Cosine theorem:
[tex]\begin{gathered} a^2=b^2+c^2-2bccosA \\ b^2=a^2+c^2-2ac\cos B \\ c^2=a^2+b^2-2ab\cos C \end{gathered}[/tex]a= 34ft
b = 20ft
c = 18ft
[tex]\begin{gathered} a^2-b^2-c^2=-2bc\cos A \\ \frac{a^2-b^2-c^2}{-2bc}=\cos A \\ \\ A=\cos ^{-1}(\frac{a^2-b^2-c^2}{-2bc}) \end{gathered}[/tex][tex]B=\cos ^{-1}(\frac{b^2-a^2-c^2}{-2ac})[/tex][tex]C=\cos ^{-1}(\frac{c^2-a^2-b^2}{-2ab})[/tex][tex]\begin{gathered} A=\cos ^{-1}(\frac{34^2-20^2-18^2}{-2(20)(18)}) \\ \\ A=\cos ^{-1}(\frac{432}{-720})=126.86 \end{gathered}[/tex][tex]\begin{gathered} B=\cos ^{-1}(\frac{20^2-34^2-18^2}{-2(34)(18)}) \\ \\ B=\cos ^{-1}(\frac{-1080}{-1224})=28.07 \end{gathered}[/tex][tex]\begin{gathered} C=\cos ^{-1}(\frac{18^2-34^2-20^2}{-2(34)(20)}) \\ \\ C=\cos ^{-1}(\frac{-1235}{-1360})=24.75 \end{gathered}[/tex]VABC:
A=126.86º
B=27.07º
C=24.75º
a=34ft
b=20ft
c=18ft
find f^-1(f(x)) for f(x)=(x-3)/2
After solving the given equation for f(x) the resultant answer is f(x)=1.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, find f(x):
When f^-1(f(x)) in f(x)=(x-3)/2.Now, calculate as follows:
f(x)=(x-3)/2f(x)=(f⁻¹-3)/2f(x)=(1/f - 3)/2f(x)=(1 -3f/f)/2f(x)=(1-3)/2f(x)=2/2f(x) = 1Therefore, after solving the given equation for f(x) the resultant answer is f(x)=1.
Know more about equations here:
https://brainly.com/question/28937794
#SPJ1
AХХ14DС1016BABBCCDAD0-14=1016 Х10x= 224x= 22.4
we get that
[tex]\frac{10}{16}=\frac{x}{14}\rightarrow x=14\cdot\frac{10}{16}=\frac{35}{4}=8.75[/tex]Which single transformation below would have the same effect as rotating the point (-3,4) by 180 degrees around the origin and then reflecting it in the y-axis?
First i will draw the original point in red
the rotation of 180° will give us the point (3,-4) the blue point
next, we reflect this point in the y-axis, the green point
if we see only the red point and the green point the transformation is equivalent to a reflection in the x-axis
the correct answer is 1
Find S3 of the sum of the geometric series. az = 4, a3 = 1, r= 1
Given:
a1 = 4
a3 = 1
r = ½
Let's find the S3 of the sum of the geometric series.
Apply the sum of geometric series formula below:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]Let's solve for S3.
Substitute the values into the equation.
Where: n = 3
Thus, we have:
[tex]S_3=\frac{4(1-(\frac{1}{2})^3)^{}^{}}{1-\frac{1}{2}}[/tex]Solving further:
[tex]\begin{gathered} S_3=\frac{4(1-(\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}))}{\frac{1}{2}} \\ \\ S_3=\frac{4(1-\frac{1}{8})}{\frac{1}{2}} \\ \\ S_3=\frac{4(\frac{7}{8})}{\frac{1}{2}} \\ \\ S_3=\frac{4\ast\frac{7}{8}}{\frac{1}{2}} \\ \\ S_3=\frac{\frac{7}{2}}{\frac{1}{2}} \\ \\ S_3=\frac{7}{2}\ast\frac{2}{1} \\ \\ S_3=7 \end{gathered}[/tex]Therefore, the S3 of the sum of the given geometric series is 7
ANSWER:
7
1. Describe the shape of
distribution A:
Answer choices:
Symmetric
Negatively skewed
Positively skewed
Uniform
The shape of the distribution A is Negatively skewed.
What is a negatively skewed distribution?\
A negatively skewed distribution sometimes referred to as a left-skewed distribution, is a type of distribution where more values are concentrated on the right side (tail) of the distribution graph and the left tail of the distribution graph is longer.
The idea of skewness is used in finance to analyze the distribution of investment returns. An investor may anticipate frequent tiny wins and a few significant losses, according to the distribution's negative skewness. In fact, traders frequently use trading methods that are based on distributions that are negatively skewed.
To learn more about negatively skewed distribution, use the link given
https://brainly.com/question/28164315
#SPJ1
pol: Practice & Problem Solving 2.PS-22 Question Help Three sisters are saving for a special trip. The ratio of Helga's savings to Maurice's savings is 8:3 and the ratio of Maurice's savings to Nora's savings is 3:4. Together all 3 sisters have saved $60. How much has each girl saved? Answer questions 3–4. IS 4 squares long. Then, use the diagrams to show $60. (Type whole numbers.) 4. Complete the table. Helga's savings Maurice's savings Nora's savings $8 $ $24 $32 $ $6 $ $ 12 $4 $ $ $16 + Vi 1 1,0 More Enter your answer in the edit fields and then click Check Answer. 1 pant Clear All Check Answer remaining
Answer:
Explanation:
We know that the ratio of Helga's savings to Maurice's savings is 8:3 and the ratio of Maurice's savings to Nora's savings is 3:4.
It means that if Helga has $8, Maurice has $3 and Nora has $4
In the same way, we can multiply one quantity by 2, and all the quantities will be multiplied by 2, so if Helga has $16, Maurice has $6 and Nora has $8
Because:
$8 x 2 = $16
$3 x 2 = $6
$4 x 2 = $8
So, following the same logic, we can complete the table as:
Therefore, the complete table is:
50 POINTS!!!!!!
1. Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 109.6°.
A) 250.4°
B) 63.2°
C) 70.4°
D) 19.6°
Answer:
C) 70.4°Step-by-step explanation:
We know supplementary angles add up to 180°:
A + B = 180°Find the missing one:
A + 109.6° = 180°A = 180° - 109.6°A = 70.4°Correct choice is C.
2) Hazel McCurry offered $419,400 for a home that had been priced at $439,500. The seller agreed to the offer. If she made a $44,000 down payment, what is the mortgage loan amount?
ANSWER
$375,400
EXPLANATION
The price of the home was $439,500, but Hazel offered $419,400 so that was the selling price. The down payment was $44,000. Hence, the mortgage loan amount is,
[tex]\text{Mortgage Loan Amount}=419,400-44,000=375,400[/tex]I need help answering the “explain how you found the slope and y intercept question. I did not know how to do this and mainly guessed and got the right answer so I need help explaining please
When we are given a straight line drawn on the cartesian graph, i.e, having x and y coordinates, the gradient/slope is the change on the y-axis relative to change on the x-axis.
The x-axis is the horizontal axis and the y-axis is the vertical axis.
To get the gradient, we simply pick two points on the line and name them points 1 and 2. Thus, they will have the following attributes:
[tex]\begin{gathered} Point1=(x_1,y_1) \\ Point2=(x_2,y_2) \end{gathered}[/tex]The gradient of a straight line is:
[tex]s=\frac{y_2-y_1}{x_2-x_1}[/tex]So, in our question, we can pick our points 1 and 2 at
Point 1 = (-2, 6), (1,-3),
Point 2 = (0, 0), (2,-6)
Applying our formulae, we get:
[tex]\begin{gathered} s=\frac{0-6}{0-(-2)_{}}=-\frac{6}{2}=-3 \\ s=\frac{-6-(-3)}{2-1}=-\frac{3}{1}=-3 \\ \text{Any two points will give us a gradient of -3} \end{gathered}[/tex]The gradient is -3.
As for the intercept on the y-axis, this is the point on the vertical axis where the graph cuts the graph. It can be visibly seen from our graph as occurring at y = 0.
However, it can be calculated via a formula to give us the form: y = mx + c.
where: m is the gradient/slope and c is the intercept on the y axis.
Formulae for getting conventional line equation is:
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \frac{y-6}{x-(-2)}=-3 \\ -3x-6=y-6 \\ \text{Adding 6 to both sides gives:} \\ -3x=y \end{gathered}[/tex]The line equation is therefore: y = -3x + 0
Slope = -3 AND
y-intercept = 0
f(x) is a linear function. f(0) = 7 and f(3) = 5. Find the equation for f(x).
Let us calculate the slope of the line. We get two points (0,7) and (3,5)
[tex]m=\frac{7-5}{0-3}=-\frac{2}{3}[/tex]given the slope we have that
[tex]f(x)=-\frac{2}{3}x+7[/tex]so the function is:
[tex]f(x)=-\frac{2}{3}x+7[/tex]Use the point-slope formula to write an equation of the line that passes through 4, 2 and 6,5.Write the answer in slope-intercept form (if possible).
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
point 01 (4 , 2)
point 02 (6 , 5)
Step 02:
equation of the line:
slope:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{5-2}{6-4}=\frac{3}{2}[/tex]Point-slope form of the line
(y - y1) = m (x - x1)
[tex]\begin{gathered} (y-2)=\frac{3}{2}(x-4) \\ \\ (y-2)=\frac{3}{2}x\text{ -}\frac{12}{2} \\ \\ y-2=\frac{3}{2}x-6 \\ \\ y=\frac{3}{2}x-6+2 \\ \\ y=\frac{3}{2}x-4 \end{gathered}[/tex]The answer is:
y = 3/2 x - 4
the figures in each pair are similar. Find the unknown measures.
3/4 is 70% of what number
3/4 is 70% of what number, Let the number is x:
So, the expression will be :
70% of x = 3/4
[tex]\begin{gathered} \text{ 70\% of x = }\frac{3}{4} \\ \frac{70\times x}{100}=\frac{3}{4} \\ 70x=\frac{3}{4}\times100 \\ x=\frac{3\times100}{4\times70} \\ x=\frac{300}{280} \\ x=\frac{30}{28} \\ x=\frac{15}{14} \\ x=1.07142 \end{gathered}[/tex]x = 1.07142
The number is 1.07142
Question 3X1127INXRewrite in simplest rational exponent form VxVx. Show each step of your process.
Given
[tex]\sqrt[]{x}\cdot\sqrt[4]{x}[/tex]So, we have that
[tex]\begin{gathered} \sqrt[]{x}=x^{\frac{1}{2}} \\ \sqrt[4]{x}=x^{\frac{1}{4}} \end{gathered}[/tex]Therefore, the expression given is
[tex]x^{\frac{1}{2}}\cdot x^{\frac{1}{4}}[/tex]Apply the laws of exponents
[tex]x^{\frac{1}{2}+\frac{1}{4}}=x^{\frac{3}{4}}[/tex]Answer:
[tex]x^{\frac{3}{4}}[/tex]Y S 18. Graph triangle DEF with vertices D(-5,2), E(1.3), and F(-4,-3). Then graph the image of the triangle after it is translated 4 units right and 3 units down. What are the vertices of triangle D'E'F? 4 3 2 1 o 1 2 J 4 SX YTY
Graphing the triangle DEF, we have:
Now, translating the triangle 4 units right and 3 units down, we have the new vertices:
[tex]\begin{gathered} D(-5,2)\to D^{\prime}(-5+4,2-3)=D^{\prime}(-1,-1) \\ E(1,3)\to E^{\prime}(1+4,3-3)=E^{\prime}(5,0) \\ F(-4,-3)\to F^{\prime}(-4+4,-3-3)=F^{\prime}(0,-6) \end{gathered}[/tex]Graphing the triangle D'E'F', we have:
A boutique sells t-shirts for $30. They pay $12.50 for each shirt and spend $740 for the right to sell the brand in their store. How many t-shirts do they have to sell to break even?
First let's find the profit for each t-shirt, by subtracting the selling price and the buying price:
[tex]30-12.5=17.5[/tex]So they have a profit of $17.5 per t-shirt sold.
Now, to find the number of t-shirts they have to sell to break even, we just need to divide the right cost of $740 by the profit value of one t-shirt:
[tex]\frac{740}{17.5}=42.29[/tex]So they need to sell approximately 43 t-shirts to break even.
two scouts are camping at a national park. They were hiking when one of them sprains his ankle. They mark off their locations on the map below. How far will they have to travel to reach the medical center?
The distance the scouts have to travel to the clinic, found using Pythagorean Theorem is about 7.07 unit distance
What does the Pythagorean Theorem states?Pythagorean Theorem indicates that in a right triangle, the square of the hypotenuse side is the sum of the square of the other two sides.
The points on the graph are;
Campsite (8, 7)
Sprained ankle (3, 7)
Medical center (8, 2)
The distance between the point where the scout sprained his ankle and the Medical center is from (3, 7) to (8, 2)
The vertical distance the scouts have to travel = 2 - 7 = -5
The horizontal distance the scouts have to travel = 8 - 3 = 5
With the above vertical and horizontal distance, the scouts have to travel to reach the medical center, the direct distance can be calculated using Pythagorean theorem as follows;
Direct distance = √((-5)² + 5²) = 5·√2 ≈ 7.07
The distance the scouts have to travel is about 7.07 unit distance
Learn more about Pythagorean Theorem in mathematics here:
https://brainly.com/question/28227806
https://brainly.com/question/21926466
https://brainly.com/question/22203660
#SPJ1
It takes Jenny 8.4 minutes to sweep a porch.Mofor can sweep the same porch in 13.3minutes. If they worked together how longwould it take them?
Rate of Jenny = 1/ 8.4 minutes
Rate of Mofor = 1/13.3 minutes
We know time and rate are inverses of each other.
So, if they work together, their rates would be:
[tex]\frac{1}{8.4}+\frac{1}{13.3}[/tex]The time they will take will be the inverse of this, thus:
[tex](\frac{1}{8.4}+\frac{1}{13.3})^{-1}[/tex]So, let's calculate it:
[tex]\begin{gathered} (\frac{1}{8.4}+\frac{1}{13.3})^{-1} \\ =5.1484 \end{gathered}[/tex]That is around 5.15 minutes.
Bianca bought a baseplate of 12inches length and 10inches width. find the area of the baseplate
Solution.
Length of the Baseplate = 12inches
Width of the Baseplate = 10inches
[tex]\begin{gathered} \text{Area = Length }\times\text{ Breadth(Width)} \\ \text{ = 12 }\times10 \\ \text{ = 120 in}^2 \\ \end{gathered}[/tex]Final Answer = 120
solving compound qualities
S = {x ∈ R : 3≤x≤12}
1) To solve a compound inequality, we must do it one by one.
Let's start with
1.1) 0≤1/3x -1
1≤1/3x-1+1
1≤1/3x Multiplying both sides by 3
3≤x Flipping it
x≥3
1.2) 1/3x -1≤3
1/3x -1+1≤3+1
1/3x≤4
x≤12
2) Let's find out the solution, by graphing on three lines. The first one for the first solution, the second for the second inequality's solution, and the third for the intersection of the above:
So the Solution set is S = {x ∈ R : 3≤x≤12}
1 and ∠2 are complementary angles. The measure of ∠1 is 14°. The measure of ∠2 is 4x°. Find the value of x. The figure is not drawn to scale
1 and ∠2 are complementary angles. The measure of ∠1 is 14°. The measure of ∠2 is 4x°. Find the value of x.
Remember that
the sum of complementary angles is 90 degrees
so
<1+<2=90
substitute given values
14+4x=90
solve for x
4x=90-14
4x=76
x=19A cosmetics company makes small, cylindrical bars of soap, and wraps them in plastic prior to packing them in boxes for shipping. Each bar of soap has a diameter of 5 cm and is 2 cm in height.a. How much soap material is used to make each bar of soap?b. How much plastic is required to wrap each bar of soap, assuming it is shrink-wrapped tightly around each bar?C.The company wants to be able to ship a minimum of 60 bars per box to save on shipping costs. What will be the dimensions of the box if the soap must be stacked no more than 5 bars high?d. Find the capacity of the box in litres.
a. In order to determine how much soap material is used for each bar of soap, consider that the shape of the bar is a cylinder, then, use the folowing formula for the volume of a cylinder:
V = π r² h
where r is the radius of the base and h is the height.
The diameter is 5 cm, then, the radius is r = d/2 = 5 cm/2 = 2.5 cm
The height is h = 2 cm
replace the previous values into the formula for V:
V = (3.14)(2.5 cm)²(2 cm)
V = 39.25 cm³
Hence, 39.25 cm³ of soap material is used to make each bar.
b. In this case it is necessary to calculate the suface area of the plastic used. As before, take into account that the bar has a cylindrical shape. Then, use the following formula for the surface area of a cylinder:
S = 2πr² + 2πrh
replace the values of the parameters to find S:
S = 2π(2.5 cm)² + 2π(2.5cm)(2cm)
S = 70.68 cm²
Hence, 70.68 cm² of plastic is required to wrap each bar
c. Take into account that the soap must be stacked no more than 5 bars high, and that the company wants to ship a minimum of 60 bars.
If there are 5 bars high x 3 bars length, in one face of the box you have 15 bars. Moreover, if there are 4 bars width, then, you have a total of 15x4 = 60 bars in one box, which is what the company wants.
The height of the box is given by 5 times the height of one bar (because there are 5 bars high). The length is given by 3 times the diameter of one bar and the width of the box is given by 4 times the diameter of one bar:
height of the box = 5(2 cm) = 10 cm
length of the box = 3(5 cm) = 15 cm
width of the box = 4(5 cm) = 20 cm
d. First, calculate the volume of the box, as follow:
V = h x l x w = (10 cm)(15 cm)(20 cm) = 3,000 cm³
take into account the conversion 1,000 cm³ = 1 L, then, the capacity of the box is:
V = 3,000 cm³ = 3L
An expression is given.
2 x² + zx - 10
The expression can be written as (x+q) (q + r), where q, r, and z are integers.
What are possible integer values of q, r, and z?
In the text box, type your answer in this format:
q =
r =
z =
Expressions are mathematical statements without the equation sign
The possible integer values of q, r, and z are 1, -5 and 8
The expressions are given as:
[tex]2x^{2} + zx - 10[/tex] (say eq. 1)
(x + q)(x + r)
Both expressions are equal.
So, we have:
[tex]2x^{2} + z x - 10 = (x+q)(x+r)[/tex]
we know that , roots of a quadratic equation ([tex]ax^{2} + bx + c = 0[/tex]) are ,
[tex]m = \frac{-b + \sqrt{b^{2} - 4ac } }{2a} , n = \frac{-b - \sqrt{b^{2} - 4ac } }{2a}[/tex]
on comparing [tex]ax^{2} + bx + c = 0[/tex] with eq . 1 , we get
a = 2 , b = z , c = -10
Therefore , [tex]m = \frac{(-z) + \sqrt{}(z^{2} - 4.2.(-10) ) }{2.2} = \frac{-z + \sqrt{}z^{2} + 80 }{4}[/tex],
[tex]n = \frac{(-z) - \sqrt{}(z^{2} - 4.2.(-10) ) }{2.2} = \frac{-z - \sqrt{}z^{2} + 80 }{4}[/tex]
Now , we can express eq. 1 as ,
(x-m)(x-n)
By comparison, we have:
q = -m
r = -n
or
[tex]q = \frac{-z + \sqrt{}z^{2} + 80 }{4}\\r = \frac{-z - \sqrt{}z^{2} + 80 }{4}[/tex]
Assume that q = 1.
So, we have:
[tex]1 = \frac{-z + \sqrt{}z^{2} + 80 }{4}\\or\\4 = -z + \sqrt{z^{2} + 80 } \\[/tex]
Rearranging and Squaring both sides ,
[tex](z+4)^{2} = (\sqrt{z^{2} + 80 }) ^{2} \\z^{2} + 16 + 8z = z^{2} + 80\\8z = 64[/tex]
This gives , z = 8
Substitute , z= 8 in r
So, we have:
[tex]r = \frac{-8 - \sqrt{8^{2} + 80 } }{4} = \frac{-8 - \sqrt{144} }{4} = \frac{-8 - 12}{4} = -5[/tex]
Hence, the possible integer values of q, r, and z are 1, -5 and 8.
Learn more about expressions at:
brainly.com/question/4344214
#SPJ1
how to find the center and scale factor of #5?
SOLUTION:
Case: Enlargement
Method:
Scale factor: The scale factor is the 3, because the image is three times the size of the object.
From the tracing, the center of dilation is at C(-2, -2).
Final answer:
Center = (-2, 2)
Scale factor = 3
Calculate the area of the square JKLM if KM = 42 mm.
Calculate the area of the square JKLM if KM = 42 mm.
given that KM=42 mm
KM is also the diagonal of the square.
Also, the diagonal KM is the hypotenuse of a right triangle with sides JK and JM the Pythagoras theorem.
Now , let's remember that the angle formed by two sides of a square is equal to 90 degrees, this means, that the angle formed by the diagonal and any side must be the half, it is 45 degrees
so, if we solve the right triangle MLK we will find the length of the s
[tex]\begin{gathered} \text{cos}\emptyset=\frac{x}{\text{Hypotenuse}} \\ x=\text{Hypotenuse }\cdot\text{ cos}\emptyset \\ x=42\cdot\cos 45 \\ x=29.69 \end{gathered}[/tex]Now, is it a square, so the sides are equal, and the area is given by
[tex]\begin{gathered} \text{Area}=x^2 \\ A\text{rea}=(29.698)^2 \\ \text{Area}=882\text{ square milimeteres} \end{gathered}[/tex]so, the answer is 882 square millimeters
what is the slope for a line that is perpindicular to the line y=4x+8
The slope for a line that is perpendicular to the line y=4x+8 is m = [tex]-\frac{1}{4}[/tex]
The given equation is y=4x+8
this equation is of the form y = mx + c
where on comparing we get the values as :
m or the value of the slope =4
and the constant is 8
Thus to find the perpendicular to the given slope
we simply have to find the negative reciprocal of the given slope
the given slope as mentioned above = 4
thus slope of perpendicular = [tex]-\frac{1}{4}[/tex]
To know more about perpendicular and slope you may visit the link which is mentioned below:
https://brainly.com/question/21167969
#SPJ1
in a stable there are H horses 6 of them are taken into the the yard to exercise ⁰how many are left in the stable
Explanation:
If there are H horses and 6 are taken into the yard, then we have 6 horses less in the stable.
Answer:
There are (H - 6) horses left in the stable
Cassius is purchasing flower baskets to be placed on each table at a volunteer appreciation lunch. Store Acharges $19.25 per flower basket plus a $15.00 delivery fee. Store B charges $17.50 per flower basket plusa $30.00 delivery fee. Which inequality can determine x, the maximum number of flower baskets that canbe ordered for the total cost at Store A to be cheaper the total cost from Store B?O 19.25 + 15x > 17.5 + 30xO 19.25 + 15x < 17.5 + 30x19.25x + 15 < 17.5x + 30O 19.25x + 15 > 17.5x + 30
We will have the following expressions for store A and B respectively:
[tex]19.25x+15[/tex][tex]17.50x+30[/tex]From this, we can see that after certain ammount of flowers the price will be better if we arrage it as follows:
[tex]19.25x+15>17.50x+30[/tex]what is the time it took to reach maximum height? round the answer to the nearest whole second.
3 seconds
Explanation
we have a graph where
x-axis: indicates the time
y-axis:indicates the height
to solve this we need to find the time, where the maximum heigth is reached
Step 1
check the coordinate where the maximum heigth is reached
and go down vertically to intersect the x-axis:
so, we have , it took around 3 seconds to reach the maximum heigth
I hope this helps you
Question 5 of 9Translate the phrase into a variable expression. Use the letter m to name thevariable. If necessary, use the asterisk (*) for multiplication and the slash(/) for division.... the total number of minutes billed on the phone bill split between 3phones...Answer here
SOLUTION
From the question, let the total number of minutes billed on the phone bill be m
Splitting this into 3 phones, we have
[tex]\frac{m}{3}[/tex]Hence the answer is m/3