From cosecant identity the expression cos(x)+sin(x)/ sin(x) =1+cot(x) was verified.
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) , where:
sin (x) = [tex]\frac{opposite\ leg}{hypotenuse}[/tex]
cos(x)=[tex]\frac{adjacent\ leg}{hypotenuse}[/tex]
tan (x) = [tex]\frac{\frac{opposite\ leg}{hypotenuse} }{\frac{adjacent\ leg}{hypotenuse} } = \frac{opposite\ leg}{adjacent\ leg}[/tex]
The question gives the following identity: [tex]\frac{cos (x)+sin(x)}{sin(x)}[/tex]
First, you should rewrite the identity using the cosecant identity - csc(x)= 1/sin(x) . Then,
(cos(x)+sin(x)) * csc(x)
After that, you should expand the previous expression.
cos(x)*csc(x) + sin(x) * csc(x)
cos(x)*1/sin(x) + sin(x) * 1/sin(x)
cos(x)/sin(x) + sin(x)/sin(x)
cot(x) + 1
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45.6 divided by 0.03
Answer:
1,520
Step-by-step explanation:
13. The model represents an equation. 1 1 1 1 À AC X DOOD D0000 solue.) What value of x makes the equation true? 15.
Answer:
The equation is true when x = 2.25
Explanation:
On the left side of the equation, there are 3 triangles with value -x and 10 triangles with value 1. So, the expression for the left side of the equation is:
3*(-x) + 10*(1)
-3x + 10
For the right side, we have 5 triangles with value x and 8 triangles with value -1. So, the expression for the right side is:
5*x + 8*(-1)
5x - 8
Now, we can write the equation as:
-3x + 10 = 5x - 8
So, solving for x, we get:
-3x + 10 + 3x = 5x - 8 + 3x
10 = 8x - 8
10 + 8 = 8x - 8 + 8
18 = 8x
18/8 = x
2.25 = x
Therefore, the equation is true when x is equal to 2.25
Jasmine is helping her father plant trees to create a border around the back yard. Jasmine plants a tree every 25 minutes, and her father plants a tree every 15 minutes. If they started together, how long before they would finish planting a tree at the same time?
Find the equation (in terms of x) of the line through the points (-3,-3) and (4,-2) II
Given:
The coordinates of the points through which the line passes,
(x1, y1)=(-3, -3).
(x2, y2)=(4, -2).
The two point form of the equation of a line can be expressed as,
[tex]y-y1=\frac{y2-y1}{x2-x1}(x-x1)[/tex]Substitute the known values in the above equation.
[tex]\begin{gathered} y-(-3)=\frac{-2-(-3)}{4-(-3)}(x-(-3)) \\ y+3=\frac{-2+3}{4+3}(x+3) \\ y+3=\frac{1}{7}(x+3) \\ 7(y+3)=x+3 \\ 7y+7\times3=x+3 \\ 7y+21=x+3 \\ 7y=x+3-21 \\ 7y=x-18 \\ y=\frac{1}{7}x-\frac{18}{7} \end{gathered}[/tex]Therefore, the equation of the line is,
[tex]y=\frac{1}{7}x-\frac{18}{7}[/tex]find the reciprocal -16/5
Remember that the reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number).
Thereby, the reciprocal of
[tex]-\frac{16}{5}[/tex]is
[tex]-\frac{5}{16}[/tex]Is the sequence an arithmetic sequence? 2. -12,4,0, 2....... Yes or No 3. -6,0, 6, 12 ..... Yes or No
For a sequence to be an arithmetic sequence the terms have to have a constant difference between them
2) We have the sequence: -12, 4, 0, 2...
The difference between the terms is not constant, so this is not a arithmetic sequence.
For example, from 4 to 0, there is -4 and from 0 to 2, is 2.
3) The sequence -6,0, 6, 12,... is an arithmetic sequence, because it has a constant difference between the terms (it always add 6 in each step).
Answer:
2. -12,4,0, 2....... No
3. -6,0, 6, 12 ..... Yes
8x – 12y = – 24 a. x-intercept: b. y-intercept: 10+ C. graph 9 8 7 6 5 4 13 2 -10 -9 -8 -7 -6 -5 -4 -B-2 -1 2 15 4 SI 6 8 9 10 -2 3 -6 -7 -8 9 10 Clear All Draw:
To determine the x- and y-intercepts is best to write the equation in slope-intercept form.
Given
[tex]8x-12y=-24[/tex]-Pass the x-term to the right side of the equation by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 8x-8x-12y=-8x-24 \\ -12y=-8x-24 \end{gathered}[/tex]-Divide both sides of the equal sign by -12
[tex]\begin{gathered} \frac{-12y}{-12}=\frac{-8x}{-12}-\frac{24}{-12} \\ y=\frac{2}{3}x+2 \end{gathered}[/tex]So the equation in slope-intercept form is:
[tex]y=\frac{2}{3}x+2[/tex]a) The x-intercept is the point where the line crosses the x-axis, at this point, the y-coordinate is equal to zero. To determine the x-coordinate of the intercept, you have to equal the equation to zero and calculate the corresponding value of x:
[tex]0=\frac{2}{3}x+2[/tex]-Subtract 2 to both sides of the equal sign
[tex]\begin{gathered} 0-2=\frac{2}{3}x+2-2 \\ -2=\frac{2}{3}x \end{gathered}[/tex]-Multiply both sides of the expression with the reciprocal fraction of 2/3
[tex]\begin{gathered} (-2)\frac{3}{2}=(\frac{2}{3}\cdot\frac{3}{2})x \\ -3=x \end{gathered}[/tex]The x-intercept is (-3,0)
b) The y-intercept is the point where the line crosses the y-axis, at this point, the x-coordinate is equal to zero. To determine the y-intercept, replace the equation with x=0 and calculate the corresponding value of y:
[tex]\begin{gathered} y=\frac{2}{3}x+2 \\ y=\frac{2}{3}\cdot0+2 \\ y=2 \end{gathered}[/tex]The y-intercept is (0,2)
c) To graph the line, plot both intercepts on the coordinate system and then link both points with a line:
Elsa is saving money to buy a game. So far she saved $24, which is two-thirds of the total cost of the game. How much does the game cost?
Elsa is saving money to buy a game.
So far she saved $24, which is two-thirds of the total cost of the game.
let the cost of the game is $x
Then, two -third of the total cost = 2/3 x
Since, it is given that 24 is the two-thirds of the total cost of the game.
i.e.
[tex]\frac{2}{3}x=24[/tex]Simplify the expression for x;
[tex]\begin{gathered} \frac{2}{3}x=24 \\ \text{ Apply cross multiplication;} \\ 2x=24\times3 \\ x=\frac{24\times3}{2} \\ x=12\times3 \\ x=36 \end{gathered}[/tex]x = 36
Total cost of the game is $36
....
Hello! I need some help with this homework question, please? The question is posted in the image below. Q11
A one-to-one function means that there are no two elements in the domain of the function that corresponds to the same element in the range,
Mathematically since
[tex]\begin{gathered} x\text{ is the input or the domain, then} \\ f(x)\text{ is the output} \end{gathered}[/tex]A one-to-one follows that
[tex]\text{if }x_1\text{ and }x_2\text{ are two different inputs of a function }f,\text{ then }f(x_1)\neq f(x_2)[/tex]If five boys can eat 16 slices of pizza, then how many slices can 20 boys eat?
Please help me complete this table
Bill owns land but has no access to water so he has to pay for well water from Jim.
Jim charges him $8 per month plus $0.80 per gallon.
During any given summer month, his water bill costs between $48 and $72.
Write and solve a compound inequality to determine how much water Bill is using.
Martin eats 3/8 of a pizza. Felix eats 2/5of a pizza of
same size. Who eats more pizza? How much more pizza
does he eat?
4. What is the value of x such that 5x + 2a > 2x-a?
a. x < -a
b. x > -a
C. x < a
d. x > a
Answer:
D: x > a
Step-by-step explanation:
We have 5x - 2a > 2x-a
We can rewrite this equation by subtracting 2x on both sides, which gives:
5x - 2x -2a > 2x - 2x - a,
so 3x - 2a > a
We now add 2a on both sides, which gives:
3x -2a + 2a > a + 2a, so 3x > 3a
We nog divide both sides by 3, which gives:
3x/3 > 3a/3, so x>a
The correct answer is D
A 12-quart cooling system is tested and found filled with a 60% antifreeze solution. The ideal mixture should be a 50% antifreeze solution. How many quarts of solution need to be drained and replaced with pure water to reach the ideal mixture?
Answer:
2 quarts
Explanation:
Let the number of quarts to be drained and replaced = x
From the given problem:
60% of (12-x)=50% of 12
[tex]\begin{gathered} 0.6(12-x)=0.5\times12 \\ 0.6(12-x)=6 \\ 12-x=\frac{6}{0.6} \\ 12-x=10 \\ x=12-10 \\ x=2 \end{gathered}[/tex]2 quarts of the solution needs to be drained and replaced with pure water to reach the ideal mixture.
Please see image attached on using the diagram to name the ray
Given:
Find - Name of rays
Sol:
Ray:- In geometry, a ray can be defined as a part of a line that has a fixed starting point but no endpoint can extend infinitely in one direction. On its way to infinity, a ray may pass through more than one point.
So rays is
[tex]=\vec{AE}[/tex]Select the names of the sides of the triangle. The 2 answer options are leg and hypotenuse.
Given:
[tex]\text{side(c)}=\text{Hypotenus}[/tex][tex]\text{side(a)}=\text{lag}[/tex][tex]\text{side(b)}=\text{lag}[/tex]Given that events A and B are independent with P(A)=0.85 and P(B) = 0.3,determine the value of P(A|B), rounding to the nearest thousandth, if necessary.
The Solution.
Given that
[tex]\begin{gathered} P(A)=0.85 \\ P(B)=0.3 \end{gathered}[/tex]The conditional probability P(A/B) is given as
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]But for independent events, we have that
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Hence, it follows that
[tex]\begin{gathered} P(A|B)=\frac{P(A)\times P(B)}{P(B)}=P(A)=0.85\approx0.850 \\ \text{though the nearest thousandth is not necessary.} \end{gathered}[/tex]Therefore, the correct answer is 0.85 ( 0.850 if you consider it necessary)
A rectangular room is 4 meters longer than it is wide, and its perimeter is 24 meters. Find the dimension of the room.The length is : meters and the width is meters.
We are given the following information
Perimeter of the rectangular room = 24 meters
The rectangular room is 4 meters longer than it is wide.
Let L be the length and W be the width of the rectangular room.
[tex]L=4+W[/tex]The perimeter of a rectangular shape is given by
[tex]P=2(L+W)[/tex]Substitute P = 24 and L = 4 + W into the above equation
[tex]\begin{gathered} P=2(L+W) \\ 24=2(4+W+W) \\ 24=2(4+2W) \\ 24=8+4W \\ 24-8=4W \\ 16=4W \\ \frac{16}{4}=W \\ W=4\;m \end{gathered}[/tex]So, the width of the rectangular room is 4 meters.
[tex]\begin{gathered} L=4+W \\ L=4+4 \\ L=8\;m \end{gathered}[/tex]So, the length of the rectangular room is 8 meters.
Length = 8 meters
Width = 4 meters
Example Problem:
Suppose that perimeter is 1055 meters.
The length is 45 meters longer than the width of the rectangle.
[tex]L=45+W[/tex]Now, substitute P = 1055 and L = 45 + W into the equation for the perimeter of the rectangle.
[tex]\begin{gathered} P=2(L+W) \\ 1055=2(45+W+W) \\ 1055=2(45+2W) \\ 1055=90+4W \\ 1055-90=4W \\ 965=4W \\ W=\frac{965}{4} \\ W=241.25\;m \end{gathered}[/tex]So, the width of the rectangle is 241.25 meters.
[tex]\begin{gathered} L=45+W \\ L=45+241.25 \\ L=286.25\;m \end{gathered}[/tex]So, the length of the rectangle is 286.25 meters
The Product of twice a number and six is the Same as the difference of eleven times the number and 5/7. Find the number
The number x = - 5/7 .
How do you frame an equation?The following steps are necessary to construct a linear equation in one variable from the provided word problem:
Step I: Read the problem attentively and make separate notes for the provided and necessary quantities.
Step II: Use 'x', 'y', 'z', etc. to represent the unknowable quantities.
Step III: Next, convert the issue into a mathematical formulation or statement.
Step IV : Utilizing the conditions provided in the problem, form a linear equation in one variable in
Step V: Verify the equation for the unknown quantity
Let the number be x
Thus according to the question :
( twice a number) × 6 = 11 (number) - 5/7
(2x)6 = 11 x - 5/7
12x = 11 x- 5/7
x= - 5/7
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Hello! I need some assistance with this homework question, pleaseQ16
we have the function
[tex]y=\sqrt[]{x}[/tex]shifted down 10 units, is the same that apply the rule
(x,y) -----> (x,y-10)
therefore
the new function is
[tex]y=\sqrt[]{x}-10[/tex]The answer is the first optionTracey paid $180 for an item that was originally priced at $560. What percent of the original price did Tracey pay?
To find the percentage that Tracey paid, we can use the rule of three:
Now, the original price $560 represent the 100%.
If $560 ----------- 100%
then $180----------- x
where x =($180*100)/$560
x = 32.14
Therefore, the percent that Tracey paid was 32.14%
The answer is rounded to the nearest hundredth.
The radius of a circle is 6 centimeters. What is the area of a sector bounded by a 150 degree arc?Give the exact answer in simplest form._____ square centimeters
Concept
[tex]\text{Area of a sector = }\frac{\theta}{360}\text{ }\times\text{ }\pi r^2[/tex][tex]\begin{gathered} \theta\text{ is the angle subtend at the center} \\ r\text{ is the radius} \end{gathered}[/tex]Step 1: List the given data
[tex]\begin{gathered} \theta=150^o \\ r\text{ = 6cm} \\ \pi\text{ = }\frac{22}{7} \end{gathered}[/tex]Step 2: Substitute the values to find the area of the sector.
[tex]\begin{gathered} \text{Area of the sector = }\frac{150}{360}\text{ }\pi\text{ }\times6^2 \\ =\text{ }\frac{150\text{ }\pi\text{x 36}}{360\text{ }} \\ =15cm^2 \end{gathered}[/tex]Ok
what is the solution to the equation 5x-1+7x=11
the expression is
5x - 1 + 7x = 11
5x + 7x = 11 + 1
12x = 12
x = 12/12
x = 1
so the answer is x = 1
Use the angle relationships present to find angle P
Answer:
65 degress
Step-by-step explanation:
I did a problem like this before
Peter hired two combine operators to harvest his 260 acres of wheat. He expected a yield of 50 bushels per acre. The first operator had a 3% grain loss, and the second operator had 5% grain loss. Each operator harvested the same number of acres in the same time. How much was saved by the first operator if wheat sold for $11.97 perbushel?
Answer:
The amount in dollars of wheat saved by the first operator is;
[tex]\text{ \$1,556.10}[/tex]Explanation:
Given that Peter hired two combine operators to harvest his 260 acres of wheat.
And it yeilds 50 bushels per acre.
The total amount of bushels of wheat on the field is;
[tex]\begin{gathered} T=260\times50 \\ T=13,000\text{ bushels} \end{gathered}[/tex]Since each operator harvest the same amount;
[tex]\text{opertor 1= Operator 2 = }\frac{13000}{2}=6500\text{ bushels each}[/tex]If operator 1 loss 3%, the remaining amount is;
[tex]\begin{gathered} A_1=6500-3\text{ \% of 6500} \\ A_1=6500-(0.03)6500 \\ A_1=6305\text{ bushels} \end{gathered}[/tex]Operator 2 loss 5%, the remaining amount is;
[tex]\begin{gathered} A_2=6500-0.05(6500) \\ A_2=6175\text{ bushels} \end{gathered}[/tex]The amount of bushels save by the first operator compared to the second operator is;
[tex]\Delta A=A_1-A_2=6305-6175=130\text{ bushels}[/tex]if wheat is sold for $11.97 per bushel, the amount in dollars of wheat saved by the first operator is;
[tex]\begin{gathered} C=130\text{ bushels }\times\text{ \$11.97 per bushel} \\ C=\text{ \$1,556.10} \end{gathered}[/tex]The amount in dollars of wheat saved by the first operator is;
[tex]\text{ \$1,556.10}[/tex]The following table represents the highest educational attainment of all adult residents in a certain town. If a resident who is aged 0 - 39 is chosen at random, what is the probability that they bave completed a bachelor's degree and no more? Round your answer to the nearest thousandth .
ANSWER:
The probability is 0.107 or 10.7%
STEP-BY-STEP EXPLANATION:
The probability is calculated with the number of people who are in that age range and meet the study conditions and the total number of people.
We can determine both data in the table, therefore
[tex]p=\frac{1707}{15921}=0.107\cong10.72\text{\%}[/tex]The pie chart below shows how the annual budget for a certain company is divided by department. If the amount budgeted for sales and research combined is 75,000,000. What is the total annual budget?
$150,000
1) In that pie chart, we can tell that the Sales and Research department combined responds to 50% (35%+15% =50%)
2) Thus, we can tell that:
[tex]\begin{gathered} 0.35x+0.15x=75000 \\ 0.5x=75000 \\ x=\frac{75000}{0.5} \\ x=150,000 \end{gathered}[/tex]So, since 50% of that budget corresponds to $75,000 we can tell that 100% (the total budget) corresponds to twice that figure, which yields 150,000
Can a table with the same Input and output be a function ?
In this relation table value of x = ( 2,5,7,-4) are following same pattern .
but x = 5 is not input and output of a function.
What is input and output of a function in math?
A function can be represented as an input-output table, such as the one below. According to the same function rule, every pair of integers in the table is connected.The input and output of a function are, respectively, what goes into it and what it produces. Also known as the domain and range, respectively, are the input variable and output variable. The collection of all values that the function will accept as inputs, or its domain, is what makes up the function.x = 2 * 1 = 2 , y = 2
x = 5 * 1 = 5 , y = 5
x = 7 * 1 = 7 , y = 7
x = -4 * 1 = -4 , y = -4
x = 5 * 2 + 1 = 11 , y = 11
In this relation table value of x = ( 2,5,7,-4) are following same pattern .
but x = 5 is not .
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URGENT!!!!!!!!!
Thank you to whoever solves it right!
Answer:
D
Step-by-step explanation:
The plane was at 24,000+ feet above the ground and then it ROSE (indicating an addition of feet to the original) 7,00+ feet.
Hope that helps
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:Let r be the number of rides and g be the number of games.
2.50g + 4.00r = 52.50
r = 2g
Step-by-step explanation:
Answer:
lol no
Step-by-step explanation: