Answer:
30
Step-by-step explanation:
a^2 + b^2 = c^2
(8sqrt(3))^2 + b^2 = 16^2
64 * 3 + b^2 = 256
192 + b^2 = 256
b^2 = 64
b = 8
The ratio of the lengths of the sides of this triangle is
8 : 8sqrt(3) : 16
which reduces to
1 : sqrt(3) : 2
This is the ratio of the lengths of the sides of a 30-60-90 triangle.
m<W = 30 deg
Expand the following:
a) x(x + 2)
b) x(2x - 5)
c) 2x(3x + 4)
d) 6x(x - 2)
Answer:
[tex]a. \: {x}^{2} + 2[/tex] [tex]b. \: 2 {x}^{2} - 5x[/tex] [tex]c. \: 6 {x}^{2} + 8x[/tex] [tex]d. \: 6 {x}^{2} - 12x[/tex]solution,
[tex]a. \: x(x + 2) \\ \: \: = x \times x + 2 \times x \\ \: \: = {x}^{2} + 2x[/tex]
[tex]b . \: x(2x - 5) \\ \: = x \times 2x - x \times 5 \\ \: \: = 2 {x}^{2} - 5x[/tex]
[tex]c. \: 2x(3x + 4) \\ \: = 2x \times 3x + 2x \times 4 \\ \: \: = 6 {x}^{2} + 8x[/tex]
[tex]d. \: 6x(x - 2) \\ \: \: = 6x \times x - 6x \times 2 \\ \: \: = 6 {x}^{2} - 12x[/tex]
Hope this helps...
Good luck on your assignment..
On piece of paper, graph f(x) =5• (0.4)^x
Answer:
When we use a graphing calc, we should see that we get A as our best choice.
Step-by-step explanation:
What is the quotient? StartFraction a minus 3 Over 7 EndFraction divided by StartFraction 3 minus a Over 21 EndFraction StartFraction negative (a minus 3) squared Over 147 EndFraction StartFraction (a minus 3) squared Over 147 EndFraction 3 –3
Answer:
Correct answer is
[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]
Step-by-step explanation:
Let us rephrase the given statement mathematically.
We are given the fractions as:
[tex]\dfrac{a-3}{7}[/tex]
to be divided by:
[tex]\dfrac{3-a}{21}[/tex]
To find:
[tex]\dfrac{a-3}{7}\div\dfrac{3-a}{21}[/tex]
Now, let us have a look at the division rule in fractions:
[tex]\dfrac{a}{b} \div \dfrac{c}{d}[/tex]
is equivalent to
[tex]\dfrac{a}{b} \times \dfrac{d}{c}[/tex]
In other words, we say that the second fraction [tex]\frac{c}{d}[/tex] is changed to [tex]\frac{d}{c}[/tex] and [tex]\div[/tex] is changed to [tex]\times.[/tex]
Now solving the given fraction by applying above rules:
[tex]\dfrac{a-3}{3}\div\dfrac{3-a}{21}[/tex]
[tex]\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{3-a}\\\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{-(a-3)}\\\Rightarrow \dfrac{1}{1}\times \dfrac{3}{-1}\\\Rightarrow -3[/tex]
So, correct answer is:
[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]
Answer:
d on edg
Step-by-step explanation:
taking test rn
This system of equations is shown on the graph: 2y − 4x = 6 y = 2x + 3 Which statement about the system is true?
Answer:
The system has infinity many solutions
Step-by-step explanation:
If it had no solutions there would be another like that does not go through it....if it was one solution it would have another like going through the other line....and since it has two lines that are on top of each other in the same point it's infinity solutions
Answer:
likely Option: DStep-by-step explanation:
If \$1000 is deposited into an account that earns 3.25\% simple interest per year, how much money will be in the account after 7 years? PLEASE SHHOW WORK
======================================================
Explanation:
The simple interest formula to use is
A = P*(1+r*t)
where,
A = account value after t years (original deposit + interest)
P = 1000 = amount deposited (principal)
r = 0.0325 = annual interest rate in decimal form
t = 7 = number of years
So,
A = P*(1+r*t)
A = 1000*(1+0.0325*7)
A = 1227.50
Side note: you've earned A-P = 1227.50-1000 = 277.50 dollars in total interest
Can someone help me out with these math questions?
You can pick one to answer or chose to answer both!
I’d appreciate the help thank you!
Evaluate: [tex]3-2^2+4*3+5[/tex]
Answer:
16
Step-by-step explanation:
Apply PEMDAS:
Solve the exponent, multiply from left to right, and then subtract and add from left to right.
[tex]3-2^2+4*3+5\\\\3-4+4*3+5\\\\3-4+12+5\\\\-1+12+5\\\\11+5\\\\\boxed{16}[/tex]
Answer: 16
Step-by-step explanation:
The important thing to remember here is the Order of Operations
The Order of Operations states that first solve Parentheses, then Exponents, then Multiplication and Division, then Addition and Subtraction.
There are no parentheses.
Exponents: 3 - 4+4*3+5
Multiplication and Division: 3 - 4 + 12 + 5
Addition and Subtraction:
-1+12+5
11+5
16
Hope it helps <3
in a box of chocolates, 1/5 of the chocolates contains nuts. the rest do not.
write down the ratio of the number of chocolates that contains nuts to the number of chocolates that do not contain nuts .
give you answer in the form 1: n
Answer:
the ratio would be 1:4
Step-by-step explanation:
ratio of those who has nuts:
1/5
ratio of those who dont:
1-1/5=4/5
one against another:
1/5 : 4/5 = 1:4 = with : without
IMAGES BELOW! Which graph shows the system of equations 4 x + y = 3 and 2 x minus 3 y = 3?
Answer:
1st Graph
Step-by-step explanation:
Simply use a graphing calculator and plug in the systems of equations into the graph. We then choose the closest-resemblanced graph.
Answer:
Its the first graph
Step-by-step explanation:
got it right on the test
What is the value of x?
Answer:
68 Degrees
Step-by-step explanation:
A triangle is 180 degrees. So,
Add 75 + 37 = 112
Subtract 112 from 180 = 68
Answer: 68°
Step-by-step explanation: To find the missing angle measure, represented by x, it's important to understand that the sum of the measures of the angles of a triangle is 180°
So to find the value of x, we can
setup the equation x + 75° + 37° = 180°.
Solving from here, we first simplify the left side of the equation.
So 75 + 37 is 112 and we have x + 112° = 180°
Next, to get x by itself, we subtract 112° from both sides.
On the left, the 112's cancel out and we are left with x.
On the right, 180° - 112° is 68°.
So x = 68°.
This means that the missing angle
measure in the triangle shown is 68°.
Two students have devised a dice game named “Sums” for their statistics class. The game consists of choosing to play odds or evens. Roll 2 3 4 5 6 7 8 9 10 11 12 P(roll) StartFraction 1 Over 36 EndFraction StartFraction 2 Over 36 EndFraction StartFraction 3 Over 36 EndFraction StartFraction 4 Over 36 EndFraction StartFraction 5 Over 36 EndFraction StartFraction 6 Over 36 EndFraction StartFraction 5 Over 36 EndFraction StartFraction 4 Over 36 EndFraction StartFraction 3 Over 36 EndFraction StartFraction 2 Over 36 EndFraction StartFraction 1 Over 36 EndFraction Each person takes turns rolling two dice. If the sum is odd, the person playing odds gets points equal to the sum of the roll. If the sum is even, the person playing evens gets points equal to the sum of the roll. Note that the points earned is independent of who is rolling the dice. If Jessica is challenged to a game of Sums, which statement below is accurate in every aspect in guiding her to the correct choice of choosing to play odds or evens? E(evens) will be more because there are more even numbers that result from rolling two dice. Therefore, Jessica should play evens. E(odds) will be more because the probability for each odd number being rolled is greater. Therefore, Jessica should play odds. E(evens) will be more because the value of the even numbers on the dice are more. Therefore, Jessica should play evens. E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
Answer:
(D)E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
Step-by-step explanation:
The table of the probability of rolling the sums is presented below.
[tex]\left\begin{array}{ccccccccccccc}$Roll&2&3&4&5&6&7&8&9&10&11&12\\\\$Prob&\frac{1}{36}&\frac{2}{36}&\frac{3}{36}&\frac{4}{36}&\frac{5}{36}&\frac{6}{36}&\frac{5}{36}&\frac{4}{36}&\frac{3}{36}&\frac{2}{36}&\frac{1}{36} \end{array}\right[/tex]
P(an even sum)
[tex]=\frac{1}{36}+\frac{3}{36}+\frac{5}{36}+\frac{5}{36}+\frac{3}{36}+\frac{1}{36} \\\\=\frac{18}{36}[/tex]
Therefore, P(an odd sum) [tex]=\frac{18}{36}[/tex]
Therefore, E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
Answer:
D /Even-odds
Step-by-step explanation:
just took test on edge 2020
Evaluate 3|−5| − 2|−2|. Question 22 options: −11 −19 11 19
Answer:
11
Step-by-step explanation:
3|−5| − 2|−2|
Absolute value means take the non-negative value
3 * 5 -2 * 2
15 - 4
11
Find the least common multiple of x2 + 4x + 3 and x2 + 7x + 12.
Answer:
( x+1) (x+3) (x+4)
Graphically represent the increase in emission of greenhouse gasses in India over a period of 5 years.
Answer:
Check it below
Step-by-step explanation:
According to GHG platform India, in the period between [2011-2015] there was a growth of emissions in tons of Carbon Dioxide. As it follows below.
The Energy sector is the segment that contributes the most with this, followed by the Agricultural and the Industries and the Waste.
Greg is designing a clock face. Using the center of the clock face as the origin, he keeps its diameter at 10 units. Match the positions of the hours on the clock face to their corresponding coordinates. 3 o'clock (0, -5) 6 o'clock (5, 0) 9 o'clock (0, 5) 12 o'clock (-5, 0)
Answer:
3 o'clock (5, 0)
6 o'clock (0, -5)
9 o'clock (-5, 0)
12 o'clock (0, 5)
Step-by-step explanation:
Given that diameter of clock = 10 units
We know that:
[tex]Radius =\dfrac{Diameter}{2}[/tex]
Radius = 5 units
The length of face will be equal to radius of clock i.e.
Length of face = 5 units
For the question, we need to visualize the clock time 3 o'clock, 6 o'clock, 9 o'clock and 12 o'clock on the coordinate xy axis.
Please refer to the attached graph to have a better understanding.
In every 3 hours the face will move [tex]90^\circ[/tex] i.e. one quadrant as per the location of clock faces.
At 3 o'clock the face will be on the positive x axis.
So coordinate (5, 0)
At 6 o'clock the face will be on the negative y axis.
So coordinate (0, -5)
At 9 o'clock the face will be on the negative x axis.
So coordinate (-5, 0)
At 12 o'clock the face will be on the positive y axis.
So coordinate (0, 5)
So, the answer is:
3 o'clock (5, 0)
6 o'clock (0, -5)
9 o'clock (-5, 0)
12 o'clock (0, 5)
Answer:
12 o'clock (0,5)
3 o'clock (5,0)
6 o'clock (0,-5)
9 o'clock (-5, 0)
Step-by-step explanation:
Two random samples were done to determine how often
people in a community go to the dentist.
The first sample surveyed 10 people as they entered
their workplaces. The first sample found that the mean
time between visits to the dentist was 7.5 months.
The second sample surveyed 50 people as they entered
the local grocery store. The second sample found that
the mean time between visits to the dentist was 18.1
months.
Complete question:
Two random samples were done to determine how often people in a community go to the dentist the first sample surveyed 10 people as they enter their workplaces. The first sample found that the mean time between visits to the dentist with 7.5 months. The second sample survey 50 people as they enter the local grocery store. The second simple found that the mean time between visits to the dentist is 18.1 months. Which statements are true check all that apply
1) The first sample is likely to be more representative of the population.
2) The second sample is likely to be more representative of the population.
3)The second sample will give a better representation because it is larger.
4) The first sample is not biased.
5) Community members probably visit the dentist about once every 18 months.
Answer:
2,3,5
Step-by-step explanation:
2) The second sample is likely to be more representative of the population, this is because the number of observations in the second sample is more than the number of observations in the first. And the more the sample observation, the more representative it is about the population.
3.) The second sample will give a better representation because it is larger, the size of the second sample is the sole factor which gives it a better representative edge than the first sample.
5.) Community members probably visit the dentist about once every 18 months, from the question, the avarage time visit of community members to the dentist is 18.1 months which is approximately 18 months, the mean gives the average value of a distribution
Pls, help. Trigonometry. Please answer in short sentences I'm not picking. Please answer a-i.
Answer:
a . See attachment
b. because we will find the distance from the bottom of the ladder to the base of the building.
c. sin 60 = opposite side / hypotenuse
d.sin 60 = x / 10
e . 8.66 ft =x
f. see attachment
i. cos 60° = adjacent side / hypotenuse
Step-by-step explanation:
a . See attachment
b. because cos 60° = adjacent side / hypotenuse, the hypotenuse is equal to the length of the ladder (10), and the adjacent side that we will find is the distance from the bottom of the ladder to the base of the building. not the height that the ladder reaches .
c. sin 60 = opposite side / hypotenuse
Because we will find the opposite side which is the height that the ladder reaches.
d.sin 60 = x / 10
e .
0.866025403 = x/10
10 (0.866025403) =x
8.66 ft =x
f. see attachment
i. cos 60° = adjacent side / hypotenuse
Because we will find the adjacent side which is the distance from the bottom of the ladder to the base of the building.
HELP ME PLEASE PLEASE
Answer:
x=0 , y=4
Step-by-step explanation:
3x - 3y = -12 - eq1
4x + 3y = 12 - eq 2
Add eq 1 and 2
3x - 3y + 4x +3y = -12 + 12
7x = 0
x = 0
By substituting the value of x in eq 2
4x + 3y = 12
4(0) + 3y = 12
3y = 12
y = 12 / 3
y = 4
Answer:
(x,y)=(24,-28)
Step-by-step explanation:
1. Multiply both sides by -1
3x+3y=-12
-4x-3y-=-12
2. Elimnate one variable by adding the equations
-x=-24
3. Change the signs
x=24
4. Susbstitue the value of x in the equation 3x+3y=-12
3 x 24 + 3 y = -12
y=-28
5. Check the solution by plugging in the values.
(x,y)=(24,-28)
How is this wrong? Reflect shape A in the x-axis.
Answer:
Your answer is wrong because you reflected it over the y-axis, not the x-axis. To find the correct answer, plot a triangle with vertices at (1, -1), (4, -1) and (4, -3). Note that we switch the sign of the y-coordinate when reflecting over the x-axis.
What are the factors of the function represented by this graph?
710
+6
+
+2
-10
-6
8
8
10
-2
4
-6
-8
+-10
A
(x-4) and (x-8)
B
(x-4) and (x+8)
C.
(x+4) and (x-8)
(x + 4) and (x+8)
Answer:
C. (x+4) (x-8)
Step-by-step explanation:
Take the graph for example both x values are -4 & positive 8
This recipe makes 6 portions of potato soup. Richard follows the recipe but wants to make 18 portions. Complete the amounts of each ingredient that he needs. Recipe: Serves 6 60 ml oil 80 g onions 450 g potatoes 600 ml milk
Answer:
1080 ml oil
240 g onions
1350 g potatoes
1800 ml milk
Step-by-step explanation:
18 ÷ 6 = 3
every ingredient x 3
60 x 6 = 360 , 360 x 3 = 1080 ml oil
80 x 3 = 240 g onions
450 x 3 = 1350 g potatoes
600 x 3 = 1800 ml milk
which best describes how the graph of g(x) = radical 25/9x
relates to the graph of the parent function, f(x)= radical x?
Answer:
Step-by-step explanation:
g(x) = radical 25/9x would be clearer if written as g(x) = radical (25/9)x. Note that radical (25/9) = (5/3).
The graph of g(x) = radical (25/9)x would have the same shape as that of g(x) = radical x EXCEPT that it would be stretched vertically by a factor of (5/3).
Answer: g(x) = radical 25/9x would be clearer if written as g(x) = radical (25/9)x. Note that radical (25/9) = (5/3).
The graph of g(x) = radical (25/9)x would have the same shape as that of g(x) = radical x EXCEPT that it would be stretched vertically by a factor of (5/3).
Step-by-step explanation:
Determine the intercepts of the line.
find the probability of rolling a seven first and then a four when a pair of dice is rolled twice
Answer:
1/72
Step by step:
The probability of rolling a seven is 1/6 as there are 36 combinations you can roll on two dice, and six of them add up to 7. The probability of rolling a 4 is 1/12 as there are 3 ways to roll a 4. Multiplying these together you get 1/72.
The question is in the picture attached
Answer:
≈ 10.7 ft
Step-by-step explanation:
We have 2 secants to a circle from an external point.
The product of the measure of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant.
let the internal part of the right secant be x , then
6(6 + x) = 4(4 + 12) = 4 × 16 = 64 ( divide both sides by 6 )
6 + x ≈ 10.7 ( subtract 6 from both sides )
x ≈ 4.7
length of pass = 6 + 4.7 = 10.7
HELP ME PLZ!!!!!!!! Brainliest will be given, THANK YOU!!!!
Answer:
Step-by-step explanation:
5*2=10, 10*2=20...
it is a geometric progression with ratio= 2
a11=a10*2=2560* 2=5120
Solve using derivatives.
I have no clue where to start on this I really need help please.
Please show steps and diagram.
Answer:
Below in bold.
Step-by-step explanation:
The surface area of the box
= x^2 + 4hx where x = a side of the square base and h is the height.
So x^2 + 4hx = 8
The volume of the box
V = x^2h
From the first equation we solve for h
4hx = 8 - x^2
h = (8 - x^2) / 4x
Now we substitute for h in the formula for the volume:
V = x^2 * (8 - x^2) / 4x
V = 8x^2 - x^4 / 4x
V = 2x - 0.25x^3
Finding the derivative:
V' = 2 - 0.75x^2 = 0 for max/mimn values
x^2 = 2/ 0.75 = 2.667
x = 1.633.
So the length and width of the base is 1.633 m and the height
= ( 8 - 2.667) / (4*1.633)
= 0.816 m
The maximum volume = 0.816 * 2.667 = 2.177 m^2.
The answers are correct to the nearest thousandth.
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 100 degrees and the low temperature of 70 degrees occurs at 5 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. Assume the next low is 24 hours later.
Answer:
The function for the outside temperature is represented by [tex]T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right][/tex], where t is measured in hours.
Step-by-step explanation:
Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:
Amplitude
[tex]A = \frac{100\º-70\º}{2}[/tex]
[tex]A = 15\º[/tex]
Mean temperature
[tex]\bar T = \frac{70\º+100\º}{2}[/tex]
[tex]\bar T = 85\º[/tex]
Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:
[tex]T(t) = \bar T + A \cdot \sin \left[2\pi\cdot\frac{t-6\,h}{\tau} \right][/tex]
Where:
[tex]\bar T[/tex] - Mean temperature, measured in degrees.
[tex]A[/tex] - Amplitude, measured in degrees.
[tex]\tau[/tex] - Daily period, measured in hours.
[tex]t[/tex] - Time, measured in hours. (where t = 0 corresponds with 5 AM).
If [tex]\bar T = 85\º[/tex], [tex]A = 15\º[/tex] and [tex]\tau = 24\,h[/tex], the resulting function for the outside temperature is:
[tex]T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right][/tex]
PLZ HELP PLZ
I WOULD APPRECIATE IT PLZ
19 and 20
let given points be
(x1,y1)=(-3,-3)
and(x2,y2)=(3,1)
equation of given line ,
(y-y1)= ((y2-y1)/(x2-x1))×(x-x1)
therefore, 2x-3y+3=0.........(i)
comparing (i ) with ax+by+c=0 we get
a=2
b= -3
c=3
then the line parallel to (i) is
ax+by+k=0 where k = -bc
that is, 2x-3y+9=0 is the required equation
Answer:
19. y = 2/3x - 10/3
20. y = -3/2x - 4
Step-by-step explanation:
First off, we need to find the equation of the line shown. There are two coordinates given. The slope of the line is (1 - -3) / (3 - -3) = 4 / 6 = 2/3. The line obviously intersects the y-axis at -1, so the equation of the line is y = 2/3x - 1.
19. If a line were to be parallel to the given line, the line would have to have a slope of 2/3. So, we have y = 2/3x + b.
To solve for b, all you need to do is substitute the coordinates given, (2, -2), and solve.
-2 = (2/3) * 2 + b
b + 4/3 = -2
b = -6/3 - 4/3
b = -10/3.
So, the equation of the line is y = 2/3x - 10/3.
20. If a line were to be perpendicular to the given line, the line would have a slope that is the negative reciprocal of the given line's slope. The slope would be -3/2. So, we have y = -3/2x + b.
To solve for b, once again, put in the given coordinates, (-4, 2), and solve.
2 = (-3/2) * (-4) + b
b + 6 = 2
b = -4
So, the equation of the line is y = -3/2x - 4.
Hope this helps!
Given f(x) = 3x - 1 and g(x)=2x-3, for which value of x does g(x) = f(2)?
2
O X-2
xe
O X4
Answer:
i hope it will help you...