Answer:
x ≈ 1.987
Step-by-step explanation:
You want x = side 'a' of triangle ABC with A=35°, C=85°, and b=3 units.
Law of sinesThe law of sines tells you side lengths are proportional to the sine of the opposite angle. To find x (side 'a'), we need to know a side and an its opposite angle.
Only one side is give, but the opposite angle is not. Its value is ...
B = 180° -A -C = 180° -35° -85°
B = 60°
Now we know ...
a/sin(A) = b/sin(B)
x = sin(35°)·3/sin(60°) ≈ 1.986927
Side x is about 1.987 units.
Given STUV is a square, with SI = 2x + 13 and WU =
8.2 - 41, find x.
S
I
x=
x = 9
all sides in a square is similar.solve:
2(x) + 13 = 8(x) - 412(x) - 8(x) = -41 -13-6(x) = -54x = 9Diagonals bisect eachother
\(\\ \rm\Rrightarrow 2x+13=8x-41\)
\(\\ \rm\Rrightarrow 6x=54\)
\(\\ \rm\Rrightarrow x=54/6\)
\(\\ \rm\Rrightarrow x=9\)
Rhonda just got promoted in her job as a physical therapy assistant. She will now earn $20.70 per hour. This is 115% of her hourly salary before her promotion. What was her hourly salary before her promotion?
As a result, Rhonda was paid $18 per hour before to being promoted; nevertheless, she will now be paid $20.70 per hour.
what is unitary method ?Finding a single unit value and applying it to ratio and proportional problem solving is known as the unitary method in mathematics. It is frequently employed in order to resolve issues involving either direct proportion, inverse proportion, or both. In the unitary technique, the ratio of the quantities' corresponding unit values is used to indicate the relationship between the quantities. The desired value is then achieved by multiplying or dividing the unit value, as necessary.
given
Let x be the hourly wage Rhonda received prior to her promotion.
The issue states that her new hourly wage is equal to 115% of her previous wage:
20.70 = 1.15x
We can divide both sides by 1.15 to find x:
x = 20.70 / 1.15
x = 18
As a result, Rhonda was paid $18 per hour before to being promoted; nevertheless, she will now be paid $20.70 per hour.
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Show what a monomial expression looks like
Give me a monomial expression and solve it, step-by-step, thoroughly, show your work and explain with each step how your doing it
(New to this, thanks in advance for the extra help!!!)
Answer:
Refer to the step-by-step explanation.
Step-by-step explanation:
Come up with a monomial expression and solve it.
What is a monomial expression?A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.
Here are a few examples of an monomial expression:
5x-2xy²3a⁵7m³n²\(\hrulefill\)
Let's work with the monomial expression, 3x²y³z.
To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.
Plug these values into the expression:
3x²y³z
=> 3(3)²(2)³(1)
=> 3(9)(8)(1)
=> 27(8)(1)
=> 216(1)
=> 216
Thus, the expression is solved.
Find the slope of the line. Describe how one variable changes in relation to the other. A. 2; distance increases by 2 miles per hour B. 2; distance decreases by 2 miles per hour C. 1/2; distance increases by 1 mile every 2 hours D. 1/2; distance decreases by 1 mile every 2 hours
The line's slope is \(\frac{1}{2}\) and the distance increases by 1 mile every 2 hours.
What is a good example of a line's slope?
The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.
A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.
B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.
C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.
D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.
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If one angle of a parallelogram is 40°, what are the measures of the other angles?
The angle measures of the other angles of the parallelogram would be: 40°, 140°, and 140°.
What is a Parallelogram?A parallelogram is a quadrilateral that has two pairs of opposite sides that have the same length (congruent sides) and has two pairs of opposite angles that are congruent to each other.
Also, consecutive angles of a parallelogram are said to be supplementary to each other. That is, consecutive angles sum up to 180 degrees.
Given that one of the interior angles of a parallelogram equals 40 degrees, therefore, the angle that is opposite to 40 degrees would also be equal to 40 degrees.
The angle that is consecutive to angle 40 degrees would be: 180 - 40 = 140 degrees.
The last angle in the parallelogram which is opposite to angle 140 degrees would also be equal to 180 degrees.
Therefore, the angle measures of the other angles of the parallelogram would be: 40°, 140°, and 140°.
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(5x3)+(nx4)=5(3+4) write each missing number.
Answer:
5
Step-by-step explanation:
5 x 3 = 15
n x 4 = 4n
3 + 4 = 7
(5 x 3) + (n x 4) = 5(3 + 4)
15 + 4n = 5*7
15 + 4n = 35
4n = 35 - 15
4n = 20
n = 20/4
n = 5
Hence, the value of missing number (n) is 5.
If Janet rolls a fair 6-sided number cube 300 times, what is a reasonable prediction
on how many times she will roll a 5?
There are 50 predicted rolls for 5 in 300 times of rolls.
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Given that, Janet rolls a 6-sided number cube 300 times,
Probability = (Favourable Outcomes)/(Possible Outcomes)
Favourable Outcomes: 5 (1 total)
Possible Outcomes: 1,2,3,4,5,6 (6 total)
Probability of a 5 in any given roll of a die = 1/6
1/6x300 = 50 = 50 predicted roll with 5.
Hence, There are 50 predicted rolls for 5 in 300 times of rolls.
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what is the area of the figure
Answer:
A = 2184 cm²
Step-by-step explanation:
the area (A) of the figure is calculated as
A = \(\frac{1}{2}\) h(b₁ + b₂)
where h is the perpendicular height between the bases b₁ and b₂
here h = 42 , b₁ = 52 , b₂ = 52 , then
A = \(\frac{1}{2}\) × 42 × (52 + 52) = 21 × 104 = 2184 cm²
Answer:
A = 2184 cm2
Step-by-step explanation:
Area of a parallelogram:
\(A = b*h\)
\(b=52,h=42\)
\(A=(42)(52)=2184cm^{2}\)
Hope this helps.
HELP PLEASE!!
Quadrilateral CDEF is a rhombus. What is m
Answer:
∠ BDC = 29°
Step-by-step explanation:
the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then
∠ BCD = ∠ BED = 61°
• the diagonals are perpendicular bisectors of each other , then
∠ CBD = 90°
the sum of the 3 angles in Δ BCD = 180°
∠ BDC + ∠ CBD + ∠ BCD = 180°
∠ BDC + 90° + 61° = 180°
∠ BDC + 151° = 180° ( subtract 151° from both sides )
∠ BDC = 29°
In the following exercises, simplify.
Answer:
2.625
Step-by-step explanation:
If it is supposed to be answered in fractional form convert into a fraction then simplify, but this is decimal.
HURRY!!!!!!!!!!!!!!!
The table shows the proportional relationship between the number of tickets required per game at a carnival. Games 4 7 10 Tickets 20 35 50 Determine the constant of proportionality.
Correct answer will get brainiest
Answer:
Therefore, the constant of proportionality for the given proportional relationship is 5.
Step-by-step explanation:
To determine the constant of proportionality in the given proportional relationship, we can use the formula:
Constant of Proportionality = Tickets / Games
Let's plug in the values from the table:
For the first set of values (4 games and 20 tickets):
Constant of Proportionality = 20 / 4 = 5
For the second set of values (7 games and 35 tickets):
Constant of Proportionality = 35 / 7 = 5
For the third set of values (10 games and 50 tickets):
Constant of Proportionality = 50 / 10 = 5
In all three cases, the constant of proportionality is equal to 5.
Therefore, the constant of proportionality for the given proportional relationship is 5.
3 less than a number his -12.
Answer:
-9
Step-by-step explanation:
Cellular phone usage grew about 22% each year from 1995 (about 34 million) to 2003. Write a function to model cellular phone usage over that time period. What is the cellular usage in 2003?
Answer:
Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:
`y = a * b^(x - h) + k`
where:
- `y` is the quantity you're interested in (cell phone usage),
- `a` is the initial quantity (34 million in 1995),
- `b` is the growth factor (1.22, representing 22% growth per year),
- `x` is the time (the year),
- `h` is the time at which the initial quantity `a` is given (1995), and
- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).
So, our specific model becomes:
`y = 34 * 1.22^(x - 1995)`
To find the cellular usage in 2003, we plug 2003 in for x:
`y = 34 * 1.22^(2003 - 1995)`
Calculating this out will give us the cellular usage in 2003.
Let's calculate this:
`y = 34 * 1.22^(2003 - 1995)`
So,
`y = 34 * 1.22^8`
Calculating the above expression gives us:
`y ≈ 97.97` million.
So, the cellular phone usage in 2003, according to this model, is approximately 98 million.
Select all that apply.
Choose all the metric units of length.
millimeter
kilometer
kilogram
mile
meter
centimeter
inch
liter
Answer:
a,b,c,e,h
Step-by-step explanation:
Answer:
millimeters, centimeters, meters, and kilometers
Step-by-step explanation:
These are the metric units that measure length. The question throws you off and answers that are metric that measure weight as well but the question asks for metric that measures length.
A Father is three times as old as his son. Five years later he will be only 2 ½ times older than his son: Find their present age
Answer: the present age of son is 15 years, and the present age of father is 45 years.
Step-by-step explanation:
Let the age of son be 'x' and that of his father be 'y'.
So according to the question, the 1st equation that can be formed will be:
y = 3(x) ->(1)
[as father's age is 3 times the age of son]
Now after 5 years:
Age of son = (x+5)
Age of father = (y+5)
So according to the question, the 2nd equation that can be formed will be:
(y+5) = 2.5×(x+5) ->(2)
[as father is now two and half times old as his son]
Substituting the value of equation (1) in (2), we get:
(3x+5) = 2.5×(x+5)
=> 3x + 5 = 2.5x + 12.5
=> 3x - 2.5x = 12.5 - 5
=> 0.5x = 7.5
=> x = 7.5/0.5 = 15
Thus, the present age of son is 15 years.
Note : we can calculate the age of father by putting the value of x in equation (1) or (2):
y = 3(x) = 3 × 15 = 45 (putting x in equation 1)
Thus, the present age of father is 45 years.
Please help
what is the measure in degrees of the highlighted ( the middle one) angle
Answer:
8x+7x+44.4=180
15x=180-44.4
15x =135.6
X=9.04
8x=9.04×8=72.32
Plz help me well mark brainliest if correct!!...
Answer:C
Step-by-step explanation:
Extinct species tend to be fully gone or not seen in the wild for quite some time endangered would be a better answer for A
Hope this helps
2. The sprinklers run 5 hours each day. The monthly (30 days) water bill is $500. How much
does it cost to run the sprinklers for an hour? Round your answer to the nearest cent.
6RI2
Answer:
$3.33 (rounded) per hour
Step-by-step explanation:
The sprinklers run 5 hours each day. The monthly (30 days) water bill is $500. How much does it cost to run the sprinklers for an hour? Round your answer to the nearest cent.
hours run per month = daily hours × days in month
hours run per month = 5 × 30
hours run per month = 150
if the total bill was $500 for 150 hours then:
$500 ÷ 150 = $3.33 (rounded) per hour.
some students have a goal of collecting 200 leaves for a science project. what does the 0% mean in this situation?what does 100% mean
0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves.
Why is percentage important?In mathematics, a percentage is a quantity or a ratio that is expressed as a fraction of 100. Calculating a percentage involves multiplying a quantity by 100 and dividing it by the total.
To determine "how much" or "how many," utilise the percentage. Calculating the precise quantity or figure that is being discussed is made easier with the use of a percentage. We compare fractions. determining a percentage rise or fall aids in calculating profit and loss margins.
In this case, 0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves for the project.
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which of the following functions grows fastest? group of answer choices n log n n log n n / log n n - log n n log n
In the following option n log n seems to grow the fastest amongst all according to the size of inputs.
In computer science and mathematics, the running time or complexity of an algorithm is often measured in terms of the size of the input, usually denoted by n. The notation O(f(n)) is used to describe the upper bound on the running time of an algorithm, where f(n) is a function of n.
In the context of comparing growth rates of functions, we usually only consider the highest-degree term of the function. For example, we would say that f(n) = n^2 + n grows as O(n^2), because n^2 grows much faster than n and dominates the running time as n grows larger.
Now, let's consider the functions n, n / log n, n - log n, n log n, and n^2. As n grows, each of these functions grows at a different rate.
1. n grows linearly with n, so it takes more time as the size of the input grows.
2. n / log n grows faster than n, but slower than n log n. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n / log n grows faster.
3. n - log n grows slower than n and n / log n, because log n grows much slower than n, so as n grows larger, n - log n becomes closer to n.
4. n log n grows faster than n, n / log n, and n - log n, but slower than n^2. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n log n grows faster.
5.n^2 grows much faster than n, n / log n, n - log n, and n log n, so as n grows larger, n^2 becomes much larger than any of these functions.
So, of the options given, n log n grows the fastest, meaning that an algorithm that takes time proportional to n log n will become slower faster as the size of the input grows than an algorithm that takes time proportional to n, n / log n, or n - log n.
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If you are given an equilateral triangle, how many lines of symmetry does it have?
Lines of simetry of a triangle
are lines that divide figure in 2
An equilateral triangle have
3 LINES OF SYMETRY
PROOF
The Miller family is taking a road trip to visit some relatives. With a full gas tank, the car has a range of 456 miles. Mr. Miller wants to stop to fill up when the range reaches 57 miles remaining. If the car averages 28.5 miles per gallon, then the equation 456 - 28.5g represents how many gallons of gas they will use before they need to fill up. How many gallons of gas will they use before they need to fill up? 57
Answer:
14 gallons
Step-by-step explanation:
456 - 28.5g = 5
28.5g =399
G=14
Given the equation x(x - 1)²(x + 5)³, the degree is
07
0 3
05
6
Answer:
Dear Friend
the answer is 6
Step-by-step explanation:
Just see the highest possible degree x in each term being multiplied and add the degree
that is
x has a degree 1
(x-1)² has a highest possible x degree as 2
for (x+5)³ it is 3
1+2+3=6
If using the method of completing the square to solve the quadratic equation
x2 + 3x +9 = 0, which number would have to be added to "complete the square"?
Answer:
0.555
Step-by-step explanation:
you simply follow the linear equation rule and fill in
An increase from $27 to $35.10 what percent of increase?
Answer:
30% increase
Step-by-step explanation:
percentage increase is calculated as
\(\frac{increase}{original}\) × 100%
increase = $35.10 - $27 = $8.10 , then
percentage increase = \(\frac{8.10}{27}\) × 100% = 0.3 × 100% = 30%
Answer:
Step-by-step explanation:
step 1: 35.10-27 =8.1
step 2: 8.1/27 x 100 = 30%
so therefore = 30% increase
A cell culture currently contains 4 thousand cells, and is growing at a rate of r (t) = 8e^0.18t thousand cells per hour, where t is the number of hours since now. Find the total cell count after 3 hours. Give your answer accurate to at least 2 decimal places.
Answer:
20.00 thousand cell
Step-by-step explanation:
The problem can be solved using integration
\(\begin{aligned} r &=4+\int_{0}^{3} 8 e^{0.18 t} d t \\ &=4+3 \cdot\left[\frac{e^{0.18t}}{0.18}\right]_{0}^{3} \\ &=4+\frac{3}{0.18}\left(e^{0.18(3)}-e^{0.18(0)}\right) \\ &=19.9996 \end{aligned}\)
\(\approx 20.00\) thousand cells
the correct answer upto 2 decimal place.
Use the remainder theorem to find P(-3) for P(x) = 2x° +5x² +5.
Specifically, give the quotient and the remainder for the associated division and the value of P(-3).
on a piece of paper graph y=-2x^2+10x-12 and identify the zeros. Select the choice that matches the graph that you drew and correctly identifies the zeros
Answer:
C. 2 and 3 opens down
Step-by-step explanation:
see graph
What is the perimeter of the triangle?
Answer:
this triangle is a acute angel so it 3
What percent of the front page is taken up by the
prom story, including the prom photograph?
A. 20%
B. 22%
C. 25%
D. 45%
E. 60%
The percent of the front page taken up by the prom story is 20%
Calculating the percent of the front page taken up by the prom storyFrom the question, we have the following parameters that can be used in our computation:
The front page
From the front page, we have
Area front page = 5 * 4
Area front page = 20
Also, we have
Prom = 2 * 2
Prom = 4
So, we have
Percentage = 4/20 * 100%
Evaluate
Percentage = 20%
Hence, the percent of the front page taken up by the prom story is 20%
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