Answer:
arccos(51/100)
Step-by-step explanation:
By the Law of Cosines,
[tex]a^2 = b^2 + c^2 - 2bc \cos A \\ \\ a^2 - b^2 - c^2=-2bc \cos A \\ \\ \cos A=\frac{b^2 + c^2 - a^2}{2bc} \\ \\ m\angle A=\arccos \left(\frac{b^2 + c^2 - a^2}{2bc} \right) \\ \\ =\arccos \left(\frac{10^2 + 5^2 - 8^2}{2(5)(10)} \right) \\ \\ =\arccos(51/100)[/tex]
Simplify each expression using the imaginary unit i . 2 √-24+6 .
The simplification of the given expression 2 √-24+6 is 9.8 i + 6.
What is a complex number?Complex numbers are helpful in finding the square root of negative numbers.
A complex number is the sum of a real number and an imaginary number.
Given the expression,
2 √-24+6
Now,
2 √-24+6 = 2√(-1 × 24) + 6
⇒ 2 √(-1) × √24 + 6
Since √(-1) is an imaginary number and is denoted by "i".
So,
2 √(-1) × √24 + 6 = 2i × √24 + 6
⇒ 2√24 i + 6
⇒ √4 × √24 i + 6
⇒ √(4×24) i + 6
⇒ √96 i + 6
⇒ 9.8 i + 6
Hence "The simplification of the given expression 2 √-24+6 is 9.8 i + 6".
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5. Use the expression to answer th
-18-(-x)
Part A: Jerry claims this expression is equivalent to -18 + x. Do you agree or disagree? Explain.
Part B: Jerry claims this expression is equivalent to x-18. Do you agree or disagree? Explain.
Answer:
part A agree because two negatives cancel each other making a positive
part B agree x is still positive and 18 is still negative
ESTIMATING RESULTS The figures show the number of taxpayers and the federal tax revenue for the United States in 2018.
Estimate the United States federal tax revenue per taxpayer.
US TAXPAYERS
122,176,626
T
US FEDERAL TAX REVENUE
$3,307,673,720,131
Answer:
$27,072.88
Step-by-step explanation:
$3,307,673,720,131 ÷ $122,176,626
Write the function rule g(x) after the given transformations of the graph of f(x) = 9x.
reflection in the x-axis; vertical compression by a factor of 1/3
g(x) = []
On reflecting f(x) = 9x in the x-axis and vertical compression by a factor of 1/3 we get the transformation g(x) where, g(x) = -3x
What is transformation of a function?Transformation of the function means that the curve representing the graph either moves to the left or right or up or down or expansion , compression or reflection of graph happens.
Rules for reflection over x axis : for an curve y = f(x) , replace y by -y and keep x as it is, we get -y = f(x) or y = - f(x)
Rules for vertical compression by a factor α : y becomes αy .If f(x) is compressed by a factor of 1/2 the the transformations becomes 1/2(f(x))
Given function is f(x) = 9x
When we reflect f(x) over x axis then the transformations becomes some h(x) where h(x) = -f(x) =-9x
Now we want to vertically compress it by a factor of 1/3 , then this transformation will become g(x) = 1/3(h(x)) = 1/3(-9x) =(-9/3)x =-3x
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2. Write and simplify an expression showing how many times farther Neptune is from the Sun
than Mercury. Write the result in scientific notation. (2 points)
The sun is [(1.974) * (10^1)] times farther from Neptune, than Mercury, mentioned in scientific notation.
As per the question statement, there is no information provided about the actual distance of the sun from Neptune, or from Mercury. Hence, let us consider that the actual distance of the sun from Neptune is [4.5 * (10^9)] kilometers, while that from Mercury is [2.28 * (10^8)] kilometers.
We are required to calculate the number of times, which the sun is times farther from Neptune, than Mercury, and express our desired answer in proper scientific notation.
Considering that, the sun is "x" times farther from Neptune, than Mercury, we can state that,
[{2.28 * (10^8)} * x] = {4.5 * (10^9)}
or, x = [{4.5 * (10^9)}/{2.28 * (10^8)}]
or, x = [{4.5 * 10 * (10^8)}/{2.28 * (10^8)}]
or, x = [{45 * (10^8)}/{2.28 * (10^8)}]
or, x = (45/2.28)
or, x = 19.7368
or, x = 19.74
or, x = [(1.974) * (10^1)]
Scientific Notation: In Mathematics, Scientific Notation is an efficient method of expressing a number, which is too large or too small, by using the form of power of (10).To learn more about Scientific Notation, click on the link below.
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Given the function f(x) = -x² - x + 7, find each of the following.
f(1), f(-7), f(y + 2)
f(1) = 7
f(-7)= -35
f(y + 2) =
(Simplify your answers. Type an integer or a fraction.)
...
The value of f (1) is 5.
The value of f (-7) is - 35.
The value of f (y + 2) is (-y²- 5y + 1).
What is Function?
A relation between a set of inputs having one output each is called Function.
The function is given as;
⇒ f(x) = -x² - x + 7
Now, To find value of f (1), substitute the value of x = 1 in given function and then calculate as;
⇒ f(x) = -x² - x + 7
⇒ f (1) = - (1)² - 1 + 7
⇒ f (1) = - 1 - 1 + 7
⇒ f (1) = 5
Hence, The value of f (1) is 5.
To find value of f (-7), substitute the value of x = -7 in given function and then calculate as;
⇒ f(x) = -x² - x + 7
⇒ f(-7) = -(-7)² - (-7) + 7
⇒ f(-7) = -49 + 7 + 7
⇒ f(-7) = - 35
Hence, The value of f (-7) is - 35.
To find value of f (y + 2), substitute the value of x = y+2 in given function and then calculate as;
⇒ f(x) = -x² - x + 7
⇒ f(y + 2) = -(y + 2)² - (y + 2) + 7
⇒ f(y + 2) = - (y² + 4y + 4) - y - 2 + 7
⇒ f(y + 2) = - y² - 4y - 4 - y - 2 + 7
⇒ f(y + 2) = - y² - 5y + 1
Hence, The value of f (y + 2) is (-y²- 5y + 1).
So, The value of f (1) is 5.
The value of f (-7) is - 35.
The value of f (y + 2) is (-y²- 5y + 1).
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Solve for u.
−7+4u = − 35
for the equation - 7 + 4 u = - 35, we get the value of u after solving it as - 7.
We are given the equation:
- 7 + 4 u = - 35
We need to solve the equation for u.
- 7 + 4 u = - 35
Add 7 to both the sides, we get that:
- 7 + 4 u + 7 = - 35 + 7
4 u = - 28
Divide both the sides by 4, we get that:
4 u / 4 = - 28 / 4
u = - 7
Therefore, for the equation - 7 + 4 u = - 35, we get the value of u after solving it as - 7.
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Brainliest and 40 points! Hurry!
Answer: 6
Step-by-step explanation:
What is another way to name line \ellℓell?
Since no line segment or reference diagram is provided in the question statement, considering ourselves a line as shown in the picture attached hereby, another name of the line "l" is UM.
As per the question statement, we are required to determine another name of the line, but no no line segment or reference diagram is provided, on whose basis, we were supposed to answer. Hence, we consider a line ourselves, as shown in the picture attached hereby, and then try to answer as per the question statement,
From the picture attached hereby, we can clearly see that, although the line "l" is a ray, it has two points "U" and "M" at the extremes, i.e., points U and M lie on the line. Hence, line "l" can be referred to as "UM" also.
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What is the solution to this inequality?
x/12 + 3 < 7
OA. x≤ 48
OB. x≤ 81
OC. x ≥ 48
O D. x≥ 81
x/12 + 3 < 7 = x<48 this is the only one i can do because i cant do the others sorry
A system of equations is shown.
{9x - y = 4
9x - y = -4
Which statement about the system of equations is true?
Answer:
No solution.
Step-by-step explanation:
There is not an number that I can put in for x and y and get the answer 4 and -4.
Answer:
No solutions
Step-by-step explanation:
Given system of equations:
[tex]9x - y = 4 \\ 9x - y = -4[/tex]
Let us substitute the equation 9x - y = 4 into the second equation:
[tex]\implies 9x - y = -4[/tex]
[tex]\implies 4 = -4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [9x - y} = 4} ][/tex]
But 4 = -4 is not possible, as they are opposite integers. Since 4 ≠ -4, there are no solutions for the given system of equations.
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Suppose J is between H and K. Use the segment Addition Postulate to solve for x. Then find the length of the segment.
HJ=4x+9, Jk=3x+3, HK=33
The length of the segment when J is between H and K will be HJ = 21 and JK = 12.
How to illustrate the information?From the information given, J is between H and K and we want to use the segment addition Postulate to solve for x.
It should be noted that:
HJ=4x+9,
Jk=3x+3,
HK=33
Therefore, we will equate the values. This will be:
4x + 9 + 3x + 3 = 33
7x + 12 = 33
Collect like terms
7x = 33 - 12
7x = 21
Divide
x = 21 / 7
x = 3
HJ=4x+9, = 4(3) + 9 = 21
Jk=3x+3 = 3(3) + 3 = 12
Therefore, the length of the segment when J is between H and K will be HJ = 21 and JK = 12.
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thats it, ima be also posting more if i dont get the question
The equation of this straight line is y = 50x + 100.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
How to determine the equation?In order to determine the equation from this graph of a linear equation, we would find the slope of the straight line by using this formula as follows:
[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Slope, m = 100/2
Slope, m = 50.
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m is the slope.c is the intercept.At point (4, 300), we have:
y = mx + c
300 = 50(4) + c
300 = 200 + c
c = 300 - 200
c = 100.
Therefore, the equation of this straight line is y = 50x + 100.
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Solve each equation. Check your answers.
ln (t-1)²=3
t = 5.48 in ln (t - 1)² = 3, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
In ln ( t -1 )² = 3, by property of logarithm ( [tex]log_b(a)^m=m(log_b(a))[/tex]),
=> 2 ( ln (t -1) ) = 3
=> ln (t - 1) = [tex]\frac{3}{2}[/tex]
=> t - 1 = [tex]e^\frac{3}{2}[/tex]
=> t = [tex]e^\frac{3}{2}[/tex] + 1 = 4.48 + 1 = 5.48
Hence, t = 5.48 in ln (t - 1)² = 3, by properties of logarithm.
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An elephant charged 13.3 meters in 15 seconds. At this rate, how far would the elephant move if it could charge for one minute? (15 seconds = 1\3 minute)
The elephant can move 53.2 meters if it is charged for 1 minute.
Given,
The time that the elephant charged = 15 seconds
The distance that the elephant can travel by this charge = 13.3 meters
We have to find the distance moved by the elephant if it is charged for 1 minute:
That is,
15 seconds = 13.3 meters
Then,
1 minute (60 seconds) = x
Therefore;
15 × x = 13.3 × 60
x = (13.3 x 60) / 15
x = 798 / 15
x = 53.2
That is, the elephant can move 53.2 meters if it is charged for 1 minute.
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Using the scale:
1/4 in = 2 ft, what would be the real-life measurement of an object that measures 4 inches on a scale drawing?
An object that appears to be 4 inches on a scale illustration actually measures 32 feet.
What is drawing to scale?A representation of a real thing with correct sizes that has been scaled back or blown up slightly (called the scale).
The scale is represented by the length in the drawing, a colon (":"), and then the actual length that corresponds to it.
A measurement of 150 mm on the picture would be 1500 mm on the actual horse since this drawing has a scale of "1:10," meaning that everything represented with a size of "1" would have an the actual world, a size of "1" corresponds to a size of "10."
based on the facts provided;
4 in =1/4 in 2ft
= 16*2 ft
= 32 ft
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emir is standing in a treehouse and looking down at a swingset in the yard next door. the angle of depression from emir's eyeline to the swingset is 30.26°, and emir is 14 feet from the ground. how many feet is the base of the tree from the swingset? round your answer to the nearest foot.
The distance between base of tree and swing set is 24 feet.
We are given the angle of depression and the vertical height. Joining the three points, which are top and base of tree and swing set forms a right angled triangle. The height of tree will be perpendicular of triangle and base will be the distance between base of tree and swing set.
The angle at the swing set will be equal to 30.26°, as alternate angles are equal.
So, the angle formed can be related with perpendicular and base by -
tan theta = perpendicular ÷ base
Keep the values in formula to find the value of base
Base = perpendicular ÷ tan theta
Base = 14 ÷ tan 30.26°
Base = 14 ÷ 0.5834
Performing division
Base = 24
Hence, the distance between base of tree and swing set is 24 feet.
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Amir has 3 jars of sweets
Jar a contains 205 sweets
Jar c contains 175 sweets
Jar a has the most sweets and Jar c has the least of sweets how many sweets could be in jar b explain how you know this
The sweets in jar B in the box with Amir will be 190 sweats.
How to calculate the number?From the information, Jar A contains 205 sweets. Jar c contains 175 sweet. Also, jar a has the most sweets and Jar c has the least of sweets.
The deets in jar B will be:
= (205 + 175) / 2
= 380 / 2
= 190
Therefore, the sweets in jar B in the box with Amir will be 190 sweats.
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Solve. 3(x+3)³/₄=81
x = 78
The equation given is
3[tex](x + 3)^{3/4}[/tex]= 81
first we will divide 3 of the right side to left side number which is 81
i.e 81/3 = 27
So we get the equation
[tex](x + 3)^{3/4}[/tex] =27
We can also write the equation as
[tex](x + 3)^{3/4}[/tex]= [tex]3^{3}[/tex]
[tex][(x + 3)^{1/4]^{3}[/tex]= [tex]3^{3}[/tex]
So from, this we get
[tex](x + 3)^{1/4}[/tex] = 3
Now we have to side with the multiply both power of four(4)
[tex][ (x + 3)^{1/4}]^{4}[/tex]= [tex]3^{4}[/tex]
we get
x + 3 = 81
x = 78
So the value of x is 78.
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Can ya'll help me with this please?
Answer: C.
Step-by-step explanation:
4. A standard die is rolled four times. What
is the probability that it shows a number
divisible by three all four times?
36,2 B
A 1/3
1
81
C
Apply
6
11/22
Answer:
C - 1/81
Step-by-step explanation
There are 6 sides on a standard die (1, 2, 3, 4, 5, 6). Out of these numbers, only 3 and 6 are divisible by 3. Therefore, 2/6 numbers would be divisible by 3. As the die is rolled 4 times, we multiply 2/6 4 times - (2/6)(2/6)(2/6)(2/6) to get 1/81. The probability that the die shows a number divisible by three all four times is 1/81. Hope that helps!
my dog spent 4 days in the veterinary hospital.I spent 1585 dollars for the surgery,16.25. a day for board, and 49.75 for medicine.what is my total bill
Answer:
1651
Step-by-step explanation:
Add up the numbers, and you get your answer. [tex]1585+16.25+49.75=1651[/tex]
6x + 9 +x+7
7x + 4 - 2x + 14
4+ 7x -x + 10
12+3x + 4x + 6
5x + 18 +2x - 2
x + 20 +4x -2
10x - 3x + 8 +6
12x + 10-5x + 8
12+3x+4x+6
Combining like terms
Matching Game
Set 1
Unmatched
Math idea galaxy
Directions: Simplify the
expression. Then, drag
each card next to its
matching pair. There
will be one without a
match.
565x + 2043
I am writing this extra because the app says the answer is to short :)
Use the Change of Base Formula to rewrite each expression using common logarithms.
log₄9
The logarithmic expression changed by the base formula is ㏒₁₀9/㏒₁₀4.
What s defines as the logarithmic functions?A number's logarithm is the exponent that a fixed value known as the base should be raised in order to generate that number. For example, because 1000 is 10 to a third power, the log of 1000 to base 10 is 3.
The y-intercept does not exist.A vertical asymptote is x = 0. *Note: An asymptote is a line which a graph approaches as the absolute value of x or y increases.There is no horizontal asymptote for a logarithmic function.The x-intercept is equal to one.The function is expanding across the domain.The function decreases out over domain if the base between 0 and 1.Some rule of the logarithmic functions are-
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, as per the sated condition of the log function;
= log₄9
Now, use the Base Rule to re-write the expression;
= ㏒ₓ9/㏒ₓ4
or, for the base 10 this could be written as;
= ㏒₁₀9/㏒₁₀4
Therefore, the given logarithmic expression converted by the base formula is ㏒₁₀9/㏒₁₀4.
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Work out the median of these numbers:
7, 24, 3, 37, 14, 32
Please help! What is the range of the function shown in the graph below?
Step-by-step explanation:
the range of a function is the interval or set of all valid y (function result) values.
so, what values is this function creating ?
we see that y never gets larger than -4.
but it will clearly go and go and go ... further down without any limit.
so, the range is
-infinity < y <= -4
96 multiplyed by 12 multyplied by 6
Answer: 6912
Step-by-step explanation:
96x12=1,152
1,152x6=6912
Use natural logarithms to solve each equation.
e²x=12
In [tex]e^{2x}=12[/tex], x = 1.24, by the properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
In [tex]e^{2x}=12[/tex], taking natural logarithm on both side.
=> [tex]log_e(e^{2x})=log_e(12)[/tex]
=> 2x = 2.48 (approx)
=> x = 1.24
Hence, In [tex]e^{2x}=12[/tex], x = 1.24, by the properties of logarithm.
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Which expression is equivalent to quantity y raised to the negative second power times z raised to the third power end quantity over quantity z raised to the negative fourth power times y raised to the fifth power end quantity all raised to the negative second power?
The simplification of the given expression using laws of Indices is :
[tex]\frac{y^{14}}{z^{14}}[/tex]
How to use Laws of Indices?
We want to simplify the expression y raised to the negative second power times z raised to the third power end quantity over quantity z raised to the negative fourth power times y raised to the fifth power end quantity all raised to the negative second power.
The above can be expressed as :
[(y⁻² * z³)/(z⁻⁴ * y⁵)]^(-2)
Collecting like terms and When two terms that are divided have the same base and different exponents, we keep the base and subtract the exponents, hence :
= [(y⁻² * z³)/(z⁻⁴ * y⁵)]²
= [(z⁻⁴ * y⁵)/(y⁻² * z³)]²
= [(z⁻⁴/z³) x (y⁵/y⁻²)]²
= [z^{-4-3} x y^{5+2}]²
= [z^{-7} x y^{7}]²
Then both numerator and denominator exponents multiply by 2, hence the equivalent expression is :
= [tex][\frac{y^{7}}{z^{7}}]^{2} = \frac{y^{14}}{z^{14}}[/tex]
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is -3.5 a whole number integer or ratinoal
Answer:
Rational
Step-by-step explanation:
its not a whole number