Match the identities to their values taking these conditions into consideration sinx=sqrt2 /2 cosy=-1/2 angle x is in the first quadrant and angle y is in the second quadrant. Information provided in the picture. PLEASE HELP
Answers
Answer:
[tex]\boxed{\vphantom{\dfrac{\sqrt{2}}{2}}\quad \cos(x+y)\quad }\longleftrightarrow \boxed{\quad \dfrac{-(\sqrt{6}+\sqrt{2})}{4}\quad }[/tex]
[tex]\boxed{\vphantom{\dfrac{\sqrt{2}}{2}}\quad \sin(x+y)\quad }\longleftrightarrow \boxed{\quad\dfrac{\sqrt{6}-\sqrt{2}}{4}\quad }[/tex]
[tex]\boxed{\quad \tan(x+y)\quad }\longleftrightarrow \boxed{\quad\sqrt{3} -2\quad }[/tex]
[tex]\boxed{\vphantom{\sqrt{3}}\quad \tan(x-y)\quad }\longleftrightarrow \boxed{\quad-(2+\sqrt{3})\quad }[/tex]
Step-by-step explanation:
To find the values of the given trigonometric identities, we first need to find the values of cos x and sin y using the Pythagorean identity, sin²x + cos²x ≡ 1.
Given values:
[tex]\sin x = \dfrac{\sqrt{2}}{2}\qquad \textsf{Angle $x$ is in Quadrant I}\\\\\\\cos y=-\dfrac{1}{2}\qquad \textsf{Angle $y$ is in Quadrant II}[/tex]
Find cos(x):
[tex]\sin^2 x+\cos^2 x=1\\\\\\\left(\dfrac{\sqrt{2}}{2}\right)^2+\cos^2 x=1\\\\\\\dfrac{1}{2}+\cos^2 x=1\\\\\\\cos^2 x=1-\dfrac{1}{2}\\\\\\\cos^2 x=\dfrac{1}{2}\\\\\\\cos x=\pm \sqrt{\dfrac{1}{2}}\\\\\\\cos x=\pm \dfrac{\sqrt{2}}{2}[/tex]
As the cosine of an angle is positive in quadrant I, we take the positive square root:
[tex]\cos x=\dfrac{\sqrt{2}}{2}[/tex]
Find sin(y):
[tex]\sin^2 y + \cos^2 y = 1 \\\\\\ \sin^2 y + \left(-\dfrac{1}{2}\right)^2 = 1 \\\\\\ \sin^2 y + \dfrac{1}{4} = 1 \\\\\\ \sin^2 y = 1-\dfrac{1}{4} \\\\\\ \sin^2 y = \dfrac{3}{4} \\\\\\ \sin y =\pm \sqrt{ \dfrac{3}{4}} \\\\\\ \sin y = \pm \dfrac{\sqrt{3}}{2}[/tex]
As the sine of an angle is positive in quadrant II, we take the positive square root:
[tex]\sin y = \dfrac{\sqrt{3}}{2}[/tex]
The tangent of an angle is the ratio of the sine and cosine of that angle. Therefore:
[tex]\tan x=\dfrac{\sin x}{\cos x}=\dfrac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}=1[/tex]
[tex]\tan y=\dfrac{\sin y}{\cos y}=\dfrac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=-\sqrt{3}[/tex]
Now, we can use find the sum or difference of two angles by substituting the values of sin(x), cos(x), sin(y), cos(y), tan(x) and tan(y) into the corresponding formulas.
[tex]\dotfill[/tex]
cos(x + y)[tex]\cos(x+y)=\cos x \cos y - \sin x \sin y \\\\\\ \cos(x+y)=\left(\dfrac{\sqrt{2}}{2}\right) \left(-\dfrac{1}{2}\right) - \left(\dfrac{\sqrt{2}}{2}\right) \left(\dfrac{\sqrt{3}}{2}\right) \\\\\\ \cos(x+y)=-\dfrac{\sqrt{2}}{4} - \dfrac{\sqrt{6}}{4} \\\\\\ \cos(x+y)=\dfrac{-\sqrt{2}-\sqrt{6}}{4} \\\\\\ \cos(x+y)=\dfrac{-(\sqrt{2}+\sqrt{6})}{4} \\\\\\ \cos(x+y)=\dfrac{-(\sqrt{6}+\sqrt{2})}{4}[/tex]
[tex]\dotfill[/tex]
sin(x + y)[tex]\sin(x+y)=\sin x \cos y + \cos x \sin y \\\\\\\sin(x+y)=\left(\dfrac{\sqrt{2}}{2}\right) \left(-\dfrac{1}{2}\right) + \left(\dfrac{\sqrt{2}}{2}\right) \left(\dfrac{\sqrt{3}}{2}\right) \\\\\\\sin(x+y)=-\dfrac{\sqrt{2}}{4} + \dfrac{\sqrt{6}}{4} \\\\\\ \sin(x+y)=\dfrac{-\sqrt{2}+\sqrt{6}}{4} \\\\\\ \sin(x+y)=\dfrac{\sqrt{6}-\sqrt{2}}{4}[/tex]
[tex]\dotfill[/tex]
tan(x + y)[tex]\tan(x+y)=\dfrac{\tan x + \tan y}{1-\tan x \tan y} \\\\\\ \tan(x+y)=\dfrac{1 + (-\sqrt{3})}{1-(1) (-\sqrt{3})} \\\\\\ \tan(x+y)=\dfrac{1 -\sqrt{3}}{1+\sqrt{3}} \\\\\\ \tan(x+y)=\dfrac{(1 -\sqrt{3})(1 -\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})} \\\\\\ \tan(x+y)=\dfrac{1-2\sqrt{3}+3}{1-\sqrt{3}+\sqrt{3}-3} \\\\\\ \tan(x+y)=\dfrac{4-2\sqrt{3}}{-2} \\\\\\ \tan(x+y)=-2+\sqsrt{3} \\\\\\ \tan(x+y)=\sqrt{3} -2[/tex]
[tex]\dotfill[/tex]
tan(x - y)[tex]\tan(x-y)=\dfrac{\tan x - \tan y}{1+\tan x \tan y} \\\\\\\tan(x-y)=\dfrac{1 - (-\sqrt{3})}{1+(1) (-\sqrt{3})} \\\\\\\tan(x-y)=\dfrac{1 +\sqrt{3}}{1-\sqrt{3}} \\\\\\\tan(x-y)=\dfrac{(1 +\sqrt{3})(1 +\sqrt{3})}{(1-\sqrt{3})(1+\sqrt{3})} \\\\\\ \tan(x-y)=\dfrac{1+2\sqrt{3}+3}{1+\sqrt{3}-\sqrt{3}-3} \\\\\\ \tan(x-y)=\dfrac{4+2\sqrt{3}}{-2} \\\\\\ \tan(x-y)=-2-\sqrt{3}\\\\\\\tan(x-y)=-(2+\sqrt{3})[/tex]
Related Questions
a triangular course for a canoe race is marked with buoys. the first leg is 3/10 mi, the second leg is 1/2 mi, and the third leg is 2/5 mi. how long is the race?
(the numbers are fractions)
Answers
Answer:
1 1/5 mi
Step-by-step explanation:
We need to add the three legs together
3/10 + 1/2 + 2/5
The common denominator is 10
3/10 =3/10
1/2 *5/5 = 5/10
2/5 *2/2 =4/10
3/10 + 5/10+4/10 = 12/10
10/10 = 10/10+2/10 = 1+2/10 = 1 1/5 mi
Answer:
Length of race = 1.2 miles
Step-by-step explanation:
Length of race is given by the perimeter of triangle.
Refer the given figure.
The first leg is 3/10 mi, the second leg is 1/2 mi, and the third leg is 2/5 mi.
[tex]\texttt{Perimeter =}\frac{3}{10}+\frac{1}{2}+\frac{2}{5}=\frac{3}{10}+\frac{5}{10}+\frac{4}{10}=\frac{3+5+4}{10}\\\\\texttt{Perimeter =}\frac{12}{10}=1.2 miles[/tex]
Length of race = 1.2 miles
Only the function represented by graph has an inverse function.
Answers
Answer:
Only the function represented by graph 2 has an inverse function
Step-by-step explanation:
* Lets explain the inverse of the function
- The Function is a relation between x-coordinates and the y-
coordinates of the order pairs under the condition every
x-coordinate has only one y-coordinate
- Ex: R = {(2 , 3) , (1 , 5) , (-2 , -3)} is a function because every x-
coordinate has only one y-coordinate and R = {(2 , 3) , (-1 , 4) ,
(2 , 5)} not a function because the x-coordinate 2 has two y-
coordinates 3 and 5
- We use the vertical line to test the graph is function or not, if
the vertical line intersects the graph in one point then the
graph is function if intersects it in more than one point then the
graph is not function
- We have two types of function one-to-one function and
many-to-one function
# one-to-one function means every x-coordinate has only 1 y-coordinate
# many-to-one function means some x-coordinates have only 1
y-coordinate
- We find the inverse function by switching x and y, then one-to-
one function has inverse but many-to-one has not inverse
because when we switched x and y it will be one-to-many
means one x-coordinate has many y-coordinates and this is not
a function
- We use the horizontal line to test the graph of the function has
inverse or not, if the horizontal line intersects the graph in one
point then the function of the graph has inverse if it intersects
the graph in more than one point ,then the function of the
graph has no inverse
* Now lets test all the graphs by using the horizontal line
# graph 1
∵ The horizontal line cuts the graph in more than 1 point
∴ The function of graph 1 has no inverse
# graph 2
∵ The horizontal line cuts the graph in just 1 point
∴ The function of graph 2 has inverse
# graph 3
∵ The horizontal line cuts the graph in more than 1 point
∴ The function of graph 3 has no inverse
# graph 4
∵ The horizontal line cuts the graph in more than 1 point
∴ The function of graph 4 has no inverse
* Only the function represented by graph 2 has an inverse function
6. Which of the following pairs of numbers contains like fractions?
A.3 1/2 and 4 4/4
B.3/2and 2/3
C.6/7and 1 5/7
D.5/6 and 10/12
Answers
Answer:
D.5/6 and 10/12
Step-by-step explanation:
A.3 1/2 and 4 4/4
3 1/2 and 4+1
3 1/2 and 5
not equal
B.3/2and 2/3
2/2 + 1/2 and 2/3
1 1/2 and 2/3
not equal
C.6/7and 1 5/7
6/7 and 1 5/7
not equal
D.5/6 and 10/12
5/6*2/2 and 10/12
10/12 and 10/12
equal
Sam and Jo created a grocery list. To make it easier to look at, they each split the list into equal groups. Sam splits the list into groups of 4 and Jo splits the list into groups of 6. What is the smallest number of items that could be on the grocery list?
Answers
Answer:
12
Step-by-step explanation:
The least common multiple of 4 and 6 is what we are looking for
4,8 ,12,16,20
6,12,18
The smallest number is 12
find the solution of x-13=25 and verify you solution using subtraction
Answers
Answer:
x = 38
Step-by-step explanation:
Add 13 to both sides, to isolate x: x = 38
We verify this solution using substitution (not subtraction):
Is 38 - 13 = 25 true? Yes, it is.
Answer:
X-13=25
get coefficient X by itself by adding 13 to both sides
X=-13+13=25+13
X=38
Tom just received a new job offer. He is told that his starting salary will be $75,000 per year. He is told his salary will probably be $81,000 in four years. We'll use this information to try to anticipate his future earnings in any given year.Assume that Y= Tom's salary amount in dollars and x= the number of years worked. Step 1.Use the data given to find the rate of change, or the salary increase per year.( hint: compute the slope.) We are now going to use a line to model Tom's salsry growth. Step 2. Use the data given and the slope value from Step 1 to write the slope-intercept form of the line. Step 3. Based on your equation from Step 2, What will Tom's salary be in ten years?
Answers
Answer:
Part 1) The rate of change is [tex]2,000\ \$/year[/tex]
Part 2) The equation of the line into slope intercept form is [tex]y=2,000x+73,000[/tex]
Part 3) Tom's salary would be [tex]\$93,000[/tex] in ten years
Step-by-step explanation:
Let
x ------> the number of years worked
y -----> Tom's salary amount in dollars
we have the points
A(1, 75,000) and B(4,81,000)
step 1
Find the rate of change (slope)
The slope is equal to
[tex]m=(81,000-75,000)/(4-1)=2,000\ \$/year[/tex]
step 2
Find the equation of the line into slope-intercept form
we know that
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have that
[tex]m=2,000\ \$/year[/tex]
point A(1, 75,000)
substitute
[tex]75,000=(2,000)(1)+b[/tex]
[tex]b=75,000-2,000=73,000[/tex]
The equation of the line is
[tex]y=2,000x+73,000[/tex]
step 3
What will Tom's salary be in ten years?
For x=10 years
Substitute in the linear equation
[tex]y=2,000(10)+73,000=\$93,000[/tex]
Answer:
The increment in salary is $1500 each year. The slope intercept form is [tex]y=1500x+75000[/tex] and the salary in 10 years will be $90000.
Step-by-step explanation:
Consider the provided information.
The starting is $75,000 per year.
Let x is the number of years worked and y is Tom's salary amount in dollars.
When he has 0 yr of experience, his salary is $75000 per year.
it can be written as (0,75000).
His salary will probably be $81,000 in four years.
It can be written as (4,81000).
STEP 1:
Find the rate of change by using the formula slope=[tex]m=\frac{rise}{run}[/tex].
Determine the rise by subtracting 75000 from 81000.
Rise = 81000 - 75000 = 6000
Now determine the run by subtracting 0 from 4.
Run = 4 - 0 = 4
Substitute the respective values in the above formula.
[tex]slope=m=\frac{6000}{4}\\slope=m=1500[/tex]
Therefore, the rate of change, or the salary increase per year is $1500.
STEP 2:
Write the slope intercept form by using the formula:
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute m = 1500 and [tex](x_1,y_1)=(0,75000)[/tex] on the above formula.
[tex](y-75000)=1500(x-0)\\y-75000=1500x\\y=1500x+75000[/tex]
Thus, the slope intercept form is [tex]y=1500x+75000[/tex].
STEP 3:
The salary in 10 years. can be calculated as:
Substitute the value of x = 10 in [tex]y=1500x+75000[/tex].
[tex]y=1500(10)+75000\\y=15000+75000\\y=90000[/tex]
Hence, the salary in 10 years will be $90000.
The radius of the cone is 1.75 inches, and its height is 3.5 inches. If the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice?
Answers
Answer:
=11.155 in³
Step-by-step explanation:
Given data:
Radius= 1.75 inches
Height = 3.5 inches
Diameter= 0.5 inches
To find the volume of a cone we will apply the formula:
Volume of a cone = 1/3 πr²h
Substitute the values:
V= 1/3* 3.14 *(1.75)² * 3.5
V=1/3 *3.14*(3.0625)* 3.5
V= 33.66/3
V=11.22 in³
Now find the volume of the bubble gum:
Volume of bubble gum = 4/3 π*r³
Substitute the values:
V= 4/3*3.14*(0.5/2)³
V=4/3*3.14(0.25)³
V=4/3*3.14(0.015625)
V=0.19625/3
V=0.0654 in³
Now subtract the volume of bubble gum ball from the volume of a cone
=11.22 - 0.0654
=11.155 in³
Thus the closest approximation of the volume of the cone that can be filled with flavored ice is 11.155 in³....
Answer:
11.15 in³
Step-by-step explanation:
Consider the function represented by the equation x - y = 3. What is the equation written in function notation, with x as the
ndependent variable?
O f(x) = y + 3
Of(x) = -y-3
Of(x) = -x + 3
f(x) = X-3
Answers
Answer:
f(x)=x-3
Step-by-step explanation:
You are given x-y=3 and you want to rewrite in function notation with x being the independent. That means we need to solve for y so y can depend on x.
x-y=3
Subtract x on both sides:
-y=-x+3
Multiply both sides by -1:
y=x -3
So function notation would be f(x)=x-3
The function notation of the equation x - y = 3, with x as the independent variable, is f(x) = x - 3.
Explanation:The equation x - y = 3 is in standard form. To express this equation in function notation with x as the independent variable, we need to solve for y in terms of x. By moving y to the other side of the equation and 3 to the opposite side, we get y = x - 3. In function notation, where y is usually replaced by the function f(x), the equation becomes f(x) = x - 3.
Learn more about function notation here:https://brainly.com/question/5025688
#SPJ3
veronica takes 1/3 of an hour to write 1/4 of a page of
calligraphy. how long will it take veronica to write one page?
Answers
Answer:
4/3 hours or 1 hour 20 minutes.
Step-by-step explanation:
1/4 page takes 1/3 hour to write.
By proportion 1 page will take 1/3 / 1/4
= 1/3 * 4
= 4/3 hours.
Answer:
[tex]1\frac{1}{3}\text{ hours}[/tex]
Step-by-step explanation:
Given,
Time taken to write 1/4 of a page = [tex]\frac{1}{3}[/tex] hour,
i.e. the ratio of time taken and number of pages wrote = [tex]\frac{1/3}{1/4}=\frac{4}{3}[/tex]
Let x be the time taken to write a full page,
So, the ratio of time taken( in hours ) and page wrote = [tex]\frac{x}{1}[/tex]
[tex]\implies \frac{x}{1}=\frac{4}{3}[/tex]
[tex]x=1\frac{1}{3}[/tex]
Hence, the time taken to write 1 page is [tex]1\frac{1}{3}[/tex] hours.
Find the arc length of the given circle.
Answers
Answer:
Arc length = (30/360)(2π)(14)
= (7/3)π cm = about 7.33 cm
if trapezoid JKLM is translated according to the rule (x, y) -> (x + 8, y - 3), what are the coordinates of point L'?
A. (1, -5)
B. (-10, 6)
C. (-5, 3)
D. (6, -8)
Answers
Answer:
D.
Step-by-step explanation:
First step: Identify the point for L.
L is at (-2,-5).
We are plugging this (x,y) into (x+8,y-3) to see where it takes us.
(-2+8,-5-3)=(6,-8).
The solution is D.
Answer: OPTION D
Step-by-step explanation:
You can observe in the figure that the coordinates of the point L are:
[tex]L(-2,-5)[/tex]
You know that the trapezoid rule applied for the translation of the trapezoid JKLM is:
[tex](x, y)[/tex]→[tex](x + 8, y - 3)[/tex]
Therefore, in order to find the coordinates of the point L', you need to add 8 to the x-coordinate of the point L and subtract 3 from the y-coordinate of the point L.
Then:
[tex]L'(-2 + 8, -5 - 3)\\\\L'(6,-8)[/tex]
1. Write the standard equation for a circle that has a center of (-5.-2) and a radius of 25.
Answers
Answer:
[tex](x+5)^2+(y+2)^2=625[/tex]
Step-by-step explanation:
The center-radius form a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]. Okay, it is called standard form. But I like to call it center-radius form because it tells us the center (h,k) and the radius,r.
So we are given the following information r=25 and center=(h,k)=(-5,-2).
So we just plug this in like so:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](x--5)^2+(y--2)^2=25^2[/tex]
[tex](x+5)^2+(y+2)^2=625[/tex]
Choose the equation that represents the graph below:
Answers
Answer:
y = -2x/3 + 6
Step-by-step explanation:
y = mx+b
m = y2-y1/x2-x1
m = 2 - 6/6 - 0
m= -4/6 = -2/3
b = y-intercept = 6
Please help ASAP
this table shows how many students from high schools attended a foot ball game.
A student is randomly selected.
what is the probability that a student attended the game, given that the student is from North Beach? Round your answer to two decimal places.
Answers
In total, there are 200 students from North Beach.
Of those 200 students, 110 attended the game.
Because it is only asking for the probability that a student from North Beach attended, the answer would be 110 / 200, or 0.55.
Therefore, the answer would be C.
Hope this helps! :)
Answer:
0.314
Step-by-step explanation:
Given:
total number of students=350
total number of students that attented= 170
students that attended from North beach =110
probability that a student attended the game, given that the student is from North Beach= 110/350
=0.314 !
Which statement can be combined with its converse to form a true biconditional?
A) if the measure of an angle is 30, then it is an acute angle
B) if two lines intersect, then the two lines are not Skew.
C) if the rat is the perpendicular bisector of the segment, then the raid devices segment into two congruent segments.
D) if an angle is a straight angle, then it’s sides are opposite rays.
Answers
Statement C can be combined with its converse to form a true biconditional because both statements are true.
Explanation:In order for a statement and its converse to form a true biconditional, both statements must be true. Let's analyze the given statements:
A) If the measure of an angle is 30, then it is an acute angle.
B) If two lines intersect, then the two lines are not skew.
C) If the ray is the perpendicular bisector of the segment, then it divides the segment into two congruent segments.
D) If an angle is a straight angle, then its sides are opposite rays.
Out of these options, statement C can be combined with its converse to form a true biconditional because both statements are true:
If the ray is the perpendicular bisector of the segment, then it divides the segment into two congruent segments.
If the segment is divided into two congruent segments, then the ray is the perpendicular bisector of the segment.
Consider the following system of equations. -10x2-10y2=-300 5x2+5y2=150 Which statement describes why the system has infinite solutions?
Which statement describes why the system has infinite solutions?
The equations represent parabolas that result in graphs that do not intersect.
The equations represent circles that result in graphs that do not intersect.
The equations represent parabolas that result in the same graph.
The equations represent circles that result in the same graph.
Answers
Answer:
The equations represent circles that result in the same graph.
Step-by-step explanation:
we have
[tex]-10x^{2}-10y^{2}=-300[/tex]
Divide by -10 both sides
[tex]x^{2}+y^{2}=30[/tex] -----> equation A
This is the equation of a circle centered at origin with radius [tex]r=\sqrt{30} \ units[/tex]
and
[tex]5x^{2}+5y^{2}=150[/tex]
Divide by 5 both sides
[tex]x^{2}+y^{2}=30[/tex] -----> equation B
This is the equation of a circle centered at origin with radius [tex]r=\sqrt{30} \ units[/tex]
equation A and equation B are equal
therefore
The system has infinite solutions, because the equations represent circles that result in the same graph.
In set-builder notation, how do you write the solutions of 2x − 7 ≥ 11?
Answers
Answer:
{ x ∈ R | x ≥ 9 }
Step-by-step explanation:
we have
[tex]2x-7 \geq 11[/tex]
solve for x
Adds 7 both sides
[tex]2x\geq 11+7[/tex]
[tex]2x\geq 18[/tex]
Divide by 2 both sides
[tex]x\geq 18/2[/tex]
[tex]x\geq 9[/tex]
The solution is the interval -----> [9,∞)
In set builder notation
{ x ∈ R | x ≥ 9 }
All real numbers greater than or equal to 9
In one store, bananas cost 60 cents per pound. The cost, in dollars, of x pounds of bananas is 0.6x. What is the cost of 2.50 pounds of bananas?
Answers
Final answer:
The cost of 2.50 pounds of bananas is 1.50 dollars.
Explanation:
To find the cost of 2.50 pounds of bananas, we need to multiply the weight of the bananas by the cost per pound. In this case, the cost per pound is 60 cents.In the store, bananas cost 60 cents per pound, and the cost in dollars for x pounds of bananas is given by the equation 0.6x. To find the cost of 2.50 pounds of bananas, you simply substitute x with 2.50 in the equation: 0.6 times 2.50. So, we multiply 2.50 pounds by 0.60 dollars per pound:
2.50 pounds x 0.60 dollars/pound = 1.50 dollars.
Therefore, the cost of 2.50 pounds of bananas is 1.50 dollars.
What’s the value of x
Answers
Answer:
The correct answer is last option 3√2 units
Step-by-step explanation:
From the figure we can see that two small right angled triangle.
These two triangle combined to form a large right angled triangle.
To find the value of x
Consider the small triangle with hypotenuse x and one side 3 units.
The angles of this triangle be 45°, 45° and 90°, then the sides are in the ratio 1 : 1 : √2
Therefore we can write,
3 : 3 : x = 1 : 1 : √2
x = 3√2
The correct answer is last option 3√2 units
In a survey of more than 4000 people, 91% of
the respondents claimed to prefer Pedro's
Perfect Pizza over any other brand of pizza.
Answers
Answer: people who have had Pedro’s perfect pizza delivered to their house in the last month
Step-by-step explanation:
I guessed and got lucky lol
Solve this equation for x. Round your answer to the nearest hundredth. 0.75=logx
Answers
Answer:
Step-by-step explanation:
[tex]10^.^7^5=10^l^o^g^(^x^)\\=10^.^7^5=x\\=10^\frac{3}{4}=\sqrt[4]{10^3} =\sqrt[4]{1000} =5.6=x[/tex]
To solve the equation 0.75 = log(x), we exponentiate both sides with base 10, resulting in x = 10^0.75. The calculated value of x to the nearest hundredth is approximately 5.62.
Explanation:To solve the equation 0.75 = log(x), we need to understand that the logarithm function here is the common logarithm, which means it has a base of 10. The equation essentially states that 10 raised to the power of 0.75 equals x. To find x, we simply need to perform the inverse operation of taking the logarithm, which in this case is exponentiation.
We use the fact that if logb(a) = c, then bc = a, where b is the base, a is the result, and c is the exponent. Therefore, we can rewrite our original equation as:
x = 100.75
Using a calculator, we can find that:
x ≈ 5.62
This is the value of x, rounded to the nearest hundredth, as the question requested.
Given a triangle with a = 12, A = 13°, and B = 12°, what is the length of c? Round to the nearest tenth.
Answers
Answer:
=5.1 units
Step-by-step explanation:
To use the sine rule to find the length of c we first need to find the angle at C.
C=180-(13+12)
C=180-25
C=155°
a/Sin A=c/Sin C
Calculating for the value of c using the sine rule:
12/Sin 13=c/Sin 155
c=12 sin 155
=5.07 units
Thus to 1 decimal places, the value of c is 5.1 units.
At the carpet store where you work, a customer wants to buy carpet for a room that is 16 1/2 feet by 18 1/2 feet in size. The carpet ,pad,and installation will cost $17.50 per square yard. To the nearest dollar,how much will it cost to carpet the room?
Answers
Answer: 595 Dollars
Step-by-step explanation:
16 1/2 times 18 1/2 = 305.25
one square yard = nine feet
305 devided by nine 33.9166667 (round to 34)
34 times 17.50 = 595
Answer:
$593
Step-by-step explanation:
We have been that a customer wants to buy carpet for a room that is 16 1/2 feet by 18 1/2 feet in size.
First of all, we will find area of carpet by multiplying both side lengths as:
[tex]\text{Area of carpet}=16\frac{1}{2}\text{ ft}\times 18\frac{1}{2}\text{ ft}[/tex]
Convert mixed fraction into improper fraction:
[tex]16\frac{1}{2}\Rightarrow \frac{16\times2+1}{2}=\frac{32+1}{2}=\frac{33}{2}[/tex]
[tex]18\frac{1}{2}\Rightarrow \frac{18\times2+1}{2}=\frac{36+1}{2}=\frac{37}{2}[/tex]
[tex]\text{Area of carpet}=\frac{33}{2}\text{ ft}\times \frac{37}{2}\text{ ft}[/tex]
[tex]\text{Area of carpet}=\frac{1221}{4}\text{ ft}^2[/tex]
[tex]\text{Area of carpet}=305.25\text{ ft}^2[/tex]
1 square feet equals 0.111 square yards.
[tex]305.25\text{ ft}^2=305.25*0.1111\text{ yards}^2[/tex]
To find the cost to carpet the room, we will multiply area of carpet by cost $17.50 per square yards.
[tex]305.25\times 0.1111\text{ yards}^2\times\frac{\$17.50}{\text{ yard}^2}[/tex]
[tex]305.25\times 0.1111\times\$17.50[/tex]
[tex]\$593.4823125\approx \$593[/tex]
Therefore, the cost to carpet the room would be $593.
What is the median of this set of data values?
10, 14, 15, 17, 20, 21, 22, 25
Answers
Answer:
18,5
Step-by-step explanation:
middle numbers --> (17+20)/2 = 18,5
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Answer: 18.5
Step-by-step explanation:
Step 1) To find the median in a set of data values you must first arrange them from least greatest to greatest. Luckily, it's already done for you!
Step 2) Then, take the two middle numbers (17 and 20) and add them.
17+20 = 37
Step 3) Now, just divide by two
37/2 = 18.5
Let me know if you have any more questions!
help please can’t find the answer
Answers
Answer:
[tex]\large\boxed{V=99\pi}[/tex]
Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have 2r = 6 → r = 3, H = 11.
Substitute:
[tex]V=\pi(3^2)(11)=99\pi[/tex]
Can you guys please help me with this two questions
Answers
Answer:
1. C) 5.50x + 10
2. 54
Step-by-step explanation:
1. C) 5.50x + 10
You have a static fee of $10 which does not need to be attached to a variable as it will not change. You also have a fee of $5.50, which may be charged depending on the amount of classes. Since this is dependent on something, it includes a variable.
Therefore, your terms are:
5.5x
10
Simply add them together for your equation.
[tex]5.5x+10[/tex]
2. 54
To solve, simply plug in 8 to your equation which you created in part 1. This is possible because x stands for the amount of classes and, as the question tells us, 8 is the amount of classes.
[tex]5.5(8)+10\\44+10\\54[/tex]
Describe the translation. y=(x+3)2+4 → y=(x+1)2+6
Answers
Answer:
Shift +2 units to the right and +2 units up
Step-by-step explanation:
y = (x+3)² + 4 has a horizontal shift of -3 and a vertical shift of +4.
y = (x+1)² + 6 has a horizontal shift of -1 and a vertical shift of +6.
So do translate the first equation to the second, shift +2 units to the right and +2 units up.
Suppose a triangle has sides a, b, and c, and that a2 + b2 < c. Let o be the
measure of the angle opposite the side of length c. Which of the following
must be true? Check all that apply.
Answers
Step-by-step explanation:
if a^2 +b^2 <c^2,
then abc is not a right triangle since for a right triangle a^2+ b^2 = c^2
The following features of the triangle are found: A. a² + b² - c² = 2 · a · b · cos θ, B. cos θ < 0, C. The triangle is not a right triangle.
How to analyze the features of a triangle
In this question we must infer all features from a triangle such that a² + b² < c². Then, the triangle is not a right triangles since relationship between side lengths is different from the relationship described by Pythagorean theorem. Then, triangle is described by law of cosine:
a² + b² - c² = 2 · a · b · cos θ
If a² + b² < c², then a² + b² - c² < 0 and 2 · a · b · cos θ < 0. Thus, we get the following result: cos θ < 0.
The shortest path from point A to point B goes through a pond. To avoid
the pond, you must walk straight 23 meters along one edge of the pond,
then take a 90-degree turn, and again walk straight 57 meters along
another edge of the pond to reach point B. If you could walk through the
pond, what would be the distance from point A to point B?
Answers
Final Answer:
The direct distance from point A to point B, considering a straight path through the pond, is 80 meters. This is obtained by applying the Pythagorean theorem to the right-angled triangle formed by walking 23 meters and then 57 meters along the edges of the pond. Subtracting the initial 23 meters provides the actual direct distance.
Step-by-step explanation:
In this scenario, we can apply the Pythagorean theorem to find the direct distance from point A to point B. Let's denote the sides of the right-angled triangle formed by walking along the edges of the pond as follows: the first leg (along one edge) is \(a = 23\) meters, the second leg (along the other edge) is [tex]\(b = 57\)[/tex] meters, and the hypotenuse (direct distance from A to B, walking through the pond) is (c). According to the Pythagorean theorem, [tex]\(c^2 = a^2 + b^2\).[/tex]
Substituting the given values, we get [tex]\(c^2 = 23^2 + 57^2\).[/tex] Calculating this gives [tex]\(c^2 = 529 + 3249\)[/tex], resulting in [tex]\(c^2 = 3778\)[/tex]. Taking the square root of both sides gives [tex]\(c ≈ \sqrt{3778} ≈ 61.47\)[/tex]. Therefore, the direct distance from point A to point B, walking through the pond, is approximately 61.47 meters.
However, since the question asks for the distance considering walking straight through the pond, we need to add the lengths of both sides of the pond. Thus, [tex]\(61.47 + 23 + 57 = 80\)[/tex]. Therefore, the final answer is 80 meters. This approach considers the direct path, incorporating the lengths of the edges and the hypotenuse, providing the most accurate measurement for the distance from point A to point B.
Solve for x in the picture please
Answers
Answer: [tex]x=1[/tex]
Step-by-step explanation:
In order to find the value of "x", it is important to remember that:
[tex]Tangent\ chord\ angle=\frac{1}{2}(Intercepted\ arc)[/tex]
We can identify in the figure that:
[tex]Tangent\ chord\ angle=(43x)\°\\\\Intercepted\ arc=AB[/tex]
Then:
[tex]43x=\frac{1}{2}AB[/tex]
Solving for AB:
[tex]2(43x)=AB\\\\AB=86x[/tex]
Now, since there are 360° in a circle, we know that:
[tex]AB+(272x+2)=360[/tex]
Then we can substitute [tex]AB=86x[/tex] into [tex]AB+(272x+2)=360\°[/tex] and solve for "x". This is:
[tex](86x)+(272x+2)=360\\\\358x=360-2\\\\x=\frac{358}{358}\\\\x=1[/tex]