Answer:
Step-by-step explanation:
The standard form equation for a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where h and k are the coordinates of the center. Our center is given as (-6,7) and the radius is given as 9, so that information fits into our standard form like this:
[tex](x-(-6))^2+(y-7)^2=9^2[/tex] and simplified, it looks like this:
[tex](x+6)^2+(y-7)^2=81[/tex]
That's choice C
x-13=x+1
Please help mee
I offer to give you $40 if you can flip a coin and have it land on heads 2 times in a row. If you get tails, you have to pay me $10. What is the probability that you will win this bet
Answer:
25%
Step-by-step explanation:
Each flip has a 50% probability of landing heads. Two in a row would be (50%)*(50%) = 25%
[Note: 25% of $40 is $10]. Don't waste your time.
At a sale this week, a desk is being sold for $336. This is a 36% discount from the original price.
What is the original price?
Answer:
$525
Step-by-step explanation:
We can find the original price by using the formula x - 0.36x = 336, where x is the original price, 0.36 is the discount percentage (converted to decimal form), and 336 is the total amount paid after the discount is applied:
[tex]x-0.36x=336\\0.64x=336\\x=525[/tex]
To check and further understand why the formula works, we can simply apply the discount to the original price and subtract the number from the original price:
525 * 0.36 = 189
525 - 189 = 336
Modeling the first formula gives us:
525 - (0.36 * 525) = 336
525 - 189 = 336
I NEED HELP WITH MY MATH PLEASE
What is the slope of the line that passes through the points (6, 2) and
(
-18, 2)? Write your answer in simplest form.
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, 2 ) and (x₂, y₂ ) = (- 18, 2 )
m = [tex]\frac{2-2}{-18-6}[/tex] = [tex]\frac{0}{-24}[/tex] = 0
The slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
m = ( y₂ - y₁) / (x₂ - x₁)
It is given that the two points are (6, 2) and (-18, 2).
The two-point can be represented as,
(x₁, y₁ ) = (6, 2)
(x₂, y₂ ) =(-18, 2)
The slope of the line can be obtained as,
m = ( y₂ - y₁) / (x₂ - x₁)
m = (2-2) / (-18-6)
m =0 / -24
m =0
Thus, the slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.
Learn more about the slope here:
brainly.com/question/3605446
#SPJ2
RSM wants to send 4 of its 18 teachers into a conference. How many ways can they do this?
There are 18c4 ways that RSM wants to send 4 of its 18 teachers into a conference. that means there are 3060 ways to send
there are 18 teachers and RSM wants to send 4 mem out of 18
so, we use combinatorics for this
Combinatorics is the branch of Mathematics dealing with the study of finite or countable discrete structures. It includes the enumeration or counting of objects having certain properties. Counting helps us solve several types of problems such as counting the number of available IPv4 or IPv6 addresses.
It is used to find solutions easily for possible ways of a problem
For that we are using the formula for combinatorics
NCr = n!/ (r! (n – r)!)
similarly 18c4 = 18!/ (4! (18 – 4)!)
= 3060
Therefore , there are 3060 ways that RSM wants to send 4 of its 18 teachers into a conference.
Learn more about combinatorics here
https://brainly.com/question/23694222
#SPJ4
I NEED HELP ASAP! The two cylinders below are similar. What is the volume of the larger cylinder?
Answer:
E
Step-by-step explanation:
We can find the volume either by finding the scale factor between the two figures and multiplying the first cylinder's volume by it or simply finding the diameter of the second cylinder and doing the equation for volume of a cylinder.
I chose the second way to work out.
Since the two cylinders are similar, we can simply set up a proportion to find the diameter, d, of the second cylinder:
[tex]\frac{6}{d}=\frac{4.5}{6}\\ \\ 4.5d=36\\ d=8[/tex]
The formula for volume of a cylinder is [tex]V=\pi r^2h[/tex]
The radius is simply d/2 so the radius of the second cylinder is 8/2 or 4.
Thus, we have
[tex]V=\pi *4^2*6\\V=\pi *16*6\\V=96\pi \\V=301.59[/tex]
A sequence is defined by the recursive function f(n 1) = one-halff(n). if f(3) = 9 , what is f(1) ?
[tex]f(1)[/tex] is [tex]81.[/tex]
What is a recursive function?A recursive function generates a series of phrases by repeating or using its own prior term as input.Problems that can be split down into smaller, repeating problems are ideal for recursion to solve. It is particularly useful when working on issues with numerous potential solutions that are too complex to handle iteratively. Searching a file system is an effective illustration of this.A recursive formula is one that defines each term in a sequence by reference to the one before it.To find f(1):
f(n 1) = one-half(n).
f(3) = 9.
[tex]f(3) = 9If n = 1,f(2) = 9×3f(2) = 27If n = 0,f(1) = 27 ×3f(1) = 81[/tex]
A sequence is defined by the recursive function [tex]f(1)[/tex] is [tex]81.[/tex]
To learn more about recursive functions, refer to:
https://brainly.com/question/11316313
#SPJ4
Answer:
36
Step-by-step explanation:
Assuming I understand the question correctly
[tex]\text{one-halff(n)} = \frac{1}{2} f(n)[/tex]
We have the recursive relationship
[tex]f(n+1) = \frac{1}{2} f(n)[/tex]
[tex]f(3) = 9[/tex]
[tex]f(3) = \frac{1}{2} f(2)[/tex]
[tex]f(2) = \frac{1}{2} f(1)[/tex]
So
[tex]f(3) = \frac{1}{2} (\frac{1}{2} f(1) = \frac{1}{4} f(1) \\[/tex]
So [tex]f(1) = 4f(3) = 4(9) = 36[/tex]
Verifying
If f(1) = 36 then f(2) = (1/2)f(1) = (1/2)36 = 18
f(3) = (1/2) f(2) = (1/2)(18) = 9
Consider a function that goes through the two points (0, 5) and (1, 20). Find the formula for the function if(a) the function is linear (of the formf(x) =mx b)
The formula for the linear function which is passing the points (0, 5) and (1, 20) is f(x) = 15x + 5.
According to the given question.
The linear form of the function is
f(x) = mx + b
Also, the function is passing through the points (0, 5) and (1, 20).
So, the given points (0, 5) and (1, 20) must satisfy f(x) = mx + b.
Now,
At (0, 5)
f(0) = m(0) + b
⇒ 5 = 0 + b
⇒ b = 5 ..(i)
Also,
at (1, 20)
f(1) = m(1) + b
⇒ 20 = m + 5 (from i)
⇒ m = 20 - 5
⇒ m = 15
Therefore, the formula for the linear function which is passing the points (0, 5) and (1, 20) is given by
f(x) = 15(x) + 5 (on substituting the vale of m and b in f(x) = mx + b).
⇒ f(x) = 15x + 5
Hemce, the formula of the function is f(x) = 15x + 5.
Find out more information about function here:
https://brainly.com/question/21107621
#SPJ4
Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:
A support structure is shown in which a right triangle PQR is formed with the right angle at Q. The length of PQ is shown as 14 feet, and the length of QR is shown as 6 feet..
Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer, stating the theorem you used. Show all your work. (5 points)
Part B: The length of rod PR is adjusted to 16 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)
Part A
Using the Pythagorean on the right triangle PQR, with PQ and QR as the legs and PR as the hypotenuse,
[tex]14^2 +6^2 =(PR)^2\\\\(PR)=\sqrt{14^2 +6^2}\\\\PR \approx \boxed{15.23 \text{ ft}}[/tex]
Part B
[tex](QR)^2 +6^2 =16^2\\\\(QR)^2 =16^2 -6^2\\\\QR=\sqrt{16^2 -6^2}\\\\QR \approx \boxed{14.83 \text{ ft}}[/tex]
G(x)=2x-8, f(x)=5-g(x) what is the value of f(10)
Answer:
-7
Step-by-step explanation:
[tex]f(10) = 5-g(10)\\=5-(2(10)-8)\\=5-(20-8)\\=5-(12)\\=-7[/tex]
The sum of two numbers is 84. The square of the first number is 6 more than the second number.
Write a system of equations to find the value of x, the first number, and y, the second number.
y = -x +
y = x² +
The system of equations to find the value of x, the first number, and y, the second number are;
y = -x + 84
y = x² + 6
System of equationThe system of equation are equations that contains more than two equation and unknown.
Let the two unknown numbers x and y
If the sum of two numbers is 84, hence;
x +y = 84
y = -x + 84
If the square of the first number is 6 more than the second number, hence;
x² = y + 6
Substitute equation 2 into 2 to have:
x² = y + 6
x² = (-x+84) + 6
x² = -x+84 + 6
x² +x+84 + 6 = 0
x² +x + 90 = 0
Hence the system of equations to find the value of x, the first number, and y, the second number are;
y = -x + 84
y = x² + 6
Learn more on system of equation here; https://brainly.com/question/12861087
#SPJ1
help on this math problem!! if there is any work that can be shown it would be great thanks!!!
Answer:
4230.44
Step-by-step explanation:
Which digit is in the hundredths place?
18.36
8
3
1
6
Answer:
6.becuase after the decimal or "." it goes 00.tenth, hundredth, thousandth, and so on
Step-by-step explanation:
PLEASE GIVE BRAINLIEST OR 5 ⭐
f(x) = 4x² - 7x - 15
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the
coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers
obtained in Part A and Part B to draw the graph. (5 points)
(10 points)
Look at the attached image above ☝️for explanation
Hope it helps! and if it's not pls tell me on the comment.
Which situation will likely have no correlation?
Answer:
The third one as they have no links really
For a given rabbit population, the relationship between the number of adult female rabbits, F, and the number of offspring, R, that survive to maturity, is given by this equation: R=3+(350F/F+625)
Considering the given function in the problem, it is found that:
a. 9.6 offspring survive to maturity when there are 12 female rabbits in the population.
b. At least 18 female rabbits are required for there to be 13 offspring.
What is the given function in this problem?The function gives the relationship between the number of adult female rabbits F and the number of offspring R as follows:
[tex]R = 3 + \frac{350F}{F + 625}[/tex]
When there are 12 female rabbits, we have that F = 12, hence:
[tex]R = 3 + \frac{350 \times 12}{12 + 625} = 9.6[/tex]
9.6 offspring survive to maturity when there are 12 female rabbits in the population.
For at least 13 offspring, we have that the number of rabbits needed is given as follows:
[tex]R \geq 13[/tex]
[tex]3 + \frac{350F}{F + 625} \geq 13[/tex]
[tex]\frac{350F}{F + 625} \geq 10[/tex]
[tex]350F \geq 10F + 6250[/tex]
[tex]F \geq \frac{6250}{340}[/tex]
[tex]F \geq 18[/tex]
At least 18 female rabbits are required for there to be 13 offspring.
More can be learned about functions at https://brainly.com/question/25537936
#SPJ1
NEED HELP ASAP
let h(x)=-1/3x+2. Find -4h(9)
Answer:
4
Step-by-step explanation:
h(x) = -1/3x+2 where we need to find -4h(9)
h(9): x = 9
h(x) = -1/3(9) + 2
h(x) = -3 + 2
h(x) = -1
-4h(9) is -4h(x):
-4(-1) = 4
A bucket contains exactly 3 marbles, one red, one blue and one green. a person arbitrarily pulls out each marble one at a time. What is the probability that the last marble removed is non-red?
The probability that the last marble removed is non-red is 2/3.
According to the given question.
Total number of marbles in a bucket = 3
And, a person arbitary pulls out each marble one at a time.
So, there are 6 possible sequences of removing 3 marbles.
Let R be the red marble, B be the blue marble and G be the green marble.
The possible sequences or sample space for removing marbles are: {RBG, RGB, BGR, BRG, GRB and GBR}.
Let A denotes the event of removing the non-red marbles at the last.
The favorable cases for event A are: RBG, RGB, BRG and GRB.
As, we know that probability of any event is calculated as by taking the ratio of total number of favorable outcomes to the total number of outcomes.
Thereofre,
The probability that the last marble removed is non-red
= 4/6
= 2/3
The probability that the last marble removed is non-red is 2/3.
Find out more information about probability here:
https://brainly.com/question/11234923
#SPJ4
In the right triangular prism below, BG Perpendicular FC
A right triangular prism is shown. Triangles A E D and B F G are the base triangles. A perpendicular bisector is drawn from point B to point G on side F C.
The volume of the prism is 900 cubic centimeters. The height of the prism is 15 centimeters and the height of the triangular base is 10 centimeters. What is the length of edge FC?
cm
The length of edge FC in the triangular prism is: 12 cm.
What is the Volume of a Right Triangular Prism?Volume of a right triangular prism = 1/2(Length of triangular base × height of triangular base × height of the prism).
Considering the image given showing a right triangular prism, we have the following:
Volume of triangular prism = 900 cubic centimeters
Length of triangular base = FC = ?
Height of triangular base = 10 centimeters
Height of the prism = 15 centimeters
Plugin the values
900 = 1/2(FC × 10 × 15)
900 = 1/2(FC × 150)
Multiply both sides by 2
2(900) = 2(1/2(FC × 150))
1,800 = FC × 150
Divide both sides by 150
1,800/150 = FC × 150/150
12 = FC
FC = 12 cm
The length of edge FC is: 12 cm.
Learn more about the volume of triangular prism on:
https://brainly.com/question/21173224
#SPJ1
Answer: 12
Step-by-step explanation:
Solve the right triangle. Round decimals to the nearest tenth
Answer: 42
Step-by-step explanation:
angle t is 42 degrees
Answer:
∠T = 42°
PT = 14.4
QT = 19.4
Step-by-step explanation:
An angle and its adjacent side are given in the right triangle. The other two sides can be found using trig relations. The third angle can be found using the angle sum theorem.
Trig relationsThe mnemonic SOH CAH TOA is intended to remind you of the relations between sides of a right triangle and the trig functions of its angles. The relations relevant to this triangle are ...
Cos = Adjacent/Hypotenuse ⇒ Hypotenuse = Adjacent/Cos
Tan = Opposite/Adjacent ⇒ Opposite = Adjacent×Tan
Then the missing side lengths are ...
QT = QP/cos(Q) = 13/cos(48°) ≈ 19.4282 ≈ 19.4
PT = PQ×tan(Q) = 13×tan(48°) ≈ 14.43796 ≈ 14.4
Angle sumThe angle sum theorem tells you the sum of angles in a triangle is 180°. This means the acute angles in a right triangle are complementary.
∠T = 90° -48° = 42°
The solution to the triangle is ...
∠T = 42°
PT = 14.4
QT = 19.4
__
Additional comment
The attachment shows the solution from one of many available triangle solvers. Some calculators have triangle solver functions built in.
The length of a spring with no applied force acting on it is 10.00 centimeters. Juanita applied different forces to the spring and recorded the new lengths of the spring in a table. She also graphed a scatterplot from the results in the table. Based on the scatterplot, which equation BEST represents these data?
Answer:
the second option L = 0.05F + 10
Step-by-step explanation:
the first one
F = 0.05L + 10
does not make any sense, as for length = 10 the force has to be 0. but this function here gives us
0.05×10 + 10 = 0.5 + 10 = 10.5
which is clearly not 0. so, this is wrong.
the second one is correct.
L = 0.05F + 10
it is not perfect, but it is the only one describing the first data points well. like, when F = 0, then L = 10.
the third
L = 0.05F
fails already at the beginning F = 0, as it gives us L = 0 instead of 10. this is wrong.
the fourth
F = 0.05L
fails also already at the beginning. for L = 10 we need to have F = 0. but instead we get F = 0.5. this is wrong.
find the gradient of 15y-6x=8
Answer:
2/5 or 0.4
Step-by-step explanation:
First we have to make equation into the gradient slope form :
y=mx+c m is gradient and c is y-intercept
15y-6x=8
First we add 6x to both sides :
15y = 6x+8
Now we divide both sides by 15 :
y = 6x+8 / 15
Split the fraction on the right :
y = 6x/15 + 8/15
6x/15 = 6/15x
Our gradient will be 6/15 = 2/5 or 0.4
Hope this helped and have a good day
A complex point of the form a 3i has a distance of 29 units from –9 24i. what is the value of a? –1 5 11 19.8
The value of a = 11
What is complex numbers ?
Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).Let a + i b = (a,b)
c + i d = (c , d)
the distance between two points = [tex]\sqrt{( a - c)^{2} + (b -d )^{2} }[/tex]
put values in the formula -
[tex]\sqrt{(a- (-9))^{2} + (3 - 24 )^{2} }[/tex] = 29
square both sides
[tex]{(a + 9)^{2} + (21)^{2} } = 29^{2}[/tex]
(a + 9)² = 841 - 441 ⇒ 400
(a + 9) = √400 = + 20
a = +20 -9
So, a = -29 or 11
Therefore, the value of a = 11
Learn more about complex number
brainly.com/question/28007020
#SPJ4
use an integer to represent 15 feet and below sea level
Answer:
-15 would be the answer because if it's below sea level it would have a negative sign in front of 15
Step-by-step explanation:
Five pounds is equal to 2.268 kilograms. How many kilograms is 2 pounds?
Mass is the amount of matter that a body possesses and its unit in the international system of units is the kilogram.
How many kilograms is 2 pounds?Knowing that 1 pound is 2.205 kilograms.Therefore ⇒ 2 lb * 1 kg / 2.205 lb = 0.907 kgAnswer: In 2 pounds there are 0.907 kilograms.
The height and weight of adults can be related by the equation y=48.3x−127 where x is height in feet and y is weight in pounds.
What does the slope of the line represent?
A. the average number of pounds per foot tall
B. the number of pounds heavier an adult one foot taller would weigh
C. the height of an adult weighing zero pounds
D. the number of adults in the sample
we conclude that the correct option is A, the slope is:
"the average number of pounds per foot tall"
What does the slope of the line represent?The linear equation:
y = 48.3*x - 127
Relates the height, x, and the weight, y of an adult.
Then the slope, which is 48.3, should have units of mass over height.
Now, if x is in feet and y is in pounds, then the slope has units of pounds/feet.
Then it represents the mean number of pounds per feet. So we conclude that the correct option is A:
"the average number of pounds per foot tall"
If you want to learn more about slopes:
https://brainly.com/question/1884491
#SPJ1
Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
The surface area of the pyramid is 34.8 in²
How to find the surface area of the figure?Since the figure is a square pyramid, its surface area, A = 4 × area of triangular face + area of square base.
The area of triangular face
Area of triangular face A' = 1/2bh where
h = height = 4.3 in and b = base = 3 in.So, A' = 1/2 × 4.3 in × 3 in
A' = 1/2 × 12.9 in²
A' = 6.45 in²
The area of square base
Area of square base A" = L² where L = length of base = 3 in
So, A" = (3 in)²
= 9 in²
The Surface area of pyramid.
Surface area of pyramid, A = 4A' + A"
= 4 × 6.45 in² + 9 in²
= 25.8 in² + 9 in²
= 34.8 in²
So, the surface area of the pyramid is 34.8 in²
Learn more about surface area of pyramid here:
https://brainly.com/question/22744289
#SPJ1
If you have 66 data observations in a sample, how many classes (bins) does the sturges' rule recommend for you to construct a frequency distribution?
According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7
Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.
Given,
n = 66
We know that,
According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:
[tex]k=1+log_{2} n[/tex]
Here, n is equal to 66 and by substituting the value to the equation we get:
[tex]k=1+log_{2} (66)[/tex]
k = 7.0444
k ≈ 7
Learn more about Sturge's rule here: https://brainly.com/question/28184369
#SPJ4
Shaking wants to write 2/6 as a decimal. which method could she use divide 6 by 2. divide 2 by 6. multiply 6 by 2. multiply 2 by 6
she should use 2 by 6
Step-by-step explanation:
2 divided by 6 will give 0.3 in 1d.p