The center of the circle that circumscribe about DABC is [tex](h,k) = (1, 5)[/tex].
A circle can be modelled after a expression of the form:
[tex]A\cdot x + B\cdot y + C =-x^{2}-y^{2}[/tex] (1)
We can determine all coefficients by knowing three distinct points on plane.
If we know that [tex](x_{1}, y_{1}) = (2, 8)[/tex], [tex](x_{2}, y_{2}) = (0, 8)[/tex] and [tex](x_{3}, y_{3}) = (2, 2)[/tex], then the solution of the system of linear equations is:
[tex]2\cdot A + 8\cdot B + C = -68[/tex] (2)
[tex]8\cdot B + C = -64[/tex] (3)
[tex]2\cdot A + 2\cdot B + C = -8[/tex] (4)
[tex]A = -2, B = -10, C = 16[/tex]
Now we proceed to complete squares and factor each resulting perfect square trinomial in order to determine the coordinates of the center of the circle:
[tex]x^{2}+y^{2}-2\cdot x -10\cdot y +16 = 0[/tex]
[tex](x^{2}-2\cdot x +1)-1+(y^{2}-10\cdot y +25)-25 +16 = 0[/tex]
[tex](x-1)^{2}+(y-5)^{2}= 10[/tex]
The center of the circle that circumscribe about DABC is [tex](h,k) = (1, 5)[/tex].
To learn more on circles, we kindly invite to check this verified question: https://brainly.com/question/11833983
Solve 4,200 ÷ 70 = ________. Rewrite as a fraction to help you.
FIRST CORRECT ANSWER GETS BRAINLIEST:
In the African nation of Niger, French is the official language, while in Nigeria, English is the official language. Why would these two countries have different official languages that are European In
origin?
They were colonized by different European countries
They are historically at war with one another.
They needed a lingua franca to be able to communicate.
Step-by-step explanation:
They needed a lingua franca to be able to communicate.
y=-1,X+2y=9 solve by substitution show all work
Answer:
x = 11
Step-by-step explanation:
Substitute y = -1 into the equation.
x+2y = 9
; x+2(-1) = 9
x+(-2) = 9
x-2 = 9
x = 9+2
x = 11
Joan is thinking of a number. She adds 5 and multiplies it by 4. She then subtracts n of her original number and divides by 20. She wants the answer to always be 1. What is the value of n?
Answer:
5
Step-by-step explanation:
(4n+5)-n/20=1 cross multiply:(4n+5)-n=204n+5=20+n4n-n=20-53n=15Divide both sides by coefficient of nn=5Identify the two irrational numbers
Answer:
Your answer is in picture hope it helps
Step-by-step explanation:
help please..
Select the correct image.
Given triangle A in the coordinate plane, which image shows a dilation of triangle A by a factor of 2 centered at the origin?
Answer:
C
Step-by-step explanation:
C because each point is twice as far from the origin
Answer:
c
Step-by-step explanation:
2y=8x-6 Find the Slope
Answer:
Slope is 4
Step-by-step explanation:
2y=8x-6
divide by 2
y=4x-3
y=mx+b
m is slope
m=4
The product of the roots of the equation ax^2+x-24=0 is equal to -2 2/5. Find the value of a in the equation. Please help 100 points and branliest.
[tex]ax^2 + x -24 =0\\\\\text{If the roots are}~ \alpha ~ \text{and}~ \beta,\\\\\alpha \beta = -\dfrac{24}a \\\\\implies -2 \dfrac 25 = -\dfrac{24} a\\\\ \implies 2 \dfrac 25 = \dfrac{24} a\\\\\implies \dfrac{12}5 = \dfrac{24}a\\\\\implies 12a = 120\\\\\implies a =\dfrac{120}{12} =10[/tex]
radius=12 round up to the nearest tenth
Answer:
12.0
Step-by-step explanation:
Answer:
452.4
Step-by-step explanation:
A line with a slope of 1/10 passes through the point (10, 1) What is its equation in slope-intercept form?
Hello there! :)
We are given the slope of the line: 1/10.We are also given the point that the line passes through.So, with the given information, we can use Point-Slope form:y-y1=m(x-x1)y-1=1/10(x-10)y-1=1/10x-1y=1/10xTherefore, that's the equation.Hope it helps. Use the comment section to clarify any doubts.
Answered by
~A teen who adores helping others
#LetItSnow
Good luck.
the equation of line which passes through point (10, 1) and having slope 1/10 is y = x/10 + 0.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
y = mx + b
In which the coefficients are described as follows:
• The coefficient m is the slope of the function, representing the rate of change of the function.
• The coefficient b is the y-intercept of the function, representing the value of y when the function crosses the y-axis(x = 0).
Here, it is given that line passes though point (10,1) and having slope of 1/10.
Now, Let us find the equation of the line using point-slope equation of line :
(y-y₁) = m(x-x₁)
Substituting all the values in above equation to get the equation of line :
(y-1) = 1/10(x-10)
y - 1 = x/10 - 1
y = x/10 + 0
Therefore, the equation of line which passes through point (10, 1) and having slope 1/10 is y = x/10 + 0.
check and know more about line here :
brainly.com/question/14914699
#SPJ2
Lily has $2. 75 in her pocket, consisting of dimes and quarters. If there are 17 coins in all, how many of each does she have?.
Answer:
Lily has 7 Quarters and 10 Dimes
Step-by-step explanation:
Let's use pennies instead of $.
Let D and Q stand for the numbers of Dimes and Quarters, respectively.
We are told that there are 17 coins total:
D + Q = 17
We also learn that they amount to 275 (pennies). We can write that as:
10D + 25Q = 275 [Each D is worth 10 pennies, etc.]
We have two equations and two unknowns. We can rearrange one equation to find the value of either of the unknowns, and then use that it the second equation.
I'll rearrange the first:
D + Q = 17
D = 17 - Q
Now use this value of D in the second equation:
10D + 25Q = 275
10(17-Q) + 25Q = 275
170 - 10Q + 25 Q = 275
15Q = 105
Q = 7 : 7 Quarters.
Since D + Q = 17:
D + 7 = 17
D = 10 Dimes
==========================================
Let's check these results:
Q = 7 Quarters
D = 10 Dimes
1. Is this 17 coins in total? (7+10 = 17) YES
2. Does this add to $2.75? (10*10) + (7*25) = 275 cents?
(100 + 176) = 275 (cents) YES
============================
Lily has 7 Quarters and 10 Dimes
What is -2 1/2 times 3 3/4?
Answer:
-6 3/8
Step-by-step explanation:
Step-by-step explanation:
-2 1/2 mixed number change fraction= -3/-4 = 3/4.
3 3/4 = 15/12 = 5/4.
3/4 x 5/4= 15/16.
The value of y varies directly with x.If x=25 then y=20 .a. find the value y when x=8 b. find the value of x when y=32
is that two problems in one?
Please help! I highly appreciate it! :D
Here's some required measures !
1 ft = 12 inches 0.4 ft = 0.5 × 12 = 6 inchesLet's calculate its surface area ~
[tex] \sf2[(12 \times 10) + (11 \times 12) + (10 \times 11) ] - 2(7 \times 7) [/tex][tex] \sf2[120 + 132 + 110 ] - 2(49) [/tex][tex] \sf{2(362)} - 98[/tex][tex] \sf724 - 98[/tex][tex]6 \sf26 \: \: in {}^{2} [/tex]solve similar triangles (advanced)
Answer: 18/7
This approximates to 2.5714
=====================================================
Explanation:
The two triangles are similar. We can use the AA (angle angle) theorem to prove this claim.
Because [tex]\triangle ABC \sim \triangle ADE[/tex], this means:
side AB corresponds to side AD. The letters from AB are the first two letters of ABC while AD are the first two letters from ADE.side BC corresponds to DE. We have BC as the last two letters of ABC and DE the last two letters of ADEAs those bullet points above mention, the order of ABC and ADE matters to allow us to pair up the corresponding angles and corresponding sides.
From that, we can form the proportion below to solve for x
AB/AD = BC/DE
3/(3+4) = x/6
3/7 = x/6
3*6 = 7*x
18 = 7x
7x = 18
x = 18/7
You could convert this to the approximate decimal form 18/7 = 2.5714, but I think it's better to keep it as a fraction.
To make a certain shade of paint, Anya mixed 2/3
cups of white paint with 2 and 2/3
cups of blue paint.
How many cups of blue paint should she mix with 3/4
cups of white paint to make the same shade?
Answer:
She needs 3 cups of white paint
Step-by-step explanation:
She has 1:4 ratio with the white and blue paint.
1/4:1
3/4:3
How many solutions does this system of equations
have?
Infinite
None
One
Answer:
Step-by-step explanation:
None
The hint is in the slopes which is the number in front of x. Both equations have a slope of 1/2
The y intercepts are different (4 for the top one 2 for the bottom one). That tells you that you have two lines and not one of top of the other. These two lines never meet, because the slopes are the same. Therefore there are no values that both lines have in common.
That makes the answer none.
At a school, 40% of the sixth-grade students said that hip-hop is their favorite kind of music. If 100 sixth-grade students prefer hip hop music, how many sixth-grade students are at the school? Explain or show your reasoning.
Answer:
250 because 250 times .4 equals 100
Step-by-step explanation:
Estimate the quotient of 57.87 ÷ 5 A) 9 B) 10 C) 11 D) 12
Answer:
C, 11
Step-by-step explanation:
What is the degree of 3x^4-4x^2?
Answer:
the degree is 4
Step-by-step explanation:
the largest exponent of x
Jared and Casey splurged on a special dinner for their anniversary. Their dinner cost $262.57,
and the local sales tax is 4%. If they left a 20% tip on the $262.57, how much in total did
they pay?
They paid a total of $325.5868
Find the value of x so that the function has the given value. g(x)=8x-11;(x)=5
Answer:
29
Step-by-step explanation:
please helpp im timed!!!
Answer:
Answer A is correct
Step-by-step explanation:
what is 2^3 x 2^18 simplified
Answer:
2097152 or 2^21
Step-by-step explanation:
Answer: [tex]2^{21}[/tex]
Step-by-step explanation: Exponents are combined when simplifying a multiplication equation.
Alg 2 the problem is below please help !!!
pls help me with math asap pls no links thx
Answer:
8
Step-by-step explanation:
Divide 192 by 24 and you'll get 8 classes per grade as the answer
Answer:
8 classes
Step-by-step explanation:
To find the minimum amount of classes, you divide 192 by 24 and you get 8 classes.
The square root of 1.85
Answer:
around 1.36
Step-by-step explanation:
2. What is the x-intercept for the equation -2x + 5y = -10?
Answer:
Step-by-step explanation:
X intercept occurs when y = 0
-2x + 5(0) = -10
x = -10/-2
x = 5
Tyrone received the same score on each hand in a card game. His score on each hand was −18. He played 6 hands.
What was Tyrone's final score?
Enter your answer in the box.
points
-108 points
How?
Because -18×6=-108
------(Showed you some proof from above)
Write an equation in point-slope form of the line that passes through the point (−3,6) and has a slope of 5.
Answer:
Below in bold.
Step-by-step explanation:
Point slope form is y - y1 = m(x - x1)
where m = the slope of the line and (x1, y1) is a point on the line.
Here m = 5, x1 = -3 and y1 = 6.
So we have:
y - 6 = 5( x - (-3))
y - 6 = 5(x + 3) (Answer)