Answers
[tex]\sin(60) = \dfrac{x}{8} [/tex]
[tex]x = 8\sin(60) [/tex]
[tex]x = \dfrac{8 \sqrt{3} }{2} [/tex]
[tex]x = 4 \sqrt{3} [/tex]
x = 4sqrt3
Related Questions
can you please help me on this worksheet and try to show the work
Answers
180° = π radians
13. (105°)*(π radians)/180° = 7π/12 radians
14. 5π/6 radians * 180°/(π radians) = 150°
15. (The geometry shown cannot actually exist. The total of subtended arcs on any linked sprockets must be 360°.)
a.
The arc length on the smaller sprocket is (12 in)*(160/360) = 5 1/3 in.
The arc length on the larger sprocket is (20 in)*(185/360) = 10 5/18 in.
The total chain length is 5 6/18 +10 + 10 5/18 + 10 = 35 11/18 in. Rounded to the nearest tenth inch, the chain length is 10.3 inches.
b.
10.3/0.5 ≈ 20.6 ≈ 21
The chain has about 21 links. (There are no "teeth" on a chain.)
1. The radius can be found by looking at the distance between the origin and the line 8x+6y-48=0. That distance is |-48|/√(8²+6²) = 4.8.
Since the radius of the circle is 4.8, so its circumference is ...
9.6π cm, about 30.159 cm.
2. s = rθ
s = (12 cm)(π/3 radians) = 4π cm
The length of arc AB is 4π cm, about 12.566 cm.
The shorter leg of a right triangle is 7 inches shorter than the longer leg. The hypotenuse is 17 inches longer than the longer leg. Find the side lengths of the triangle.
Answers
Or round them all up.
a² + b² = c²
c² - a² = b²
17² - 7² = x² ↓
289 - 49 = √240
√240 = 15.49193338482967 (rounded 15.49 or 15.5)
Hope this helps,
♥A.W.E.S.W.A.N.♥
PLEASE HELP ME
If the maximum density of killer whales per cubic foot is 0.000011142, what is the maximum number of killer whales allowed in the main show tank at any given time? You must explain your answer using words, and you must show all work and calculations
Answers
Given that the the tank has a radius of 70 ft;
The volume of the sphere will be:
V=1/4[4/3*pi*r^3]
v=1/4[4/3*3.14*70^3]
V=359,006.6675
b] The maximum number of whales will be given by:
density=mass/volume
thus
0.000011142=x/(359006.6675)
thus
x=0.000011142*359006.6675
x=4
thus the maximum number of whale would be 4
if (x+1) is a factor of x^3+2x^2-x-2, find the remaining factors.
Answers
Answer:
The other factors are (x-1) and (x+2).
On a scatter plot what does it mean when both variables are increasing
Answers
Help with algebra 2 please!!!!!!!
Answers
a boy flies a kite with a 100 foot long string. the angle of elevation of the string is 48 degrees. how high is the kite from the ground?
Answers
in a right triangle
sin ∅=opposite side angle ∅/hypotenuse
opposite side angle ∅=hypotenuse*sin ∅
in this problem
angle ∅=48°
hypotenuse=100 ft
opposite side angle ∅=?----> height of the kite from the ground
opposite side angle ∅=100*sin 48°------> 74.31 ft
the answer is
74.31 ft
Solve system by elimination
y=x^2
y=x+2
SHOW YOUR WORK
Answers
y=x²----> equation 1
y=x+2-----> equation 2
multiply equation 1 by -1
-y=-x²
add equation 1 and equation 2
-y=-x²
y=x+2
------------
0=-x²+x+2-------------> -x²+x+2=0-----> x²-x-2=0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(x²-x)=2Complete the square. Remember to balance the equation by adding the same constants to each side
(x²-x+0.5²)=2+0.5²
Rewrite as perfect squares
(x-0.5)²=2+0.5²(x-0.5)²=2.25-----> (x-0.5)=(+/-)√2.25-----> (x-0.5)=(+/-)1.5
x1=1.5+0.5-----> x1=2
x2=-1.5+0.5---- > x2=-1
for x=2
y=x²----> y=2²----> y=4
the point is (2,4)
for x=-1
y=x²----> y=(-1)²---> y=1
the point is (-1,1)
the answer is
the solution of the system are the points
(2,4) and (-1,1)
A man has 25 25 coins in his pocket, all of which are dimes and quarters. if the total value of his change is $ 4.45 $4.45, how many dimes and how many quarters does he have?
Answers
$1.95/$0.15 = 13
quarters.
The man has 12 dimes and 13 quarters.
_____
Check:
12*$0.10 +13*$0.25 = $1.20 +3.25 = $4.45 . . . (answer checks OK)
On a map, 1 inch equals 9.2 miles. two houses are 3.5 inches apart on the map. what is the actual distance between the houses? use pencil and paper. show how you can represent the scale with two different ratios. what ratio is more helpful for solving the problem? explain.
Answers
The actual distance between the houses is 18.9 miles.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
Given that On a map, 1 inch equals 9.2 miles. Two houses are 3.5 inches apart on the map.
To find the actual distance between the houses.
Given that,
1 inch = 9.2 miles
Therefore,
∴ we get
3.5 inches = 3.5 × 9.2 miles
= 13.8 miles
The actual distance is 13.8 miles.
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Final answer:
To find the actual distance between the houses, we can set up a proportion using the given map scale. The actual distance between the houses is 32.2 miles. Using the ratio 1 inch/9.2 miles = 3.5 inches/x is more helpful in solving the problem.
Explanation:
To find the actual distance between the houses, we need to use the scale of 1 inch equals 9.2 miles. We are given that the two houses are 3.5 inches apart on the map.
First, we can set up a proportion to find the actual distance:
1 inch / 9.2 miles = 3.5 inches / x
Cross-multiplying, we have:
1x = 3.5 * 9.2 miles
Simplifying, we get:
x = 32.2 miles
The actual distance between the houses is 32.2 miles.
To represent the scale with two different ratios, we can use the proportion:
1 inch / 9.2 miles = 3.5 inches / x
This ratio is more helpful for solving the problem as it allows us to directly calculate the actual distance using the given map distance and the scale ratio.
A field goal post in football is 3.33 yards above the ground. If a football player kicks the ball at a 10 degree square angle in a straight line toward the goal post what is the distance away in yards where the ball barely goes over the goal post
Answers
because tan(10)=opposite/adjacent=3.33/x and x is distance
x=3.33/tan(10)=18.9 yd
Blue marbles, green marbles and red marbles are in a ratio of 5 to 7 to 8 in a box. if the total number of marbles is 240, how many green marbles are in the box?
Answers
= ⁷/₂₀
If there are 240 marbles in the box, then the number of green marbles = (240 × ⁷/₂₀) = 84 marbles
∴ 84 of the marbles in the bag are green.
describe the steps you would use to solve the following inequality
Answers
[tex] \frac{x + 1}{2x - 3} > 2 \\ x + 1 > 2(2x - 3) \\ x + 1 > 4x - 6 \\ - 3x + 1 > - 6 \\ - 3x > - 7x \\ x < \frac{7}{3} [/tex]
Answer:
Rewrite the inequality so there is a single rational expression on one side, and 0 on the other.
Combine under a common denominator.
Test points in the critical regions.
Construct the solution.
Step-by-step explanation:
Answer Above
i really need help. please help
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4^−x and y = 8^(−x−1) intersect are the solutions of the equation 4^−x = 8^(−x−1). (4 points)
Part B: Make tables to find the solution to 4^−x = 8^(−x−1). Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4^−x = 8^(−x−1) graphically? (2 points)
Answers
The answer to B is forming a table. This is quite easier than you think :D.
Start with x on one side (3) and go all the way down to -3 like this:
(x) 4^-x 8^-x-1
-3 64 (Do the same with this)
-2 16
-1 4
0 1
1 1/4
2 .0625
3 .015625
So basically you just fill in the x variable with every number between 3 and -3. After that, it's just a bit of math and you've done it!
C is a bit misguided. I think it would be quite simple to just use a graphing calculator, but you would have to actually input all the x and y values from the table. After that, you will have a graph.
I hope I helped! Good luck and good day!
does anyone know the surface area for this problem. if so i will mark brainliest.
Answers
From the given volume, we know that the ratio is:
[tex]\text {Ratio of yellow eraser to white eraser = } \sqrt[3]{ \dfrac{16}{2} } [/tex]
From the given area, we know that the ratio is:
[tex]\text {Ratio of yellow eraser to white eraser = } \sqrt{ \dfrac{52}{x} } [/tex]
Equate the two ratio and solve for x:
[tex]\sqrt[3]{ \dfrac{16}{2} } = \sqrt{ \dfrac{52}{x} } [/tex]
Cube both sides:
[tex]\dfrac{16}{2} = \bigg(\sqrt{ \dfrac{52}{x} }\bigg)^3[/tex]
Square both sides:
[tex]\bigg(\dfrac{16}{2} \bigg)^2 = \bigg( \dfrac{52}{x} }\bigg)^3[/tex]
Simplify each term:
[tex]\dfrac{16^2}{2^2} = \dfrac{52^3}{x^3} [/tex]
Cross multiply:
[tex]256x^3 = 562432[/tex]
Divide both sides by 256:
[tex] x^3 = 2197[/tex]
Cube root both sides:
[tex] x = 13[/tex]
How many degrees is w?
Answers
w = 180 -38 - 49
w = 93
Answer
w = 93°
find the greatest common factor 9x^2a + 9xa^2
Answers
9x^2a+9xa^2
factor out 9 we get:
9(x^2a+xa^2)
=factoring out x we get
9x(xa+a^2)
factoring out a we get
9ax(x+a)
therefore the GCF is 9ax
Which of these is an example of continuous random variable
A. Number of flights leaving an airport
B. Distance of a javelin throw
C. Pieces of mail in your mailbox
D. Attendance at a sporting event
Answers
A continuous random variable is a variable that can be any number between the integers not just the integers themselves.
For example, the distance for a javelin throw could be 6.70819203 feet.
However, you would not say that you have 6.70819203 flights, pieces of mail or people at a sporting event.
The B. distance of a javelin throw is an example of a continuous random variable.
Explanation:A continuous random variable is a variable that can take any value within a specified range, often associated with measurements and quantities. Unlike discrete variables, it can assume an infinite number of values, typically represented by intervals on the real number line.
Out of the given options, the distance of a javelin throw is an example of a continuous random variable. A continuous random variable is one that can take on any value within a given range. In the case of a javelin throw, the distance can be any real number value within a certain range, such as 0 to infinity. This is in contrast to the other options, which are discrete random variables that can only take on specific whole number values.
Write an algebraic expression for the verbal description. the distance a car travels in t hours at a rate of 50 miles per hour
Answers
d=50t
Where; d is the distance covered in miles
t is the time taken in hours
The algebraic expression is D = 50t where D is the distance covered in miles and t is the time taken in hours.
What is the distance?Distance is defined as the product of speed and time.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operations is called arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
Given that the distance a car travels in t hours at a rate of 50 miles per hour
Let the distance covered in miles = D
And t is the time taken in hours
Since distance is defined as the multiplication of speed and time.
So an algebraic expression for the verbal description as
⇒ D = 50t
Hence, the algebraic expression is D = 50t where D is the distance covered in miles and t is the time taken in hours.
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If the ratio of the radii of two spheres is 8:9, what is the ratio of the volumes of the two speheres
Answers
A------------> smaller sphere
B----------> larger sphere
radius of sphere A-------> rA
radius of sphere B----> rB
we know that
rA/rB=8/9
the scale factor is equal to 8/9
volume smaller sphere A=[scale factor]³*volume larger sphere B
volume smaller sphere A/volume larger sphere B=[scale factor]³
volume smaller sphere A/volume larger sphere B=[8/9]³----> 512/729
the answer is
512/729
divide r+5/ r^2+5r-14 by r^2+4-21/r-2
Answers
The first thing we are going to do is factor the denominator of the first fraction and the denominator of the second one:
- For our first fraction:
[tex]r^2+5r-14=(r+7)(r-2)[/tex]
Now we can rewrite our first fraction:
[tex]\frac{r+5}{r^2+5r-14} = \frac{r+5}{(r+7)(r-2)} [/tex]
- For our second fraction:
[tex]r^2+4r-21=(r+7)(r-3)[/tex]
Now we can rewrite our second fraction:
[tex] \frac{r^2+4r-21}{r-2} = \frac{(r+7)(r-3)}{r-2} [/tex]
Last but not least, we can express our division as a fraction and simplify:
[tex] \frac{\frac{r+5}{(r+7)(r-2)}}{ \frac{(r+7)(r-3)}{r-2}} = \frac{(r+5)(r-2)}{(r+7)(r-2)(r+7)(r-3)} = \frac{r+5}{(r+7)^2(r-3)} [/tex]
We can conclude that the result of dividing r+5/ r^2+5r-14 by r^2+4r-21/r-2 is: [tex] \frac{r+5}{(r+7)^2(r-3)} [/tex]
Use the given graph to determine the limit, if it exists.
Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x.
Answers
As the value of x approaches 2 from the positive side i.e. the right hand side, the value of function approaches -4
Since the Right hand limit and the Left hand limit as x approaches 2 are not the same, the limit does not exist at x = 2
Find the area of the shaded region.
Answers
Area of bigger rectangle
A = (x+1)(x+1) = x^2 + 2x + 1
2)
Area of smaller rectangle
A = 5(x - 7) = 5x - 35
3)
The difference:
(x^2 + 2x + 1) - (5x - 35)
= x^2 + 2x + 1 - 5x +35
= x^2 - 3x + 36
area of the shaded region = x^2 - 3x + 36
You first have to find the area of the bigger rectangle
You find this by multiplying the sides
(x + 1)(x + 1) = x^2 + 2x + 1
Next you have to find the area of the smaller rectangle
(x - 7) * 5 = 5x - 35
Subtract the two polynomials
(x^2 + 2x + 1) - (5x - 35) = x^2 - 3x + 36
The answer is [tex] x^{2} -3x + 36[/tex]
Hope this helps!
The length of a rectangle is 4 feet shorter than its width. the area of the rectangle is 42 square feet. find the length and width. round your answer to the nearest tenth of a foot
Answers
Length is [tex]\boldsymbol{4.4}[/tex] feets and width is equal to [tex]\boldsymbol{8.8}[/tex] feets.
Area of a rectangleThe area of a two-dimensional region, form, or planar lamina in the plane is the quantity that expresses its extent.
A quadrilateral having four right angles is known as a rectangle.
Let [tex]\boldsymbol{w}[/tex] feets denotes width of a rectangle.
Length of a rectangle [tex]=\boldsymbol{w-4}[/tex] feets
Area of a rectangle [tex]=\boldsymbol{42}[/tex] square feet
Length [tex]\times[/tex] Width [tex]=42[/tex]
[tex]w(w-4)=42[/tex]
[tex]w^2-4w-42=0[/tex]
[tex]w=\frac{4\pm \sqrt{16+168}}{2}[/tex]
[tex]=2\pm \sqrt{46}[/tex]
As dimension can not be negative, [tex]2-\sqrt{46}[/tex] is rejected.
So,
[tex]w=2+ \sqrt{46}[/tex]
[tex]=\boldsymbol{8.8}[/tex] feets
Length [tex]=8.8-4[/tex]
[tex]=\boldsymbol{4.4}[/tex] feets
So, length is [tex]4.4[/tex] feets and width is equal to [tex]8.8[/tex] feets.
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Rewrite with only sin x and cos x. Sin2x-cos2x
Answers
So sin2x-cos2x = 2sinxcosx - ([tex]cos^{2} x - sin^{2} x[/tex]) in terms of sinx and cosx
Write the inverse function for the function, ƒ(x) = x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.
ƒ -1(x) = _________ x ___________ ______
ƒ -1(4) = _____________
Answers
Answer: The required values are
[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]
Step-by-step explanation: We are given the following function f(x) :
[tex]f(x)=x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the values of [tex]f^{-1}(x)[/tex] and [tex]f^{-1}(4).[/tex]
Let us consider that
[tex]y=f(x)~~~~~~~~\Rightarrow x=f^{-1}(y).[/tex]
So, from equation (i), we get
[tex]f(x)=x+4\\\\\Rightarrow y=f^{-1}(y)+4\\\\\Rightarrow f^{-1}(y)=y-4\\\\\Rightarrow f^{-1}(x)=x-4.[/tex]
Substituting x = 4 in the above equation, we get
[tex]f^{-1}(4)=4-4=0\\\\\Rightarrow f^{-1}(4)=0.[/tex]
Thus, the required values are
[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]
Find the values of b such that the function has the given maximum value. f(x) = −x2 + bx − 14; Maximum value: 86
Answers
[tex]y_{max}\ \text{is in the vertex of the parabola}.[/tex]
[tex]\text{The coordinates of the vertex of the parabola}\ f(x)=ax^2+bx+c:\\\\V\left(\dfrac{-b}{2a};\ \dfrac{-(b^2-4ac)}{4a}\right)[/tex]
[tex]\text{We have:}\\\\f(x)=-x^2+bx-14\to a=-1;\ b=b;\ c=-14[/tex]
[tex]\text{Substitute:}\\\\\dfrac{-\left(b^2-4\cdot(-1)\cdot(-14)\right)}{4\cdot(-1)}=86\\\\\dfrac{b^2-56}{4}=86\ \ \ \ |\cdot4\\\\b^2-56=344\ \ \ \ |+56\\\\b^2=400\to b=\pm\sqrt{400}\\\\b=-20\ \vee\ b=20[/tex]
Answer: b = -20 or b = 20.
To find the value of 'b' that gives the maximum value of 86 for the function f(x) = -x² + bx - 14, substitute the x-coordinate of the vertex (-b/2a) into the function, equate it with 86 and solve for 'b'.
Explanation:To find the values of b for which the quadratic function f(x) = -x² + bx - 14; Maximum value: 86 holds true, we need to utilize the properties of quadratic functions. In a quadratic function in the form f(x) = ax² + bx + c, the maximum value occurs at the vertex of the parabola. The x-coordinate of the vertex is given by -b/2a.
Given that our quadratic is a maximum (opens downwards since a=-1), the y-coordinate of the vertex, which is our maximum value, is 86. Substituting these into our function, we get f(-b/2a) = 86, replacing a=-1, this reduces to -b²/4 -14 = 86. Simplifying this equation will give you the value of b.
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SOLVE FOR X one question 20 points
Answers
a^2 + b^2 = c^2 (c^2 is the hypertenuse)
The equation will look like this:
14^2 + 14^2 = x^2
196 + 196 = x^2
x^2 = 392
So the answer is the square root of 392:
14[tex] \sqrt{2} [/tex]
If you want a decimal form:
14 * 1.414 = 19.796
Answer:
ANSWER IS
Step-by-step explanation:
Given y = 4x + 3, what effect does changing the equation to y = 2x + 3 have on the slope?
Answers
Hope this helps!
can I get a brainleist pls!
Changing the slope of the equation from 4 to 2 reduces the steepness of the line in the graph, with the y-intercept remaining constant at 3.
Explanation:The student asked about the effect on the slope of the linear equation when changing from y = 4x + 3 to y = 2x + 3. The slope of the first equation is 4, which can be seen from the coefficient of x, indicating a rise of 4 on the vertical axis for every increase of 1 on the horizontal axis. When the equation changes to y = 2x + 3, the slope is reduced to 2, which means there is a rise of 2 on the vertical axis for every increase of 1 on the horizontal axis. This change in the slope would cause the line to rotate clockwise when graphed on a coordinate plane. The y-intercept remains the same at 3 since it is unchanged in both equations. Therefore, changing the equation has the effect of decreasing the steepness of the line, but the location where the line crosses the y-axis does not change.
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:f(t) = −16t2 + 48t + 100The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.
Answers
f (t) = -16t2 + 48t + 100
The average rate of change is:
(f (t2) - f (t1)) / (t2 - t1)
We have then:
For t1 = 3:
f (3) = -16 * (3) ^ 2 + 48 * (3) + 100
f (3) = 100
For t2 = 5:
f (5) = -16 * (5) ^ 2 + 48 * (5) + 100
f (5) = -60
Substituting values:
AVR = (-60 - 100) / (5 - 3)
AVR = -80
Answer:
The average rate of change of f (t) from t = 3 seconds to t = 5 seconds is -80 feet per second.