If the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units
The length of the hypotenuse = 13.5 units
The angle = 41 degrees
Here we have to use the trigonometric function
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
tan θ = Opposite side / Adjacent side
In this question hypotenuse and angles are given and we have to find the opposite side.
sin θ= opposite side / Hypotenuse
Substitute the values in the equation
sin 41 = Opposite side / 13.5
Opposite side = sin 41×13.5
= 8.86 units
Hence, if the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units.
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Exterior angle, theorem, and triangle sum theorem
Answer:
x = 4Step-by-step explanation:
It is assumed you are looking for the value of x.
According the diagram, we have:
∠JEF is exterior angle to triangle EFG and ∠F and ∠G are remote interior angles.Property of exterior angle - it is same as the sum of remote interior angles.
Set equation:
m∠F + m∠G = m∠JEF16x + 4 + 14x + 6 = 13030x + 10 = 13030x = 120x = 4It is easy to calculate the unknown angle measures if needed:
m∠F = 16*4 + 4 = 68m∠G = 14*4 + 6 = 62can anyone tell my how they came up with the net force? (purple arrow)
Answer:
5 m/s
Step-by-step explanation:
1. 3² + 4² = 25
2. √25 = 5
is 4.887888 a rational number
What is the least common multiple of 10 and 20?
Answer:
20
Step-by-step explanation
We need to find the multiples of 10 and 20 (multiples of 10 = 10, 20, 30, 40; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 10 and 20, i.e., 20.
Answer:
20
Step-by-step explanation:
First, find the factors of both 10 and 20
Factors of 10: 1, 2, 5, 10
Factors of 20: 1, 2, 4, 5, 10, 20
Notice any common factors?: 1, 2, 5, 10
Now multiply the greatest common factor, 10, with another even number to hopefully get 20: 10*2=20.
Hence, the least common multiple is 20.
Monica made strawberry lemonade to serve at her birthday party. In a large pitcher, she mixed 8 ounces of strawberry puree and 40 ounces of lemonade. She had some strawberries left over, so she made another smaller batch. She mixed 5 ounces of strawberry puree and 20 ounces of lemonade in a small jug. Which container's strawberry lemonade had a stronger strawberry flavor?
The container's strawberry lemonade that had a stronger strawberry flavor is the more compact bottle and has a more robust taste.
This is further explained below.
What is the stronger strawberry flavor?Generally, in a bid to understand the context of the scenario we must first write the rato of the flavor's relationship
x=8:40
y=5:20
Therefore
x=8:40
y=10:40
In conclusion, This helps us decipher that Larger container: We add eight ounces of strawberry puree for every forty ounces of lemonade that we make.
We have 10 ounces of strawberry puree for every 40 ounces of lemonade that we have.
Therefore, the more compact bottle has a more robust taste.
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Lisa and Joey just became parents to their son, David. They want to start saving for their newborn’s college, so they open a new, empty savings account. They agree that they will put an equal amount of money every month, so that as David gets older and time goes by, the account gets filled with money for David’s future. Describe what is happening to the variables here (hint: time is almost always on the x-axis). Is this a variation equation?
If Lisa and Joey put the same amount of money every month in the savings account for David's future and the situation is plotted in a graph where time is on the x-axis, then there will be straight line with a constant slope.
As per the question statement, Lisa and Joey just became parents to their son, David and they decided to start a savings account for their newborn's future, where they agreed to put an equal amount of money every month.
We are required to determine the condition of the variables if the above-mentioned situation is plotted into graph and the account gets constantly filled with money as David grows older.
To solve this question, first let us consider the time to be plotted on the X-axis (As mentioned in question statement that "Time" is almost always on the x-axis) and the money collected to be plotted on the Y-axis.
Since, an equal amount of money is put into the account every month, therefore, taking 1 month as unit time to plot our graph, the money will grow diagonally in a straight line with a constant slope. Hence, both the variables (abscissa and ordinates) will increase on a constant ratio along the first quadrant.
Slope of a Line: In mathematics, the slope or gradient of a line is a value that describes both the direction and the steepness of the line and is calculated by the change in y coordinate with respect to the change in x coordinate.To learn more about Slope of a Line, click on the link below.
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I need help with qeustion 36 please
Answer:
8 + 2(x + 3) = 2x + 14
Would be infinitely many solutions.
Step-by-step explanation:
8 + 2x + 6 = 2x + 14
2x + 14 = 2x + 14
0 = 0; True
All real numbers
The coordinates of point T are (0,5). The midpoint of ST is (5,-8). Find the coordinates of point S.
The other endpoint is
(Type an ordered pair.)
... HELP PLS!!!!
In 3–5 sentences, explain why the moon appears to be less bright than the sun despite its very close distance to Earth. PLEASE DO NOT COPY OTHER PEOPLE AND RIGHT THISBased on scientific observations and findings, the reasons the moon appears to be less bright than the sun despite its very close distance to earth are the following:
Moon doesn't produce its light but rather takes or reflects the light from the Sun.
Moon only reflects about 12 percent maximum of lights that shines on it from the sun.
Externally, Moon is made of dark-colored soil often referred to as lunar soil. This is unlike the Sun which is made of hydrogen and helium, whose atoms are very light.
Also, Sun is about 400 times bigger than the Moon.
Hence, in this case, it is concluded that there are many reasons the moon appears to be less bright than the sun despite its very close distance to earth. MAKE IT SIMPLE
Answer:
Since the moon has no atmosphere, all wavelengths of sunlight reach the ground by traveling straight through space. Our sun appears white because it produces all visible wavelengths approximately equally. The sun will appear the same size whether viewed from Earth or the Moon since Earth and the moon are relatively close to the sun. The sun and moon both have an apparent size of one-half of a degree when viewed from Earth.
Step-by-step explanation:
A city is paving a bike path. The same length of path is paved each day. After 4 days, 15 miles of path remain to be paved. After 6 more days, 12 miles of path remain to be paved. Find the average rate of change.
15 km of walkway still need to be paved after 4 days. There are still 12 miles of trail to be paved after another 6 days. The average rate of the change is 24.
Given that,
The paving of a bike route by a city. Every day, the same amount of the path is paved. 15 km of walkway still need to be paved after 4 days. There are still 12 miles of trail to be paved after another 6 days.
We have to find the average change rate.
1st we find the slope with the points (4,15) and (6,12).
Slope =[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Slope=[tex]\frac{12-15}{6-2}[/tex]
Slope=-3/4
Now,
y=mx+b
15=-3/4(4)+b
b=15+3
b=18
We got the equation of line as y=-3/4x+18
Now take y=0
0=-3/4x+18
-3/4x=-18
x=(18×4)/3
x=72/3
x=24
Therefore, the average rate of the change is 24.
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pleaseee help, question what is the sum of 4x^2 + 2x - 5 and 7x^2 - 5x + 2
Answer:
Add the expressions.
11x2−3x−3
Step-by-step explanation:
Simplification of polynomials.
Polynomials are mathematical expressions made up of many terms.To simplify a polynomial the most, you must collect all like terms and rearrange them from highest to lowest power.
4x² + 2x -5 + 7x² - 5x+24x² + 2x -3 + 7x² - 5x+211x² + 2x - 3 - 5x11x² - 3x - 3 ====> Option "A"What's 4/9+9/18 please help with this thanks you
After solving the equation 4/9+9/18, we have to come to find the solution is 1.57.
What is an equation?An equation can be defined in a number of different ways. An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." There are one or more variables in even the most fundamental and straightforward algebraic equations.
The value of the variable that makes the equation a true statement is the solution of the equation.
We have been asked to solve the equation 4/9 + 9/8
Lets solve
⇒ 4/9 + 9/8
⇒ (32+81)72 (finding the LCM of denominators and multiplying with
⇒ (32+81)72 numerators)
⇒ 113/72
⇒ [tex]1\frac{41}{72}[/tex]
⇒ 1.57
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Can someone help. fill fill
Answer:
x = 13
calculations in the pic hope it helps
Answer is 13
Step by step
1.4 + x / 6 = 2.4
We want to get rid of the 6 first
It is a divide so we want to do the inverse, which is multiply both sides by 6
1.4 + x * 6/ *6 = 2.4 * 6
Combine (the 6/6 becomes 1)
1.4 + x = 14.4
Now we want to isolate the x
Subtract 1.4 from both sides to solve for x
1.4 - 1.4 + x = 14.4 - 1.4
Combine
x = 13
LeeAnn is taking care of her 3 brothers.
She has four pieces of toast and wants
to divide them equally among her
brothers.
How much toast does each get?
Each gets [tex]\frac{1}{4}[/tex] pieces of toast.
What is fraction?A number that is stated 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. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.
Given Data
LeeAnn is taking care of her 3 brothers. She has four pieces of toast and wants to divide them equally among her brothers.
So,
Total pieces of toast = 4
Each gets = 1
Fraction of toast each gets = [tex]\frac{1}{4}[/tex]
Each gets [tex]\frac{1}{4}[/tex] pieces of toast.
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a researcher is interested in the sleeping habits of students at the local state college. the average number of hours spent sleeping each night for the entire set of students enrolled at the college is an example of a .
One example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.
What do we mean by a parameter?In mathematics, a parameter is a variable whose range of possible values identifies a number of unique cases in a problem. A parametric equation is any equation that is expressed in terms of parameters. To describe the entire population under study, a parameter is used. For instance, we are interested in learning the typical length of a butterfly. This information about the entire butterfly population makes it a parameter. The local state college's students' sleeping patterns are of interest to a researcher. One example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.Therefore, one example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.
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The correct question is given below:
A researcher is interested in the sleeping habits of students at the local state college. The average number of hours spent sleeping each night for the entire set of students enrolled at the college is an example of a ____.
I need this answered please
Answer:
x=45
Step-by-step explanation:
20-.24=9.2
mp Learning
A fair costs $28 for admission plus $3 for each roller coaster ride.
Given that x represents the number of roller coaster rides, choose the algebraic expression that models this situation.
A
B
D
E
28x + 3
31x
31
28 + 3x
You answer is: 28 + 3[tex]x[/tex]
Since $28 is a one-time fee and does not have to be paid again for each and every ride, it does not need a variable in front of.
But for every ride you want, you pay $3 so you need the variable "[tex]x[/tex]" which represents how many times you ride.
For example, if you ride the roller coaster once, your total amount, in dollars, will be:
T = 28 + 3 * (1)
T = $31
But if you ride the roller coaster 3 times, your cost, in dollars, will be:
T = 28 + 3 * (3)
T = 28 + 9
T = $37
90 is what percent of 81?
Step-by-step explanation:
did you change the reference number ?
I think the original question was "90 is how many % of 80 ?"
now it is 81.
in % calculations the most important things to identify :
what are 100% (or any other reference % level).
then what is 1%.
and then multiply this 1% by the desired number of % or divide the target number by this 1% to find out how many % the target number is.
in our case here
100% = 81
1% = 100%/100 = 81/100 = 0.81
how many % are 90 ?
well, as many as how often 1% fits into these 90 :
90/0.81 = 111.111111111... %
when the reference was 80, then we had
90/0.8 = 112.5%
Describe the slope of the line. (0, 3) (5,-1) m= The slope is negative Find the slope.
Answer:
Step-by-step explanation:
Slope formula: m=[tex]\frac{rise}{run}[/tex] so m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_1[/tex]=3
[tex]y_2[/tex]=-1
[tex]x_1[/tex]=0
[tex]x_2[/tex]=5
So the formula is, [tex]\frac{(-1)-3}{5-0}[/tex] = [tex]\frac{-4}{5}[/tex]
Slope is negative.
Slope is -4/5
what is7.9 times 0.99
Answer:
7.821 or 7821/1000
Step-by-step explanation:
Answer:
7.821
Step-by-step explanation:
A family is taking a trip to a maill 45 miles away. They have seven gallons of gas in their car's fuel tank and the car gets 22 miles per gallion on this trip. Explain why it is okay to estimate the fuel supply for the trip.
Trip of 45miles with seven gallons of gas in a car and car gets 22 miles per gallon ,estimate fuel supply for trip is 2 gallons.
As given in the question,
Total distance covered in family trip is 45 miles
Total fuel in car is seven gallons
Average of the on trip=22 miles per gallon
Estimate fuel supply for trip =(45 miles )/(22 miles per gallon)
=2.04545gallons
≈2gallons(approximately)
As the fuel used in the trip is 2.04545.. gallons which is nearest to the 2 gallons, it is okay to estimate the fuel supply.
Therefore, trip of 45 miles with 7gallons of gas in a car with average 22 miles per gallon ,estimate fuel supply for trip is 2 gallons.
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A line that includes the points (c, -10) and (-8,-8) has a slope of -1/8 what is the value of c
Answer:
gradient= y2-y1/x2-x1
-8+10/-8-c=-1/8
2/-8-c=-1/8
-1(-8-c)=8(2)
8+c=16
c=16-8
c=8
equation. h(x) = x - 11
Answer:
6
Step-by-step explanation:
Let the required input be y.
[tex]h(y)=y-11=-5 \\ \\ y=6[/tex]
What is the right answer
No solution is the answer of inequality.
What is inequality
The relationship between two values in an imbalanced algebraic statement is represented by an inequality in mathematics. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality. Make use of the following steps to solve an inequality: Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the integers on the other by adding or subtracting quantities.
Given Data
[tex]\frac{4}{3}[/tex]g - 3< g + [tex]\frac{2}{3}[/tex] - [tex]\frac{1}{3}[/tex]g
([tex]\frac{4}{3}[/tex]g - g) + [tex]\frac{1}{3}[/tex]g <( [tex]\frac{2}{3}[/tex] + 3)
Taking LCM,
[tex]\frac{4e+3e+1e}{3}[/tex] < [tex]\frac{2+9}{3}[/tex]
8g < 11
g < [tex]\frac{11}{8}[/tex]
No solution is the answer of inequality.
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The angle of elevation of the top of the building at a distance of 50 Marin it’s foot on a horizontal plane is found to be 60.Find the height of the building
Answer:
If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?
Step-by-step explanation:
Reflect point M across the axis
Answer:
coordinates (-4,6)
Answer:
C the answer is v
Step-by-step explanation:
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Last year, Ken bought a mountain bike for $400. It is now worth $320. What percent
did the value of Ken's bike depreciate over the past year, to the nearest whole
percent?
The percent by which the value of Ken's bike depreciated over the past year is 20%.
What is the percentage deprecation?
Depreciation is the decline in the value of an asset with the passage of time. Depreciation is as a result of wear and tear of an asset. The price of an item would decline when it depreciates.
Percentage is the fraction of an amount that is expressed as a number out of hundred. Percentage is used to measure the frequency of data. The sign that represents percentage is %. To convert a number to percentage, multiply the number by 100.
Percent depreciation = (value of the mountain bike today / value of the mountain bike last year) - 1
($320 / $400) - 1 = -0.20
0.20 x 100 = 20%
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A table showing Rate in kilometers per hour, Time in hours, and Distance in kilometers. The first row shows, Trip 1, and has 40, 0.9 minus x, and 40 left-parenthesis 0.9 minus x right-parenthesis.
Talia took the bus from her home to the bank and then walked back to her home along the same route. The bus traveled at an average speed of 40 km/h and she walked at an average speed of 5 km/h. To determine the time, x, that it took Talia to walk home, she used the equation
40(0.9 – x) = 5x.
The time of Trip 2 is
hours.
The distance of Trip 1 is
km.
Answer:The time of Trip 2 is
⇒ 0.8 hours.
The distance of Trip 1 is
⇒ 4 km.
The time of Trip 2 is 0.8 hours
The distance of trip 1 is 32 km
Given,
The speed of the bus = 40 km/h
Talia's walked at a speed = 5 km/h
To determine the time,x for her walk here used the equation; 40(0.9 – x) = 5x.
We have to find the time from Talia's home to bank in bus and the distance.
Here,
Equation is already given, we can simplify it and get x which is the time.
40(0.9 – x) = 5x.
36 - 40x = 5x
36 = 40x + 5x
36 = 45x
x = 36/45
x = 0.8 hours = 0.8 x 60 = 48 minutes
Now,
Distance from Talia's home to bank;
Speed = distance/time
Distance = speed x time = 40 x 0.8 = 32 km
That is,
The time of Trip 2 is 0.8 hours
The distance of trip 1 is 32 km
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a new test has been developed to determine whether a given student is overstressed. this test is 95% accurate if the student is not overstressed, but only 85% accurate if the student is in fact overstressed. it is known that 99.5% of all students are overstressed. given that a particular student tests negative for stress, what is the probability that the test results are correct, and that this student is not overstressed?
The probability that the test results are correct, and that this student is not overstressed is mathematically given as
3.08%
This is further explained below.
What is probability?Generally,
Let A: student is overstressed
B: The test is positive. Given
[tex]P(\bar{B} / \bar{A})=0.95, P(B / A)\\P(\bar{B} / \bar{A}) =0.85, P(A)\\P(\bar{B} / \bar{A})=0.995, \\[/tex]
[tex]P\left(\frac{\text { correctresult }}{\text { Test negative }})=P(\bar{A} / \bar{B}) \\\\ =\frac{P(\bar{A} \cap \bar{B})}{P(\bar{B})} \\\\ =\frac{P(\bar{A} \cap \bar{B})}{P(\bar{A} \cap \bar{B})+P(A \cap \bar{B})}\right.[/tex]
[tex]=\frac{P(\bar{B} / \bar{A}) P(\bar{A})}{P(\bar{B} / \bar{A}) P(\bar{A})+P(\bar{B} / \bar{A}) P(A)} \\\\=\frac{0.95 \times 0.005}{0.95 \times 0.005+0.15 \times 0.995} \\[/tex]
=0.0308
=3.08%
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A cube is being compacted. Given that the volume decreases at a rate of 2 cubic meters per minute, find the rate of change of an edge of the cube when the volume is exactly 27 cubic meters.
The rate of change of an edge of the cube is 0.074 m/min.
What is the rate of change of volume of cube?The rate at which the volume of the cube changes is calculated as follows;
dv/dt = 2 m³/min
where;
v is the volume of the cubeThe length of edge of the cube will be denoted with a, and it is related to the volume of cube in the following equation.
v = a³
a = v^¹/₃
where;
a is the length of the edgeThe change in the edge with volume;
da/dv = 1/3 (1/v)^2/3
The change in edge of the cube with time is given as;
da/dt = da/dv . dv/dt
da/dt = 1/3 (1/v)^2/3 x 2 m³/min
da/dt = 1/3 (1/27)^2/3 /m² x 2 m³/min
da/dt = 1/27 x 2 m/min
da/dt = 2/27 m/min
da/dt = 0.074 m/min
Thus, the rate at which the edge of the cube changes with time is smaller compared to the volume.
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