Answer:
the nearest value of the mass is 3.27 grams
it s near 3.25
answer is c
prove tan(pi/4 x) - tan(pi/4-x)/tan(pi/4 x) tan(pi/4-x)=2sinxcosx
To prove the given equation involving tangent, we use trigonometric identities and simplification techniques to show that both sides of the equation are equal.
Explanation:To prove the given equation: tan(π/4 x) - tan(π/4-x)/tan(π/4 x) tan(π/4-x) = 2sin(x)cos(x).
We can simplify this equation using the trigonometric identities for tan:
tan(a) = sin(a)/cos(a)tan(π/4) = 1By substituting these identities, we get:
1 - 1/(tan(π/4-x)tan(π/4 x)) = 2sin(x)cos(x)
From here, we can simplify further and use the following trigonometric identities:
sin(2a) = 2sin(a)cos(a)tan(a)tan(b) = sin(a+b)/cos(a+b)Using these identities, we can simplify the equation to:
-2sin(x)cos(x) = -2sin(x)cos(x)
Therefore, the given equation is proved to be true.
a surveyor standing 64 meters from the base of a building measures the angle to the top of building and finds it to be 39 degrees . the surveyor then measures the angle to the top of the radio tower on the building and finds that it is 48 degrees. how tall is the radio tower?
To calculate the height of the radio tower, trigonometry is used to first determine the building height and then the total height including the tower. Subtracting the building height from the total height gives the height of just the radio tower.
Explanation:To determine the height of the radio tower, we must first use trigonometry to find the height of the building. We use the tangent of the angle and the distance from the surveyor to the building:
Tan(39°) = Height of Building / 64 metersHeight of Building = 64 meters * Tan(39°)After calculating the height of the building, we use the same approach to find the total height to the top of the radio tower:
Tan(48°) = Total Height / 64 metersTotal Height = 64 meters * Tan(48°)Finally, to find the height of the radio tower alone, we subtract the height of the building from the total height.
Height of Radio Tower = Total Height - Height of Building
By following these steps, we can calculate the height of the radio tower.
A laptop computer sells for $850. the sales tax is 7%. what is the total cost of the laptop?
Answer:
$909.50
Step-by-step explanation:
$850 x 7% = $59.50 (tax amount)
850 x (1+ 0.07) = $909.50
Input the equation for the following line in standard form Ax + By = C. Reduce all fractional answers to lowest terms.A line that passes through the origin and is parallel to x + y = 6. Input the equation for the following line in standard form Ax + By = C. Reduce all fractional answers to lowest terms.A line that passes through the origin and is parallel to x + y = 6.
Pablo deposited 57 into a savings account for which interest is compounded quarterly according to the rule 72 what interest rate will cause his money to double is approximately 44 years
To find the interest rate that will cause Pablo's money to double in approximately 44 years, we can use the rule of 72. The interest rate is approximately 1.64%.
Explanation:To find the interest rate that will cause Pablo's money to double in approximately 44 years, we can use the rule of 72. The rule of 72 states that dividing 72 by the interest rate will give you the approximate number of years it takes for money to double. In this case, we need to find the interest rate that makes the money double in 44 years. So, we divide 72 by 44 to get the interest rate.
Interest rate = 72 / 44 ≈ 1.6363636363636363
Therefore, the interest rate that will cause Pablo's money to double in approximately 44 years is approximately 1.64%.
in the diagram below Bd is parallel to XY . what is the value of x
Answer: The correct option is (B) 60.
Step-by-step explanation: Given that the line BD is parallel ti the line XY.
We are to find the value of x.
We know that
if two parallel lines are cut by a transversal, then the measures of the alternate interior angles are equal.
In the given figure, BD is parallel to XY and they are cut by a transversal.
So, the angles with measures x° and 60° are alternate interior angles.
Therefore, we must have
[tex]x^\circ=60^\circ\\\\\Rightarrow x=60.[/tex]
Thus, the value of x is 60.
Option (B) is CORRECT.
What is (are) the apparent x-intercept(s) of the function graphed above?
–4, –2, and 6
115 and –9
–3 and 3
50
For this case what we must do is observe the cut points of the function with the x axis.
The cut points with the horizontal axis are:
(-4, 0)
(-2, 0)
(6, 0)
Therefore, the intersections with the axis are:
x = -4
x = -2
x = 6
Answer:
The apparent x-intercept (s) of the function graphed are:
-4, -2, and 6
Trayvon bought 2 gallons of milk at the supermarket. How many quarts did he buy
Bob has a tree house at a height of 20 ft. When he's feeling adventurous he uses a rope to climb the tree house instead of the ladder. If the weight of the rope is 32 lb, then how much work must Bob do to pull the rope up once he has entered the house? ...?
f=uv/u+v
Make v the subject of the equation showing your working f=uv/u+v
Make v the subject of the equation showing your working
If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.
Check my answer? Will Upvote!
A scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 35 • 3x models the number of bacteria after x hours. Estimate when there will be about 550 bacteria in the culture.
I think it's about 2.5 hours.
Other answer options:
about 5.5 hours
about 4.5 hours
about 3.5 hours
Answer:
The answer to your question is about 5.5 hours.
Step-by-step explanation:
The equation is y = 35(3x)
Data
# of bacteria = 550 = y
time = ? h
Then 550 = 35(3x) substitution
550 = 105x simplifying
x = 5.23 h.
2.5 – 3.1 – 3.86 + 2.7 – 4.01 (simplify the expression)
-5.77 is the answer
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Final answer:
The expression 2.5 – 3.1 – 3.86 + 2.7 – 4.01 simplifies to -5.77 by adding the positive numbers together, adding negative numbers together, and then combining the two results.
Explanation:
To simplify the expression 2.5 – 3.1 – 3.86 + 2.7 – 4.01, we need to perform the subtraction and addition operations in sequence.
Combine the positive numbers (2.5 + 2.7 = 5.2).Combine the negative numbers (-3.1 - 3.86 - 4.01 = -10.97).Add the results from steps 1 and 2 (5.2 + (-10.97) = -5.77).The simplified result of the expression is -5.77.
Explain why the square root of a number is defined to be equal to that number to the 1/2 power.
Answer:
Sample Response: Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.
(3.2b+0.8)+1.9b simplify the expression.explain each step
To simplify the expression (3.2b+0.8)+1.9b, combine like terms by adding the coefficients. The simplified expression is 5.1b + 0.8.
Explanation:
To simplify the expression (3.2b+0.8)+1.9b, we can combine like terms by adding the coefficients. The variable b remains unchanged. So, we have:
(3.2b + 1.9b) + 0.8
Combine the coefficients: 3.2 + 1.9 = 5.1
The simplified expression is therefore 5.1b + 0.8.
Learn more about Simplifying expressions here:https://brainly.com/question/29003427
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Which best explains why all equilateral triangles are similar?
A. All equilateral triangles can be mapped onto each other using dilations.
B. All equilateral triangles can be mapped onto each other using rigid transformations.
C. All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.
D. All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.
Answer: A. All equilateral triangles can be mapped onto each other using dilations.
Step-by-step explanation:
We know that all equilateral triangles are similar to each but not congruent because they all have same measure of corresponding angles 60° but do not have same side-lengths.
So, equilateral triangles can be mapped onto each other using dilation because they maps similar shapes (sometimes congruent) where as rigid transformations always map congruent shapes so we cannot map all equilateral triangles by using rigid transformations.
tom has 6 quarters and 12 dimes in his pocket how many coins does he need to take out his pocket to make sure he has 4 quarters
lyn has as much money as jo. together they have $63.how much money does each have
take 63 and divide it by 2.
63÷2= 31.5
so they each had $31.5
There are 96 students in a speech contest. Yesterday, 1/4 of them gave their speeches. Today, 1/8 of the remaining students gave their speeches. How many students still haven't given their speeches?
Given the diagram at the right, which of the following must be true?
A. xfs = xtg
B. sxf = gxt
C. fxs = xgt
D. fxs = gxt
Answer:
SXF ~= GXT
Step-by-step explanation:
SX corresponds to GX,
XF corresponds to XT,
so SF corresponds to GT.
How many solutions does the following system of equations have? y=5/2x+2 2y=5x+8
Zero Solutions
Since the two lines have equal slopes and different intercepts
The system of equations has no solution.
Explanation:First, let's rewrite the second equation in slope-intercept form:
2y = 5x + 8
y = (5/2)x + 4
Now we can see that both equations have the same slope (5/2), but different y-intercepts (2 and 4). Since the slopes are the same, the lines are parallel and will never intersect. Therefore, this system of equations has no solution.
x= 1, 2, 3, 4, 5. y=11\4, 25\4, 39\4, 53\4, 67\4. what equation relates y to x in the values x and y?
The ratio of boys to girls in Mrs. Ronilo's math class is 3 to 1. What PERCENT of the class is girls?
Answer:25 %
Step-by-step explanation: there are 4 parts and 1 of those is girls 1 divided by 4 is 0.25, which is 25%
The percent of the class that is girls is 75%
Ratios and proportionGiven the ratio of boys to girls in Mrs. Ronilo's math class is 3 to 1, the total ratio will be:
Total ratio = 3 + 1Total ratio = 4The percent of the class that is girls = 3/4 * 100
The percent of the class that is girls = 75%
Hence the percent of the class that is girls is 75%
Learn more on percentage here: https://brainly.com/question/24304697
A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? (Use x as the independent variable.) ...?
What is the vertex and the equation of the axis of symmetry of the graph of y=x2-6x-7?
Answer:
The vertex is (3,-16) and axis of symmetry is 3
Step-by-step explanation:
The vertex of a quadratic equation [tex]f(x)=ax^{2}+bx+c[/tex] is calculated as [tex](\frac{-b}{2a},f(\frac{-b}{2a}))[/tex]
and the axis of symmetry is [tex]\frac{-b}{2a}[/tex]
Compare equation [tex]y=x^{2}-6x-7[/tex] with [tex]f(x)=ax^{2}+bx+c[/tex]
Where a= 1 and b = -6
so, [tex]x=\frac{-b}{2a}=\frac{-(-6)}{2}[/tex]
[tex]x=3[/tex]
Now, put the value of x=3 in [tex]y=x^{2}-6x-7[/tex]
[tex]y=(3)^{2}-6(3)-7[/tex]
[tex]y=9-18-7[/tex]
[tex]y=-16[/tex]
Therefore, the vertex is (3,-16) and axis of symmetry is 3
Use the distributive property to create an equivalent expression to 7x 56
The measures of the angles in a triangle have a ratio of 2:9:1. How do you find the measures of these angles
Final answer:
To find the measures of the angles with a ratio of 2:9:1, represent the angles as 2x, 9x, and x, set up the equation 2x + 9x + x = 180, solve for x, and then use x to calculate each angle. The measures of the angles are 30 degrees, 135 degrees, and 15 degrees.
Explanation:
To find the measures of the angles in a triangle with a given ratio, we apply the fact that the sum of the angles in a triangle is always 180 degrees. If we have the ratio of 2:9:1, we can represent the angles as 2x, 9x, and x, respectively. Since the angles must add up to 180 degrees, we can write the equation 2x + 9x + x = 180, which simplifies to 12x = 180.
Divide both sides of the equation by 12 to find the value of x: x = 180 / 12 = 15 degrees. Now, we can find each angle by multiplying x by the respective ratio number:
The first angle is 2x, which equals 2(15) = 30 degrees.
The second angle is 9x, which equals 9(15) = 135 degrees.
The third angle is 1x, which equals 1(15) = 15 degrees.
Therefore, the measures of the angles in the triangle are 30 degrees, 135 degrees, and 15 degrees.
Write the expression in standard form.
five divided by quantity three minus fifteen i.
Answer:
[tex]\frac{4}{229}+\frac{30i}{229}[/tex]
Step-by-step explanation:
If your chemistry grade is broken down so that 70% of it is exams, 20% is a lab, and 10% is homework, and your average scores out of 100 points in each area are:
exams 85
labs 75
homework 96
Calculate your weighted average.
some of the fastest growing occupations in the United States are in which field
a. retail
b. agriculture
c. health care
d. manufacturing