Answer: [tex]\sqrt{2}[/tex]
======================================================
Explanation:
Rewrite each trig function terms of sine and/or cosine. Then use the unit circle to find that,
[tex]\cot(90^{\circ})\cos(45^{\circ}) + \sec(45^{\circ})\\\\\frac{\cos(90^{\circ})}{\sin(90^{\circ})}\cos(45^{\circ}) + \frac{1}{\cos(45^{\circ})}\\\\\frac{0}{1}*\frac{\sqrt{2}}{2} + \frac{1}{(\sqrt{2})/2}\\\\\frac{2}{\sqrt{2}}\\\\[/tex]
Now rationalize the denominator
[tex]\frac{2}{\sqrt{2}}\\\\\frac{2\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\\frac{2\sqrt{2}}{\sqrt{2*2}}\\\\\frac{2\sqrt{2}}{\sqrt{4}}\\\\\frac{2\sqrt{2}}{2}\\\\\sqrt{2}[/tex]
Which is the exact value of [tex]\sec(45^{\circ})[/tex]
The portion [tex]\cot(90^{\circ})*\cot(45^{\circ})[/tex] evaluates to 0 and goes away.
Which equation represents the
value of 0 in a triangle when all
oth er angle information is
known?
Answer:
theta = 180 -(A +B)
Step-by-step explanation:
The sum of the angles of a triangle is 180
theta + A + B = 180
solve for theta
Subtract ( A + B) from each side
theta +A+B -(A +B) = 180 -(A +B)
theta = 180 -(A +B)
solve 4w–3w+2w=24
Please
We need to simplify the left side first.
On the left side, all the terms can be combined.
So 4w - 3w + 2w is 3w.
So we have 3w = 24.
Next, dividing both sides by 3, we have w = 8.
So our solution is w = 8.
Answer
[tex] \boxed{ \huge{ \bold{ \sf{ \boxed{w = 8}}}}}[/tex]
Step by step explanation
[tex] \sf{4w - 3w + 2w = 24}[/tex]
Collect like terms
⇒[tex] \sf{w + 2w = 24}[/tex]
⇒[tex] \sf{3w = 24}[/tex]
Divide both sides of the equation by 3
⇒[tex] \sf{ \frac{3w}{3} = \frac{24}{3} }[/tex]
Calculate
⇒[tex] \sf{w = 8}[/tex]
Hope I helped!
Best regards!!
Terri graphed a system of linear inequalities. Which ordered pairs are a part of the solution set for this system of linear inequalities? Select two that apply.
(-1, 5)
(2, -4)
(7, -1)
(4, 6)
(5, 2)
Answer: (2, -4) and (7, -1)
Step-by-step explanation:
Ok, the solutions of the system of inequalities are all the points that lie on the blue shaded part of the graph or in the solid line.
So, in order to see if the points are solutions of the system, then you need to locate the point in the graph and see if it is inside the shaded region or in the solid line (only in the segment that "touches" the shaded region).
Now, we want to find the equation of the solid line, we can see that it passes through the points (0, 6) and (6, 0)
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then, in this case, the slope is:
a = (0 - 6)/(6 - 0) = -1.
And to find the value of b, we have that when x = 0, y = 6.
y = 6 = -1*0 + b
6 = b
The equation is:
y = -1*x + 6
(-1, 5) is not in the blue region nor in the solid line, so this is not a solution.
(7, - 1) this point is near the solid line, let's test it:
y(7) = -1*7 + 6 = -1
So the point (7, -1) is on the solid line, and is the other solution of the system.
Can you tell I suck at math?
Answer:
B). 34.85°
Step-by-step explanation:
From trigonometric ratios:
[tex] \sin(C) = \frac{opposite}{hypotenuse} [/tex]
Opposite = 16
Hypotenuse = 28
[tex] \sin(C) = \frac{16}{28} \\ \\ C = { \sin}^{ - 1} ( \frac{16}{28} ) \\ \\ C = 34.85 \degree[/tex]
a plane is a _ figure
What is the simplest form of the fraction 120/150?
Answer:
4/5
Step-by-step explanation:
120/30=4
150/30=5
120/150=4/5
Answer:
4/5
Step-by-step explanation:
120/150
Both 120 and 150 are divisible by 30
So we divide both number by 30
120 ÷ 30 = 4
150 ÷ 30 = 5
So therefore the answer is
4/5
Hope this helps!
The Boeing777-300ER flies between Auckland and Los Angeles. It has 246 Economy
class seats, 50 Premium Economy seats and 44 Business Premier seats. Out of the 340
seats in total, what percentage are Economy seats?
Answer:
72.35%
Step-by-step explanation:
246/340 = .723529
Just multiply it by 100 to get the percentage
.723529 x 100 = 72.3529
A map is drawn using 2cm:100 mi. On the map town B is 3.5 cm from town a in town see is 2 cm past town be how many miles apart or town a in town c
Answer:
275 miles
Step-by-step explanation:
I assume all towns are on the same line. Then, town C is 5.5 cm from town A on the map since 3.5 cm + 2 cm = 5.5 cm.
The real distance can be calculated with a proportion.
2/100 = 5.5/x
2x = 5.5 * 100
2x = 550
x = 275
Answer: 275 miles
solve for x 13(x-3)=39
Answer:
x=6
Step-by-step explanation:
13(x-3)=39
Divide each side by 13
13/13(x-3)=39/13
x-3 = 3
Add 3 to each side
x-3+3 = 3+3
x = 6
Answer:
x=6
Step-by-step explanation:
expanding we get
13x-39=39
13x=39+39
13x=78
x=78/13
x=6
FOLLOW THE STEP: reduce to simplest form
-7/12 + 3/8 = ______
Answer:
-5/24
Step-by-step explanation:
get a common denominator = 24
-14/24 + 9/24 = -5/24
Answer:-5 /24 ez
Step-by-step explanation:
Please answer quickly! A radio telescope has a parabolic surface, as shown below. A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 1 meter and its width from left to right is 20 meters. If the telescope is 1 m deep and 20 m wide, how far is the focus from the vertex?
Answer:
Basing on the description, a parabola checking with vertex at origin, the formula with vertex at origin can be used, x^2 = 4py. p is the focus therefore with the dimensions given, we get yourself a 0.25 and this is the distance of the focus to the vertex.
Write the following statement in equation form using variables x and y. "Sum of two numbers is 15 and difference is 11.
Answer:
see explanation
Step-by-step explanation:
Using x and y to represent the 2 numbers with x > y , then
x + y = 15 → (1)
x - y = 11 → (2)
Adding the 2 equations term by term to eliminate y
2x = 26 ( divide both sides by 2 )
x = 13
Substitute x = 13 into (1)
13 + y = 15 ( subtract 13 from both sides )
y = 2
The 2 numbers are 13 and 2
Given the equation y = 2x + 3 what is the slope?
x
3
2
idk
Answer:
The slope is 2Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question the equation is
y = 2x + 3
Comparing this equation with the general equation above
Slope / m = 2
Hope this helps you
(7)
* 8. Evaluate Mahesh rides a bus to work. The number of minutes his daily
bus ride took over a two-week period are recorded below:
M T W Th F
Week 1 12 8 10 9 12
Week 2 8 7 12 9 10
a. Find the mean, median, mode, and range of the data.
b. Which measure would Mahesh use to describe how many minutes
the duration of his bus ride may differ from day to day?
a. From the data recorded for the number of minutes Mahesh bus ride took over a two-week period, Mean = 9.7 minutes, Median = 9.5 minutes, Mode = 12 minutes, Range = 5 minutes.
b. The measure Mahesh will use to describe how many minutes the duration of his bus ride may differ from day to day is the range.
From the question,
The data for the first week are
Week 1: 12, 8, 10, 9, 12
and for the second week
Week 2: 8, 7, 12, 9, 10
Putting the data together, we have
12, 8, 10, 9, 12, 8, 7, 12, 9, 10.
Now,
]a. To determine the mean of the above data,
Mean is the average of the numbers. The mean can be determined by adding up the numbers and then dividing by the count of the numbers.
From the above, we have 10 numbers
∴ [tex]Mean = \frac{12+8+10+9+12+8+7+12+9+10}{10}[/tex]
[tex]Mean = \frac{97}{10}[/tex]
Mean = 9.7 minutes
For the median of the data
The median of a given set of numbers is the middle value when the numbers are sorted either in the ascending or descending order.
For the data 12, 8, 10, 9, 12, 8, 7, 12, 9, 10
Arranging in ascending order, we get
7, 8, 8, 9, 9, 10, 10, 12, 12, 12.
Since we have two numbers (9 and 10) in the middle, the median can be determined by the finding the average of these numbers.
∴ [tex]Median = \frac{9+10}{2}[/tex]
[tex]Median = \frac{19}{2}[/tex]
Median = 9.5 minutes
For the mode of the data
The mode is the value that occurs most often.
From the data, 12 occurs most often (three times)
∴ Mode = 12 minutes
For the range of the data
Range is the difference between the highest and lowest values.
From the data
Highest value = 12
Lowest value = 7
∴ Range = 12 - 7
Range = 5 minutes
b. For the measure Mahesh will use to describe how many minutes the duration of his bus ride may differ from day to day.
Here, we are talking about measures of dispersion. The only measure of dispersion from above is range.
∴ The measure Mahesh will use to describe how many minutes the duration of his bus ride may differ from day to day is the range.
Hence,
From the data recorded for the number of minutes Mahesh bus ride took over a two-week period, Mean = 9.7 minutes, Median = 9.5 minutes, Mode = 12 minutes, Range = 5 minutes
and the measure Mahesh will use to describe how many minutes the duration of his bus ride may differ from day to day is the range.
Learn more here: https://brainly.com/question/16882439
the perimeter of a rectangle is 68 feet the length is 5 inches shorter than twice the width what are the dimensions of the rectangle
Answer:
Step-by-step explanation:
The perimeter formula is P = 2L + 2W. If the perimeter is given as 68 feet, then our P will be filled in with 68. If the length is "5 inches shorter than twice the width" is an expression that looks like this, keeping in mind that "shorter" means subtraction, "twice" means doubled, and the word "is" means equals:
L = "length is"
2W is "twice the width"
5 inches shorter is " - 5". Putting it all together:
L = 2W - 5. Now we can fill in the perimeter formula:
68 = 2W + 2(2W - 5) and
68 = 2W + 4W - 10 and
68 = 6W - 10 and
78 = 6W so
W = 13. The width is 13 inches and the length is
L = 2(13) - 5 so the length is
L = 21 inches.
Tricia starts school at 7:00 AM and has lunch at 12:00 PM. She wants to make sure she has something to eat in between. Determine what time she should eat her snack if she is to eat at exactly a time between starting school and eating lunch. (Hint: Set up a horizontal number line as a timeline.) A. A. 9:30 AM
B. 10:00 AM
C. 9:00 AM
D. 10:30 AM
Answer:
D) 9:00 am
Step-by-step explanation:
Because 9:00 is the midpoint of 7 and 12
need help on this one
The length of a rectangular field is 6 metres longer than its width. If the area of the field is 72 square metres, What are the width and the length of the field?
Answer:
The length is 12metres, the width is 6metres
Step-by-step explanation:
Suppose the width is x, the length is x+6
The square is 72. The square of rectangular field is equal to product of length and width.
so x(x+6)=72
x^2+6x-72=0
a=1 b=6 c=-72
D= b^2-4ac= 6*6+288= 36+288= 324
sqrtD= 18
x1= (-b-sqrtD)/2a=(-6-18)/2= -12 (it is negative, but width is only positive. So this root doesn't match)
x2=(-b+sqrtD)/2a= (-6+18)/2= 12/2=6 - the width
The length is 6+6=12
The difference between the annual and semi-annual compound interest on a sum of money is Rs 482 at the rate of 20 % per annum for 2 years. Find the sum.
One hundred people, ages 11-15, were randomly surveyed to find their opinion of their favorite leisure time activity. Sixty-four percent of them said they liked to spend time watching TV. If there are 1500 students in your school, about how many of them would you predict would enjoy watching t.v. A.2343 B.960 C.640 D.500
Answer:
If there are 1500 students in your school then 960 students would enjoy watching TV
Step-by-step explanation:
Step 1: We know that 64% of kids aged from 11 to 15 enjoy watching TV and there is 1500 students in your school
Step 2: We now want to find 64% of 1500, we can rewrite 64% as 0.64. We multiple 1500 by 0.64 to find out how many students enjoy watching TV
0.64 x 1500 = # of students who like watching TV
960 = # of students who like watching TV
Therefore out of 1500 students, 960 would enjoy watching TV
HELP ILL MARK YOU BRAINLIEST (40PTS)!! Which number line best shows how to solve −6 − (−8)? A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 6. Another arrow points from negative 6 to 2. A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 6. Another arrow points from negative 6 to 8. A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to 6. Another arrow points from 6 to negative 8. A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 6. Another arrow points from negative 6 to negative 2.
Answer:
i think it is 6 but not sure
Step-by-step explanation:
Answer:
A is the answer hope i could help
Step-by-step explanation:
Simplify
2x + 5x^3 + 3x - 4x^3
Answer:
x³ + 5x
Step-by-step explanation:
2x+5x3+3x−4x3
=2x+5x3+3x+−4x3
Combine Like Terms:
=2x+5x3+3x+−4x3
=(5x3+−4x3)+(2x+3x)
=x3+5x
Answer:
[tex]\large \boxed{x^3+5x}[/tex]
Step-by-step explanation:
[tex]2x + 5x^3 + 3x - 4x^3[/tex]
[tex]\sf Group \ like \ terms.[/tex]
[tex]5x^3 - 4x^3+2x+3x[/tex]
[tex]\sf Combine \ like \ terms.[/tex]
[tex]x^3+5x[/tex]
If the domain of a function f is {x|0≤x≤7} and the domain of a function g is {x|-2≤x≤5}, then the domain of the sum of the function f+g is ______
Answer:
-2 ≤ x ≤ 6
Step-by-step explanation:
For function f:
x - 7 ≤ 0 and x ≥ 0
For function g:
x + 2 ≥ 0 and x - 5 ≤ 0
The sum of the f + g:
x - 7 + x - 5 ≤ 0
2x - 12 ≤ 0
2x ≤ 12
∴ x ≤ 6
Also, x + 2 ≥ 0
x ≥ -2
Hence, -2 ≤ x ≤ 6
A building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground. Could you use lines and text to draw and label a diagram that represents this situation?
Greetings from Brasil...
Its attached the diagram of the situation.....
The ground is 8 feet from the bottom edge of the window
How far up from the ground is the bottom edge of the window?We start by representing the building, the ladder and the ground in a sketch.
See attachment for diagram
From the diagram, the distance (d) from ground to the bottom edge of the window is calculated using Pythagoras theorem:
10^2 = d^2 + 6^2
Evaluate the squares
100 = d^2 + 36
Evaluate the like terms
d^2 = 64
Take the square root of both sides
d = 8
Hence, the ground is 8 feet from the bottom edge of the window
Read more about Pythagoras theorem at:
https://brainly.com/question/343682
#SPJ6
Find the area of a circle with a diameter of 4.
Either enter an exact answer in terms of it or use 3.14 for 7 and enter your answer as a decimal.
units?
area of circle =22/7×4=12.56
Score for Question 3: of 5 points)
. What is the area of triangle BCD to the nearest tenth of a square centimeter? Use special right triangles to
help find the height. Show your work.
Answer:
[tex] \frac{25 \sqrt{3} }{2} [/tex]
Step-by-step explanation:
Height = 5 * tan 60°
[tex]height \: = 5 \sqrt{3} [/tex]
[tex]area = \frac{1}{2} \times 5 \times 5 \sqrt{3 } = \frac{25 \sqrt{3} }{2} [/tex]
What is the median for the set of data? 6, 7, 10, 12, 12, 13
Answer choices:
6
7
10
12
12
13
Answer:
11
Step-by-step explanation:
If the set of numbers are not in least to greatest first set them up into their positions. But since this set is already in least to greatest we can go to the next step.
6, 7, 10, 12, 12, 13
Cross off all numbers until you get to the middle:
6, 7, 10, 12, 12, 13
Find the mean of the numbers in the middle:
10 + 12 = 22
22 / 2 = 11
The answer is 11
Hope this helped.
Answer:
11
Step-by-step explanation:
10+12=22
22÷2=11
median is equal to the middle number after being arranged in ascending order.
what is the coefficient of x in the equation of 32+2x=10
solve after finding the coefficient
Answer:
x= -11
Step-by-step explanation:
the coefficient is variable that appears before a number . bearing this in mind, the coefficient of x is therefore 2 .
the value of x is:
>32+2x=10
>2x=10-32
>2x= -22
>x= -11
Answer:
Step-by-step explanation:
Coefficient of x = 2
32 + 2x = 10
Subtract 32 from both side
32 + 2x -32 = 10 - 32
2x = - 22
Divide both sides by 2
2x/2 = -22/2
x = -11
inscribed angles. help asap!
Answer:
20°
Step-by-step explanation:
The measure of the inscribed angle is equal to the half of the arc it sees
Since AC is the diameter the measure of arc ABC is 180°
and since A sees arc BC and C sees the arc AB
A< + C< = 90° so angle C = 20°
Which of these expressions is equivalent to 3x(x-1)-5(x-1)? Select all that apply.
3x^2-8x+5
x-1(3x-5)
(3x-5)(x-1)
(x-1)(3x+5)
Answer:
3x(x-1)-5(x-1)
=3x²-3x-5x+5 (we can count it one by one)
=3x²-8x+5 (we can calculate the same variable)
#i'm from indonesia
hope it helps.
Answer:
[tex]\boxed{3x^2 -8x+5}[/tex]
[tex]\boxed{(3x-5)(x-1)}[/tex]
Step-by-step explanation:
[tex]3x(x-1)-5(x-1)[/tex]
Expand brackets.
[tex]3x(x)+3x(-1)-5(x)-5(-1)[/tex]
[tex]3x^2 -3x-5x+5[/tex]
Combine like terms.
[tex]3x^2 -8x+5[/tex]
[tex]3x(x-1)-5(x-1)[/tex]
Take x-1 as a common factor.
[tex](3x-5)(x-1)[/tex]