in triangle ABC, point E (5, 1.5) is the circumcenter, point He (4.3, 2.3) is the incente, and point I (3.6, 2.6) is the centroid.what is the approximate length of the radius that circumscribes triangle ABC?
Answers
1) Gathering the data
E (5,1.5) Circumcenter
H (4.3,2.3) incenter
I (3.6, 2.6) is the centroid.
2) Examining the figure we can see point C and B as the vertices of the
triangle, to find the radius let's use the distance formula between point E and C
E(5, 1.5) and C(3,5)
[tex]\begin{gathered} d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)}^2 \\ \\ d=\sqrt[]{(5-3_{})^2+(1.5_{}-2.6_{})}^2 \\ d=2.28 \end{gathered}[/tex]Since the radius is a line segment from the origin to the circumference then the distance BC = radius of the circumscribed triangle
Radius = 2.28
Related Questions
Hello I could really use help with this problem please!
Answers
Answer:
C
[tex]A=2\pi\text{ square units; }h=2\text{ units}[/tex]Explanation:
Given:
Volume of a cylinder (V) = 4pi cubic units
To find:
Base area(A) and height(h)
Recall that the volume of a cylinder(A) is usually given as;
[tex]\begin{gathered} V=A*h \\ \end{gathered}[/tex]So let's go ahead and try each of the options and see which gives us 4pi on the left-hand side as we have on the right-hand side for Volume.
For option A;
We have that A = 1 and h = 2, so we'll have;
[tex]\begin{gathered} V=A*h \\ 4\pi=1*2 \\ 4\pi\ne2 \end{gathered}[/tex]For option B;
We have A = 2pi and h = 1, so we'll have;
[tex]\begin{gathered} 4\pi=2\pi *1 \\ 4\pi\ne2\pi \end{gathered}[/tex]For option C;
We have A = 2pi and h = 2, so we'll have;
[tex]\begin{gathered} 4\pi=2\pi *2 \\ 4\pi=4\pi \end{gathered}[/tex]We can see from the above that option C is the right option.
From 1999 to 2009, the number of dogs [tex]D[/tex] and the number of cats [tex]C[/tex] (in hundreds) adopted from animal shelters in the United States are modeled by the equations [tex]D = 2n+3[/tex] and [tex]C = n +4[/tex], where [tex]n[/tex] is the number of years since 1999.
a. Write a function that models the total number [tex]T[/tex] of adopted dogs and cats in hundreds for that time period.
b. If this trend continues, how many dogs and cats will be adopted in 2013?
Answers
The functions that models the number of adopted dogs and cat is T = 3n + 7.
If the trend continues, the number of cats and dog that will be adopted by 2013 is 4600.
How to find the function that models a problem?From 1999 to 2009, the number of dogs D and the number of cats C (in hundreds) adopted from animal shelters in the United States are modelled by the equations D = 2n + 3 and C = n + 4, where n is the number of years since 1999.
Therefore, the functions that models the total number T of the adopted dogs and cats in hundreds for that time period can be represented as follows:
T = D + C
where
D = 2n + 3
C = n + 4
where
n = number of yearsT = 2n + 3 + n + 4
T = 3n + 7
b. If the trends continues the number of cats and dogs that will be adopted in 2013 can be calculated as follows:
n = 2013 - 1999 = 13Hence,
T = 3(13) + 7
T = 39 + 7
T = 46
Recall it's represented in hundred's
Therefore, 4600 dogs and cat will be adopted by 2013
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find the ranges of values for which x²-5+6<0
Answers
Answer:
The range of values of x for which the function is < 0 is:
2<x<3.
Step-by-step explanation:
x²-5x+6<0
First find the critical points:
x^2 - 5x + 6 = 0
(x - 2)(x - 3) = 0.
x = 2, 3.
The critical points are 2 and 3.
Make a table of values:
x x<2 2<x<3 x >3
x -2 < 0 >0 >0
x -3 <0 <0 >0
(x - 2)(x - 3) >0 <0 >0
reduce 45/10 to halves
Answers
How does g(t) = 4t change over the interval t = 3 to t = 4?
Answers
Over the interval t = 3 to t = 4, g(t) increases.
The increasing factor (f) is computed as follows:
[tex]f=\frac{g(4)}{g(3)}[/tex]where g(4) is g(x) at t = 4, and g(3) is g(x) at t = 3. Substituting with the formula of g(t) and evaluating each expression, we get:
[tex]\begin{gathered} f=\frac{4^4}{4^3} \\ f=\frac{4\cdot4^3}{4^3} \\ f=4 \end{gathered}[/tex]Then, g(t) increases by a factor of 4
The dimensions and the weight of several solids are given. Use the density information to determine what element is the solid made up of.
Answers
Given:
Dimensions and weight of a solid is given.
Height (h) of a cylinder (in cm) =
[tex]h=5[/tex]Radius (r) of a cylinder (in cm) =
[tex]r=5[/tex]Mass (m) of solid (in grams)=
[tex]m=3090.5[/tex]Density of several elements is given.
Cobalt=8.86, Copper=8.96, Gold=19.3, Iron=7.87, Lead 11.3, Platinum=21.5, Silver=10.5, Nickel=8.90.
Required:
What element is the solid made up of.
Answer:
Let us find the volume (V) of cylinder (in cubic cm).
[tex]\begin{gathered} V=\pi\times r^2\times h \\ V=3.14\times\left(5\right)^2\times5 \\ V=3.14\times25\times5 \\ V=392.5 \end{gathered}[/tex]Using formula of density (D), we get,
[tex]\begin{gathered} D=\frac{m}{V} \\ D=\frac{3090.5}{392.5} \\ D=7.87 \end{gathered}[/tex]Hence, the density of the solid is 7.87 grams per cubic cm.
From the given information of density of several elements, we see that the solid is made up of Iron.
Final Answer:
The solid is made up of Iron.
32. Recall the pattern that you found in the diamond problems from Ready, Set, Go #2. Use the pattern you discoveredto complete each diamond below.8-121-724ISet
Answers
Answer:
Step-by-step explanation:
What is the intermediate step in the form (x+a)^2=b(x+a)
2
=b as a result of completing the square for the following equation?
x^2+6x+19=4x
Answers
The intermediate step in the form (x + a)² = b when you solve the given quadratic equation by using completing the square method is (x + (√3 - 2)/2)² = 77/4.
The standard form of a quadratic equation.In Mathematics, the standard form of a quadratic equation is given by:
ax² + bx + c = 0.
In this exercise, you're required to determine the intermediate step in the form (x + a)² = b when you solve the given quadratic equation by using completing the square method. Therefore, we would re-write the quadratic equation by subtracting 19 from both sides as follows:
x² + 6x + 19 = 4x
x² + 6x + 19 - 19 = 4x - 19
x² + 6x = 4x - 19
x² + 6x - 4x = 19
x² + 2x = 19
In order to complete the square, we would have to add (half the coefficient of the x- term)² to both sides of the quadratic equation as follows:
x² + 2x + (1/2)² = 19 + (1/2)²
x² + 2x + 1/4 = 19 + 1/4
(x + (√3 - 2)/2)² = 77/4
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Complete Question:
What is the intermediate step in the form (x + a)² = b as a result of completing the square for the following equation?
x² + 6x + 19 = 4x
пеу Fabric Sale At a fabric store, fabrics are sold by the yard. A dressmaker spent $46 on 5 yards of silk and cotton fabrics for a dress. 1 x + y = 5 117x + 4y = 46) Silk is $17 per yard and cotton is $4 per yard. Here is a system of equations that represent the constraints in the situation. What does the solution to the system represent?
Answers
It is said that the dressmaker bought 5 yards of cotton and silk. Let's see the first equation of the system:
[tex]x+y=5[/tex]And that he spent $46 on those 5 yards. Also, it is said that silk costs $17 per yard and cotton $4 per yard. Let's see the second equation of the system:
[tex]17x+4y=46[/tex]If 46 is how much the dressmaker spent, and 17 and 4 represent how much silk and cotton cost PER YARD then we know that x and y represent how much of each fabric did the dressmaker bought. Also, in the first equation you see that the total is 5 yards. So, if you solve this system you will find that 'x' is how many yards of silk the dressmaker bought and 'y' is how many yards of cotton he bought.
In summary, the solution of this system represents how may yards of silk (x) and cotton (y) the dressmaker bought.
Ms. Wong sold 28 cars. She sold 8 fewer cars that 3/4 as many cass as Mr. Diaz. Which equation can be used to find the number of cars that Mr. Diaz sold,c?
Answers
The equation that we can be used to find the number of cars that Mr. Diaz sold is [tex]\frac{3}{4}x[/tex]−[tex]8=28[/tex].
Ms Wong sold cars = 28.
She sold [tex]8[/tex] fewer cars that is 3/4 as many cars as Mr. Diaz.
Let Mr. Diaz sold [tex]x[/tex] cars.
Cars is 3/4 as many cars as Mr. Diaz so the term [tex]3/4x[/tex].
She sold 8 fewer cars.
Now from the statement the Ms Wong sold cars [tex]\frac{3}{4}x[/tex]−[tex]8[/tex].
As it is given that Ms Wong sold 28 cars.
So the equation must be
[tex]\frac{3}{4}x[/tex]−[tex]8=28[/tex]
So equation that we can be used to find the number of cars that Mr. Diaz sold is [tex]\frac{3}{4}x[/tex]−[tex]8=28[/tex].
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Three times a number decreased by 1 is 10 Three times the difference of a number is 1 is 10One less than three times a number is 10The quotient of a number and 3 is 10
Answers
Three times a number decreased by 1 is 10:
X is the number.
3x = three times a number.
3x - 1 = 10 (Three times a number decreased by 1 is 10)
3x = 10 + 1
3x = 11
x = 11/3
Is the prime factor of 85 17x5
Answers
Given data:
The given number is 85.
The given number 85 can be expressed in terms of their prime factors as,
[tex]85=5\times17[/tex]Thus, yes 85 can be expressed in terms of their prime factors as 17x5.
I need to find out what sine cosine and cotangent is, if this is my reference angle in the picture
Answers
We will use the following trigonometric identities
[tex]\begin{gathered} \tan \Theta=\frac{sin\Theta}{\cos \Theta} \\ \cot \Theta=\frac{1}{\tan \Theta} \end{gathered}[/tex]Using these identities we can identify
[tex]\begin{gathered} \tan \Theta=\frac{12}{5} \\ \sin \Theta=12 \\ \cos \Theta=5 \\ \cot \Theta=\frac{1}{\frac{12}{5}}=\frac{5}{12} \end{gathered}[/tex][tex]\begin{gathered} \Theta=\tan ^{-1}(2.4) \\ \Theta=67.38º \\ \sin \Theta=0.92 \\ \cos \Theta=0.38 \end{gathered}[/tex][tex]\begin{gathered} \tan \Theta=\frac{opposite}{\text{adjacent}}^{} \\ \text{opposite}=12 \\ \text{adjacent}=5 \\ \text{hippotenuse=}\sqrt[\square]{12^2+5^2} \\ \text{hippotenuse=}13 \end{gathered}[/tex][tex]\begin{gathered} \sin \Theta=\frac{12}{13} \\ \cos \Theta=\frac{5}{13} \end{gathered}[/tex]Jim can choose plan A or plan B for his long distance charges. For each plan, cost (in dollars)depende on minutes used (per month) as shown below.(a)If Jim makes 40 minutes of long distance calls for the month, which plan costs more? How much more does it cost than the other plan?(b) For what number of long distance minutes do the two plans cost the same?
Answers
Answer:
• Plan B, by $4
,• 140 minutes
Explanation:
Part A
From the graph, at 40 minutes, the costs of the plans are:
• Plan A: $4
,• Plan B: $8
[tex]\begin{gathered} \text{Difference}=8-4 \\ =\$4 \end{gathered}[/tex]Plan B costs more by $4.
Part B
The point where the costs are the same is the time at which the two graphs intersect.
When the number of minutes = 140 minutes
• Cost of Plan A = $14
,• Cost of Plan B = $14
Thus, the two plans cost the same for 140 minutes of long-distance call.
• If the time spent is less than this amount, Plan B costs more.
Looking to receive help on the following practice question thank you.
Answers
use the definition of sec and write it in terms of cos
[tex]r=4\cdot\frac{1}{\cos \theta}[/tex]multiply both sides by cos
[tex]r\cos \theta=4[/tex]then we know that r*cos is equal to x in the cartesian
[tex]x=4[/tex]Find the perimeter of the following quadrilateral.The bottom side measures 2 ft.
Answers
The perimeter of a quadrilateral is given by the sum of all the sides.
In order to add mixed numbers, let's rewrite them as a sum of the integer part and the fraction part.
So we have:
[tex]\begin{gathered} P=1\frac{5}{12}+3\frac{3}{4}+2\frac{1}{6}+2 \\ P=1+\frac{5}{12}+3+\frac{3}{4}+2+\frac{1}{6}+2 \\ P=(1+3+2+2)+(\frac{5}{12}+\frac{9}{12}+\frac{2}{12}) \\ P=8+\frac{16}{12} \\ P=8+1+\frac{4}{12} \\ P=9+\frac{1}{3} \\ P=9\frac{1}{3}\text{ ft} \end{gathered}[/tex]Therefore the perimeter is 9 1/3 ft.
Hello, I really need help on this assignment I don't understand what to do.
Answers
Answer:
-2 and -10
Explanation:
There are two numbers at a distance of 4 units from -6, the number that is 4 units to the right and the number that is 4 units to the left.
So, the number that is 4 units to the right is equal to
-6 + 4 = -2
And the number that is 4 units to the left is equal to
-6 - 4 = -10
Therefore, the numbers are -2 and -10 and they are represented as
What is the inverse function of y = (x-4)^2+2
Answers
One way to find the inverse of a function is by first swapping x and y, then solving for y, like this:
[tex]\begin{gathered} y=(x-4)^2+2\text{ }\Rightarrow x=(y-4)^2+2 \\ \end{gathered}[/tex]Now, let's solve for y, like this:
[tex]\begin{gathered} x=(y-4)^2+2 \\ x-2=(y-4)^2+2-2 \\ (y-4)^2=x-2 \\ \sqrt[]{\mleft(y-4\mright)^2}=\sqrt[]{x-2} \\ y-4=\sqrt[]{x-2} \\ y-4+4=\sqrt[]{x-2}+4 \\ y=\sqrt[]{x-2}+4 \end{gathered}[/tex]Then, the inverse function of y = (x-4)^2+2 is:
[tex]y=\sqrt[]{x-2}+4[/tex]A company orders business cards for their employees. The company pays $9.00 per 100 cards ordered. The company orders2,000 business cards for Karen and 2,500 business cards for Lamar. How much more do the business cards for Lamar cost than thebusiness cards for Karen?$9$45$450d $500
Answers
Take into account what the company pays per 100 cards ordered, which is $9.00.
To determine the cost of the cards for Karen and Lamar
Brookner's Grocery Store sells bars of chocolate in cartons. There are 39 bars of
chocolates in each box. There are 25 boxes in each carton. Last weekend
Brookner's Grocery sold 48 cartons of chocolates. How many bars of chocolate did
the Brookner's Grocery sell last weekend? Explain your thinking.
Answers
1,200 boxes of chocolate
1,200 x 39 = 46,800 bars of chocolate.
Answer is 46,800.
Step - By - Step Explanation:
Multiply the cartons sold with how many boxes are in each carton to find how many boxes was sold.
Multiply the amount of boxes they sold with how much bars is in each box to find the solution.
The difference between two numbers is 28. The sum of the two numbers is 56. Let x be the larger number and y be the smaller number. Which system of equations represents this proble O y - x = 28 I + y = 56 O x=y= 28 x + y = 56 Oy - 2 = 56 x + y = 28 - y = 56
Answers
Since x is the larger number and y is the smaller number
Since their sum is 56
That means add x and y then equate them by 56
[tex]x+y=56(1)[/tex]Since the difference between them is 28
That means subtract y from x and equate the answer by 28
[tex]x-y=28(2)[/tex]Look at the answer to find the correct answer
It is B
x - y = 28 and x + y = 56
50% of $277 is $144True or False
Answers
Answer:
FALSE
Explanation:
Given the expression
50% of $277
This can also be written as;
= 50/100 * 277
= 1/2 * 277
= 277/2
= 138.5
Therefore 50% of $277 is $138.5 not $144 rendering the question FALSE
4x + 3x = 56. What is the value of x?
Answers
Given
The expression is given as
[tex]4x+3x=56[/tex]Explanation
To find x, add the expression.
[tex]\begin{gathered} 7x=56 \\ x=\frac{56}{7} \end{gathered}[/tex][tex]x=8[/tex]Answer
Hence the value of x is 8.
[tex]4x + 3x = 56\\7x = 56\\x = 56/7\\x = 8[/tex]
The answer is X=8
Dylan invested $93,000 in an account paying an interest rate of 3% compoundedquarterly. Assuming no deposits or withdrawals are made, how much money, to thenearest cent, would be in the account after 17 years?
Answers
The formula to calculate compound interest is given to be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
[tex]\begin{gathered} A=\text{ final amount} \\ P=\text{ initial amount (principal)} \\ r=\text{ interest rate} \\ n=\text{ number of times interest applied per time period} \\ t=\text{ number of time period elapsed} \end{gathered}[/tex]The following parameters are given in the question:
[tex]\begin{gathered} P=93000 \\ r=\frac{3}{100}=0.03 \\ n=4(quarterly) \\ t=17\text{ years} \end{gathered}[/tex]We can substitute these values into the formula to calculate the final amount as follows:
[tex]A=93000(1+\frac{0.03}{4})^{4\times17}[/tex]Solving, we get:
[tex]\begin{gathered} A=93000\times1.0075^{68} \\ A=154,577.64 \end{gathered}[/tex]The amount after 17 years is $154,577.64
To achieve mastery of this lesson, make sure you develop responses to the following questions: How are exponential functions graphed? How do you compare exponential functions? How do you transform exponential functions? help
Answers
For exponential functions, it is found that:
They are graphed looking at the asymptote, the intercept, the rate of change and the end behavior.They are compared by the rate of change.They are transformed with translations and stretching/compression.What is an exponential function?An exponential function is modeled according to the rule presented as follows:
[tex]y = ab^x + c[/tex]
In which the coefficients of the rule are given as follows:
a is the intercept of the function, the value of y when it crosses the y-axis.b is the rate of change of the function.c is the asymptote of the function.To graph the function, along with the coefficients of the function, the end behavior of the function is needed, as follows:
Limit of y when x goes to negative infinity: gives the behavior at the left end of the graph.Limit of y when x goes to positive infinity: gives the behavior at the right end of the graph.They are compared by their rate of changes, if they are increasing/decreasing, and which one increases faster.
The transformations are as follows:
Translation: a constant is added to either x or y(changing the asymptote if y), meaning that the function can be moved down, up, left or right.Stretching: a constant multiplies x or y, meaning that the graph can be either compressed or stretched vertically or horizontally.More can be learned about exponential functions at https://brainly.com/question/25537936
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what is 9=-1/4x+4 in standard form
Answers
The standard form in which the equation must be written is -1/4x = 5
Standard Equation FormStandard form is just another way to write a linear equation equation along with slope intercept form and point slope form.
Standard form appears in the form ax + by = c
Where a, b and c are integers and a must be positive
In the given equation 9 = -1/4x + 4, we can rewrite this into standard equation of line by
-1/4x + 4 = 9
-1/4x + 4 - 9 = 0
-1/4x - 5 = 0
-1/4x = 5
The standard form of the equation is -1/4x = 5
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Liz attended class every day since she started school as a kindergarten. She said she has been in school for about 1,000 days.What numbers could be the actual number of school days if Liz rounded to the nearest ten?4 grade student
Answers
Solution.
Given that Liz attended class every day since she started school as a kindergarten and that she said she has been in school for about 1000 days (by rounding up the actual number of days to the nearest ten)
The actual number is a number that when rounded up, we would arrive at 1000.
This number falls between the numbers 995 and 1004.
Answer: Any of the numbers below could be the actual number:
995, 996, 997, 998, 999, 1000, 1001, 1002, 1003, 1004
What is the slant height and surface area of the pyramid
Answers
we have that
The surface area of the pyramid is equal to the area of its square base plus the area of its four triangular faces
step 1
Find out the area of the square base
A=15^2
A=225 ft2
step 2
Find out the area of one triangular face
the area of a triangle is equal to
A=(1/2)(b)(h)
we have
b=15 ft
h ----> is the slant height
To find out the slant height, apply the Pythagorean Theorem
h^2=10^2+(15/2)^2
h^2=100+56.25
h=12.5 ft
therefore
A=(1/2)(15)(12.5)
A=93.75 ft2
step 3
The surface area is equal to
SA=225+4(93.75)
SA=600 ft2 and the slant height is 12.5 ftState the number of complex zeros and the possible number of real and imaginary zeros for each function. Then find all zeros. show all work
Answers
We have a cubic function
[tex]f(x)=x^3-3x^2-47x-87[/tex]One way to find all the zeros is by factoring, we can easily find the first zero using the divisors test if we have an independent term, at our case it's -87, one of the divisors may be a zero. The divisors of -87 is 1, 3, 29 and 87.
If we check for all of the divisors we will see that -3 is a zero. (Check with both signals).
If -3 is a zero, the D'Alembert theorem tells us that f(x) is divisible by (x+3), if we do that division we'll have a quadratic function where we can just apply the quadratic formula, then
There's a theorem that says that, if f(a) is a zero, i.e f(a) = 0, and f(x) is a polynomial, then f(x) is divisible by (x-a), in other words, we can divide f(x) by (x-a) and the rest of the division will be 0.
Therefore, let's divide our function by (x+3)
Then we can write our function as
[tex]f(x)=(x+3)(x^2-6x-29)[/tex]Look that now we have a quadratic function, and we can easily find its zeros, applying the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]We have a = 1, b = -6 and c = -29. Then
[tex]\begin{gathered} x=\frac{6\pm\sqrt[]{36+4\cdot29}}{2} \\ \\ x=\frac{6\pm\sqrt[]{156}}{2} \\ \\ x=\frac{6\pm2\sqrt[]{38}}{2} \\ \\ x=3\pm\sqrt[]{38} \end{gathered}[/tex]Now we have all the zeros of f(x), it's
[tex]\begin{gathered} x=-3 \\ \\ x=3+\sqrt[]{38} \\ \\ x=3-\sqrt[]{38} \end{gathered}[/tex]As we can see there's no complex zero, all the zeros are real numbers.
The max number of complex zeros is 2 because the complex zeros always come in pairs, so if we have 1 complex zero, automatically we have another, for a 3-degree equation, there's a maximum of 2 complex zeros and 1 real zero, or all the of them are real.
Then the correct answer is A)
(blank)+(7x+24)=180
7x + (blank)+ = 180
7x =
x =
Answers
Answer:
first blank: 72°
2nd blank: 96
next line: 84
last: 12
Step-by-step explanation:
The two marked angles are called same-side interior angles or consecutive angles.
They add up to 180°
Thats how you know how to set up the equation.
72° + 7x + 24 = 180
Add the plain numbers (the 72 and 24)
7x + 96 = 180
subtract 96 from both sides.
7x = 84
Divide both sides by 7.
x = 12
