Answers
The sine relation is given by the length of the opposite leg to the angle over the length of the hypotenuse.
So, for the given triangle, we have:
[tex]\begin{gathered} \sin A=\frac{BC}{AC}\\ \\ \sin A=\frac{20}{29} \end{gathered}[/tex]Therefore the value of sin A is 20/29.
Related Questions
Solve. Your answer should be in simplest form. (2 1/6)(1 1/3) HELP!!!!
Answers
The simplified form of the expression (2 1/6 ) × (1 1/3) is 26/9.
What is the simplified form of the given expression?Given the expression in the question;
(2 1/6 ) × (1 1/3)
To simplify, first convert from mixed to improper fraction.
(2 1/6 ) × (1 1/3)
( (2×6 + 1)/6 ) × (1 1/3)
( (12 + 1)/6 ) × (1 1/3)
( 13/6 ) × (1 1/3)
( 13/6 ) × (1×3 + 1/3)
( 13/6 ) × (3 + 1/3)
( 13/6 ) × (4/3)
Now, cancel the common factor 2.
13/6 × 4/3
13/3 × 2/3
( 13 × 2 ) / ( 3 × 3 )
( 26 ) / ( 9 )
26/9
Therefore, the simplified form is 26/9.
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what is the domain and range of {(1,0), (2,0), (3,0) (4,0), (5,0)}
Answers
We have the following:
The domain is the input values or the values of x and the range is the output values or the values of y
Therefore:
[tex]\begin{gathered} D=\mleft\lbrace{}1,2,3,4,5\mright\rbrace \\ R=\mleft\lbrace0\mright\rbrace \end{gathered}[/tex]Sally deposits $2,500 at 8% interest for 3 years . How much can she withdraw at the end of that period
Answers
ANSWER
$3100
EXPLANATION
Sally deposits $2500 at 8% interest for 3 years.
We want to find the amount she can withdraw at the end of the period.
To know this, we have to first find the interest.
Simple Interest is given as:
[tex]\begin{gathered} SI\text{ = }\frac{P\cdot\text{ R }\cdot\text{ T}}{100} \\ \text{where P = principal = \$2500} \\ R\text{ = rate = 8\%} \\ T\text{ = 3 years} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} SI\text{ = }\frac{2500\cdot\text{ 8 }\cdot\text{ 3}}{100} \\ SI\text{ = }\frac{60000}{100} \\ SI\text{ = \$600} \end{gathered}[/tex]Therefore, after 3 years the interest will be $600.
The amount she can withdraw after this period is therefore the sum of the principal and the interest:
$2500 + $600 = $3100
She can withdraw $3100 at the end of the period.
find the values of x y and z.The answers are in degrees.
Answers
Answer
x = 35°
y = 145°
z = 25°
Explanation
We are told to solve for x, y and z.
Considering the first triangle with angles 55°, x° and the right angle (90°).
The sum of angles in a triangle is 180°.
So,
x° + 55° + 90° = 180° (Sum of angles in a triangle is 180°)
x° + 145° = 180°
x = 180° - 145° = 35°
Then, we can solve for y. Angles x and y are on the same straight line, and the sum of angles on a straight line is 180°
x° + y° = 180°
35° + y° = 180°
y° = 180° - 35°
y° = 145°
We can then solve for z°. The big triangle has angles (55° + 10°), z° and the right angle (90°).
The sum of angles in a triangle is 180°.
So,
55° + 10° + z° + 90° = 180°
z° + 155° = 180°
z = 180° - 155°
z° = 25°
Hope this Helps!!!
Watch the video and then solve the problem given below.Click here to watch the video.Solve the inequality both algebraically and graphically. Give the solution in interval notation and draw it on a number line graph.x−54
Answers
Given the inequality below:
[tex]\frac{x-5}{4}<\frac{9}{5}[/tex]Solving algebraically as shown below:
[tex]\begin{gathered} \frac{x-5}{4}<\frac{9}{5} \\ \text{Lcm of the denominator(4 and 5) is 20} \\ \text{mltiply through by the Lcm(20)} \\ 20\times\frac{(x-5)}{4}<20\times\frac{9}{5} \end{gathered}[/tex][tex]\begin{gathered} 5(x-5)<4\times9 \\ 5x-25<36 \\ 5x<36+25 \\ 5x<61 \\ x<\frac{61}{5} \\ x<12.2 \end{gathered}[/tex]Solving graphically as shown below the plotting of x < 12.2
The number line graph is the number line showing x < 61/5, as shown below:
The interval notation of the solution is (- ∞, 61/5) or (- ∞, 12.2)
Create a polynomial of degree 6 that has no real roots. Explain why it has no real roots.
Answers
Answer:
Explanation:
We're asked to create a polynomial of degree 6 that has no real roots.
Let's consider the below polynomial;
[tex]x^6+1=0[/tex]To determine its roots, we'll follow the below steps;
Step 1: Subtract 1 from both sides of the equation;
[tex]undefined[/tex]Consider these functions:
ƒ(x) = 1/3 x² + 4
g(x)=9x - 12
What is the value of g(f(x))?
Answers
The value of the composite function g(f(x)) is 1 / 3 (81x² - 216x + 144) + 4
How to solve composite function?A composite function is a function that depends on another function. In a composite function, the output of one function becomes the input.
Therefore, let's solve the function as follows;
f(x) = 1 / 3 x² + 4
g(x) = 9x - 12
The value of g(f(x)) can be found as follows:
To find g(f(x)) we have to substitute the f(x) in g(x).
Therefore,
g(f(x)) = 1 / 3 (9x - 12)² + 4
(9x - 12)(9x - 12) = 81x² - 108x - 108x + 144
(9x - 12)(9x - 12) = 81x² - 216x + 144
Therefore,
g(f(x)) = 1 / 3 (81x² - 216x + 144) + 4
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Write a quadratic equation in standard form with the given roots. a. Write a quadratic equation with a double root of -5.
Answers
a quadratic function has any root when replacing that number the equation is equal to zero
so
[tex](x+5)(x+5)[/tex]now solve the multiplication
[tex]\begin{gathered} (x\times x)+(x\times5)+(5\times x)+(5\times5) \\ x^2+5x+5x+25 \\ x^2+10x+25 \end{gathered}[/tex]Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of this function:h(x) = (x − 1)^2− 9.
Answers
The function is
[tex]h(x)=(x-1)^2-9[/tex]1) x-intercept(s)
The x-intercepts refer to the points on which the function intercepts with the x-axis, in other words, when y=h(x)=0
So, given that condition, we get
[tex]\begin{gathered} h(x)=0 \\ \Rightarrow(x-1)^2-9=0 \\ \Rightarrow x^2-2x+1^{}-9=0 \\ \Rightarrow x^2-2x-8=0 \\ \Rightarrow(x-4)(x+2)=0 \end{gathered}[/tex]Therefore, there are two x-intercepts, and those are the points
[tex](4,0),(-2,0)[/tex]2) y-intercepts
The y-intercepts happen when x=0. So,
[tex]\begin{gathered} x=0 \\ \Rightarrow h(0)=(0-1)^2-9=1-9=-8 \end{gathered}[/tex]So, there is only one y-intercept and it's on the point (0,-8)
3) Vertex
The general equation of a parabola is
[tex]y=f(x)=a^{}x^2+bx+c[/tex]There is another way to express the same function, which is called the 'vertex form':
[tex]\begin{gathered} y=f(x)=a(x-h)^2+k \\ \Rightarrow y=ax^2-2ahx+ah^2+k \end{gathered}[/tex]What is particularly useful of this vertex form is that the vertex is the point (h,k)
So, transforming h(x) into vertex form:
[tex]\begin{gathered} h(x)=(x-1)^2-9=a(x-h)^2+k \\ \Rightarrow\begin{cases}a=1 \\ h=1 \\ k=-9\end{cases} \end{gathered}[/tex]Therefore, the vertex is the point (h,k)=(1,-9)
4) Axis of symmetry
In general, the equation of the axis of symmetry is given by
[tex]x=-\frac{b}{2a};y=f(x)=ax^2+bx+c[/tex]Therefore, in our particular problem,
[tex]\begin{gathered} h(x)=x^2-2x-8=ax^2+bx+c \\ \Rightarrow\begin{cases}a=1 \\ b=-2 \\ c=-8\end{cases} \\ \end{gathered}[/tex]Thus, the equation of the line that is the axis of symmetry is
[tex]x=-\frac{b}{2a}=-\frac{(-2)}{2\cdot1}=-\frac{(-2)}{2}=1[/tex]Then, the axis of symmetry is the line x=1.
Summing up the information in the four previous steps, we get
Line / contains the points (-4, -1) and (1, 1) asshown below.432-10x-212-1P-2--3-Line m will be drawn perpendicular to line I andcontaining point P. Identify the coordinates ofanother point on line m.(-1, 4)O (1,3)(-2,-4)(5,3)
Answers
Let's begin by listing out the information given to us:
Line m is perpendicular to line P
Line P: (x, y) = (-4, -1), (1, 1)
We will proceed to calculate for the slope of the line P (as shown below):
Slope (m) = Δy/Δx
Slope (m) = (1 - - 1)/(1 - - 4) = 2/5
Slope (m) = 2/5
The slope of a parallel line is the negative reciprocal of the slope of the line.
Line m: slope (m) = -1/(2/5) = -5/2
Line m: slope (m) = -5/2
We calculate for the equation of the line using the point-slope equation. We have
y - y1 = m(x - x1) ⇒
(x1, y1) = (1, 1)
y - 1 = 2/5 (x - 1) ⇒ y - 1 = 2/5x - 2/5
y = 2/5x - 2/5 + 1
y = 2/5x + 3/5
We will proceed to put the value of the new slope into the equation. We have:
y = -5/2x + b ; (x, y) = (1, 1) ⇒ 1 = -5/2(1) + b
⇒ b = 5/2
Substitute the value of b into the point-slope equation, and we obtain the equation of line m. We have:
y = -5/2x + 5/2
The proof below may or may not be correct. If the proof is incorrect, determine the first step number that is not justified and the reason it is not justified.
Answers
The first step number that is not justified and the reason it is not justified:
From the attached image
[tex]<\text{ECF}\congStep 1: is said to be correct cause all the range are equivalent and parallel
Step 2: is said to be correct AECF is a parrelologram because it is a quadilateral with two opposite equal sides
Step 3: is correct
[tex]\begin{gathered} \Delta BEC\cong\Delta\text{ECF}\ldots\text{..} \\ \text{parallel lines cut by a transverse form congruent alternate interior angle.} \end{gathered}[/tex]Step 4: is correct
[tex]<\text{BEC}\congStep 5: is correct [tex]<\text{BEC}\congStep 6 : is not correct , because corresponding parts of the congruent triangle are not congruent.
Step 7: is correct , because its a rhombus.
How do I know which score is the highest frequency? how do I figure the scores had a frequency of 2?
Answers
To determine the score which presents the highest frequency, we need to check the last column, the frequency one, and find the highest value among them. The score which is in the same row that this value will be the score with the highest frequency.
In the present problem, there are values of frequency equal to 1, 2, 3, and 4. The one with frequency 4 is the one with the highest frequency. (8th row). And the Score related to it is Score 8.Once we check the frequency column once again, we see that the 2nd, the 4th, and the 7th rows have a frequency equal to 2.
Checking the Scores of the related rows, we are able to say that the scores with frequency 2 are: 2, 4, and 7.If we have a system of two linear equations in two variables that has no solution, what would we see on the graph?
Answers
Answer:
The graph will have two lines which will never intersect
How do we determine the strength of a correlation?
OA. The more closely two variables follow the general trend, the stronger the correlation (which may be positive or negative).
GB. Negative correlation is stronger than no correlation. Positive correlation is stronger than negative correlation.
OC. The more closely two variables follow the general trend, the weaker the correlation (which may be positive or negative).
OD. No correlation is stronger than negative correlation. Positive correlation is stronger than no correlation
Answers
We can determine the strength of a correlation by A. The more closely two variables follow the general trend, the stronger the correlation (which may be positive or negative).
What is correlation?Correlation is a statistical term that reflects how closely two or more variables are related to one another. Correlation is measured on a scale of -1 to +1, with 0 indicating a negative correlation and > 0 indicating a positive correlation. A value of 0 implies that there is no association.
A positive correlation is a two-variable association in which both variables move in lockstep. A positive correlation exists when one variable declines while the other increases, or when one variable increases while the other falls. The number one represents a perfect positive association.
If there is an increase or decrease in one variable results in increase or decrease in the other then there is correlation. If the value of correlation is close to either extremities (+1 or +1) then there is strong correlation.
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VIP at (-2,7) dropped her pass and moved to the right on a slope of -9. Where can you catch up to her to return her VIP pass? I know the answer is (-1 ,-2) my question is how do you solve to get the answer?
Answers
we are told that VIP is located at (-2,7) and then she drops her pass. Then she moves on a slope of -9. To determine where you can catch up, we simply analyze what would be the next position by incrementing x by 1.
In this case, we are told that the slope is -9.
Recall that given points (a,b) and (c,d) the slope of the line that joins this points is given by
[tex]m=\frac{d-b}{c-a}=\frac{b-d}{a-c}[/tex]Lets call the next point (-1,y) . So using this, we have
[tex]\text{ -9=}\frac{y\text{ - 7}}{\text{ -1 -(-2)}}=\frac{y\text{ -7}}{2\text{ -1}}=y\text{ -7}[/tex]So, by adding 7 on both sides, we get
[tex]y\text{ = -9+7 = -2}[/tex]So, the next position, following a slope of -9 and starting at (-2,7) is (-1,-2)
A family eats at a restaurant. The bill is $42. The family leaves a tip and spends $49.77. How much was the tip as a percentage of the bill?
Answers
Percentage of the bill = 0.185*100=18.5%
Write a recursive formula for an and the nth term of the sequence 4, 10, 16, 22, ...
Answers
Here we have an arithmetic sequence with a common difference of 6, so the recursive formula is:
Tₙ = Tₙ₋₁ + 6
Where T₁ = 4.
How to find the recursive formula?Here we have the following sequence:
4, 10, 16, 22, ...
This seems to be an arithmetic sequence, to check this, we need to take the difference between consecutive terms and see if this is constant.
10 - 4 = 6
16 - 10 = 6
22 - 16 = 6
So yes, this is an arithmetic sequence and the common difference is 6, this means that each term is 6 more than the previous one, so the recursive formula is:
Tₙ = Tₙ₋₁ + 6
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Clarence is saving money to buy a skateboard that costs $97.50. He has $15.05 already saved and plans to save $5.50 each week from his allowance. He also earns $15.60 every two weeks for walking dogs. Suppose Clarence wants to spend some of the money from walking dogs on other things. To the nearest dollar, how much would he need to save from walking dogs each week in order to buy the skateboard 4 weeks earlier than if he just saves his allowance?
Please explain. Thanks!
Answers
Answer:88
Step-by-step explanation:
Select the correct answer from the drop-down menu.Find the polynomial,{4'" is the solution set of
Answers
Let P(x) be the polynomial such that the given set is its solution set.
Now notice that:
[tex]\begin{gathered} x=-\frac{1}{3}\Rightarrow x+\frac{1}{3}=0\Rightarrow3x+1=0, \\ x=4\Rightarrow x-4=0. \end{gathered}[/tex]Therefore (x-4) and (3x+1) divide to P(x), then:
[tex]\begin{gathered} Exists\text{ k such that:} \\ P(x)=k(x-4)(3x+1). \end{gathered}[/tex]Simplifying the above result we get:
[tex]P(x)=k(3x^2-11x-4).[/tex]Setting k=1 we get that:
[tex]P(x)=3x^2-11x-4.[/tex]Answer: Second option.
Is 7.787887888... a rational number?Highlight the correct answer below.a) Yes; it has a pattern which is repeatingb) Yes; it has a pattern which isterminatingc) No; it has a pattern which isterminatingd) No; it has a pattern which is repeating
Answers
A)
If This number 7.787887888... could be written as a ratio
[tex]\frac{a}{b}[/tex]Then it is called rational.
Since it has 7.78788788788... is an infinite number, with a repeating pattern notice it in bold. Then the only possible answer is:
Yes, it as a rational number, with a repeating pattern.
A.
Which equation has the same solution as x2 + 8x – 17 = -8? Submit Answer (3-4)2 = -7 O (2+4)2 = 25 O (x – 4)2 = 25 (x - 1)² = -7 problem 3 out of max 6
Answers
Given
[tex]x^2+8x-17=-8[/tex]
Procedure
[tex]\begin{gathered} x^2+8x+16-16-17=-8 \\ (x+4)^2=16+17-8 \\ (x+4)^2=25 \end{gathered}[/tex]
The answer would be (x+4)^2 = 25
If he paints 1/2 of the wall blue, hoy many square feet will be blue?
Answers
To determine how much of the wall is blue we first need to find its area. The wall is a rectangle, then its area is the product of its height and length:
[tex]\begin{gathered} A=(8\frac{2}{5})(16\frac{2}{3}) \\ A=(\frac{42}{5})(\frac{50}{3}) \\ A=(14)(10) \\ A=140 \end{gathered}[/tex]Hence, the area of the wall is 140 square ft. To determine how much of the wall is already painted we multiply this by 1/2, then:
[tex](140)(\frac{1}{2})=70[/tex]Therefore, 70 square ft are blue.
Select the statement that accurately describes the following pair oftriangles.
Answers
In any pair of similar triangles, (side side side )
Each correspondent side has the same ratio so let's examine
ΔCDE and ΔFGH
Susan has a job selling cars, and earns 1.25% commission on the first $100,000 in sales,The commission increases to 4.95% on the next $200,000. Last month her total sales were$387,000. How much was her commission if she received 7.25% for any sales over $300,000
Answers
Solution:
Susan earns a commission based on car sales made.
Given:
Total sales made for the month = $387,000
Her commission is calculated based on levels and commision rate for each level.
On the first $100,000, she earns 1.25% commission.
Total sales at this level is $100,000
[tex]\begin{gathered} \text{Commision made on the first \$100,000 is;} \\ \frac{1.25}{100}\times100000=\text{ \$1,250} \\ =\text{ \$1,250} \end{gathered}[/tex]On the next $200,000, she earns 4.95% commission.
Total sales at this level is $300,000
[tex]\begin{gathered} \text{Commision made on the next \$200,000 is;} \\ \frac{4.95}{100}\times200000=\text{ \$9,900} \\ =\text{ \$9,900} \end{gathered}[/tex]On the next $87,000, total sales at this level is $387,000. She earns 7.25% commission for sales above $300,000.
[tex]\begin{gathered} \text{Commision made on the next \$87,000 is;} \\ \frac{7.25}{100}\times87000=\text{ \$6,}307.50 \\ =\text{ \$6,}307.50 \end{gathered}[/tex]Therefore, Susan's total commission received for the month is;
[tex]\begin{gathered} \text{ \$1250 + \$9900 + \$6307.50} \\ =\text{ \$17,457.50} \end{gathered}[/tex]Hence, her commission received in total for the sales made is $17,457.50
First find the circumference. Do you need to divided by two? Find X. Then show all work to calculate the composite perimeter.
Answers
We are given the radius of the circle =5
then the circumference is given by
[tex]C=2\pi *r[/tex][tex]C=2\pi *5[/tex][tex]C=10\pi[/tex]then the cicumference of the semicircle is
[tex]\frac{C}{2}=\frac{10\pi}{2}=5\pi[/tex]Now let's find X
given the radius=5
the diameter = 2r = 5*2 = 10 in
then X is given by
[tex]X=4+10+4.5[/tex][tex]X=18.5[/tex]now the lateral side of the rectangle is given by
12-5= 7 in
then
the composite perimeter is
[tex]P=\frac{C}{2}+4.5+7+X+7+4[/tex][tex]P=5\pi+4.5+7+18.5+7+4[/tex][tex]P=5\pi+41[/tex][tex]P=56.70\text{ in}[/tex]then the composite perimeter is 56.7 in
How do I tell if a parabola has a minimum or a maximum?
Answers
We can write the equation of a parabola in two different ways:
The standard form:
[tex]\begin{gathered} y=ax^2+bx+c \\ a\ne0 \end{gathered}[/tex]And the vertex form:
[tex]y=a(x-h)^2+k[/tex]If the parabola has a minimum or a maximum depends on the leading coefficient (the coefficient of x²) or in both cases the coefficient a.
Let's see the cases:
[tex]a>0_{\text{ }}(a_{\text{ }}is_{\text{ }}positive)[/tex]If a is positive, the parabola opens upwards, so the parabola has a minimum.
[tex]a<0_{\text{ }}(a_{\text{ }}is_{\text{ }}negative)[/tex]If a is negative, the parabola opens downwards, so the parabola has a maximum
I'll send a pic of it
Answers
Solution:
Since the slope of the given function represents the rate at which the temperature changes, the answer is the slope of the equation, that is, the correct solution would be:
[tex]0.7[/tex]
NEED HELP ASAP
What is the value of X? Justify each step
Answers
The value of x = 3 ,where ,
AC = 32 , AB = 2x , BC = 6x + 8 .
Solution:Here given,
AB = 2x
BC = 6x + 8
AC = 32
AC = (AB + BC) (Rule of addition).
So ,
2x + 6x + 8 = 32 (by applying substitution rule) .
In the equation AB + BC = AC, substitute for AB, BC, and AC.
Simplifying,
8x + 8 = 32
2x + 6x + 8 = 32 (when simplified by incorporating similar terms).
8x = 24
8x = 32 - 8
8x = 24
On dividing both sides by 8
8x / 8 = 24/8
x = 3
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Write an addition equation and a subtraction equation
to represent the problem using? for the unknown. Then solve.
There are 30 actors in a school play. There are 10 actors from second grade. The rest are from third grade. How many actors are from third grade?
a. Equations:
b. Solve:
Answers
The Equation is 10 + x= 30 and 20 actors are from third grade.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
There are 30 actors in a school play.
There are 10 actors from second grade.
The rest are from third grade.
let the actors in third grade is x.
Equation is:
Actors from second grade + Actors from third grade = Total actors
10 + x= 30
Now, solving
Subtract 10 from both side
10 +x - 10 = 30 - 10
x = 20
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(b) The area of a rectangular window is 6205 cm .If the width of the window is 73 cm, what is its length?Length of the window: 0cm
Answers
We have that the area is 6205 cm^2 and the widht is 73 cm.
since it is a rectangle, we must use
[tex]A_{rect}=widht\cdot length[/tex]Now, we only replace values and find the value of the length
[tex]\begin{gathered} 6205cm^2=73\operatorname{cm}\cdot length \\ \text{length }=\frac{6205\operatorname{cm}}{73\operatorname{cm}} \\ \text{length }=85cm \end{gathered}[/tex]The length of the window is 85 cm.