Answer:12.5
Step-by-step explanation:
Answer question in picture
The given graph can be expressed as an equation of f(x) = tan(-x) - 2.
What is a graph of a trigonometric function?
In these trigonometry graphs, the x-axis values of the angles are in radians, and the y-axis value of the function at each given angle is taken as f(x).
The given graph is of a negative angle of a tangent.
So if we draw the graph of the tangent of a negative angle, the graph will pass through the origin, but
If we subtract 2 from the graph of the tangent of the negative angle then we will get the same graph as shown in the given figure.
So the equation would be f(x) = tan(-x) - 2.
Hence, the equation of the graph will be f(x) = tan(-x) - 2.
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Daiy i given a cale drawing with the route to her campite. The route to the campite i 28 cm on the drawing. The cale on the drawing i 1 : 300. What i the actual length of the route?
metre
According to scale drawing, the actual length of route is 84 metres.
The calculations will be based on the concept of ratio and proportion -
Ratio in real :: Ratio of scale drawing
Let us assume the actual length of route be x.
28 : x :: 1 : 300
Writing the ratio as fraction
28/x = 1/300
Cross multiplying the fraction
x = 28 × 300
Performing multiplication on Right Hand Side of the equation
x = 8400 cm
Converting centimetres to meters. As per the known fact, 100 cm = 1 metre
8400 cm = 84 meters
Thus, the actual length is 84 meters.
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A group of 60 people are going on a trip to an amusement park that has dollar coasters and water rides. The number of people who like roller coasters is 42, the number who do not like water rides is 23 and the number who do not like either kind of ride is 8. Determine which Venn diagram accurately represents the people going on the trip.
The no. of people whole likes only roller coasters is 19.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Let N(U) be the no. who likes at least one of the rides which is
N(U) = (60 - 8) = 52 as 8 people do not like either kind of ride.
Given, The number of people who like roller coasters is 42 and the number who do not like water rides is 23.
∴ The no. of people who only likes roller coasters is (42 - 23) = 19.
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Estimate each square root to the nearest tenth. 1. √10 3.4
Step 1: Estimate
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2.
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2.
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: Divide
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: Average
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667 Step 4: Repeat
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667 Step 4: RepeatTo get a more accurate number, keep repeating step 2 and 3.
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667 Step 4: RepeatTo get a more accurate number, keep repeating step 2 and 3.
Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667 Step 4: RepeatTo get a more accurate number, keep repeating step 2 and 3. You should get a final answer of 3.16.
6. The mass of Mars is 6.42 x 1023 kilograms. The mass of Mercury is 3.3 x 1023 kilograms.
a. What is the combined mass of Mars and Mercury expressed in scientific notation
b. What is the difference in the mass of the two planets expressed in scientific notation?
a) The combined mass of Mars and Mercury expressed in scientific notation is 9.72 x 10²³
b) The difference in the mass of the two planets expressed in scientific notation is 3.12 x 10²³
Scientific Notation:
Scientific method is the method of expressing numbers in terms of a decimal number between 1 and 10, but not 10 itself multiplied by a power of 10.
Given,
The mass of Mars is 6.42 x 10²³ kilograms. The mass of Mercury is 3.3 x 10²³ kilograms.
Here we need to find the following,
a) The combined mass of Mars and Mercury expressed in scientific notation
b) The difference in the mass of the two planets expressed in scientific notation
a) The combined mass of Mars and Mercury expressed in scientific notation is calculated by add the both masses then we get,
=> (6.42 x 10²³) + (3.3 x 10²³)
Here we have to take the exponent term as common, then we get,
=> (6.42 + 3.3) x 10²³
=> 9.72 x 10²³
b) The difference mass of Mars and Mercury expressed in scientific notation is calculated by subtract the both masses then we get,
=> (6.42 x 10²³) - (3.3 x 10²³)
Here we have to take the exponent term as common, then we get,
=> (6.42 - 3.3) x 10²³
=> 3.12 x 10²³
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Why is the area of a triangle 1/2 Bxh?.
By using the rectangle, we proved that area of triangle is half the area of rectangle that is 1/2 (base×height).
Some properties of rectangle are ?The opposite sides are parallel and equally spaced apart, and each internal angle is 90 degrees.360 degrees are equal to the total of all internal angles.Both of the diagonals are identical in length and parallel to one another.A rectangle's perimeter is equal to 2a+2b units if its sides are of lengths a and b.A rectangle with sides that are a and b long has an area that is equal to ab sin 90 square units.Diagonally is the diameter of the circumference of a rectangle.To Prove:- Area of a triangle= 1/2 (base×height)
Diagonals of the rectangle divide it into two parts of equal areas.
Let ABCD be a rectangle.
In ΔABC and ΔADC,
AC=AC
By Alternate Interior Angles:
∠BAC=∠CAD
∠BCA=∠CDA
Hence, ΔABC≅ΔACD
∴ar(ΔABC) =ar(ΔACD)
Let ΔABC,
We draw a line AD perpendicular to BC, line EF parallel to BC passing through A and lines BE and CF , perpendicular to BC passing through B and C respectively.
In rectangle ADBE,
we get,
ar(ΔABE)=ar(ΔADB)
Similarly, in rectangle ADCF,
ar(ΔADC)=ar(ΔACF)
Now, area of rectangle BCFE, from axiom,
=(length)⋅(breadth)
=AB⋅BC
=AD⋅BC
Also,
ar(BCFE)
=ar(ADBE) + ar(ADCF)
=2⋅ar(ΔADC) + 2⋅ar(ΔADB)
=2(ar(ΔADC) + ar(ΔADC)
=2(ar(ΔABC))
From (1) and (2),
2(ar(ΔABC)) = AD⋅BC
ar(ΔABC) = 1/2AD⋅BC
ar(ΔABC) = 1/2(base)⋅(height)
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(-3, -9) and (4, -2)
What is the Linear Equation?
Pls help asap! Tysm if u do!
The equation of the line is y=x-6 when the points are (-3,-9) and (4,-2).
Given that,
The points are (-3,-9) and (4,-2).
We have to find the linear equation.
We know the formula of the equation of the line is,
y=mx+b
The slope of the line is m that is rise by run.
m=-2+9/4+3
m=7/7
m=1
The slope of the line is 1.
Now, b is intercept.
-9=1(-3)+b
-9=-3+b
b=-9+3
b=-6
The equation of the line is y=x-6.
Therefore, The equation of the line is y=x-6 when the points are (-3,-9) and (4,-2).
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Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4. 31.4n + 8.4 = 24 –8.4n + 31.4 = 24 24 = 31.4n + (–8.4) 24 – 31.4 = –8.4n
The corerect equation for the given linear equation in one variable is 24 = 31.4n + (-8.4)
What is Linear Equation in One Variable?
A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable of the form an x + b = 0 are solved using simple algebraic techniques.
Solution:
According to the word problem,
The formation of Linear Equation will be
24 = 31.4n + (-8.4)
and it can be also written as
24 = 31..4n - 8.4
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I WILL MARK BRAINLIEST!!!
Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
4. The graph of the correct system of equations is shown. Find how many days it will take Amir to catch up to Jesse and how many pages they each will have read. (3 points)
Answer:
It will take 6 days to catch up and they both will have read 210 pages
Step-by-step explanation:
to find this out we just find where the line intersects
It intersects at 6 days and 210 pages
Hopes this helps please mark brainliest
Answer: i put this here so you can mark the other person brainliest
Step-by-step explanation:
Evaluate 23x-1 for x = 1.
A: 4
B: 1
C: 7
D: 8
Answer:
23-1=22
Step-by-step explanation:
I really need the answer to this question. What is n take away 5 times by 4? or: n-5*4
Answer: n-20
Step-by-step explanation: just multiply 5 and 4.
hope this helps!
please give brainliest!
9
105°
C
Α΄
B
6
Calculate the measure of ZC in ABCA to the nearest tenth of a degree.
By using the law of sine, the measure of ∠C is 39°
Law of sine:
Law of sine refers the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.
Given,
Here we have the triangle.
Now, we have to find the angle ∠C.
While we looking into the given diagram,
We have the length of,
AB = 6
AC = 9
∠B = 105°
So, based on the law of sine it can be written as,
=> sin 105° / 9 = sin x°/6
Apply the value of sin 105° = 0.97, then we get,
=> 0.97/9 = sin x° / 6
Cross multiply them, then we get,
=> 5.82/9 = sin x°
=> 0.64 = sin x°
=> x = sin⁻¹ (0.64)
=> x = 39°
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a local ice cream shop has a special deal on thursdays. buy a waffle cone for $3 and get each scoop for $1.50. what would be the rate of change in this word problem?
Answer: the rate change in this problem would be by 1.50
Step-by-step explanation:
The rate of change in this word problem will be 2.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
A local ice cream shop has a special deal on Thursdays. buy a waffle cone for $3 and get each scoop for $1.50.
Now,
The rate of change will be find as;
The rate of change = $3 / $1.50
= 2
Thus, The rate of change in this word problem will be 2.
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Chloe is in the business of manufacturing phones. She must pay a daily fixed cost of $300 to rent the building and equipment, and also pays a cost of $75 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
The table of values and the equation for C, in terms of p, representing the total cost, in dollars are
p C(p)
0 300
1 375
2 450
3 525
4 600
and so on.
Given,
Chloe is in the business of manufacturing phones.
She pay a daily cost $300 to rent for the building and equipment.
and, also pays a cost of $75 per phone produced for materials and labor.
Now, According to the question;
How to make a table of values and the equation for C, in terms of p, representing the total cost, in dollars?
The given parameters are:
Cost per phone = $75
Fixed cost of labor and material = $300
The total cost is represented as;
C(p) = Fixed cost + Cost per phone x Number of phones
So, we have
C(p) = 300 + 75 * p
Evaluate
C(p) = 300 + 75p
Hence, Using the above equation, the table of values is
p C(p)
0 300
1 375
2 450
3 525
4 600
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Find the area of the figure. Express the answer in terms of x and then
round to the nearest tenth.
Find the area of the figure in terms of x.
A=
C...
A≈
(Type an exact answer, using a as needed.)
Find the area of the figure rounded to the nearest tenth.
Square
6 cm
Answer:
Step-by-step explanation:
Area of the square = 6^2 = 36 cm^2
radius = 6 : 2 = 3 cm
Area of the four semicircles = 3^2 * π * 2 = 18 π cm^2
Total area in terms of π= 36 + 18π = 18(2+π) cm^2
Total area = 18(5.141593) = 92.548668 = 92.5 cm^2
Stuart owns a window washing business. He can wash the windows on 9 houses in 4 hours. At this rate, how long would it take him to wash the windows on 45 houses? How many houses could he wash in 12 hours
Answer:
20hours;
27houses.......................
find the sum of the interior angles of a polygon with 28 sides
The sum of the interior angles of a polygon with 28 sides is 4680°.
According to the question,
We have the following information:
The number of sides of a polygon = 28
We know that the following formula is used to find the sum of the interior angles of a polygon:
(n-2)*180 where n is the number of sides
Putting the value of n in this formula for the given polygon:
(28-2)180
We will first solve the bracket and then we will multiply the obtained result by 180:
26*180
4680°
Hence, the sum of the interior angles of a polygon with 28 sides is 4680°.
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3.
How many times the value of the 7 in 107 is the value of the 7 in 170?
Answer:
14
Step-by-step explanation:
What is
66/200 as a decimal
Answer:
0.33
Step-by-step explanation:
hope this helps :)
You decide at 14 years old you want to begin saving for a car for when you're 17. It's 3 months until your 15th birthday and you can afford to put $60 a month in a savings account. How much will you have for a car on your 17th birthday?
Answer:
180
Step-by-step explanation:
If you are 14 you are 3 years away from 17 Wich would mean $60 would have to be multiplied by 3
60x3
3x6= 18
18x10= 180
(sorry if this is wrong)
John was setting up nametags for a business meeting. His supervisor placed the first three rowsthe first row has 3 nametags, the second row has 5 nametags, and the third row has 8 nametags.
How many nametags should be in the fourth row?
The number of nametags that should be in the fourth row is 12
How to calculate the value?It should be noted that this information illustrates sequence.
In this case, the supervisor placed the first three rowsthe first row has 3 nametags, the second row has 5 nametags, and the third row has 8 nametags.
The difference will be:
5 - 3 = 2
8 - 5 = 3
Therefore, the next one will have a difference of 4. This will be:
= 8 + 4
= 13
Check: 12 - 8 = 4
Therefore, the nametags should be 12.
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solve for X in the angle diagram
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
The interior angles of a triangle add up to 180 degrees.
So we have [tex]108+47+(2x+11)=180[/tex]
Solve for x.
[tex]47+(2x+11)=72[/tex]
[tex]2x+11=25[/tex]
[tex]2x=14[/tex]
[tex]x=7[/tex]
Answer:
7
Step-by-step explanation:
108+47=155
180-155=25
25-11=14
14/2=7
Find the 97th term of the arithmetic sequence -16, 2, 20, ...
Answer: 1712
Step-by-step explanation:
[tex]a_{n} = a_{1} + d(n -1)[/tex]
[tex]a_{1} = -16[/tex]
[tex]d = 2 - (-16) = 18\\[/tex]
[tex]20 - 2 = 18[/tex]
[tex]-16 + 18(n+1)[/tex]
[tex]-16 + 18(97+1)[/tex]
[tex]-16 + (1728)\\[/tex]
[tex]1712[/tex]
The distance traveled by a cruise ship varies directly with the number of hours it travels. After 2 hours, a cruise ship travels 30 miles. After 4 hours, a cruise ship travels 60 miles. Determine the time it would take the cruise ship to travel 75 miles.
It will take the ship 5 hours to travel 75 miles
What is variation?A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.
if it takes 2 hours to cover 30 miles by the ship and 4 hours to cover 60 miles.
let d be the distance covered in miles and t time taken in hours
The d ∝ t
introducing a constant
d = kt
when d = 30, t = 2
30 = 2k
k = 30/2
k = 15
The equation relating d and t is
d = 15t
to find t when d = 75, making t the subject of the equation
t = d/15
t = 75/15
t = 5 hours
In conclusion, 5 hours is the time taken to cover 75 miles.
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each side of a square is increasing at a rate of 6 cm/s. at what rate (in cm2/s) is the area of the square increasing when the area of the square is 16 cm2?
The area of the square increasing when the area of the square is 16 cm² by the rate of 48cm²/s.
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
Here,
A = s²
(dA)/(dt)
(dA/ds)*(ds/dt)
(ds)/(dt) = 6 cm/s
When A = 16 cm²
16 = s²
s = √(16)
s = 4 cm
(dA)/(dt) = 2 × 4 × 6 = 48 cm²/s
When the square is 16 cm², its area grows by 48cm²/s, or one-fourth of its initial size.
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Work out an estimate for
√4.98 +2.16×7.35
The estimated value of √4.98 +2.16×7.35 = 18.1075
Mathematical Operations:Operators are Mathematical methods that emphasize particular actions like adding, dividing, and adding multiple times are known as Mathematical Operations. The basic mathematical operations are 4 types they are Addition, Subtraction, Multiplication, and Division.
While we use mathematical operations to solve a problem we will use the BODMAS rule as given below
B - Brackets (Calculating numerical parts in brackets comes first )
O - Orders (Simplify powers and square roots)
D - Division (Complete division parts )
M - Multiplication (complete multiplication)
A - Addition (complete additions part )
S - Subtraction ( End with subtractions )
Here we have
√4.98 +2.16×7.35
Here the value of √4.98 = 2.2315 (approximately)
From above value
=> √4.98 +2.16×7.35
=> 2.23 + 2.16 × 7.35
By using the BODMAS rule
=> 2.23 + 15.876 [ Do multiplication ]
=> 18.106 [ Do adding ]
Therefore,
The estimated value of √4.98 +2.16×7.35 = 18.106 (approx)
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Factor [tex]6x^{2} -2x=0[/tex]
6x^2 - 2x = 0
-> 2x ( 3x - 1 ) = 0
For this equation to hold true, either 2x or 3x-1 must be equal to 0.
-> 2x = 0 - > x = 0
-> 3x - 1 = 0 -> x = 1/3
Members of a lacrosse team raised $1775. 50 to go to a tournament. They rented a bus for $901. 50 and budgeted $46 per player for meals. Write and solve an equation which can be used to determine xx, the number of players the team can bring to the tournament.
The number of players the team can bring to the tournament = 19 .
Given : amount raised by team = $1775.50
rent of bus = $901.50
budget for meal per player = $46
To find : the number of players the team can bring to the tournament
Equation :
taking bus charge as y - intercept ( since it does not depend on the no . of members riding on it )
taking meal amount as slope ( since it depends on the no . of members a team can bring to the tournament )
Let x be the no . of players a team can bring to the tournament .
Therefore , the equation is :
1775.50 = 46 x + 901.50
874 = 46 x
x = 19
Hence , the number of players the team can bring to the tournament = 19 .
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Determine the relationship between the two triangles and whether or not they can be proven to be congruent.
See two attachments
The relationship between the triangles is angle angle side.
What is the relationship between the triangles?We know that triangles could be related in certain ways. The way that a triangle is related to each other can be used to determine the relationship then the several ways that triangles could be related to eacjh other are;
Side angle side
Angle angle side
side side side.
We can see that the angles and the sides of this triangles are the same so the relationship between then can be said to be on the basis of angle side angle.
Looking at the images, it is clear that the triangles are congruent because there are two sides and an angle that are equal.
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Decide whether the triangles are similar. if so, determine the appropriate expression to solve for x. triangles abc and edf, where triangle abc has angle a measuring 47 degrees, angle c measuring 62 degrees, side ac labeled as y, side ab labeled as w, and side bc labeled as x and triangle edf has angle d measuring 71 degrees, angle e measuring 47 degrees, side de labeled z, side ef labeled u, and side df labeled r the triangles are not similar; no expression for x can be found. δabc ~ δdef; x equals r times w over u δabc ~ δedf; x equals r times w over u δabc ~ δedf; x equals r times w over z
The option that describes the similarity relationship between the triangles is the option; The triangles are not similar, no expression for x can be found.
What are similar triangles?Similar triangles are triangles that have all three interior angles of one triangle, congruent to the three angles of the other triangle.
The parameters of the triangles can be presented as follows;
ΔABC
∠A = 47°
∠C = 62°
AC = y
AB = w
BC = x
The measure of angle ∠B = 180° - 47° - 52° = 81°
ΔDEF
∠D = 71°
∠E = 47°
DE = z
EF = u
DF = r
Therefore;
∠F = 180°- 71° - 47° = 62°
The angles of triangle ΔABC are not congruent to the angles of triangle ΔDEF, therefore; triangle ΔABC and triangle ΔDEF are not similar.
Therefore;
The triangles are not similar, no expressions for x can be found.
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