We have that the distance in meters of the object is
[tex]d=687.55m[/tex]
From the Question we are told that
Angular diameter [tex]d_a= 30 arcseconds[/tex]
Linear diameter [tex]d_l= 10 cm=0.10m[/tex]
Generally the equation for Linear diameter is mathematically given as
[tex]d_l=\frac{d_a*d}{206265}[/tex]
Therefore
[tex]d=\frac{0.10m*206265}{30}[/tex]
[tex]d=687.55m[/tex]
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Which represents a function?
Answer:
B
Step-by-step explanation:
For a function to be a function, every x value can only equal a single y value. A has two y values for one x value, and so does C and D. This leaves only B.
20. In the above figure, ZAOB = 80°. What does ZACB equal?
A. 10°
B. 160°
C. 80°
O
D. 40°
Answer:
D. 40
Step-by-step explanation:
A central angle is equal to the measure of its corresponding arc.
angle AOB is a central angle and it's corresponding arc is arc AB
this means that arc AB = measure of angle AOB
If angle AOB = 80 degrees then arc AB equals 80 degrees too.
An inscribed angle is equal to half the measure of its intercepted arc.
Angle ACB is an inscribed angle and the arc it intercepts is arc AB
This means that angle ACB = 1/2 of arc AB
We have found that the measure of arc AB is 80 degrees.
This means that angle ACB = 1/2 of 80 which is 40
50 Points to correct answer!!!
what is the average rate of change from 2 to 9 of the function represented by the graph?
Answer:
-3/7
Step-by-step explanation:
It is asking to find the slope of the secant line going through points (2,f(2)) and (9,f(9)).
We must find f(2) by looking at the curve at x=2. We should see that y=2 there so f(2)=2.
We must find f(9) by looking at the curve at x=9. We should see that y=-1 there so f(9)=-1.
The slope of a line is calculated by finding the ratio of the change of y to the change of x.
(-1-2)/(9-2)
(-3)/(7)
-3/7
Could someone please solve this using a^2+b^2=c^2
Step-by-step explanation:
it is shown in the above process.
hope you understand
Anyone know how to solve it?
Answer:
[4 -2 -19]
[-1 1 8]
Step-by-step explanation:
[ 2 5] * [a b c] = [3 1 2]
[ 1 3] ld e f] [1 1 5]
[2a+5d 2b+5e 2c+ 5f] = [3 1 2]
[a+3d b + 3e c + 3f] [1 1 5]
Solving systems of equations:
2a + 5d = 3
a + 3d = 1
2a + 6d = 2
Subtract -d = 1 so d = -1
and a = 1 - 3d = 1 - 3(-1) = 4
So d = -1 and a = -4.
In the same way we find that b = -2, e = 1, c = -19, f = 8.
find the real numbers x&y so that (x^2+2xy)+i(y-1) = (x^2-2x+2y) - i(x+y)
Answer:
[tex]\displaystyle x_1 = 2-\sqrt{3} \text{ and } y_1 = \frac{\sqrt{3}-1}{2}[/tex]
Or:
[tex]\displaystyle x _ 2 = 2 + \sqrt{3} \text{ and } y _ 2 = -\frac{1+\sqrt{3}}{2}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle (x^2 + 2xy) + i(y-1) = (x^2 -2x + 2y) - i(x +y)[/tex]
And we want to find the values of x and y such that the equation is true.
First, distribute:
[tex]\displaystyle (x^2 + 2xy) + i(y-1) = (x^2 -2x + 2y) +i(-x -y)[/tex]
If two complex numbers are equivalent, their real and imaginary parts are equivalent. Hence:
[tex]\displaystyle x^2 + 2xy = x^2 - 2x +2y \text{ and } y - 1 = -x -y[/tex]
Simplify:
[tex]\displaystyle 2xy = -2x +2y \text{ and }x = 1 - 2y[/tex]
Substitute:
[tex]\displaystyle 2(1-2y)y = -2(1-2y) + 2y[/tex]
Solve for y:
[tex]\displaystyle \begin{aligned} 2(y - 2y^2) &= (-2 + 4y) + 2y \\ 2y - 4y^2 &= 6y -2\\ 4y^2 + 4y - 2& = 0 \\ 2y^2 + 2y - 1 &= 0 \\ \end{aligned}[/tex]
From the quadratic formula:
[tex]\displaystyle \begin{aligned} y &= \frac{-(2)\pm\sqrt{(2)^2 - 4(2)(-1)}}{2(2)} \\ \\ &= \frac{-2\pm\sqrt{12}}{4} \\ \\ &= \frac{-2\pm2\sqrt{3}}{4}\\ \\ &= \frac{-1\pm\sqrt{3}}{2} \end{aligned}[/tex]
Hence:
[tex]\displaystyle y_1 = \frac{-1+\sqrt{3}}{2} \text{ or } y_2 = \frac{-1-\sqrt{3}}{2}[/tex]
Then:
[tex]\displaystyle x _ 1 = 1 - 2\left(\frac{-1+\sqrt{3}}{2}\right) = 1 + (1 - \sqrt{3}) = 2 - \sqrt{3}[/tex]
And:
[tex]\displaystyle x _ 2 = 1 - 2\left(\frac{-1-\sqrt{3}}{2}\right) = 1 + (1 + \sqrt{3}) = 2 + \sqrt{3}[/tex]
In conclusion, the values of x and y are:
[tex]\displaystyle x_1 = 2-\sqrt{3} \text{ and } y_1 = \frac{\sqrt{3}-1}{2}[/tex]
Or:
[tex]\displaystyle x _ 2 = 2 + \sqrt{3} \text{ and } y _ 2 = -\frac{1+\sqrt{3}}{2}[/tex]
2. Which type of variation is represented by the following equation?
indirect variation
Verification
[tex]\\ \rm\Rrightarrow s\propto \dfrac{1}{y}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{s_1}{t_2}=\dfrac{s_2}{t_1}[/tex]
[tex]\\ \rm\Rrightarrow s_1t_1=s_2t_2[/tex]
Does anyone know how to finish this equation?
Janice is building a model volcano for the science fair. To find the right ratio, she starts by mixing small amounts of baking soda and vinegar. She finds that adding 1.5 teaspoons of baking soda for every fluid ounce of vinegar produces the best eruption. If Janice plans to us 0.5 cups of vinegar for her project, how many tablespoons of baking soda should she use?
Answer:
6 tablespoons of baking soda
Step-by-step explanation:
There are 8 fluid ounces in 1 cup and shes going to use half a cup so that means shes going to use 4 fluid ounces of vinegar. To find how much baking soda she is going to use, we are going to multiply.
1.5 * 4 = 6
Best of Luck!
Answer:
3 Tablespoons, 6 teaspoons
Step-by-step explanation:
In order to find the right ratio of Baking Soda to Vinegar we have to find ratio given,... they tell us that for every 1.5 teaspoon of baking soda, you must add 1 fluid ounce or vinegar,... thus the ratio of Baking Soda to Vinegar is (1.5 teaspoon / 1 Fluid ounce)
There are:
3 teaspoons = 1 Tablespoons
8 fluid ounces = 1 cup
So if you use 0.5 cups of Vinegar as they tell us we do than that is the same thing as using 4 Fluid ounce, and because your problem say 1.5 teaspoon of baking soda for every Fluid ounce of vinegar all you have to do it multiply your 1.5t by your 4 to get how many teaspoons of Baking Soda you will need,...
1.5 * 4 = 6
You need 6 teaspoons or 3 Tablespoons,...
Hope that helps,... and I'll see you in life,... well not, literally, but you get what I mean,... Chow!
x ^ 2 − 17x − 60
Which expression is equivalent to the expression above?
(Please explain in simple terms cause, it's usually hard for me to understand)
[tex] {x}^{2} - 17x - 60 \\ (x + 3)(x - 20)[/tex]
First we put parentheses and in each bracket we put (X) and then we put the signs x² is positive and the 17X before it is a negative q is positive with negative —> negative, and negative before 17X and negative before the 60 —> positive. And then the number that does not have (x) where did it come from, for example 60 came from 20 x 3 or 30 x 2...etc. We can verify this by multiplying the parentheses together and the same number comes out .
Or it can be checked by multiplying the first bracket 3 with x from the second parenthesis comes out 3X and negative 20 from the second parenthesis with X from the first parenthesis and subtract 3X from –20xcomes out –17X .
I hope I helped you^_^
Name the red line. Select ALL that apply.
1. PN
2. PW
3. WN
4. line d
5. NW
6. line P
Answer:
1. PN
Step-by-step explanation:
Is the function given by f(x)=3x-2 continuous at x=5?
Answer:
Yes the function is continuous f(5) = 13
Step-by-step explanation:
Replace the variable x with 5 in the expression
Simlify the results
f(5) = 3(5)-3
f(5) = 15=3
f(5) = 13
Plotting on a graph gives a coninous line with a positive gradient
y intercept (0,-2)
Please view the attached graph
f. 40% of students use the Math Lab on a consistent basis. If 1,250 students are
enrolled, about how many use the Math Lab on a consistent basis?
Hi
it's means multiplicate your number by 40/100 ie : 0.4
have a try. Math is all about method and practice.
It took Emma 3/4 hour to rake the leaves. It took her 1/5 hour more to
weed the garden than it took to rake the leaves. It took her 0.2 hour
more to mow the lawn than it took to weed the garden. Discuss a
strategy you can use to find the answer. Then determine how long it
took her to do all three chores.
9514 1404 393
Answer:
total: 2.85 hours = 2 17/20 hours
Step-by-step explanation:
Strategy: convert all fractions to decimals, determine weeding and mowing times, and add the three times to find the total.
3/4 = 0.75
1/5 = 0.2
Solution:
raking time: 0.75 hours
weeding time: 0.75 +0.2 = 0.95 hours
mowing time: 0.95 +0.2 = 1.15 hours
__
Total time: 0.75 +0.95 +1.15 = 2.85 hours = 2 17/20 hours
_____
Additional comment
You may recognize that 0.95 is the middle of three equally-spaced values. Then the total will be 3×0.95 = 2.85 hours.
-(7-4x)=9
can somebody help me with this, and if you could, can you show work?
Answer:
x=4
Step-by-step explanation:
Simplifying
-1(7 + -4x) = 9
(7 * -1 + -4x * -1) = 9
(-7 + 4x) = 9
Solving
-7 + 4x = 9
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '7' to each side of the equation.
-7 + 7 + 4x = 9 + 7
Combine like terms: -7 + 7 = 0
0 + 4x = 9 + 7
4x = 9 + 7
Combine like terms: 9 + 7 = 16
4x = 16
Divide each side by '4'.
x = 4
Answer:
x = 4
Step-by-step explanation:
-(7 - 4x) = 9 (Given)
-7 + 4x = 9 (Distributed)
-7 + 4x + 7 = 9 + 7 (Add 7 on both sides)
4x = 16 (Simplify)
4x/4 = 16/4 (Divide 4 on both sides)
x = 4 (Simplify)
I =∫▒dx/(x^2 √(x^2+4))
brainiest to whoever right.
Answer:
The problems listed are all the formulas for 2d figures:
Area of a Triangle: 1/2 B*H
Area of a Square: S^2
Area of a Rectangle: l*w
Perimeter of a Square: 4s
Perimeter of a Triangle: a+b+c
Perimeter of a Rectangle: 2l+2w
plz help me do this thanks
A missile was fired from a submarine from 220 feet below sea level. If the missile reached a height of 10400 feet before exploding, what was the change in the altitude of the missile?
Answer:
10,620
Step-by-step explanation:
Since it reached a height of 10,400 before exploding and was 220 feet below sea level we need to add the two numbers together to get the total change in altitude.
You can think of it as sea level = 0 so 220 feet below sea level is -220 and 10,400 above sea level is +10,400 so what's the difference between the two.
Finding the Difference
10400 - (-220)
= 10400 + 220
= 10620
Solve for r: 3r+2-r=-4
Answer:
r = -3
Step-by-step explanation:
3r + 2 - r = -4
2r + 2 = -4
2r = -6
r = -3
Answer:
r = -3
Step-by-step explanation:
3r + 2 - r = -4 (Given)
2r + 2 = -4 (Simplify)
2r + 2 - 2 = -4 - 2 (Subtract 2 on both sides)
2r = -6 (Simplify)
2r/2 = -6/2 (Divide 2 on both sides)
r = -3 (Simplify)
Which set of ordered pairs represents a function?
{(5, -8), (8,-1), (8,7), (-4,2)}
{(-9,-9), (7, -9), (-7, -7), (9,-8)}
{(4,7), (-7,-4), (6,8), (-7,6)}
{(0,8), (-7,2), (4, -9), (4, -3)}
Answer: The second one
Step-by-step explanation:
That's the only set where there is only one output for every input.
Find the area and the circumference of a circle with radius 7 ft.
Answer:
Area is 307.72 ft^2
Circumference is 43.96 ft
Step-by-step explanation:
Area is 2pir^2
Circumference is 2rpi
pi is about 3.14
A=2pi(7)^2
A= 98pi which is about 307.72 ft^2
C= 2(7)pi
C= 14pi which is about 43.96 ft
(I'm not sure whether they want the answer left in terms of pi or not)
Point V is on line segment UW. Given VW = 5x - 4, UV = 2x, and UW = 5x, determine the numerical length of VW
Answer:
VW = 6
Step-by-step explanation:
To find x, set up the following equation:
(5x - 4) + (2x) = 5x
Solve out left side
7x - 4 = 5x
Subtract 5x from both sides
2x - 4 = 0
Add 4 to both sides
2x = 4
Divide both sides by 2
x = 2
Plug into 5x - 4
5(2) - 4
10 - 4
6
Answer:
6
Step-by-step explanation:
5x - 4 + 2x = 5x
7x - 4 = 5x
-4 = -2x
2 = x
5(2) - 4
10 - 4
6
Find the area of this triangle.
8 m
14 m
A = [?] m2
Answer:
A = 56 m^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh where b is the base and h is the height
A = 12 (14)(8)
A = 56 m^2
The product of 2 more than 5 times a number and 4 less than three times a number
Sorry I'm not sure if I'm right just my thinking...
set the number to be x so that (5x+2)(3x-4)??
Which expression can be used to find the slope of a line containing the points (–3, 2) and (7, –1)?
A. (Image 092552)
B. (Image 092607)
C. (Image 092618
D. (Image 092630)
Answer:
C. (Image 092618
Step-by-step explanation:
[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1} } [/tex]
y1 is 2
y2 is -1
x1 is -3
x2 is 7
substitute:
[tex]slope = \frac{ - 1 - 2}{7 - ( - 3)} [/tex]
2.
It takes Troy 3 hours to mow his family's large lawn. With his little brother's help, he can
finish the job in only 2 hours. How long would it take the little brother to mow the entire
lawn alone ?
(A) 4 hr
(B) 5 hr
(C) 5.5 hr
(D) 6 hr
(E) 6.75 hr
Answer:
It takes four hours because the little bro is alone and only one lawn mower is used
Solve for x in the equation below.
-3x + 2 = -7
Answer:3
Step-by-step explanation:
-3x+2=-7
subtract 2 from both sides
-3x+2-2-(-7-2
simplify the arithmetic
-3x=-7-2
simplify the arithmetic aging
-3x=-9
=3
The formula d=rt is used to calculate the distance traveled by an object moving at a constant average speed during an elapsed time . How long would it take a pilot to fly 1240 miles at an average speed of 220 mph?
Answer:
Approx 5.64 hours
Step-by-step explanation:
d=rt
t=d/r
To find the time, divide distance by velocity
1240 / 220 = approx 5.64 hours
Identify the equation of the circle that has its center at (9, 12) and passes through the origin.
Answer: [tex](x-9)^2 + (y-12)^2 = 225\\\\[/tex]
This is the same as writing (x-9)^2 + (x-12)^2 = 225
========================================================
Explanation:
Any circle equation fits the template of [tex](x-h)^2 + (y-k)^2 = r^2\\\\[/tex]
The center is (9,12) which tells us the values of h and k in that exact order.
h = 9
k = 12
To find the radius r, we need to find the distance from the center (9,12) to a point on the circle. The only point we know on the circle is the origin (0,0).
Apply the distance formula to find the distance from (9,12) to (0,0)
[tex]d = \sqrt{ (x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{ (9-0)^2+(12-0)^2}\\\\d = \sqrt{ (9)^2+(12)^2}\\\\d = \sqrt{ 81+144}\\\\d = \sqrt{ 225}\\\\d = 15\\\\[/tex]
The distance from (9,12) to (0,0) is 15 units. Therefore, r = 15
An alternative to finding this r value is to apply the pythagorean theorem. The distance formula is effectively a modified version of the pythagorean theorem.
---------------------
Since h = 9, k = 12 and r = 15, we can then say:
[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-9)^2 + (y-12)^2 = 15^2\\\\(x-9)^2 + (y-12)^2 = 225\\\\[/tex]
which is the equation of this circle.
