/tex]
By the application of algebraic procedures and logarithm properties, the roots of the logarithmic equation [tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex] are x = 2 and x = -1.
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How to subtract negative number from 1
when you subtract a negative number from any platitude number the equation changes to addition so you would add the value of the negative number to 1.
To subtract a negative number from one you will need to set it up like this
1- (-x) x equals the negative number you're talking about
so we use the method KCC (keep change change)
So we KEEP the positive one, CHANGE the subtraction sign in to a plus sign "+" then CHANGE the negative number to a positive
lets say the negative number is 2
1-(-2)
1+ (+2)
1+2 = 3
A pink crayon is made with 12\text{ mL}12 mL12, start text, space, m, L, end text of red wax for every 5\text{ mL}5 mL5, start text, space, m, L, end text of white wax. Which of the following wax mixtures will create the same shade of pink? Choose 2 answers: Choose 2 answers:
Mixtures D and E have a ratio of 5:12 and will create the same shade of pink. Options D and E are correct.
What is the difference between a ratio and a proportion?A ratio is an ordered pair of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two ratios are specified to be equal.
Given data;
red wax = 12 ml
white wax = 5 ml
A red wax: white wax = 5:12
B. red wax: white wax=4:1
C red wax white wax = 13: 6
D. red wax: white wax=12:5
E. red wax white wax=12:5
Hence, mixtures D and E have a ratio of 5:12 and will create the same shade of pink.
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1. In a class of 24, 3 students were absent, What fraction of class is present
2. Karen taped a television show that lasted 1h 30mins. On the same tape she recorded another 2 shows that were 5/6h each. What time was still left on the 4h tape.
3. Steve ordered 12 lengths of timber, each 6m long. He cut 6 lengths into 1 1/2m pieces and the other 6 lengths into 3/4 pieces A. How many pieces together is this? B. Was there any waste?
Problem 1
Answer: 7/8 of the class is presentReason:
24 people total with 3 absent. So 24-3 = 21 are present
21/24 = (7*3)/(8*3) = 7/8
==========================================================
Problem 2
Answer: 50 minutes left on the tape.Work Shown:
1 hour = 60 min
(5/6)*(1 hour) = (5/6)*(60 min)
5/6 of an hour = 50 min
1 hr + 30 min = 60 min + 30 min = 90 min
The first show is 90 minutes. Add on two more shows that are 50 min each to get 90+50+50 = 190 minutes used up
4 hours = 4*60 = 240 min
240 - 190 = 50 min
There are 50 minutes left on the tape.
==========================================================
Problem 3
Answer: 72 pieces; not enough info to calculate the wasteExplanation:
1 1/2 = 1 + 1/2 = 1 + 0.5 = 1.5
6/(1.5) = 4
Each 6 meter board is cut into 4 equal pieces each 1.5 meters long
There are 6 boards this applies to which means so far that's 6*4 = 24 pieces
Now to the other 6 boards.
3/4 = 0.75
6/(0.75) = 8
Each of the other 6 boards are cut into 8 equal pieces of 0.75 meters each
That's another 6*8 = 48 pieces
In total there are 24+48 = 72 pieces
When cutting into wood, there always is a small sliver that is discarded. While small, these slivers do add up. So yes there is some waste. Unfortunately, we don't have enough info to calculate. We would need to know the width of the saw blade.
help its TIMED
WHICH OF THE FOLLOWING MAY BE TRUE ABOUT f(x)
All three are possible.
The table tells us that for certain x and y, we have f(x) < f(y) if x < y. There's also no evidence that f(x) = f(y) for some points x ≠ y in the interval, so f(x) could easily be monontonically increasing. (I is true)
If we assume f(x) is strictly increasing (which does not contradict the given table) on the entire interval, we have f'(x) > 0. A positive function can be strictly increasing. (II is true)
A function is concave up on an interval if its derivative is increasing on that interval. This follows from statement (II) if it happens to be true. (III is true)
(E)
Solve by elimination
show your work
y = 3x + 10
y = 2x - 8
im giving brainlyest
Answer:
[tex]x=-18, y=-44[/tex]
Step-by-step explanation:
[tex]y=3x+10\\y=2x-8\\\\3x+10=y\\2x-8=y\\3x-y=-10\\2x-y=8\\\\-2(3x-y=-10)\\3(2x-y=8)\\\\-6x+2y=20\\6x-3y=24\\-y=44\\y=-44\\-44=3x+10\\-54=3x\\x=\frac{-54}{3} \\x=-18\\\\x=-18, y=-44\\[/tex]
CHECK
[tex]-44=3(-18)+10\\-44=-54+10\\-44=-44\\\\-44=2(-18)-8\\-44=-36-8\\-44=-44[/tex]
help the question is on the image.
Answer:
[tex]\boxed {tan\theta = \frac{2}{3}}[/tex]
Step-by-step explanation:
Let's derive a formula :
⇒ Area (triangle) × 3 = Area (square)
⇒ 1/2(bh) × 3 = a²
∴ But a = h (shown in diagram)
⇒ 3/2(bh) = h²
⇒ h = 3b/2
Now, taking tan θ :
⇒ tan θ = b/h
⇒ tan θ = b/(3b/2)
⇒ tan θ = 2b/3b
⇒ tan θ = 2/3
HELP ME!! FIND X AND Y.
Answer:
x = 26
y = 72°
Step-by-step explanation:
Finding x:Alternates angles are equal.(4x - 16)° = (3x + 10)°
Subtract 3x to both sides
4x - 3x - 16 = 10
x - 16 = 10
Add 16 to both sides
x = 10 + 16
x = 26
Finding y:Angles on a straight lines add up to 180 degrees.(4x - 16)° + y° = 180°
4x - 16 + y = 180
4(26) - 16 + y = 180
104 - 16 + y = 180
88 + y = 180
Subtract 88 to both sides
y = 180 - 88
y = 72°
[tex]\rule[225]{225}{2}[/tex]
Reflect shape A in the x-axis.
I have 20 min to complete this
Answer:
Step-by-step explanation:
Which expression is equal to the polynomial
below?
2x + 5x38x - 20
Ox³(2x + 5) + 4(2x - 5)
Ox³(2x + 5)- 4(2x + 5)
Ox³(2x-5)-4(2x - 5)
Ox³(2x + 5) + 4(2x + 5)
The expression 2x⁴ + 5x³ - 8x - 20 can be express as follows;
x³(2x + 5) - 4(2x + 5)
How to factorise an expression?2x⁴ + 5x³ - 8x - 20
Therefore,
2x⁴ + 5x³ - 8x - 20
x³(2x + 5) - 4(2x + 5)
Hence, the expression 2x⁴ + 5x³ - 8x - 20 can be express as follows:
2x⁴ + 5x³ - 8x - 20 = x³(2x + 5) - 4(2x + 5)
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Jaime makes the following claim.
An angle with a measure of π/3 radians in a circle with a radius of 3 inches is smaller than an angle with a measure of π/3 radians in a circle with a radius of 6 inches. This is because the radian measure is based on the length of the radius of the circle and a radius of 3 inches is smaller than a radius of 6 inches.
1. Review Jaime’s statement and what you know about angles and radians.
a. Explain whether you agree with Jaime’s statement or not.
b. Provide examples to support your whether you agree or disagree.
Jaime is incorrect, the angle does not depend on the radius of the circles.
Is Jaime correct?Remember that an angle that defines an arc on a circle, does not depend on the radius of the circle.
So, if we have an angle with a measure of π/3 radians in a circle with a radius of 3 inches and an angle with a measure of π/3 radians in a circle with a radius of 6 inches, these two angles are exactly the same thing.
The radius of the circle only has an impact on the length of the arc defined by the angle.
So Jaime is clearly incorrect.
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Selena is preparing for her eighth-grade graduation party. she must keep within the budget set by her parents. which is the best price for her to purchase ice cream? a. $3.99/ 24 oz carton b. $4.80/ one-quart carton c. $11.00 / one gallon tub d. $49.60/ five gallon tub
Answer:
Basically find the unit rate by doing 3.99/24 = $0.16625/1oz
1 quart = 32 ounces so 4.8/32 = $0.15/1oz
1 gallon = 153.722 ounces so 11/153.722 = 0.07
49.6/768.61 = 0.06
Step-by-step explanation:
D.
The coefficient of 8 · 2N is
Answer:
the leading coefficent is 16 or 16n (leading term)
Step-by-step explanation:
The length of a rectangle is twice its breadth. If its length is decreased half of the 10 cm and the breadth is increased by half of the 10 cm cm, the area of the rectangle is increased by 5 sq cm, more than 70 sq cm. Find the length of the rectangle.
Also....any armies, stays and blinkss?
Since the length of this rectangle is twice its breadth, the length is equal to 40 cm.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
Area = Length × Width
Based on the information provided, we have:
Its length is decreased half of the 10 cm ⇒ (length - 5)Its breadth is increased by half of the 10 cm ⇒ (breadth + 5)Its area is increased by 75 cm ⇒ (area + 5)Substituting the parameters into the formula, we have:
LB + 75 = (L - 5)(B + 5)
2B² + 75 = (2B - 5)(2B + 5)
2B² + 75 = 2B(B + 5) - 5(B + 5)
2B² + 75 = 2B² + 10B - 5B - 25
5B = 75 + 25
5B = 100
B = 100/20
B = 20 cm.
For the length, we have:
L = 2B
L = 2 × 20
L = 40 cm.
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Which transformations could have taken place? Select two options.
The two options are R₀ 270 , R₀ 90 , Option C and D .
The complete question is attached in the image.
What are the two types of Transformations ?There are two types of transformations namely , Rigid Transformation and Non- Rigid Transformation
The rigid transformations do not change the shape and size of the preimage .
The non Rigid transformation do not change the shape but change the size of the preimage.
The rule rotating the origin , 270 degree is
(x,y) ----> (y , -x)
as (x,y) is (0,5)
Therefore after 270 degree transformation
(y,-x) is (5 , 0)
So, the clockwise rotation is 90 degree about origin
(x,y) ----> (y , -x)
as (x,y) is (0,5)
Therefore after 90 degree transformation
(y,-x) is (5 , 0)
Therefore the two options are R₀ 270 , R₀ 90 , Option C and D .
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The ratio of players to soccer balls at practice sessions is 5:2. How many soccer balls are needed for 20 players?
Answer:
8 soccer balls
Step-by-step explanation:
Since the ratio of players to soccer balls is 5:2, we can conclude that:
Players = 5 peopleSoccer balls = 2 ballsThe question asks to find how many soccer balls are needed for 20 players.
Multiply both players and soccer balls by 4, this will get:
Players = 20 peopleSoccer balls = 8 ballsHenceforth, 8 soccer balls are needed for 20 players.
what is the volume of a triangular prisim if the length is 4cm heigght is 3cm and width is 11cm
Volume is a three-dimensional scalar quantity. The volume of the triangular prism is 66cm².
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the length of the triangle is 4cm, while the width of the triangle is 11cm, therefore, the area of the base of the triangle will be,
Area of triangle = 0.5 × 4cm × 11cm
Area of triangle = 22 cm²
Now, the volume of the prism with a base area of 22cm² and a height of 3 cm is,
Volume of the triangular prism = 22cm² × 3cm = 66cm³
Hence, the volume of the triangular prism is 66cm².
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what is the cos? trigonometry
Answer:
Cos, a abreviation of cosine is used in trigonometry, and it represents the ratio of the hyptenuse and the adjacent side of a right triangle (a triangle with a right/90 degree angle). The formula for evaluating cosine/cos is the length of the adjacent side of the triangle divided by length of the hypotenuse of the triangle. To be clear, the hypotenuse is the side of the triangle the 90 degrees is facing, and the adjacent side is the side across the hypotenuse.
Step-by-step explanation:
Answer:
A trigonometric function that for an acute angle is the ratio between the leg adjacent to the angle when it is considered part of a right triangle and the hypotenuse.
What is cos law?
The cos law or cosine law defines the relationship between the sides and the angles of the triangle. This law is also known as the law of cosine or cosine rule. According to this law,
c2 = a2 + b2 − 2ab cos α
Where a, b and c are the sides of the triangle.
the slope of the line is 4. which of the following is the point-slope form of the line
The point slope form of line is y+4 = -4( x+3)
What is point slope of form?The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
Given:
m=4
We know the general form is
y - b = -4(x - a)
So, from the graph attached below
b= -4, a= -3
So, y-(-4)= -4(x-(-3))
y+4 = -4( x+3)
Hence, point slope form of line is y+4 = -4( x+3).
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Pls help quickly!!!
Find the coordinates of the vertex of the graph of the function.
y=3x^2-4x+3
Answer:
vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )
Step-by-step explanation:
given the equation of a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 3x² - 4x + 3 ← is in standard form
with a = 3 , b = - 4 , then
x = - [tex]\frac{-4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
substitute x = [tex]\frac{2}{3}[/tex] into the equation for corresponding y- coordinate of vertex
y = 3([tex]\frac{2}{3}[/tex] )² - 4([tex]\frac{2}{3}[/tex] ) + 3
= 3([tex]\frac{4}{9}[/tex] ) - [tex]\frac{8}{3}[/tex] + 3
= [tex]\frac{4}{3}[/tex] - [tex]\frac{8}{3}[/tex] + [tex]\frac{12}{3}[/tex]
= [tex]\frac{8}{3}[/tex]
vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )
Fraction:
23
100
Decimal: 0.23
Percent: 30 %
Answer: Below is the correct data.
Fraction: [tex]\frac{23}{100}[/tex]
Decimal: 0.23
Percent: 23%
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