If the radius of the planet is given by R, and the height above the surface is given by h, use the figure below, and the Pythagorean Theorem to derive the formula for the distance, d, to the horizon tangent point, assuming that the triangle is a right triangle.
Please answer the second one too
Applying the pythagroean theorem, the formula to find the horizontal distance, d, is: [tex]\mathbf{d = \sqrt{h^2 - R^2} }[/tex]
What is the Pythagorean Theorem?The pyhagroean theorem is given as, c² = a² + b², where h is the longest side of the right triangle.
Given the following:
c = ha = db = RThe formula derived would be:
h² = d² + R²
Make d the subject fo the formula
[tex]\mathbf{d = \sqrt{h^2 - R^2} }[/tex]
Learn more about the pythagorean theorem on:
https://brainly.com/question/654982
#SPJ1
6
Mr. Jones determined that the equation y = 98 - 15 x could be used to predict his
students' unit test scores, based on the number of days, x, a student was absent
during the unit. What is the meaning of the y-intercept of the function?
A. A student who was not absent during the unit should score about 98.
B. A student who was not absent during the unit should score about 94.5.
C. A student's test score should increase by about 3.2 points for each day the
student is absent.
D. A student's test score should decrease by about 3.2 points for each day the
student is absent.
HELP ME!!!!!!
The data represents the yearly salary, in thousands of dollars, for 9 managers.
{68, 54, 104, 183, 72, 84, 75, 108, 71}
What is the five-number summary?
A. Minimum = 54Q1= 69.5Median = 75Q3= 106Maximum = 183
B. Minimum = 54Q1= 72Median = 74.5Q3= 104Maximum = 183
C. Minimum = 54Q1= 71Median = 74.5Q3= 108Maximum = 183
D. Minimum = 54Q1= 70Median = 74.5Q3= 106Maximum = 183
Answer:
A. Minimum = 54, Q1= 69.5, Median = 75, Q3= 106, Maximum = 183
Step-by-step explanation:
Arranging the data set in order from least to greastest we get:
54, 68, 71, 72, 75, 84, 104, 108, 183
From this, we can see that the minimum value is 54 and the maximum value is 183.
Taking a number off one by one on each side of the data set gives the median. In the middle lies 75, so that is our median
To find quartile ranges, split the data set into two where the median lies, then, find the median of those two data sets. The medians will be the values of the upper (Q3) and lower quartiles (Q1).
Q1: 54, 68, 71, 72
68 + 71 = 139
139 ÷ 2 = 69.5
-----
Q3: 84, 104, 108, 183
104 + 108 = 212
212 ÷ 2 = 106
Option A is the only answer with all of these values, therefore, it is the answer.
hope this helps!
5. F-LE.1.2
Two terms from a sequence are two terms from a sequence are shown in
the table below. Which formula does not
generate these terms?
A, an = 2n
B. an = 2(n-1) + 2
C. An=2"
D. an = 2n-1 + 2
Answer:
A, an = 2n. B. an = 2(n-
Step-by-step explanation:
can you brainlist me
Please help. Will mark brainlyest!
T.True F.False While on your Limited Learner Permit (Level 1), you are required to keep a Driving Log and record a minimum of 60 hours of driving time.
It is true that you are required to keep a Driving Log and record a minimum of 60 hours of driving time, while on level 1
How to determine the truth value?There are 5 requirements a driver must fulfil before progressing to level 2 of learner permit.
One of these requirements is that the driver must spend at least 60 hours driving.
This means that the minimum driving time is 60 hours
Hence, the statement is true
Read more about speed and time at:
https://brainly.com/question/4931057
#SPJ1
What is the probability of rolling numbers that add to 8 when rolling two standard number cubes? Use the chart to help you solve the problem
A 7/36
B 5/36
C 11/26
D 1/6
Answer:
It's 3/18 becasue in total there are 18 choices but only 3 add up to 8
help quick!
Jennifer is collecting cans of food for a food drive at her school. On
week one, she collected 4 cans. On week two she had 5 cans. By
week five, she had 8 cans. How many cans will she have collected by
week twelve?
Answer:
make me brainliest pls hope it helps :)
Step-by-step explanation:
week 1 = 1+3=4
week 2= 2+3=5
week 5=8+3=11
11 cans
which transformation of y = f(x) moves the graph 9 units to the left and 5 units down
Answer:
y=f(x+9)-5
Step-by-step explanation:
to move the graph 9 units to the left, you would need to add 9 to the variable (which is x) - so that transformation for y=f(x) would look like this:
y=f(x+9)
then, to move the graph 5 units down, you would need to subtract 5 from f(x), so the transformation for y=f(x) that moves the graph 5 units down would be:
y=f(x)-5
now, you would put that all together and it would look like this:
y = f (x+9) -5
i hope this helps.
Graph the system of equations below on a piece of paper. What is the solution? TW y=x-1 y=-2x+5
A system of equations
y= x-1y= -2x+5To find↷The solution to the system of equationsAnswer↷(2,1)Solution↷y = x -1 _ _ _ _ _ _(1)
y=-2x+5_ _ _ _ _ _(2)
subtracting equation 2 from equation 1,we get,
x -1 = y
-(-2x +5 = y)
__________
3x -6 = 0
3x = 6
x = 6/3
x = 2
___________
Plugging the value of x in equation 1,y= 2-1
y= 1
hence, the solution of this system of equation is (2,1)We will solve this through graphical way
Graph both equations
Solution is
(2,1)Graph attached
What is the value of x?
Enter your answer in the box.
x =
The figure shows 2 right triangles, triangle A B C with right angle B and triangle B D C with right angle D. The measure of angle B A C is 45 degrees. The measure of angle D B C is 60 degrees. The length of side C A is 6 square root 2. The length of side B D is x.
Answer:
x=3
Step-by-step explanation:
I took the test and I got it right but if you want an explanation see bellow.
so triangle ABC is a 45- 45 -90 and we are given the hypotenuse of [tex]6\sqrt{2}[/tex]
and on a 45-45-90 triangle we know that the hypotenuse is always [tex]s\sqrt{2}[/tex] s standing for the lengths of both of the legs since they are both equal, so this tells us that line segment AB and BC are equal to 6, SO triangle BCD hypotenuse is equal to 6.Triangle BCD is a 60-90-30 triangle as we can tell by the measures given, and in a 60-90-30 triangle the hypotenuse is equal to S and it's shorter length known as line segment BD on this triangle is equal to [tex]\frac{s}{2}[/tex] and since we know s=6 we can do [tex]\frac{6}{2}[/tex] giving us our answer 3.
Using the sine ratio and the cosine ratio, the value of x in the given triangle is calculated as: x = 6.
How to Find the Value of x?Using the sine ratio, find BC:
sin ∅ = opposite/hypotenuse
Given the following:
∅ = 45°
hypotenuse = 6√2
opposite = BC
Substitute:
sin 45 = BC/6√2
sin 45 = BC/6√2
√2 = BC/6√2 [sin 45 = √2]
BC = √2 * 6√2
BC = 12 units
Use the cosine ratio to find x:
cos ∅ = adjacent/hypotenuse
Thus, we have:
cos 60 = x/12
1/2 = x/12 [cos 60 = 1/2]
2x = 12
x = 6.
Learn more about sine ratio on:
https://brainly.com/question/2920412
#SPJ2
What is the area of the trapezoid at the right
Answer:
144
Step-by-step explanation:
8•6 because two triangles make a square and they are the same size, so there is no need to divide by half
then 8•12 for the square in the middle
what is the simplest way to explain how to do this?
Answer:
96
Step-by-step explanation:
area of a triangle = h x b/2 which means ill do
8 x 8 = 64
then 64/2
32
8x8 (again) = 64
64+32 = 96
Answer:
96 in^2. Find the area of the square, then the area of the triangle. After that, add them together.
Step-by-step explanation:
First, let's find the area of the square:
A = lw
A = 8 x 8
A = 64
Now, let's find the area of the triangle.
A = 1/2lh
A = 1/2(8)(8)
A = 1/2(64)
A = 32
Now, all we have to do is add 64 and 32 to get the total area
64 + 32 = 96
The lengths of the sides of triangle XYZ are written in
terms of the variable m, where m 2 6.
Which is correct regarding the angles of the triangle?
Omzx <'
mzz
Х
m +8
OmZY
m-3
OmZY
2m + 3
Omzz
Z
Answer:
its the 3rd one i think but don't trust me cuz ion know
The correct regarding the angles of the triangles are,
⇒ m ∠Y < m ∠Z < m ∠X
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Since, Given that;
m ≥ 6, we will substitute 6 in for m.
This makes;
XZ = m-3 = 6-3 = 3.
XY = m+8 = 6+8 = 14.
YZ = 2(6)+3 = 12+3 = 15.
Hence, This makes the sides, in order from least to greatest as;
XZ < XY < YZ.
Thus, The angles associated with these are opposite their corresponding sides; XZ corresponds with Y; XY corresponds with Z; and YZ corresponds with X.
This means correct regarding the angles of the triangles are,
⇒ m ∠Y < m ∠Z < m ∠X
Thus, The correct regarding the angles of the triangles are,
⇒ m ∠Y < m ∠Z < m ∠X
Learn more about the angle visit:;
https://brainly.com/question/25716982
#SPJ7
what is 339.12 rounded to the nearest hundreth
Answer:
339.12 rounded to the nearest hundreth is 339
Because the hundreth place right now is 1 so anything below five keep the same
Please consider brainliest <3
Step-by-step explanation:
Answer: 339.10
Step-by-step explanation: The value of 2 is the hundredth and it is rounded up to 0
Use the rule y = -2x + 5 to answer the questions below.
a. What is the slope of the line?
Answer:
-2
Step-by-step explanation:
Slope-intercept form: y = mx + b, in which:
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
~
Note the numbers that replace the given variables:
y = mx + b ; y = -2x + 5
y = y
m = slope = -2
x = x
b = y-intercept = 5
-2 is your answer for slope.
~
Answer:
The slope is -2.
Step-by-step explanation:
I hope this helps! :)
The formula is y=mx+b, where m (in the place of -2) is the slope.
You might need:
Calculator
Problem
The following shape has 111 pair of parallel sides.
What is the area of the shape?
Answer:
56
Step-by-step explanation:
First I would get the area of the entire figure as if it were a Rectangle
10x7 = 70 Area if the figure was a rectangle.
We can form a triangle with the cut out space, the height of the triangle is 10-6 which is 4 and has a base of 7.
7x4= 28
28/2 = 14 Area of triangle cutout
Now you subtract the two figures
70-14= 56
56 Is the area
The area of the given shape is 56 square units.
What is an area?The quantity of space within a two-dimensional figure or form is measured by its area. It is a number that describes the size or extent of a surface, like the surface of a flat plane or the contours of an area on a map.
First I would get the area of the entire figure as if it were a Rectangle
10x7 = 70 Area if the figure was a rectangle.
Form a triangle with the cutout space, the height of the triangle is 10-6 which is 4, and has a base of 7.
7 x 4= 28
28/2 = 14 Area of triangle cutout
Now you subtract the two figures
70-14= 56 Square units
To know more about the area follow
https://brainly.com/question/21135654
#SPJ2
Find the measurement of the missing angle of this quadrilateral.
Answer:
x= 81°
Step-by-step explanation:
the interior angles of a quadrilaterial add up to 360°
143+80+56+x=360
condense left side: 279+x=360
isolate x: 279-279+x=360-279
x= 81°
What is the answer ?
Answer:
The answer for Q35 is : 176 cubic feet
Step-by-step explanation:
V = 16×3×2+16×5
= 96 + 80
= 176 cubic feet
Systolic blood pressure for a group of women is normally distributed, with a mean of 121 and a standard deviation of 9. Find the probability that a woman selected at random has the following blood pressures. (Round your answers to four decimal places.) (a) greater than 136 (b) less than 114 (c) between 114 and 128
the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.
What is a Z-table?A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.
Given the mean is 121 while the standard deviation of the women is 9. Therefore, Using the z-table, the probability can be found.
(a) The probability that a woman selected at random has blood pressures greater than 136.
[tex]P(x > 136) = 1 - P(x < 136)\\\\P(x > 136) = 1 - P(z < \dfrac{x-\mu}{\sigma})[/tex]
[tex]=1 - P(z < \dfrac{136-121}{9})\\\\=1 - P(z < 1.667)\\\\=1-0.9515\\\\=0.0485[/tex]
(b) The probability that a woman selected at random has a blood pressure less than 114.
[tex]P(x < 114)= P(z < \dfrac{114-121}{9})\\\\[/tex]
[tex]= P(z < -0.77)\\\\= 0.2206[/tex]
(c) The probability that a woman selected at random has a blood pressure between 114 and 128.
[tex]P(114 < x < 128)= P(\dfrac{114-121}{9} < z < \dfrac{128-121}{9})\\\\[/tex]
[tex]= P(-0.77 < z < 0.77)\\\\= P(z < 0.77)-P(z < -0.77)\\\\= 0.7794 - 0.2206\\\\=0.5588[/tex]
Hence, the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.
Learn more about Z-table:
https://brainly.com/question/6096474
#SPJ1
WILL GIVE BRANLIEST
Which number is irrational? Question 2 options:
A fraction
A terminating decimal
The square root of an imperfect square
Zero
Answer:
The square root of an imperfect square
Step-by-step explanation:
Paula bicycled for 20 minutes and covered 5 miles. What is her speed in miles per hour?
A sequence is defined by an = -5+ (n - 1) 14, where n is a positive integer. What is the value of 410?
The sequence an = -5 + (n - 1)14 is an arithmetic sequence
The value of a10 is 121
How to determine the the a10-th term?The sequence is given as:
an = -5 + (n - 1)14
To calculate the value of a10, we set n = 10
So, we have:
a10 = -5 + (10 - 1) * 14
Evaluate the difference
a10 = -5 + 9 * 14
Evaluate the product
a10 = -5 + 126
Evaluate the sum
a10 = 121
Hence, the value of a10 is 121
Read more about sequence at:
https://brainly.com/question/6561461
Which of the following are factors of 6x^2+30x-36? Select all that apply.
Answer choices:
1. X-1
2. X+2
3. 2
4. 3
5. X+6
6. X-6
7. X-2
Answer:
Step-by-step explanation:
If Deb cleans a 9100 square foot building for a total of $306.00, what is the amount Deb gets paid for a building half that size? (Hint: You will need to calculate the square footage of the building before you set up the ratio.)
A. 4550
B. 153
C. 306
D. 4397
Answer:
Answer choice B: 153
Step-by-step explanation:
Find the equation of a line that passes through the point (4,2) that is perpendicular to the line y=4/3x
Answer:
Step-by-step explanation:
The a line that is perpendicular to the reference line will have a slope that is the negative inverse of the slope of the reference line. We'll look for a line that has the form y=mx+b, where m is the slope and b is the y-intercept. The reference line y=(4/3)x has a slope of (4/3) and a y-intercept of 0 (it crosses the y axis at x = 0).
The negative inverse the the slope (4/3) would be -(3/4).
The new line will be y = -(3/4)x + b.
To find point, use the given point and solve for b:
y = -(3/4)x + b
y = -(3/4)x + b for point (4,2)
2= -(3/4)(4) + b
2= -3 + b
b = 5
The equation of the perpendicualr line is y = -(3/4)x + 5
See attached graph.
please solve the given problem
Find the value of x and y
If
5x-2y=0
5x+10y=100
Answer:
The answer is given in the picture
Step-by-step explanation:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
Answer:
x = 10/3 , y = 25/3
Step-by-step explanation:
Let's solve your system by substitution.
5x−2y=0 ; 5x+10y=100
Step 1: Solve 5x−2y=0 for x:
5x−2y=0
5x−2y+2y=0+2y (Add 2y to both sides)
5x=2y
5x=2y
5x/5=2y/5 (Divide both sides by 5)
x=2y/5 (Simplify)
Step 2: Substitute 2y/5 for x in 5x+10y=100:
5x+10y=100
5 2/5y +10y=100
12y=100 (Simplify both sides of the equation)
12y/12=100/12 (Divide both sides by 12)
y=25/3
Step 3: Substitute 25/3 for y in x=2/5y
x=2/5y
x=2/5 * 25/3
x=10/3 (Simplify both sides of the equation)
At the end we have the following answers :
x = 10/3
y = 25/3
find the product 867 and 49
Answer:
42483
Step-by-step explanation:
867*49 = 42483
The area of the base of a cone is 36π square centimeters. The height of the cone is 20 centimeters. What is the closest to the volume of the cone?
A.740 cm ³
B.750 cm ³
C.800 cm ³
D.775 cm ³
Answer:
the answer is d because i have dont it b4
Step-by-step explanation:
Write the correct ratio (fraction) for each triangle.
Answer:
21/20
20/29
21/20
20/29
21/29
20/21
Step-by-step explanation:
Use Soh Cah Toa for each, using the right equation for the right angle
e.g for sin(z) we use the opposite/adjacent for that angle
the hypotenuse is the biggest sizethe opposite is the side opposite to the angle you are usingthe adjacent is the other side