Answer:
b = 8sqrt(3)
Step-by-step explanation:
The triangle has a 30-deg angle and a right angle, so the third angle measures 60 degrees making this a 30-60-90 degree right triangle.
You don't mention which method to use to solve the problem.
You can use trigonometry ratios or the ratios of the lenghts of the sides of a 30-60-90 triangle
I'll use the second method.
In a 30-60-90 triangle, the lengths of the sides are in the ratio:
1 : sqrt(3) : 2
The long leg measures 12 and corresponds to sqrt(3) in the ratio, so we can find the length of the short leg by dividing 12 by sqrt(3).
12/sqrt(3) = [4 * sqrt(3) * sqrt(3)]/sqrt(3) = 4sqrt(3)
The hypotenuse is twice the length of the short leg.
b = 2 * 4sqrt(3) = 8sqrt(3)
The value of b is 8√3 because cos is the ratio of side adjacent to the angle to side opposite to the angle.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We have a right angle triangle shown in the picture.
From the cos ratio:
cos30 = 12/b
b = 12/cos30
b = 12/(√3/2)
After factorization:
b = (24√3)/3
b = 8√3
Thus, the value of b is 8√3 because cos is the ratio of side adjacent to the angle to side opposite to the angle.
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Amy has a triangle with side lengths of 6 and 8. What is the length of the
hypotenuse.
Hello There!
The length of the hypotenuse is 10.
We know what 2 sides are 6 and 8.
To find the third side we use the formula a^2 + b^2 = c^2
So we multiply 6 by 6 which equals 36 and then multiply 8 by 8 which equals 64.
Next we add 64 and 36 together and we get 100.
Next, we square root 100 and get 10.
10 is the length of the hypotenuse.
Write the equations of the line contains E and F in:
A) slope-intercept form
B) standard form
C) point-slope form
Answer:
A) y=4x-12
B) y-4x=-12
C) y+4=4(x-2)
Step-by-step explanation:
Sorry it took you so long to be answered, but I hope this helps! :D
Answer with explanation:
Coordinate of Point E and F are = (4,4) and (2,-4).
Two Point form of line, that is equation of line Passing through two points is given by:
[tex]\rightarrow \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}_x_{1}}\\\\\rightarrow \frac{y-4}{x-4} =\frac{4+4}{4-2}\\\\\rightarrow \frac{y-4}{x-4} =4\\\\ \rightarrow y-4=4 x-16\\\\\rightarrow 4 x-y -16+4=0\\\\\rightarrow 4 x -y-12=0[/tex]
Standard Form : 4 x-y-12=0
Slope-intercept form
[tex]\rightarrow 4 x-y-12=0\\\\\rightarrow 4 x- y=12\\\\\rightarrow \frac{4 x-y}{12}=1\\\\\rightarrow \frac{4x}{12}-\frac{y}{12}=1\\\\\rightarrow \frac{x}{3} +\frac{y}{-12}=1[/tex]
Point-slope form
[tex]\rightarrow \frac{y-4}{x-4} =\frac{4+4}{4-2}\\\\\rightarrow \frac{y-4}{x-4} =4[/tex]
Plz help me with this
Answer: A) 13
Step-by-step explanation:
Mean - 1 SD: 20.2 - 2.4 = 17.8 --> (18)
Mean + 1 SD: 20.2 + 2.4 = 22.6 --> (23)
Now, find the values on the histogram for 18 through 23:
2 + 3 + 4 + 3 + 1 + 1 = 13
A(n) ____ is NOT an example of an agreement.
A) Lease
B) Month-to-month
C) Annual
D) Fine Print
Answer:
D) Fine Print
Fine print is part of an agreement but technically isnt one.
Final answer:
The correct answer is D) Fine Print. Fine Print is not an agreement but refers to the small, often hard-to-read text in a contract that contains important legal provisions.
Explanation:
The correct answer is D) Fine Print. A lease is a contractual agreement between a lessor and a lessee that gives the lessee the right to use a property owned by the lessor for a specific period in exchange for payment. A month-to-month agreement is a type of lease which automatically renews each month until either party decides to terminate it. An annual agreement typically refers to a contract or lease that is renewed once per year.
Write the equation 4x + 2y = 5 in the form y = mx + b.
Answer:
4x+2y-5=0
Step-by-step explanation:
since you have to put the problem in that order you take 5 from both sides
Answer:
The correct answer is y = -2x + 5/2
Step-by-step explanation:
y = mx + b. is the y intercept form of a line.
To find the y = mx + b. form
It is given that,
4x + 2y = 5
2y = -4x + 5
Dividing both sides by 2 we get,
2y/2 = (-4x + 5)/2
y = -4x/2 + 5/2
y = -2x + 5/2
Here m = -2 and b = 5/2
-4v+-12=-12-4v simplified
The answer would be 0.
you would add -4v on the left to -4v to the right to get 0. Then you would add -12 on the left to -12 on the right to get 0.
Find the value of x in the triangle shown
Answer:
the answer is A the square root of 80.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
What is the measure of ∠JSM?
A) 12°
B) 17°
C) 23°
D) 31°
I think it would be “B”
Answer:
Option B.
Step-by-step explanation:
Given information: [tex]m\angle A=48^{\circ},\angle E=90^{\circ},\angle EMS=59^{\circ}[/tex].
According to the angle sum property of a triangles, the sum of interior angles of a triangle is 180°.
Apply angle sum property on triangle AEJ.
[tex]\angle A+\angle E+\angle J=180^{\circ}[/tex]
[tex]48^{\circ}+90^{\circ}+\angle J=180^{\circ}[/tex]
[tex]138^{\circ}+\angle J=180^{\circ}[/tex]
Subtract 138 from both sides.
[tex]\angle J=180^{\circ}-138^{\circ}[/tex]
[tex]\angle J=42^{\circ}[/tex]
The measure of angle J is 42°.
According to exterior angle property, the sum of two interior angles of a triangle is equal to the third exterior angle.
Apply exterior angle property on triangle JMS.
[tex]\angle EJA+\angle JSM=\angle EMS[/tex]
[tex]42^{\circ}+\angle JSM=59^{\circ}[/tex]
Subtract 42 from both sides.
[tex]\angle JSM=59^{\circ}-42^{\circ}[/tex]
[tex]\angle JSM=17^{\circ}[/tex]
The measure of ∠JSM is 17°.
Therefore, the correct option is B.
a. y=1/2x-2
b. y=-1/2x+3
c. y=2x+1
d. y= -2x+4
d. y=-2x+4
this is because in the formula used y=mx+b, b is represented as the the "y" intersept, which is 4. the slope, which is -2, is represented as x in this formula. therefore, D. y=-2x+4 is the correct answer
a refund of $3.15 on a $8.64 bill
8.64 - 3.15 = $5.49 if this is what you are asking
Answer:
Step-by-step explanation:
3.15-8.64 is5.49 hope this helps
A game is played with a deck of 50 cards numbered from 1 to 50. At the end of each round, players calculate their score by adding the numbers on their cards.
What is the least score a player could have if he or she has 7 cards remaining at the end of a round?
Answer:
28, 329, 11
Step-by-step explanation:
What is the least score a player could have if he or she has 7 cards remaining at the end of a round?
28 pointsWhat is the greatest score a player could have if he or she has 7 cards remaining at the end of a round?
329 pointsGlenna needs to get 60 points in the next round to win the game. What is the least number of cards Glenna needs to be guaranteed a win?
11The least score a player could have is if he or she has 7 cards remaining at the end of round 28.
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Calculation:-
Addition of the first 7 natural number (out of 50 cards)
In order to get the minimum value
⇒1+2=3+4+5+6+7=28
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The denominator of the seventh term is
125
216
343
512
343 will be your answer
Answer: Thus, Third option is correct.
Step-by-step explanation:
Since we have given that
[tex]1,\dfrac{1}{8},\dfrac{1}{27},\dfrac{1}{64},...............\dfrac{1}{n^3}[/tex]
So, we can see the pattern:
General term of the series is given as
[tex]\dfrac{1}{n^3}[/tex]
So, we just put the value of n = 7, to get the required denominator:
[tex]\dfrac{1}{7^3}=\dfrac{1}{343}[/tex]
Hence, the denominator of the seventh term is 343.
Thus, Third option is correct.
I’m thinking of a number. The square of this number is the same as the number times 4. What could my number be?
Answer:
4
Step-by-step explanation:
4 squared equals 16 and 4 times 4 equals 16
how much dog food does dobby eat in a week
Answer:
We do not know much details for your question. Please add numbers or something. This question could be deleted if we don't know how to solve something like this.Chris spent $8 on lunch. 75% was spent on a sub ad the rest was used to buy two cookies. How much was each cookie?
Answer:
1 dollar.
Step-by-step explanation:
"Chris spent $8 on lunch. 75% was spent on a sub ad the rest was used to buy two cookies. How much was each cookie?"
.75=75%
8*.75=cost of sub=6
total cost- cost of sub=cost of cookies
8-6=2
The cost of 2 cookies is 2 dollars
Now to find the cost per cookie we take the total cost of the cookies, and divide it by the amount of cookies-
2/2=cost per cookie=1
It cost $1 for each cookie.
[WILL GIVE BRAINLIEST ANSWER] f(x)=(x-5)(5x+2) write the smaller solution first and the smaller solutuon second
Answer:
x = - [tex]\frac{2}{5}[/tex], x = 5
Step-by-step explanation:
Given
f(x) = (x - 5)(5x + 2)
To obtain the solutions set f(x) = 0, that is
(x - 5)(5x + 2) = 0
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5 ← larger x
5x + 2 = 0 ⇒ 5x = - 2 ⇒ x = - [tex]\frac{2}{5}[/tex] ← smaller x
Please help with this probability question and if you could explain how to get the answer in order for me to understand!
Thank you
Answer:
Expected value = $8.89
Step-by-step explanation:
cost of playing game = $1
winning if sum is odd = $10
winning if sum is 4 or 8 = $5
winning if sum is 2 or 12 = $50
two dice rolled, possible outcomes =
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
total no. of outcomes = 36
now according to the table of outcome with respect to winning money, we can calculate expected value by multiplying the probability of each roll with winning amount associated with each roll. and subtract the amount that we paid for the game that is $1.
E(x) = 1/36*($50) + 1/18*($10) + 1/12*($5) + 1/9*($10) + 5/36*($0) + 1/6*($10) + 5/36*($5) + 1/9*($10) + 1/12*($0) + 1/18*($10) + 1/36*($50)
= 25/18 + 5/9 + 5/12 + 10/9 + 0 + 5/3 + 25/36 + 10/9 + 0 + 5/9 + 25/18
Expected value = $8.89
Subtract the amount that was paid to play the game that is $1.
$8.89 - $1 = $7.89
A profit of $7.89 is expected every-time the game is played.
11. Determine whether the triangles are similar. If so, what is the similarity statement and the
postulate or theorem used?
(please answer ASAP if you have the all of the questions for the semester exam I'll take them too please)
A.>TRS~>TPQ;SSS~
B.>TRS~>TPQ;SAS~
C.>TRS~>PQR;SAS~
D.The triangles are not similar
Answer:
Option B
Step-by-step explanation:
we know that
SAS Similarity Theorem: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
In this problem
∠STR is congruent with ∠QTP
Verify if the corresponding sides are proportional
[tex]\frac{42}{42+6}=\frac{28}{28+4}[/tex]
[tex]\frac{42}{48}=\frac{28}{32}[/tex]
[tex]42*32=48*28[/tex]
[tex]1,344=1,344[/tex] ----> is true
therefore
The triangles TRS and TPQ are similar by SAS
In the expression a = k/b, what is k
Answer:
k=ab
Step-by-step explanation:
a=k/b
a(b)=(k/b)(b)---multiple b to both sides to isolate k
k=ab
Answer:
k is the constant of variation.
Step-by-step explanation:
In direct variation:
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
In inverse variation:
[tex]y\propto \frac{1}{x}[/tex]
[tex]y=\frac{k}{x}[/tex]
[tex]yx=k[/tex]
In both cases k is the constant of variation
The given equation is
[tex]a=\frac{k}{b}[/tex]
We need to find the value of k in this equation.
First we have to isolate k on one side of the equation.
Multiply both sides by b to isolate k on right side.
[tex]a\times b=\frac{k}{b}\times b[/tex]
Cancel out the common factors.
[tex]ab=k[/tex]
Interchange the sides of the equation.
[tex]k=ab[/tex]
It means a and b are inversely proportional.
Therefore, the k is the constant of variation.
Could someone check over me? Thanks!
Answer:
Yes, I agree with A. :)
Step-by-step explanation:
By how much does the median of the data set 12, 9, 9, 11, 14, 28 change if the outlier is removed?
Hi there! Here's the answer and how I got that answer!!
Answer:
11
The change in the Median would be 11 instead of 11.5 because the total amount of numbers became odd when the outlier is removed. This allowed for the step of having to solve for two middle numbers to be avoided and therefore only leave you with the answer simple as 11 instead of having to solve between two numbers!
Step-by-step explanation:
With all the numbers (including the outlier) the median would be 11.5.
Here's how:
First sort least to greatest and cancel out the numbers until you get to the one on the middle.
9, 9, 11, 12, 14, 28
If you have two middle numbers add them together and then divide by two.
11+12=23
23/2= 11.5
So your median with the outlier is 11.5.
Now if you take out the outlier, which in this case I'm assuming its 28. Let's re-look for the median once more!
First sort least to greatest and cancel out the numbers until you get to the one on the middle.
9, 9, 11, 12, 14
Now because there is an odd amount of numbers your left to only one middle number, 11.
This means if the outlier is removed the median would change to be 11.
I hope this helps, have a stupendous day!! ☆*:.。.o(≧▽≦)o.。.:*☆
please help with this inequality 4+6x<4x-18
Answer:
x < - 11
Step-by-step explanation:
Given
4 + 6x < 4x - 18 ( subtract 4x from both sides )
4 + 2x = - 18 ( subtract 4 from both sides )
2x < - 22 ( divide both sides by 2 )
x < - 11
Use the distributive property to remove the parentheses.
-5(6y - u - 2)
Answer:
-30y+5u+10
Hope this helped
Find the area of the trapezoid.
75
15×6÷2+10×6÷2
90÷2+60÷2
45+30
75
The answer is 75.
Hope this helps!
A right rectangular prism has a length of 10 in., a width of 12 in., and a height of 16 in. The dimensions of the prism are halved. What is the surface area of the reduced prism? Enter your answer in the box. in²
Answer:
[tex]S.A=236in^2[/tex]
Step-by-step explanation:
The given prism has dimension;
[tex]L=10in.,W=12in.,H=16in.,[/tex]
If the dimensions of the prism are halved then;
[tex]l=5in.,w=6in.,h=8in.,[/tex]
The surface area of the reduced prism will be;
[tex]S.A=2(lw+lh+wh)[/tex]
[tex]S.A=2(5(6)+5(8)+6(8))[/tex]
[tex]S.A=2(30+40+48)[/tex]
[tex]S.A=2(118)[/tex]
[tex]S.A=236in^2[/tex]
Answer:
236in²
Step-by-step explanation:
Given in the question,
length of rectangular prism = 10 in
width of rectangular prism = 12 in
height of the prism = 16 in
Since the dimensions are reduced to half so the new dimensions are
length of rectangular prism = 5 in
width of rectangular prism = 6 in
height of the prism = 8 in
Formula to calculate the surface area
2(lw + lh + wh)
2 ((5x6) + (8x5) + 2(6x8))
236 in²
Which statements are true about polygons?
The statements that are true about polygons are:
All sides and all angles in a polygon are congruent. In a polygon, all segments with a common endpoint are collinearThe sides of a polygon are segments that intersect exactly two other segments, one at each endpoint.What are polygons?A closed polygonal chain of connected line segments makes up a polygon, a plane shape. The edges or sides of a closed polygonal chain are the individual pieces. The polygon's vertices or corners are the places where two edges converge.
Each side of a polygon is the same length, and each angle is the same size. For instance, in a square, every side is the same length and every angle is 90 degrees. There is at least one interior angle that is more than 180 degrees in a concave polygon. A concave polygon will have at least one point that is inside it if a side or diagonal is expanded.
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The perimeter of the triangle below is 4x + 3y. Find the measure of the missing side. (Picture of triangle)
Answer: 2x+3y
Step-by-step explanation: look at picture
To find the missing side in a triangle with a given perimeter, subtract the lengths of the known sides from the total frame. This is based on the sum of the lengths of all sides of a triangle, which equals its circumference.
Explanation:We need to understand a simple rule about triangles to find the missing side of a triangle where the perimeter is 4x + 3y. The sum of all sides of a triangle equals its edge. So, if we know the length of the other two sides, we can subtract their sum from the total circumference to find the size of the missing side.
For example, if we know that the other two sides of the triangle are 2x and y, respectively, the missing side would be calculated by subtracting the sum of these sides from the given perimeter.
4x + 3y = perimeter
2x + y = known sides
missing side = (4x + 3y) - (2x + y)
Note: This method assumes that x and y values are provided. If they're unknown, we will require additional equations to solve for x and y before calculating the length of the missing side.
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Helpppppp PLZZZZZZZZZZZZ
Answer:
Final answer is m∠D = 61°.
Step-by-step explanation:
Given that m∠C = 98°,
m∠B = 140°,
m∠A = m∠D ,
Using those information we need to find the value of m∠D.
We know that sum of all 4 interior angles of a quadrilateral is always 360°.
So we can write equation:
m∠A +m∠B +m∠C +m∠D = 360°
m∠A + 140° + 98° +m∠D = 360°
m∠D + 140° + 98° +m∠D = 360°
2(m∠D) + 140° + 98° = 360°
2(m∠D) + 238° = 360°
2(m∠D) = 360° - 238°
2(m∠D) = 122°
m∠D = 122°/2
m∠D = 61°
Hene final answer is m∠D = 61°.
Answer:
the answer is 61°
Step-by-step explanation:
360- 98- 140 = 122 ÷2 = 61
What is the measure of the missing angle?
A. 40
B. 75
C. 35
D. 115
Answer:
D) 115
the inside angles of a triangle always (ALWAYS) add up to 180, add 75 and 40. You get 65. Then you know that a straight line means it is 180 degrees so you subtract 65 from 180. you get 115 degrees
Missing angle is 115
Does anyone know this?! Pls help
Answer:
Step-by-step explanation:
we are given the angles of XYR = 40, ZXY = 130, and SRY = 40 degrees.
angle ZXY is half of angle ZAY, so angle ZXY is 65 degrees.
imagine a line XA (not on the diagram). then ZXA is 32.5 degrees since it is half of YXZ. Angle XZA and ZXA are equal, so XZA is 32.5 degrees. RZA = XZA + RZX = 32.5 + 40 degrees (assuming the upper left stated degree belongs to angle XZA), or simply RZA is 72.5 degrees.
since ZRA = RZA, then ZRA is 72.5 degrees. since angle ZRS = SRY + ZRA, finally ZRA = 40 + 72.5 degrees or simply, ZRS = 112.5 degrees. which visually is blantantly wrong as it appears to be less than 90 degrees.