Consider the triangle shown below where m∠C=50∘, b=11 cm, and a=23 cm.Use the Law of Cosines to determine the value of x (the length of AB in cm).x=
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The Law of Cosines is:
[tex]c^2=a^2+b^2-2ab\cdot\cos C[/tex]Where "a", "b" and "c" are sides of the triangle and "C" is the angle opposite side "c".
In this case you know that:
[tex]\begin{gathered} m\angle C=50\degree \\ b=11\operatorname{cm} \\ a=23\operatorname{cm} \\ c=x \end{gathered}[/tex]Then, you can substitute values as following:
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cdot\cos C \\ x^2=(23\operatorname{cm})^2+(11\operatorname{cm})^2-2(23\operatorname{cm})(11\operatorname{cm})\cdot\cos (50\degree) \end{gathered}[/tex]Finally, evaluating, you get that the answer is:
[tex]\begin{gathered} \\ x\approx18.02\operatorname{cm} \end{gathered}[/tex]Related Questions
Attached is my question, thank you. And x^2=squared i just can’t find the button to do it.
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From the question we are given
[tex]\text{Profit }=Total\text{ Revenue }-total\text{ cost}[/tex]Annual total cost in $ is given by
[tex]C(x)=3600+100x+2x^2_{}[/tex]And an Annual total revenue in $ is given as
[tex]R(x)=500x-2x^2[/tex]Where x is the number of pairs of boots sold
We are to find the profit function
Using the detains given we have
Profit function P(x) is
[tex]P(x)=R(x)-C(x)[/tex]Therefore,
[tex]\begin{gathered} P(x)=500x-2x^2-\lbrack3600+100x+2x^2\rbrack \\ P(x)=500x-2x^2-3600-100x-2x^2 \\ P(x)=-4x^2+400x-3600 \end{gathered}[/tex]Therefore, the profit function is
[tex]P(x)=-4x^2+400x-3600[/tex]Next we are to find determine the number of pair of boots that will maximize annual profit
Plotting the graph of the Profit function we have
Hence, at maximum we have the points (50, 6400)
Therefore, x = 50
This implies that the number of boots that will maximize the annual profit is 500
How does graphing the line help us represent the value of k (constant of proportionality)?
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Answer:
The graph of the line shows that the value of k is the y-coordinate of the point where the x-coordinate is equal to 1.
k = 2.5
1 seagull eats 2.5 pounds of garbage.
Explanation:
First, we need to draw the point (4, 10) on the graph because 4 seagulls eat 10 pounds of garbage. Then, we need to draw a line that passes through this point, and through (0, 0). Finally, we need to identify the number of pounds of garbage when the number of seagulls is 1 or identify the point (1, k). So, we get:
Therefore, the value of k = 2.5 is the constant of proportionality and tell us the number of pounds of garbage that each seagull eat.
So, the graph of the line shows that the value of k is the y-coordinate of the point where the x-coordinate is equal to 1. Also, k represents the slope of the line.
Question 5 of 10 Which function is increasing? O A 19-(0) OB. Rx) = 5* O C. f( 10w -() OD. (X) = (0.5)
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Increasin function:
f(x) = a^x
Where a must be greater than 1:
A. 1/15 = 0.06 NO
B. 5 YES
C. 1/5 NO
D. 0.5 NO
Correct option B.5
5>1
27, 9, 3, 1, 1/3,1/9....What is the value of the 10th term in the sequence?
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1. Identify if the sequence has a common difference or a common ratio.
Common difference: subtract each term from the next term:
[tex]\begin{gathered} 9-27=-18 \\ 3-9=-6 \\ 1-3=-2 \end{gathered}[/tex]There is not a common difference.
Common ratio: Divide each term into the previous term:
[tex]\begin{gathered} \frac{9}{27}=\frac{1}{3} \\ \\ \frac{3}{9}=\frac{1}{3} \\ \\ \frac{1}{3}=\frac{1}{3} \\ \\ \frac{\frac{1}{3}}{1}=\frac{1}{3} \\ \\ \frac{\frac{1}{9}}{\frac{1}{3}}=\frac{3}{9}=\frac{1}{3} \end{gathered}[/tex]The common ratio is 1/3; it is a geometric sequence.
2. Use the next fromula to write the formula to find the nth term in the sequence:
[tex]\begin{gathered} a_n=a_1*r^{n-1} \\ \\ r:common\text{ }ratio \end{gathered}[/tex][tex]a_n=27*(\frac{1}{3})^{n-1}[/tex]Evaluare the formula above for n=10 to find the 10th term:
[tex]\begin{gathered} a_{10}=27*(\frac{1}{3})^{10-1} \\ \\ a_{10}=27*(\frac{1}{3})^9 \\ \\ a_{10}=27*\frac{1}{3^9} \\ \\ a_{10}=27*\frac{1}{19683} \\ \\ a_{10}=\frac{27}{19683} \\ \\ a_{10}=\frac{1}{729} \end{gathered}[/tex]Then, the 10th term is 1/729Evaluate log3/8 91 using the change of base formula. Round your answer to one decimal place.
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We have to apply the change of base formula:
[tex]\log _b(a)=\frac{\log _x(a)}{\log _x(b)}[/tex]We can apply this to our expression as:
[tex]\log _{\frac{3}{8}}(91)=\frac{\ln(91)}{\ln(\frac{3}{8})}=\frac{\ln (91)}{\ln (3)-\ln (8)}\approx\frac{4.511}{1.099-2.079}=\frac{4.511}{-0.980}\approx-4.6[/tex]Answer: -4.6
Using the explicit formula, find the 3rd term f(n)=5+4(n-1)
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Answer:
13
Explanation:
The explicit formula of a sequence is given below:
[tex]f\mleft(n\mright)=5+4\mleft(n-1\mright)[/tex]When n=3
[tex]\begin{gathered} f\mleft(3\mright)=5+4\mleft(3-1\mright) \\ =5+4(2) \\ =5+8 \\ =13 \end{gathered}[/tex]The 3rd term of the sequence is 13.
Solving a proof I know how to start it just confused how to put it all together
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Given that ABCD is a parallelogram, prove that
[tex]\begin{gathered} \bar{AB}\cong\bar{CD} \\ \bar{BC}=\bar{DA} \end{gathered}[/tex]step 1: Sketch the parallelogram
step 2: The diagonal AC, divides the parallelogram into two triangles
[tex]\begin{gathered} \Delta ADC\text{ and }\Delta ABC \\ Note\text{ that,} \\ \angle DAC=\angle ACB\text{ ( the angles are alternate)} \\ \angle DCA=\angle BAC\text{ (the angles are alternate)} \\ side\text{ AC = AC (common sides for both triangles)} \end{gathered}[/tex]step 3: By the ASA (Angle-Side-Angle) congruency theorem,
[tex]\begin{gathered} \Delta ADC\cong\Delta ABC \\ (The\text{ two triangles are congruent)} \end{gathered}[/tex]Hence, by CPCT (corresponding parts of congruent triangles)
[tex]\begin{gathered} \bar{AB}\cong\bar{CD}\text{ } \\ \bar{BC}\cong\bar{DA} \end{gathered}[/tex]can you find the domain of a piecewise functuon
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a piecewise function
x+ 4 , if -4 ≤x <3
. 3 ≤ x < 6
Then ,answer is [ -4,6)
Select all the lines that are perpendicular to 3x – y = 10. A. y = 3x + 5 B. y = –13x + 17 C. x + 3y = 27 D. y – 2 = 13(3x + 36)
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The lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).
Line equation:
3x - y = 10
y = 3x - 10
here slope m = 3.
perpendicular line slope = -1/m = -1/3
so the perpendicular line must have slope m = -1/3
A.
y = 3x + 5
here slope m = 3
This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
B.
y = -13x + 17
here slope m = -13
This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
C.
x + 3y = 27
3y = -x + 27
y = -1/3(x) + 27/3
y = -1/3(x) + 9
here slope m = -1/3
This line is perpendicular to the 3x - y = 10 because here slope is equal to -1/3.
D.
y - 2 = 13(3x+36)
y = 39x + 468 - 2
y = 39x + 466.
here slope m = 39.
So this line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
Therefore the lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).
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Which of the follwoing shows the area of circle with a diameter of 8 km? a. 16 km2 50.27km2 X b. 4tkm? ~ 12.57km? c.21km? ~ 6.28km? d. Akm? ~ 3.14km2
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The formula of the area of a circle is
[tex]A=\pi r^2[/tex]where r is the radius
in this case, we have the length of the diameter, the diameter is twice the radius
d= diameter
d=2r
therefore
r=d/2
r=8/2
r=4
we substitute the value of the radius in the formula
[tex]A=\pi r^2=\pi(4)^2=16\pi=50.27\operatorname{km}^2[/tex]the area of a circle with a diameter of 8km is 16pi km^2 or 50.27km^2
William bought 3 pizzas for himself and 6 friends. Each pizza has m slices. Select all of the following expressions that represent the number of slices of pizza per person. Al (m + m + m) 7 m7 3m 7
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12
From the information given,
Wiliam bought 3 pizzas and each had m slices. This means that the total number of slices in the 3 pizzas is 3 * m = 3m
He bought the the pizzas for himslef and 6 friends. This means that the total number of people that shared 3m slices of pizzas is 1 + 6 = 7
Thus, the expression that represent the number of slices of pizza per person are
c) 3m/7
"You are solving a system of equations of two linear equations in two variables, and you discover that there are no solutions to the system"
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"You are solving a system of equations of two linear equations in two variables, and you discover that there are no solutions to the system"
So, it will mean the lines are parallel
so, the graph which describe the system is pink
The answer is option D
A spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds the amplitude has decreased to 13 cm. The spring oscillates 14 times each second. Find a function that models the distance, D the end of the spring is below equilibrium in terms of seconds, t, since the spring was released.
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The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
What is equilibrium?A state of balance between opposing forces or actions that is either static (as in a body acted on by forces whose resultant is zero) or dynamic (as in a reversible chemical reaction when the rates of reaction in both directions are equal).
Given that, a spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds, the amplitude has decreased to 13 cm. The spring oscillates 14 times each second.
Amplitude begins at 17 cm, [tex]A_{0}[/tex] = 17 cm
The amplitude decreases by 13/3 = 4.33 per second = 0.043%
The amplitude function can be then modelled as =
A(t) = [tex]A_{0}[/tex][tex](1-0.043)^{t}[/tex]
A(t) = [tex]A_{0}[/tex][tex]0.957^{t}[/tex]
The spring oscillates 14 times each second, therefore,
T = 1/14
2π/B = 1/14
B = 28π
The graphical equation is;
D(t) = [tex]A_{cos}[/tex](Bt-C)+D
Horizontal shift = 0
Vertical shift = 0
Hence, The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
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Give the equation of the transformed quadratic toolkit function shown below.()=−(+1)2+2()=−(−1)2+2()=−(+1)2+2()=(−1)2−2
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The Solution:
Given:
Required:
Determine the function of the given graph.
The required equation is:
[tex]y=-\left(x-1\right)^{2}+2[/tex]Answer:
[option 2]
Find f[2) if f(x) = (x+ 1)^2 O9O6 O5
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You have the following function:
f(x) = (x + 1)²
In order to determine the value of f(2) you replace the value x = 2 in the given function and make the operations, just as follow:
f(2) = (2 + 1)² simplify inside parenthesis
f(2) = (3)² 3² is the same as 3x3=9
f(2) = 9
Hence, the value of the function when x = 2 is f(2) = 9
Hello everybody! Can anyone help me with this? I just need to know if it's a Direct variation, a inverse variation, or neither? (Look at the photo) Thanks!
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Remember that
A relationship between two variables, x, and y, represent a proportional variation (direct variation) if it can be expressed in the form y=Kx
An equation of the line that passes through the origin
A relationship between two variables, x, and y, represents an inverse variation if it can be expressed in the form y=1/x
There is a vertical asymptote at x=0
therefore
Looking at the graph
we have an inverse variationanswer is IWhat angle will make a rotational symmetry?A. 8B. 50C. 45D. 60
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To find the angle, we will simply divide 360 by the number of sides
Number of sides = 8
That is;
Angle = 360 / 8 = 45 degree
write each fraction in simplest form 3/12
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3/12 is 1/4 in its simplest form
Ming prepared three chemical solutions with temperatures -5, -4, and -3. what is the correct compares of the three temputures?
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So we will like to compare the three numbers -5, -4 and -3. We will like to compare the three temperatures. To know wich numbers is less than the other we can draw the real line
The more to the left the number are the lesser it is therefore
[tex]-5<-4<-3[/tex]The cost to manufactute a hair clip is $.50. With a markip of 200 percent,what is the selling price of this hair clip?
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The selling price of this hair clip will be $ 1.50.
Cost price of the clip is = $ 0.50
Markup price = 200 percent
Mark up price = 200 % of 0.5
Mark up price = 200 / 100 × 0.50
Mark up price = 2 × 0.50
Mark up price = $ 1
Selling price of the product will be:
SP = $ 0.50 + $ 1
SP = $ 1.50
Therefore, we get that, the selling price of this hair clip will be $ 1.50.
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Your question was incomplete. Please refer the content below:
The cost to manufacture a hair clip is $0.50. With a markup of 200 percent, what is the selling price of this hair clip?
The table below shows the probability distribution of a random variable Z. Z P(Z) -11 0.06 -10 0.36 -9 0.43 -8 0.03 -7 0.02 -6 0.1 What is the mean of the probability distribution? Write your answer as a decimal. Submit
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The mean (μ) of a discrete random variable (z) is calculated as follows:
[tex]\mu=\Sigma z\cdot P(z)[/tex]Substituting with data:
[tex]\begin{gathered} \mu=-11\cdot0.06-10\cdot0.36-9\cdot0.43-8\cdot0.03-7\cdot0.02-6\cdot0.1 \\ \mu=-0.66-3.6-3.87-0.24-0.14-0.6 \\ \mu=-9.11 \end{gathered}[/tex]Example 1: Choose a point in Quadrant 2, 3, or 4 to be on the terminal arm of an angle in standard position. Determine the principal angle in radians. Include a sketch.Example 2: Using a different quadrant than in Example 1 (but still not Quadrant 1), choose a reciprocal trig ratio. Determine all of the primary and reciprocal ratios for that angle, as well as the principal angle in radians.
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Example 1:
The quadrants with their numbering (I, III,III, and IV) are shown below.
Now let us draw an angle in quadrant II.
We have drawn the angle above such that its measure from the positive x-axis is 135° . The angle 135° in radians is 3π/4.
Example 2:
Let us now choose an angle in the 3rd quadrant.
7. Marco was asked to rotate thecoordinate P(3,-4) 180 degrees about theorigin. Then, he decided to perform atranslation of (x, y+2) followed by adilation of 2. Marco was convinced thatP and P'" had the same coordinates. IsMarco correct? Explain your reasoning.
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Let's take this, step by step.
First step:
Rotate the coordinate 180 degrees about the origin.
When a 180 degrees rotation about the origin is performed the coordinates (x, y) changes to (-x, -y)
Thus, P(3, -4) changes to P'(-3, 4)
Second Step:
Perform a translation of (x, y+2)
P'(-3,4) = P''(-3, 4+2) = P''(-3, 6)
Third step:
Perform a dilation of 2.
P''(-3, 6) = P'''(-3*2, 6*2) = P'''(-6, 12)
We can see that,
P(3, -4) while P'''(-6, 12)
Therefore, P and P''' do not have the same coordinates
simplifying like terms and distributive property7b + 2(46 - 3)
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We will solve as follows:
[tex]7b+2(46-3)=7b+92-6[/tex][tex]=7b+86[/tex]So, the solution is 7b + 86.
6) Identifyas amonomial, binomial, or trinomial.4x2 – y + 0z4 binomial monomial Trinomial
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For this problem we have the following expression given:
[tex]4x^2-y+0z^4[/tex]Since any number multiplied by 0 is 0 then our expression becomes:
[tex]4x^2-y[/tex]And since we have two terms we can categorize the expression as a binomial.
Write the following equation x2 +9y2 + 10x – 18y + 25 = 0 in vertex form.Identify the type of conic section and its direction.
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The equation of the conic section is:
[tex]x^2+9y^2+10x-18y+25=0[/tex]Square terms are positive and have different coefficients. Then, we can say it is an ellipse.
To find the vertex form, we need to group x and y:
[tex](x^2+10x)+(9y^2-18y)+25=0[/tex]The grouped terms of y can be factored:
[tex](x^2+10x)+9(y^2-2y)+25=0[/tex]It will be convenient to group the 25 with the group of x, since we can have a perfect square trinomial (since the square root of 25 is 5, which is half ten):
[tex](x^2+10x+25)+9(y^2-2y)=0[/tex]We can factor the first goup:
[tex](x+5)^2+9(y^2-2y)=0^{}[/tex]Now, we can try to make another perfect square trinomila from the second term. We need a number whose square root multiplied by 2 gives us 2 (the coefficient of y) This number will be one. Then, we can sum 1 inside the parenthesis, but we need to substract 9 outside it in order not to alter the equation. (it is 9 because we added 1 inside a parenthesis that is multiplied by 9).
[tex](x+5)^2+9(y^2-2y+1)-9=0^{}[/tex]Now, we can factor the second group of terms and reorganize:
[tex](x+5)^2+9(y-1)^2=9^{}[/tex]Now, to get the equation in the vertex form, we need a 1 in the right side of the equation. Then, we can divide everything (both sides) by 9:
[tex]\frac{(x+5)^2}{9}+(y-1)^2=1[/tex]The equation of the ellipse is now on its vertex form. Since the number dividing the x term (9) is higher than the number dividing the y term (1) we can say that the direction of the ellipse is horizontal. It´s longer axis is parallel to the x axis of the plane.
Can you please help me with this question from math? A) He will receive a refund of $435.B) He will receive a refund of $442.C) He will pay $435.D) He will pay $442.
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ANSWER:
A) He will receive a refund of $435.
STEP-BY-STEP EXPLANATION:
According to the table for your income and marital status you must pay a total of $4091
If you already paid a total of $4,526, then:
[tex]\begin{gathered} t=4526-4091 \\ \\ t=435 \end{gathered}[/tex]Which means, they owe you a total of $435 back.
Therefore, the correct answer is A) He will receive a refund of $435.
What volume of ice cream is contained in a 10 cm-high ice cream cone with a base radius of 4 cm?
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We would find the volume of the ice cream contained in the cone by applying the formula for determining the voume of a cone which is expressed as
Volume = 1/3 x pi x radius^2 x height
From the information given,
height = 10
radius = 4
pi is a constant whose value is 3.142
Thus,
Volume = 1/3 x 3.142 x 4^2 x 10
Volume = 167.57
rounding to the nearest whole number,
Volume = 168 cubic cm
What is the new equation 1 when youmultiply by -1?
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the equation will be
-x - y = 7
Abc is isosceles triangle and right angled at C then TanA
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When we have a right angled triangle, it means the triangle has a right angle and two acute angles all equally summing up to 180 degrees.
When we have an isosceles triangle, it means there are two equal acute angles.
Therefore, by combining these two statements, we can get the value of the acute angles. A plot is given below.
[tex]\begin{gathered} 90+x+x=180 \\ 90+2x=180 \\ \text{Subtract 90 from both sides to get:} \\ 2x=90 \\ \text{Divide both sides by 2 to get:} \\ x=45^o \end{gathered}[/tex]Next step is to get Tan A.
We can use trigonometric ratios and Pythagoras theorem to get:
[tex]\begin{gathered} AB^{}=\sqrt[]{AC^2+BC^2} \\ AB=\sqrt[]{1^2+1^2} \\ AB=\sqrt[]{2} \end{gathered}[/tex]For Tan A, we employ the Soh Cah Toa to get:
[tex]\begin{gathered} \tan A=\frac{\text{opposite}}{\text{adjacent}} \\ \tan A=\frac{1}{1}=1 \end{gathered}[/tex]Therefore, Tan A = 1