Starting with the equation:
[tex]\tan (\theta)=1[/tex]take the inverse tangent function to both sides of the equation:
[tex]\begin{gathered} \arctan (\tan (\theta))=\arctan (1) \\ \Rightarrow\theta=\arctan (1) \\ \therefore\theta=\frac{\pi}{4} \end{gathered}[/tex]Yet another value can be found for this equation to be true since the period of the tangent function is π:
[tex]\begin{gathered} \theta_1=\frac{\pi}{4} \\ \theta_2=\frac{\pi}{4}+\pi=\frac{5}{4}\pi \end{gathered}[/tex]Starting with the equation:
[tex]7\tan (\theta)=-15[/tex]Divide both sides by 7:
[tex]\Rightarrow\tan (\theta)=-\frac{15}{7}[/tex]Take the inverse tangent to both sides of the equation:
[tex]\begin{gathered} \Rightarrow\arctan (\tan (\theta))=\arctan (-\frac{15}{7}) \\ \Rightarrow\theta=\arctan (-\frac{15}{7}) \\ \therefore\theta=-1.13416917\ldots \end{gathered}[/tex]The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:
[tex]\begin{gathered} \theta_1=-1.13416917\ldots+\pi \\ =2.007423487\ldots \end{gathered}[/tex]We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:
[tex]\begin{gathered} \theta_2=\theta_1+\pi \\ =5.14901614\ldots \end{gathered}[/tex]Therefore, for each equation we know that:
[tex]\begin{gathered} \tan (\theta)=1 \\ \Rightarrow\theta=\frac{\pi}{4},\frac{5\pi}{4} \end{gathered}[/tex][tex]\begin{gathered} 7\tan (\theta)=-15 \\ \Rightarrow\theta=2.007423487\ldots\text{ , }5.14901614\ldots \end{gathered}[/tex]Starting with the equation:
[tex]\tan (\theta)=1[/tex]take the inverse tangent function to both sides of the equation:
[tex]\begin{gathered} \arctan (\tan (\theta))=\arctan (1) \\ \Rightarrow\theta=\arctan (1) \\ \therefore\theta=\frac{\pi}{4} \end{gathered}[/tex]Yet another value can be found for this equation to be true since the period of the tangent function is π:
[tex]\begin{gathered} \theta_1=\frac{\pi}{4} \\ \theta_2=\frac{\pi}{4}+\pi=\frac{5}{4}\pi \end{gathered}[/tex]Starting with the equation:
[tex]7\tan (\theta)=-15[/tex]Divide both sides by 7:
[tex]\Rightarrow\tan (\theta)=-\frac{15}{7}[/tex]Take the inverse tangent to both sides of the equation:
[tex]\begin{gathered} \Rightarrow\arctan (\tan (\theta))=\arctan (-\frac{15}{7}) \\ \Rightarrow\theta=\arctan (-\frac{15}{7}) \\ \therefore\theta=-1.13416917\ldots \end{gathered}[/tex]The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:
[tex]\begin{gathered} \theta_1=-1.13416917\ldots+\pi \\ =2.007423487\ldots \end{gathered}[/tex]We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:
[tex]\begin{gathered} \theta_2=\theta_1+\pi \\ =5.14901614\ldots \end{gathered}[/tex]Therefore, for each equation we know that:
[tex]\begin{gathered} \tan (\theta)=1 \\ \Rightarrow\theta=\frac{\pi}{4},\frac{5\pi}{4} \end{gathered}[/tex][tex]\begin{gathered} 7\tan (\theta)=-15 \\ \Rightarrow\theta=2.007423487\ldots\text{ , }5.14901614\ldots \end{gathered}[/tex]pls help with whats in image!!!
The slope of the line will be positive 9. Then the correct option is C.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope is given as,
Slope = m = (y₂ - y₁) / (x₂ - x₁)
Determine whether a line's slope, which represents the linear connection, is positive, negative, zero, or undefined without using a graph. Next, locate the slope. A babysitter may make $9 per hour and $36 per 4 hours.
Slope = (36 - 9) / (4 - 1)
Slope = 27 / 3
Slope = 9
The slope of the line will be positive 9. Then the correct option is C.
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Suppose that two lines, AB and CD, are intersected by a transversal.
Which of the following reasons alone could be used to show that the lines are parallel?
The CORRECT ANSWER is
Alternate exterior angles converse
The answer is NOT
Linear pair theorem
Consecutive interior angles theorem
Congruent supplements
The reason that can be used to show that the lines are parallel is: alternate exterior angles converse.
What is the Alternate Exterior Angles Converse?The alternate exterior angles converse can be defined as rule that states that if two exterior angles that lie on each of the lines that is crossed by a transversal are congruent, then the lines can be said to be parallel lines.
The diagram below shows two lines that are intersected by a transversal. It also shows two pairs of alternate exterior angles, a and d, and b and c.
If angles a and d are congruent or angles b and c are congruent, then both lines can be proven to be parallel to each other by the alternate exterior angles converse.
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What is the slope of -2,1 and 2,1
Is should be 50% slope
Answer:
m=0
Step-by-step explanation:
(-2,1) (2,1)
x1=-2,x2=2,y1=1,y2=1
Gradient/slope
m=y2-y1/x2-x1
m=1 - 1/2-(-2)
m=0/2+2
m=0/4
m=0
Calvin wants to sell a basic badminton kit to his friends. In that kit, he puts two rackets worth
140 each and a shuttlecock worth 280. He wants to have a profit of 25%.
For how much should Calvin sell the kit?
Answer:
realto, hindi ako sure eh
Step-by-step explanation:
tama yan
Can someone please help! And thank you!
Answer:
x = 20
Step-by-step explanation:
X = 20 Because the values are Corresponding Angles This means that they are congruent
5. Which might be your first step if you want to solve the
system by elimination?
1st equation: 5x + 4y = 7
2nd equation: 2x - 3y = 3
A) Substitute -10y + 7 for x in the second equation.
B) Substitute 3y + 3 for x in the second equation.
C) Multiply the first equation by 3, multiply the second
equation by 4, then add the resulting equations
together.
D Multiply the first equation by 2, multiply the second
equation 5, then add the resulting equations together.
Answer:
C)
Step-by-step explanation:
elimination is not substitution.
therefore, A and B are out.
D does not work, because in the described way the x terms don't get different signs, and the addition does not eliminate any variable.
C brings both y terms to the same absolute value, and their signs are different, so the addition will eliminate the y terms leaving us with one equation in x that we can solve :
15x + 12y = 21
8x - 12y = 12
---------------------
23x 0 = 33
23x = 33
x = 33/23
Answer:
a is the right answer for you
You are a grant writer for an organization that helps adults complete their high school educations. For the last 5 years, you have applied for and received $45,000.00 in grants. Your boss would like you to try to increase that amount to $60,000.00. How much of an increase does the new amount represent over the previous amount?
Based on the amount you have received in grants, and the amount the boss wants to increase it to, the increase the new amount represents over the previous amount is $15,000 or 33.3%.
How to find the increase?Your boss wants to increase the grants to $60,000 from the current amount of $45,000.
This means that the new amount will represent an increase over the previous amount by:
= 60,000 - 45,000
= $15,000
In percentage terms this is:
= Increase over previous amount / Previous amount x 100%
= 15,000 / 45,000 x 100%
= 33.3%
In conclusion, the difference between the grants applied for in the past 5 years and the amount the boss is asking for, gives the increase of $15,000.
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Help please i need it for a grade
Answer:
(3,13 ) & (-1,5)
Step-by-step explanation:
a. 2x + 7 = x^2 + 4
b. move all terms to the left side and set equal to zero. then set each factor equal to zero. which gives you the x values 3, -1
c. substitute x with the x values to get y. 2(3) + 7 = -1^2 + 4
d. the solution is (3,13 ) & (-1,5)
Checks: 32.96,121.03 and 24.70;cash:22 one dollar bills, 5 ten dollar bills, and 15.21 in coins; less $20 cash recieved
The balance of the checks and cash (receipts and payments) is -$245.90.
How is the balance determined?The balance is the difference between receipts of cash and payments of checks and cash.
Using addition and subtraction operations, the balance is determined as follows:
Check Payments:32.96
121.03
24.70
Total checks = $178.69
Cash Payments:22 one dollar bills = $22.00 (22 x $1)
5 ten dollar bills $50.00 (5 x $10)
15.21 in coins $15.21
Total cash payments = $87.21
Cash Receipts:$20 cash received
Total cash = $67.21
Balance = -$245.90 [$20 - ($87.21 + $178.69)]
Thus, the balance of the checks and cash totals -$245.90, showing that payments outstripped receipts.
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Question Completion:How much is the balance between receipts and payments?
YAbisects ZXYZ. Which statement is false?A. YXYZB. ZXYA and ZZYA each measure 63º.C. ZXYA: ZZYAD. The total measure of ZXYA and ZZYA is 126º.
Given that
[tex]\vec{YA}\text{ bisesects}\angle XYZ[/tex]Then,
[tex]\begin{gathered} \angle XYA\text{ and }\angle ZYA\text{ each measure 63degr}ees \\ \angle XYA\cong\angle ZYA \\ \text{ The total measure of }\angle XYA\text{ and }\angle ZYA\text{ }is\text{ }63+63=126^{\text{0}} \end{gathered}[/tex]Therefore, the statement
[tex]\begin{gathered} \bar{YX}\cong\bar{YZ}\text{ is false} \\ The\text{ answer is Option A} \end{gathered}[/tex]Natalia and her friends held a bake sale to benefit a local charity. The friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale. They collected $60 on the first day and $88 on the second day. Write an equation to represent the amount R Natalia and her friends raised after selling c cakes.
In linear equation, R = 4c is an equation to represent the amount R Natalia and her friends raised after selling c cakes.
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as .
Where,
y = R (amount of cake sold in dollars)
x = c (cakes sold)
m = slope
b = y-intercept.
The equation would look like
R = mc + b
We need to find the value of m and b, to get an equation to represent the situation.
The first point we have from the information given is (15, 60) => 15 cakes sold for $60.
The second point is (22, 88) => 22 cakes sold for $88.
Slope(m) = 88 - 60/22 - 15 = 28/7 = 4
To find b, substitute c = 15, R = 60 and m = 4, into R = mc + b
60 = 4(15) + b
60 = 60 + b
b = 0
Since b = 0, this means there is a proportional relationship between R and c.
Substitute m = 4 and b = 0 into R = mc + b to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.
R = 4c + 0
R = 4c
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Question Progress
Homework Progress
7/21 Marks
Solve the equation
3x-2
4
-
2x-5
3
=
1+x
6
Answer: x= 1.20833
The way it was written was a little confusing but hope this helps, This may be wrong just re write it for me and it should be correct next time.
Step-by-step explanation:
Step 1: Make parentheses
( 3x - 2 ) 4 ( -2x - 5 ) 3 = ( 1 + x ) 6
Step 2: Solve parentheses ( Multiplication and division first )
(4 * 3x = 12x) - (4 * 2 = 8) -> 12x - 8
(-2x * 3 = -6x) - (3 * 5 = 15) -> -6x - 15
(6 * 1 = 6) + (6 * x = 6x) -> 6 + 6x
New and improved equation:
-12x - 8 - 6x - 15 = 6 + 6x
Step 3: add like terms
-12x - 6x = -18x
-8 - 15 = -23 so...
-18x - 23 = 6 + 6x
Step 4: solve it
-18x - 23 = 6 + 6x
+ 23
-18x = 29 + 6x
-6x
-24x = 29
x= 1.20833
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Write the equation of the line in y=mx+b form using the following two points:
(-2,-1) and (-1,-2)
Enter you equation here: type your answer....
10 points
Answer: The slope-intercept form for a line with the coordinates of (-2,-1) and (-1,-2) is:
y= -1.00x + -3.00
(results are in decimal form, rounded to the nearest 100th)
i hope i helped it is for if it was for like slope intercept form
Step-by-step explanation:
3|y|+(y-x²)
if x = -1 and y = -5
the admission fee at a local zoo is $ 1.50 for children and $ 5.00 for adults. on a certain day, 2000 people enter the zoo and $ 7 , 550.00 is collected. how many children and how many adults attended?
There are [tex]700[/tex] children and [tex]1300[/tex] adults.
What is system of linear equations?
A System of Linear Equations is when we have two or more linear equations working together.
Let [tex]x[/tex] be number of children and [tex]y[/tex] be number of adults.
Since [tex]2000[/tex] people enter the zoo then [tex]x+y=2000.[/tex]
The admission fee at a local zoo is $ [tex]1.50[/tex] for children and $ [tex]5.00[/tex] for adults and $[tex]7550.00[/tex] collected then [tex]1.5x+5y=7550[/tex].
Thus there are two linear equations to solve.
Substitute [tex]x=2000-y[/tex] in [tex]1.5x+5y=7550.[/tex]
[tex]1.5(2000-y)+5y=7550[/tex]
[tex]3000-1.5y+5y=7550[/tex]
[tex]3000+3.5y=7550[/tex]
[tex]3.5y=7550-3000[/tex]
[tex]3.5y=4550[/tex]
[tex]y=\frac{4550}{3.5}[/tex]
[tex]y=1300[/tex]
So [tex]x=2000-y=2000-1300=700.[/tex]
Therefore there are [tex]700[/tex] children and [tex]1300[/tex] adults.
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PLEASE HELPPPPPPP I NEED THIS DONE
50 POINTS
Answer:
y to the power of -8
:) hope this help
Answer: y^8
Step-by-step explanation:
You see that the equation has two negative numbers, so it will become positive.
(y^-2)^-6 = y^8
The base of it will cancel each other out and left with y^8
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Select the correct answer.
Find the inverse of function f.
f (x) = 9x + 7
A. f^{\small -1}(x)\ =\ 7x\ +\ 9
B. f^{\small -1}(x)\ =\ -9x\ -\ 7
C. f^{\small -1}(x)\ =\ \frac{1}{9}x\ -\ \frac{7}{9}
D. f^{\small -1}(x)\ =\ \frac{7}{9}x\ -\ \frac{1}{9}
Answer:
[tex]\dfrac{x-7}{9}[/tex]
which corresponds to choice
C : [tex]f^{\small -1}(x)\ =\ \frac{1}{9}x\ -\ \frac{7}{9}[/tex]
Step-by-step explanation:
The inverse of a function y = f(x) can be found by interchanging x and y and solving for y
Let y = f(x)
y = 9x + 7
Interchange x and y:
x = 9y + 7
9y + 7 = x (switch sides)
subtract 7 both sides
→ 9y + 7 - 7 = x - 9
→ 9y = x - 9
Divide both sides by 9
→ [tex]y = \dfrac{x - 7}{9} = \dfrac{x}{9} - \dfrac{7}{9}[/tex]
which corresponds to choice C
In Arizona, a minimum temperature of - 40.0°C was recorded at Hawley Lake in 1971. A maximum recorded temperature of 53.3°C was recorded at Lake Havasu City in 1994. Find the difference between these maximum and minimum temperatures.
Answer:
Your answer is 93.3.
Step-by-step explanation:
[tex]53-[/tex][tex](-40) = 93.3[/tex]
How to solve this question, I have an idea of what to do but I’m confused on solving it
ANSWER
R1, R2, R3, R4, G1, G2, G3, G4. Option B.
Describe the end behavior of the graph of the following polynomial function:
We will have the following:
From the polynomial we will have that:
*It falls to the left and rises to the right.
This can be seeing as follows:
What is the image of (0,-8) after a reflection over the line y=x
the reflection over the line y=x tells us to swap the points.
Therefore the point (0,-8) becomes (-8,0)
Use the graph or table to find the equation that represents the relationship.
Answer:
1) y = 3x + 5
2) y = -12x + 2
3) y = 5/4 - 5
4) y = -6x + 3
Step-by-step explanation:
Can someone please answer this!
Considering the situation described, it is found that:
a) The numeric values of the piecewise function are as follows:
W(30) = $300.W(40) = $400.W(47) = $505.W(52) = $580.b) The new piece-wise function is:
W(h) = 10h, 0 ≤ h ≤ 38.W(h) = 15(h - 38) + 380, h > 38.c) The new piece-wise function is:
W(h) = 12h, 0 ≤ h ≤ 40.W(h) = 18(h - 40) + 480, h > 40. What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
In this problem, the rule is one for times up to 40 hours, and another for times greater than 40 hours, hence the numeric values are given as follows:
W(30) = 10 x 30 = $300.W(40) = 10 x 40 = $400.W(47) = 15 x (47 - 40) + 400 = $505.W(52) = 15 x (52 - 40) + 400 = $580.For item b, the new reference is of 38 hours, hence the function is:
W(h) = 10h, 0 ≤ h ≤ 38.W(h) = 15(h - 38) + 380, h > 38. (the earnings for the first 38 hours are of 38 x 10 = $380).For item c, the new hourly wage is of 12 hours, hence the rule is:
W(h) = 12h, 0 ≤ h ≤ 40.W(h) = 18(h - 40) + 480, h > 40. (pay and half = 12 x 1.5 = 18, wage for the first 40 hours of 40 x 12 = 480).More can be learned about piecewise functions at brainly.com/question/19358926
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Simplify by dividing
Answer: -27/40
Step-by-step explanation:
13) Which of the following algebraic representations would result in a reduction dilation?A. (x,y) → x,y)C. (x,y) →x,0.75y)AnswerB. (x,y) → (-2x.-2y)D. (x,y) →x,y)acxiy) (tx, tyTriangles JKN and MKL are shown below.KMN14) Which of the following congruency statements is true about the two triangles?Angwer BA. L and ZN ZM B. ZNZL and ZK-ZK2N and CL areCongruentC. ZNZL and ZMD. UN and ZMZL Eck and Zk aze congruen15) Are triangles JKN and MKL similar?Yes16) If you answered YES for question 15, explain how you know they are similar. If you answered NO forquestion 15, explain how you know they are not similar.
16) We know that the triangles are similar because the three angles are equal in both triangles:
The angles in K are opposite by the vertex, so they are equal.
We also know that angles L and N are equal too.
By the rule of the sum of the angles in a triangle, we know that the third angle has to be equal.
Also, the side opposite to the angle N and L in each triangle have the same measure, so we can conclude that the triangles are similar.
In the triangle below, suppose that mV = (x - 2)",mW = (x - 2)°, and m ZX=(4x+4)*Find the degree measure of each angle in the triangle.(x - 2)(4x + 4)m ZV =Х5?m ZW =001Xm 2x =(x - 2)°
SOLUTION
Consider the image given below.
From the image above,
[tex]\begin{gathered} \angle V=(x-2)^0 \\ \angle W=(x-2)^0 \\ \angle X=(4x+4)^0 \end{gathered}[/tex]To find the measures of each angle, we need to obtain the value of small x in the diagram.
Applying the rule: Sum of angle in a triangle is 180 degrees
[tex]\angle V+\angle W+\angle X=180^0[/tex]Then substitute the given expression, we have
[tex]\begin{gathered} (x-2)^0+(x-2)^0+(4x+4)^0=180^0 \\ Then \\ x-2+x-2+4x+4=180^0 \end{gathered}[/tex]Collect like terms and add
[tex]\begin{gathered} x+x+4x-2-2+4=180^0 \\ 6x-4+4=180^0 \\ \text{then} \\ 6x=180 \end{gathered}[/tex]Divide both sides by 6, we have
[tex]\begin{gathered} \frac{6x}{6}=\frac{180}{6} \\ hence \\ x=30 \end{gathered}[/tex]hence, x=30
Then substitute the value of x to obtain the measure of each angles.
[tex]\begin{gathered} \angle V=(x-2)^0 \\ \text{Then x=30} \\ \angle V=30-2=28^0 \end{gathered}[/tex]Since the triangle is an issoceles triangle, then
[tex]\angle W=28^0[/tex]Hence
[tex]\begin{gathered} \angle X=(4x+4)^0 \\ \angle X=(4\times30+4)^0=(120+4)=124^0 \\ \text{hence} \\ \angle X=124^0 \end{gathered}[/tex]Therefore
Answer : ∠V= 28°, ∠W=28°, ∠X=124°
What’s the answer plss
Opposite Q is length PR
Adjacent is 7
Hypotenuse is 19
We got AH - which is CAH or cos
Cos-1( 7/19) = 68.38....
It's 68.4 degrees
The closest answer to this is B. So, choose that because it maybe due to a typing error.
Hope this helps!
Can someone help me with this?
Answer:
y = 77
Step-by-step explanation:
[tex]\frac{7}{3}[/tex] = [tex]\frac{y}{33}[/tex] ( cross- multiply )
3y = 7 × 33 = 231 ( divide both sides by 3 )
y = 77
The answer to this math question is 77
Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.)2 cos 2x − 1 = 0
Given:
The function is:
[tex]2\cos2x-1=0[/tex]Find-:
The value of "x"
Explanation-:
The value of x is:
[tex]\begin{gathered} 2\cos2x-1=0 \\ \\ 2\cos2x=1 \\ \\ \cos2x=\frac{1}{2} \\ \end{gathered}[/tex]Solve for x is:
[tex]\begin{gathered} \cos2x=\frac{1}{2} \\ \\ 2x=\cos^{-1}(\frac{1}{2}) \\ \\ 2x=\frac{\pi}{3}+2\pi n\text{ and }2x=\frac{5\pi}{3}+2\pi n \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} 2x=\frac{\pi}{3}+2\pi n \\ \\ x=\frac{\pi}{2\times3}+\frac{2\pi n}{2} \\ \\ x=\frac{\pi}{6}+\pi n \end{gathered}[/tex]Another value of "x" is:
[tex]\begin{gathered} 2x=\frac{5\pi}{3}+2\pi n \\ \\ x=\frac{5\pi}{3\times2}+\frac{2\pi n}{2} \\ \\ x=\frac{5\pi}{6}+\pi n \end{gathered}[/tex]So, the answer is:
[tex]x=\frac{\pi}{6}+\pi n,\frac{5\pi}{6}+\pi n[/tex]2, What method of data collection would you use to collect data for a study where adrug was given to 10 patients and a placebo to another group of 10 patients todetermine if the drug has an effecton a patient's illness?A) take a censusb) use sampling c) use a simulation d) perform an experiment e) none
I would say that using a survey gives you the perfect way to collect the data you need for the drug effect. So,
