Answer:
m∠1 = 30°
m∠2 = 120°
m∠3 = 30°
w = 52
x = 104 (approximately)
y = 156 (approximately)
z = 180
Step-by-step explanation:
Step 1: Label your diagram with variables to make solving easier
Step 2: Solve for the missing degrees
*Note: A triangle adds up to 180°m∠1 = 180° - 90° - 60° = 30°*Note: A line adds up to 180°m∠2 = 180° - 60° = 120°m∠3 = 180° - 120° - 30° = 30°Step 3: Solve for the missing side lengths
*Note: SOH CAH TOA: sin = [tex]\frac{opposite}{hypotenuse}[/tex], cos = [tex]\frac{adjacent}{hypotenuse}[/tex], tan = [tex]\frac{opposite}{adjacent}[/tex]x can be solved by using sineThe angle opposite of 90 is 60°, so [tex]sin(60)=\frac{90}{x}[/tex]Then isolate x to one side, [tex]x=\frac{90}{sin(60)}[/tex]Finally solve for x, x ≈ 104 (means x is approximately 104)w can be solved by using sineThe angle opposite of w is 30° and the hypotenuse is 104, so [tex]sin(30)=\frac{w}{104}[/tex]Then isolate w to one side, [tex]w=104(sin(30))[/tex]Finally solve for w, w = 52z can be solved by using cosine*Note: 30° + 30° = 60°The angle adjacent to 90 is 60°, so [tex]cos(60)=\frac{90}{z}[/tex]Then isolate z to one side, [tex]z=\frac{90}{cos(60)}[/tex]Finally solve for z, z = 180y can be solved by using cosineThe angle adjacent to y is 30° and the hypotenuse is 180, so [tex]cos(30)=\frac{y}{180}[/tex]Then isolate y to one side, [tex]y=180(cos(30))[/tex]Finally solve for y, y ≈ 156 (means y is approximately 156)A bag contains 6 blue marbles, 5 red marbles, 3 green marbles, and 2 yellow marbles. If 2 marbles are removed from the bag one at a time, without being replaced, what is the probability of selecting 2 red marbles in a row?
The probability of selecting 2 red marbles in a row is 1/12.
A bag contains 6 blue marbles, 5 red marbles, 3 green marbles, and 2 yellow marbles. Two marbles are removed from the bag one at a time without being replaced. We need to find the probability of selecting 2 red marbles in a row. Let the probability be represented by the variable "P".
The probability that the first selected marble will be red is given below :
P1 = 5/(6 + 5 + 3 + 2) = 5/16
The probability that the second selected marble will be red is given below :
P2 = 4/(6 + 4 + 3 + 2) = 4/15
The probability that both of the selected marbles will be red is given below :
P = P1*P2 = (5/16)*(4/15) = 1/12.
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Please help :( PQRS is a quadrilateral and M is the midpoint of PS.
PQ=a QR=b AQ=a-2b
Show that PS =2b
Answer as fast as possible please
Answer: B)
Could you please merk me as "Brainliest"
From 1987 to 2009, the number
B
of federally insured banks could be approximated by
B
(
t
)
=
−
327.4
t
+
13715
where t is the year and t=0 corresponds to 1987.
Answer:
12100
Step-by-step explanation:
If the number B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 from 1985 to 2007 where t = 0 correspond to year 1985
In order to determine the amount of federally insured banks that were there in 1990, we will first calculate the year range from initial time 1985 till 1990
The amount of time during this period is 5years. Substituting t = 5 into the modeled equation will give;
B ( t ) = − 329.4 t + 13747
B(5) = -329.4(5) + 13747
B(5) = -1647+13747
B(5) = 12100
This shows that there will be 12100 federally insured banks are there in the year 1990.
What is 348,962 rounded to the nearest ten thousand?
Answer:
i think its 350000
Step-by-step explanation:
hope it helps! :)
What should the height of a can of fruit juice used as a prop be if it's actual height is 7 inches
The height of a can of fruit juice used as a prop, if it's actual height is 7 inches, should be of:
3.85 inches.
What is a proportional relationship?A proportional relationship is a linear function that has intercept of zero and hence it has the output variable y as the multiplication of the input variable x and the constant of proportionality k, as follows:
y = kx.
The input and the output variables in this problem are given as follows:
Input variable: Actual height.Output variable: Height on set.From the table given at the end of the answer, the constant is given as follows:
k = 44/80
k = 0.55.
Hence the equation is:
y = 0.55x.
Then the height on the set when the actual height is of 7 inches is given by:
y = 0.55(7) = 3.85 inches.
Missing InformationThe table is given by the image at the end of the answer.
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8 9/10-3 2/3
Step by step if you want to
Answer:
The answer for that question is 5.233
The 3 is repetitive
helppppppppppppppppp plssssssss
The "zero of a function" refers to the input value that makes the function's output equal to 0.
For this problem, write the numbers in scientific notation. 6,000 A. 6 × 103 B. 6 ×104 C. 6× 102
Answer:
Step-by-step explanation:
6,000 = 6 × 1000 = 6 × 10³
thirty seconds after a bowl begins to leak, the bowl is losing 0.28 ounces of liquid per second. let l(t) represent the amount of liquid that has leaked at any given time, and let t be measured in seconds. which of the following expressions represents this scenario?
The expression that represents this scenario would be l(t) = 0.28t. This expression states that the amount of liquid that has leaked at any given time is equal to 0.28 times the number of seconds that have passed.
What are linear equations?Linear equations are mathematical equations of the type y = mx + b, with and x and y being variables. These equations represent a straight line on a graph and are referred to be "linear" since the maximum power of the variable is 1. For example, the equation y = 2x + 3 is a linear equation since the maximum power of the variable x is 1. Linear equations are useful for representing a broad range of real-world events, such as the link between the distance an object travels and the time it takes to traverse that distance. They are a common tool in many disciplines, including physics, engineering, and economics. They are also quite simple to answer.
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HURRY!! What is the distance between points G and H?
Points G (-5,-8) and H (3,7) are plotted on a coordinate grid.
___ units
The distance between Points G (-5,-8) and H (3,7) are plotted on a coordinate grid will be 17 units.
What is distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations. The distance formula is typically employed to determine the separation between two places. The Pythagoras theorem is used to help create a triangle and to derive the formula.
It is given that the points are plotted on a coordinate grid. are, G (-5,-8) and H (3,7).
The distance between the two points is obtained for the point (x₁.y₁) and (x₂,y₂) is,
[tex]\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
The distance between the points G (-5,-8) and H (3,7).
[tex]\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\ GH = \sqrt{(3-(-5))^2 + (7-(-8))^2} \\\\ GH = \sqrt{289} \\\\ GH = 17 \ units[/tex]
Thus, the distance between Points G (-5,-8) and H (3,7) plotted on a coordinate grid will be 17 units.
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PLEASR HELP!!! What is the name for this angle below
•HJI
•HIJ
•IJH
help me its due today and its 9:42 2^3 x 5^111
Round the decimal two hundred twenty-one and five hundred seventy-four thousandths to the nearest tenth.
What value of x will make a0nm similar to ASRQ by the SAS similarity theorem?.
The value of x is 25 will make ΔONM similar to ΔSRQ by the SAS similarity theorem.
Given:
∠ONM is similar to ∠SRQ
From the figure
NM = 10
SR = 20
NO = 8
QR = x
SAS Similarity Theorem:
if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
Both the triangles are similar by SAS if
NO/NM = SR/QR
Now substitute the values
8/10 = 20/x
cross multiplication
8x = 200
dividing both sides by 8
x = 25
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for a summer bbq you have 30 friends coming over. how many picnic tables do you need if you can seat 4 people at each picnic table?
Answer:
You need 8 picnic tables.
Step-by-step explanation:
You need 8 picnic tables because there are 30 friends and 4 sits at each table, and 4 x 8 is 32. There is 2 more extra seats. But it does fit all 30 friends.
What is an equation of the line that passes through the points (8, -3) and (4, 2)?
Answer:y
=5/4x+-3
Step-by-step explanation:
first you find the slope which is 5/4 then you do y=mx+b but replace the y and the x with points on the line giving you 2=5/4•4+b then you solve for b and get -3 giving you your answer.
Answer: -5/4x+7
Step-by-step explanation:
1)First find the slope passing through (8,-3) (4,2) using this formula
y2-y1/x2-x1 (this: 2--3/4-2) to get -1.25 or -5/4. this is your slope.
2) Then to get the y-intercept choose one of your points (doesn't matter which I chose (8,3) but you can choose any of the two) and create this formula y=mx+b.
3) Input your x and y from the point you chose and your slope (m) to create this -3=(8)+b.
4) Now solve for b. This should get you Postitve 7 (REMEMBER it is VERY IMPORTANT if you result is negative or positive. One mess up could make the whole thing wrong.)
5) Finally take your slope and y-intercept and put it together to get:
y=-5/4x+7
Follow those steps every time you get a problem like this and it should help :)
Jemmy throws the dice twice. What is the probability of getting 3 on the top for both dice?.
The probability of getting 3 on both of the dice is 1/36.
What is probability?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. An event's possibility is a number between 0 and 1, where, practically speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Main Body:
The probability of getting 3 on a dice = 1/6
As Jemmy throws the dice twice
P( 3 on both dice) =(1/6)*1/6
P ( 3 on both dice) = 1/36.
Hence the probability of getting 3 on both dice = 1/36.
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Which set of coordinates represents Figure MNOP reflected across the x-axis?
The set of coordinates after the reflection is (c) M' = (-3, -4) N' = (2, -3) O' = (1, -1) P' = (-2, -2)
How to determine the coordinates after the reflection?The graph represents the given parameter
On the graph, we have the following coordinate points
M = (-3, 4)
N = (2, 3)
O = (1, 1)
P = (-2, 2)
The rule of the reflection is given as:
Reflection across the x-axis
Mathematically, this is represented as
(x, y) ⇒ (x, -y)
When this is applied to the points, we have the following representation
M' = (-3, -4)
N' = (2, -3)
O' = (1, -1)
P' = (-2, -2)
Hence, the set of coordinates is (c)
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Carter feeds each of his dogs 1/5 of a can of food each day. He uses a total of 2/5 of a can of food each day. How many dogs does Carter have?
Answer:
Artur has 2 dogs
Step-by-step explanation:
we know he feeds the one fifth per dog so two fifth will be 2 dogs
Answer Two dogs,
Step-by-step explanation:
1/5 + 1/5 = 2/5 I mean cmon now that's easy
Caroline leaves her house and walks north 6 blocks. She turns and heads east 8 blocks until she reaches mattie’s house. What is the shortest distance between caroline’s and mattie’s houses?.
The shortest distance between Caroline's and Mattie's houses is 10 block.
Let Caroline started from point A and goes towards north 6 blocks to O. and goes to B 8 blocks in east.
AO = 6
BO = 8
Formula for the Shortest distance can be solve by pythagoras theorem:
[tex]AB^{2} = AO^{2} +OB^{2}[/tex]
[tex]AB^{2} = 6^{2} +8^{2}[/tex]
[tex]AB^{2} = 36+64[/tex]
[tex]AB^{2} = 100[/tex]
[tex]AB = \sqrt{100}[/tex] can
[tex]AB = 10[/tex].
The shortest distance AB = 10 block.
#1234
10 blocks are the shortest distance between Caroline and Mattie's homes.
Given data,
Caroline steps outside and makes a 6 block trek to the north. To go to Mattie's house, she does a turn and travels 8 blocks to the east.
To get the shortest distance between Caroline and Mattie's houses we need to it as a triangle and apply the Pythagorean theorem.
Pythagorean theorem:
The well-known geometric axiom is that the hypotenuse (the side across from the right angle) of a right triangle is equal to the sum of the squares on its legs. Or, in popular algebraic form, a² + b² = c².
The shortest distance (c);
Let, a = 6
b = 8
⇒ a² + b² = c²
6² + 8² = c²
36 + 64 = c²
c = [tex]\sqrt{100}[/tex]
c = 10
Therefore, the shortest distance between Caroline’s and Mattie’s houses is 10 blocks.
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Select the correct answer.
Jackie is selling smoothies at a school fair. She starts the day with $15 in her cash box to provide change to her customers. If each smoothie costs $3.75, which graph represents the balance of the cash box, y, after Jackie sells x smoothies?
Answer:
the expression for the graph would be y = 3.75x + 15.
There aren't answer choices so this is the most I could do with the information provided.
Hope this at least helps you find the correct graph.
Have a nice day! :)
Step-by-step explanation:
A bakery sold 76 mocha cupcakes in a day, which was 95% of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
126 cupcakes
Step-by-step explanation:
75 is equal to 94.5%
and if it was 127 cupcakes it would be 95.25%
but it would most likely have to be under 95%
so it would be 126 cupcakes
i need help on this thanks
The value of x that makes m ║n is 60 degree.
What is consecutive interior angles?
Pairs of angles that are between two lines and on the same side of the line that cuts through the lines are referred to as consecutive internal angles.
The "consecutive interior angle theorem" asserts that each pair of consecutive interior angles is supplementary, meaning that the sum of the consecutive interior angles equals 180°, if a transversal intersects two parallel lines.
Here to make m ║n the angles x and 2x are consecutive interior angles.
Since consecutive interior angles are supplementary.
So,
x + 2x = 180
3x = 180
x = 180/3
x = 60 degree.
Therefore, the value of x is 60 degree that makes m ║n.
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2. What is the 20th term of the arithmetic sequence?
2, 10, 18, 26,...
Answer:
154
Step-by-step explanation:
The difference is 8.
4 8 12
A B
++++
24 32
C
48
What number does C stand for?
D
56 60
Answer:
The answer is 40
Step-by-step explanation:
You are counting by 4's
prove that
tan x / (1 +secx) + (1+secx)/tanx = 2 csc x
The trigonometric expression [tex]\left(\dfrac{tan( x)}{1+sec( x)} +\dfrac{1+sec( x)}{tan( x)}\right)[/tex] can be simplified to prove that it equals 2·csc(x), by plugging in [tex]\left(tan(x) = \dfrac{sin(x)}{cos(x)}\right)[/tex],
[tex]\left(sec(x) = \dfrac{1}{cos(x)}\right)[/tex] and [tex]\left(csc(x) = \dfrac{1}{sin(x)}\right)[/tex] to give the following
trigonometric identity;
[tex]\dfrac{tan( x)}{1+sec( x)} +\dfrac{1+sec( x)}{tan( x)} = 2\cdot csc(x)[/tex]What are trigonometric identities?Trigonometric identities are equations of trig functions which are valid for all values of the input variable at which the expressions on both sides of the equality are defined.
The trigonometric expression in the question is simplified as follows;
[tex]\dfrac{tan( x)}{1+sec( x)} +\dfrac{1+sec( x)}{tan( x)} = \dfrac{tan( x)}{1+\dfrac{1}{cos(x)} } +\dfrac{1+\dfrac{1}{cos(x)}}{tan( x)}[/tex]
[tex]\dfrac{tan( x)}{1+\dfrac{1}{cos(x)} } +\dfrac{1+\dfrac{1}{cos(x)}}{tan( x)} = \dfrac{cos(x)\times tan( x)}{cos(x)+1} } +\dfrac{cos(x)+1}{cos(x)\times tan( x)}}[/tex]
[tex]\dfrac{cos(x)\times tan( x)}{cos(x)+1} } +\dfrac{cos(x)+1}{cos(x)\times tan( x)}} = \dfrac{sin(x)}{cos(x)+1} } +\dfrac{cos(x)+1}{sin( x)}}[/tex]
[tex]\dfrac{sin(x)}{cos(x)+1} } +\dfrac{cos(x)+1}{sin( x)}} = \dfrac{sin^2(x)+(cos(x)+1)^2}{sin( x)\cdot (cos(x)+1)} }[/tex]
[tex]\dfrac{sin^2(x)+(cos(x)+1)^2}{sin( x)\cdot (cos(x)+1)} }=\dfrac{sin^2(x)+cos^2(x)+2\cdot cos(x)+1}{sin( x)\cdot (cos(x)+1)}[/tex]
[tex]\dfrac{2\cdot cos(x)+2}{sin( x)\cdot (cos(x)+1)} =\dfrac{2\cdot (cos(x)+1)}{sin( x)\cdot (cos(x)+1)} = \dfrac{2}{sin( x)}[/tex]
[tex]\dfrac{2}{sin( x)} = 2\cdot csc(x)[/tex]
[tex]\therefore \dfrac{tan( x)}{1+sec( x)} +\dfrac{1+sec( x)}{tan( x)} =2\cdot csc(x)[/tex]
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What is the equation of the line that is perpendicular to the given line and passes through the point (2,6).
The equation of the line passing through the point (2,6) and perpendicular to the given line is y = 6.
Given data;
The line is horizontal, and the slope of the line is infinity.
The slope of the line perpendicular will be expressed as [tex]\frac{-1}{∞}[/tex] = 0
To get the equation of the line and passes through the point (2,6),
A line's equation in point-slope form is written as;
[tex]m = \frac{y-yo}{x-xo}[/tex]
As m is the slope of the line then,
The required equation will be:
y - 6 = 0*(x-2)
y - 6 = 0
y = 6
Hence, the equation of the line that is perpendicular to the given line and passes through the point (2,6) is y = 6.
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a particular 12 -hour digital clock displays the hour and minute of a day. unfortunately, whenever it is supposed to display a 1 , it mistakenly displays a 9. for example, when it is 1 : 16 pm the clock incorrectly shows 9 : 96 pm . what fraction of the day will the clock show the correct time?
1/2 fraction of the day will the clock show the correct time when it is supposed to display a 1 , it mistakenly displays a 9.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Here,
=2/3(1-15/60)
=2/3(3/4)
=2/4
=1/2
When the clock should be displaying a 1, but instead shows a 9, the correct time will be displayed for 1/2 of the day.
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When Arianna, left her house, her cell phone was 45% charged started losing charge at a constant rate. 4 hours after leaving her house, the battery had 15% remaining battery life. Write an equation for B, in terms of t, representing the charge remaining in Arianna's battery, as a percentage, t hours after Arianna left her house.
The answer, Arianna's battery, as a percentage, 3.75t hours after Arianna left her house.
What is percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The % sign is used to denote it.
The initial charge of Arianna's phone = 45%
now the charge remaining in Arianna's battery = 15%
If after 4 hours of leaving her house, the battery had 15% remaining battery life, then the battery is discharging at the rate of ( 15% / 4 hours)
=3.75% per hour.
Thus, the charge remaining in Arianna's battery after she left her house will be, B = 3.75t
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if the reference angle was . what are the angle in the 4 quadrants. make sure to explain how you get the angles.
Answer:
Step-by-step explanation:31542