Answers
Answer:
[tex] \boxed{\sf Length \ of \ leg \ y = 13} [/tex]
Step-by-step explanation:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
[tex] \therefore \\ \sf \implies {84}^{2} + {y}^{2} = {85}^{2} \\ \\ \sf {84}^{2} = 7056 : \\ \sf \implies 7056 + {y}^{2} = {85}^{2} \\ \\ \sf {85}^{2} = 7225 : \\ \sf \implies 7056 + {y}^{2} = 7225 \\ \\ \sf Substract \: 7056 \: from \: both \: sides : \\ \sf \implies (7056 - 7056) + {y}^{2} = 7225 - 7056 \\ \\ \sf 7056 - 7056 = 0 : \\ \sf \implies {y}^{2} = 7225 - 7056 \\ \\ \sf 7225 - 7056 = 169 : \\ \sf \implies {y}^{2} = 169 \\ \\ \sf 169 = {13}^{2} : \\ \sf \implies {y}^{2} = {13}^{2} \\ \\ \sf \implies y = \sqrt{ {13}^{2} } \\ \\ \sf \implies y = {13}^{ \cancel{2} \times \frac{1}{ \cancel{2}} } \\ \\ \sf \implies y = 13 [/tex]
So,
Length of leg y of the right triangle = 13
EXPLANATION:
(Using Pythagoras Theorem)
c^2 - a^2 = b^2
85^2 - 84^2 = b^2
7225 - 7056 = b^2
169 = b^2
√169 = b
b= 13
I HOPE THIS HELPED:)
Related Questions
11/10= x+2/5 Please Explain
Answers
Answer:
x=7/10
Step-by-step explanation:
2/5=4/10
11/10=x+4/10
11/10-4/10=x
7/10=x
Answer:
x=7/10 or 0.7
Step-by-step explanation:
I turned the fractions into decimals
so
1.1=x+0.4
subtract 0.4 from 1.1 to get 0.7
Turn it into a fraction which is 7/10
Si tienes 24 tubos de 6 metros de longitud cada uno para unir dos puntos que conducen agua , si los tubos fueran de 8 metros ¿ cuantos tubos se necesitarían?
Answers
Answer:
Se necesitarían:
18 tubos
Step-by-step explanation:
La longitud total de la tubería con 24 tubos de 6 metros cada uno es:
24*6 = 144 metros
si los tubos fuesen de 8 metros:
144/8 = 18
Se necesitarían:
18 tubos
Volume of a Triangular Prism
Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
Answers
Answer:
348 km³
Step-by-step explanation:
The volume of the triangular prism can be calculated using the formula, Volume = base area of the prism*the length of the prism
Base area of the prism = area of triangle = ½*base of the triangle*height of the triangle
Base of the triangle = 12 km
Height of the traingle = 5.8
Therefore,
Base area = ½*12*5.8
= 6*5.8
Base area = 34.8 km²
Length of prism = 10 km
Volume of prism = base area*prism length
= 34.8*10
Volume of triangular prism = 348 km³
Sketch the graph of y = (x - 3)2 - 16, then select the graph that corresponds
to your sketch.
10
-20
20
-5
5
. 10
10
20
A. Graph A
B. Graph B
C. Graph C
Ο Ο
D. Graph D
Answers
Answer:
Please look at the attached graph and select the appropriate answer.
Step-by-step explanation:
Make sure that the graph shows a parabola with branches up, and the vertex situated at the point (3, -16) which corresponds to the double root x = 3, and the vertical shift that lowers that vertex 16 units below the x-axis.
Please look at the attached picture.
Answer: Graph B
Step-by-step explanation:
I need the answer and maybe someone can tell me how to do it? Please and Thanks!! :))
Answers
Answer:
83
Step-by-step explanation:
The 126 angle is an exterior angle of the triangle.
The 43 and x angles are the two remote interior angles of the 126 angle.
Theorem:
The measure of an exterior angle of a triangle equals the sum of the measures of the remote interior angles.
x + 43 = 126
x = 83
Answer:
x = 83
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
126 = x+43
Subtract 43 from each side
126-43 = x+43-43
83 = x
what is the measure of arc angle EG
Answers
Answer:
80 = EG
Step-by-step explanation:
Inscribed Angle = 1/2 Intercepted Arc
40 = 1/2 EG
Multiply each side by 2
80 = EG
Answer:
80 deg
Step-by-step explanation:
Theorem:
The measure of an inscribed angle is half the measure of the intercepted arc.
m<EFG = (1/2)m(arc)EG
40 deg = (1/2)m(arc)EG
m(arc)EG = 2 * 40 deg
m(arc)EG = 80 deg
which is the equation of a line that passes through the point (3,2) and is parallel to the line in the graph?
Answers
Answer:
A. 3x - 2y = 5
Step-by-step explanation:
Given line in the graph has the following properties:
using point (2,3)
m = slope = (y2-y1)/(x2-x1) = (5-2)/(2-0) = 3/2
New line passes through y0(3,2), so use the point-slope form
(y-y0) = m (x-x0)
substitute in value y0(3,2)
y - 2 = (3/2) (x - 3)
multiply by 2 on each side
2y - 4 = 3x - 9
simplify and rearrange
3x - 2y = -4 + 9 =5
3x - 2y = 5
Classify the following triangle. Check all that apply.
A. Obtuse
B. Isosceles
C. Scalene
D. Equilateral
E. Acute
F. Right
Answers
Answer:
isosceles
Step-by-step explanation:
Find the slope and y-intercept of each line:
a. (x+2)(x+3)=(x-2)(x-3)+y
b. x=my+b
Please show workings, and I won't accept nonsense answers! Don't answer the question if you don't know what it means!!
Answers
Answer:
See below
Step-by-step explanation:
Part A:
[tex](x+2)(x+3) = (x+2)(x-3) + y[/tex]
Resolving Parenthesis
[tex]x^2+3x+2x+6=x^2-3x-2x+6+y\\x^2+5x+6 = x^2-5x+6+y[/tex]
Subtracting [tex]x^2[/tex] and 6 to both sides
[tex]5x= -5x+y[/tex]
Adding 5x to both sides
[tex]y = 5x+5x\\y = 10x[/tex]
Comparing it with [tex]y = mx+b[/tex] where m is the slope while b is the y-intercept
So,
Slope = m = 10
Y-intercept = b = 0
Part B:
[tex]x = my+b[/tex]
Subtracting b to both sides
[tex]my = x-b[/tex]
Dividing both sides by m
[tex]y = \frac{x-b}{m}\\ y = \frac{x}{m} - \frac{b}{m}[/tex]
Comparing it with [tex]y = mx+b[/tex] where m is the slope while b is the y-intercept
So,
Slope = m = [tex]\frac{1}{m}[/tex]
Y-intercept = b = [tex]-\frac{b}{m}[/tex]
What the answer now hurry up and answer fast question
Answers
Answer:
927.0 cm²
Step-by-step explanation:
Step 1: find Z
m < Z = 180 - (28 + 118) (sum of ∆)
= 180 - 146
Z = 34°
Step 2: Find side XY using the law of sines
[tex] \frac{XY}{sin(34)} = \frac{42}{sin(28)} [/tex]
Cross multiply
[tex] XY*sin(28) = 42*sin(34) [/tex]
[tex]XY*0.469 = 42*0.559[/tex]
Divide both sides by 0.469
[tex]\frac{XY*0.469}{0.469} = \frac{42*0.559}{0.469}[/tex]
[tex]XY = 50.06[/tex]
XY ≈ 50 cm
Step 3: find the area.
Area of ∆ = ½*XY*YZ*sin(Y)
XY ≈ 50 cm
= ½*50*42*sin(118)
= 25*42*0.8829
Area = 927.045
Area ≈ 927.0 cm² (nearest tenth)
what is the value of 24% of 800?
Question of mathematics
Answers
We simply multiply 800 and 24% (0.24)
800(0.24) = 192
Answer:
[tex] \huge \boxed{192}[/tex]Step-by-step explanation:
[tex]24\% \: of \: 800[/tex]
By definition of p% = p/100
[tex] = \frac{24}{100} \times 800[/tex]
Reduce the numbers with Greatest Common Factor 100
[tex] = 24 \times 8[/tex]
Multiply the numbers
[tex] = 192[/tex]
Hope I helped!
Best regards!!
Rewrite [tex]\frac{200x - 300}{x}[/tex] as a sum of two fractions, and simplify.
Answers
Answer:
We can rewrite this as [tex]\frac{200x}{x} + \frac{-300}{x}[/tex].
[tex]\frac{200x}{x}[/tex] simplifies to 200 after eliminating x from the numerator and denominator and [tex]\frac{-300}{x}[/tex] becomes [tex]-\frac{300}{x}[/tex] so the final answer is [tex]200 - \frac{300}{x}[/tex].
If you flip a coin three times in the air, what is the probability that tails lands up all three times? A. 1/2 B. 1/8 C. 1/4 D. 1/6
Answers
Answer: A) 1/2
Step-by-step explanation:
Answer:
If you flip a coin three times in the air, what is the probability that tails lands up all three times?
Step-by-step explanation:
1/2
Find the tangent of the angle in between the lines 2x+3y–5=0 and 5x=7y+3?
Answers
Answer:
tanФ = 2.6363636
Step-by-step explanation:
To find the tangent of the angle in-between the lines we will follow the steps below:
We are going to use the formula;
tanФ = |m₂ - m₁ / 1 + m₁m₂|
We can get the slope m₁ from the first equation
2x+3y–5=0
we will re-arrange it in the form y=mx + c
3y = -2x + 5
Divide through by 3
y = -[tex]\frac{2}{3}[/tex]x + [tex]\frac{5}{3}[/tex]
comparing the above equation with y=mx + c
m₁ = -[tex]\frac{2}{3}[/tex]
We will proceed to find the second slope m₂ using the second equation
5x=7y+3
we will re-arrange it in the form y=mx + c
7y = 5x -3
divide through by 7
y = [tex]\frac{5}{7}[/tex] x - [tex]\frac{3}{7}[/tex]
comparing the above with y=mx + x
m₂ = [tex]\frac{5}{7}[/tex]
we can now go ahead and substitute into the formula
tanФ = |m₂ - m₁ / 1 + m₁m₂|
tanФ = | [tex]\frac{5}{7}[/tex] - (-[tex]\frac{2}{3}[/tex] ) / 1 + (-[tex]\frac{2}{3}[/tex]₁)( [tex]\frac{5}{7}[/tex])|
tanФ = | [tex]\frac{5}{7}[/tex] +[tex]\frac{2}{3}[/tex] / 1 - [tex]\frac{10}{21}[/tex]|
tanФ = | [tex]\frac{29}{21}[/tex] / [tex]\frac{11}{21}[/tex]|
tanФ = | [tex]\frac{29}{21}[/tex] × [tex]\frac{21}{11}[/tex]|
21 will cancel-out 21
tanФ =[tex]\frac{29}{11}[/tex]
tanФ = 2.636363
x=y-y and 2x+4y=10 solve using substitution
Answers
Answer:
(0, 2.5)
Step-by-step explanation:
Well we substitute y-y into x in the following equation,
2x + 4y = 10
2(y-y) + 4y = 10
2y - 2y + 4y = 10
Combine like terms
2y - 2y = 0
4y = 10
10/4
y = 2.5
If y is 2.5 we can plug those into y.
2x + 4(2.5) =10
2x + 10 = 10
-10
2x = 0
0/2
x = 0
A sphere has a diameter of 12 ft. What is the volume of the sphere? Give the exact value in terms of pi
Answers
Answer:
288π
Step-by-step explanation:
V=4 /3πr^3 is the formula. We have the diameter, so the radius is half (6). We now have V=4 /3π(6)^3 = 4/3π216 = 288π.
What is the simplified form of m-4+m
Answers
Answer:
2m - 4
Step-by-step explanation:
Add m and m.
Hope this helps :)
Answer:
[tex]\boxed{2m+4}[/tex]
Step-by-step explanation:
[tex]m-4+m[/tex]
Combine like terms.
[tex]m+m-4[/tex]
[tex]2m-4[/tex]
PLs answer ASAP will make you brainlist
Answers
Answer:
[tex]\boxed{\sf A. \ 36}[/tex]
Step-by-step explanation:
The triangles are congruent. The sides are proportional.
Let x be the length of FQ.
[tex]\frac{24}{18} =\frac{x}{27}[/tex]
[tex]\sf Multiply \ both \ sides \ by \ 27.[/tex]
[tex]\frac{24}{18}(27)=\frac{x}{27}(27)[/tex]
[tex]36=x[/tex]
Simplify $\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}.$
Answers
Let [tex]x=\sqrt[3]{3}[/tex] and [tex]x^2=\sqrt[3]{9}[/tex]. Then
[tex]\dfrac{2\sqrt[3]{9}}{1+\sqrt[3]{3}+\sqrt[3]{9}}=\dfrac{2x^2}{1+x+x^2}[/tex]
Multiply the numerator and denominator by [tex]1-x[/tex]. The motivation for this is the rule for factoring a difference of cubes:
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
Doing so gives
[tex]\dfrac{2x^2(1-x)}{(1+x+x^2)(1-x)}=\dfrac{2x^2(1-x)}{1-x^3}[/tex]
so that
[tex]\dfrac{2\sqrt[3]{9}}{1+\sqrt[3]{3}+\sqrt[3]{9}}=\dfrac{2\sqrt[3]{9}(1-\sqrt[3]{3})}{1-3}=\sqrt[3]{9}(\sqrt[3]{3}-1)=3-\sqrt[3]{9}[/tex]
Which triangle’s area can be calculated using the trigonometric area formula?
Answers
Explanation:
In order for a triangle to be calculated by using trigonometric area formula that triangle must be given 2 sides and 1 angle (SAS)
Answer:
Triangle klm
Step-by-step explanation:
edg 2020
Identify whether the relations given in the options are functions or not.
Answers
Answer:
Graphs 1, 2, and 3 are not functions. Graph 4 is a function.
Step-by-step explanation:
Use the vertical line test.
Imagine a vertical line moving from left to right.
If in any position of the vertical line, it intersects more than one point on the graph, then it is not a function.
In graphs 1 and 2 it is clear that there are many vertical lines than would intersect the graph at more than one point.
In graphs 3, a vertical line would intersect the vertical parts of the graph at more than 1 point, so graph 3 is not a function.
The only function is graph 4.
The relations given in options 1, 2, and 3 are not functions only Graph 4 is a function.
What is the function?A function is an expression, or rule that defined the relation between two variables.
If we use the vertical line test.
Imagine a vertical line moving from left to right.
If in any position of the vertical line, it intersects more than one point on the graph, then it is not a function.
In graphs 1 and 2 it is clear that there are many vertical lines than would intersect the graph at more than one point.
In graph 3, a vertical line would intersect the vertical parts of the graph at more than 1 point, so graph 3 is not a function.
Learn more about function here;
https://brainly.com/question/21145944
Which is the mean for this data? 1,2,5,5,6,6,7,8
Answers
Answer:
5
Step-by-step explanation:
First you need to add all the digits so 1 +2+5+5+6+6+7+8 = 40
Then, divide that by the number of digits which is 8.
Therefore, 40/8 = 5, which is the answer.
I hope this helped!
Suppose there is a bond in ABC Company that that pays coupons of 8.5%, and suppose that these coupons are paid annually.
Suppose the face value of the ABC bond is $1000 and the maturity is 11 years.
a) If the appropriate discount rate for this bond is 6%, what would you be willing to pay for ABC’s bond?
b) If a comparable company, XYZ, has a 7.0% coupon bond with a maturity of 9 years and a face value of 1000, and that bond is trading in the market for $994.50, what would you be willing to pay for ABC’s bond?
c) Suppose you find that the true fair value for ABC bond is $1200.00, but you see that the bond trading for $1051.00, what would you recommend?
Answers
Answer:
$1197.17185
Step-by-step explanation:
ABC bond :
Par value of bond (FV) = 1000
Period (n) = 11 years
Coupon rate (r) = 8.5% annually
Discount rate (r) = 6% = 0.06
The coupon price = 8.5% of par value
Coupon price (C) = 0.085 * 1000 = 85
Current price of bond can be computed using the relation:
= C * [1 - 1 / (1 + r)^n] / r + (FV / (1 + r)^n)
85 * [1 - 1/(1+0.06)^11]/0.06 + 1000/(1 + 0.06)^11
85 * 7.8868745 + 526.78752
670.38433 + 526.78752 = $1197.17185
Anita plans to cover a solid cone with construction paper for a science project. The cone has a diameter of 11 inches and a slant height of 28.5 inches. How many square inches of paper will she need to cover the entire cone? (Use 3.14 for Pi and round to the nearest hundredth. Recall the formula S A = pi r l + pi r squared.) 492.20 in.2 587.18 in.2 982.82 in.2 984..39 in.2
Answers
Answer:
587.18 in²
Step-by-step explanation:
In the above question, we are given the following values
Diameter = 11 inches
Radius = Diameter/2 = 11 inches/2 = 5.5 inches
Slant height = 28.5 inches.
We were asked to find how many square inches of paper will she need to cover the ENTIRE cone.
To solve for this, we would use formula for Total Surface Area of a Cone
Total Surface Area of a Cone = πrl + πr²
= πr(r + l)
Using 3.14 for π
Total Surface Area of a Cone
= 3.14 × 5.5( 5.5 + 28.5)
= 3.14 × 5.5 × (34)
= 587.18 in²
Therefore, Anita will need 587.18 square inches of paper to cover the entire cone.
Answer:
B
Step-by-step explanation: Just trust me bro
A Prince came to an Evil Wizard to ask for the release of his beloved Princess, who is locked behind one of three doors. The Evil Wizard offered to release the Princess if the Prince was able to correctly guess which door she was behind. And with this offer, the Evil Wizard gave three hints: 1) The Princess is locked behind door 1 2) A fire-breathing Dragon is locked behind door 2. 3) There is also someone locked behind door 3 The Prince realized that all three hints were false, and with the help of logic, understood which door the Princess was locked behind. Which door was it?
Answers
Answer:
Princess is behind 2
Step-by-step explanation:
If all 3 hints are false, then the princess is not behind 1 ( so it must be 2 or 3)
The dragon is not behind 2 ( so it must be 1 or 3)
The is no one behind 3
That means the princess cannot be behind 3 and the dragon cannot be behind 3
The princess is behind 2 and the dragon is behind 1
given that sin x equals to a over b then what is tan x
Answers
Answer:
Hey there!
Sine is equal to opposite/hypotenuse
Tangent is equal to opposite/adjacent
opposite=a
hypotenuse=b
adjacent=c
Thus, tangent x= a/c.
Hope this helps :)
Answer:
tan x = a/sqrt(b^2 - a^2)
Step-by-step explanation:
sin x = a/b = opp/hyp
tan x = opp/adj
adj^2 + opp^2 = hyp^2
adj^2 + a^2 = b^2
adj = sqrt(b^2 - a^2)
tan x = a/sqrt(b^2 - a^2)
Sunland Mining Company purchased land on February 1, 2020, at a cost of $975,900. It estimated that a total of 57,600 tons of mineral was available for mining. After it has removed all the natural resources, the company will be required to restore the property to its previous state because of strict environmental protection laws. It estimates the fair value of this restoration obligation at $110,700. It believes it will be able to sell the property afterwards for $123,000. It incurred developmental costs of $246,000 before it was able to do any mining. In 2020, resources removed totaled 28,800 tons. The company sold 21,120 tons.
Answers
Sunland Mining Company purchased land on February 1, 2020, at a cost of $975,900. It estimated that a total of 57,600 tons of mineral was available for mining. After it has removed all the natural resources, the company will be required to restore the property to its previous state because of strict environmental protection laws. It estimates the fair value of this restoration obligation at $110,700. It believes it will be able to sell the property afterwards for $123,000. It incurred developmental costs of $246,000 before it was able to do any mining. In 2020, resources removed totaled 28,800 tons. The company sold 21,120 tons.
Calculate :
a. Per unit mineral cost.
b. Total material cost of December 31, 2020, inventory
c. Total materials cost in cost of goods sold at December 31, 2014.
Answer:
a. Per unit mineral cost is $21
b. Total material Cost of ending inventory is $161280
c. Total materials cost in cost of goods sold is $443520
Step-by-step explanation:
The Per unit mineral cost can be computed as follows:
Details Amount ($)
Cost of land 975900
Add: Restoration obligation 110700
Add: Development cost 246000
1332600
Less: Resale value of property 123000
Total cost of land 1209600
Divide:Total estimated cost 57600
of minerals
Per unit mineral cost 21
b. The ending inventory cost on December 31, 2020 can be calculated as follows:
Ending inventory = Total mined tons - sold tons
Ending inventory = 28800 - 21120
Ending inventory = 7680
Cost per ton= $21
Cost of ending inventory = 7680 × $21
Cost of ending inventory = $161280
c.To calculate the cost of goods sold in December 2020; we have:
Cost per ton = $21
Total units sold = 21120
Cost of goods sold = 21120 × $21
Cost of goods sold = $443520
Please help me with this question. refer to the image first.
5. The diagram below shows three circles. Circle A has a radius of 2 cm and circle B has a
radius of 1 cm.
PQ is a common tangent and all circles touch one another. Find the radius of the smallest
circle. PL5
Answers
Answer: The radius of the small circle is about 0.85 cm - 0.95 cm
Explanation: I am not completely sure but I drew the same figure with the same lengths as given and between both circles there is almost a gam of 2.5 - 3 cm and when we draw a circle between them the diameter is about 1.7 - 1.9 so dividing the diameter by 2 to get the radius we get 0.85 cm - 0.95 cm.
Answer:
o.85 to 0.95
Step-by-step explanation:
I got to go so I don' have time to explain!
Find the area of the triangle.
Answers
Answer:
10.5 cm^2
Step-by-step explanation:
Since we have two sides and the angle between those sides, we can use the alternative area formula:
[tex]A=\frac{1}{2}ab\sin(C)[/tex]
a and b are the two sides while C is the angle in between the two sides.
Plug in the numbers:
[tex]A=\frac{1}{2}(7)(6)\sin(150)[/tex]
Recall the unit circle. Sin(150) is 1/2.
[tex]A=21(\frac{1}{2})[/tex]
[tex]A=21/2=10.5cm^2[/tex]
Will give BRAINLIEST to best answer One way to explore a career opportunity is to work as a trainee in your field of interest to gain practical experience. In this experience you would be known as a(n). A intern B. mentor C. tutor D. volunteer
Answers
Answer:
A. Intern
Step-by-step explanation:
Usually as a intern, you go around gaining experience about something. For example, if your a fresh graduate , you would first be hired as an intern to gain experience in the job you want.
Answer:
B:Mentor
Step-by-step explanation: