10x3y5,
-15x4y8,
20x5y6
[tex]undefined[/tex]greatest common factor of 10, 15, and 20 is 5
greatest common factor of x^3, x^4 and x^5 is x^3
greatest common factor of y^5, y^8 and y^6 is y^5
Therefore the greatest common factor of all is:
5x^3y^5
[tex]5x^3y^5^{}[/tex]The value of a stock decreases by an average of 10 dollars each week. Which of the following represents the total average decrease in the stock after 8 weeks?
O 1-101-181=2 dollars
O -8110) = 80 dollars
O 1-101-8=2 dollars
0 81-101 = 80 dollars
The following describes the total moderate decrease in the wares after 8 weeks is 8 | -10 |= 80 dollars.
What is meant by value?The value refers to the worth of each digit in relation to its position in the number. We compute it by multiplying the digit's place and face values. Place Value + Face Value = Value. As an example: If we look at the number 45. In this case, digit 4 is in the tens column. Values are benchmarks or ideals against which we judge actions, people, things, or situations. Many people support values such as beauty, honesty, justice, peace, and generosity. The actual population value obtained with perfect measuring instruments and without committing any type of error, both in collecting primary data and in performing mathematical operations.
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Determine the period PLEASE HELP
The period of the wave = 3 units of the x-variable.
From the Graph,
The period of a wave is the time taken to complete a cycle of motion of the wave
In the given figure, the graduations of the x-axis, which is the usually time axis = 1 unit
At the origin, (0, 0), the vertical displacement of the wave = 0
The maximum value of the wave function is between x = 0 and x = 1
The minimum value of the wave function is between x = 2 and x = 3
The time elapsed for two consecutive occurrences of the same result is called period.
At the point (3, 0) the value of the wave function is again 0, and a cycle of the wave is completed
Therefore, the period of the wave = 3 units of the x-variable.
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Answer:
2
Step-by-step explanation:
The Period goes from one peak to the next (or from any point to the next matching point).
What is the wavelength change of a radio signal changes if the emitting source is moving away at 3,000 km/s. The lab (rest) wavelength of this radio signal is 1 meter
The change in wavelength of the radio signal is 100m
What is Wavelength ChangeThe change in wavelength of the radio can be calculated using the velocity of the given radio signal.
[tex]c = v \lambda\\[/tex]
c = speed of lightv = velocity y = wavelengthLet's substitute the values and solve.
But then, we have to convert the velocity from km to m
[tex]1km = 1000m\\3000km = x\\x = 3000000m[/tex]
Let's proceed to solve this.
[tex]c = \lambda v\\3.0*10^8 = \lambda * 3.0^6\\\lambda = \frac{3.0*10^8}{3.0*10^6} \\\lambda = 1.0*10^2m\\\lambda = 100m[/tex]
The wavelength of the radio signal is 100m.
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I find 4heb diagram.
We are asked to find the volume of the given pyramid.
Recall that the volume of a pyramid is given by
[tex]V=\frac{1}{3}\cdot B\cdot h[/tex]Where B is the area of the base and h is the height of the pyramid.
As you can see from the figure, the base of the pyramid is rectangular
The length is 23 yd and the width is 14 yd of the rectangular base.
So, the area of the rectangular base is
[tex]\begin{gathered} B=l\cdot w \\ B=23\cdot14 \\ B=322\: yd^2 \end{gathered}[/tex]The height of the pyramid is 25 yd
So, the volume of the pyramid is
[tex]\begin{gathered} V=\frac{1}{3}\cdot B\cdot h \\ V=\frac{1}{3}\cdot322\cdot25 \\ V=2683.3\: yd^3 \end{gathered}[/tex]Therefore, the volume of the rectangular pyramid is 2683.3 cubic yards.
The type of pyramid is the rectangular pyramid.
Joel wants to find the best model for a bivariate data set that he is working with. He used a calculator to create a linear model, a quadratic model, and an exponential model. The coefficient of determination for the linear model was 0.45. The coefficient of determination for the quadratic model was 0.38, and the coefficient of determination for the exponential model was 0.51. Which model should he use to represent the data set? Justify your response in at least 2 sentences.
Answer:
exponential
Step-by-step explanation:
just took the test
What is the remainder when 2x2 - 3x + 5 is divided by x - 1?10-10-44
Explanation
Given the expression
[tex]f(x)=2x^2-3x+5[/tex]The remainder when it is divided by x-1 can be seen below.
[tex]\begin{gathered} r=2(1)^2-3(1)+5 \\ r=2-3+5 \\ r=4 \end{gathered}[/tex]Answer: 4
Two questions! Please help! Multiple choice.
Answer:
8) a. Use center G and the same radius
9) b. WX ≅ JK
Step-by-step explanation:
8) You want to know the next step in constructing a perpendicular bisector.
9) You want to know how WX relates to JK.
8)A perpendicular bisector of GH is the set of points equidistant from G and H. The arc shown is a set of points at some distance from H. We want to find two points on that arc that are the same distance from G, so the next step is ...
a) Using G as a center, draw an arc with the same radius as the first arc
9)All of the points on the arc are the same distance from W as J is from K. Point X is a point on the arc, so WX will have the same length as JK.
b) WX is congruent to JK
selecting from milligram, gram, kilogram, and tonne, determine the best unit of measure to express a butterfly weight
Solution
For this case we can conclude that the best answer for this case is:
gram
Since a butterfly can weight about 0.04-1 grams
Find the standard deviation for n = 10 and p = 0.6 when the conditions for the binomial distribution are met. (Round your answer to two digits after the decimal point.)
Given the values of n and p to be;
[tex]\begin{gathered} n=10 \\ p=0.6 \end{gathered}[/tex]We can calculate the standard deviation using the formula below;
[tex]\sigma=\sqrt[]{n\cdot p\cdot(1-p)}[/tex]substituting the given values;
[tex]\begin{gathered} \sigma=\sqrt[]{10\cdot0.6\cdot(1-0.6)} \\ \sigma=\sqrt[]{2.4} \\ \sigma=1.55 \end{gathered}[/tex]Therefore, the standard deviation for the distribution is;
[tex]\sigma=1.55[/tex]a blow up pool in your backyard has a diameter of 8 ft what is the circumference of the pool round to the nearest hundredth
A blow-up pool in your backyard has a diameter of 8 ft.
We are asked to find the circumference of the pool. (rounded to the nearest hundredth)
Recall that the circumference of a circular shape is given by
[tex]C=\pi\cdot D[/tex]Where π is a constant and D is the diameter.
Let us substitute the given values into the above formula
[tex]\begin{gathered} C=\pi\cdot D \\ C=\pi\cdot(8) \\ C=25.13\: ft \end{gathered}[/tex]Therefore, the circumference of the pool is 25.13 feet (rounded to the nearest hundredth)
Write the equation of the line that passes through the points (-2,-8)(−2,−8) and (9,8)(9,8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The equation of a line is y + 8 = 16/11 (x + 2).
Here we have to find the equation of a line which are passing through points (-2, -8) and (9, 8).
Slope of a line = [tex]\frac{y_{2} - y_{1} }{x_{2}- x_{1} }[/tex]
([tex]x_{1} , y_{1}[/tex]) = (-2, -8)
([tex]x_{2} , y_{2}[/tex]) = ( 9, 8)
The slope(m) = [tex]\frac{8-(-8)}{9-(-2)}[/tex]
= 16/ 11
The equation of a straight line is:
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
The point ([tex]x_{1} , y_{1}[/tex]) = ( -2, -8)
y - (-8) = 16/11( x -(-2))
y + 8 = 16/11(x + 2)
Therefore the equation of a line is y + 8= 16/11( x +2).
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Choose the appropriate pattern and use it to find the product: (p4−q4)(p4+q4).
The expression can be solved by expanding the bracket and multiplying out the terms
[tex](p^4-q^4)(p^4+q^4)[/tex][tex]\begin{gathered} =p^4(p^4+q^4)-q^4(p^4+q^4) \\ =p^8+p^4q^4-p^4q^4-q^8 \\ =p^8-q^8 \end{gathered}[/tex]Therefore, the expression can be simplified as;
[tex]p^8-q^8[/tex]Alternatively, using the theorem of difference of two squares, which is
[tex]a^2-b^2=(a-b)(a+b)[/tex]Hence,
[tex]p^8-q^8=(p^4)^2-(q^4)^2[/tex]
The table below shows primary school enrollment for a certain country. Here, x represents the number of years after 1820, and y represents the enrollment percentage. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places.
See uploaded table in screenshots below
Linear slope formula,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex] (Equation-1)
We can table-1,
(x , y) = (0 , 0.1)
(x , y) = (5 , 0.1)
So,
We can write,
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (0 , 0.1)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (5 , 0.1)
We can substitute equation-1,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
k = [(0.1) - (0.1)]/5-0
k = 0/5
k = 0
y = kx + b
y = (0)x + b
y = 0+b
y = b
After (x , y) = (0 , 0.1)
Substituting point,
0.1 = b
b = 0.1
Hence,
The slope and intercept to two decimal places are k = 0 ; y = b
We can table-2,
(x , y) = (55 , 3.0)
(x , y) = (60 , 4.5)
So,
We can write,
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (55 , 3.0)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (60 , 4.5)
We can substitute equation-1,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
k = [(4.5) - (3.0)]/60-55
k = 1.5/5
k = 0.3
y = kx + b
y = (0.3)x + b
y = 0.3x + b
After (x , y) = (55 , 3.0)
Substituting point,
3.0 = (0.3)(55) + b
3.0 = 16.5 + b
b = -13.5
Hence,
The slope and intercept to two decimal places are k = 0.3 ; y = 0.3x + b
We can table-3,
(x , y) = (110 , 16.6)
(x , y) = (115 , 17.5)
So,
We can write,
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (110 , 16.6)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (115 , 17.5)
We can substitute equation-1,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
k = [(17.5) - (16.6)]/115-110
k = 0.9/5
k = 0.18
y = kx + b
y = (0.18)x + b
y = 0.18x + b
After (x , y) = (110 , 16.6)
Substituting point,
16.6 = (0.18)(110) + b
16.6 = 19.8 + b
b = -3.2
Hence,
The slope and intercept to two decimal places are k = 0.18 ; y = 0.18x + b
We can table-4,
(x , y) = (160, 63.2)
(x , y) = (165 , 75.0)
So,
We can write,
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (160, 63.2)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (165 , 75.0)
We can substitute equation-1,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
k = [(75.0-63.2)]/165-160
k = 11.8/5
k = 2.36
y = kx + b
y = (2.36)x + b
y = 2.36x + b
After (x , y) = (160, 63.2)
Substituting point,
63.2 = (2.36)(160) + b
63.2 = 377.6 + b
b = -314.4
Hence,
The slope and intercept to two decimal places are k = 2.36 ; y = 2.36x + b
We can table-5,
(x , y) = (185, 100.0)
(x , y) = (190 , 100.0)
So,
We can write,
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (185, 100.0)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (190 , 100.0)
We can substitute equation-1,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
k = [((100-100)]/190-185
k = 0/5
k = 0
y = kx + b
y = (0)x + b
y = b
After (x , y) = (185, 100.0)
Substituting point,
100 = (0)(185) + b
100 = 0 + b
b = 100
Hence,
The slope and intercept to two decimal places are k = 0 ; y = b
Therefore,
The slope and intercept to two decimal places are k = 0 ; y = b The slope and intercept to two decimal places are k = 0.3 ; y = 0.3x+bThe slope and intercept to two decimal places are k = 0.18 ; y = 0.18x+bThe slope and intercept to two decimal places are k = 2.36 ; y = 2.36x+bThe slope and intercept to two decimal places are k = 0 ; y = bTo learn more about information visit Slope :
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How many of the justices were 65 or older in 2017?
The dot plot shows the frequency of the ages of the judges and each dot tells us that there is a judge of that age.
From 65 and beyond, we can count 5 dots meaning that we have 5 judges in that range.
OPTION D
Kurt is flying his airplane over a campground. he spots a small fire below at an angle of depression of 32°. If the horizontal d9stance from Kurt's plane to the fire is 3600 feet, find the approximate altitude of his plane.
ANSWER:
A. 2,250 feet
STEP-BY-STEP EXPLANATION:
We can calculate the value of the height thanks to the tangent trigonometric function, which relates the opposite leg (altitude) and the adjacent leg (horizontal), as follows:
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \theta=32\text{\degree} \\ \text{opposite = x} \\ \text{adjacent = 3600} \end{gathered}[/tex]Replacing and solving for x:
[tex]\begin{gathered} \tan 32=\frac{x}{3600} \\ x=3600\cdot\tan 32 \\ x=2249.53\cong2250 \end{gathered}[/tex]The altitude value is 2250 feet
River Rafting Company A costs $18 for a rental and has an
additional charge of $5 each hour. River Rafting Company B
costs $22 for a rental and has an additional charge of $3 each
hour. Let y represent the total cost and a represent the number
of hours. Which system of equations could you use to find
when the total cost of renting a raft will be the same?
Answer:
$28 on 2 hours of additional charges.
Step-by-step explanation:
Hello! Let's help you with your question here!
To begin, let's start writing these in terms of system of equations. Given your parameters we can split it up!
River Rafting Company A:
Here, we have a $18 cost for rental and an additional charge of $5 each hour. The $18 cost is essentially our flat rate, we have to pay this regardless and it's a one-time payment. The $5 each hour is our variable cost as we are unsure of how long people are going to be renting them for. So we can write the equation as:
[tex]y = 5a + 18[/tex]
River Rafting Company B:
Over on this side, we have a $22 cost for rental and an additional charge of $3 each hour. The explanation is the exact same as the previous one. We have a higher flat rate of $22 but a lower variable cost of $3 each hour. Therefore, the equation is:
[tex]y = 3a + 22[/tex]
Now that we have equations for both companies, we can solve using systems of equations to get y, since we are trying to get the total cost of both companies to be same. For this, let's solve with substitution.
Solve by Substitution:
Okay! Let's take [tex]y = 3a+22[/tex] (Equation 1) and substitute it into [tex]y = 5a+18[/tex] (Equation 2). To do this, we just essentially have substitute y in Equation 2 with the values that it equals to in Equation 1, so it becomes:
[tex]3a+22=5a+18[/tex]
Now, we solve for a, we move everything over to one side and then collect like terms. For this, I will be moving everything to the right. So it becomes as follows:
[tex]0 = 5a+18-3a-22[/tex]
[tex]0 = 2a - 4[/tex]
From here, we divide x and -4 by 2 to isolate a. We finally get [tex]a=-2[/tex]. Time cannot be negative which means it has to be [tex]a = 2[/tex] instead.
Now that we finally have the value of a, we can use that value and substitute it into Equation 1 to get the total cost y. So that would be:
[tex]y=3(2)+22[/tex]
[tex]y=28[/tex]
Let's try this for the second equation to verify that the cost are the same:
[tex]y=5(2)+18[/tex]
[tex]y=28[/tex]
Here, both y values are equal to 28. Therefore, you use solve by substitution to figure out that the total cost for both equals $28 when under the additional charge of 2 hours.
Solve the equation on the interval 0<=theta<2pi2 sin^2 theta-V3 sin theta = 0
Given the equation
[tex]2\sin ^2\theta-\sqrt{3}\sin \theta=0[/tex]We can rewrite the given equation as:
[tex]2\sin ^{}\theta\sin ^{}\theta-\sqrt{3}\sin \theta=0[/tex]Factoring, we obtain:
[tex]\sin ^{}\theta(2\sin ^{}\theta-\sqrt{3})=0[/tex]Therefore, we can say:
[tex]\begin{gathered} \sin ^{}\theta=0\: \implies\theta=0 \\ \text{Similarly} \\ 2\sin ^{}\theta-\sqrt{3}=0 \\ \implies2\sin ^{}\theta=\sqrt{3} \\ \implies\sin ^{}\theta=\frac{\sqrt{3}}{2} \\ \implies\theta=\sin ^{-1}\frac{\sqrt{3}}{2} \\ \implies\theta=\frac{\pi}{3} \end{gathered}[/tex]Therefore, the solution set in the given interval is:
[tex]\left\lbrace 0,\frac{\pi}{3}\right\rbrace [/tex]If Jason eats 3/6 of a birthday cake and Mike eats 2/6 of the same cake, how much of the birthday cake was eaten?
a.5/6
b.5/12
If a pizza is divided into 8 equal slices and Lily eats 3/8 of the pizza, how much of the pizza is left?
a.3/6
b.5/8
There are 10 t-shirts. 7/10 of the tee-shirts are blue. The rest are green. How many t-shirts are green?
a.7
b.3
1. The quantity of the birthday cake eaten by Jason and Mike is a. 5/6 or 83.3%.
2. The quantity of the pizza left after Lily has eaten 3/8 is b. 5/8.
3. The number of green t-shirts is b. 3.
How are the numbers determined?The various numbers are determined using the mathematical operations of subtraction, addition, multiplication, and division.
These basic mathematical operations result in the difference, sum, product, and quotient, respectively.
a) Birthday Cake:The quantity of the birthday cake = 1 or 6/6
The amount consumed by Jason = 3/6
The amount consumed by Mike = 2/6
The total quantity consumed by Jason and Mike = 5/6 (3/6 + 2/6)
b) Pizza:The quantity of the pizza = 1 or 8/8
The amount consumed by Lily = 3/8
The amount left unconsumed = 5/8 (1 - 3/8)
c) T-shirts:The total number of t-shirts = 10
The fractional size of blue t-shirts = 7/10
Since the rest are green, the fractional size of the green t-shirts = 3/10 (1 - 7/10)
3/10 of 10 = 3
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√98-√18
how would I get the answer to this
SURDS
The value of √98-√18 in surds will be 4✓2.
Whet is surds?A surd simply means an expression that include the square root, the cube root or other root symbols.
In this case, the value given is illustrated as:
√98-√18
= ✓(2 × 49) - ✓(2 × 9)
= 7✓2 - 3✓2
= 4✓2
The value is 4✓2.
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Complete these sentences to describe the rules of dividing signed numbers.
The quotient of two integers with same sign is always
The quotient of two integers with different signs is always
Answer:
1) Positive, 2) NegativeStep-by-step explanation:
The quotient of two integers with same sign is always positive, because:
Positive / positive = positive andNegative / negative = positiveThe quotient of two integers with different signs is always negative, because:
Positive / negative = negative andNegative / positive = negativeAnswer:
1) Positive (+)
2) Negative (-)
Step-by-step explanation:
1) Positive
→ (+) ÷ (+) = (+)
→ (-) ÷ (-) = (+)
Hence, it is proved.
2) Negative
→ (+) ÷ (-) = (-)
→ (-) ÷ (+) = (-)
Hence, it is proved.
Janice is going to go buy dinner but she wants to use all the change that she has collected in her purse. She has a total of $12.10 in quarters, nickels and dimes. She has double the amount of quarters compared to nickels. The number of dimes is 5 less than twice the number of nickels. q: quarters d: dimes n: nickels Choose the correct verbal expressions for problems into a system of equations or inequalities.
x=2y
z+5=2y
0.25x+0.05y+0.10z=12.10
Explanation
Step 1
Let
She has a total of $12.10 in quarters, nickels and dimes.=
[tex]\text{total = 1}2.10[/tex]a quarter =0.25 usd
a nickels=0.05 usd
a dime=0.10 usd
x= amount of quartes
y=amount of nickels
z=amount of dimes
total=0.25x+0.05y+0.10 z
Step 2
She has double the amount of quarters compared to nickels, in other words you have to multiply the amount of nickes by 2 to obtain the amount of quarters
[tex]x=2y[/tex]Also, The number of dimes is 5 less than twice the number of nickels, in other words, you have to add 5 to the number of dimes to obtain twice the number of nickels
[tex]z\text{ +5=2y}[/tex]Step 3
total
[tex]0.25x+0.05y+0.10z=12.10[/tex]and that's all, now you have a system of 3 equations and 3 variables(x,y,z)
(a)A child has a box full of colored building blocks. She will choose one block without looking. The odds against choosing a blue block are 5/12 . What is the probability of choosing a blue block?
Ivanna is playing a role-playing game with her friends. She will roll dice to determine if her character unlocks a treasure chest. The probability of her character unlocking the treasure chest is 9/20 . Find the odds in favor of her character unlocking the treasure chest
(a) 12/17 is the probability of choosing a blue block.
b )The odds in favor of her character unlocking the treasure chest are 9/11
What is probability?
probability has to do with the chance of a particular thing happening.
a)
We need the probability of choosing a blue block,
Odds:
The odds of an event is the ratio of the probability of an event to the probability of its complement. In other words, it is the ratio of favorable outcomes to unfavorable outcomes.
The odds against choosing a blue block are 5/12 means. In 12 chances, 5 events will happen in which blue block will not be chosen and 12 events will happen in which blue blocks will be chosen.
So, the probability of not choosing the blue block is 12/17.
Probability of choosing blue block: complement of 5/12 which is equal to 12/17.
(b)
The probability of Ivanna character unlocking the treasure chest is 9/20
It means, in 20 total chances, 9 times an event will happen where Amanda's character unlocks the treasure chest while the rest 11 times, her character would not open treasure chest.
Favorable events: 9
Unfavorable events: 11
Hence, the odds in favor of her character unlocking the treasure chest are 9/11
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PLEASE HELP
Solve for m.
-6m = −9(2m - 4)
m =
Answer: m=3
That's the correct answer
Answer:
m = 3
Step-by-step explanation:
-6m = -18m +36
12m = 36
m = 3
What is the slope intercept equation for the following line.
to get the equation of any straight line, we simply need two points off of it, let's use those ones in the picture below
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-2)}}} \implies \cfrac{-4 +2}{2 +2} \implies \cfrac{ -2 }{ 4 } \implies - \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{(-2)}) \implies y +2= -\cfrac{ 1 }{ 2 } (x +2) \\\\\\ y+2=-\cfrac{ 1 }{ 2 }x-1\implies {\Large \begin{array}{llll} y=-\cfrac{ 1 }{ 2 }x-3 \end{array}}[/tex]
The triangles shown below are similar.Similar Help30Sole for
Here, we want to find the value of x
From the question, we have that the two triangles are similar
When two triangles are similar, the the ratio of their corresponding sides are equal
Thus, we have it that;
[tex]\begin{gathered} \frac{24}{30}\text{ = }\frac{8}{x} \\ \\ 24\text{ }\times\text{ x = 30}\times8 \\ x\text{ =}\frac{30\times8}{24} \\ x\text{ = 10} \end{gathered}[/tex]Solve for the angles of the triangle described below. Express all angles in degrees and round to the nearest hundredth.a = 6, b = 6,C = 8l
ANSWER:
A = 48.19°
B = 48.19°
C = 83.62°
STEP-BY-STEP EXPLANATION:
Given:
a = 6, b = 6, c = 8
We can calculate the angles by means of the law of cosines, just like this:
[tex]A=\cos^{-1}\left(\frac{b^2+c^2-a^2}{2bc}\right)[/tex]We apply in each case to calculate the 3 angles, as follows:
[tex]\begin{gathered} A=\cos^{-1}\left(\frac{6^2+8^2-6^2}{2\left(6\right)\left(8\right)}\right)=\cos^{-1}\left(\frac{2}{3}\right) \\ \\ A=48.19^{\circ\:} \\ \\ B=\cos^{-1}\left(\frac{6^2+8^2-6^2}{2\left(6\right)\left(8\right)}\right)=\cos^{-1}\left(\frac{2}{3}\right) \\ \\ B=48.19^{\operatorname{\circ}} \\ \\ C=\cos^{-1}\left(\frac{6^2+6^2-8^2}{2\left(6\right)\left(6\right)}\right)=\cos^{-1}\left(\frac{1}{9}\right) \\ \\ C=83.62^{\circ\:} \end{gathered}[/tex]Therefore, the angles are the following:
A = 48.19°
B = 48.19°
C = 83.62°
Find the greatest common factor of the following monomials50a^5b^2 6a^3b^4 12a^4b^4
From the question;
We are to find the greatest common factor of the following monomials
[tex]\begin{gathered} 50a^5b^2 \\ 6a^{3^{}}b^4 \\ 12a^4b^4 \end{gathered}[/tex]solution
By prime factorisation
[tex]\begin{gathered} 50a^5b^2\text{ = 2 }\times5\times5\times a\times a\times a\times a\times a\times b\times b \\ 6a^3b^4\text{ = 2}\times3\times a\times a\times a\times b\times b\times b\times b \\ 12a^4b^4\text{ = 2 }\times2\times3\times a\times a\times a\times a\times b\times b\times b\times b \end{gathered}[/tex]From the above factorisation
The Greatest common factor is
[tex]\begin{gathered} G\mathrm{}C\mathrm{}F\text{ = 2}\times a\times a\times a\times b\times b \\ G\mathrm{}C\mathrm{}F=2a^3b^2 \end{gathered}[/tex]Therefore the greatest common factor is
[tex]2a^3b^2[/tex]Score on last try: 0 of 10 pts. See Details for more. > Next question Get a similar question You can retry this question below 2 Write the following in inequality notation: 3 Inequality notation solution: No solution Question Help: M Message instructor Submit Question
Given the following:
[tex]\text{ (}\frac{2}{3},\infty)[/tex]Since both ends are in parenthesis ( ), therefore, it means that it is not equal to.
Writing this will be:
[tex]\text{ (}\frac{2}{3},\infty)\text{ = }\frac{2}{3}\text{ }<\text{ x }<\text{ }\infty[/tex]Question 2
I measure the length of a building 10 times, using a tape measure. Use the following observations to
determine the 50% Error of this sample.
26.583m
26.454m
26.858m
26.808m
26.819m
26.573m
26.466m
26.826m
26.872m
26.319m
O 0.1295
0.2024
0.3329
10 pts
0.1365
(Real-World Proportional Problems MC)
Three students have summer jobs. The proportional relationship between their pay and the hours they work is shown.
Student A:
Time (hours) 5 11
Pay (dollars) 63.75 140.25
Student B: $147.00 for 12 hours
Student C: The equation p = 12.5h, where p represents total pay and h represents hours worked
Which student is paid the most for 20 hours of work?
Student A paid the most for 20 hours of work.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
Given that;
Condition for A;
Time (hours) = 5 11
Pay (dollars) = $63.75 $140.25
Condition for B;
$147.00 for 12 hours.
Condition for C;
The equation, p = 12.5h
Where, p represents total pay and h represents hours worked
Now, For student A;
The amount of money raised for 1 hours of work will be;
⇒ $63.75 / 5
⇒ $12.75
So, The amount of money raised for 20 hours of work will be;
= $12.75 × 20
= $255
Hence, The amount of money raised for 20 hours of work = $255
For student B;
The amount of money raised for 1 hours of work will be;
= $147.00 / 12
= $12.25
Hence, The amount of money raised for 20 hours of work will be;
= $12.25 x 20
= $245
So, The amount of money raised for 20 hours of work = $245
For student C;
The amount of money raised for 1 hours of work will be;
p = 12.5h
p = 12.5 x 1
p = 12.5
Hence, The amount of money raised for 20 hours of work will be;
p = $12.5 x 20
p = $250
So, The amount of money raised for 20 hours of work = $250
Therefore,
Student A raised the least amount of money after walking 8 miles.
Learn more about the ratio visit;
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Answer: Student A, who is paid $255 for 20 hours of work
Step-by-step explanation: Since Student A gains $63.75 every 5 hours, and 5 x 4 = 20, then that means this $63.75 x 4 = $255 is logical and trustworthy
