By using trigonometric properties, we will see that:
tan(x) = 3/4.
How to find the value of tan(x)?
Remember that the sine of the difference is:
sin(a - b) = sin(a)*cos(b) - sin(b)*cos(a).
Here we have:
sin(90° -x ) = 0.8
Expanding the sine:
sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°)
We know that:
sin(90°) = 1 and cos(90°) = 0, then:
sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°) = cos(x).
Then we have:
cos(x) = 0.8
And we want to find the tangent of x, which is:
[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]
We already know that cos(x) = 0.8
Now, remember that:
[tex]sin(x)^2 + cos^2(x) = 1\\\\sin(x) = \sqrt{1 - cos^2(x)} \\[/tex]
Because x is an acute angle, sin(x) > 0, that is why we choose the positive root.
Replacing cos(x) we get:
[tex]sin(x) = \sqrt{1 - 0.8^2} = \sqrt{1 - 0.64} = \sqrt{0.36} = 0.6[/tex]
Then the tangent of x is:
[tex]tan(x) = \frac{0.6}{0.8} = \frac{6}{10}*\frac{10}{8} = 6/8 = 3/4[/tex]
If you want to learn more about trigonometric functions:
https://brainly.com/question/8120556
#SPJ1
33. Three consecutive
integers exist such that five
times the first number is
equal to one more than twice
the sum of the second and
third numbers.
Which equation accurately
solves for the integers?
Let n represent the first
number.
The equation which accurately solves for the integers is; 5n = 2(2n +3) +1.
Which equation accurately solves for the integers?It follows from the task content that the first number is represented by n.
On this note, it follows that the second, and third numbers are; (n+1) and (n+2) respectively.
On this note, since five times the first number is equal to one more than twice the sum of the second and third numbers; we have;
5n = 2(n+1+n+2) +1
5n = 2(2n+3)+1.
Read more on word problems;
https://brainly.com/question/13818690
#SPJ1
what is the perimeter of a rectangle with the of 10cm and width 20cm
Solve inequality -8x+4≤36.
[tex]\bf{-8x+4\leq 36 }[/tex]
Subtract 4 from both sides.
[tex]\bf{-8x\leq 36-4 }[/tex]
Subtract 4 from 36 to get 32.
[tex]\bf{-8x\leq 32 }[/tex]
Divide both sides by −8. Since −8 is <0, the inequality direction is changed.
[tex]\bf{x\geq \dfrac{32}{-8} }[/tex]
Divide 32 by −8 to get −4.
[tex]\bf{x\geq -4 \ \ \Rightarrow \ \ \ Answer }[/tex]
{ Pisces04 }Question :
Solve inequality -8x + 4 ≤ 36Solution :
⇒ -8x + 4 ≤ 36
⇒ -8x ≤ 36 - 4
⇒ -8x ≤ 32
⇒ -x ≤ 32 / 8
⇒ -x ≤ 16 / 4
⇒ -x ≤ 8 / 2
⇒ -x ≤ 4
⇒ x ≥ -4
For the given functions f and g find f•g and state it’s domain
f(x) = 3x - 6; g(x) = 8x +4
f.g and its domain is 24x²-36x-24; all real numbers.
Given, f(x) = 3x - 6; g(x) = 8x +4.
We need to find the value of f.g
What is a domain?The domain of a function; In mathematics, the domain of a function is the set of inputs accepted by the function.
Now, (f.g)(x)=(3x-6)(8x+4)
=24x²-48x+12x-24
=24x²-36x-24
Therefore, f.g and its domain is 24x²-36x-24; all real numbers.
To learn more about the domain of a function visit:
https://brainly.com/question/13113489.
#SPJ1
Write the arithmetic series 3+9+15+21+27 using summation notation
Answer:
_ t&byds
ty grk gtrwwfh
Let sets A and B be defined as follows.
A= {c,d,e,f}
B is the set of odd numbers greater than 5 and less than 23 (a) Find the cardinalities of A and B. n(A) = n(B)=
There are 4 elements in the set A and 8 elements in set B that is n(A) = 4 and n(B) = 8
Cardinality of a setThis is the total number of elements in a set. Given the following sets;
A = {c, d, e, f}
B = {odd numbers greater than 5 and less than 23}
B = {7,9,11,13, 15, 17, 19, 21}
Since there are 4 elements in the set A and 8 elements in set B hence n(A) = 4 and n(B) = 8
Learn more on cardinality of set here: https://brainly.com/question/23976339
#SPJ1
Given the function r(x)=x−4x 9, find the values of x that make the function less than or equal to zero. write the solution in interval notation.
Inequalities help us to compare two unequal expressions. The solution that will make the value of the function r(x) less than equal to 0 is [3,∞).
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
To find the value of x that will make the function r(x)=x-4x+9 less than or equal to 0 solve the inequality,
x - 4x + 9 ≤ 0
x - 4x ≤ -9
-3x ≤ -9
x ≥ (-9)(-3)
x ≥ 3
Hence, the solution that will make the value of the function r(x) less than equal to 0 is [3,∞).
Learn more about Inequality:
https://brainly.com/question/19491153
#SPJ1
A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 8 ft above the bow. The rope is hauled in at the rate of 1 ft/sec. Complete parts (a) and (b). a. How fast is the boat approaching the dock when 10 ft of rope are out? ft/sec (Type an integer or a simplified fraction.) b. At what rate is the angle changing at this instant? rad/sec (Type an integer or a simplified fraction.)
a) The speed of the boat is 3/5 ft/sec
b) The rate at which the angle changes is 8/125 rad/sec
What is a right angled triangle?A right angled triangle is a type of the triangle with one of its angles 90°.
The longest side of the triangle is called the hypotenuse which is the side that faces the right angle. other sides are called the adjacent sides.
Analysis:
The analysis is in the attached file below.
Learn more about right angled triangles: brainly.com/question/64787
#SPJ1
HELP................................................
Answer:
D. g(x) = 5x^2
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
A point of the function g(x) is known: (1, 5)
The proper function is
[tex]g(x)=5x^{2}[/tex]
Demonstration calculating g(1)
[tex]g(1)=5(1)^{2} =5(1)=5[/tex]
The point (1, 5 ) belongs to this function
Hope this helps
Alexander is working two summer jobs, making $10 per hour washing cars and $8 per hour landscaping. Last week Alexander worked twice as many hours washing cars as he worked hours landscaping hours and earned a total of $84. Write a system of equations that could be used to determine the number of hours Alexander worked washing cars last week and the number of hours he worked landscaping last week. Define the variables that you use to write the system.
The system of equations is:
x = 2y
x*$10 + y*8 = $84
Solving it, we see that he worked 3 hours landscaping and 6 hours washing cars.
How to write the system of equations?
First, we need to define the variables:
x = number of hours washing cars.y = number of hours landscaping.We know that Alexander worked twice as many hours washing cars as he worked hours landscaping, then:
x = 2y
We also know that he earned a total of $84, then:
x*$10 + y*8 = $84
So the system of equations is:
x = 2y
x*$10 + y*8 = $84
To solve it, we just replace the first equation into the second one:
(2y)*$10 + y*8 = $84
y*$28 = $84
y = $84/$28 = 3
So He worked 3 hours landscaping, and:
x = 2*y = 2*3 = 6
6 hours washing cars.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
A formula for the normal systolic blood pressure for a man age A , measured in mmHg, is given as P=0.006A2−0.02A+120 . Find the age of a man whose normal blood pressure measures 128 mmHg.
The age of the man whose normal pressure measures 128 mmHg is approximately 38 years.
How do we determine the age of the man using a quadratic equation?The quadratic formula can be used to determine the age of a man whose normal blood pressure measures 128 mmHg. This can be expressed mathematically as:
[tex]\mathbf{ \dfrac{-b \pm\sqrt{b^2 - 4ac}}{2a}}[/tex]
From the given equation:
P = 0.006A² - 0.02A + 120
where;
P = 128128 = 0.006A² - 0.02A + 120
= 0.006A² - 0.02A + 120 - 128
= 0.006A² - 0.02A - 8
where:
a = 0.006 , b = - 0.02, and c = -8[tex]\mathbf{ \dfrac{-(-0.02) \pm\sqrt{(-0.02)^2 - 4(0.006)(-8)}}{2(0.006)}}[/tex]
[tex]\mathbf{ = \dfrac{(0.02) \pm 0.43863}{0.012}}[/tex]
= 38.2195 or -34.8862
Taking the positive integer value, the age of the man whose normal pressure measures 128 mmHg is approximately 38 years.
Learn more about using the quadratic formulas to solve quadratic equations here:
https://brainly.com/question/8649555
#SPJ1
A principal of $5500 is invested in an account paying an annual rate of 7%. Find the amount in the account after 4 years if the account is compounded semiannually, quarterly, and monthly.
Answer:
Formulae is Future value, see in picture I've done example 1 for u.
Choose the proportion that is true.
3/8=15/40
12/13=2/3
9/13=27/36
16/49=4/7
Answer:
3/8=15/40
Step-by-step explanation:
Multiply both the numerator and the denominator of the first term by 5 and you'll see that it's the same fraction.
Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
The given graph is a function.
The correct option is (B).
What is vertical line test?The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
As we draw the vertical line then for one input x there is one output.
Hence, the given graph is function.
Learn more more vertical line test here:
https://brainly.com/question/11579929
#SPJ1
g(x)= l2xl +2
find domain and range
The domain of the function g(x)=l2xl +2 is all real numbers and the range is from (0,∞).
Given g(x)= l2xl +2
First of all we know that modulas gives two values for x<0 and x>=0.
The function g(x) if opened gives two values.
for x>=0 g(x)=2x+2
for x<0 g(x)=-2x+2
because we have not told about the description about x so we can put any value in the function.
So the domain is all real numbers.
Now when we take g(x)=2x+2 for x>=0
putting x=0 we get 2 and rest are positive values so the value of g(x) keeps increasing as we increase the value of x. So here range is [2,∞).
Now take g(x)=-2x+2 for x<0
putting smallest number starting from zero but not 0 we will get a number near to 0 but not zero and because when a negative number multiplies with -2 it becomes positive and increase the value of g(x) so here the range becomes (0,∞).
When we talk about overall range it will be [2,∞) ∪(0,∞)
it will be (0,∞).
Hence the domain of the function g(x) is all real numbers and range is from 0 to infinity.
Learn more about domain and range at https://brainly.com/question/2264373
#SPJ10
Last week Sharon's mother order 60 roses for her shop this week she will order five times as many roses how many roses will she order write an expression and then find the solution
Answer:
60(5) = 300 :D
Step-by-step explanation:
First lets make the equation :)
Orders 60 roses
This week will order 5x as many as last week
60 x 5 OR 60(5)
60(5) = 300 :)
Have an amazing day!!
Please rate and mark brainliest!!
find the length of segment AC if AB=7.8 cm and BC=25 mm. how many solutions are there in each case? Point B lies on segment AC
Answer:
10.3. and One solution
Step-by-step explanation:
I had this question, tho it might be different
Find the x-intercept of the graph of the linear equation y = −1
2
x + 3.
x-intercept
Answer:
Step-by-step explanation:
x intercept equals pi
Answer:
x intercept= 6
Step-by-step explanation:
Area of a Parallelogram
i 13 cm
20 cm
15 cm
View One Minute Version
Overview
Answer:
260 cm^2
Step-by-step explanation:
The area of a parallelogram is calculated by multiplying its height and base:
The base for this parallelogram is given as 20 and the height is 13
13*20 = 260
The area is stated in square units so the answer is 260 cm^2
Find the h.c.f of
[tex] {x}^{3} + {y}^{3} \: and \: \: {x}^{2} - xy + {y}^{2} [/tex]
The greatest common factor will be (x² – xy + y²).
Greatest common factorThis is a value or expression that can divide the given expressions without leaving a remainder.
Given the following expressions
x^3+^3 and x^2 - xy + y^2
Expand x^3+y^3
x^3+y^3 =(x + y)(x² – xy + y²).
Since (x² – xy + y²) is common to both expression, hence the greatest common factor will be (x² – xy + y²).
Learn more on GCF here: https://brainly.com/question/902408
#SPJ1
► Math and Gymnastics
In a gymnastics competition, gymnasts compete
in events such as the balance beam, parallel bars,
vault, and floor exercise,
Leigh earned the following scores from the judges
for her balance beam routine.
9.30 9.20
Follow these steps to find Leigh's final score.
1. Order the scores from least to greatest.
9.20
9.30
9.20
9.00
Answer:
9.00,9.20,9.30
Step-by-step explanation:
What happens when you reflect an object over intersecting line( combination of reflection)?
Answer:
Step-by-step explanation:
The Compositions of Reflections Over Intersecting Lines Theorem states that if we perform a composition of two reflections over two lines that intersect, the result is equivalent to a single rotation transformation of the original object.
hope it helps! (✿◠‿◠)
The result concluded is equivalent to a single rotation transformation of the original object.
Explanation of how reflection across axis works?When a graph is reflected along an axis, say x-axis, then that leads the graph to go just on the opposite side of the axis as if we're seeing it in a mirror.
The Compositions of Reflections Over Intersecting Lines states that if we perform a composition of two reflections over two lines that intersect.
The result concluded is equivalent to a single rotation transformation of the original object.
Learn more about reflection;
https://brainly.com/question/15487308
#SPJ2
Question 1
At room temperature, one liter of water can dissolve over 300 grams of salt.
What is the solvent in this solution?
temperature
water
salt
grams
It's the water
The salt would be the solute that dissolves in the solvent.
Temp - is a factor
(affecting rate at which salt dissolves)
grams - unit of measure
Hope this helps!
Can someone please assist me with this problem
The category in the pie chart that was chosen by 1/8 of those that were surveyed is documentary.
How to illustrate the pie chart?From the pie chart, it can be seen that comedy and drama have the highest fraction as they have 1/4 each.
Therefore, the percentage of those who choose comedy or drama will be:
= (1/4 + 1/4) × 100
= 2/4 × 100
= 50%
Lastly, if 24% chose news, the others that choose others will be:
= 1/3 × 24
= 8%
Learn more about pie charts on:
brainly.com/question/26851221
#SPJ1
The area of a rectangle is 119 square units. Find the length and width of the rectangular
Answer: 7 and 17
Step-by-step explanation:
Since the area of a rectangle is the product of the two sides, the product of these two numbers must be 119.
The factors pairs of 119 are 1 and 119, and 7 and 17.
x+7 and x-3 have a difference of 10. The difference of 7 and 17 is also 10. Hope this helped!
In the future, please take a less blurry photo because I had to guess the part where I think it said x-3.
In a story about a doctor trying to treat a patient with mysterious symptoms, which scene would most likely be the climax?
represent the complex number graphically, and find the trignometric form of the number. 1 + 3i
The trigonometric form of the complex number 1 + 3i is 3.16[cos(71.57)° + isin(71.57°)]
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Complex number is in the form z = a + bi, where a, b are real numbers.
Given the complex number z = 1 + 3i
In polar form: r = √(1² + 3²) = 3.16
Ф = tan⁻¹ (3/1) = 71.57⁰
The trigonometric form of the complex number 1 + 3i is 3.16[cos(71.57)° + isin(71.57°)]
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
HELP
17x - 32y + 2.78y - 11,345x + 1/5x
Answer:
i think this is the answers
Step-by-step explanation:
-13.78xy
Suppose that F(x) = x² and G(x) = 2/5 x². Which statement best compares the
graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically and
flipped over the x-axis.
B. The graph of G(x) is the graph of F(x) stretched vertically.
C. The graph of G(x) is the graph of F(x) compressed vertically and
flipped over the x-axis.
OD. The graph of G(x) is the graph of F(x) compressed vertically.
Answer: The graph of G(x) is the graph of F(x) compressed vertically.
Step-by-step explanation:
See attached image.
Giving Brainliest to the first person who can accurately answer and explain these questions.
Answer:
It's A 48,736
Step-by-step explanation:
Answer:
48,856.11
Step-by-step explanation:
Compound interest is generally written as: [tex]A=P(1+\frac{r}{n})^{nt}[/tex] where P = principle amount, r = interest rate, n=compound periods, t = time. This is compounded continuously which can be defined as: [tex]A=Pe^{rt}[/tex]. If you're confused what e is, one of the definitions, is [tex]\lim_{x\to\infty}{(1+\frac{1}{x})^x[/tex]. This is essentially the very definition of continuous compound. It's when the amount of compounds (n in the equation) goes towards infinity. So using the previous defined equation simply plug the values into the equation.
[tex]A=(40000)e^{0.025*8}[/tex]
Multiply inside the exponent
[tex]A=(40000)*e^{0.2}[/tex]
raise e to the power of 0.2
[tex]A\approx40000*1.221[/tex]
Multiply
[tex]A=48,856.11[/tex]