Find the value of a in the diagram of the right triangle. Round to the nearest tenth.
the options are
A) 21.6 in.
B) 24.2 in.
C) 5.0 in.
D) 12.3 in.
Answers
Answer:
The answer is the option B
[tex]a=24.2\ in[/tex]
Step-by-step explanation:
we know that
In the right triangle of the figure
[tex]sin(27\°)=\frac{11}{a}[/tex]
Solve for a
[tex]a=\frac{11}{sin(27\°)}[/tex]
[tex]a=24.2\ in[/tex]
Related Questions
What is the sum of square root -2 and squareroot -18
Answers
1.414i + 4.234i = 5.657i
The 'i' is included because the sqrt of a negative number is imaginary.
The sum of the square roots of -2 and -18 is [tex]\( 4\sqrt{2}i \)[/tex], where i is the imaginary unit.
The sum of the square roots of -2 and -18 involves complex numbers because both -2 and -18 are negative.
The square root of a negative number is not a real number, but it can be expressed using imaginary units.
The square root of -2 can be represented as [tex]\( \sqrt{-2} = \sqrt{2}i \),[/tex] where i is the imaginary unit, defined as [tex]\( i = \sqrt{-1} \).[/tex]
Similarly, the square root of -18 can be written as [tex]\( \sqrt{-18} = \sqrt{18}i \).[/tex]
Now, to find the sum of these square roots:
[tex]\[ \sqrt{-2} + \sqrt{-18} = \sqrt{2}i + \sqrt{18}i \][/tex]
[tex]\[ = \sqrt{2}i + \sqrt{2 \times 9}i \][/tex]
[tex]\[ = \sqrt{2}i + 3\sqrt{2}i \]\\\\ = (\sqrt{2} + 3\sqrt{2})i \][/tex]
[tex]\[ = 4\sqrt{2}i \][/tex]
So, the sum of[tex]\( \sqrt{-2} \) and \( \sqrt{-18} \)[/tex] is [tex]\( 4\sqrt{2}i \).[/tex]
Solve the system by the elimination method. Check your work. 2a + 3b = 6 5a + 2b - 4 = 0
Answers
2a + 3b = 6
5a + 2b - 4 = 0
multiply thru the top equation by 2
Multiply thru the bottom equation by 3
4a + 6b = 12
15a+ 6b = 12
Subtract and solve for "a":
11a = 0
a = 0
Solve for "b" using 2a + 3b = 6
2*0 + 3b = 6
b = 2
Answer:
Step-by-step explanation:
a=0
b=2
answer (0,2)
Estimate the volume of material in a cylindrical shell with height 30 in., radius 2 in., and shell thickness 0.5 in.
Answers
Ray is 2 inch taller than Lin, and Ray is 3 inch taller than Sam. What is the average height of ray, Lin and Sam? The median height of Ray, Lin and Sam?
Answers
r - Ray's height
l - Lin's height
s - Sam's height
Ray is 2 inch taller than Lin: r = l + 2 ⇒ l = r - 2
Ray is 3 inch taller than Sam: r = s + 3 ⇒ s = r - 3
The average is the sum of all values divided by the number of values:
[tex]A= \frac{r + l + s}{3} [/tex]
Since l = r - 2 and s = r - 3, then:
[tex]A= \frac{r + (r-2) + (r-3)}{3} = \frac{r+r-2+r-3}{3} = \frac{3r-5}{3} = \frac{3r}{3} - \frac{5}{3} =r-\frac{5}{3}[/tex]
The median means the middle value. Let's first rearrange values so we can find the middle one:
Ray is taller than Lin and Sam, so Ray is the tallest.
Sam is much shorter than Ray comparing to Lin, so Sam is the shortest.
Therefore, values are from the lowest to the highest:
(s, l, r)
⇒ (r-3, r-2, r)
Median of these values is in the middle, so the median height is r-2.
What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5?
Answers
f(x) = 5(2)^x
f(1) = 5(2)^1
f(1) = 10
So the point (1,10) is on this curve
Do the same for x = 5
f(x) = 5(2)^x
f(5) = 5(2)^5
f(5) = 160
The point (5,160) is also on the curve
Use the slope formula now
m = (y2-y1)/(x2-x1)
m = (160-10)/(5-1)
m = 150/4
m = 37.5
The average rate of change is 37.5
If two angles of a triangle measure 43 degrees and 48 degrees the triangle is
Answers
The third angle for the triangle is equal to 89°.
What is geometry?Geometry is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a geometer.
A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C.
Given that the two angles of a triangle measure 43 degrees and 48 degrees. the value of the third angle will be calculated as,
Third angle = 180 - 43 - 48
Third angle = 89°
The complete question is given below.
If two angles of a triangle measure 43 degrees and 48 degrees what is the third angle of the triangle?
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100 plus the product of a number and -2 equals 50 What is the number?
Answers
100 + (-2 * x ) = 50
100-2x = 50
2x = 100-50
x = 50/2
x= 25
So, your final answer is 25
Hope this helps!
What is 7.58E8 expressed in standard notation?
Answers
how many solutions are there to this equation?
9x - 16 = 9x - 23
a. infinitely many
b. 0
c. 1
Answers
Answer: the correct option is
(b) 0.
Step-by-step explanation: We are given to find the number of solutions for the following linear equation :
[tex]9x-16=9x-23~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the number of solutions of the given equation, we must try to solve the equation and find the value of x.
From equation (i), we have
[tex]9x-16=9x-23\\\\\Rightarrow 9x-9x=-23+16\\\\\Rightarrow 0=-7,[/tex]
which can never be possible.
Thus, the given equation has NO solution.
Option (b) is CORRECT.
Kayla notices that she can buy snacks and candy in bulk at the grocery store. The snacks she wants to buy cost $1.29 per kilogram.
Answers
Leslie can determine which option will give her more yogurt by comparing the weights of the two options.
Explanation:To determine which option will give Leslie more yogurt, she needs to compare the weights of the two options. First, she needs to convert the weight of the first option from pounds to ounces. Since 1 pound is equal to 16 ounces, the 2 pound container is equal to 32 ounces. Next, she can compare the weights of the two options. The first option is 32 ounces and the second option is 5 containers of 6 ounces each, which is a total of 30 ounces. Therefore, the first option will give Leslie more yogurt.
round 624 to the nearest hundred
Answers
A number decreased by 10 is greater than -5.
How can I write this in an inequality?
Answers
simplified:
x>5
Which expression is equaivalent to mn+z
nm+n
z+mz
mz+n
z+nm
Answers
Answer:
D. z+nm
Step-by-step explanation:
Equaivalent to mn+z: Just switch the letters around and you get z+nm
For any positive number b not equal to 1 and any number or variable n, evaluate the following expression.
logb(b^n) =
with logb being the base
Answers
If: [tex]log_x(y^{z}) = z*log_x(y) [/tex]
Then: [tex]log_b( b^{n}) = n*log_b(b) [/tex]
If: [tex]log_x(y) = \frac{log_z(y)}{log_z(x)} [/tex]
Then: [tex]log_b(b) = \frac{log_z(b)}{log_z(b)} =1[/tex]
Therefore:
[tex]log_b( b^{n}) = n*log_b(b) =n*1=n[/tex]
Answer:
[tex]log_{b} b^{n}[/tex] = n.
Step-by-step explanation:
Given : [tex]log_{b} b^{n}[/tex] , b is any positive number not equal to 1 and n is any number.
To find : Evaluate the expression [tex]log_{b} b^{n}[/tex].
Formula used : [tex]log_{b} x^{y}[/tex]. = y ∙ [tex]log_{b}[/tex](x) and
[tex]log_{b}(b) = 1.
Solution : We have [tex]log_{b} b^{n}[/tex].
By logarithm rule : [tex]log_{b} x^{y}[/tex]. = y ∙ [tex]log_{b}[/tex](x).
Then [tex]log_{b} b^{n}[/tex] = n∙ [tex]log_{b}[/tex](b).
By logarithm rule : [tex]log_{b}(b) = 1.
Now, n∙ [tex]log_{b}[/tex](b) = n.
Therefore, [tex]log_{b} b^{n}[/tex] = n.
What is the median distance jumped 7.48, 7.60, 7.15, 7.44, 7.73, 7.72
Answers
out of a swarm of bees one fifth part settled on a kadamba blossom; one third on a silihindra flower; three times the difference of those numbers flew to the bloom of a kutaja. one bee, which remained, hovered about in the air. tell me, charming woman, the number of bees
Answers
let x be the # of bees in the swarm, then
[tex]\frac{x}{5}+\frac{x}{3}+3(\frac{x}{3}-\frac{x}{5})+1=x[/tex]
multiply across by 15
[tex]3x+5x+3(5x-3x)+15=15x[/tex]
[tex]8x+3(2x)+15=15x[/tex]
[tex]8x+6x+15=15x[/tex]
[tex]14x+15=15x[/tex]
[tex]15=x\leftrightarrow x=15[/tex]
Water is pumped out of a holding tank at a rate of 6-6e^-0.13t liters/minute, where t is in minutes since the pump is started. If the holding tank contains 1000 liters of water when the pump is started, how much water does it hold one hour later?
Answers
1) Integrate the function, from t =0 to t = 60 minutues to obtain the number of liters pumped out in the entire interval, and
2) Substract the result from the initial content of the tank (1000 liters).
Hands on:
Integral of (6 - 6e^-0.13t) dt ]from t =0 to t = 60 min =
= 6t + 6 e^-0.13t / 0.13 = 6t + 46.1538 e^-0.13t ] from t =0 to t = 60 min =
6*60 + 46.1538 e^(-0.13*60) - 0 - 46.1538 = 360 + 0.01891 - 46.1538 = 313.865 liters
2) 1000 liters - 313.865 liters = 613.135 liters
Answer: 613.135 liters
Expression as a decimal number 6x0.1 6x0.01 1x0.001
Answers
Final answer:
To express the given multiplications as decimal numbers: 6 times 0.1 equals 0.6, 6 times 0.01 equals 0.06, and 1 times 0.001 equals 0.001. Moving the decimal point due to multiplication by powers of 10 is the underlying concept.
Explanation:
The student's question involves expressing multiplications involving decimals in decimal form. To convert each term:
6 x 0.1 is moving the decimal point one place to the left in the number 6, which results in 0.6.6 x 0.01 is moving the decimal point two places to the left in the number 6, giving 0.06.1 x 0.001 is moving the decimal point three places to the left in the number 1, resulting in 0.001.When numbers are multiplied by powers of 10, the decimal point is shifted to the right for positive exponents and to the left for negative exponents. Scientific notation is often used for this purpose.
Here are examples demonstrating the use of scientific notation:
0.006 can be expressed as 6 x 10-3 (moving the decimal point three places to the left).0.0000045 becomes 4.5 x 10-6 (the decimal point moves six places to the left).Negative exponents indicate the decimal point moves to the left, whereas positive exponents indicate it moves to the right. For instance, 2.4 x 10-2 is equivalent to 0.024 as the decimal has moved two places to the left.
To solve a three-variable system of equations, you can use a combination of the elimination and substitution mehtods.
True or False ...?
Answers
This is the best way to solve these kinds of equations, as you get rid of the unnecessary variables.
Final answer:
True, a combination of the elimination and substitution methods can solve a three-variable system of equations.
Explanation:
The statement is True. We can use a combination of the elimination and substitution methods to solve a three-variable system of equations. In the elimination method, we aim to eliminate one variable by adding or subtracting the equations, allowing us to solve for the remaining variables. This method works well when the coefficients of one variable are opposites in two equations.
In the substitution method, we solve one equation for one variable and substitute this expression into the other equations. This allows us to solve for the remaining variables. This method is more straightforward when one equation can be easily solved for one variable.
When sam breathes in, his chest expands, causing air to fill his lungs. which structure causes his chest to expand?
Answers
If xy^2 = 20, and x is decreasing at the rate of 3 units per second, the rate at which y is changing when y = 2 is nearest to?
Answers
[y^2]' = [20/x]'
2y [dy/dt] = [-20/x^2] [dx/dt]
dy/dt = [-10/yx^2] [dx/dt]
[dx/dt] = - 3 u/s ....(the negative sign was included to account for decreasing)
y = 2 => x(2)^2 = 20 => x = 20/4 = 5
dy/dt = [-10/(2*5^2)] [- 3]
dy/dt = [-1/5][- 3] = 3/5
Answer: dy/dt = 3/5 units/s
Write an equation of the direct variation that includes the point (9, –12).
(A.) y = 1 1/3x (B.) y = - 1/12x (C.) y = 1 1/3x (D.) -3/4x ...?
Answers
The equation of direct variation for the point (9, -12) would be y = -1 1/3x. The constant of variation, 'k', is found by dividing 'y' by 'x'. Therefore, 'k' is -12/9, which simplifies to -1 1/3.
Explanation:In a direct variation, the equation can be represented in the form y = kx, where 'k' is the constant of variation. Here, 'k' can be found by dividing 'y' by 'x'. So, in the given point (9, -12), 'k' would be -12/9, which simplifies to -4/3 or -1 1/3. Therefore, the equation of the direct variation that includes the point (9, -12) would be y = -1 1/3x. The provided options don't include this equation, so it might be a mistake in the question options. Remember, the correct equation should always have 'y' and 'x' directly vary, and 'k' have the same sign as the given 'y' value.
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Your iron works has been contracted to design and build a 500-ft3 square-based, open-top, rectangular steel holding tank for a paper company. The tank is to be made by welding half-inch-thick stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible. What dimensions do you tell the shop to use?
Answers
To minimize the weight of the tank, the base length should be (4/3) times the height. The height should be (3/4)^(1/4) times the fourth root of (2V/π).
Explanation:To find the dimensions that will make the tank weight as little as possible, we need to consider the volume and weight of the tank. Since the tank is square-based, the volume can be calculated by V = bh^2, where b is the length of one side of the base and h is the height.
The weight of the tank can be calculated by multiplying the volume by the density of the stainless steel. W = V * density. Since we want to minimize the weight, we want to minimize the volume.
To do this, we can differentiate the volume equation with respect to b and set it equal to zero. Solving for b, we find that b = (4/3) * h. Substituting this value into the volume equation gives: V = (4/3) * h^3.
To further minimize the volume, we can take the derivative of the volume equation with respect to h and set it equal to zero. Solving for h, we find that h = (3/4)^(1/4) * (2V/π)^(1/4).
appleseed a tech company spends a fixed cost of $1500 to manufacture the wristbands for their new appleseed watch plus $100 per unit manufactured solution
Answers
The y-intercept is 1500. It represents the fixed cost to manufacture the wristbands.
a. The slope is 100. It shows the cost per wristband.
b. The y-intercept is 1500. It shows the fixed cost for manufacturing the wristbands.
Given that,
The fixed cost of $1,500 for manufacturing the wristbands. And, there is $100 per unit.Based on the above information, we can conclude that
a. The slope is 100. It shows the cost per wristband.
b. The y-intercept is 1500. It shows the fixed cost for manufacturing the wristbands.
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Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?
Answers
Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece m = 90 - 6d
Answer:
m=90-6 days or b
Step-by-step explanation:
i got a hundred on the quiz...
What is the median of this set of data? 66, 51, 77, 68, 60, 75, 54, 80
Answers
67````````````````````````
Help me please !
Scores on a statewide standardized test are normally distributed with a mean of 12.89 and a standard deviation of 1.95. Certificates are given to students whose scores are in the top 2% of those who took the test. This means that they scored better than 98% of the other test takers. Marcus received his score of 13.7 on the exam and is wondering why he didn’t receive a certificate. Show all work to determine whether Marcus’ score was high enough to earn a certificate. Write a letter to Marcus explaining whether or not he will be receiving a certificate. Include a brief summary of your statistical analysis in your letter.
Answers
The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?
A. 13
B. 1
C. 2
D. 12
Answers
Answer:
2 students failed in the final exam.
Step-by-step explanation:
The scores on a final exam were approximately normally distributed.
We know that,
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
X = raw score = 60
μ = mean = 82
σ = standard deviation = 11
Putting the values,
[tex]Z=\dfrac{60-82}{11}=-2[/tex]
From Normal distribution table, we get
[tex]P(-2)=0.0227=2.27\%[/tex]
Hence, 2.27% of 85 students failed the final exam.
So the number of students who failed the exam is,
[tex]=85\times 0.0227=1.9295\approx 2[/tex]
carla looks from the top of a diving board, and lines up a ball floating on the surface of the water with the bottom of the opposite corner of the pool. calculate the total distance across the surface of the pool. explain your reasoning
Answers
Below is the solution:
12/x = 10/9
10x/ 20 = 108/10
x = 10.8
9 + 10.8 = 19.8 ft
Calculate the average rate of change for the function f(x) = −x4 + 4x3 − 2x2 + x + 1, from x = 0 to x = 1.
0
1
2
7
Answers
Answer:
I believe the answer is (C.2)
Step-by-step explanation:
The answer isn’t 1. I took the test and ‘B’ is incorrect
Final answer:
C: 2
To find the average rate of change of the function f(x) from x = 0 to x = 1, we compute (f(1) - f(0)) / (1 - 0), which results in (3 - 1) / 1 = 2. The average rate of change is therefore 2.
Explanation:
To calculate the average rate of change for the function f(x) = −x⁴ + 4x³ − 2x² + x + 1 from x = 0 to x = 1, we use the formula:
Average rate of change = ∆f/∆x = (f(x_2) - f(x_1)) / (x_2 - x_1)
First, we need to find the values of f(x) at x = 0 and x = 1:
f(0) = −(0)⁴ + 4(0)³ − 2(0)² + (0) + 1 = 1f(1) = −(1)⁴ + 4(1)³ − 2(1)² + (1) + 1 = 3Using these values, we calculate the average rate of change:
Average rate of change = (3 - 1) / (1 - 0) = 2 / 1 = 2
Therefore, the average rate of change of the function from x = 0 to x = 1 is 2.