a=1.9 in, A=46.5°, C=90°Solve the right triangle. Round side lengths one decimal place.
Answers
SOLUTION
Given the following
[tex]a=1.9in,A=46.5^0,C=90^0[/tex]Consider the image below
To solve the right triangle, we need to find the following:
[tex]b=\text{?,c}=\text{?and B=?}[/tex]To find B, we use the sum of angles in a triangle
hence
[tex]\begin{gathered} A^0+B^0+C^0=180^0^{} \\ \text{where A=46.5}^0,C=90^0 \end{gathered}[/tex]Substituting into the equation we have,
[tex]\begin{gathered} 46.5^0+B+90^0=180^0 \\ 136.5+B=180^0 \end{gathered}[/tex]Subtract 136.5 from both sides
[tex]\begin{gathered} 136.5+B-136.5^0=180^0-136.5^0 \\ \text{Then} \\ B=180^0-136.5 \\ B=43.5^0 \end{gathered}[/tex]hence
B = 43.5°
To find b, we use the trigonometry ratio for tangent
From the triangle above
[tex]\begin{gathered} \tan A=\frac{a}{b} \\ \text{Where A=46.5in, a=1.9in, b=?} \end{gathered}[/tex]Substituting into the equation
[tex]\begin{gathered} \tan 46.5=\frac{1.9}{b} \\ \text{Then } \\ b=\frac{1.9}{\tan46.5} \\ \text{Where tan46.5=1.0538} \end{gathered}[/tex]Then
[tex]b=1.8030[/tex]hence
b = 1.8in to 1 decima place
To find c, we also apply trigonometry ratio for sine of an angle
[tex]\begin{gathered} \text{sinA}=\frac{opposite}{\text{hypotenuse}} \\ \text{Where } \\ A=46.5^0,\text{ opposite =1.9in},\text{ hypotenuse =c} \end{gathered}[/tex]Substituting the values into the equation we have,
[tex]\begin{gathered} \sin 46.5=\frac{1.9}{c} \\ Multiply\text{ both sides by c, we have } \\ c\times\sin 46.5=\frac{1.9}{c}\times c \\ \text{Then } \\ c\times\sin 46.5=1.9 \end{gathered}[/tex]Divide both sides by 1.9, we have
[tex]\begin{gathered} c=\frac{1.9}{\sin 46.5}=\frac{1.9}{0.7254} \\ \text{Then} \\ c=2.6193 \end{gathered}[/tex]hence
c = 2.6 in
Therefore, to solve the right triangle, we have
Answer; B = 43.5°, b = 1.8in, c = 2.6 in
Related Questions
What is the domain and range? What does it mean in terms of the graph?
Answers
The domain of the graph is [0,14] and the range of the graph is [0, 7]
In this question, we have been given a graph of height of a falling object.
In this graph, x-axis represents the time in seconds and y-axis represents the height in meters.
We know that, the domain of a graph consists of all the input values which are on the x-axis and the range is the set of possible output values, which are shown on the y-axis.
In this graph we can see that the input (time) takes the values between [0, 14] and the output (height) has values in the interval [0, 7]
Therefore, the domain of the graph is [0,14] and the range of the graph is [0, 7]
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The average of three test scores of the first two scores are 77 and 89
Answers
Answer:
A = (166+s)/3
Step-by-step explanation:
Average test-score:
Sum of all scores divided by the number of tests.
In this question:
First two tests: 77 and 89.
Third test: s
Number of tests: 3
Average:
Finding the sum: 77 + 89 + s = 166 + s
The average is:
A = (166+s)/3
At a local restaurant, the amount of time that customers have to wait for their food isnormally distributed with a mean of 12 minutes and a standard deviation of 2minutes. Using the empirical rule, determine the interval of minutes that the middle99.7% of customers have to wait.
Answers
By the empirical rule 99.7% of the customers fall within the interval bounded by
[tex]\bar{x}-3\sigma\text{ and }\bar{x}+3\sigma[/tex]In this case,
[tex]\begin{gathered} \bar{x}=12\min \text{ and} \\ \sigma=2\min \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \bar{x}-3\sigma=12-3(2)=12-6=6\min s \\ \bar{x}+3\sigma=12+3(2)=12+6=18\min s \end{gathered}[/tex]Hence, the interval of minutes that the middle 99.7% of customers have to wait is given by
(6mins, 18mins)
The perimeter of a rectangle is equal to 138. The width of the rectangle is 5 less than the length . What is the area the rectangle?
Answers
Step 1: Concept
Perimeter of a rectangle = 2( L + W)
L = length
W = width
Area of a rectangle = Lenght x Width
Step 2:
Given data
The perimeter of a rectangle = 138
Length L = m
Width W = m - 5
Step 3:
[tex]\begin{gathered} \text{Use the perimeter of the rectangle to find the length(L) and width(W).} \\ \text{Perimeter = 2(L + W)} \\ 138\text{ = 2(m + m - 5)} \\ 138\text{ = 2m + 2m - 10} \\ 138\text{ = 4m - 10} \\ \text{Collect similar terms} \\ 138\text{ + 10 = 4m} \\ 148\text{ = 4m} \\ m\text{ = }\frac{148}{4}\text{ = 37} \end{gathered}[/tex]Step 4:
Length = 37
Width = 37 - 5 = 32
Step 5:
Find the area
Area = length x width
Area = 37 x 32
Area = 1184
Final answer
Area of the rectangle = 1184
Writing an equation of a hyperbola give me the Foci and vertices
Answers
Given the Foci of the hyperbola:
[tex]\begin{gathered} (-1,-9) \\ (-1,9) \end{gathered}[/tex]And the Vertices:
[tex]\begin{gathered} (-1,-3) \\ (-1,3) \end{gathered}[/tex]You can plot the Foci on a Coordinate Plane:
Notice that the blue line represents the Vertical Transverse Axis. Then, the equation has this form:
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]You need to find the Center using the Midpoint Formula, in order to find the Midpoint between the Foci and the Midpoint between the vertices:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]- For the Foci:
[tex]M=(\frac{-1-1}{2},\frac{-9+9}{2})=(-1,0)[/tex]- For the Vertices:
[tex]M=(\frac{-1-1}{2},\frac{-3+3}{2})=(-1,0)[/tex]Therefore:
[tex]\begin{gathered} h=-1 \\ k=0 \end{gathered}[/tex]Now you need to find "a". This is the distance from the center to the vertices:
[tex]a=3-0=3[/tex]Find "b" with this formula:
[tex]b^2=c^2-a^2[/tex]Knowing that "c" is the distance from the Foci to the center:
[tex]c=9[/tex]You get:
[tex]b^2=9^2-3^2=72[/tex]Therefore, you can write this equation:
[tex]\frac{y^2}{9}-\frac{(x+1)^2}{72}=1[/tex]Hence, the answer is:
[tex]\frac{y^2}{9}-\frac{(x+1)^2}{72}=1[/tex]Add.
Your answer should be an expanded polynomial in
standard form.
(-4b³ + b − 1) + (6b - 6) =
Answers
Answer:
-4b^3 + 7b - 7
Step-by-step explanation:
We have to look at terms which look like each other, for example 1b and 6b.
We can add and subtract terms which have the same degree of b.
In this question, we can safely add -1 and -6, and also b and 6b,
which gives us (-4b^3 + b - 1 ) + 6b - 6) = -4b^3 + (1+6)b +( -1 - 6) = -4b^3 + 7b - 7
The three remaining terms all have different degrees of b's (respectively 3, 1, 0), so we can't add those up any further, which tells us that this is the right answer.
Answer:
Step-by-step explanation:
CAN SOMEONE PLS HELP ME WITH MY PRACTICE MATH QUESTIONS!!!
Answers
some fhdf
djfsirsisdsjfsd
fdfjjjf9d094--djjf9939=3030395944./445335
What is the product?
1/2•(12 64)
(78 30)
Answers
How do I calculate the shaded area of this shape ?
Answers
SOLUTION:
We are to calculate the shaded area of the given shape.
CONCEPT:
This is a triangle that a rectangle was cut out from.
To calculate the shaded area of the given shape, we are to find the area of the triangle and then subtract the area of the recangle that was cut out.
[tex]\begin{gathered} \text{Area of Triangle:} \\ A\text{ = }\frac{1}{2}\text{ base }\times\text{ height} \\ \\ A\text{ = }\frac{1}{2}\text{ }\times\text{ 6m }\times7m\text{ } \\ \\ A=21m^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of Rectangle:} \\ A=L\text{ }\times\text{ W } \\ A\text{ = 4m }\times\text{ 2m} \\ A=8m^2 \end{gathered}[/tex]The shaded area = Area of the triangle - Area of the rectangle
[tex]\begin{gathered} \text{Shaded area = 21 m}^2-8m^2 \\ \text{Shaded area = 13 m}^2 \end{gathered}[/tex]O EXPONENTIAL AND LOGARITHMIC FUNCTIONSExpanding a logarithmic expression: Problem type 1
Answers
Given:
a logarithm is given as
[tex]log(z^5x)[/tex]Find:
we have to expand the given logarithm expressionusing properties of logarithm.
Explanation:
we know from the properties of logarithm that
[tex]\begin{gathered} log(m^n)=nlog(m) \\ and \\ log(mn)=log(m)+log(n) \end{gathered}[/tex]we will use above properties to expand the given logarithm expression as follows
[tex]log(z^5x)=logz^5+logx=5logz+logx[/tex]Therefore, the expansion of the given logarithm is 5 log(z)+ log(x)
Create your own thought experiment explaining why a negative divided by a negative is a positive.
Answers
Dividing two negative numbers results in a positive number.A negative number divided by a negative number produces a positive result since two negatives equal a positive.
Explaining why a negative divided by a negative is a positive
The quotient is positive when two negative values are divided.The same guidelines apply to multiplication. Divided by another negative integer, a negative number always yields a positive number.divided equally by.The solution cannot be or any other negative number because it is positive. Divide two negative numbers, and you'll always get a positive number as the result.For instance, dividing -4 by -2 yields 2.The negatives cancel out when both numbers are negative, hence the outcome is always a positive number. Consider that you are taking part in a game that uses red and black chips.You will win one dollar (+1) at the end of the game for each black chip you have.You must pay one dollar for every red chip you possess.Assume that at some time throughout the game you have numerous bags of black chips and several bags of red chips. These chips are currently bundled together in bags of five.You make $15 if someone offers you three bags of black chips.(3)(5)=15.You lose 15 bucks if someone steals three of your bags of black chips.(-3)(5)=-15.You lose $15 if someone gives you three bags of red chips.(3)(-5)=-15.You lose $15 if someone gives you three bags of red chips.(3)(-5)=-15.You make 15 bucks if someone steals three of your bags of red chips.(-3)(-5)=15.The crucial concept is that negative numbers signify variations rather than totals.Saying that you have four slices of bread is illogical.However, it makes logical to state that since you had 4 slices of bread, the new number of slices you possess is 4.
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Using the graph below, write two ordered pairs to show that the equation y = 15x represents the data.
Answers
By using the points (2, 30) and (4, 60) that we can see on the graph, we can see that the linear equation that models the data is:
y = 15*x
How to find the equation that models the data?A general linear equation is of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂), the slope is given by:
a = (y₂ - y₁)/(x₂ - x₁)
In this case we can use two points that appear on the graph, I will use the first two ones:
(2, 30) and (4, 60)
Then the slope is:
a = (60 - 30)/(4 - 2) = 30/2 = 15
Thus, the line is of the form:
y = 15*x + b
To find the value of b we use the point (2, 30), replacing these values we get:
30 = 15*2 + b
30 = 30 + b
30 - 30 = b
0 = b
We conclude that the linear equation that models the data is y = 15*x
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If 2(x-8)= - 4x+2 , then x=
A) -7
B) -5
C) 3
D) 9
Answers
Answer:
C) 3
Step-by-step explanation:
2(x - 8) = -4x + 2
2x - 16 = -4x + 2
6x - 16 = 2
6x = 18
x = 3
2+4-2÷3 please help
Answers
A easy way to operate fractions is convert the integer in a fraction, to operate fractions with the same denominator:
[tex]6\cdot\frac{3}{3}-\frac{2}{3}=\frac{18}{3}-\frac{2}{3}=\frac{16}{3}[/tex]Question 2 George is 5 feet 8 inches tall. How many inches tall is he? (1foot = 12 inches) 58 inches O 60 inches O 68 inches O 12 inches
Answers
Answer:
68
Step-by-step explanation:
1 foot = 12 inches
Multiply 5 by 12 inches
5 feet = 60 inches
Add the extra 8 inches
60 + 8 = 68 inches
George is 68 inches tall.
Answer:
Step-by-step explanation:
George is 5 feet and 1 foot equals 12 inches, so do 12x5 + the actual 8 inches
12x5=60
60+8=68 inches total
Consider the steps James uses to solve the equation 2(x – 10) = 24. Equation: 2(x - 10) = 24 Step 1: 2x - 10 = 24 Step 2: 2x = 34 Step 3: x = 17 In which step, if any, did James make an error? A. Step 1 B. Step 2 C. Step 3 D. James did not make an error.
Answers
In the steps that James uses to solve the given equation he made a mistake:
We have:
[tex]2\cdot(x-10)=24\Rightarrow2x-20=24[/tex]James needed to apply the distributive property in the first step. However, he did not.
Therefore, James made an error in Step 1, that is, option A.
PLS HELP WILL MARK BRAINLIEST
Answers
Answer:
l = [tex]\frac{P-2w}{2}[/tex]
Step-by-step explanation:
P = 2l + 2w ( subtract 2w from both sides )
P - 2w = 2l ( isolate l by dividing both sides by 2 )
[tex]\frac{P-2w}{2}[/tex] = l
line segment QR is parallel to line segment ST. x = ___ m
Answers
In order to find the value of x, consider that triangles PQR and PST are similar. Then, you have the following equivalence:
PQ/PS = PR/PT
Where:
PQ = x
PS = 45m
PR = 16m
PT = 36m
replace the previous values of the length of the segments and solve for x, just as follow:
x/45 = 16/36 multiply by 45 both sides
x = (16/36)45
x = 20
Hence, the value of x is x = 20
classify the triangle with the given side lengths as acute, right, obtuse, or not a triangle 11, 13, 25
Answers
Notice that if a = 11 and b = 13 are two sides of the triangle, then:
[tex]a+b=11+13=24[/tex]since the larger side measures 25 units, then we cannot write a triangle with the given measures, since a + b cannot be less than the larger side. Therefore, it is not a triangle
Determine the perimeter of this rectangle. » 526 m 78 m P = I on m m
Answers
1) Since the Perimeter (2P) is the sum of all sides of a rectangle. And this rectangle has 526m w and 78 m. And also, a rectangle is a parallelogram that has the property of having a pair of congruent sides. Then
2) Then we can state:
2p = 526 +526+78+78
2p =1052+156
2p= 1208 meters
30 60 90° triangles find the measure of the missing two sides for each figure below leave answer and rationalize and simple light form
Answers
Given : 30 60 90 triangle as shown in the following figure :
As shown : the hypotenuse of the triangle = 28√5
The side length opposite to the angle 30 =
[tex]\frac{1}{2}\cdot28\sqrt[]{5}=14\sqrt[]{5}[/tex]The side length opposite to the angle 60 =
[tex]\frac{\sqrt[]{3}}{2}\cdot28\sqrt[]{5}=\frac{28}{2}\sqrt[]{3\cdot5}=14\sqrt[]{15}[/tex]Help me please!! I don’t understand
Answers
Answer:
-3
Step-by-step explanation:
To find the answer, you need to use the formula y2-y1/x2-x1.
2-17/2-(-3)
2-17=-15
2-(-3)=5
-15/5=
-3
Hope this helps :D
10. Sydney wants to buy soda and juice for her birthday party. A bottle of soda costs $1.99 each and a jug of juice costs $2.49 each. If Sydney has $30, what equation could be used to find how many soda bottles and how many jugs of juice she can purchase? let x = let y = Equation
Answers
ANSWER
1.99x + 2.49y = 30
EXPLANATION
A bottle of soda costs $1.99 each and a jug of juice costs $2.49.
Sydney has $30.
Let x be the number of bottles of soda she can get.
Let y be the number of jugs of juice that she can buy.
This means that the cost of x bottles of soda is:
1.99 * x = $1.99x
This also means that the cost of y jugs of juice is:
2.49 * y = $2.49y
The total cost must be equal to $30, so this means that the total cost of bottles of soda and jugs of juice she can purchase is:
1.99x + 2.49y = 30
That is the equation that represents it.
I don't understand this at all.
Answers
Answer:
P1V1T2
T1= _______
P2V2
Step-by-step equation:
You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $3500 per month. You have access to an account that pays an APR of 4.8% compounded monthly. This requires a nest egg of $610,823.48.
What monthly deposits are required to achieve the desired monthly yield at retirement? (Round your answer to the nearest cent.)
Answers
The monthly deposit that is required to achieve the desired monthly yield at retirement is $1,056.71.
What is the monthly deposit?An annuity is a series of payment that is made over a period of time. The annuity in this question would last for 25 years. When an investment is compounded monthly, it means that the investment would grow at an exponential rate once in a month.
The formula that would be used to determine the monthly payment is:
Monthly payment = future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = monthly interest rate = 4.8% / 12 = 0.4%n = number of periods = number of compounding x number of years: 12 x 25 = 300$610,823.48 ÷ [{(1.004^300) - 1} / 0.004] = $1,056.71
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What is a valid conclusion that can be reached by reading the graph?A.Joel and Nancy own 62 cards when you add their cards together.B.Joel and Nancy own more cards than Jim when you add their cards together.C.Nancy and Ricardo own more cards than Jim when you add their cards together.D.Tina owns 350 cards.
Answers
Answer:
C. Nancy and Ricardo own more cards than Jim when you add their cards together.
Explanation:
Taking into account the graph, we can conclude the following:
Nancy and Ricardo own more cards than Jim when you add their cards together
This is because, Nancy and Ricardo have bars with heights that are greater than 40, when we add their cards, we will get a bar with a height greater than 80, and 80 is greater than the height of Jim's bar.
Therefore, the answer is
C. Nancy and Ricardo own more cards than Jim when you add their cards together.
E Match the corresponding congruent parts.(G.6)(6 point) DE DF / A Lc ZB EF
Answers
By definition:
Congruent figures in geometry are identical in shape and size.
This means that two figures are congruent with each other even if they are rotated, flipped or trasnlated as long as they have the identical shape and size.
For example, look at the following picture
We notice that the triangle has the same size and shaped, hence they are congruent. Furthermore we can say that the side BC is congruent to the side ZY and so on.
The Sugar Sweet Company is going to transport its sugar to market. It will cost $5500 to rent trucks plus $125 for each ton of sugar transported. The total cost,
C (in dollars), for transporting n tons is given by the following.
C=125n+5500
Answer the following questions.
(a) What is the total cost of transporting 11 tons?
(b) If the total cost is $8125, how many tons is the company transporting?
Answers
C=125*11+5500
C=1375+5500
C=$6875
(B) For this part you follow the same concept as part a just change what and where you are substituting since the question gives you total cost C you plus 8125 in for C and solve for n
C=125n+5500
8125=125n+5500 (subtract 5500 from BOTH sides)
2625=125n (divide BOTH sides by 125 to get n alone)
n= 21 tons
Match the two lines that are parallel and the two lines that are perpendicular. Then, match the equations.
Answers
Step-by-step explanation:
A and C are parallel. equations G and E.
B and D are perpendicular (standing at a right angle = 90° to each other). equations F and H.
parallel means that both lines have the same slope.
the slope is the factor a of x when the equations look like
y = ax + b (slope-intercept form)
or
y - y1 = a(x - x1) (point-slope form)
"a" being the slope, b being the y-intercept (the y- value when x = 0), (x1. y1) being a point on the line.
the slope is specified as ratio (y coordinate difference / x coordinate difference) when going from one point to another.
the perpendicular slope to y/x is the upside down ratio and the sign is flipped.
e.g. the perpendicular slope to 5/4 is -4/5.
equation E is already in point-slope form.
the slope is 2/3, and the point (-9, -2) must be on the line.
only one line goes through the point (-9, -2) : C.
equation H is already in slope-intercept form.
the slope is 3/2, and the y-intercept is 5, meaning the line goes through the point (0, 5).
only one line goes through that point : D
equation F
2x + 3y = -21
3y = -2x -21
y = (-2/3)×x - 7
the slope is -2/3, which is perpendicular to 3/2 (equation H).
the y-intercept is -7, meaning the line goes through the point (0, -7).
only one line goes through that point : B
equation G
-2x + 3y = -6
3y = 2x - 6
y = (2/3)×x - 2
the slope is 2/3 (parallel to equation E).
the y-intercept is -2, meaning the line goes through the point (0, -2).
only one line goes through that point : A
kind of confused with this whole probability concept, i just need help with these here
Answers
Solution
For this case we have 0-9 possible digits (10) and 4 spaces for the code
Part a
The number of ways are using the multiplication principle:
10x9x8x7= 5040
Part b
p= 1/5040
Part c
If digits can be repeated we have this:
10x10x10x10= 10000