Answers
Answer:
The coordinates of point C are (a,0).
Step-by-step explanation:
Given information: ABC is right isosceles triangle.
From the given figure it is noticed that the side BC is hypotenuse of the triangle ABC.
By pythagoras theorem,
[tex]hypotenuse^2=leg^2+leg^2[/tex]
[tex]hypotenuse^2=2leg^2[/tex]
[tex]hypotenuse=leg\sqrt{2}[/tex]
Therefore hypotenuse cannot be equal to leg. So, we can say that in triangle ABC,
[tex]AB=AC[/tex]
Length of AB is
[tex]AB=\sqrt{(a-0)^2+(0-0)^2}=a[/tex]
From the figure it is noticed that the point C lies on the x-axis, therefore the y-coordinates of C is 0.
Let the coordinates of C be (x,0) and length of AC must be a.
[tex]AC=\sqrt{(x-0)^2+(0-0)^2}[/tex]
[tex]a=x[/tex]
Therefore coordinates of point C are (a,0).
Related Questions
find the missing lenghts of the sides
Answers
Answer:
See attached picture
Step-by-step explanation:
The ratios of sides in a 30°-60°-90° triangle are ...
... 1 : √3 : 2
Multiplying these ratio units by 3 inches, we get the side lengths to be ...
... 3 in : 3√3 in : 6 in
Thus, a = 3 in; b = 3√3 in.
_____
Alternate solution
Or, you can work from your memorized values of the trig functions of 30° and 60°.
... sin(30°) = a/(6 in) = 1/2 . . ⇒ . . a = (1/2)·6 in = 3 in
... cos(30°) = b/(6 in) = (√3)/2 . . ⇒ . . b = (√3)/2·6 in = 3√3 in
The frequency (F) and length (L) of a wave are related by the following formula: F x L = 3.0 x 1010. Consider that the wavelength of violet light is 1.3 x 10−8. What is the frequency of violet light?
Answers
Answer:
2.3 × 10^18
Step-by-step explanation:
Your formula tells you ...
... F × (1.3 × 10^-8) = 3.0 × 10^10
Dividing by the coefficient of F, you have ...
... F = 3.0/1.3 × 10^(10-(-8))
... F ≈ 2.3 × 10^18
If (2−√3) is a root of a polynomial with integer coefficients, which of the following must be another root?
2√3
√3−2
2+√3
3−√2
Answers
Answer:
2+√3
Step-by-step explanation:
We know that roots with square roots come in pairs
so if we have a+ sqrt(b), we will also have a - sqrt(b)
Since one of the roots is 2 -sqrt(3), it must have another root of 2+ sqrt(3)
The conjugate of the root (2-√3) for a polynomial with integer coefficients is (2+√3), which must also be a root of the polynomial.
If (2-√3) is a root of a polynomial with integer coefficients, then by the Conjugate Root Theorem (which is a consequence of the Complex Conjugate Root Theorem), if the polynomial has real coefficients and a non-real root, then its complex conjugate must also be a root. However, since √3 is a real number and our expression involves only real numbers, in this context, we look for the conjugate in terms of radicals. Thus, the conjugate of (2-√3) would be (2+√3), which must also be a root of the polynomial.
The other options given, such as 2√3, √3-2, and 3-√2, do not satisfy the criteria of being the conjugate of (2-√3). They might be roots of some polynomial, but without the constraint of integer coefficients or known conjugate pairs, we cannot confirm that.
Your class wants to know to most typical age of student in your class. It collects the ages of all students and the teacher. Which measures of central tendency would give you the best typical student age
Answers
Answer:
Median.
Step-by-step explanation:
Assuming the teacher is not of similar age to the students, their higher age would pull the mean higher than if the teacher were not included, where the median would not be pulled by this extreme value.
Which equation is equivalent to y=23x−6?
A. 2x + 3y = −6
B. 3x − 2y = 6
C. 3x − 2y = 12
D. 2x − 3y = 18
Answers
D. 2x -3y = 18
Step-by-step explanation:Multiply by 3, then rearrange.
... y = 2/3x -6
... 3y = 2x -18 . . . . . multiply by 3
... 0 = 2x -3y -18 . . . subtract 3y
... 18 = 2x -3y . . . . . add 18
... 2x - 3y - 18 . . . . . swap sides to match the form of the answers
once out of every two weeks of the year would be how may days through out the year
Answers
Answer:
26 most years; 27 some years
Step-by-step explanation:
1 day out of 14 is 1/14 of the number of days in a year.
The number of days in a year depends on the year or years you're talking about. In all cases, there are not an integer number of weeks in a year, so days are left over. 365/14 = 26 1/14.
For example, if you're concerned with every other Monday, most years, there will be 26 of them, but every few years there will be 27. Over a period of 800 years, there will be exactly 71 years with 27 days of interest instead of 26. 800 is not divisible by 71, so the spacing will be uneven.
A punter kicks a football upward with an initial velocity of 48 feet per second. After how many seconds does the ball hit the ground? Use the formula h=rt−16t2, where h represents height in feet and r represents the initial velocity (rate) in feet per second.
A. 3
B. 6
C. 8
D. 12
Answers
A. 3
Step-by-step explanation:Fill in the given values in the formula (h=0, r=48) and solve for t.
... 0 = 48t -16t²
... 0 = 16t(3 -t)
This is true for t = 0 and for t = 3.
The ball will take 3 seconds to hit the ground.
Answer:
A.3
Step-by-step explanation:
That would the answers be for this question
Answers
[tex]\mathsf{We\;know\;that : \dfrac{a^m}{a^n} = a^m^-^n}[/tex]
[tex]\mathsf{Given : \dfrac{3^-^8}{3^-^4}}[/tex]
[tex]\mathsf{\implies 3^-^8^+^4}[/tex]
[tex]\mathsf{\implies 3^-^4}[/tex]
[tex]\mathsf{\implies \dfrac{1}{3^4}}[/tex]
[tex]\mathsf{So,\;The\;Given\;Expression\;can\;be\;written\;as : 3^-^4\;(or)\; \dfrac{1}{3^4}}[/tex]
A ladder leaning against a wall makes a 60o angle with the ground. The base of the ladder is 4 m from the building. How high above the ground is the top of the ladder?
Answers
h = 4 tan (60°)
h =6.93 m
A computer printer cost $100. Ink cartridges for the printer cost $25 each. How could you determine the overall cost of printer?
Answers
Answer: does the printer come with a starter pack of ink? how many ink cartridges does it take? A standard printer takes pink, blue, black, and yellow.
Step-by-step explanation:
1) $100 for printer
2) $25 for each cartridge
total cost if take 4 cartridges:
$200
Answer:
25*x+100
Step-by-step explanation: You do 25 multiplied by the number of cartridges (x) and then add 100 for the cost of the printer. For example, if you buy 5 cartridges, it would be, 25*5+100 and then it would equal 225 or 225 dollars for the overall cost of the printer.
Plz Help ASAP WILL MARK BRAINIEST Solve for x:
Answers
Answer:
The correct answer is 5.34
Step-by-step explanation:
you can double check this by multiplying .6 and 8.9
Answer:
x = 5.34
Step-by-step explanation:
x/ .6 = 8.9
We want to solve for x, which means we want x by itself.
Multiply each side by .6
x/ .6 * .6= 8.9 * .6
x = 5.34
If f(x) = x^3 – x^2 – 3, which of the following is equal to g(x) = f(2 – x)?
–x^3 + 5x^2 – 8x + 1
–x^3 + 7x^2 – 16x – 15
x^3 + 5x^2 + 8x + 1
x^3 – 7x^2 + 16x – 15
Answers
Answer:
–x^3 + 5x^2 – 8x + 1
Step-by-step explanation:
You can observe that expanding f(2-x) will give you a sum that includes (2-x)³, so will have a -x³ term. This narrows the choices to one of the first two.
If x=0, then you have ...
... f(2) = 2^3 -2^2 -3 = 8 - 4 - 3 = 1 . . . . corresponds to the first selection
_____
Worked in detail
f(2-x) = (2-x)³ -(2-x)² -3 . . . . substitute 2-x for x in the expression for f(x)
... = (2³ -3·2²x +3·2x² -x³) -(2² -2·2x +x²) -3
... = -x³ +5x² -8x +1 . . . . . matches the first selection
_____
Using ...
... (a+b)³ = a³ + 3a²b +3ab² +b³
... (a+b)² = a² +2ab +b²
Select linear or nonlinear to correctly classify each function.
Answers
Answer:
okiii i got the answers right here i hope this helps!
Step-by-step explanation:
oki so for the first one liner
the second it non liner
third is also non liner
and the lasst one is liner
In triangle $ABC$, let angle bisectors $BD$ and $CE$ intersect at $I$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 17$, $AC = 24$, and $BC = 33$, then find the perimeter of triangle $AMN$.
Thanks!
Answers
Answer:
41
Step-by-step explanation:
If you work through a series of obscure calculations involving area and the radius of the incircle, they boil down to a simple fact:
... For MN║BC, perimeter ΔAMN = perimeter ΔABC - BC = AB+AC
.. = 17+24 = 41
_____
Wow! Thank you for an interesting question with a not-so-obvious answer.
_____
A little more detail
The point I that you have defined is the incenter—the center of an inscribed circle in the triangle. Its radius is the distance from I to any side, such as BC, for example.
If we use "Δ" to represent the area of the triangle and "s" to represent the semi-perimeter, (AB+BC+AC)/2, then the incircle has radius Δ/s. The area Δ can be computed from Heron's formula by ...
... Δ = √(s(s-a)(s-b)(s-c)) . . . . where a, b, c are the side lengths
For this triangle, the area is Δ = √38480 ≈ 196.1632 units². That turns out to be irrelevant.
The altitude to BC will be 2Δ/(BC), so the altitude of ΔAMN = (2Δ/(BC) -Δ/s). Dividing this by the altitude to BC gives the ratio of the perimeter of ΔAMN to the perimeter of ΔABC, which is 2s.
Putting these ratios and perimeters together, we get ...
... perimeter ΔAMN = (2Δ/(BC) -Δ/s)/(2Δ/(BC)) × 2s
... = (2/(BC) -1/s) × BC × s = 2s -BC
... perimeter ΔAMN = AB +AC
The perimeter of triangle AMN is found using the angle bisector theorem to determine the lengths of AM and AN, and recognizing that MN = BC due to the parallelism. After calculating, the approximate perimeter of triangle AMN is found to be 54.86.
In triangle ABC, the angle bisectors BD and CE intersect at I. A line through I parallel to BC intersects AB at M and AC at N. Perimeter of triangle AMN is found by adding lengths AM, MN, and NA. Since IM is parallel to BC and bisectors divide the angles proportionally, we have:
AM/AB = AI/AD, where D is the intersection of angle bisector BD with BC.
AN/AC = AI/AD, using similar logic.
MN is parallel to BC, so MN = BC due to the properties of parallelograms.
Using AB = 17, AC = 24, and BC = 33, find AM and AN using the proportional segments:
AM = (AI/AD) * AB
AN = (AI/AD) * AC
The perimeter of triangle AMN is AM + MN + AN.
To solve for AI/AD, we use the angle bisector theorem which gives us AI/AD = AB/BC = 17/33. Substituting this into the equations for AM and AN we get:
AM = (17/33) * 17
AN = (17/33) * 24
Computing these we find:
AM = 8.77 (approximately)
AN = 13.09 (approximately)
Lastly, we add AM, AN, and BC to find the perimeter:
Perimeter = AM + AN + MN
Perimeter = 8.77 + 13.09 + 33 = 54.86 (approximately)
This is the approximate perimeter of triangle AMN.
In kite JKLM , MJ=JK and ML=KL . Diagonals JL¯¯¯¯¯ and MK¯¯¯¯¯¯¯ intersect at point P, m∠MLK=48∘ , and m∠JKM=30∘ . What is m∠JML ?
Answers
Answer:
96°
Step-by-step explanation:
ΔKLM is isosceles, so base angle KML will be half the supplement of ∠MLK, or ...
.... ∠KML = (180° -48°)/2 = 66°
ΔKJM is also isosceles, so base angle JMK will be the same measure as ∠JKM, 30°.
∠JML = ∠JMK + ∠KML = 30° +66°
∠JML = 96°
Lucien is going to move to a new house he needs to figure out how much each packing box will hold which formula can lucien use to figure out how much the box will hold h=40cm w=45cm l=70 cm NEED HELP PLEASE QUICK GOOD AMOUNT OF POINTS!!!!!!!!!!
Answers
Volume - the amount of space that a substance or object occupies, or that is enclosed within a container.
Volume is length × breadth × height
The volume of the box will be 40 × 45 × 70
= 126000 cubic centimeters
Please help me answer this question, thank youuu
Answers
PLZ HELP WILL MARK BRAINLEST SOLVE FOR X
Answers
[tex]\frac{x}{8} + 19 = 30[/tex] - subtract 19 from both sides
[tex]\frac{x}{8} = 11[/tex] - multiply both sides by 8
[tex]x = 88[/tex]
In this equation, x = 88.
Which expression represents the phrase?
Answers
Answer to your question:
C.7n+4 represents the phrase as
Number is n.
Seven times the number means 7n.
Adding four we get,
7n+4
Hope it helps *_*
Answer:
It would be C
Here's Why:
Sum means addition"Seven times the sum of a number" meaning a number times another number which represents 7nfind thevmissing value. please
Answers
y=69°
x=104°
Finding the missing value in mathematics usually involves solving an equation. The process can vary depending on whether the problem involves algebra, geometry or another mathematical principle.
Explanation:In mathematics, finding the missing value typically involves solving an equation where a variable represents the unknown, or missing, value. The task requires understanding of the mathematical principle being applied. For example, if you have an equation like 2x = 10, you can solve for the missing value (x) by dividing both sides of the equation by 2, which gives x = 5. If the problem involves a geometric figure, understanding the relevant formulas for area, volume, perimeters, etc. is key.
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find the scale factor please.
Answers
Answer:
5/2
Step-by-step explanation:
The scale factor for linear measures, such as perimeter, is the square root of the scale factor for areas. The ratio of larger area to smaller is ...
... 75/12 = 25/4
so the ratio of the larger perimeter to the smaller is ...
... √(25/4) = 5/2
2x 2 - 4x + 6 = 0 is in general form.
Answers
2x² - 4x + 6 = 0 /:2
x²-2x+3=0
Δ=(-2)²-4·1·3=4-12=-8<0
x∈∅
False. A, B, and C does not have a greatest common factor of 1 which means this ewuation is not in general form.
Trevon is making payments on a car that costs $26,555. He makes 36 equal payments. If he rounds the equal payments up to the nearest whole dollar, about how much will he overpay after 36 months? Show your work to justify your answer.
Answers
Answer:
$13
Step-by-step explanation:
$26,555 ÷ 36 = 737.6388889 ≈ $738 per month
36 × 738 = $26,568
= $13
Answer:
$13 will be overpaid after 36 months if payments are rounded of to nearest whole number dollar.
Step-by-step explanation:
We are given the following in the question:
Total cost of car = $26,555
Number of equal installments made = 36
Payment of 1 installment =
[tex]\displaystyle\frac{\text{Toatl cost}}{\text{Number of installments}} = \frac{26555}{36} = 737.6389\$[/tex]
Rounding of to nearest whole number, payment of one installment = $738
Value of 36 installments of $738 each =
[tex]36\times 738 = 26568\$[/tex]
Money overpaid after 6 months =
[tex]26568 - 26555 = 13\$[/tex]
Thus, $13 will be overpaid after 36 months if payments are rounded of to nearest whole number dollar.
Pat bounces a basketball 25 times in 30 seconds. At that rate, approximately how many fimes will Pat bounces the ball in 150 seconds?
Answers
Answer:
125 times
Step-by-step explanation:
Set up the proportion
25 times/ 30 seconds = x / 150 seconds Multiply by 150
25 * 150 / 30 = x
3750 / 30 = x
x = 125
He will be able to bounce the ball 125 times
Answer:
The ball will bounce 125 times
Step-by-step explanation:
We can use ratio's to solve this problem. I will put how many times the basketball is bounced on top and how many seconds on the bottom.
25 times x times
------------- = ----------------
30 seconds 150 seconds
Using cross products
25 * 150 = 30 * x
Divide each side by 30
25*150/30 =30*x/30
25 * 5 = x
125 =x
What is 8 3/4% expressed as a fraction?
8/100
7/80
7/40
8/25
Answers
7 / 80
8 3/4% expressed as a fraction is 7 / 80.
STEP-BY-STEP EXPLANATION:
Write 8 3/4% as a percentage with a decimal:
= 8.75%
Convert 8.75% to a fraction:
= 8.75% ÷ 100
= 8.75 / 100
Make the numerator a whole number by multiplying both the numerator and denominator by a 100:
= ( 8.75 × 100 ) / ( 100 × 100 )
= 875 / 10000
Divide the numerator and denominator in the fraction by their highest common factor ( HCF ):
HCF = 125
THEREFORE:
= ( 875 ÷ 125 ) / ( 10000 ÷ 125 )
= 7 / 80
Final answer:
To convert 8 3/4% to a fraction, you transform the mixed number into an improper fraction, which equals 875%. Then, scale it by dividing by 100 to get 8.75%, and express this as 8.75/100. Simplify by dividing numerator and denominator by 25 to finally get 7/16.
Explanation:
To express 8 3/4% as a fraction, we first convert the mixed number to an improper fraction. There are 4 quarters in a whole, so 8 3/4 is the same as 8 + 3/4, which equals 35/4. To convert this into a percent, we need to consider that 1 whole is the same as 100%, so 35/4 as a percent is 35/4 * 100%. Simplifying this, we multiply 35 by 25 (100% divided by 4), which gives us 875%. Since we want to express 8 3/4%, not 800 3/4%, we divide by 100 to get back to the correct scale. So, 875% divided by 100 is 8.75%, which is the same as 8 3/4%.
Now, to convert 8.75% to a fraction, we can write it as 8.75/100. To simplify this fraction, we recognize that both the numerator and the denominator are divisible by 25. Dividing both by 25, we get 7/4 divided by 1 which simplifies to 7/4 divided by 100/25. This simplifies to 7/4 * 25/100, which equals 7/16 when simplified.
Thus, 8 3/4% as a fraction is 7/16.
Agora chess club has 16 members and gains a new memeber every month. The key club has 4 members and gains 4 new members every month. How many months will it take for the clubs to have the same amount of members
Answers
Answer:
4 months and you can check for yourself by plugin in 4 in both equations (e.g. 1(4)+16=4(4)+4
Step-by-step explanation:
To do this: Agora = 1x+16
Key Club = 4x+4
1x+16=4x+4
1x+12=4x
12=3x
4=x
if x equals 8 and y equals 0 are the lines perpendicular? Yes or no?
Answers
Answer:
yes it's perpendicular line
Step-by-step explanation:
The radius of a circular ring is 4 feet. What is the circumference?
A. 12.15 feet
B. 12.56 feet
C. 30.43 feet
D. 25.12 feet
Answers
The radius of a circular ring is 4 feet. What is the circumference?
Answer: D.) 25.12 feet
Step-by-step explanation:
We apply the formula to calculate the circumference knowing the radius. We consider π = 3.14
C = 2 x π x Radius = 2 x 3.14 x 4 feet = 25.12 feet
Answer : D.) 25.12 feet
[tex]\textit{\textbf{Spymore}}[/tex]
The circumference of the circle is 25.12 feet.
The radius of a circular ring is 4 feet.
We have to determine the circumference
We apply the formula to calculate the circumference by knowing the radius.
We consider π = 3.14
What is the formula for the circumference of the circle?
C = 2 x π x Radius
use the given values in the above formula so we get,
C= 2 x 3.14 x 4 feet
C= 25.12 feet
Therefore option D is correct.
The circumference of the circle is 25.12 feet.
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Simplify (2p+3)2 - (2p-3)2 (Give proper detailed answer with all steps)
Answers
Answer:
[tex]24p[/tex]
Step-by-step explanation:
There's a very useful pattern in factoring and multiplying binomials called a difference of squares, and it looks like this:
[tex](x+y)(x-y)=x^2-y^2[/tex]
We can use this difference of squares to factor the expression we've been given, setting [tex]x=2p+3[/tex] and [tex]y=2p-3[/tex] to obtain the expression
[tex](2p+3)^2-(2p-3)^2=[(2p+3)+(2p-3)][(2p+3)-(2p-3)][/tex] (1)
tackling each of the multiplicands on the right:
[tex](2p+3)+(2p-3)=2p+2p+3-3=4p[/tex] (Left)
[tex](2p+3)-(2p-3)=2p-2p+3-(-3)=3+3=6[/tex] (Right)
This simplifies the expression on the right of (1) to [tex]4p\cdot6[/tex], or simply [tex]24p[/tex].
a random generator is used to select an integer from 1 to 3 inclusive. What is the difference between the estimated probability that a 3 is generated and the actual probability that a 3 is generated?
1 2 3 3 3 2 2 1 1 1 2 3 1 1
A. 0.29
B. 0.33
C. 0.05
D. 0.04
Answers
Answer:
option no D
Step-by-step explanation:
AS it given that it is a random generator
so it will generate random integers between 1 and 3
so
possible sample space = {1,2,3}
Total no of out comes = 3
Estimated probability that 3 will occur will be obtained by dividing total no of outcomes with total no of possible events to occur
as the occurrence of event is only 1
so
Estimated probability = 1 /3 = 0.33333
Now
The experiment is performed
total outcomes = 14
Total no of like able events that 3 occurred = 4
Actual probability = 4 / 14
= 0.2857
Difference between actual and estimated probability is = 0.3333-0.2857
=0.0421
≅0.04
which is option D
Final answer:
The actual probability of a 3 being generated is 1/3, and the estimated probability from the given sequence is 4/14. The difference between the two probabilities is roughly 0.05, which corresponds to answer choice C.
Explanation:
The question refers to the probability of a random generator selecting the number 3 from a set of integers ranging from 1 to 3, where each number has an equal chance of being selected. The actual probability of the random generator selecting a 3 is 1/3, as there are three possible outcomes and each is equally likely. To find the estimated probability, we can look at the frequency of the number 3 in the provided set of generated numbers: (1 2 3 3 3 2 2 1 1 1 2 3 1 1). In this set, there are 4 occurrences of the number 3 out of 14 total numbers. Therefore, the estimated probability is 4/14 or approximately 0.2857. The difference between the estimated and actual probabilities is 0.3333 (actual) - 0.2857 (estimated) = 0.0476. When rounded to two decimal places, the difference is approximately 0.05. Thus, the correct answer to the question would be C. 0.05.