The diagram shows a right angled triangle. 7cm and 11cm and x degrees. Find the size of angle x. Give your answer correct to 1 decimal place.
Answers
The size of the unknown angle "x".
Solution:We'll have to check which one is appropriate from SOHCAHTOA.
In this question we'll have to use cos because hypotenuse and adjacent is given.
[tex]\large\boxed{cos(A)=\frac{adj}{hyp}}[/tex]
Substitute according to the formula.
[tex]cos \: x= \frac{7}{11}[/tex]
We'll have to use cos inverse.
[tex]x={cos}^{-1}(\frac{7}{11})[/tex]
[tex]x=50.47880364[/tex]
[tex]\large\boxed{x=50.5°}[/tex]
Therefore, the size of the unknown angle "x" is 50.5°
The required measure of the angle x is given as 50°.
Given that,
The diagram shows a right-angled triangle. 7cm and 11cm and x degrees.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Apply cosine equation,
cosx = 7 / 11
cosx = cos50
x = 50°
Thus, the required measure of the angle x is given as 50°.
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Related Questions
How many classrooms would be necessary to hold 1,000,000 inflated balloons? (Assume one balloon is about 1 ft3 and a typical classroom is about 35 ft × 50 ft × 15 ft. Round your answer to the nearest number of classrooms.)
Answers
One balloon = 1 cube ft. Using this value and multiplying it by 1,000,000, we can find how much space all of these would take up. Since 1 times anything is just the unchanged value,
• a million inflated balloons = 1000000 ft^3.
The classroom has dimensions 35, 50, and 15 ft. We can use these values to find the classroom’s volume. The equation for Volume of a rectangular prism: V = lwh, where l is length, w is width, and h is height. Substitute given dimensions into this equation:
• V = 35*50*15 = 26250 ft^3.
now, what times 26250 will equal 1000000? Well, let’s set up an equation and solve for x, the number of classrooms.
• 26,250x = 1,000,000. Divide both sides by 26250 to get x alone:
• x = 38.0952.
Approximately 38 classrooms are necessary to hold 1,000,000 inflated balloons.
Check: when x is 38: 26,250(38) = 997,500 ft^3. When x is 39: 26,250(38) = 1,023,750 ft^3. x = 38 is more accurate.
**(I will note, however, that I’m not sure if you’re instructed to round according to the decimal rules or round UP a whole number because that extra .0952 needs to be included).
To hold 1,000,000 inflated balloons,
38 classrooms are needed.
What is volume?In three-dimensional space,
the amount of space taken by an object is the volume of that object.
The volume of the cubic,
= length x width x height
Given:
The dimensions of the normal classroom are 15 ft × 50 ft × 35 ft.
The volume of the classroom,
= 15 ft by 50 ft by 35 ft.
= 26250 cubic feet.
The number of classrooms,
= 1,000,000 / 26250
Simplifying the fraction,
we get,
= 38.09
≈ 38 to the nearest whole number.
Therefore, 38 classrooms are required.
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Find the circumference of a circle that has a diameter of 2 ft. Use 3.14 for pi.
5.14 ft
6.28 ft
12.56 ft
7.14 ft
Answers
Answer:
6.28 ft
Step-by-step explanation:
using the formula [tex]\pi d[/tex] to find the circumference of the circle, you substitute the numbers. 3.14(2). 3.14 x 2 = 6.28 hence the answer
-28=8x+2(x+6) im so lost
Answers
[tex]\bf{Swap \ sides \ 8x+2(x+6)=-28 }[/tex]
[tex]\bf{Expand \ 2(x+6): \ \ \ \ 2x+12}[/tex]
[tex]\mathrm{Set \ the \ variables \ using: \ \ \ a(b+c)=ab+ac}[/tex]
[tex]a=2,\:b=x,\:c=6[/tex]
[tex]=2x+2\cdot \:6[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:6=12[/tex]
[tex]=2x+12[/tex]
[tex]8x+2x+12=-28[/tex]
[tex]\mathrm{Add\:similar\:elements:\:8x+2x=10x}[/tex]
[tex]10x+12=-28[/tex]
[tex]\mathrm{Subtract\:}12\mathrm{\:from\:both\:sides}[/tex]
[tex]10x+12-12=-28-12[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]10x=-40[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}10[/tex]
[tex]\dfrac{10x}{10}=\dfrac{-40}{10}[/tex]
[tex]\mathrm{Simplify \ \dfrac{10x}{10}: \ \ x }[/tex]
[tex]\mathrm{Divide:}\:\dfrac{10}{10}=1[/tex]
[tex]=x[/tex]
[tex]\mathrm{Simplify \ \dfrac{-40}{10}: \ \ -4 }[/tex]
[tex]\rm{Apply \ the \ properties \ of \ fractions \ to \ fractions: \ \ \dfrac{-a}{b}=-\drac{a}{b}}[/tex]
[tex]=-\dfrac{40}{10}[/tex]
[tex]\rm{split: \ \dfrac{40}{10}=4 }[/tex]
[tex]\bf{x=-4 \ \ \to \ \ \ Answer }[/tex]
What is the equation of the line that passes through the point (6, 1) and has a slope
of -1/2
Answers
Answer:
y = 6x + [tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
I think take this with a grain of salt
please help anyone i really need it
Answers
Answer:
Median: 21
Eric took the longest
Ed took 18 minutes longer than Mike
Oscar took the shortest amount of time to solve the puzzle
Step-by-step explanation:
The median is the middle amount of the numbers, line them up from smallest to largest and find the number in the middle...the largest number is the person who took the longest...subtract Ed's score (25) from Mike's score (4) to get the answer...and the smallest number is the person who took the shortest amount of time
Calculate the area of the alarm clock.
Answers
Given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².
What is the area of the alarm clock?Note that: Area of a circle is expressed as;
A = πr²
Where r is radius and π is constant pi ( π = 3.14 )
Given that;
Diameter d = 70cm Radius r = d/2 = 70cm/2 = 35cmArea = ?A = πr²
A = 3.14 × ( 35cm )²
A = 3.14 × 1225cm²
A = 3846.5cm²
Therefore, given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².
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Find the probability of rolling a 66 -sided dice and getting a number that is a divisor of 2020
Answers
Answer:
2/3 or 0.66 repeated
Step-by-step explanation:
Since 2022 is only divisible by 1,2,4, and 5, the probability of getting a number that is a divisor of 2020 is 4/6, simplified to 2/3 or %0.66.
Julia can sell a certain product for $75 per unit. Total cost consists of a fixed overhead of $4000 plus production costs of $50 per unit. How many units must be sold for Julia to break even?
Answers
Reason is 75 sell price less cost per unit = $25 profit per unit
Overhead cost is $4000. Divide fixed overhead cost $4000 by profit per unit $25 = 160
A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field
[tex]F(x,y,z) = z^2i+5xyj+2y^2k[/tex]
Use Stokes Theorem to find the work done:
Answers
A particle moves along line segments from the origin to the points, work done is mathematically given as
W=184.5units
What is the solution of an equation that matches the model.?Considering line segments from (0,0,0)origin to (2,0,0) , (2,5,1) and (0,5,1) under the infulence of force
Generally, the equation for force is mathematically given as
F = z2i + 5xyj + 2y2k
Therefore, Considering u*v
[tex]u * v = (u_1j+u_2j+u_3k) * (v_1i+v_2j+v_3k)[/tex]
[tex]u* v = u_1v_1(i * i) + u_1v_2(i * j)+u_1v_3(i * k) + u_2v_1(j * i) + u_2v_2(j * j)+u_2_3(j* k) + u_3v_1(k * i) + u_3v_2(k * j)+u_3v_3(k * k)[/tex]
Where
[tex]i * i = j *j=k * k=0[/tex]
Hence
[tex]u* v = u_1v_2k-u_1v_3j-u_2v_1k+u_2v_3i +u_3v_1j - u_3v_2i[/tex]
[tex]u = (u_1,u_2,u_3) = (0,5,1)\\\\v = (v_1,v_2,v_3) = (-3,0,0)[/tex]
The normal equation formed
-2y + 15z = 0
z= (1/5)y
Considering the level surface and differential surface area
h(x,y,z) = -y + 5z =0
[tex]dS = |grad(h)| dA[/tex]
In terms of the x and y coordinates of (2,0,0) and (2,5,1) and (0,5,1), we can state that the ranges are 0 to 3 and 5 respectively we have
[tex]0 \leq x \leq 2 \ and \ 0 \leq y \leq 5[/tex]
Using strokes theorem to evaluate
[tex]F = z2i + 5xyj + 2y2k[/tex]
[tex]curl \ F = 4yi+2zj+5yk = (4y,2z,5y)[/tex]
[tex]curl \ F * nds= \frac{1}{5}(-2z + 25y)\ dy \ dx[/tex]
In conclusion, The work done is
[tex]W=\int _CF *dr[/tex]
[tex]\int _C F * dr = \int \int curl \ F * n ds[/tex]
[tex]\int _C F *dr = \frac{123}{2}\int_0^3 \ dx[/tex]
[tex]\int _C F * dr = \frac{123*3}{2}[/tex]
W= 184.5units
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how to Solve for x. -1/2 (x + 2) + 1 1/2 x = 3
Answers
find the slope of the line that passes through (9,-3) and (9,-8)
Answers
Answer:
The line has no slope. I hope this helps
Gerald will be finishing his payments on his 5-year, $45,000 student loan and wants to know the amount of interest that he
paid over the course of the loan. The student loan has a 4.1% fixed interest rate that is compounded monthly. Calculate the
total amount of interest Gerald paid, rounding to the nearest cent.
Answers
Answer: 538
Step-by-step explanation: en verdad no sé pero eso fuelo que me salio
You are trying to bulk and gain muscle. Your trainer says your daily calorie intake should increases based on hours you spend exercising and can be represented by the following equation: T=2000+500h.
Answers
a) T - Calories, 2000 - Minimum calories, 500 - Additional calories per exercise hour, b) We should consume 3500 calories to spend three hours exercising.
How to analyse a linear function of calorie gain in terms of the exercise time
In this question we have a linear function where the independent variable is the exercise time (h), in hours, and the dependent variable is the calorie gain (T), in calories. The constant "2000" is the minimum calorie consumption and the constant "500" represents the amount of additional calories per each hour of exercise.
Now we proceed to respond the questions of the part a):
(i) T - Amount of calories needed, (ii) 2000 - Minimum calorie consumption, (iii) 500 - Amount of additional calories per hour of exercise.
b) And lastly we calculate the amount of calories by evaluating the function:
T = 2000 + 500 · 3
T = 2000 + 1500
T = 3500
We should consume 3500 calories to spend three hours exercising.
Remark
The statement is incomplete, the complete form is shown below:
You are trying to bulk up and gain muscle. Your trainer says that your daily calorie intake should increase based on the hours you spend exercising and can be represented by the following equation: T = 2000 + 500 · h
a) What does each part of this expression represent? (i) T = , (ii) 2000, (iii) 500, (iv) h
b) If you spend 3 hours exercising, how many calories should you consume?
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Find the 66th term in the following
arithmetic sequence:
-92, -85, -78, -71, ...
Answers
Answer: 363
Step-by-step explanation:
The common difference is 7, so the explicit formula is [tex]a_{n}=-92+7(n-1)[/tex].
Substituting in n=66,
[tex]a_{66}=-92+7(66-1)=\boxed{363}[/tex]
OK so I don't know why but I enjoy giving away points, so if anyone has the right answer then please put it in, if not please DO NOT put it in, this is for helping others, not for greed.
Lakima has a spinner divided into 5 equal sections that are labeled 1 though 5. She wants to compare the theoretical probability and the experimental probability of spinning an odd number. She spins the spinner 6 times and records the results in this list. {2, 4, 1, 5, 3, 4} Drag and drop the answers into the boxes to correctly complete the sentences. The theoretical probability of spinning an odd number is equal to . The experimental probability of spinning an odd number is equal to Response area. Therefore, the theoretical probability of spinning an odd number is the experimental probability of spinning an odd number.
Answers
The theoretical probability of getting an odd number is 0.6, but the experimental probability was 0.5.
What is the theoretical probability?Total of numbers in the spinning wheel: 5Total of odd numbers: 3 (1,3,5)Probability of getting an odd number: 3/5 = 0.6 or 60%
What is the experimental probability?Number of times the wheel was spinned: 6 timesNumber of times she got an odd number: 3 times6 times = 1003 times = xx = 3 x 100/ 6x = 50% or 0.50What can be concluded?The experimental probability is lower than the theoretical probability.
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Answer:
Answer in pic below
Step-by-step explanation:
Question 18
Let set A = { even numbers}
set B = {odd numbers}
Find A U B
Answers
Answer: all integers
Step-by-step explanation:
[tex]A \cup B[/tex] denotes the union of the two sets, and is thus the set of all integers.
find the solution set. 4x^2+x=3
Answers
Answer:
[tex]x=\frac{3}{4},\:x=-1[/tex]
Keys:
For this problem, you need the quadratic formula(listed below).
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex][tex]1^a=1[/tex][tex]\sqrt[n]{a}^n=a[/tex]When you see ± in a quadratic equation, you must know there is going to be at least 2 solutions.
Step-by-step explanation:
solving for x₁ and x₂
[tex]4x^2+x=3\\4x^2+x-3=3-3\\4x^2+x-3=0\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot 4\left(-3\right)}}{2\cdot 4}\\[/tex]
[tex]1^2=1\\=\sqrt{1-4\cdot \:4\left(-3\right)}\\=\sqrt{1+4\cdot \:4\cdot \:3}\\=\sqrt{1+48}\\=\sqrt{49}\\=\sqrt{7^2}\\\sqrt{7^2}=7\\=7[/tex]
[tex]x_{1,\:2}=\frac{-1\pm \:7}{2\cdot \:4}\\x_1=\frac{-1+7}{2\cdot \:4},\:x_2=\frac{-1-7}{2\cdot \:4}\\[/tex]
solve for x₁
[tex]\frac{-1+7}{2\cdot \:4}[/tex]
[tex]=\frac{6}{2\cdot \:4}[/tex]
[tex]=\frac{6}{8}[/tex]
[tex]= \frac{6\div2}{8\div2}[/tex]
[tex]=\frac{3}{4}[/tex]
solve for x₂
[tex]\frac{-1-7}{2\cdot \:4}[/tex]
[tex]=\frac{-8}{2\cdot \:4}[/tex]
[tex]=\frac{-8}{8}[/tex]
[tex]=-\frac{8}{8}[/tex]
[tex]=-1[/tex]
Hope this helps!
If f(x)=x2−4x+4 , then f(3)=
Answers
Answer:
f(3) = 1
Step-by-step explanation:
substitute x = 3 into f(x) , that is
f(3) = 3² - 4(3) + 4 = 9 - 12 + 4 = 1
Answer:
1
Step-by-step explanation:
Substitute 3 for x in your equation leaving you with (3)^2-4(3)+4.
9-12+4
-3+4=1
Date:
Name:
Refocus
Directions: Solve the problems by building the figure with algebra tiles and writing an equation.
A rectangle has a length that is twice the width. The perimeter of the rectangle is 12 feet.
What is the width? What is the length?
Equation:
Width:
Length:
Answers
Answer:
Equation: 2w + 2(2w) = 12
width = 2
length = 4
Step-by-step explanation:
Width is w
Length is 2 * width = 2w
Perimeter is 2w + 2l
Substitute 2w for L.
Perimeter is now 2w + 2(2w) = 12
Distribute the 2 to the parentheses.
2w + 4w = 12
Combine Like terms
6w = 12
Divide by 6 to solve for w.
w = 2
If w = 2, then the length = 4.
Find the fist 4 terms of a geometric series with first term of 8 and the sum to infinity of 12
Answers
Step-by-step explanation:
the sum of an infinite geriatric series with |r| < 1 is
s = a1/ (1 - r)
in our case we have
a1 = 8
12 = 8/(1 - r)
12(1 - r) = 8
1 - r = 8/12 = 2/3
-r = -1/3
r = 1/3
so, the first 4 terms (I added a5 too, just in case your teacher meant the NEXT 4 terms) are
a1 = 8
a2 = a1 × 1/3 = 8/3
a3 = a2 × 1/3 = 8/9
a4 = a3 × 1/3 = 8/27
a5 = a4 × 1/3 = 8/81
...
Answer:
[tex]8,\quad \dfrac{8}{3},\quad \dfrac{8}{9},\quad\dfrac{8}{27}[/tex]
Step-by-step explanation:
Sum to infinity of a geometric series:
[tex]S_\infty=\dfrac{a}{1-r} \quad \textsf{for }|r| < 1[/tex]
Given:
[tex]a[/tex] = 8[tex]S_\infty[/tex] = 12Substitute given values into the formula and solve for [tex]r[/tex]:
[tex]\implies 12=\dfrac{8}{1-r}[/tex]
[tex]\implies 1-r=\dfrac{8}{12}[/tex]
[tex]\implies r=1-\dfrac{8}{12}[/tex]
[tex]\implies r=\dfrac{1}{3}[/tex]
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
Substitute the found values of [tex]a[/tex] and [tex]r[/tex]:
[tex]\implies a_n=8\left(\dfrac{1}{3}\right)r^{n-1}[/tex]
The first 4 terms:
[tex]\implies a_1=8\left(\dfrac{1}{3}\right)r^0=8[/tex]
[tex]\implies a_2=8\left(\dfrac{1}{3}\right)r^1=\dfrac{8}{3}[/tex]
[tex]\implies a_3=8\left(\dfrac{1}{3}\right)r^2=\dfrac{8}{9}[/tex]
[tex]\implies a_4=8\left(\dfrac{1}{3}\right)r^3=\dfrac{8}{27}[/tex]
The universal set, &, and the sets A and B are defined below.
= {3, 4, 6, 8, 9, 12, 15, 16, 20}
A = {6, 9, 12, 15}
B = {multiples of 4}
Write down all the elements of AB'.
Answers
Answer:
wedg
Step-by-step explanation:
ed
Find a3, a4, and a5.
a₁ = 5
a₂ = 2
an =-2an -1 + an-2
Answers
Answer:
A1 5×3 = 15
A2 = 2×4= 8
an=I don't know that one
9) A furniture store is having a spring sale-15% off of everything in the store.
What is the price of a table that regularly costs $159.98 if it is bought on sale?
Answers
Answer:
$135.98
Step-by-step explanation:
15% of $159.98 = 0.15 × $159.98 = $24.00
$159.98 - $24.00 = $135.98
what is a parralel line
Answers
Answer:
A parallel line is something that is equivalent on the other end. This mean if you cut a shape, a square for example, in half,the sides will be of equal length.
Answer:
a parallel line is diagonal
Find x. Round your answer to the nearest tenth of a degree.
36
X
19
+
Answers
Answer: 36.9
Step-by-step explanation:
what is the volume of the rectangular prism each is 1/3
Answers
Answer:
The answer is 7
Step-by-step explanation:
To find the volume you multiply the width, height, and the length.
Length= 7/3
width= 3/3
height= 9/3
When you multiply you then have to simplify which is 7/1 or 7.
Mark this correct to help me gain!!
ITS URGENT I WILL YOU GIVE BRAINLEST(if you are the first and the best)!!!
Answers
Answer:
2 Hours
Step-by-step explanation:
First you have to add up all the points which would be;
1 1/2 + 1 1/2+ 2 1/2+ 2 1/2= 8 hours
Then you have to divide by how many points to find the average;
8 hours divided by 4 points= 2 hours average
In total, she will practice 2 hours every day
At time t=0 a woman tosses an apple straight up into the air. At time t= 0.5, it begins to fall back to her hand. She catches the apple at t=1.0. Treat motion upward a positive. which of the follwong graphs could represent the motion of the apple?
Answers
The graph that could represent the motion of the apple is graph B.
What is a graph?A graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.
Here, the speed of apple at time t is given by v=0 + at which is a straight line of slope a that passes through origin because constant is zero. At time t=0 its initial speed is 0 and it will increase constantly with time. Therefore, graph (B) is correct
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Which statement is true?
a.All rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, all rectangles have 2 pairs of parallel sides.
b.Only some rectangles are parallelograms. Parallelograms have exactly 1 pair of parallel sides. Therefore, only some rectangles have exactly 1 pair of parallel sides.
c.Only some rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, only some rectangles have 2 pairs of parallel sides.
d.All rectangles are parallelograms. Parallelograms have exactly 1 pair of parallel sides. Therefore, all rectangles have exactly 1 pair of parallel sides.
Answers
Answer:
All rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, all rectangles have 2 pairs of parallel sides.
Step-by-step explanation:
A line intersects the points (3,6) and (5, -4). m=-5 write an equation in point-slope form using the point (3,6)y - [?] = __ (x -__)
Answers
Answer:
y -6 = -5(x -3)
Step-by-step explanation:
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
__
substituting given valuesYou have been given ...
m = -5
(h, k) = (3, 6)
Putting the given values into the point-slope form gives the equation you want:
y -6 = -5(x -3)