Answer:
1.2 cm
Step-by-step explanation:
The area of sircumscribed quadrilateral over a circle is equal to
[tex]A=s\cdot r,[/tex]
where s is semi-perimeter of the quadrilateral and r is the radius of the circle.
Use property of circumscribed quadrilateral: The sums of the opposite sides are equal.
So, if the sum of two opposite sides of the circumscribed quadrilateral is 10 cm, then the sum of another two sides is also 10 cm and the perimeter of the quadrilateral is 20 cm. Hence,
[tex]s=\dfrac{20}{2}=10\ cm[/tex]
Now,
[tex]A=s\cdot r\\ \\12=10r\\ \\r=\dfrac{12}{10}=1.2\ cm[/tex]
We will see that the radius of the inscribed circle is 1.2 cm.
How to get the radius?Remember that for a rectangle of length L and width W, the area is:
A = L*W
In this case we know that the sum of two opposite sides is 10cm, then we can have:
2*L = 10cm
L = 10cm/2 = 5cm
And the area is 12 cm, so we can solve:
12cm = 5cm*W
12cm/5cm = W = 2.4cm
Now, the circle must be inside of the rectangle, so its diameter is equal to the smaller side of the rectangle, which is 2.4cm
Then we have:
D = 2.4cm
And the radius is half of the diameter, so the radius is:
R = 2.4cm/2 = 1.2 cm
If you want to learn more about circles, you can read:
https://brainly.com/question/1559324
[02.05] Solve for x: 3 − (2x − 5) < −4(x + 2) x < −8 x > −8 x < −3 x > −3
ANSWER
[tex]x \: < \: - 8[/tex]
EXPLANATION
The given inequality is
[tex]3 - (2x - 5) \: < \: - 4(x + 2)[/tex]
Expand:
[tex]3 - 2x + 5 \: < \: - 4x - 8[/tex]
Group similar terms, to obtain:
[tex] - 2x + 4x\: < \: - 8 - 5 - 3[/tex]
Combine similar terms:
[tex]2x\: < \: - 16[/tex]
Divide both sides by 2 to get,
[tex]x \: < \: - 8[/tex]
I need help so this is so hard and this is not me
Answer:
No answer
Step-by-step explanation:
I don't think this equation has an answer.
Normally, you'd try to combine like terms
3 3/4 = 2 + 3/4
3 3/4 = 2 3/4
3 and 3/4 is not equal to 2 and 3/4.
So, I believe this equation has no answer
I need a lot of help with many questions help
Answer:
2 cake donuts
Step-by-step explanation:
This is a question on probability, which means that we can find:
# of wanted outcomes/total outcomes.
Wanted outcomes: Vicky ate 3 cake donuts, so our value is 3.
Total outcomes: Vickey ate 3 + 4 + 8 = 15 donuts, so our value is 15.
Plug in: 3/15
Simplify: 1/5
So 1/5 of donuts Vicky eats will probably be cake donuts.
1/5 * 10 = 2
Need help with this question any help would be very appreciated
Answer:
Between A and B : Decreasing
Between B and C : Increasing
Between C and D : Decreasing
Between D and E : Constant
Step-by-step explanation:
If graph goes downward between two points then it indicates function is decreasing.
If graph goes upward between two points then it indicates function is increasing.
If graph goes parallel to the x-axis between two points then it indicates function is constant.
Then final answer is given by:
Between A and B : Decreasing
Between B and C : Increasing
Between C and D : Decreasing
Between D and E : Constant
WILL MARK BRANLIEST!! part a: Abe rented a bike at $36 for five days. If he rents the same bike for eight days, he has to pay a total rent of $48.
did I do this correctly?
Answer:
No, The answer should be 240
Step-by-step explanation:
The first step to finding the Surface Area was done well and was right but you got confused when trying to add the area of each shapeThere is 3 Rectangles and 2 Traingles. Let's start with the area of the triangles. 1/2bh is the formula for finding area of Traingles. 1/2(4)(6) = 12. We have two Traingles so that would be 24. Now we have three rectangles with different lengths we need to calculate. Rectangle 1 = 12 * 8 = 96Rectangle 2 = 12 * 6 = 72 Rectangle 3 = 12* 4 = 4824+96+72+48 = 240. So, the surface area of the rectangular prisim is 240Write an equation that represents a vertical translation 7 units down of the graph of g(x) = 21.
h(x) -
Answer:
h(x) = 14Step-by-step explanation:
f(x) + n - translation n units up
f(x) - n - translation n units down
f(x + n) - translation n units to the left
f(x - n) - translation n units to the right
===========================================
g(x) = 21
translation 7 units down: g(x) - 7 = 21 - 7 = 14
Moving a graph or function vertically down is as simple as subtracting the number of units you wish to move from the original function. The function g(x) = 21 moved 7 units down resulting in h(x) = 14.
Explanation:A vertical translation in a graph is a shift in the graph either up or down along the y-axis. In the case of the function g(x) = 21, which is a horizontal line at y = 21, a vertical translation 7 units down would yield the new function h(x) = 21 - 7 = 14. Therefore, the equation that represents this translation is h(x) = 14.
Learn more about Vertical Translation here:https://brainly.com/question/12463306
#SPJ3
If x = 2 calculate the value of x squared- x
Formula to find the missing number Faces:15 vertices:15 edges:?
Answer:
Step-by-step explanation:
Euler's formula is
V - E + F = 2
Givens
V = 15
E = 15
F = ?
Solution
15 - 15 + F = 2
F = 2
I'm not sure this makes sense, but it is what the formula gives you.
The student can calculate the number of edges in a polyhedron by using Euler's formula for polyhedra. Given the number of faces and vertices, both being 15, we solve for edges and find that the polyhedron would have 28 edges.
Explanation:The student wants to calculate the missing number of edges in a geometrical shape given the number of faces and vertices. This can be solved in mathematics using Euler's formula for polyhedra which is Faces + Vertices - Edges = 2. In the current situation, where the shape has 15 faces and 15 vertices, you can solve for edges. Inserting these values into Euler's equation yields: 15 (faces) + 15 (vertices) - Edges = 2. As a result, Edges = 15 + 15 - 2 = 28 edges.
Learn more about Euler's formula here:
https://brainly.com/question/34369062
#SPJ12
you deposit $1500 in an account that pays 5% interest yearly. How much money do you have after 6 years?
Answer: $1,950 explanation: 1500 x 0.05 =75 75 x 6 years = 450. 1500+450=1950
assuming simple interest.
[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &6 \end{cases} \\\\\\ A=1500[1+(0.05)(6)]\implies A=1500(1.3)\implies A=1950[/tex]
If F(x) = x+ 6 and G(x) = x^4, what is G(F(x))?
O
A. A +x+6
B. (X+6)^4
C.x^4+6
D.x^4(x+6)
ANSWER
B.[tex] (x + 6)^{4} [/tex]
EXPLANATION
The given functions are:
f(x)=x+6
and
[tex]g(x)= {x}^{4} [/tex]
We want to find
[tex]g(f(x)) = g(x + 6)[/tex]
This is the composition of functions, where one function becomes the input of the second function.
We plug in x+6 into the expression for g(x) to obtain,
[tex]g(f(x)) = (x + 6)^{4} [/tex]
The correct answer is B.
Billy has swimming lessons on every 3rd day and piano lessons every 12th day when will he have both on the same day
on the twelfth day because 3-6-9-12 and 12
Billy will have both swimming and piano lessons on the same day every 12th day.
To determine when Billy will have both swimming and piano lessons on the same day, we need to find the least common multiple (LCM) of the two schedules. Billy has swimming lessons every 3rd day and piano lessons every 12th day.
The LCM of 3 and 12 is the smallest number that both 3 and 12 can divide into without leaving a remainder. The prime factorization of 12 is [tex](2^2 \times 3\))[/tex], and the prime factorization of 3 is simply 3 . To find the LCM, we take the highest powers of all prime factors that appear in the factorization of both numbers:
For 3: [tex]\(3^1\)[/tex]
For 12: [tex]\(2^2 \times 3^1\)[/tex]
The LCM is [tex]\(2^2 \times 3^1 = 4 \times 3 = 12\)[/tex].
Since the LCM of 3 and 12 is 12, Billy will have both lessons on the same day every 12th day. This is because every 12th day is a day when both his 3-day swimming lesson cycle and his 12-day piano lesson cycle align.
Brand Y Cola sponsors a survey of 15,559 residents of Texas to determine which brand of cola they prefer. Forty percent say they prefer Brand X, and 60 percent say they prefer Brand Y. Which of the following is the population sample?
Answer:
B. the 15,559 residents
Step-by-step explanation:
I just took the final exam
Can anybody please help me ?
1 The average salary for a professional baseball player in the United States can be approximated by = 283(1.2)^t where t=0 represents the year 1984. Using this approximation, find the ratio of an average salary in 1988 to the average salary in 1994.
2 Find and correct the error(s) in the problem below. Explain your correction(s).
x^-9/x^-3=x^-9-3
=x^-12
=1/x^-12
Here the answer is in this picture
Answer:
1. Ratio is 1 : 3
Step-by-step explanation:
1. The average salary for a professional baseball player in the United States can be approximated by = [tex]283(1.2)^{t}[/tex]
Where t = 0 represents the year 1984.
Salary in year 1988 = [tex]283(1.2)^{4}[/tex] [t = 4 years]
Salary in year 1994 = [tex]283(1.2)^{10}[/tex] [t = 10 years]
Ratio of the average salary in 1988 to the average salary in 1994 = [tex]\frac{283(1.2)^{4}}{283(1.2)^{10}}=\frac{(1.2)^{4}}{(1.2)^{10}}[/tex]
= [tex]\frac{1}{(1.2)^{10-4}}=\frac{1}{(1.2)^{6}}[/tex]
= [tex]\frac{1}{3}[/tex]
2. Corrected form
[tex]\frac{x^{-9} }{x^{-3}}[/tex]
= [tex]x^{-9+3}[/tex][since [tex]\frac{a^{1}}{a^{1}}=a^{1-1}=a^{0}=1[/tex]]
= [tex]x^{-6}[/tex]
= [tex]\frac{1}{x^{6}}[/tex] [ since [tex]\frac{1}{a^{1}}=a^{-1}[/tex] ]
Now we can compare the corrections and errors in the highlighted form.
Expression needs correction
[tex]\frac{x^{-9} }{x^{-3}}[/tex]
= [tex]x^{-9-3}[/tex]
= [tex]x^{-12}[/tex]
= [tex]\frac{1}{x^{-12}}[/tex]
Subtract. negative 10.0 minus left parenthesis negative 2.3 right parenthesis
If you mean -10.0 - (-2.3) then the answer is -7.7
Final answer:
To subtract -10.0 - (-2.3), you change the subtraction of the negative number to addition and calculate -10.0 + 2.3, resulting in -7.7.
Explanation:
Subtracting a negative number from another negative number is equivalent to adding the absolute value of the number being subtracted. To solve the given problem, we can visualize it as negative 10.0 plus 2.3.
The subtraction of two negative numbers can be transformed into an addition problem by remembering that subtracting a negative is the same as adding a positive. Here is how you would calculate it step-by-step:
Start with the first number: -10.0.
Change the subtraction to addition because subtracting a negative is like adding a positive.
Add the absolute value of the second number: +2.3.
Combine both numbers: -10.0 + 2.3 = -7.7.
So, negative 10.0 minus (negative 2.3) equals -7.7.
Fill in the blank to make the fractions equivalent.
8/12 = _/3
Kylie needs to pack her baton for a color-guard competition. The baton is 38 inches long. Will it fit in a rectangular box with a base of 13 inches by 35 inches and a height of 13 inches?
What is the diagonal??
Also, use the Pythagorean theorem
I really need it ASAP
Answer:
The baton will not fit in the rectangular box
Step-by-step explanation:
step 1
Find the diagonal of the base of the rectangular base and then compare with the length of the baton
Applying the Pythagoras Theorem
Let
x ----> the length of the diagonal base of rectangular box
we know that
[tex]x^{2}=13^{2}+35^{2} \\ \\x^{2} =1,394\\ \\x= 37.3\ in[/tex]
[tex]38\ in > 37.3\ in[/tex]
therefore
The baton will not fit in the rectangular box
Simplify the expression
Answer:
the answer is c
Step-by-step explanation:
Find the length of Lw
Answer:
[tex]LW=17.5\ units[/tex]
Step-by-step explanation:
we know that
In the right triangle LAY
Find the measure of side LY applying the Pythagoras Theorem
[tex]LY^{2} =3.5^{2}+ 7.0^{2} \\ \\ LY^{2} =61.25\\ \\ LY=\sqrt{61.25}\ units[/tex]
Find the cosine of angle ALY
[tex]cos(<ALY)=\frac{LA}{LY}[/tex]
[tex]cos(<ALY)=\frac{3.5}{\sqrt{61.25}}[/tex] -----> equation A
In the right triangle LWY
[tex]cos(<ALY)=\frac{LY}{LW}[/tex]
[tex]cos(<ALY)=\frac{\sqrt{61.25}}{LW}[/tex] -----> equation B
equate equation A and equation B and solve for LW
[tex]\frac{3.5}{\sqrt{61.25}}=\frac{\sqrt{61.25}}{LW}[/tex]
[tex]LW=(\sqrt{61.25})(\sqrt{61.25})/3.5[/tex]
[tex]LW=17.5\ units[/tex]
Answer:
There
Step-by-step explanation:
The difference of the same side interior angles of two parallel lines is 50°. Find all angles.
Answer:
The angles are 65° and 115°
Step-by-step explanation:
Let
x,y ----> the two side interior angles of two parallel lines
we know that
x+y=180° ----> equation A
x-y=50° ----> equation B
Adds equation A and equation B
x+x=180°-50°
2x=130°
x=65°
Find the value of y
x+y=180° -----> 65°+y=180° ----> y=180°-65°=115°
therefore
The angles are 65° and 115°
Y’all answer this question
ANSWER
[tex]x = 11[/tex]
EXPLANATION
According to the exterior angle theorem, the sum of remote interior angles equal an exterior angle.
This implies that,
[tex](7x + 7) \degree + 66 \degree =(1 2x + 18) \degree[/tex]
We group the similar terms to get:
[tex]7 + 66 - 18 = 12x - 7x[/tex]
[tex]55= 5x[/tex]
Divide both sides by 5.
[tex]x = \frac{55}{5} [/tex]
[tex]x = 11[/tex]
PLZ HELP ME!!!!!!!!!!!!!!
Answer:
It's B. 1/6^9
Step-by-step explanation:
It is simplified to 6^-9 which is equal to 1/6^9.
Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first 8 terms of the geometric sequence: -8, -16, -32, -64, -128,
Answer:
-2040
Step-by-step explanation:
[tex]S_n=a_1\dfrac{r^n-1}{r-1} \qquad\text{for first term $a_1$ and common ratio r}\\\\S_8=-8\dfrac{2^8-1}{2-1}=-2040[/tex]
The sum of the first 8 terms is -2040.
Brainist and 40 pt please help
And show your work
Answer:
n > 2
Step-by-step explanation:
-10 − -3n > -4
-10 + 3n > -4
3n > 6
n > 2
Check our answer: if n = 3:
-10 − -3(3)
-10 − -9
-10 + 9
-1
-1 > -4
-10 - (-3n) > -4 ---> -10 + 3n > -4
^^^^ -3n became positive because a negative times a negative gives a positive
Step 1: Combine like terms
normal numbers go with normal numbers. This would be -10 and -4. To get -10 to the right side of the inequality you must add 10 to both sides
(-10 + 10) + 3n > (-4 + 10)
(0) + 3n > 6
3n > 6
Step 2: Isolate n by dividing 3 to both sides of the inequality
[tex]\frac{3n}{3} > \frac{6}{3}[/tex]
n > 2
Hope this helped!
The center of a circle represented by the equation (x − 5)2 + (y + 6)2 = 42 is
Answer:
(5,-6)
Step-by-step explanation:
When you write the equation of a circle in the form
[tex](x-x_0)^2+(y-y_0)^2=r^2[/tex]
Then the center of the circle will be [tex](x_0,y_0)[/tex] and the radius will be [tex]r[/tex].
Answer: The center of the given circle is (5, -6).
Step-by-step explanation: We are given to find the center of the circle represented by the following equation :
[tex](x-5)^2+(y+6)^2-4^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the STANDARD equation of a circle with center (h, k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex](x-5)^2+(y+6)^2=4^2\\\\\Rightarrow (x-5)^2+(y-(-6))^2=4^2.[/tex]
Comparing with the standard form, we get that the center of the given circle is (h, k) = (5, -6).
Thus, the center of the given circle is (5, -6).
Solve the inequality. Graph the solution set. 26 +6b>2(3b+4)
Answer:
True for all b
Interval notation; (-∞, ∞)
Step-by-step explanation:
We have been given the following inequality;
26+6b>2(3b+4)
The first step is to open the brackets on the right hand side;
26+6b>6b+8
26-8>6b-6b
18>0
Since 18 is actually greater than 0, the solution set to the inequality is;
True for all b.
PLEASE ANSWER ASAP What is the value of x in the equation 1.8-3.7x=-4.2+0.3?
Answer:
X=57/37 , X=1.540
A sandwich shop has 18 tables. Each table seats up to 4 people. To find the greatest number of people that can be seated, you can solve p4 ≤ 18. Which step is the best way to solve the inequality?
Answer:
I did this test. The answer to this question is c.multiply each side by 4
Step-by-step explanation:
I PROMISE BRINLIEST THIS IS VERY EASY I JUST DON'T KNOW!!!!!!!!!! Simplify the polynomial
3x2 + 5x – 5x2 – 4x + 5 – 2
A.)–8x2 – 9x + 3
B.)2x2 + x + 3
C.)–2x2– 9x + 3
D.)–2x2 + x + 3
Answer:
x-1
Step-by-step explanation:
(3)(2)+5x-(5)(2)-4x+5-2
=6+5x-10-4x+5-2
=x-1
Answer:
-2x2+x+3
Step-by-step explanation:
you have to combine like terms
-5x2+ 3x2= -2x2
5x-(-4x)= x
5-2=3
-2x2+x+3
Andre picks blocks out of a bag 60 times and notes that 43 of them were green. What should Andre estimate for the probability of picking out a green block from this bag?
43/60 would be the probability
The required estimation is [tex]P(A)=\frac{43}{60}[/tex]
Important information:
Number of observation=60
Number of expected outcomes =43
Probability: Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed between zero and one. So, the formula probability is,
P(A)=Expected observation/number of observations
Now, substituting the given values into the above formula we get,
[tex]P(A)=\frac{43}{60}[/tex]
Learn more about the topic probability:
https://brainly.com/question/14642847