Find the angles and sides of the right triangle B = 70 degrees, b= 19ft. Please round to the nearest degree.
Answers
Data:
• B = 70°
,• b = 19ft
,• C = 90°
Procedure:
• Finding the angles
We know that C = 90° as the image shows the symbols. Also, we know that the sum of the interior angles of a triangle are 180°. Then, to get A we have to do the following:
[tex]A+B+C=180[/tex]Isolating for A:
[tex]A=180-B-C[/tex]Replacing the values we know:
[tex]A=180-70-90[/tex][tex]A=20[/tex]• Finding side ,a
Using trigonometric functions, we can get a.
[tex]\tan (A)=\frac{a}{b}[/tex]As we already know the value of A and b, we can isolate for a:
[tex]a=b\cdot\tan (A)[/tex]Replacing the values:
[tex]a=19\cdot\tan (20)\approx6.92[/tex]• Finding side ,c
Finally, using the Pythagorean Theorem, we can calculate c:
[tex]c^2=a^2+b^2[/tex]Isolating for c:
[tex]c=\sqrt[]{a^2+b^2}[/tex]Replacing the values:
[tex]c=\sqrt[]{6.92^2+19^2}[/tex][tex]c\approx20.22[/tex]
Answer:
• A = 20°
• a = 6.92 ft
,• c = 20.22 ft
Related Questions
i need help with this please:-))
Answers
When two lines are perpendicular, their slopes have the following relation:
[tex]m_1=\frac{-1}{m_2}[/tex]If we rewrite this expression, we have:
[tex]m_1\cdot m_2=-1[/tex]The product of each slope is equal to -1.
Therefore the correct option is the fourth one.
how do you tun the area of a rectangle into its side lengths?
Answers
In order to find what factors could represent the length and the width, we need to factor the polynomial that represents the area.
To do so, first let's find the zeros a1 and a2, then we can factor as follows:
[tex]k(a-a_1)(a-a_2)[/tex]Where k is the coefficient of the quadratic term (so k = 12).
Using the quadratic formula, we have:
[tex]\begin{gathered} 12a^2+4a-5=0 \\ a_{}=\frac{-4+\sqrt[]{4^2-4\cdot12\cdot(-5)}}{2\cdot12} \\ a_1=\frac{-4+16}{24}=\frac{1}{2} \\ a_2=\frac{-4-16}{24}=-\frac{5}{6} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 12(a-\frac{1}{2})(a+\frac{5}{6}) \\ =(2a-1)(6a+5) \end{gathered}[/tex]Therefore the factors are 2a-1 and 6a+5.
What is the image point of (0,5)(0,5) after the transformation r_{y=x}\circ R_{180^{\circ}}r y=x ∘R 180 ∘ ?
Answers
The image of the point is (0, -5) after applying the geometric transformation, the answer is (0, -5).
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The point is (0, 5)
As we know, the
The rule for the above transformation:
(x, y) → (-x, -y)
(0, 5) → (0, -5)
Thus, the image of the point is (0, -5) after applying the geometric transformation, the answer is (0, -5).
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Calculate your take-home pay (net pay) for the following situation. Gross Salary: $3,500 per month. You are paid once a month. Federal Income Tax Withholding = 20% of Gross Salary. State Income Tax Withholding = 12% of Gross Salary. Social Security Tax Withholding = 8.25% of Gross Salary. 401k Contribution = 4% of Gross Salary.
What is the amount of Federal Income Tax Withholding each month?
What is the amount of State Income Tax Withholding each month?
What is the amount of Social Security Tax Withholding each month?
What is the amount contributed to the 401k each month?
What is the net pay (take-home pay) each month?
What is the total take-home pay for a full-year?
Answers
Using proportions, the amounts are given as follows:
Federal Income Tax Withholding each month: $700.State Income Tax Withholding each month: $420.Social Security Tax Withholding each month: $288.75.Amount contributed to the 401k each month: $140.The take-home pay for the month is $1,951.25.The take-home pay for the year is $23,415.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.
One example of application is for percentage problems, as the equivalent amount can be found multiplying the equivalent decimal by the total amount.
The amount of Federal Income Tax Withholding each month is given by:
0.2 x 3500 = $700.
The amount of State Income Tax Withholding each month is given by:
0.12 x 3500 = $420.
The amount of Social Security Tax Withholding each month is given by:
0.0825 x 3500 = $288.75.
The amount contributed to the 401k each month is:
0.04 x 3500 = $140.
The take-home pay for the month is the $3,5500 subtracted by all the with holdings, hence:
3500 - (700 + 420 + 288.75 + 140) = $1,951.25.
A year has 12 months, hence the take-home pay for the year is given by:
12 x 1951.25 = $23,415.
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2. Ying sees this flyer. She decides to buy 12 of these boxes for her shoes. What total volume will these boxes occupy in her closet?
Answers
Step 1. Find the volume of just one box.
To find the volume V of one box, we multiply all of the dimensions of the box:
In this case, the volume of one box is:
[tex]V=29.5cm\times18cm\times9.5cm[/tex]The result is:
[tex]V=5,044.5cm^3[/tex]Step 2. We are told that Ying bought 12 boxes, so the total volume that the boxes occupy will be the volume of one box multiplied by 12:
[tex]12\times5,044.5cm^3=\boxed{60,534cm^3}[/tex]Answer:
[tex]\boxed{60,534cm^3}[/tex]What is 7,984 -9,151 =
Answers
Explanation:
Literally anyone can do this
Last year cost 24500 today worth 14300 what is the percentage change
Answers
The most appropriate choice for percentage will be given by- Percentage change in cost = 37.09 %
What is percentage?
A number or ratio which can be expressed as just a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a portion per hundred. Per 100 is what the word percent means. The letter "%" stands for it. As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any subject have been calculated in terms of percentages in academics. Ram, for instance, scored 78% on his final exam. This rate is computed based on Ram's overall grade point average (GPA) across all subjects.
For example 2% means [tex]\frac{2}{100}[/tex].
Here,
Cost last year = 24500
Cost today = 14300
Change in cost = 24500 - 14300
= 10200
Percentage change in cost = [tex]\frac{10200}{24500} \times 100[/tex]
= 37.09 %
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If f(x) = 2x + 1 and g(x) = x 7, find (++ g)(x). h
Answers
Therefore Option B is correct
PLSSSS HELP Which number is not in the correct location?
Answers
We can conclude that the position of the number -7 in the provided Venn diagram is incorrect as -7 is an integer but, not a whole number.
What are whole numbers?Any positive number that does not contain a fractional or decimal component is referred to as a whole number. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers, for instance, as a result. -3, 2.7, or 3 12 are examples of non-whole numbers.Integers:
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers.As we can read the definitions whole numbers do not include negative numbers and integers do include negative numbers, so we can conclude that the number -7 in the given Venn diagram is not in the correct location.
Therefore, we can infer that the position of the number -7 in the provided Venn diagram is incorrect as -7 is an integer but, not a whole number.
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The support arm, AB, is
perpendicular to a line tangent to this curve on a roller coaster at the point of tangency B.
The equation of the tangent line to the curve at B is 3x + 2y = 28.
Find the equation of the support arm, AB.
B(4,8)
Lines perpendicular to tangents to curves, at
the point of tangency, are referred to as “normals.”
Answers
Answer:
[tex]y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]
Step-by-step explanation:
The genera slope-intercept equation of a line is
y = mx + 8 where m is the slope and b the y-interecept
A perpendicular line will have a slope = -1/m ie the negative of reciprocal of the first line such that m x (-1/m ) = -1
The equation of the tangent line is
3x + 2y = 28.
1. Convert to slope-intercept form:
Subtract 3x from both sides3x - 3x + 2y = 28 - 3x
2y = 28 - 3x
y = 14 - 3/2xy = (-3/2)x + 14
So slope = -3/2
Reciprocal of -3/2 = -2/3
Negative of reciprocal = +2/3
Slope of a perpendicular line should be -1/3 and the resultant equation of the line(the support arm) should be:
y = (2/3)x + b
To calculate b for the complete line equation plug in the point B(4, 8) and solve for B
y = 8 when x = 4
=> 8 = (2/3)(4) + b
Switch sides: (does not change any signs)
8/3 + b = 8
Subtract 8/3 on both sides
b = 8 - 8/3
b = 24/3 - 8/3
b = 16/3
So equation of the support arm is
[tex]\boxed{y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]
Members of a softball team raised $1186.50 to go to a tournament. They rented a bus
for $842.50 and budgeted $21.50 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Answers
The equation to determine the number of players the team can bring is $842.50 + $21.50y = $1,186.50
The team can bring 16 players to the tournament.
To go to a tournament, softball team members raised $1186.50 and rented a bus for $842.50, and the cost of meals of each player is $21.50.
Let y represent the number of players.
$842.50 + $21.50 × y = $1,186.50
$842.50 + $21.50 × y = $1,186.50
$842.50 + $21.50y = $1,186.50
Subtracting $842.50 from each side.
$21.50y = $1,186.50 - $842.50
$21.50y = $344
Divide both side of the equation by $21.50.
x = $344 / $21.50
x = 16 players
As a result, the team is allowed to enter 16 players into the competition.
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Find the scale factor from triangle A to triangle B:
Answers
From the figure of triangles, scale factor of A and B, the value of x = 3
According to the question, given that
when two triangle are same, then we easily get missing value x
From the figure, two triangle are similar in it thus,
[tex]\frac{x}{1}[/tex] = [tex]\frac{9}{3}[/tex] {property of triangles which are similar}
x = [tex]\frac{9}{3}[/tex] .
x = 3
Therefore, we get scale factor of triangle A and B, the missing value of missing x = 3.
What is a Scale Factor?Scale factor is the proportion of an original object's scale to a new one that is a representation of it but is a different size (bigger or smaller).
For example, if we have a rectangle of sides 4 cm and 6 cm, we can enlarge it by multiplying each side by a number, say 4. The new figure we get will be similar to the original figure, but all its dimensions will be twice that of the original rectangle.
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PLSSS HELP MEEE
Classify quadrilateral RSTV. Support your answer by showing calculations.
Answers
The given quadrilateral RSTV is a kite.
What are quadrilaterals?The following characteristics apply to quadrilaterals, which are polygons.
It has four sides and four vertices surrounding four angles.A quadrilateral's interior angles add up to 360 degrees.To classify the quadrilateral calculate the length of its sides using the distance formula given as follows:
[tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }[/tex]
In the given quadrilateral RSTV,
RS = [tex]\sqrt{(2 - (-5))^{2} + (6 - 7)^{2} }[/tex] = [tex]\sqrt{50 }[/tex]
RV = [tex]\sqrt{(-4 - (-5))^{2} + (0- 7)^{2} }[/tex] = [tex]\sqrt{50}[/tex]
ST = [tex]\sqrt{(5 - 2)^{2} + (-3- 6)^{2} } = \sqrt{90}[/tex]
VT = [tex]\sqrt{(-3 - 0)^{2} + (5- (-4))^{2} } = \sqrt{90}[/tex]
The two adjacent sides of the quadrilateral are equal i.e. RS = RV and ST = VT.
A kite is a quadrilateral with two pairs of sides that are both the same length and are next to one another.
Therefore, the quadrilateral is a kite.
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What is the correct answer
Answers
1) [tex]m\angle A=76^{\circ}[/tex] (given)
2) [tex]m\angle B=76^{\circ}[/tex] (base angles theorem)
3) [tex]m\angle BCA=28^{\circ}[/tex] (sum of angles in a triangle)
4) [tex]m\angle ECD=28^{\circ}[/tex] (vertical angles)
5) [tex]m\angle DEC=90^{\circ}[/tex] (perpendicular lines)
6) [tex]m\angle D=62^{\circ}[/tex] (sum of angles in a triangle)
Use the drawing tool(s) to form the correct answers on the provided graph. F(x)=(x^4-16)(x^4+3x-18) Find the real zeros of the following function, and plot them on the graph.
Answers
The real zeros of the following function [tex]$\quad f(x)=\left(x^4-16\right)\left(x^2+3 x-18\right)$[/tex] are
2,-2,3,-6, and the graph is attached below
This is further explained below.
What are the Zeros?[tex]$\quad f(x)=\left(x^4-16\right)\left(x^2+3 x-18\right)$[/tex]
as we know the formula a^2-b^2=(a-b)(a+b)
[tex]\begin{aligned}x^4-16 &=\left[\left(x^2\right)^2-(4)^4\right]=\left(x^2-4\right)\left(x^2+4\right) \\&=\left((x)^2-(2)^2\right)\left(x^2+4\right) \\x^4-16 &=(x-2)(x+2)\left(x^2+4\right)\end{aligned}[/tex]
substituting it in equation (1) we get.
[tex]\begin{gathered}f(x)=(x-2)(x+2)\left(x^2+4\right)\left(x^2+3 x-18\right) \\\\\left(x^2+3 x-18\right)=x^2+6 x-3 x-18=x(x+6)-3(x+6) \\\\f(x)=(x-2)(x+2)(x-3)(x+6)\left(x^2+4\right) \\\\x^2+4=(x+2 i)(x-2 i)=\left[(x)^2-(2 i)^2\right] \\\\f(x)=(x-2)(x+2)(x-3)(x+6)(x+2 i)(x-2 i)\end{gathered}[/tex]
Real zuoes =2,-2,3,-6
imaginary zuroes =2 i,-2 i
In conclusion, In the question, we have to answer the real zeroes of the function f(x)
which is 2,-2,3,-6
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A 7ft board is cut into 2 pieces. If one piece is x feet long, express the other length in terms of x
Answers
Answer:
7-x
Step-by-step explanation:
If one piece is x, and the whole is 7, the missing piece would be 7-x
Hope this helps :)
Use front end rounding to round each number. Then add the rounded
numbers to get an estimated answer. Finally, find the exact answer.
35.25
197.39
+ 4.835
Answers
An estimated answer is 237.44 and the exact answer is 237.475.
The first number is 35.25.The second number is 197.39.The third number is 4.835.We need to use front end rounding to round each number and then add the rounded numbers to get an estimated answer.First, look only at the whole numbers and add the digits.35 + 197 + 4 = 236Next, look at the decimals and round them.0.25 is approximately equal to 0.2.0.39 is approximately equal to 0.4.0.835 is approximately equal to 0.84.Add the rounded decimals.0.2 + 0.4 + 0.84 = 1.44Now add the whole number part and the decimal part together.236 + 1.44 = 237.44An estimated answer is 237.44.Now we will calculate exact answer :35.25 + 197.39 + 4.835 = 237.475The exact answer is 237.475.To learn more about rounding off numbers, visit :
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What’s the correct answer answer now for brainlist better he right
Answers
Answer:
they filter the air coming into the body
Determine a, b, c ∈ N*, different two by two, so that: [tex]\frac{1}{a}+\frac{1}{b}+\frac{1}{c}[/tex] is an integer
Answers
Using a system of equations, a possible set of values for a, b and c such that it results in an integer number is given by:
a = 6, b = 3, c = 2.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.
In the context of this problem, the variables are the given ones of:
a, b and c.
An integer number is a number that has no decimal part, hence the easiest way to solve this is making the sum of 1.
Attributing a = 6, we have that:
[tex]\frac{1}{6} + \frac{1}{b} + \frac{1}{c} = 1[/tex]
[tex]\frac{1}{b} + \frac{1}{c} = \frac{5}{6}[/tex]
This is possible with these two fractions:
[tex]\frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6} = \frac{5}{6}[/tex]
Hence the other possible values are given by:
b = 2, c = 3.
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whowever does my online math homework will get 200 points it yr9 maths (grade 8) maths
Answers
Answer:
I hope the deadline hasn't passed!
Your last question got deleted
Help me with question 2, thank you!
Answers
Given the function f(x):
[tex]f(x)=3x^2-5x-4[/tex]We will find the point on the given parabola where the slope of the tangent is horizontal
The horizontal line has a slope = zero
The slope of the line is the first derivative of the function
So, we will find the first derivative and equate it to zero
[tex]\begin{gathered} f^{\prime}(x)=0 \\ 3(2x)-5(1)-(0)=0 \end{gathered}[/tex]solve the equation to find (x):
[tex]\begin{gathered} 6x-5=0 \\ 6x=5 \\ x=\frac{5}{6} \end{gathered}[/tex]substitute with the value of (x) into the given function to find the y-coordinate
[tex]y=3(\frac{5}{6})^2-5(\frac{5}{6})-4=\frac{-73}{12}[/tex]So, the answer will be the point will be as follows:
[tex](x,y)=(\frac{5}{6},\frac{-73}{12})[/tex]See the following figure:
Hello I need help please :)
Answers
Given: The system of equations below...
[tex]\begin{gathered} y=2x-2 \\ -4x-y=26 \end{gathered}[/tex]To Determine: The value of x and y
Using substitution method, Substitute for y in the second equation
[tex]\begin{gathered} -4x-y=26 \\ -4x-(2x-2)=26 \\ -4x-2x+2=26 \\ -6x=26-2 \\ -6x=24 \\ x=\frac{24}{-6} \\ x=-4 \end{gathered}[/tex]Substitute for x in the first equation to solve for y
[tex]\begin{gathered} y=2x-2 \\ y=2(-4)-2 \\ y=-8-2 \\ y=-10 \end{gathered}[/tex]ence,
x = -4; y = -10
G
please help fast how do i what property do i need to solve this
h to the 3rd power g to the -7th power
Answers
Answer: the property needed to find this is negative exponents
Step-by-step explanation: find the reciprocal of g to the -7th power which would be 1 over g to the 7th power
Find the value of p in the inequality.
three fourths times p plus 8 is greater than or equal to 3
p is greater than or equal to negative twenty over three
p is less than or equal to negative twenty over three
p is greater than or equal to negative forty four over three
p is less than or equal to negative forty four over three
Answers
Value of p for given inequality of three fourths times p plus 8 is greater than or equal to 3 is p is greater than or equal to negative twenty over three.
As given in the question,
Given inequality:
Three fourths times p plus 8 is greater than or equal to 3 is written as
(3/4)p + 8 ≥ 3
Simplify inequality to get the value of p
(3p + 32)/4 ≥ 3
⇒ 3p + 32 ≥ 12
⇒ 3p ≥ 12 -32
⇒ 3p ≥ -20
⇒ p ≥ -20 /3
Therefore, value of p for given inequality of three fourths times p plus 8 is greater than or equal to 3 is p is greater than or equal to negative twenty over three.
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What is the missing perfect square in this list?
81, 100, 121, ____, 169
A. 125
B. 160
C. 12
D. 144
Answers
Answer:
d 144
Step-by-step explanation:
Each number is the square starting with 10
10² = 100
11² = 121
12² = __?
13²=169
9x9=81
10x10=100
11x11=121
12x12=144
f(x)=4x+6 and g(x)=1/2*f(x) What is the function rule for function g?
g(x) = _________________ x+ _____________________
Answers
g(x) is a dilation of scale factor 1/2 of f(x), and the rule is:
g(x) = 2x + 3
What is the rule for function g?
Here we have the function f(x) = 4x + 6 and the function g(x) that is defined as:
g(x) = (1/2)*f(x)
So g(x) is a vertical dilation of scale factor k = 1/2 of f(x).
Replacing f(x) in there we get:
g(x) = (1/2)*(4x + 6) = (4/2)*x + 6/2 = 2x + 3
The rule for g is:
g(x) = 2x + 3
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Choose the graph that represents the following set.
the whole numbers greater than 3
O
1 2 3 4 5 6 7 8 9 ...
-1 0 1 2 3 4 5 6 7
1011H
0 1 2 3 4 5 6 7 8
Answers
Answer:
option 3
It has a zero a set of whole no has 0 in it and it start after the no 3 as it says GREATER then 3.
Find the area of the polygon with the given vertices.
X(-1, 2), Y(-1, -3), Z(4, -3)
square units
Answers
Check the picture below.
Write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence
Answers
Answer is;
[tex]a_n=3n[/tex][tex]\begin{gathered} \text{common difference (d) =6-3=3} \\ By\text{ formula, } \\ a_n=a+(n-1)d\text{ , where a=3} \\ a_n=3+(n-1)3 \\ a_n=3+3n-3 \\ a_n=3n \end{gathered}[/tex]Please explain step by step I do not explain this,
Answers
The value of f(1/2) for the given function f(x) = -3(4x² + 12) + 3/4(8x) - 2x is: -37. (None of the options are correct).
How to Evaluate a Function?If given a function, to evaluate the function for a given value of x, input the value of x in the equation and solve to evaluate the function.
Given the function, f(x) = -3(4x² + 12) + 3/4(8x) - 2x, to find the value of f(1/2), substitute x = 1/2 into the equation:
f(1/2) = -3(4(1/2)² + 12) + 3/4(8(1/2)) - 2(1/2)
Evaluate
f(1/2) = -3(4(1/4) + 12) + 3/4(4) - 1
f(1/2) = -3(1 + 12) + 3 - 1
f(1/2) = -3(13) + 2
f(1/2) = -39 + 2
f(1/2) = -37
The value of the function f(1/2) is: -37. (none of the given options are correct).
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