Answers
The side lengths of the right triangle in exact form are z = (15√3)/2, x = 15/2, y = (15√3)/4, a = 15/4 and b = 45/4.
How determine the sides of a right triangle using trigonometric ratios?Three out of the six functions used in trigonometry is expressed as;
sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent
From diagram, we solve for side z of the right triangle.
cosθ = adjacent / hypotenuse
cos( 30° ) = z / 15
Solve for z
z = cos( 30° ) × 15
z = (√3)/2 × 15
z = (15√3)/2
Next solve for side x
sinθ = opposite / hypotenuse
sin( 30° ) = x / 15
x = sin( 30° ) × 15
x = 15/2
Solve for side y
sinθ = opposite / hypotenuse
sin( 60° ) = y / 15/2
y = sin( 60° ) × 15/2
y = (15√3)/4
Solve for side a
cosθ = adjacent / hypotenuse
cos( 60° ) = a / 15/2
a = cos( 60° ) × 15/2
a = 15/4
Solve for side b
b = 15 - a
b = 15 - 15/4
b = 45/4
Therefore the length of side of b is 45/4
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Related Questions
Hi can you give me the basic answer for 12 please
Answers
Given the equation of the line:
[tex]y=-5x-\frac{1}{2}[/tex]• You can identify that it is written in Slope-Intercept Form:
[tex]y=mx+b[/tex]Where "m" is the slope of the line, and "b" is the y-intercept.
Notice that:
[tex]\begin{gathered} m_1=-5 \\ b_1=-\frac{1}{2} \end{gathered}[/tex]• By definition, parallel lines have the same slope, but their y-intercepts are different.
Therefore, you can determine that the slope of the line parallel to the first line is:
[tex]m_2=-5[/tex]You know that this line passes through this point:
[tex](-4,2)[/tex]Therefore, substituting the slope and the coordinates of that point into this equation:
[tex]y=m_2x+b_2[/tex]And solving for the y-intercept, you get:
[tex]\begin{gathered} 2=(-5)(-4)+b_2 \\ \\ 2-20=b_2 \\ \\ b_2=-18\frac{}{} \end{gathered}[/tex]Then, the equation of the line parallel to the first line is:
[tex]y=-5x-18[/tex]• By definition, the slopes of perpendicular lines are opposite reciprocal, therefore, the slope of this line is:
[tex]m_3=\frac{1}{5}[/tex]Using the same procedure used before to find the y-intercept, you get:
[tex]\begin{gathered} 2=(\frac{1}{5})(-4)+b_3 \\ \\ 2+\frac{2}{5}=b_3 \\ \\ b_3=\frac{14}{5} \end{gathered}[/tex]Therefore, its equation is:
[tex]y=\frac{1}{5}x+\frac{14}{5}[/tex]Hence, the answer is:
- Equation for the parallel line:
[tex]y=-5x-18[/tex]- Equation for the perpendicular line:
[tex]y=\frac{1}{5}x+\frac{14}{5}[/tex]There are 3 consecutive even integers that have a sum of 30. What are the integers?
Answers
Answer:
8, 10, 12
Step-by-step explanation:
x+x+2+x+4=30
3x+6=30
3x=30-6
3x=24
x=8
if we subtract 2/4 from 3/4, what isthe difference?
Answers
Answer:
-[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Ans:
In Fractional/Exact Form:
1/4
In Decimal Form:
Ans=0.25
Steps to Simplify the expression.
Step 1:Find the least common denominator
Step 2:Multiply the least common denominator
Step 3:Simplify the equation
Step 4:Solve
(3/4)-(2/4)= (3-2)/4
Exact Form:
1/4
Decimal Form:
Ans=0.25
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Solve each system of the equation by elimination method. 2x+3y=258x+5y=37
Answers
Answer:
x = -1 and y = 9
Explanation:
Given the below system of equations;
[tex]\begin{gathered} 2x+3y=25 \\ 8x+5y=37 \end{gathered}[/tex]To solve by using the elimination method, the 1st step is to multiply the 1st equation by 8 and the 2nd equation by 2, we'll have;
[tex]\begin{gathered} 16x+24y=200 \\ 16x+10y=74 \end{gathered}[/tex]The 2nd will be to subtract the 4th equation from the 3rd equation and solve for y;
[tex]\begin{gathered} 0+14y=126 \\ y=\frac{126}{14} \\ y=9 \end{gathered}[/tex]The 3rd step is to substitute y = 9 into the 1st equation and solve for x;
[tex]\begin{gathered} 2x+3(9)=25 \\ 2x+27=25 \\ 2x=-2 \\ x=\frac{-2}{2}=-1 \end{gathered}[/tex]Please reference attached image for the problem that requires solving. Thank you so much for taking the time to help.
Answers
Explanation:
The number of times the 6-sided number cube will be rolled will is
[tex]750[/tex]Let the numbers greater than 4 be represented below as
[tex]E_1[/tex][tex]\begin{gathered} E_1=\lbrace5,6\rbrace \\ n(E_1)=2 \end{gathered}[/tex]The number of sample space will be
[tex]n(S)=6[/tex]The probability of rolling a number greater than 4 will be calculated below as
[tex]\begin{gathered} Pr(E_1)=\frac{n(E_1)}{n(S)} \\ Pr(E_1)=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]Hence,
To calculate the number of times a number greater than 4 will be rolled will be calculated below as
[tex]\begin{gathered} =Pr(E_1)\times750 \\ =\frac{1}{3}\times750 \\ =250times \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow250\text{ }times[/tex]La suma de tres numeros consecutivos impares es 63
Answers
Answer:
19, 21, 23
Step-by-step explanation:
Find the area of the following circles. Leave your answer in terms of pi or round to the nearest 10th.
Answers
To find the area of a circle, we use the formula for area
A = pi r^2 where r is the radius
We are given the diameter
d = 2r
8 = 2r
Solving for r
8/2 =r
4= r
A = pi (4)^2
A = 16 pi
Triangle XYZ is translated by the rule (x + 1, y − 1) and then dilated by a scale factor of 4 centered at the origin. Which statement describes the properties of triangles XYZ and X''Y''Z'' after the transformations?
Answers
Using the given transformations, namely translation and dilation, the correct statement is given as follows:
Segments YZ and Y''Z'' are proportional after the dilation and congruent after the translation.
TranslationThe translation rule in this problem is given as follows:
(x, y) -> (x + 1, y - 1).
Meaning that the triangle was shifted:
One unit right, due to x -> x + 1.One unit down, due to y -> y - 1.The only change with the dilation was in the position of the triangle, hence the translated triangle is congruent to the original triangle.
DilationThe triangle was dilated by a scale factor of 4, meaning that the coordinates of each vertex of the triangle is multiplied by 4, changing the side lengths of the triangle, thus the dilated triangle is not congruent to the original triangle.
The angles keep the same measure for both cases, translation and dilation, hence the first two statements are incorrect.
The change in the side lengths is proportional, due to the scale factor of 4, hence the correct statement is:
Segments YZ and Y''Z'' are proportional after the dilation and congruent after the translation.
What is the missing information?The correct options are missing and are given by the image at the end of the answer.
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The circumference of a circle is 25.2 cm. Find the area of the circle correct to 1 decimal place. Area = cm²
Answers
The area of the circle is 12.56 [tex]cm^{2}[/tex].
What is area of circle?
The space occupied by a circle in a two-dimensional plane is defined as its area. A circle is a critical geometric figure found in many fields, including construction, engineering, and many others. Geometry problems involving circles necessitate the ability to calculate the area of a circle. The area of a circle is calculated as A = πr2, where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, in2, and so on.
Here the circumference of the circle is,
=> C = 25.2 cm
=> 2πr = 25.2
=> 2×3.14×r=25.2
=> r = [tex]\frac{25.2}{2*3.14}[/tex]
=> r= 4cm
Now area of the circle A= π[tex]r^2[/tex] [tex]unit^{2}[/tex]
=> A= 3.14*4 = 12.56 [tex]cm^{2}[/tex]
Hence area of the circle is 12.56 [tex]cm^{2}[/tex].
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A rectangle is placed around a semicircle as shown below. The width of the rectangle is 6 mm. Find the area of the shaded region.Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Q) In the picture we have a semi-circle inscribed in a rectangle. We see that the diameter is equal to the width of the rectangle (the horizontal side) of the rectangle (w), so we have:
[tex]d=w=6\operatorname{mm}[/tex]From the fact that the diameter is always two times the radius for every circle, we have:
[tex]r=\frac{d}{2}=\frac{6}{2}\operatorname{mm}=3\operatorname{mm}[/tex]Now, we also see from the picture:
[tex]h=r=3\operatorname{mm}[/tex]The question asks us about the area of the shaded region.
A) The shaded region can be computed in the following way:
1) First, we compute the area of the rectangle (Ar).
[tex]A_r=w\cdot h=6\operatorname{mm}\cdot3\operatorname{mm}=18mm^2[/tex]2) Secondly, we compute the area of the semi-circle (Asc), which is half of the area of the entire circle.
[tex]A_{sc}=\frac{1}{2}\cdot A_c=\frac{1}{2}\cdot\pi\cdot r^2=\frac{1}{2}\cdot3.14\cdot(3\operatorname{mm})^2=14.13mm^2[/tex]3) Finally, we compute the area of the shaded region taking the difference between the area of the rectangle and the area of the semi-circle.
[tex]A_s=A_r-A_{sc}=18mm^2-14.13mm^2=3.87mm^2[/tex]Is a triangle whose sides measure 1.25 in ,0.75 in and 1 in, a right triangle?
Answers
In a right triangle, the largest side is called the hypotenuse. Furthermore, from the Pythagorean Theorem, the following relation is satisfied:
[tex]c^2=a^2+b^2[/tex]To find if those measures correspond to a right triangle, verify if it satisfies the Pythagorean Theorem:
[tex]\begin{gathered} 1.25^2=1.5625 \\ 1^2+0.75^2=1.5625 \end{gathered}[/tex]Then:
[tex]1.25^2=1^2+0.75^2[/tex]Therefore, the sides of lengths 1.25 in, 1 in and 0.75 in are indeed the sides of a right triangle.
A health inspector from the Food and Drug Administration was tasked with oversight of a pharmaceutical company in their development of a new medication. He used a 99% confidence interval to estimate the true mean amount of propionic acid in each 800 mg pill. Propionic acid is an important ingredient in several medications, including ibuprofen. His confidence interval was (3.2 mg, 6.5 mg). Which one of the following is the best interpretation of this confidence interval?
Answers
The best interpretation of the confidence interval is given by:
We are 99% sure that the true mean amount of propionic acid in all 800 mg pills of the new medication is between 3.2 mg and 6.5 mg.
What is the interpretation of a x% confidence interval?The x% confidence interval means that it is x% likely that the population parameter(mean/proportion/standard deviation) is between the bounds a and b of the confidence interval
The bounds of the confidence interval are given by the estimate plus/minus the margin of error.
In this problem, the bounds of the problem are already given, as follows:
3.2 mg.6.5 mg.The variable of interest is given by:
Mean amount of propionic acid in all 800 mg pills of the new medication
The level of confidence is of 99%, hence, considering the variable and the bounds, the interpretation of the interval is:
We are 99% sure that the true mean amount of propionic acid in all 800 mg pills of the new medication is between 3.2 mg and 6.5 mg.
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Determine the CPI for a suit that costs $235 now and cost $90 in 1967.a. 261b. 203c. 219d. 275
Answers
Answer:
[tex]A\text{ :261}[/tex]
Explanation:
Here, we want to calculate the CPI for the cost of the suit
To do this,we use the weighted average method
What we will do here is to divide the past price by the current price and convert the value to a percentage
Mathematically, we have this as:
[tex]\frac{\text{Present cost}}{\text{Cost in 1967}}\text{ }\times\text{ 100 \%}[/tex]Substituting the values, we have:
[tex]\frac{235}{90}\text{ }\times\text{ 100 = 261}[/tex]what percent of 8,7 is 17.4
Answers
The number 17.4 is 200 percent of 8.7
How to determine the percentage?The statement is given as
"what percent of 8.7 is 17.4"
From the above statement, we have the following parameters
Dividend = 17.4
Divisor = 8.7
The percentage is then calculated as
Percentage = Dividend/Divisor x 100%
Substitute the known values in the above equation
So, we have
Percentage = 17.4/8.7 x 100%
Evaluate the quotient
Percentage = 2 x 100%
Evaluate the product
Percentage = 200%
Hence, the percentage is 200%
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The Matrix Fishing Company does fishing in Toluca Lake the first year of the company's operation it managed to catch a 190,000 fish due to population decreases the number of fish the company was able to catch decreased by 8% each year how many total fish did the company catch over the first 12 years round to the nearest whole number
Answers
Solution
For this case we can model the number of fishes with the following equation:
[tex]A=19000(1-0.08t)[/tex]And for this case we want to find the value for t =12 and replacing we got:
[tex]A=190000\cdot(1-0.08\cdot12)=7600[/tex]And then the number of fishes after 12 years would be 7600
so then they catched 182400
3x^2-4x+5-x^2+x
Combine like terms
Answers
Find the sum of the geometric series given a₁ = 2, r = -3, and n = 8.A. 1/2B.-3107OC.-3280D. -3780Reset Selection
Answers
The formula to calculate the sum of a geometric sequence is given to be:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]The question has the following parameters:
[tex]\begin{gathered} a_1=2 \\ r=-3 \\ n=8 \end{gathered}[/tex]Therefore, the sum will be:
[tex]\begin{gathered} S_8=\frac{2(1-(-3)^8)}{1-(-3)} \\ S_8=-3280 \end{gathered}[/tex]The correct option is OPTION C.
The hypotenuse of right triangle is 226 miles long. The difference between the other two sides is 194 miles. Find the missing sides. Use exact values.
Find the value of the short and ling leg.
Answers
Answer: short line: 30 miles, ling leg: 224 miles
Step-by-step explanation:
Intro:
We will be using Pythagoras theorm, which states, if we have a 90 degree triangle which has 3 side as H, B and P defined as Hypotenuse, Base and Perpendicular, then H² = B² + P²
In your case, we know that hypotenuse is 226.
We also know that (A + B)² = A² + B² + 2AB
Given:
H = 226
B - P = 194
Solution:
B = 194 + P
So
(226)² = (194 + P)² + P²
51076 = (194)² + P² + (2 x 194 x P) + P²
51076 = 37636 + 2P² + 388P
51076 - 37636 = 2P² + 388P
13440 = 2P² + 388P
6720 = P² + 194P
P² + 194P - 6720 = 0
P² - 30P + 224P - 6720 = 0
P(P - 30) + 224(P - 30) = 0
(P - 30) x (P + 224) = 0
P = 30 or -224
As miles cannot be negative, we will choose answer as 30 miles.
Now we have H = 226 and P = 30
Using Pythagoras theorm:
(226)² = (30)² + B²
51076 = 900 + B²
50176 = B²
B = 224 miles.
So the missing miles are 224 miles and 30 miles
find the surface area of the prism choose the correct units
Answers
We have a rectangular prism, with dimensions 7 ft tall, 1 ft wide and 4 ft deep.
The surface area of the prism is the sum of the area of all their faces.
We can start by listing the faces. We will have 3 pair of faces:
- One pair of 7 ft * 1 ft
- One pair of 1 ft * 4 ft
- One pair of 4 ft * 7 ft
Then, we can write and solve the expression for the surface area as:
[tex]\begin{gathered} A=2\cdot A_1+2\cdot A_2+2\cdot A_3 \\ A=2\cdot(7\cdot1)+2\cdot(1\cdot4)+2\cdot(4\cdot7) \\ A=2\cdot7+2\cdot4+2\cdot28 \\ A=14+8+56 \\ A=78\text{ ft}^2 \end{gathered}[/tex]Answer: the surface area is 78 square feet.
Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
The product of 2 and the difference of a number and 5.
Answer:
Submit Answer
attempt 1 out of 2
Answers
Answer:
2(x-5).
Step-by-step explanation:
The difference of a number and 5 is x-5.
The product means to multiply, so the answer is 2(x-5).
M(5,-10) is rotated 270 degrees what is M’?
Answers
Problem
M(5,-10) is rotated 270 degrees what is M’?
Solution
For this case we need to remember that is we have any point A =(x,y) when we apply a transformation fo 270° then the new coordinates would be:
M' = (x,-y)
And for this case if we apply this transformation we got:
M'= (5, -(-10))= (5,10)
John has a $200 gift card for laser tag. Every time he goes to the laser tag, $25.00
is removed from the gift card. Which of the following functions have the same end behavior as the function that models the money left on John’s gift card?
Answers
John can use the gift card for 9 times till his balance becomes zero dollars from $200 using the concept of arithmetic progression.
As per the question statement, John has a $200 gift card for laser tag. So every time he goes to the laser tag, $25.00 is removed from the gift card.
We are supposed to find out the number of times John can use the card till his balance becomes zero dollars from $200 and we will use the concept of arithmetic progression.
We know the formula, a(n) = a + (n-1)*d
where "a" is the first value, "a(n)" is the total value, "d" is the common difference and "n" is the number of times
The AP : 200, 175, 150,......0
Here a = 200, a(n) is 0, n is supposed to be find out and d = 25
Hence using the AP formula,
0 = 200 + (n-1) * 25
n-1 = 8
n = 9
Hence, John can use the gift card for 9 times till his balance becomes zero dollars from $200 using the concept of arithmetic progression.
Arithmetic Progression: A string of figures that fluctuate in value by the same amount throughout time.
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Line segment LN has endpoints L-2, -3) and N(3, 7).Which of the following determine the coordinates of point M located at the midpoint of LN?M= - (³2/2/², 2/³) 3-2 7-3M= =(3+2, 7+³)M = (-2-³, -3-7)M = (¹+³, 32)
Answers
The line segment LN has coordinates as follows;
[tex]\begin{gathered} L=(-2,-3) \\ N=(3,7) \end{gathered}[/tex]The midpoint of a line is derived with the following coordinates;
[tex]M=\frac{(x_1+x_2)}{2},\frac{y_1+y_2}{2}[/tex]The coordinates are thus;
[tex]\begin{gathered} (x_1,y_1)=(-2,-3) \\ (x_2,y_2)=(3,7) \end{gathered}[/tex]The midpoint, which is M, now becomes;
[tex]\begin{gathered} M=\frac{-2+3}{2},\frac{-3+7}{2} \\ \text{Also, re-written as;} \\ M=\frac{3-2}{2},\frac{7-3}{2} \end{gathered}[/tex]ANSWER:
The first option is the correct answer.
14x^2y^4-7x^5y^3 Factor with GCF method
Answers
[tex]14x^2y^4-7x^5y^3[/tex]
The GCF is
[tex]7x^2y^3[/tex]Factoring out using the GCF, we have
[tex]\begin{gathered} 7x^2y^3(\frac{14x^2y^4}{7x^2y^3}-\frac{7x^5y^3}{7x^2y^3}) \\ \\ 7x^2y^3(2y-x^3) \end{gathered}[/tex]What is the slope intercept equation for this line?
Answers
the slope for this line is 2
what is slope?The slope or gradient of a line is a number that describe both the direction and the steepness of the line. the steepness of a line is defined as the slope (or gradient). The slope is the ratio of vertical distance to the horizontal distance between any two points on a line. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).The greater the value of the slope, the "steeper" the slope is, and vice versa. So the smallest value of the absolute value of these slopes is 1/2.
So, A.T.Q:-
The formula of slopet intercept is Y2 -Y1 /X2-X1
From the question:
slope = -1-1/0-1
slope = 2
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3 years ago I was 2/3 as old as I will be 8 years from now. How old am I?
Answers
Considering the definition of an equation and the way to solve it, if 3 years ago I was 2/3 as old as I will be 8 years from now, I am 25 years old.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign. One or more unknown values appear in it, in addition to certain known data.
Solving an equation is determining the value or values of the unknowns that transform the equation into an identity. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.My ageBeing "x" the my age today, and knowing that 3 years ago I was 2/3 as old as I will be 8 years from now, the equation in this case is:
x -3= 2/3×(x +8)
Solving:
x -3= 2/3x +2/3×8
x -3= 2/3x +16/3
x - 2/3x= 16/3 + 3
1/3x= 25/3
x= 25/3 ÷ 1/3
x= 25
Finally, I am 25 years old.
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If a woman making $33,000 a year receives a cost-ofliving increase of 2.8%, what will her new salary be?
Answers
Answer:
$33,924
Step-by-step explanation:
The amou8nt of the raise is 2.8% of $33,000.
2.8% of $33,000 =
= 2.8% × $33,000
= 0.028 × $33,000
= $924
The amount of the raise is $924.
The new salary is the amount of the raise added to the original salary.
$33,000 + $924 =
= $33,924
y=-2/3 3 what is the slope of the equation entered as a fraction
Answers
The equation:
[tex]y=-\frac{2}{3}x-1[/tex]has the form:
y = mx + b
with
[tex]\begin{gathered} m=-\frac{2}{3} \\ b=-1 \end{gathered}[/tex]m is known as the slope of the line, then the slope is -2/3
The oxygen saturation level of a river is found by
dividing the amount of dissolved oxygen the river
water currently has per liter by the dissolved oxygen
capacity per liter of the water and then converting to a
percent. If the river currently has 7.3 milligrams of dis-
solved oxygen per liter of water and the dissolved
oxygen capacity is 9.8 milligrams per liter, what is the
oxygen saturation level, to the nearest percent?
Answers
Answer:
sub
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A boy sold $88.50 worth of stationery. If he received a 33 1/3% commission, what was the amount of his commission?
A) $29.50
B) $40
C) $50
D) $62.50
Answers
Work Shown:
33 & 1/3% = 0.3333... the '3's go on forever
0.3333*88.50 = 29.49705 which rounds to 29.50
Answer: A. $29.50 is the correct answer.
