In triangle $ABC,$ $AB = BC = 17$ and $AC = 16.$ Find the circumradius of triangle $ABC.$
Answer:
[tex]R = 9.63\ units[/tex]
Step-by-step explanation:
Given
[tex]AB = BC = 17[/tex]
[tex]AC = 16[/tex]
Required
Determine the circumradius, R
The circumradius is calculated as follows;
[tex]R = \frac{AB * BC * AC}{\sqrt{(AB + BC + AC)(AB + BC - AC)(AB + AC - BC)(AC + BC - AB)}}[/tex]
Substitute the values of AB, BC and AC
[tex]R = \frac{17 * 17 * 16}{\sqrt{(17 + 17 + 16)(17 + 17 - 16)(17 + 16 - 17)(16 + 17 - 17)}}[/tex]
Evaluate the denominator
[tex]R = \frac{17 * 17 * 16}{\sqrt{(50)(18)(16)(16)}}[/tex]
[tex]R = \frac{4624}{\sqrt{230400}}[/tex]
Take square root of 230400
[tex]R = \frac{4624}{480}[/tex]
[tex]R = 9.63\ units[/tex] (Approximated)
Hence, the circumradius is 9.63
Answer:
289/30
Step-by-step explanation:
Let the circumcenter be point O. We start by drawing line median BM. Since AB = BC, median BM is perpendicular to side AC.
Therefore, BM is part of the perpendicular bisector of AC and thus, must pass through point O.
We have AM = 8, so the Pythagorean Theorem applied to triangle ABM gives us BM = 15.
Let OA = x, our circumradius. Since O is equidistant from A and B, we have OB = x as well.
Therefore,
OM = BM - BO = 15 - x.
From right triangle OAM, we have (OA)^2 = (OM)^2 + (AM)^2.
Solving for x, we have 30x = 225 + 64.
So, x = 289/30.
someone please answer and give me a reason. hint: the answer isn’t 49.
Answer:
√37
Step-by-step explanation:
An irrational number is a number that never terminates nor repeats.
Let's go through each of the answer choices.
1) √100 is just 10. This is not irrational.
2) √81 is just 9. This is again not irrational.
3) √64 is 8. Not irrational.
4) √49 is 7. Again, not irrational.
5) √37 is 6.08276253... This number will never end and it doesn't repeat. Therefore, √37 is irrational.
And this is our answer.
And we're done!
Find the height H of solid
what is 21000 take away two thirds
Answer:
7000
Step-by-step explanation:
21000/0.667
=14000
21000-14000
=7000
all linear pairs and vertical pairs share the same...?
Answer:
Lines
Step-by-step explanation:
In both linear and vertical pairs share at least one line.
Hope This Helps :)
All linear pairs and vertical pairs share the same supplementary angle.
Linear pairs and vertical pairs are both types of angle pairs formed by intersecting lines or by the intersection of a line and a transversal.
1. Linear Pairs: A linear pair consists of two adjacent angles formed by two intersecting lines. The two angles in a linear pair are always supplementary, meaning their measures add up to 180 degrees. In other words, if one angle in a linear pair measures x degrees, then the other angle will measure (180 - x) degrees.
2. Vertical Pairs: Vertical angles are formed by the intersection of two lines. They are opposite angles that share a common vertex but are formed by different pairs of intersecting lines. Vertical angles are congruent, meaning they have the same measure. If one vertical angle measures x degrees, then the other vertical angle formed by the same pair of intersecting lines will also measure x degrees.
Therefore, both linear pairs and vertical pairs share the same property of having angles with equal measures. In the case of linear pairs, the angles are supplementary (their measures add up to 180 degrees), while in vertical pairs, the angles are congruent (they have the same measure).
To know more about linear pairs, refer here:
https://brainly.com/question/34190098
#SPJ2
Number 14 help I have to zoom with the answer in five minutes
Answer:
31 over -3
Step-by-step explanation:
4.7+1.6=6.3x 5 =31.5-.5=31
Answer: 28
Step-by-step explanation:
Simplify:
(XY3Z4)4
A.xy3z16
B.xy3z8
C.x4y12z16
D.x5y7z8
Answer:
C
Step-by-step explanation:
(xy^3z^4)^4 =
(x)^4 = x^4
(y^3)^4 = y^12
(z^4)^4 = z^16
Therefore the answer is C. x^4 y^12 z^16
The histogram shows the heights in meters of trees in a certain section of a park.
How many trees are less than 16 meters tall?
A histogram titled Heights of Trees with Height in meters on horizontal x-axis and Frequency on vertical y-axis
5
9
16
12
Answer:
16
Step-by-step explanation:
CAN SOMEONE HELP ME PLEASE???
Answer:
[tex]x^3[/tex]
Step-by-step explanation:
To find the greatest common factor of a set of numbers, we need to find the greatest number, that when it's used as a divisor for all the numbers, returns an integer value.
We have the numbers [tex]x^3, x^6,[/tex] and [tex]x^9[/tex].
Exponent rules tell us that [tex]a^b \div a^c = a^{b-c}[/tex].
This means that each of these values must be raised to the power of three. Therefore, each of them can be divided by [tex]x^3[/tex].
[tex]x^3 \div x^3 = 1[/tex]
[tex]x^6 \div x^3 = x^3[/tex]
[tex]x^9 \div x^3 = x^6[/tex]
So [tex]x^3[/tex] is the GCF.
Hope this helped!
Do the following ratios form a proportion? 5/8, 9/14 OR 10/16, 18/28 BRAINLIEST AND 30 POINTS
Answer:
18/28
Step-by-step explanation:
Please help!,! Once again
Answer:
the answer is "dilation by a scale factor of 2 and a rotation of 90° counter clock wise about the origin"
z−4/9−1/3=5/9 Enter your answer as a fraction in simplest form in the box. z =
Answer:
z=12/9 or 4/3 or 1 1/3
Step-by-step explanation:
1/3 needs to have a denominator of 9 so 3/9 because 3x3=9 and you have to multiply the numerator by 3 also
z-4/9-3/9=5/9
add -4/9 and -3/9 because you add two negative numbers
new equation
z-7/9=5/9
add 7/9 to 5/9
z=12/9 or 4/3 or 1 1/3
arithmetic sequences are to linear functions as geometric sequences are to
Answer:
exponential functions.
Step-by-step explanation:
5x + 8 verbal expression
Answer:
The sum of 5 times a number x and 8
Step-by-step explanation:
It could also be written as:
The sum of the product of 5 and a number x and 8
What is the perimeter of a triangle with the following side lengths?
Side 1=22x-17
Side 2=-15x+12
Side 3=-3x-5
Answer:
p=22x-17-15x+12-3x-5
4x-10
Step-by-step explanation:
hope it is helpful for you if it is follow me
what is the slope of (-5,4) and (7,8)
What is the equivalent equation to: -6=3y
the answer for your question is y=−2
Determine which letter on the numberline best represents the radical(photo attached)
Answer:
The square root of 133 is 11.53. The closest to this number would be point D.
Evaluate g(x) = 4 – 3x when x
= -3, 0, and 5.
Would anyone happen to know this?! I need help please ASAP
Answer:
nope
Step-by-step explanation:
could someone please help me
Answer:
x=16°
y=25°
Step-by-step explanation:
7x=112
x=112/7
x=16
90+y=115
y=115-90
y=25
Is −2x=38 a literal equation?
Steps to solve:
-2x = 38
~Divide -2 to both sides
x = -19
Since this equation is solvable, it is a literal equation
Best of Luck!
-2(2u-3)+3u=3(u+8)
u=?
A single card is drawn from a standard 52 card deck.
Work out the probability of choosing the "9 of
spades"
Give your answer in its simplest form
Answer:
Probability of choosing 9 of spades = 1/52
Enter a fraction equivalent to 0.8. Use only whole numbers for numerator and denominator.
Answer:
4/5
Step-by-step explanation:
=>0.8
=>8/10
=>4/5
Does every quadratic equation have at
least one real solution? Explain. (1 point)
A. Yes. When the discriminant is zero, there is exactly one solution. When the discriminant is not zero, there are two unique solutions.
B. No. When the discriminant is greater than zero, there are no real solutions.
C. Yes. When the discriminant is zero, there are two unique solutions. When the discriminant is not zero, there is exactly one solution.
D. No. When the discriminant is less than zero, there are no real solutions.
Answer:
D. No. When the discriminant is less than zero, there are no real solutions.
Step-by-step explanation:
We have to notice that quadratic equations are second order polynomials whose standard form is:
[tex]y = a\cdot x^{2}+b\cdot x + c \cdot x[/tex], [tex]\forall \,a,b,c\,\in\,\mathbb{R}[/tex]
The factorized form of this polynomial is:
[tex]y = (x-r_{1})\cdot (x-r_{2})[/tex]
Where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the roots of the quadratic equation, which may be real or complex.
If we equalize [tex]y[/tex] to zero and make algebraic handling, we can get the value of each root anatically by the Quadratic Formula:
[tex]r_{1,2} = \frac{-b\pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]
Where [tex]b^{2}-4\cdot a\cdot c[/tex] is known as the discriminant. Then, we should remember the following rules:
i) If discriminant is greater than zero, then the quadratic equation has two different real roots.
ii) If discriminant is zero, then the quadratic equation has two equal real roots.
iii) If discriminant is less than zero, then the quadratic function has two complex roots.
In consequence, we came to the conclusion that statement is false, as quadratic equation have all roots real or all complex, but not one real and the other complex.
In a nutshell, the correct answer is D.
In the quadratic formula, −b±b2−4ac√2a, what is b2−4ac called?
Answer:
Step-by-step explanation:
In the quadratic formula x = -b±√b²-4ac/2a, the expression b²-4ac inside the square root is called the discriminant. The discriminant is the function that determines the nature of the roots of the equation even without the constant a, b and c
If b²-4ac > 0, the roots of the equation will be real and distinct
If b²-4ac < 0 the roots of the equation will be complex number
If b²-4ac = 0 the roots of the equation will be real and the same
2x+4(7−x) HELP PLEASE IM DEPERATEEEEE
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 2x + 28}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{2x + 4(7 - x)}[/tex]
Distribute 4 through the parentheses
[tex] \dashrightarrow{ \sf{2x + 28 - 4x}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{2x - 4x + 28}}[/tex]
[tex] \dashrightarrow{ \sf{ - 2x + 28}}[/tex]
Hope I helped!
Best regards! :D
i’m not sure about this please help
Answer:
3
Step-by-step explanation:
Evaluate x/4 + 6 (x - 12) where x = 12:
x/4 + 6 (x - 12) = 12/4 + 6 (12 - 12)
Hint: | Reduce 12/4 to lowest terms. Start by finding the GCD of 12 and 4.
The gcd of 12 and 4 is 4, so 12/4 = (4×3)/(4×1) = 4/4×3 = 3:
3 + 6 (12 - 12)
Hint: | Look for the difference of two identical terms.
12 - 12 = 0:
6×0 + 3
Hint: | Any number times zero is zero.
0×6 = 0:
0 + 3
Hint: | Simplify the expression.
Write 3 + 0 as 3:
Answer: 3
The answer is three.
Explanation:
x/4 = 12/4 = 3. 6(x-12) = 6(12-12) = 6(0) = 03+0=3
A. 20% increase
B. 10% increase
C. 20% decrease
D. 10% decrease
Answer:
C. 20% decrease
Step-by-step explanation:
[tex]Saturday = 50\\Sunday =40\\\\50-40 =10\\\\\frac{10}{50} \times \frac{100}{1} \\= \frac{1000}{50} \\\\Cross \:cancel common \:factor; 50\\\\= 20[/tex]