Answers
1.
The question requires you to find csc of angle thetha
The formula to apply is;
[tex]co\sec \text{ }\emptyset=\frac{1}{\sin \emptyset}[/tex]So, First find sin of the angle theta, then its reciprocal
Sin theta= opposite side length / hypotenuse
[tex]\sin \emptyset=\frac{8}{8\sqrt[]{2}}[/tex][tex]\sin \emptyset=1.4142[/tex][tex]co\sec \emptyset=\frac{1}{1.4142}=0.70710678118[/tex]Answer
0.7071
Or
Using surds
[tex]\sin \emptyset=\frac{8}{8\sqrt[]{2}}[/tex]Cancel 8 both in the denominator and numerator to remain with
[tex]\sin \emptyset=\frac{1}{1\sqrt[]{2}}=\frac{1}{\sqrt[]{2}}[/tex]T
Related Questions
Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.
Cab Fare
Number of Miles Total Fee
2 $13.00
5 $17.50
7 $21.50
10 $25.00
15 $32.50
WILL GIVE BRAINLIEST TO FIRST ANSWER
What does the y-intercept mean in this situation?
For every additional mile the cab travels, the total fee increases by $10.00.
For every additional mile the cab travels, the total fee increases by $1.50.
When the cab travels 0 miles, the total fee will be $1.50.
When the cab travels 0 miles, the total fee will be $10.00.
Answers
The meaning of the y-intercept in this situation is that: D. when the cab travels 0 miles, the total fee will be $10.00.
How to calculate the slope of a line?Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
From the table, we have the following parameters:
Points (x, y) = (2, 5) and (13.00, 17.50)
Next, we would calculate the slope as follows:
Slope = (17.50 - 5)/(13.00 - 2)
Slope = 12.50/11.
Slope = 1.14.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
Where:
x and y represents the points.m represents the slope.b represents the y-intercept.Substituting the given parameters into the standard equation, we have;
y - 13.00 = 1.14(x - 2)
y - 13.00 = 1.14x - 2.28
y = 1.14x - 2.28 + 13.00
y = 1.14x + 10.72
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pottery studio gives three-hour and four-hour ceramics classes for $36 an hour. If the studio has collected $4428 for a total of 32 classes, how many three hour classes and how many four-hour classes were paid for?
Answers
Answer:
5 three hour classes and 27 four hour classes
Step-by-step explanation:
Convert these words into equations
Since one hour is 36, we can write two expressions for the 2 different classes: 108x and 144y (the amount of money from those classes)
x is the number of 3 hour classes, y is the number of 4 hour classes
Since the amount of money the studio makes is 4428, 108x+144y=4428
Since there are a total of 32 classes, x+y=32
So we now have the equations x+y=32 and 108x+144y=4428
Solve for x in the first equation (in order to substitute it into the second one)
we get x=32-y
plugging this into the second equation gives
108(32-y)+144y=4428
3456-108y+144y=4428
Combining like terms gives 36y=972
y=27
So there are 27 four hour classes, and 5 three hour classes( because 32-27=5)
Help needed! please help math
Answers
Answer:
Step-by-step explanation:
The sum of three consecutive numbers is 111. What is the smallest of the three numbers? please help show work
Answers
The sum of three consecutive numbers is 111.
Consecutive Numbers: Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Let the three consecutive numbers are : x , x + 1, x +2
Since the sum of three consecutive number is 111
x + (x +1 ) + (x +2) = 111
Simplify :
x + x + 1 + x + 2 = 111
x + x + x + 1 + 2 = 111
3x + 3 = 111
3x = 111 - 3
3x = 108
x = 108/3
x = 36
So, the first number is x : x = 36
Second number is : x + 1= 36 + 1 = 37
Third Number is : x + 2 = 36 + 2 = 38
Numbers are : 36, 37, 38
Smallest number in 36, 37 & 38 is 36
Smallest number = 36
Answer : 36
jon drove an average of 250 miles a day for three days he drove 400 miles on the first dat 125 miles on the second day
Answers
Answer:
225 miles on 3rd day
Step-by-step explanation:
400 + 125 + x /3 = 250
multiply each by 3 to get 400 +125 +x = 750
subtract 525 each to get x = 225
scale factor and dilations
Answers
The scale factor here is 3 : 2.
What is meant by scale factor and dilations?The scale factor is defined as the difference between the new image's and the old image's sizes. A fixed point in the plane is the center of dilation. The definition of the dilation transformation depends on the scale factor and the center of dilation.
A stretched image results from a scale factor of higher than 1.
The image shrinks when the scale factor falls between 0 and 1.
The resulting image is consistent with the source image if the scale factor is 1.
As a result of the dilation modifications, the following characteristics of forms don't change:
The figure's angles are all identical.
The figure's midpoints on its sides and the midpoint of the dilated shape are both preserved.
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The graph below describes the distance from home over a period of time. What is the rate of change from 70 seconds to 100 seconds?
Answers
According to the given graph, after 70 seconds it ran 40 units of distance, after 100 seconds it ran 160 units of distance. So, the points we are going to use to find the rate of change are: (70, 40) and (100, 160).
Now, we use the following formula.-
[tex]r=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing the points, we have.
[tex]r=\frac{160-40}{100-70}=\frac{120}{30}=4[/tex]Therefore, the rate of change from 70 seconds to 100 seconds is 4.4. 5.26 x 1031.37 x 10-1Which of the following pairs of numbers are between the two numbers shown?A. 294 and 0.0294B. 7,338 and 0.7388C. 5,007 and 0.5007D. 6,152 and 0.06152
Answers
Answer:
C. 5,007 and 0.5007
Explanation:
Given the two numbers:
[tex]\begin{gathered} 5.26\times10^3=5260 \\ 1.37\times10^{-1}=0.137 \end{gathered}[/tex]From the given options:
[tex]5260>5007>0.5007>0.137[/tex]All other options do not satisfy the condition.
The correct choice is C.
About 1% of 7900 commuters carpool to work. Find the number of commuters who carpool
Answers
Data
number of commuters = 7900
percent needed = 1%
Rule of three
7900 ------------------------ 100%
x
The beginning steps for determining the center and radius of a circle using the completing the square method are shown in the table.Step 1[original equation]:x2 + 8x + y2 − 6y = 11Step 2[group like terms]:(x2 + 8x) + (y2 − 6y) = 11Step 3[complete the square]:Which of the following is the correct equation for Step 3?
Answers
Solution
We want to complete the square of
[tex](x^2+8x)+(y^2-6y)=11[/tex]Firstly, let us look at how to complete a square.
Consider the illustration below
[tex]\begin{gathered} To\text{ complete the square of }(x^2+8x) \\ Add\text{ \lparen}\frac{8}{2})^2\text{ to both sides of the equation} \\ That\text{ is 4}^2=16 \end{gathered}[/tex][tex]\begin{gathered} To\text{ complete the sqaure of y}^2-6y,\text{ } \\ Add\text{ \lparen}\frac{-6}{2})^2=(-3)^2=9\text{ to both sides of the equation} \end{gathered}[/tex]Thus, we have
[tex](x^2+8x+16)+(y^2-6y+9)=11+_16+9[/tex][tex]\begin{gathered} The\text{ answer is } \\ (x^2+8x+16)+(y^2-6y+9)=11+16+9 \end{gathered}[/tex]x 1 2 3 y 16 32 48 Write an equation that represents the proportional relationship. y = 16x y = 2x y equals 1 over 16 times x y equals 1 over 2 times x Question 6(Multiple Choice Worth 2 point
Please HELP ME I WILL GIVE BRAINLYNEST
Answers
The equation which represents the proportionality relationship is:
y=16x.
Given, we have the pairs as:
(1,16),(2,32) and (3,48)
calculate the value of y/x for the ordered pairs:
For (1,16), the value of y/x is = 16/1 = 16
For (2,32), the value of y/x is = 32/2 = 16
For (3,48), the value of y/x is = 48/3 = 16
now, compare ratios:
for each ordered pair, y/x = 16
Since, k=y/x, you know that the constant of proportionality , k is 16.
Substitute 16 for k in the equation for a proportional relationship.
y = kx
y = 16x
Hence we get the equation as y=16x.
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A caterpillar eats
1400
%
1400%1400, percent of its birth mass in one day. The caterpillar's birth mass is
m
mm grams.
Answers
If a caterpillar eats 1400% percent of its birth mass in one day. The caterpillar's birth mass is 14m grams.
How to find the birth mass in grams?Given data:
Birth mass in one day = 1400%
Hence, we need to formulate an equation and then use the formulated equation to find or determine the caterpillar's birth mass in m grams
1400 / 100m
Now let find the birth mass in m grams using the equation
1400/100m
= 14m grams
Therefore we can conclude that 14m grams is the birth mass.
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Answer: 14m and 1400/100
Step-by-step explanation: just do it !!
Point J is on line segment IK. Given IK=15 and IJ=13, determine the length of segment JK.
Answers
Line segment IK includes Point J. The length of the segment IK=15 and IJ=13. The length of the segment JK is 2.
Given that,
Line segment IK includes Point J.
We have to determine the length of segment JK.
We have length of the segment IK=15 and IJ=13.
Two unique points on a line define the boundaries of a line segment. A line segment is also known as a part of a line that connects two locations. A line and a line segment vary in that a line has no ends and can continue indefinitely in any direction.
We can write as,
IK=IJ+JK
15=13+JK
JK=15-13
JK=2
Therefore, The length of the segment JK is 2.
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In the year 2016, Ethan was single and had a total income of $58,000. He took a deduction of $9,000 and had a tax credit of $1,500. Calculate the tax owed by Ethan. (Refer to the 2016 Tax Table for Singles for tax rates.)
Answers
The tax owed by Ethan is $6,521.25.
Ethan's total income was $58,000. There was a deduction of $9,000. Ethan's net income is $49,000. The tax table is attached below. Now we will calculate the tax as per the table.
From $0 to $9,275, the tax is 10%, i.e., $9,27.5.
From $9,276 to $37,650, the tax is 15%, i.e., $4,256.25.
From $37,651 to $49,000, the tax is 25%, i.e., $2,837.5.
The payable tax is the sum of the above calculated taxes. The payable tax is $8,021.25. There is a tax credit of $1,500. The tax owed is the difference between the payable tax and the tax credit. The tax owed is $8,021.25-$1,500 = $6,521.25.
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User = 1 to identify the value of each expression.Exponent Value of expression923341239
Answers
Find x in the following expressions:
9^x = 3 in this case, x has to be 1/2 (square root) in order to render 3 as an answer, given that 3^2 = 9
Then x = 1/2 in this first case
Second case:
3^x = 1 In this case, we use the property of exponent zero, which always renders 1
Last case x^3 = 9
Given the following table of values for f(x), find f(9).x−5−42489f(x)4124058
Answers
We have a table of values which contains different x-values and their related f(x).
We are searching for f(9), then we have to observe the value of the function f(x) when x=9.
In the table of values we can observe when x=9, then f(x)=8.
So f(9)=8
Step-by-step explanation:
please write the question properly
7) Solve the system graphically.y = -X-4y=x² – 2x - 6
Answers
Ok, so
We have the next system of equations:
The first equation is a line, and the second one is a parable.
If we graph, we would get the following:
Then, we notice that there's two intersection points between both graphs.
These points are located at ( -1 , -3 ), and ( 2 , -6)
Therefore, there are two solutions for this problem.
x = -1 and y = -3,
x = 2, and y = -6
Now, how to graph each equation?
First one, take the line y = -x-4
Notice that this equation tells us that the line given has its intersection with y-axis at ( 0 , -4 )
We also know that a line is formed with two points, so we could replace by any "x" number and see which value "y" takes.
For example:
If x = 1,
y = -1-4, which is y = -5
So we got other point: ( 1, -5).
Now, we just join both points and we get the line, like this:
And that's how you can graph the line.
Now, how could we graph the parable?
We know that we have to take three points to join to graph a parable. So, first, we would find its intersections with x - axis, if we equal the equation to zero.
x² – 2x - 6 = 0
If we solve this equation, we obtain that x could take two different values.
To solve it, we use the next equation:
x = 1 - √7 or
x = 1 + √7.
Then, we actually have two points.
Now, finally, we could find its vertex.
If we find the vertex of the parable, we notice that it is located in (1,-7)
Now, we just join these three points as this:
And if we put these graphs together, we obtain the first graph I drew, and notice that the solution for the system is the intersection between both functions.
Write the vector v in terms of i and j whose magnitude and direction angle are given.
Answers
The magnitude, r, of the vector, v , is given to be 4/5.
The direction angle is given to be 114 degrees.
A vector component is written in the form of:
[tex]V=ai+bj[/tex]We are going to use the given magnitude and direction angle to obtain the values of a and b.
Thus, we have:
[tex]\begin{gathered} \text{The magnitude, r, of a vector with i and j component is given as:} \\ r=\sqrt[]{a^2+b^2} \\ \frac{4}{5}=\sqrt[]{a^2+b^2} \\ \text{square both sides;} \\ (\frac{4}{5})^2=a^2+b^2 \\ \frac{16}{25}=a^2+b^2 \\ \frac{16}{25}-b^2=a^2 \\ a^2=\frac{16}{25}-b^2 \\ a=\sqrt[]{\frac{16}{25}-b^2}\text{ ----eqn i)} \end{gathered}[/tex][tex]\begin{gathered} \text{The direction angle, }\theta,\text{ of a vector is given as;} \\ \text{Tan }\theta=\frac{b}{a} \\ \text{Tan 114=}\frac{b}{a} \\ -2.2460=\frac{b}{a} \\ b=-2.2460a\text{ -----eqn }ii) \end{gathered}[/tex]Substitute for b into eqn i); thus we have:
[tex]\begin{gathered} From\text{ eqn i)} \\ a=\sqrt[]{\frac{16}{25}-b^2} \\ \text{Put b=-2.2460a into the equation, we have:} \\ a=\sqrt[]{\frac{16}{25}-(-2.2460a)^2} \\ a=\sqrt[]{\frac{16}{25}-(5.0447a^2)} \\ \text{square both sides;} \\ a^2=\frac{16}{25}-5.0447a^2 \\ a^2+5.0447a^2=\frac{16}{25} \\ 6.0447a^2=0.64 \\ a^2=\frac{0.64}{6.0447} \\ a^2=0.1058 \\ a=\sqrt[]{0.1058} \\ a=0.325 \end{gathered}[/tex]Substitute for a= 0.325 into any of the equations, we have:
[tex]\begin{gathered} \text{From eqn }ii) \\ b=-2.2460a \\ b=-2.2460(0.325) \\ b=-0.729 \end{gathered}[/tex]Hence, the vector, v, in terms of i and j is:
[tex]\begin{gathered} v=0.325i-0.729j \\ \text{This can also be written as:} \\ v=\frac{13}{40}i-\frac{729}{1000}j \end{gathered}[/tex]May get help I am terribly bad at these equations.
Answers
The distance Rhea travelled is the perimeter around the triangle.
The first step in finding the perimeter is finding the side lengths and for that, the following distance formula is used.
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]where (x_1, y_1) and (x_2, y_2) are the coordinates of the two points.
The distance between L(-1,6) and M(-4,2) is
[tex]d=\sqrt[]{(_{}-1--4)^2+(6_{}-2_{})^2}[/tex][tex]d=5[/tex]Similarly, the distance between L(-1,6) and K(2,2) is
[tex]d=5[/tex]And the distance between M(-4, 2) and L(2,2) is
[tex]d=6[/tex]Therefore, the perimeter of the triangle is
[tex]5+5+6=16[/tex]Hence, Rhea travelled 16 km.
to get the paint color moss green, 2 parts violet paint mixed with 3 parts yellow paint. how many parts yellow paint should be mixed with 5 parts violet paint. Please explain how you got to the answer and what is this topic in math called
Answers
7.5 components yellow paint should be mixed with 5 parts violet paint.
What is probability?Moss green is created by combining violet and yellow paint in a 2 to 3 ratio. You're interested in learning how many parts of yellow paint to combine with five parts of violet paint.
Proportion
There are various ways to express the proportion. The unknown value is often placed in the numerator. (x is the quantity of yellow paint in parts)
Yellow: violet equals 3: 2; x; and 5
The ratio, expressed as a fraction, is
3/5=x/5
5*3/2=X multiply by 5
15/2=x=7.5 simplify
7.5 parts yellow paint to 5 parts violet paint.
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Use algebra to solve each problem. If a diagram is not given, you MUST sketch one.Show your calculations for each question. Place your answer in the space provided.Yis between X and Z on segment XZ. XY = x + 7, XZ - 152, and YZ - 2XY. Find x to thenearest tenth.xX
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} |XY|=x+7 \\ |XZ|=152 \\ |YZ|=2|XY|\Rightarrow|XZ|=|XY|+|YZ| \\ But\colon|YZ|=2|XY|\Rightarrow|XZ|=|XY|+2|XY|\Rightarrow|XZ|=3|XY| \\ |XZ|=3|XY| \\ But\colon|XY|=x+7,|XZ|=152 \\ 152=3(x+7)\Rightarrow152=3\cdot x+3\cdot7\Rightarrow152=3x+21 \\ 152=3x+21 \\ \text{Subtract 21 from each side, we have:} \\ 152-21=3x+21-21\Rightarrow131=3x\Rightarrow3x=131 \\ 3x=131 \\ \text{Divide each side by 3, we have:} \\ \frac{3x}{3}=\frac{131}{3}\Rightarrow x=43\frac{2}{3}\approx43.667\cong43.7 \\ x=43.7(ToNearestTenth) \end{gathered}[/tex]6 Jeff bought a bottle of water for $2. He also bought some hot dogs for $3 each. Jeff didnot spend more than $14 on the hot dogs and the bottle of water. Which inequality canbe used to find h, the number of hot dogs that Jeff could have bought?F 3h - 2 s 14G 3h + 2 S 14H h - 2 2 14J 3h + 2 2 14
Answers
SOLUTION
Step1: Write out the parameters in the question
Let the number of hot dogs be h
The cost of a hot dog is $3
The cost of the bottle of water is $2
The total amount spent by jeff is $ 14
Step2: Write the inequality
The total amount spend should be less than or equal to the total amount
then
The cost of the hot dog is
[tex]3\times h=3h[/tex]The inequality will be the sum of the cost of the hot dog and the bottle of water
[tex]3h+2\leq14[/tex]Hence option G is the correct op
4-(-3/5) is equivalent to
Answers
Subtracting a negative number is the same as adding that number. In this case,
[tex]4-(-\frac{3}{5})=4+\frac{3}{5}[/tex]Help me please help me out please please
Answers
Answer:
The answer is it is true.hope the day is saved
The point (x,y) is proportional to the point (2, 5).Select all the true statements.5(x, y) is a solution to y=3x:0 (x, y) is a solution to y=x+3.The ratio of is equivalent toPoint (x,y) is the same point as (5,2).A straight line through points (2,5) and (x, y) will pass through the origin.
Answers
Since all the points proportional to (2,5) follow the equation 2y = 5x, (x,y) is a solution to y=5/2x
Accordingly 2y= 5x is the same as y/x = 5/2 . Since the equation y = 5/2x is a line with y-intercept equal to 0 , there is a line which passes through points (x,y) and (2,5). The true statements are: first, third and fifth statements.
Carson drove a distance of 120120120 kilometers. He initially had 303030 liters of fuel, and his car's fuel efficiency is 100100100 cubic centimeters per kilometer.
What calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters?
Answers
If he initially had 30 liters of fuel, and his car's fuel efficiency is cubic centimeters per kilometer. The calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters is: 30- 100/1000×120
How to determine the estimated volume?Given data:
Distance = 120 kilometers
Liters of fuel = 30 liters
Using this formula to find the remaining volume
Remaining volume = I - E × D
Where:
I = Initial volume
E = Fuel efficiency
D = Distance
First step is to formula an equation that will be use to find the remaining volume
Equation = 30- 100/1000 ×120
Now let use the formulated equation to find the remaining volume
Remaining volume = 30- 100/1000 × 120
Remaining volume = 30- 12
Remaining volume = 18
Therefore 30- 100/1000×120 can be used to determine the remaining volume.
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2x + 4y=8
graphing in standard form
Answers
Answer:
slope = -1/2
Y-intercept = (0,2)
Step-by-step explanation:
(08.01 LC)A cylinder has a height of 2 meters and a diameter that is 5 timesthe measure of the height. Using 3.14 for pi, which of the followingcan be used to calculate the volume? (6 points)
Answers
Let's begin by identifying key information given to us:
This figure is a cylinder. The formula for its volume is:
[tex]V=\pi r^2h[/tex]Height (h) = 2 m,
Diameter (d) = 5 × h = 5 × 2 = 10 m; radius (r) = d/2 = 10/2 = 5 m
pi = 3.14
The volume of the cylinder is calculated as shown below:
[tex]\begin{gathered} V=3.14\times5^2\times2 \\ V=3.14\times25\times2=157 \\ V=157m^3 \end{gathered}[/tex]3/5 of the students in the band play the flute, and another 1/5 play the clarinet. What fraction of the students in the band plays either the flute or the clarinet?
Answers
The fraction of the students in the band that play either the flute or the clarinet is 4/5.
We are given the fraction of the students that play a certain musical instrument.The fraction of the students in the band that play the flute is 3/5.The fraction of the students in the band that play the clarinet is 1/5.We need to find the fraction of the students in the band that play either the flute or the clarinet.The fraction of the students in the band that play either the flute or the clarinet is the sum of the individual fractions of the students in the band that play the flute and the students in the band that play the clarinet.The fraction of the students in the band that play either the flute or the clarinet is 3/5 + 1/5.The fraction of the students in the band that play either the flute or the clarinet is 4/5.To learn more about fractions, visit :
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5/7 - 3/5 = what? I'm don't know what is .
Answers
Answer: 4/35
Step-by-step explanation: First you need to make the fraction denominators the same so we are going to do multiply 7 x 5 which equals 35 if you don't know your multiplication you can always skip count by 5's so now since we changed the denominators the numerators need to be changes also so the new equation will be 25/35 - 21/35 that equals 4/35 and the fraction cannot be simplified because 1 is the only common divisor
Answer:
4/35
Step-by-step explanation:
Used a calculator and did the math problem in paper
5/7 - 3/5 = 4/35
