The length of the remaining sides is a = 57.50 and b = 61.93.
What are the laws of sines?The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.
The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle.
Given a triangle ABC, and ∠B = 90°
∠A = 68.2° and c = 23.0
so ∠C = 90 - ∠A
∠C = 90 - 68.2
∠C = 21.8°
according to the law of sines,
sinA/a = sinB/b = sinC/c
for a,
sinA/a = sinC/c
substitute the values
sin(68.2)/a = sin(21.8)/c
a = 23(sin68.2)/(sin21.8)
a = 57.50
and for b,
sinB/b = sinC/c
substitute the values
b = csinB/sinC
b = 23(sin90/sin21.8)
b = 61.93
Hence a = 57.50 and b = 61.93.
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Which equation represents the graph? a graph of a line that passes through the points 0 comma negative 3 and 4 comma negative 1 y equals negative one half times x plus 6 y equals one half times x minus 3 y = 2x − 3 y = −2x + 6
the equation of line passes through points (0, -3) and (4, -1) is 4y = 3x -12.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, an equation of a line in the graph.
Since the graph shows that the line passes through points (0, -3) and (4, -1).
The slope-intercept form of the equation of a line
y=mx+b,
where m is the slope
b is the y-intercept (value of y at x =0)
since
slope = (y - y')/(x -x')
In our case,
slope (m) = (-1 - (-3))/(4 -0)
m = 3/4
b = -3
Thus, the equation of the line:
y = 3/4x - 3
or, 4y = 3x -12
therefore, the equation of the line will be 4y = 3x -12.
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Describe how the graph of the function is a transformation of the original function f.
y=f(x+16)
The graph of the function y = f(x + 16) is a transformation of the original function f. This transformation has shifted the graph of f to the right by 16 units on the x-axis. This means that the value of x in the original function has been increased by 16, which has an effect on the corresponding value of y in the transformed function.
For example, if the point (a, b) is on the graph of f, then the point (a + 16, b) will be on the graph of y = f(x + 16). The x-coordinate of the point has been increased by 16, and since the transformation is a horizontal shift, the y-coordinate remains unchanged.
In summary, the graph of y = f(x + 16) is a reflection of the graph of f about the vertical axis. The transformation has the effect of shifting the graph to the right, but preserving the shape and overall form of the original function.
A solution contains furosemide (frusemide) 10 mg/mL. How many milligrams of frusemide are in 3 mL of solution?
Answer:
30mg
Step-by-step explanation:
10 mg/mL x 3 mL
13, 11, 9, 7 In the number pattern above, each term is 2 less than the previous term. Which of the following is also true about the pattern?
A. All the numbers are multiples of 3.
B. All the numbers are even.
C. All of the numbers are prime.
D. All the numbers are odd.
HURRY ITS DUE TODAY
The truth about the pattern that we have here is that all of the numbers are: odd.
What are odd numbers?In the number pattern given, each term is 2 less than the previous term. Starting from 13, we have 11 (13 - 2), 9 (11 - 2), and 7 (9 - 2). All of these numbers are odd, making answer D the correct choice.
A. All the numbers are multiples of 3: This is not true, as 9 is the only number that is a multiple of 3.
B. All the numbers are even: This is not true, as all of the numbers are odd.
C. All of the numbers are prime: This is not true, as 9 is not a prime number.
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What is the value of x in the triangle?
Answer: D. [tex]5\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\tan 30^{\circ}=\frac{x}{15}\\\\x=15 \tan 30^{\circ}\\\\x=5\sqrt{3}[/tex]
A cylinder has a volume of 243 pi
and a diameter of 18. What is its height?
Answer:
0.955
Step-by-step explanation:
Height= volume x pi x radius squared (h = V x pi x r^2)
Volume (V) = 243
Height (h) = ?
Pi = 3.14
Radius (r) = 9
Diameter to radius = 18/2 = 9
h = 243 x 3.14 x 9^2
=0.955
What is the difference in rainfall from the wettest and driest months ?
The difference in rainfall between the wettest and driest months is the amount of precipitation.
What do you mean by precipitation?Precipitation refers to any form of moisture that falls from the atmosphere to the ground, including rain, snow, sleet, hail, and other forms of precipitation. Precipitation is an important aspect of the Earth's water cycle, as it provides the water that replenishes rivers, lakes, and aquifers, and sustains the growth of plants and animals.
The amount of precipitation that falls in a given area can vary widely, depending on many factors such as geography, temperature, and prevailing weather patterns. For example, areas near the equator tend to receive more rainfall than areas located closer to the poles, and areas with high elevations tend to receive more snow than areas that are closer to sea level.
The distribution of rainfall and other forms of precipitation across a region can also be affected by the prevailing winds, air masses, and topographical features. For example, mountainous areas may receive more rainfall due to the prevailing winds and the way that air masses interact with the terrain.
The difference in rainfall between the wettest and driest months is the amount of precipitation that occurs in the wettest month minus the amount of precipitation that occurs in the driest month. This difference can vary greatly depending on the location and climate of a region.
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A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts
down the slope, its speed is 4 m/s. 3 seconds later, at the bottom of the slope,
its speed is 22 m/s. What is the cars acceleration?
solve the given initial-value problem. Dy dx + y = f(x), y(0) = 1, where f(x) = 1, 0 ≤ x ≤ 1; -1 , x ≥ 1
The general solution of the ODE is:
y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1
y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1
How did we get the values?This is a first-order linear ordinary differential equation (ODE) with constant coefficients. It can be solved using the method of integrating factors.
Let's multiply both sides by the integrating factor e^(∫p(x)dx), where p(x) = 1.
e^(∫p(x)dx) * Dy/dx + e^(∫p(x)dx) * y = e^(∫p(x)dx) * f(x)
D/dx (e^(∫p(x)dx) * y) = e^(∫p(x)dx) * f(x)
Integrating both sides, we get:
e^(∫p(x)dx) * y = ∫ e^(∫p(x)dx) * f(x) dx + C
where C is an arbitrary constant of integration.
Using the initial condition y(0) = 1, we can find the value of the constant C.
y(0) = 1 = e^(∫p(x)dx) * y(0) = e^(∫p(x)dx) * 1 = ∫ e^(∫p(x)dx) * f(x) dx + C
So, C = 1 - ∫ e^(∫p(x)dx) * f(x) dx
For 0 ≤ x ≤ 1, we have f(x) = 1 and:
∫ e^(∫p(x)dx) * f(x) dx = ∫ e^x dx = (e^x - 1) / 1
For x ≥ 1, we have f(x) = -1 and:
∫ e^(∫p(x)dx) * f(x) dx = ∫ -e^x dx = -(e^x - 1) / 1
Therefore, the general solution of the ODE is:
y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1
y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1
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Hey guys please help me with my quiz its about finding the values of letters in angles!!
The value of x is given as follows:
x = 24.
The measure of angle DFE is given as follows:
<DFE = 62º.
How to obtain the measures?To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.
The internal angle measures for this problem are given as follows:
180 - (5x - 14) -> each angle is supplementary with it's external.44º.3x - 10.Hence the value of x is obtained as follows:
180 - 5x + 14 + 44 + 3x - 10 = 180
228 - 2x = 180
2x = 48
x = 24.
The measure of angle DFE is obtained as follows:
<DFE = 3(24) - 10
<DFE = 72 - 10
<DFE = 62º.
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HELP
_______________
The correct statements regarding the translation from function f(x) to function g(x) are given as follows:
Function f is translated down 2 units.Function f is translated to left 3 units.What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The translations for this problem are defined as follows:
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Assume the following
actual machine hours during the period of 54000 hours
estimates machine hours to be worked during the coming period of 55000 hours manufacturing overhead applied to production during the period of 432000 estimated variable manufacturing overhead per machine hour of 2.7
which is the fixed MOH cost
Based on the manufacturing overhead applied to production during the period of $432,000, the fixed manufacturing overhead cost is $286,200.
What is the manufacturing overhead applied?The manufacturing overhead applied is determined as the product of the predetermined overhead rate and the actual machine hours consumed during the period.
Estimated machine hours to be worked = 55,000 hours
Actual machine hours during the period = 54,000 hours
Total manufacturing overhead applied to production = $432,000
Estimated variable manufacturing overhead per machine hour = $2.70
Total variable manufacturing overhead = $145,800 ($2.70 x 54,000)
Fixed manufacturing overhead (MOH) cost = $286,200 ($432,000 - $145,800)
Thus, the fixed manufacturing overhead cost is the difference ($286,200) between the total overhead cost applied and the variable manufacturing overhead cost.
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2. What is the difference in rainfall from the wettest and driest months?
The difference in rainfall between the wettest and driest months is 3.97 inches.
What is a bar graph?A bar graph is a graphical depiction of information, amounts, or numbers using bars or strips. They are utilized to contrast and compare various data types, frequencies, or other measurements of several categories of data.
On the graph, there are two axes. The numerical data is displayed against the category data on one axis, which is used to depict the numerical values.
Given the graph which shows the rainfall of the wettest and driest months,
here red blocks are for the driest months and blue blocks show the wettest months,
From the graph, we can see that the wettest month has a rainfall height of 2.3 inches
The driest month has a rainfall of -1.67 inches
So the difference between the two will be;
2.3 - (-1.67)
= 2.3 + 1.67 = 3.97 inches
Hence the difference is 3.97 inches.
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The complete question is,
The bar graph shows the differences in a city’s rainfall from the historical average. What is the difference in rainfall between the wettest and the driest months? Write your answer as a decimal.
The difference in rainfall between the wettest and the driest months is inches.
What is the sum of the measures of the exterior angles of the polygon shown below? If necessary, round to the nearest tenth.
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The sum of the measures of the exterior angles of the polygon is, 360°
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
Given that,
A polygon,
Having 9 equal sides,
The sum of the measures of the exterior angles of the polygon = ?
The sum of each interior & exterior angles are 180°
Suppose, interior angles are respectively
a, b, c, d, e, f, g, h, i,
Now, exterior angles are respectively
180°-a, 180°-b, 180°-c, 180°-d, 180°-e, 180°-f, 180°-g, 180°-h, 180°-i,
The sum of the measures of the exterior angles of the polygon =
180°-a + 180°-b +180°-c +180°-d + 180°-e + 180°-f + 180°-g +180°-h + 180°-i,
1620 - (a + b + c + d + e + f + g + h + i)
Sum of all the interior angles = (9-2)x180°
= 1260°
The sum of the exterior angles of the polygon = 1620 - 1260°
= 360°
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Please use the law of sines to show me how to solve the triangle please. Thank you .
Answer:
[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\[/tex]
[tex]a=38.5[/tex] ft
[tex]b=51[/tex] ft
[tex]c=76[/tex] ft
Step-by-step explanation:
Here is the formula for the Law of Sines.
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]`
In this example we are given
[tex]\angle A =27.2 \textdegree\\\angle C=115.5 \textdegree\\c=76.0[/tex]
Angle B
The sum of the interior angles in a triangle add up to 180º. Given 2 angles, we can evaluate the 3rd.
[tex]180\textdegree-115.5\textdegree-27.2\textdegree=37.3 \textdegree[/tex]
[tex]\angle B=37.3 \textdegree[/tex]
Side a
We can use the Law of Sines formula [tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex] to evaluate side a.
Inserting our values into the equation gives us
[tex]\frac{a}{\sin 27.2}=\frac{76}{\sin 115.5}[/tex]
Cross multiply to evaluate side a.
[tex]76*\sin 27.2=a*\sin 115.5[/tex]
Divide both sides by [tex]\sin 115.5[/tex].
[tex]\frac{76*\sin 27.2}{\sin 115.5} =a[/tex]
[tex]38.49=a[/tex]
Side b
We can use the Law of Sines formula [tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex] to evaluate side b.
Inserting our values into the equation gives us
[tex]\frac{b}{\sin 37.3}=\frac{76}{\sin 115.5}[/tex]
Cross multiply to evaluate side b.
[tex]76*\sin 37.3=b*\sin 115.5[/tex]
Divide both sides by [tex]\sin 115.5[/tex].
[tex]\frac{76*\sin 37.3}{\sin 115.5} =b[/tex]
[tex]51.03=b[/tex]
[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\a=38.5\\b=51\\c=76[/tex]
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sin(A) / a = sin(B) / b = sin(C) / c
where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.
Write the phrase as an expression. a number x divided by 2
Answer: x/2
Step-by-step explanation: Good morning. I am not sure what you mean by "A number x", so I suppose that is a typo.
Answer: x/2 IS CORRECT
Step-by-step explanation:
I TRIED IT :)
Find the surface area of the sphere. Use 3.14 for pi.
A. 1519.8 yd2
B. 276.3 yd2
C. 6079.0 yd2
D. 552.6 yd2
Answer:
A
Step-by-step explanation:
please memorize this formula for area of sphere
A=4π r²
so d = 22, which means r=11
so A = 4* π*11² = 4*121*π =484π = 1519.76
ria is buying plates and cubs for a party. she wants the same numbers of each.Plates are sold in packs of 8. cups are sold in packs of 12. what is the least number of plates and cups that ria can buy
The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, ria is buying plates and cubs for a party. she wants the same numbers of each. Plates are sold in packs of 8. cups are sold in packs of 12.
Plates = 8 per pack
Cups = 12 per pack
the Lowest common multiple of 8 and 12
8 = 16, 24, 32, 40, 48, 56, 64, 72, 80
12 = 24, 36, 48, 60, 72
The Lowest common multiple of 8 and 12 is 24
The least number of plates and cups she can buy is 24
Packs of plates = 24 plates / 8 per pack
= 3 packs
She will buy 3 packs of plates
Packs of cups = 24 / 12 per pack
= 2 packs
She will buy 2 packs of cup
Therefore, The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup
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evaluate without a calculator: sec 30°
Answer:
sec 30° = 1/cos 30° = 2.
Step-by-step explanation:
The secant function (sec) is the reciprocal of the cosine function. So, sec(x) = 1/cos(x). The value of cosine at 30 degrees is sqrt(3)/2, and its reciprocal is 2/sqrt(3), which can be simplified to 2. Hence, sec(30°) = 2.
How much is invested at 5% and 7%, with annual interest is $490, with a total of $8000
The amount invensted at 5% and 7% are 3500 and 4500 respectively.
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, an amount $8000, is invested at 5% and 7%, with annual interest is $490,
For this we will establish the a system of equations,
x + y = 8000......(i)
0.05x + 0.07y = 490
Multiplying by 100,
5x + 7y = 49000.....(ii)
Multiplying eq(i) by 5,
5x + 5y = 40000
Subtract eq(i) from eq(ii)
2y = 9000
y = 4500
Put y = 4500 in eq(i)
x = 8000 - 4500
x = 3500
Hence, the amount invensted at 5% and 7% are 3500 and 4500 respectively.
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The probability that a passenger is chosen for customs inspection is 10 %. Emma and Michael go through customs. What is the probability that neither of them is chosen for inspection? The probability of one passenger being chosen is independent of that of other passengers.
a) 81 %
b) 90 %
c) 99 %
d) other
The probability that neither of them is chosen for inspection is given as follows:
a) 81 %
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 2, p = 0.1.
The probability of neither is P(X = 0), hence:
P(X = 0) = (1 - 0.1)² = 0.81.
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calculate the length of AC to 1 decvimL POINT
Answer:The length of AC to one decimal place in the trapezium is 18.1 cm
Step-by-step explanation: Using Pythagoras theorem, we can find the length AC
Pythagoras theorem
c² = a² + b²
Therefore, draw a line from the point B to the line AD and call it line BX.
BX ║ CD
Therefore,
16² - 7² = BX²
256 - 49 = BX²
BX² = 207
BX = √207
BX = 14.3874945699
BX = 14.4 cm
Therefore,
11² + 14.4² = AC²
121 + 207.36 = AC²
AC = √328.36
AC = 18.120706388
AC = 18.1 cm
A museum charges $7 per person for a guided tour with a group of 1 to 14 people or a fixed $105 fee for a group of 15 or more people. Write a function relating the number of people, n, to the cost, C.
The value of function relating the number of people, n, to the cost, C is,
⇒ C (n) = 7n ; if 0 < n < 15
= 105n ; if n ≥ 15
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
A museum charges $7 per person for a guided tour with a group of 1 to 14 people or a fixed $105 fee for a group of 15 or more people.
Hence, he value of function relating the number of people, n, to the cost, C is,
⇒ C (n) = 7n ; if 0 < n < 15
= 105n ; if n ≥ 15
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I need help ASAP!!!!!
Answer:
Nope
Step-by-step explanation:
No, because if you add the angles of B and C (since they're asking for line BC), they must equal the angles of A and D (Since the other line was AD)
The sum of B and C is 90+45 which = 135
The sum of A and D is 90+135 which = 225
135 =/= 225
Write an expression to represent:
3
33 minus the product of
2
22 and
�
xx.
The expression to represent the given statement is:33 - (2 * 22 * ½x)
The expression "33 - (2 * 22 * ½x)" represents a mathematical calculation. Breaking it down, we start with the product of 2 multiplied by 22, which equals 44. Then, we multiply the result by ½x, where ½ represents one-half and x is a variable. This gives us the term 44 * ½x. Finally, we subtract this term from 33. In simpler terms, we have 33 minus half of 44 times x. The expression allows us to compute the value of the expression based on the input for the variable x, providing a way to evaluate the equation numerically.Let's dive deeper into the explanation.
The given expression is "33 - (2 * 22 * ½x)".
To simplify it, let's break it down step by step:
The term "2 * 22" is a multiplication operation that calculates the product of 2 and 22, resulting in 44.
Next, we have "½x". Here, ½ represents one-half, or 0.5. Multiplying 0.5 by x gives us 0.5x.
Putting it together, we have the term "44 * ½x". This means multiplying 44 by 0.5x, resulting in 22x.
Finally, we subtract the term "22x" from 33, giving us the expression "33 - 22x".
In summary, the expression represents the number 33 minus the product of 22 and the value of x, denoted as 22x. This expression allows us to calculate the result by substituting a specific value for x. It provides a way to compute the numerical outcome based on the given mathematical relationship.
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Find the area of the rectangle
The area of the given rectangle will be A = 9x² - 64 yards².
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
The area of the rectangle is A = a*b
Given is l =(3x+8) yards
b = (3x-8)yards
So the area of the rectangle is A = l*b
A = (3x+8)(3x-8)
A = 3x² - 8²
A = 9x² - 64
hence the area of the given rectangle will be A = 9x² - 64 yards².
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(x+2)^2=4(x+5)+y standard form
The standard form of the equation (x + 2)² = 4 (x + 5) + y is:
x² + y - 16 = 0
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The standard form of an equation is Ax + By = c.
Now,
(x + 2)² = 4 (x + 5) + y
x² + 4x + 4 = 4x + 20 + y
x² + 4 = 20 + y
x² + y = 20 - 4
x² + y = 16
x² + y - 16 = 0
Thus,
x² + y - 16 = 0 is the standard form of an equation.
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I need this for math homework anyone on tonight to help? 5/8 = x/12 x=
x = 15/2
do u need an explanation?
What is the sum of 3 of the interior angles of a regular pentagon?
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Answer: 540°.
Step-by-step explanation:
by
Celine purchased a ball of red yarn costing $2.33. She gave the cashier $7.19. How much change did the cashier give back to Celine?
Answer:
$ 4.86
Step-by-step explanation:
Subtract 7.19 and 2.33
7.19-2.33=4.86