Answers
Answer:
r=9
Step-by-step explanation:
We can use the Pythagorean to solve, since this is a right triangle
The leg lengths are r and 12
The hypotenuse is (r+6)
a^2 + b^2 = c^2
r^2 + 12^2 = (r+6)^2
Foiling out the right hand side
(r+6)(r+6_ = r^2+6r+6r+36
r^2 +144 = r^2 +12r+36
Subtracting r^2 from each side
r^2-r^2 +144 = r^2-r^2 +12r+36
144 = 12r+36
Subtract 36 from each side
144-36 = 12r+36-36
108 = 12r
Divide each side by 12
108/12 = 12r/12
9=r
AC=AB+BC
AC=6+r
AD=12
DC=r
by Pythagorus theorem
AC*2=AD*2+DC*2
(6+r)*2=12*2+r*2
36+12r+r*2=144+r*2
12r+r*2-r*2=144-36
12r=108
r=108/12
r=9
Related Questions
Find the vertical, horizontal, and slant asymptotes, if any, for f(x)=5x^3-51x^2+77x+100/x^2-11x+24
Answers
Answer:
Step-by-step explanation:
Given: f(x)=5x^3-51x^2+77x+100/x^2-11x+24
Please use parentheses to eliminate any ambiguity:
f(x) = (5x^3-51x^2+77x+100) / (x^2 - 11x + 24)
or (better yet):
5x^3-51x^2+77x+100
f(x) = ---------------------------------
x^2 - 11x + 24
The vertical asymptotes here are at the zeros of the denominator:
x^2 - 11x + 24 = 0, This quadratic equation has coefficients a = 1, b = -11 and c = 24. Thus, its roots (zeros) are:
-(-11) ± √( 121 - 4(1)(24) )
x = -------------------------------------
2(1)
or:
11 ± √( 25 )
x = --------------------
2
or: x = 8 and x = 3
The vertical asymptotes are x = 8 and x = 3.
If we attempt to divide x^2 - 11x + 24 into 5x^3 - 51x^2 + 77x + 100, we see that the first term of the quotient is 5x. As x increases or decreases without bound, 5x goes to either ∞ or -∞, so we conclude that there is no horiz. asymptote. Continuing this division results in:
5x + 4 + a fraction
This represents the slant asymptote, y = 5x + 4
Answer:
5x+4
Step-by-step explanation:
edge 2020 2021
The sum of three consecutive numbers is 72. What is the middle number?
Answers
Answer:
48
Step-by-step explanation:
Assuming that the numbers went in a pattern instead of a random order it would be 48 because 48 divided by 3 would be 24. 24 would be the first number though, so it would be 48 because 24 plus 24 is 48.
Hope this helps, have a great day!
Thhe answer is 48 :]
which pattern folds into the triangular prism above?
Answers
Answer:
the answer will be the letter Y
Step-by-step explanation:
because the darker shaded side are at the bottom and one is at the top and don't forget about the two triangles
Is .9 greater or less than 95%?
Answers
Less than 95%
Why because if you change .9 into a percentage, it turns into 90%
I hope that was correct
[tex]\text{Hey there!}[/tex]
[tex]\text{Is .9 greater or less than 95\%?}[/tex]
[tex]\bf{.9\rightarrow0.9\rightarrow\frac{18}{20}}[/tex]
[tex]\bf{95\%\rightarrow0.95\rightarrow\frac{19}{20}}[/tex]
[tex]\bf{You\ could\ reask\ yourself\ is\frac{18}{20}\ greater\ or\ less\ than\frac{19}{20}}?[/tex]
[tex]\text{Note: Solve the fractions/ decimals/ percentages to where you can}[/tex] [tex]\text{understand it better}[/tex]
[tex]\text{After that you'd find your result to your question}[/tex]
[tex]\boxed{\boxed{\text{Thus your answer will be: .9 is LESS THAN 95\%}}}[/tex] [tex]\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Please Help , Is it ABC or D
Answers
Answer:
A
Step-by-step explanation:
To determine the scale factor compare the quotient of the coordinates of the image with the original coordinates
A
[tex]\frac{2}{1}[/tex] = [tex]\frac{4}{2}[/tex] = 2
B
[tex]\frac{4}{2}[/tex] = [tex]\frac{8}{4}[/tex] = 2
C
[tex]\frac{8}{4}[/tex] = [tex]\frac{16}{8}[/tex] = 2
Hence the scale factor is 2
round 26.86 to the nearest tenth
Answers
Answer:
26.9
Step-by-step explanation:
Right now we have '8' in the tenths place. That '6' following the '8' requires us to round up. Thus, 26.86 to the nearest tenth is 26.9.
The fence is 68 feet long and 1/2 feet thick. 7 feet of space is between each post. How many posts are used for the fence. I think it’s basic division but I’m not sure what to divide by lol.
Answers
Answer:
We could say 10
Step-by-step explanation:
1) Remove unneeded info
2) Divide the length by the distance between posts
68/7
3) Will give you a decimal but ro7nd up to 10
find the exact values of sin pi/12
Answers
Answer:
[tex]\sin (\frac{\pi}{12})=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]
Step-by-step explanation:
We want to find the exact value of
[tex]\sin \frac{\pi}{12}[/tex]
We rewrite the given expression to obtain:
[tex]\sin \frac{\pi}{12}=\sin (\frac{\pi}{3}-\frac{\pi}{4})[/tex]
We use the identity:
[tex]\sin (A-B)=\sin A \cos B-\sin B \cos A[/tex]
[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\sin \frac{\pi}{3} \cos \frac{\pi}{4}-\sin \frac{\pi}{4} \cos \frac{\pi}{3}[/tex]
[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2} \times \frac{1}{2}[/tex]
[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]
The exact value of sin(π/12) is ±√(2 - √3)/2 by using half-angle formula
To find the exact value of sin(π/12), we can use the half-angle formula for sine:
sin(x/2) = ±√[(1 - cos(x))/2]
In this case, x = π/6.
Therefore, we can use the half-angle formula with x = pi/6 to find the exact value of sin(π/12).
sin(pi/12) = ±√[(1 - cos(π/6))/2]
Let's calculate the value step by step:
cos(π/6) = √3/2
sin(π/12) = ±√[(1 - √3/2)/2]
To simplify further, let's rationalize the denominator:
sin(π/12) = ±√[(2 - √3)/4]
sin(π/12) = ±√(2 - √3)/2
Therefore, the exact value of sin(π/12) is ±√(2 - √3)/2.
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The average man takes 7192 steps a day about how many steps does the average man take any year
Answers
Answer:
2625080
Step-by-step explanation:
just multiply by 365
Answer: 2,625,080
Explanation: 1 day = 7192, 365 days x 7192 = 2,625,080
Suppose that you ask three friends to go to the mall. Each one has a 0.70 chance of saying yes. What is the probability that all three friends will say they can go to the mall with you? a. 0.027 c. 0.343 b. 0.21 d. 0.657
Answers
____________________________________________________
Answer:
Your answer would be 0.343.
____________________________________________________
Step-by-step explanation:
In the probability questions like this one, in order to get the answer,we would use the multiplication rule.
In your questions, we are trying to find the probability of ALL of your friends going to the mall with you.
Lets make it easier for you.
Whenever in probability you can say and, you multiply.
This means that you would try to find if friend 1 and friend 2 and friend 3 will say yes.
That's the same as saying friend 1's probability × friend 2's probability × friend 3's probability
We know that each friend has a 0.70 chance of saying yes.
Using the multiplication rule, we would just multiply 0.7 three times.
[tex]0.7 *0.7*0.7=0.343[/tex]
When you multiply, you should get 0.343.
There is a 0.343 chance of ALL your friends saying yes to go to the mall with you.
0.343 would be your FINAL answer.
____________________________________________________
To solve this problem, you need to consider the probability of each friend agreeing to go to the mall individually, then multiply these probabilities together to find the probability that all three will say yes.
Since each friend has a 0.70 chance of saying yes, we can calculate the combined probability as follows:
For the first friend, the probability is 0.70.
For the second friend, the probability is also 0.70.
For the third friend, the probability remains 0.70.
To find the combined probability that all three friends will say yes, we multiply the individual probabilities together:
\( Probability (All Say Yes) = Probability (Friend1 says Yes) \times Probability (Friend2 says Yes) \times Probability (Friend3 says Yes) \)
\( Probability (All Say Yes) = 0.70 \times 0.70 \times 0.70 \)
When you calculate this, you get:
\( Probability (All Say Yes) = 0.343 \)
So the answer is c. 0.343.
explain why it is useful to write linear equations in equivalent form. what does each form reveal?
Answers
However, point slope equations can be awkward to use in some algebraic operations. In such cases, it may be helpful to convert the equation into a different form, the standard form. The standard form of an equation is Ax + By = C. In this kind of equation, x and y are variables and A, B, and C are integers.
Write the given equation in slope-intercept form, y=mx+b by solving for y. 4x - 2y =10
Answers
y = 2x - 5
Here’s a photo of the math
The equation will be y = 2x - 5
Given Equation: 4x - 2y = 10
Step 1: Move 4x to the other side to isolate -2y: -2y = -4x + 10
Step 2: Divide by -2 to solve for y: y = 2x - 5
Consider the following equations: −x − y = 1 y = x + 3 If the two equations are graphed, at what point do the lines representing the two equations intersect? (4 points) (−1, 2) (−2, 1) (1, −2) (2, −1)
Answers
Equation 1: -x-y = 1y, -x = 2y
Equation 2: 1y = x+3 , y = x+3
Substitute equation 2 into equation 1
-x = 2y
-x = 2(x+3)
-x = 2x + 6
-3x = 6
x = -2
Substitute x=-2 into equation 2
y = x+3
y = -2+3
y = 1
So, (x,y) = (-2,1)
What is the slope of the function?
-10, -5, 5, 10
Answers
It is -10
Because when you take two points from the table and put it into the equation y=my+b...
So for example, take (-4,-16) from the table and substitute into x and y...
-16=m(-4) + b
And then substitute all the options given in the question, so I tried -10 first and put it in the place of m( in the equation) because m is the slope.
Then the equation would look like this:
-16= -10(-4) +b
Now solve for b
B= 24
And then check your answer by the RHS and LHS Method..
-16=-40 +24
Which is equal to:
-16=-16
There fore the the slope of this equation is 10
Answer: 5
Step-by-step explanation:
The formula to find slope is given by :-
[tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given table in picture,
Take [tex]x_1=0\ ;\ y_1=4\\\\x_2=2\ ;\ y_2=14[/tex]
Then, slope of the given function will be given by :-
[tex]\text{Slope}=\dfrac{14-4}{2-0}\\\\\Rightarrow\text{Slope}=\dfrac{10}{2}=5[/tex]
Hence, the slope of the given function = 5
A coral reef grows 0.13 m every week. How much does it grow in 15 weeks
Answers
0.13 times 15 is 1.95. Which means the coral reef grows 1.95 m in 15 weeks.
For this case we have reef coral grows 0.13 meters per week, if we want to indicate how much will have grown in 15 weeks we have the following rule three:
0.13 metrs ---------------> 1 week
x -------------------------------> 15 weeks
Where "x" is the number of meters reef coral grows in 15 weeks.
[tex]x = \frac {15 * 0.13} {1}\\x = 1.95 \ m[/tex]
Thus, in 15 weeks it grows 1.95 meters.
Answer:
[tex]1.95 \ m[/tex]
What is the initial value of the function represented by this table?
x y
0 5
1 9
2 13
A) 0
B) 3
C) 4
D) 5
Answers
Answer:
Option D. 5
Step-by-step explanation:
we know that
The initial value of the function is the y-intercept, so is the value of the function when the value of x is equal to zero
In this problem observing the table
For x=0
The value of y is equal to y=5
therefore
The initial value is 5
Answer:
It is 5!
Step-by-step explanation:
I just did the test and got it correct.
Tools
Question 12
The bottom of a garage door is 2.8 meters above the ground. When a button is pushed, the door moves down at a rate of 0.6 meter per second. W
A 0.6 + 2.8t = 0
B 0.6 – 2.8t = 0
C 2.8 + 0.6t = 0
D 2.8 – 0.6t = 0
Answers
Answer: D. 2.8 - 0.6t
Step-by-step explanation:
The t represents how much time it takes. So, it goes down by 0.6 per second until it gets to 0.
A garage door's bottom is 2.8 meters above the ground. The door descends at a pace of 0.6 meters per second when a button is pressed. The equation for the above situation is 2.8 + 0.6t = 0. Option C is correct.
What is an equation?Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation.
It is given that, the bottom of a garage door is 2.8 meters above the ground. When a button is pushed, the door moves down at a rate of 0.6 meters per second.
The two expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation. The right side of an equation is typically assumed to be zero.
Suppose t represents the number of seconds, The equation for the given condition is,
2.8 + 0.6t = 0.
Thus, a garage door's bottom is 2.8 meters above the ground. The door descends at a pace of 0.6 meters per second when a button is pressed. The equation for the above situation is 2.8 + 0.6t = 0. Option C is correct.
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I think of a number, multiply it by three, and add four. I get twenty two.
Using the statement above, form an equation. Use the letter x for the unknown number.
Answers
Answer:
3x+4=22
Step-by-step explanation
So, if you minus 4 from 22 and divided by 3, there will be the answer for x. Which is 6.
The equation that could be formed using the letter x to be represent the unknown number is 3x + 4 = 22
let
x = the unknown number
multiply it by three
= x × 3
= 3x
add four
3x + 4
I get twenty two
3x + 4 = 22
solve for x
3x = 22 - 4
3x = 18
x = 18/3
x = 6
Therefore, the unknown number in the equation 3x + 4 = 22 is 6
check:
3x + 4 = 22
3(6) + 4 = 22
18 + 4 = 22
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Simplify 12√18-6√20-3√50-8√45
Answers
12√18-6√20-3√50-8√45
*Break each radical up into the product of a radical of a perfect square and a second radical*
12(√9*√2)-6(√4*√5)-3(√25*√2)-8(√9*√5)
*Simplify the radicals*
12(3√2)-6(2√5)-3(5√2)-8(3√5)
*Distribute*
36√2-12√5-15√2-24√5
*Combine like terms*
21√2-36√5
Hope this helps!!
The simplified form of the expression is 21√2-36√5.
Given,
12√18-6√20-3√50-8√45
Here,
12√18-6√20-3√50-8√45
⇒ Break each radical up into the product of a radical of a perfect square and a second radical.
Rewriting the expression,
12(√9*√2)-6(√4*√5)-3(√25*√2)-8(√9*√5)
⇒ Simplify the radicals
12(3√2)-6(2√5)-3(5√2)-8(3√5)
⇒ Distributive property
36√2-12√5-15√2-24√5
⇒ Combine like terms
21√2-36√5
Thus the simplified expression is 21√2-36√5.
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given x-5>-2 choose the solution set
Answers
x -5 > -2
Add 5 to both sides:
x > 3
The answer is the 3rd choice.
Answer:
x>3
Step-by-step explanation:
just add 5 to both sides :p
Solve m + 2/3 = 1/2
1 1/6
1/6
-1
- 1/8
Answers
Answer:
m = - 1/6
Step-by-step explanation:
Since 2/3 is larger than 1/2, m is going to be less than 0 because you have to subtract 2/3 to get to the right. That makes a and b incorrect. I can tell you that the answer doesn't appear to be there.
m + 2/3 = 1/2 Subtract 2/3
m = 1/2 - 2/3 The common denominator is 6
m = 3/6 - 4/6 Do the subtraction
m = - 1/6
You might want to check out the - 1/8.
The Answer: m = - 1/6
This is my other I need help account. So I have the bigger picture now. I hope this is better . But still ! Urgent! Help!
Answers
Answer:
A. 12 in^2
Step-by-step explanation:
Polygon ABCD is a kite. The area of a kite is equal to the product of the diagonals divided by 2.
One diagonal is segment AC.
AC = AE + CE = 2 + 2 = 4
The other diagonal is segment BD.
BD = BE + ED
BD = BE + 2BE
BD = 3BE
BD = 3(2) = 6
The diagonals measure 4 inches and 6 inches.
area = diagonal1 * diagonal2/2
area = 4 * 6 /2
area = 24/2
area = 12
Answer: A. 12 in^2
The longest chord of a circle is?
Answers
Answer:
diameter
Step-by-step explanation:
A chord is a line segment connecting any 2 points on the circumference of the circle.
The diameter connects 2 points and also passes through the centre of the circle, making it the longest chord.
Circle M has a radius of 7.0 cm. The shortest distance between P and Q on the
circle is 7.3 cm. What is the approximate area of the shaded portion of circle M? Please explain :)
Answers
Answer: C. [tex]25.6\ cm^2 [/tex]
Step-by-step explanation:
Given: Circle M has a radius = 7.0 cm.
The shortest distance between P and Q on the circle (arc length)= 7.3 cm.
Now, the central angle 'x' is given by :-
[tex]x=\dfrac{l}{r}\\\\\Rightarrow\ x=\dfrac{7.3}{7}=1.04285714286\ radian[/tex]
Now, the area of sector is given by :-
[tex]A=\dfrac{1}{2}r^2x\\\\\rightarrow\ A=\dfrac{1}{2}(7)^2(1.04285714286)\\\\\Rightarrow\ =25.55\approx25.6\ cm^2 [/tex]
Answer:
C.
Step-by-step explanation:
I did the test.
A recipe for cookies requires 2/3 cup of butter. Anna wants to make 1/4 of the recipe. How many cups of butter should Anna use to make the cookies? You must
Answers
Answer:5/12
Step-by-step explanation:2/3-1/4=5/12
For this case we must raise a rule three:
1 recipe ----------------------->[tex]\frac {2} {3}[/tex] butter
[tex]\frac {1} {4}[/tex]recipe -------> x
Where the variable "x" represents the amount of butter that requires a quarter of the cookie recipe.
[tex]x = \frac {\frac {1} {4} * \frac {2} {3}} {1}\\x = \frac {2} {12} = \frac {1} {6}[/tex]
So, Anna requires[tex]\frac {1} {6}[/tex] cup of butter
ANswer:
[tex]\frac {1} {6}[/tex]
What is the area of the triangle rounded to nearest hundredth
Answers
ANSWER
The area of the triangle is 48.6 square feet to the nearest tenth.
EXPLANATION
The area of the triangle is calculated using the formula
[tex]Area= \frac{1}{2} bc \sin(A) [/tex]
where A=94° is the included angle, b=7.5 inches and c=13 inches.
We substitute the values into the formula to obtain:
[tex]Area= \frac{1}{2} \times 7.5 \times 13 \sin(94 \degree) [/tex]
Area=48.6 ft² to the nearest tenth.
Jonathon deposits $11,000 in an account paying 6% compounded semiannually. Find the interest earned on the investment after 10 years.
$19,867.22
$8,954.20
$8,867.22
$19,954.20
Answers
Answer:
Total = Principal * (1 + 6%/2)^2*years
Total = 11,000 * (1.03)^2*10
Total = 11,000 * (1.03)^20
Total = 11,000 * 1.8061112347
Total = 19,867.22
Step-by-step explanation:
what is the volume of the cone with radius 6 inches and height 10 inches express the answer in terms of pi
Answers
Answer:
V = (1/3)(π)(6 in)²(10 in) = 120π in³
Step-by-step explanation:
The volume of a cone of radius r and height h is V = (1/3)πr²h.
Here, that volume is V = (1/3)(π)(6 in)²(10 in) = 120π in³
Answer:
120pi
Step-by-step explanation:
What is the value of x?enter your answer in the box.
Answers
Answer:
Hence final answer is x=46
Step-by-step explanation:
We need to find the value of x using given triangle.
Given that ED is angle bisector of angle E.
Then we can apply this formula
[tex]\frac{EG}{EH}=\frac{DG}{DH}[/tex]
[tex]\frac{63.8}{55}=\frac{58}{x+4}[/tex]
[tex]\frac{63.8}{55}=\frac{58}{x+4}[/tex]
Cross multiply
63.8(x+4)=55(58)
63.8(x+4)=3190[tex]x+4=\frac{3190}{63.8}[/tex]
x+4=50
x=50-4
x=46
Hence final answer is x=46
how do i graph the lines when the equations aren’t in slope intercept form????
Answers
Slope-Intercept Form: y=mx+b
Standard Form: ax+by=c
Point- Slope: (y-y1)= m(x-x1)
There are multiple answers to your question-
If you are only missing b(the y-intercept) but are given a set of points, plug the points into x and y and solve for b.If you are only missing the slope(m) but are given a set of points, plug the points into x and y and solve for m.If you are given the standard form/point-slope form, change the equation to slope intercept form. If you are given an complete form(there is an x and y; no missing variables), but are not sure what it is, plug in some numbers in x to find y, then graph.