Answer:
An angle is defined as two rays with a common endpoint, so CAB (or BAC) is an angle. A line is described as an infinite set of points that extend forever in either direction, which these rays also do.
Step-by-step explanation:
Angles are rays with a shared endpoint.
Lines extend forever in either direction.
Rays AB and AC extend forever in either direction.
A line with points C, A, and B with arrows at the endpoints can satisfy the fact that the two rays AB and AC form both a line and an angle.
A line with points C, A, and B have arrows on both endpoints.
We need to explain how the line containing the points C, A, and B has two rays AB and AC and how it can form both a line and an angle.
What are a line, ray, and angle?A line has no endpoints, it extends infinitely in both directions and both end point is denoted by an arrow.
A ray has a fixed point on one side and an arrow on the other side which extends infinitely.
An angle is formed by two rays from one common fixed point.
Let us draw the line with points C, A, and B that have arrows at the endpoints.
C A B
<----------------.-------------------->
We can say that AB is a ray since at point A we have a fixed point and at point B there is an arrow.
And AC is also a ray since at point A there is a fixed point and at point C there is an arrow.
The two rays AB and AC together form a line because on both ends sides there are arrows.
An angle can also be formed since AB and AC are two rays from one common fixed point.
Thus a line with points C, A, and B with arrows at the endpoints can satisfy the idea that the two rays AB and AC form both a line and an angle.
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A truck with 20 inch diameter wheels is traveling at 45mi/hr
Find the angular speed of the wheels in rad/min,*hint* convert miles to inches & hours to minutes:
______rad/min
How many revolutions per minute do the wheels make?
______rpm
Show your work plzzzz
A wheel with a 20 in diameter has a circumference of 2π*(20 in) = 40π in.
For every 40π in traveled, a wheel makes one complete revolution, or turns an angle of 2π rad.
We need to convert from in to mi: there are 12 in to 1 ft, and 5280 ft to 1 mi, and so there are 12*5280 = 63,360 in to 1 mi.
We also need to convert h to min: there are 60 min to 1 h.
So we have an angular speed of
(45 mi/h) * ((2π)/(40π) rad/in) * (63,360 in/mi) * (1/60 h/min) = 2376 rad/min
As mentioned before, there are 2π rad to 1 rev, so
(2376 rad/min) * (1/(2π) rev/rad) ≈ 378.152 rev/min
(where rev/min is equivalent to rpm)
400,000+60,000+5,000+100
Answer:
[tex] 400,000 + 60,000 + 5,000 + 100 [/tex]
46510 (add the zero since there are no ones)
. Leah invested some money at 4.5% annual interest and $1000 more than four times that amount at 6%. Her total annual income from these two investments was $801. How much did she invest at each rate
Answer:
The amount invested are $2600 and $11400 respectively
Step-by-step explanation:
Let the first amount be x
Given:
(First Investment)
Principal (P1) = x
Rate (R1) = 4.5%
Time (T) = 1 year
(Second Investment)
Principal (P2) = 4x + 1000
Rate (R2) = 6%
Time (T) = 1 year
Income = $801
Calculating the income from the first investment;
[tex]I_1 = \frac{P_1R_1T}{100}[/tex]
Substitute values for P1, R1 and T
[tex]I_1 = \frac{x * 4.5 * 1}{100}[/tex]
[tex]I_1 = \frac{4.5x}{100}[/tex]
Calculating the income from the second investment;
[tex]I_2 = \frac{P_2R_2T}{100}[/tex]
Substitute values for P2, R2 and T
[tex]I_2 = \frac{(4x + 1000) * 6 * 1}{100}[/tex]
[tex]I_2 = \frac{6(4x + 1000)}{100}[/tex]
[tex]I_1 + I_2 = Annual\ Income[/tex]
So:
[tex]\frac{4.5x}{100} + \frac{6(4x + 1000)}{100} = 801[/tex]
Multiply through by 100
[tex]100 * \frac{4.5x}{100} +100 * \frac{6(4x + 1000)}{100} = 801 * 100[/tex]
[tex]4.5x +6(4x + 1000) = 801 * 100[/tex]
[tex]4.5x +24x + 6000 = 80100[/tex]
Collect Like Terms
[tex]4.5x +24x = 80100 - 6000[/tex]
[tex]28.5x = 74100[/tex]
Divide through by 28.5
[tex]x = \frac{74100}{28.5}[/tex]
[tex]x = \$2600[/tex]
Recall that; the second invest
Amount Invested = 4x + 1000
This gives
[tex]Amount = 4 * \$2600 + 1000[/tex]
[tex]Amount = \$11400[/tex]
Hence;
The amount invested are $2600 and $11400 respectively
determine the quotient of 1 3/4÷2/5
Answer:
Step-by-step expl1 3/4 / 2/5 = 35
8
= 43
8
= 4.375
The radiator in a car is filled with a solution of 70 per cent antifreeze and 30 per cent water. The manufacturer of the antifreeze suggests that for summer driving, optimal cooling of the engine is obtained with only 50 per cent antifreeze. If the capacity of the raditor is 4.7 liters, how much coolant (in liters) must be drained and replaced with pure water to reduce the antifreeze concentration to 50 per cent?
Answer:
0.94 liters antifreeze is drained out and replaced with water to get a concentration to 50 per cent of the solution.
Step-by-step explanation:
Total amount of the solution is 4.7 liters.
It contains 70 percent antifreeze = 70% * of 4.7 = 3.29 liters of antifreeze
It contains 30 percent water = 30% * of 4.7= 1.41 liters water
For the solution to have 50 % antifreeze it must contain
4.7 * 50%= 2.35 antifreeze.
We have 3.29 liters and we want to have 2.35 liters of antifreeze
Therefore we will (3.29-2.35 =)0.94 liters drained out and replace it with water to get a concentration to 50 per cent.
Anna says that x 6/4× x 3/4=x 18/16 but Tim says that x 6/4× x 3/4= x 9/4 Who is correct and why?
Answer:
Anna
Step-by-step explanation:
First of all, let's look at both equations. 6x/4 multiplied by 3x/4 will equal 18x/6. Anna's equation is correct, but let's look at Tim's equation. Tim says that the answer would be 9x/4. However, he had incorrectly simplified it. Simplifying 18x/16 would be 9x/8, not 9x/4.
Answer:
Anna
Step-by-step explanation:
First of all, let's look at both equations. 6x/4 multiplied by 3x/4 will equal 18x/6. Anna's equation is correct, but let's look at Tim's equation. Tim says that the answer would be 9x/4. However, he had incorrectly simplified it. Simplifying 18x/16 would be 9x/8, not 9x/4.
Which statement correctly describes the characterization in this excerpt? Indirect characterization is used to show that Steve is confused and lonely. Indirect characterization is used to show that Steve is isolated and worried. Direct characterization is used to show that Steve is confused and lonely. Direct characterization is used to show that Steve is isolated and worried.
Answer:
The answer is B
Step-by-step explanation:
Answer: B- Indirect characterization is used to show that Steve is isolated and worried.
Step-by-step explanation:
Compute 81^3/4
Plz help :)
Answer:
531441/4
Step-by-step explanation:
Answer:
81.75!
Step-by-step explanation:
hope this helps! i worked this one out so if its wrong please tell me! シ︎
Express 120 as a percentage of 75
Answer:
62.5%
Step-by-step explanation:
75/120 x 100
= 62.5%
Bacteria vary somewhat in size, but a diameter of 1.5 μ m is not unusual.
a. What would be the volume (in cubic centimeters) of such a bacterium, assuming that it is spherical? Express your answer using two significant figures.
b. What would be the surface area (in square millimeters) of such a bacterium, assuming that it is spherical? Express your answer using two significant figures.
Answer:
a) 1.8 × 10^-12 cm³ or 1.8 × 10^-12 cubic meters
b) 7.1 × 10^-6 mm² or 7.1 × 10^-6 square millimeters
Step-by-step explanation:
a) We are assuming that the shape of the bacteria is a sphere.
Hence, Volume of the Sphere(Bacteria) = 4/3 × π × r³
Diameter = 1.5 μm
Radius = Diameter/2 = 1.5μm/2
= 0.75μm
We are told that the volume should be in cubic centimeters
Converting 0.75μm to centimeters
1 μm = 1 × 10^-4 cm
0.75 μm =
Cross Multiply
= 0.75 μm × 1 × 10^-4 cm/ 1 μm
= 0.000075cm
Volume of the Sphere(Bacteria) = 4/3 × π × r³
= 4/3 × π × (0.000075)³
= 1.767145867 × 10^-12 cm³
Approximately as 2 significant figures = 1.8 × 10^-12 cm³
b) The formula for the Surface area of a Sphere = 4πr²
Diameter = 1.5 μm
Radius = Diameter/2 = 1.5μm/2
= 0.75μm
We are told that the surface area should be in square millimeters
Converting 0.75μm to millimeters
1 μm = 0.001 mm
0.75 μm =
Cross Multiply
= 0.75 μm ×0.001mm/ 1 μm
= 0.00075mm
Surface Area of a Sphere
= 4 × π × r²
= 4 × π × 0.00075²
= 7.06858 ×10^-6 mm²
Approximately to 2 significant figures
= 7.1 × 10^-6 mm²
What is the least common multiple of 2, 5, and 10?
Submit Answer
Answer:
10
Step-by-step explanation:
The least common multiple is the smallest number that all 3 numbers will multiply properly to. In this case it is 10, because it is a multiple of all three of the numbers (2x5, 5x2, 10x1) and is the smallest as it cannot go below the largest number (10)
Hope this helped!
Answer:
10
Step-by-step explanation:
The least common multiple 10 is a product of common & odd prime factors between the integers which is divisible by each one an integer of this same group.
A short order cook can prepare 40hamburgers in 30 minutes
Answer:1.33333333333 hamburgers every minute
Step-by-step explanation:40 burgers ÷ 30minutes = 1.333333 burgers every minute
evaluate the 1/3 of 10.25
[tex]\textsf{Hey there!}[/tex]
[tex]\textsf{The word OF means MULTIPLY in mathematical terms }[/tex]
[tex]\mathsf{So, \ your\ equation\ becomes: \dfrac{1}{3}\times 10.25 }[/tex]
[tex]\mathsf{You\ can\ convert\ \dfrac{1}{3}\ into\ a\ decimal\ and\ solve\ from \ there}[/tex] [tex]\textsf{(if you want to)}[/tex]
[tex]\mathsf{\dfrac{1}{3} \times 10.25=3.416667}[/tex]
[tex]\boxed{\textsf{Thus your answer is: \boxed{\huge\text{\bf{3.416667}}}}}}\checkmark[/tex]
[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
What are the steps, in order, needed to solve 3x + 4 = 13? Divide by 3, and then subtract 4. Multiply by 3, and then add 4. Add 4, and then multiply by 3. Subtract 4, and then divide by 3.
Answer:t
Step-by-step explanation:
3x + 4 = 13
3x = 9
x = 3
Option 3
Answer:
subtract 4 then divide by three
Step-by-step explanation:
La suma de los ángulos interiores de un dodecágono es: a) 1900 b) 1800 c) 1950 d) 1960 e) 2000
Answer:
La suma de los ángulos interiores de un dodecágono es 1800°
Step-by-step explanation:
Un dodecágono es un polígono (figura plana delimitada por lados rectos, creando una figura cerrada) formado por 12 lados, 12 vértices y por consiguiente, 12 ángulos interiores.
Los ángulos interiores de un polígono son los ángulos delimitados por dos lados y que se encuentran dentro del polígono.
Los polígonos convexos son aquellos en los cuales todos los ángulos del polígono miden menos de 180º y la suma de los ángulos interiores es determinada por el número de lados que posee el polígono de la siguiente manera: 180°*(n-2)
Entonces, la suma de los ángulos interiores de un dodecágono se calcula como: 180*(12-2)= 1800
La suma de los ángulos interiores de un dodecágono es 1800°
Kevin and Randy Muise have a jar containing 100 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $15.00. How many of each type of coin do they have?
Answer:
what do we know?
we know that a quarter is $0.25 and a nickel is $0.05
4x$.25 = $1
20x$0.05 = $1
and we have 84 coin
n = the number of nickels
q = the number of quarters
(1) n + q = 84 and
(2) 5*n + 25*q = 100*11.80 (always work in cents)
(3) 5*n + 25*q = 1180
Now substitute n from equation (1) into equation (3) and get
5*(84 - q) + 25*q = 1180
420 - 5*q + 25*q = 1180
20*q = 1180 - 420
20*q = 760
q = 38
Then using equation (1), plug in q
n + 38 = 84
n = 46
now check these values.
Is (.05*38 + .25*46 = 11.80)?
Is (2.30 + 9.50 = 11.80)?
Is (11.80 = 11.80)? Yes
Step-by-step explanation:
Plz Mark me as brainliest
Answer: 7 quarters and 19 nickels
Step-by-step explanation:
find the measure of the third angle of a triangle if the measures of the other two angles are given 118.6 and 42.3
Answer:
[tex]\boxed{\bold{\huge{\boxed{\mathrm{Third\ Angle = 19.1\ degrees}}}}}[/tex]
Step-by-step explanation:
The interior angles of a triangle add up to 180 degrees. So, to find an unknown interior angle, we need to subtract rest of the two angles from 180 degrees.
So,
Third Angle = 180 - 118.6 - 42.3
Third Angle = 19.1 degrees
please respond ASAP!!!! in the diagram below, AC is parallel to DF is parallel to BH and CB is parallel to FE. (look at image) a. Find four similar triangles. Explain how you know that they are all similar. b. Using the similar triangles you found in part (a), complete the following extended proportion (look at image)
Answer:
SImilar triangles are: ABC, DBG, DEF, and BEH.
Step-by-step explanation:
There are clealy four well defined triangles in the image:
ABC, DBG, DEF, and BEH.
Given the parallelism of the mentioned lines, one can conclude that when those lines parallel to different sides of the triangle ABC for example (to sides AC and CB), intersect, they will also intersect giving similar angles . That is: angle ACB must equal angle DGB, angle DFE, and angle BHE. Apart from that, the angles around the bases of all four triangles must be equal since they come from parallel lines. That is:
(1) angles BAC, BDG, BDF, and EBH must be equal to each other, and
2) angles ABC, DBG, DEF, and BEH must be equal to each other.
Therefore we have four triangles with congruent angles, which make them similar triangles.
Solve 2g - 13 = 3.
g=
Answer:
8
Step-by-step explanation:
2g = 3 + 13
2g = 16
g = 16/2
g = 8
Answer:
g=8
Step-by-step explanation:
2g-13=3
2g-13+13=3+13
2g=16
2g/2=16/2
g=8
there are eight more women than men in a theater group. The group has a total of 44 members. How many men and how many women are in the group?
The number of men and women in the group will be 18 and 26 respectively.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that there are eight more women than men in a theater group. The group has a total of 44 members.
Let the number of men in the group be {x}. Then, the number of women will be (x + 8). We can write -
x + (x + 8) = 44
2x = 36
x = 18
Number of women : x + 8 = 26
The number of women in the group will be 26.
Therefore, the number of men and women in the group will be 18 and 26 respectively.
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e. Lindsey sold stationery to her family and her mother's friends. She deposited the $125
she earned in a savings account. The account earns 5.18% interest annually. If she does
not deposit or withdraw any money from for 18 months, how much will she have in her
account?
Answer:
$134.71
Step-by-step explanation:
This is a simple interest question
A = P(1 + rt)
A = Amount after t months or years
P = Principal or amount saved
r = interest rate = 5.18% = 0.0518
t = time.in years = 18 months
= 1 year and 6 month
= 1.5 year
A = $125( 1 + 0.0518 × 1.5)
A = $125 ( 1 + 0.0777)
A = $125(1.0777)
A = $134.71
A snack company can pack 16 granola bars in a box. How many boxes are need for 800 granola bars
Answer:
50 granola bars
Step-by-step explanation:
800 divided get 50 bars
4x+2x=24 i need the answer
Answer:
x =4Step-by-step explanation:
[tex]4x+2x=24\\\\\mathrm{Add\:similar\:elements:}\:4x+2x=6x\\6x=24\\\\\mathrm{Divide\:both\:sides\:by\:}6\\\frac{6x}{6}=\frac{24}{6}\\\\Simplify\\x=4[/tex]
Answer:
x =4
Step-by-step explanation:
[tex]4x+2x=24[/tex]
Simplify
[tex]6x = 24[/tex]
Divide both sides of the equation by 6
[tex]\frac{6x}{6} = \frac{24}{6} \\\\x = 4[/tex]
96,240 is divisible by 2, 4, and 8. true or false?
Answer:
false
Step-by-step explanation:
96,240
a-9
2,3
8,9
simplify the expression where possible (x^3 y^2) ^4
Answer:
[tex]x^{12} y^{8}[/tex]
Step-by-step explanation:
[tex](x^{3} y^{2})^{4}[/tex] You must multiply the outside exponent with the inside exponents.
[tex]x^{12} y^{8}[/tex]
What is the value of |-25|?
Answer:
25
Step-by-step explanation:
this answer is 25, essentially you just remove the negative hope this helps
Pls i need help with this
Answer:
48
Step-by-step explanation:
surface area is the outside of everything.
James is playing an arcade game with tokens. In the first
game, he hits the jackpot and doubles the number of
tokens that he has. In the second game, James wins 12
more tokens. In his third and final game, he loses 4
tokens. James now has 170 tokens. How many tokens
did he have before he started playing the game?
Answer
81 tokens
Step-by-step explanation:
x+12-4=170
x+8=170
-8 -8
x=162
162/2=81 tokens
The number of tokens he had before he started playing the game is 81 tokens.
Given,
James is playing an arcade game with tokens.
In the first game, he hits the jackpot and doubles the number of tokens that he has.
In the second game, James wins 12 more tokens.
In his third and final game, he loses 4 tokens. James now has 170 tokens.
We need to find how many tokens did he have before he started playing the game.
What does the term mean?Doubles = multiply by 2
x more than M = M + x
Loses x from M = M - x
We have,
Let the number of tokens he had initially be M.
First game:
Doubles the number of tokens
= 2M
Second game:
James wins 12 more tokens.
= 2M + 12
Third game:
Loses 4 tokens.
= 2M + 12 - 4
= 2M + 8
James now has 170 tokens
This means:
2M + 8 = 170
2M = 170 - 8
2M = 162
M = 162 / 2
M = 81
Thus the number of tokens he had before he started playing the game is 81 tokens.
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Help i dont uderstand please help :(
Answer:
-3
Step-by-step explanation:
Plug in -3
2(-3)+3
Remember PEMDAS
Parentheses first: 2(-3)=-6
-6+3=-3
Hope this helps :)
5. One January morning, the temperature was -8 degrees. By the afternoon, it rose 5 degrees. What was the temperature in the afternoon? (Only enter a number answer) * Your answer This is a required question Pa Back Next ever submit passwords through Google Forms.
Answer: -3
Step-by-step explanation: