Answer:
7.07070707E15
Step-by-step explanation:
prove that tan² 20° + tan² 40° + tan² 80° = 33
nine fewer than half a number is five more than fout times the number
If a-b=5 and a^2 - b^2= 45 find the value of a+b
Answer:
(a + b) = 9
Step-by-step explanation:
The a² - b² formula is also known as "the difference of squares formula"
It can be decomposed as follows:
a² - b² = (a - b)(a + b)
Since we are given a + b = 5 and a² - b² = 45
we have
45 = 5 (a + b)
Dividing by 5 both sides
45/5 = (a + b)
9 = (a + b)
or,
(a + b) = 9
HELP FAST PLEASE
Question one
The grid above shows the graph of the parent function
f(x)=IxI
and a translated functions graph.
Write the equation for the translated graph.
If the equation of the parent graph, shown in the reference picture attached hereby, is [f(x) = |x|], then the equation of the translated graph will be [f(x) = (|x-2| + 1)].
Along with the question statement, we are provided with a reference attachment, which is a grid, consisting of two graphs, and the equation of the parent graph is [f(x) = |x|].
We are required to calculate the equation of the other graph, which is a translated version of the parent graph.
From the reference grid, we can clearly see that, the vertex of the parent graph is at the origin (0, 0) while that of the translated graph is at (-2, 1), i.e., the vertex translated by 2 units to the left along the x-axis and then, 1 unit upwards along the y-axis. And this translation will be followed by every point of the daughter graph.
Hence, the equation of the translated graph will be [f(x) = (|x-2| + 1)].
Translation (Cartesian geometry): In Euclidean geometry, translation is a process which moves every point of a figure, shape or space by the same distance in a given direction.To Learn more about Translation, click on the link below.
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you approve your time running a course by 5 Seconds in week one, by three seconds in week two in by four seconds in week three what is the average weekly change in your running time?
The average weekly change in your running time bases on the information will be 4 seconds.
How to illustrate the information?It should be noted that the mean simply means the average of the numbers that are given.
It should be noted that in this case, the person approve your time running a course by 5 seconds in week one, by three seconds in week two in by four seconds in week three.
Therefore, the average weekly change in your running time will be:
= Total seconds / Number of weeks
= (5 + 3 + 4) / 3
= 12 / 3.
= 4 seconds
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Determine whether each function is an example of exponential growth or decay. Then find the y -intercept. y=0.1(10) x
The statement employs that Because b > 1, the function shows exponential growth. We calculate the y-intercept by substituting 0 for x and afterward solving for y.
Exponential growth is defined as:Exponential growth is the process by which quantity rises over time. It happens when the instantaneous rate of alteration of a quantity with regard to time is proportionate to the amount itself.
Apply the exponential growth formula:As a result, the exponential growth formula is: x(t) = 10,000 * (1 + 0.05)t = 10,000 * 1.05t. Here is the amount of years that have gone since 2019. In our situation, t = 11 should be used for the year 2030 because that is the lot of years between 2030 as well as the initial year 2019.
According to the given data:y=0.1(10)ˣ
y = 0.1(10)⁰
y = 0.1(1)
y = 0.1
Because b > 1, the function shows exponential growth. We calculate the y-intercept by substituting 0 for x and afterward solving for y.
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Find each real root. √0.49
The real root of the number √0.49 is given by 0.7.
We are given the expression:
√0.49
We need to find the root of the number.
For this, we will make the factors of the number and then solve the expression accordingly.
First, we know that 0.49 can also be written as 49 / 100
Now, we also know that:
49 = 7 × 7 and 100 = 10 × 10
So, the square root of 49 will be 7 and 100 will be 10.
So, we get the root of the number as:
√0.49 = 7 / 10
√0.49 = 0.7
Therefore, the real root of the number √0.49 is given by 0.7.
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Factor each expression completely. 4 x³ - 8 x²+16 x
Solve for x by factoring. Obtain the roots of the expression. Solve the quadratic form and obtain the complex solutions. Equate the expression to zero and divide by the common factor 4, and factor out x.
4x^3-8x^2+16x
4x^3-8x^2+16x = 0
x(x^2-2x+4) = 0
x =0
x^2-2x+4 = 0
by quadratic formula,
x = (-b±√(b²-4ac))/(2a)
x= (--2±√((-2)²-4(1x4))/(2)
x = (2±√(4-16))/(2)
x = (2±√-12)/(2)
Let √-12 = i , a complex root
x = (2±i)/(2)
x = (2+i)/(2)
x = (2-i)/(2)
Thus,
x = 0
x = (2+i)/(2)
x = (2-i)/(2)
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Given f(x) = 4x + 1 and g(x) = 2x² +3 , find (f ◦ g)(x)
Answer:
8x^2 + 13.
Step-by-step explanation:
(f o g)(x) is found by replacing the x in f(x) by g(x).
= 4(2x^2 + 3) + 1
= 8x^2 + 12 + 1
= 8x^2 + 13.
The sum of the measures of the angles of any triangle is 180 degrees. In triangle ABC, angles A and B have the same measure, while the measure of angle C is 81 degrees larger than each of A and B. What are the measures of the three angles?
The measure of the angles are ∠A = 33° , ∠B = 33° and ∠C = 114°
Supplementary angles are the angles whose sum is equal to [tex]180^{o}[/tex].
According to the question we have been given that the three angles that is ∠A , ∠B and ∠C are the supplementary angles that is their sum is 180°.
Let the measure of ∠A = x = ∠B
and the measure of ∠C = 81 + x
Now,
∠A + ∠B + ∠C = 180°
Putting the required values we get
x° + x° + (81 +x )° = 180°
2x° + 81° + x° = 180°
3x° = 99°
x° = 33°
Hence the measure of three angles are
∠A = 33° , ∠B = 33° and ∠C = 114°
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Can someone please help me really quick
The amount of the shed that Jack would have built when Kyle finishes the shed is 8/25.
How much shed would Jack have built?A fraction is a non- whole number that consists of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2.
When Kyle finishes building the shed, he would have finished building 1 of the shed. In order to determine the amount of shed Kyle needs to build in order to build one shed, divide 1 by 5/8.
1 ÷ 5/8
= 1 x 8/5 = 8/5
The amount of shed that Jack will have built when Kyle finishes the shed is:
8/5 x 1/5 = 8/25
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a scale drawing of a school bus has a scale of 1/2 in to 5 ft. if the length of the school bus is four and a half inches on the scale drawing, what is the actual length of the bus?
Answer:
45 feet
Step-by-step explanation:
Set up Ratios
1/2 in/5 ft = 4 1/2 in/x
Solve for x by cross-multiplying:
[tex]\frac{1/2}{5}[/tex] times [tex]\frac{4 1/2}{x}[/tex]
4 1/2 times 5 = 22 1/2
1/2 times x = 1/2x
22 1/2 = 1/2x
45 = X
Therefore the actual length of the bus is 45 feet.
Hope it helps :)
What is 3/8 as a mixed number
Answer:
3/8 is a proper fraction which means it can't be written as a mixed number
Step-by-step explanation:
If the numerator is bigger than the denominator then you can convert it to a mixed number.
Answer:
3/8 is equal to 0.375
i dont think this can be turned into a mixed number becuase the fraction isn't over 8
example: 18/8 can be changed into the mixed number 2 3/8
Step-by-step explanation:
Three integers have a mean of 9, a median of 12 and a range of 13.
Find the three integers.
If three integers have a mean of 9, a median of 12, and a range of 13, then the three integers are 1, 12, and 14.
As the median is the value that's exactly in the center of a set of values, one of the three integers is 12.
Considering the first and third integers to be x and y, the range can be given as
x - y = 13
x = 13 + y
As mean can be given as,
x + 12 + y / 3 = 9
Putting x = 13 + y in this equation,
13 + y + 12 + y / 3 = 9
25 + 2y = 9 × 3
25 + 2y = 27
2y = 27 - 25
2y = 2
y = 2/2
y = 1
As,
x = 13 + y
x = 13 + 1
x = 14
Hence the three integers are calculated to be 1, 12, and 14.
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Write each expression in simplest form. 5(x²/₃)⁻¹
The given expression can be written in its simplest form by using the rule of negative exponent.
As the negative exponent is applied to the second term, which also has a power, we will first multiply the powers. As we know that (x^n)^m=x^nm, hence,
(x^2/3)^-1=x^2/3*-1=x^-2/3
Now the expression will become 5x^-2/3
Now solving the second term for the negative exponent, the rule of negative exponent states that when a base term has a negative exponent, the negative sign can be solved by inversing the base term. We know that x^-a=1/x^a, therefore
5x^-2/3=5/x^2/3
The simplest form of the expression is 5(x²/₃)⁻¹=5/x^2/3
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A committee consisting of 6 men and 4 women are to be formed from 58 men and 42 women. In how many ways can this be done?
Answer: 21
Step-by-step explanation:
what is wrong with 4x3 7/10 = 12 7/10
The value of the fraction expression 4 x 37/10 is 14 8/10 not 12 7/10
How to determine the mistake in the computation?The equation is given as:
4 x 3 7/10 = 12 7/10
Remove the result
So, we have
4 x 3 7/10
Express 3 7/10 as an improper fraction
So, we have
4 x 37/10 = 4 x 37/10
Evaluate the product of 4 and 37
So, we have
4 x 37/10 = 148/10
Evaluate the quotient of 148 and 10
So, we have
4 x 37/10 = 14 8/10
Hence, the value of the fraction expression 4 x 37/10 is 14 8/10 not 12 7/10
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The sum of 333 consecutive even numbers is 270270270.
What is the first number in this sequence?
The numbers are 88, 90 and 92. So the first number in this sequence is 88.
Given that
The sum of 3 consecutive even numbers is 270 .
What is consecutive numbers?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.Even numbers are numbers that end with 0, 2, 4, 6 or 8. The examples of consecutive even numbers are:0, 2, 4, 6, 8, 10, 12, Odd numbers are numbers that end with 1, 3, 5, 7 or 9.Let the numbers be n, n+2, and n+4.
n+(n+2)+(n+4) = 270
3n+6 = 270
3n = 264
n = 264/3
n=88
First number = x = 88
Second number = x + 2 = 88 + 2 = 90
Third number = x + 4 = 88 + 4 = 92
Therefore, the first number is 88.
Hence, the numbers are 88, 90 and 92.
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Solve each system of equations using a matrix equation. Check your answers.
[300x-y=130 200x+y=120]
Just by adding the second row to the first one in the matrix, we can see that the solution of the system of equations is x = 0.5 and y = 20.
How to solve the system of equations?
Here we have the system of equations:
300x - y = 130
200x + y = 120
And we want to solve it using a matrix equation. Remember that we could add the two rows, subtract them, etc to remove one of the variables.
Here is really simple to see that if we add the two rows (or the two equations, depending on how you see the system) the variable y will be removed.
Then we can add the second row to the first one to get.
(300x + 200x) + (-y + y) = (130 + 120)
Now our matrix will look like:
500x + 0y = 250
200x + y = 120
With the first row we can find the value of x, it just is:
x = 250/500 = 0.5
And with taht we can find the value of y:
200*0.5 + y = 120
100 + y = 120
y = 120 - 100 = 20
Just by adding two rows, we can see that the solution of the system of equations is x = 0.5 and y = 20.
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9-(3x2)+8
how do i write this in parenthasies
What is 6 to the power of 2 subtracted by 3 (4)
Answer:
33
Step-by-step explanation:
You do 6 x 2 and you get 12 times that by 3 and get 36 and subtract that by 3 and get 33.
Answer:
Step-by-step explanation:
6 x 6 = 36
3(4) is just 3x4 which is 12
so 36 - 12 = 24
DB bisects AC at point E.
AE = 4x + 2 and AC = 40. Find x.
1) Write the equation that you will set up to solve for x. (2 points)
2) Solve for x. Show all your work
The equation setup up to solve for x is 2( 4x + 2 ) = 40 and the numerical value of x is 4.5.
What is the numerical value of x?A bisector divides segments or angles into two equal halves.
Given the data in the question;
AC is bisected at point EAE = 4x + 2AC = 40Numerical value of x = ?Since AC is bisected at point E and we know that a bisector divides segments or angles into two equal halves.
AC = 2 × AE
Hence
40 = 2( 4x + 2 )
Rewrite the equation such that x will be at the left side.
2( 4x + 2 ) = 40
To solve for x, remove the parenthesis using distributive property.
2( 4x + 2 ) = 40
2×4x + 2×2 = 40
Rewrite the equation such that x will be at the left side.
8x + 4 = 40
Subtract 4 from both sides.
8x + 4 - 4 = 40 - 4
8x = 36
Divide both sides by 8
8x/8 = 36/8
x = 36/8
x = 4.5
Therefore, the equation setup up to solve for x is 2( 4x + 2 ) = 40 and the numerical value of x is 4.5.
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6.2.5 What do Similar shapes tell us?
The values of the missing sides of the similar shapes are:
x = 7
y = 10
z = 20
How to Find the Side Lengths of Similar Shapes?Similar shapes have side lengths whose ratios are the same, or have proportional side lengths.
Use the following ratios to find the missing lengths of the two similar shapes in the given diagram:
35/14 = 17.5/x
Cross multiply
(35)(x) = (17.5)(14)
35x = 245
Divide both sides by 35
35x/35 = 245/35
x = 7
35/14 = 25/y
Cross multiply
(35)(y) = (25)(14)
35y = 350
35y/35 = 350/35
y = 10
35/14 = z/8
(35)(8) = 14z
280 = 14z
z = 280/14
z = 20
Therefore, the values of the missing sides of the similar shapes are:
x = 7
y = 10
z = 20
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I NEED HELPP!! ILL GIVE YOU 50 POINTS AND MORE
Answer:
7 = b.
8 = a.
Your revenue (in dollars) for selling x hamburgers is given by f(x) = 5x and your profit is $20 less than your revenue . What is your profit for 33 sales?
The profit for 33 sales is $145
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
Given:
f(x) = 5x is the revenue (in dollars) for selling x hamburgers.
profit = $20 less than revenue
So, the equation for the profit is
profit = 5x - 20
Now, if sales is 33 i.e., x=33 then profit will be
profit = 5(33) - 20
profit = 165-20
profit = $145
Hence, the profit is $145
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PLEASE HELP VERY IMPORTANT!!! What is the domain of the function shown in the graph below?
Answer:
(-∞, 4]
Step-by-step explanation:
Domain: x-axis
(-∞, 4]
Graph type: √-x
I hope this helps!
Khalid makes an investment at 4% simple interest. at the end of 1 year, the total value of the investment is $1560. how much was originally invested
Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit. If Khalid makes an investment at 4% simple interest. at the end of 1 year, the total value of the investment is $1560. Then the original investment is $1500.
What is simple interest?Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit.
Percent to decimal 4%=4/100=0.04
A=P(1+rt)
where A is the final amount
P is initial principle balance, t is time and r rate of interest.
1560=P(1+0.04)
1560=1.04P
P=1560/1.04
P=1500
Therefore $1500 is originally invested.
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Find the values of x and y.
X=
y=
(5x + 4)
114°
(2⁰
(3x-24)
Answer:
x=42
y=12
Step-by-step explanation:
6x-x²
——————->0
2x² - 4x - 6
Answer:
Step-by-step explanation saz mix dururtuuuutruturutrutrtru
Need help with this and I also need your work shown please and thank you.
Answer:
8x+8
Step-by-step explanation:
perimeter = lengths of all sides added up
we want all sides to add up to 6x + 4
so far, we have 2x-7 and -4x + 3
side 1 + side 2 + side 3 = perimeter = 6x + 4
2x - 7 + (-4x + 3) + side 3 = 6x + 4
-2x -4 + side 3 = 6x + 4
add (2x+4) to both sides to isolate side 3
side 3 = 8x + 8