Which of the following are equivalent to the function y = 3cOS X + 2? Check all that apply. A. y = 3cos(-x) + 2 B. y = -3cOS X-2 C. y = 3sin(x + 1) +2 + D. y = 3sin(x-7)+2
Answers
We need to plot the graphs of these functions on the same axis:
[tex]\begin{gathered} \text{From the graph, we s}e\text{ the function} \\ y\text{ = 3cosx + 2 has the same grap as } \\ y\text{ = 3sin(x + }\frac{\pi}{2})\text{ + 2} \\ \\ \text{Please note from angles in trigonometry:} \\ \sin \text{ (90 + }\theta)\text{ = cos }\theta \\ \cos x\text{ = sin (90 + x)} \end{gathered}[/tex]Hence, the correct option
[tex]y\text{ = 3sin(x + }\frac{\pi}{2})\text{ + 2 (option }C)[/tex]
Related Questions
What is the third term of the recursive sequence below
Answers
Given the sequence:
[tex]\begin{gathered} a_1=-6 \\ a_n=\frac{1}{2}a_{n-1}-n \end{gathered}[/tex]Let's find the third term of the sequence.
To find the third term, a3, we have:
First find the second term, a2:
[tex]\begin{gathered} a_2=\frac{1}{2}a_{2-1}-2 \\ \\ a_2=\frac{1}{2}a_1-2 \\ \\ a_2=\frac{1}{2}(-6)-2 \\ \\ a_2=-3-2 \\ \\ a_2=-5 \end{gathered}[/tex]The second term is -5.
To find the third term, we have:
[tex]\begin{gathered} a_3=\frac{1}{2}a_{3-1}-3 \\ \\ a_3=\frac{1}{2}a_2-3 \\ \\ a_3=\frac{1}{2}(-5)-3 \\ \\ a_3=-2.5-3 \\ \\ a_3=-5.5 \end{gathered}[/tex]Therefore, the third term of the
Determine the value for x in the equation x over 6 and 4 tenths equals 3 and 6 tenths.
Answers
Answer:
x = 23.04
Step-by-step explanation:
You want to know the value of x such that x/6.4 = 3.6.
One-step equationWe can solve this equation by multiplying by the inverse of the coefficient of x.
The coefficient of x is 1/6.4, so multiplying by 6.4 will give ...
6.4(x/6.4) = 6.4(3.6)
x = 23.04
The value for x in the equation is 23.04.
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Write the standard form of the equation
1) through: (-5, 3) and (2,-2)
Answers
What is the annual percentage yield (APY) for money invested at an annual rate of(A) 4.09% compounded monthly?(B) 4.1% compounded quarterly?
Answers
The annual percentage yield is given by the following formula:
[tex]\text{APY}=(1+\frac{r}{n})^n-1[/tex]Where r is the stated annual interest rate (in decimal form) and n is the number of times compounded.
A) APY for money invested at an annual rate of 4.09% compounded monthly.
Thus, the annual interest rate in decimal form is:
[tex]r=\frac{4.09\%}{100\%}=0.0409[/tex]And as it is compounded monthly then n=12.
Replace these values and solve:
[tex]\begin{gathered} \text{APY}=(1+\frac{0.0409}{12})^{12}-1 \\ \text{APY}=(1+0.0034)^{12}-1 \\ \text{APY}=(1.0034)^{12}-1 \\ \text{APY}=1.0417-1 \\ \text{APY}=0.0417 \end{gathered}[/tex]The APY is 0.0417=4.17%.
B) 4.1% compounded quarterly:
The annual interest rate is:
[tex]r=\frac{4.1\%}{100\%}=0.041[/tex]As it is compounded quarterly then n=4.
Replace and solve:
[tex]\begin{gathered} \text{APY}=(1+\frac{0.041}{4})^4-1 \\ \text{APY}=(1+0.0103)^{12}-1 \\ \text{APY}=(1.0103)^{12}-1 \\ \text{APY}=1.1302-1 \\ \text{APY}=0.1302 \end{gathered}[/tex]The APY is 0.1302=13.02%
–5 = –3(h − 10) + –8
Answers
Answer:
h = 9
Step-by-step explanation:
-5 = -3(h - 10) + (-8)
−5 = −3h + 22
−3h + 22 = −5
−3h = −27
h = 9
--------------
check
-5 = -3(9-10)+(-8)
-5 = -27 + 30 - 8
- 5 = -5
the answer is good
Match the correct slope-internet form of an equation with the standard form of the same equation.
Answers
Given:
-x+y=2
x-y=2
x+y=-2
-x-y=-2
To match the correct slope-intercept form of an equation, we follow the process as shown below:
Standard Form: Ax+By=C
Conversion: y= -A/Bx+C/B
So,
For -x+y=2:
A=-1
B=1
C=2
Hence,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ y=-\frac{-1}{1}x+\frac{2}{1} \\ Simplify \\ y=x+2 \end{gathered}[/tex]For x-y=2,
A=1
B=-1
C=2
So,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ =-\frac{1}{-1}x+\frac{2}{-1} \\ Simplify \\ y=x-2 \end{gathered}[/tex]For x+y=-2,
A=1
B=1
C=-2
So,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ y=-\frac{1}{1}x+\frac{-2}{1} \\ y=-x-2 \end{gathered}[/tex]For -x-y=-2,
A=-1
B=-1
C=-2
So,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ =-\frac{-1}{-1}x+\frac{-2}{-1} \\ Simplify \\ y=-x+2 \end{gathered}[/tex]Therefore, the answers are:
-x+y=2----y=x+2
x-y=2-----y=x-2
x+y=-2----y= -x-2
-x-y=-2----y= -x+2
The next model of a sports car will cost 6.2% less than the current model. The current model costs $57,000. How much will the price decrease in dollars? What will be the price of the next model
Answers
Answer:
The price will decrease $3534
The price of the next model is $53466
Step-by-step explanation:
57000 divided by 100 and then time 6.2 = $3534
Then subtract 57000 - 3534 = $53466
Answer: 53,466
Step-by-step explanation:
Do 57,000 minus 6.2 or and get 53,466.
What is 1/5 divided by 4. (Fraction)
Answers
Given the expression:
[tex]\text{ 1/5 }\div\text{ 4}[/tex]Let's determine the quotient:
Step 1: Transform the whole number into the fractional form.
[tex]\text{ 1/5 }\div\text{ 4 = }\frac{1}{5}\text{ }\div\text{ }\frac{4}{1}[/tex]Step 2: Transpose the division into multiplication and reciprocate 4/1.
[tex]\frac{1}{5}\text{ }\div\text{ }\frac{4}{1}[/tex][tex]=\text{ }\frac{1}{5}\text{ x }\frac{1}{4}[/tex][tex]\text{ = }\frac{1}{20}[/tex]Therefore, the answer is 1/20.
It Carlos sits 3 feet from the fulcrum of a see-saw, how far from the fulcrum must his baby-sister who weighs three-times his weight sit?
A. 1 foot
B. 6 feet
C. 3 feet
D. 9 feet
Answers
Answer: B: 6 feet
Step-by-step explanation: To solve this problem, we need to use the concept of leverage, which is the force applied to an object at a distance from its pivot point. In this case, Carlos is applying a force of 3 feet from the fulcrum, while his baby sister is applying a force 3 times as large, at a distance from the fulcrum.
To find the distance from the fulcrum that the baby sister must sit, we need to balance the forces applied by Carlos and his sister. This means that the product of the force applied by Carlos and the distance from the fulcrum must be equal to the product of the force applied by his sister and the distance from the fulcrum where she must sit.
We can use this information to write the equation: 3 * 3 = 3 * x
Where x is the distance from the fulcrum where the baby sister must sit. We can solve for x by dividing both sides of the equation by 3 to get: x = 6
Therefore, the baby sister must sit 6 feet from the fulcrum in order to balance the forces applied by Carlos and his sister. The correct answer is B. 6 feet.
Can someone help? :)
Answers
The slope is [tex]\frac{3}{4}[/tex]
What is slope ?
A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not. Any two clearly separated points on a line can be used to calculate the slope of any line. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined.
here the given two pints are
[tex](x_1,y_1)=(-2,4)\\(x_2,y_2)=(6,10)[/tex]
Now using slope formula,
slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = [tex]\frac{10-4}{6+2}[/tex]
=> slope m = [tex]\frac{6}{8}[/tex]
=> slope m = [tex]\frac{3}{4}[/tex]
Therefore the slope is [tex]\frac{3}{4}[/tex].
To learn more about slope
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What is the equation of the line that passes through the point (-3,-6) and has a slope of 1/3
Answers
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
How can I locate a slope?You may determine the slope of the line by determining the rise and the run using two of the line's points. The rise and the run are terms used to describe changes in height between two points. The increase divided by the run is the slope.The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) expressions of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.Formula m = rise / run = y2 - y1 / x2 - x1m = slope
(x1, y1) = coordinates of first point in the line
(x2, y2) = coordinates of second point in the line
Point (-3, 6) (-3, 6) Summary: An equation for the line through the point, which has the undefined slope m specified. x = -3 at the location (-3, 6).To Learn more About line's slope refer to:
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The bull in Ms. Garcia's pasture weighs 0.95 tons. What is the weight of the bull in pounds?
Answers
Answer:
The bull weighs 1,900 pounds.
Step-by-step explanation:
2,000 pounds = 1 ton
0.95 x 2,000 = 1,900 pounds
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 6 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer: 1,900 pounds
Step-by-step explanation:
There are 2,000 pounds in a ton, so we will multiply 0.95 tons by 2,000 to figure out the weight of the bull in pounds.
0.95 * 2,000 = 1,900 pounds
3. Select all equations that have exactly one solution.
A 5x + 8 = 5x - 15
B. 3x +4= 7x-1
c. 3 (x - 12) = 4x - 36
D. 2 (x-1) + x = 2x - 7
E. 4 (2x - 5) - 3x = 5x-20
Answers
Answer:
Step-by-step explanation:
D the reason is because I said so
If Jamal treated his family with a family brunch and the brunch costs $250 and the sales tax was 4%. If Jamal left an 18% tip on the $250. How much did he pay in total?
Answers
The total amount jamal paid is $305.
Given:
Jamal treated his family with a family brunch at the cost of $250.
The sales tax was 4%.
The tip is 18%.
to find the sales tax.
[tex]\begin{gathered} =250\cdot4\text{ \%} \\ =250\cdot\frac{4}{100} \\ =\frac{1000}{100} \\ =10 \end{gathered}[/tex]The amount he paid for sales tax is $ 10.
to find the tip.
[tex]\begin{gathered} =250\cdot18\text{ \%} \\ =250\cdot\frac{18}{100} \\ =\frac{4500}{100} \\ =45 \end{gathered}[/tex]Jamal left a tip of $45.
Thus the total amount paid by Jamal is,
[tex]250+10+45=305[/tex]Find the radian measure of θ if θ is a central angle in a circle of radius r=14in and θ cuts off an arc length s=7π in
Answers
The formula for determining the length of an arc is experessed as
arc length = θ x r
where
θ is the central angle
r is the radius of the circle
From the information given,
arc length = 7π in
r = 14 in
By substituting these values into the formula,
7π in = θ x 14 in
We would divide both sides of the equation by 14 in. We have
7π in/14 in = θ x 14 in/14 in
θ = π/2
Yesterday jack drove 38 1/2 miles. He used 1 1/4 gallons of gasoline. What is the unit rate for mile per gallon
Answers
Answer:
the unit rate for miles per gallons is 32.4 miles per gallon
Step-by-step explanation:
From the information we have, Jack drove 401/2 miles and used a total of 1 1/4 gallons of gasoline.
We need to find out how many miles he travelled per each gallon.
40 1/2 miles can be written as 40.5 miles
1 1/4 gallons can be written as 1.25 gallons.
So now we form an equation.
40.5 = 1.25
x = 1
Where x is the number of miles per gallon
We cross multiply the equation
40.5 * 1 = 1.25 * x
40.5 = 1.25x
40.5 / 1.25 = x
32.4 = x
x = 32 .4
Find the measure of the angles between the hands of the clocks at a) 8:54 b) 5:11 and c) 8:03I have the answers, but I need an explanation
Answers
I will explain to you through a drawing on how to identify 3 types of angles :
You will find the angles by placing a protractor aligning the centre with 0:00 marking the hour and the minute will be your angle formed on the watch, you can twist and turn the protractor but it will always form a measured angle .
Using the following diagram below: Find the length of TT. Round youranswer to the nearest tenth.Note: The nearest tenth means you will round to one decimal place. YouMust Show Your Work.IPoints T, T', and 7" are shown.T"T'T
Answers
Let point T the origin
so
The coordinates of point T are (0,0)
therefore
The coordinates of point T' are (-2,1)
Find out the distance TT'
Applying the formula to calculate the distance between two points
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]substitute given coordinates
[tex]\begin{gathered} TT^{\prime}=\sqrt{(1-0)^2+(-2-0)^2} \\ TT^{\prime}=\sqrt{1^2+-2^2} \\ TT^{\prime}=\sqrt{5} \\ TT^{\prime}=2.2\text{ units} \end{gathered}[/tex]The answer is TT'=2.2 unitsWhat is an equation of the line that passes through the points (2, 2) and
(1, -2)
Answers
Answer: y = 4x + -6
Step-by-step explanation:
What's the length of the hypotenuse of a right triangle if the length of one leg is 7 units and the length of the other leg is 14 units?
Answers
ANSWER:
The hypotenuse is
[tex]7\sqrt[]{5}=15.65[/tex]STEP-BY-STEP EXPLANATION:
In this case we can calculate the value of the hypotenuse by means of the Pythagorean theorem.
[tex]\begin{gathered} h^2=a^2+b^2 \\ a=7 \\ b=14 \end{gathered}[/tex]replacing
[tex]\begin{gathered} h^2=7^2+14^2 \\ h^2=49+196 \\ h=\sqrt[]{245} \\ h=7\sqrt[]{5}=15.65 \end{gathered}[/tex]Sel 9.5.37 Assigned Media Question Help D You, a A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 17 feet more than the length of the shortest side. Find the dimensions if the perimeter is 153 feet. What is the length of the shortest side?
Answers
First we can set the equations we already know
[tex]a\text{ +b +c = 153 ft}[/tex]Where a, b and c are the sides of the triangle. Then, I will assign "a" the shortes side. One side is twice the shortest side so:
[tex]b\text{ = 2a }[/tex]Now, the sentence says, the third side is 17 feet longer that the shortes side "a":
[tex]c\text{ = a + 17}[/tex]Now we have a system of three equations with three unknown variables, so it will be easy to find the value of all the variables. If we put "b" and "c" in the first equation we have:
[tex]a\text{ + (2a) + (a+17) = 153 ft}[/tex][tex]\begin{gathered} 4a\text{ = 153-17} \\ 4a\text{ = }136 \\ a\text{ = 136/4} \\ a=34 \end{gathered}[/tex]Now, since we assigned "a" as the shortest side, we are done.
Explain the error Andrew is using vector v to draw a copy of ∆ABC explain his error
Answers
We want to know the mistake is doing Andrew when he tries to draw a copy of ∆ABC using the vector v.
We see that the vector v is directed 3 units to the right, and 3 units down.
For translating the triangle ABC with the vector v, we should make the translation with every point of the triangle.
This means that you move the point A 3 units down and 3 units to the right, but Andrew just moved it 2 units down, and 3 units to the left. Also, we have:
0. The point B was moved two units down and four units to the right.
,1. The point C was moved three units down, and three units to the right
Thus, Andrew didn't move correctly the points A and B.
Geometry Match each segment, angle, or arc to its degree measure. segment ADsegment DKsegment AKsegment KLangle BDCangle DAKangle EMAangle FBAarc EJsegment DEsegment AFarc DCE
Answers
The given figure inscribed in the circle is a square.
We know from the properties of a square that all the sides and all the angles of a square are equal.
Also the diagonal bisects each other at 90 degrees.
From the figure we are given;
CD = 14.14
AJ = 10
arc BC = 90 degrees
From the figure and properties of polygons, we can say that;
arc BC = arc CD = arc DE = Arc EB = 90 degree
AJ = AK = AB = AC = AD = AE = 10 = Radius of circle
JL = EC = BD = 20 = diameter of circle (Since, diameter = 2 * radius)
BC = CD = DE = EB = 14.14 = sides of the squares
Thus, the given figure inscribed in the circle is a square.
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What is the GCF of 12, 48, 36, 24, and 60. Will mark BRAINLIEST!!!!!
Answers
Answer: 6
Step-by-step explanation:
Answer: Hi the answer to your question would be
GCF = 12
for the values 12, 24, 36, 48, 60
Here is an explanation!
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Then the greatest common factor is 12.
Hope this helps Ihsan!
Order these numbers from least to greatest. 143 7 7.116, 6.67 20
Answers
We are given the following numbers
[tex]7\frac{1}{9},\: 7.116,\: \frac{143}{20},\: 6.67[/tex]We are asked to arrange these numbers from least to greatest.
As you can see, the numbers are in different forms (decimal, fraction)
So, first we need to convert them into a single form then we can compare them
Let us convert all the numbers into decimals
[tex]\begin{gathered} 7\frac{1}{9}=\frac{7\cdot9+1}{9}=\frac{63+1}{9}=\frac{64}{9}=7.111 \\ \frac{143}{20}=7.15 \end{gathered}[/tex]So the order from least to greatest is
6.67, 7.111, 7.116, 7.15
Now write the numbers in their original form
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Answers
Answer: 2.5, 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]
Select all of the scenarios below that correctly identify the independent variable. A. Charlie gets paid by the hour. The number of hours he works is the independent variable. B. Oscar likes to go for drives in the car. The cost of the trip increases as the distance he travels increases. The distance is the independent variable. C. How much Caleb weighs is relative to the amount he eats. The amount he weighs is the independent variable. D. The more Mark practices his golf swing, the better he becomes at hitting the ball. The amount of time he practices is the independent variable.
Answers
Independent varible are variable that dosent depend on any factor that afftect the scenarios.
the scenarios that identify the independent variable.
A. Charlie gets paid by the hour. The number of hours he works is the independent variable.
B. Oscar likes to go for drives in the car. The cost of the trip increases as the distance he travels increases. The distance is the independent variable.
D. The more Mark practices his golf swing, the better he becomes at hitting the ball. The amount of time he practices is the independent variable.
What two numbers add to give 3 and multiply to give -18
Answers
-3 and 6
Explanation:
-3 + 6 = 3
-3 • 6 = -18
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W. Checkpoint: Solve lines 1) Tell whether each equation has exactly one solution, infinitely many solutions, or no solutions no exactly one solution Infinitely many solutions solutions 7(x-2) 9x - 2 9x + 3 = 3(3x + 1) 3x + 2 = 7(x-2)
Answers
7(x-2) = 9x - 2
open the parenthesis
7x - 14 = 9x - 2
collect like term
9x - 7x = -14 + 2
2x = -12
Divide both-side of the equation by 2
x = -6
It has exactly one solution
9x+3 =3(3x+1)
9x + 3 = 9x + 3
Since the left-hand side is exactly the same as the right hand side, then it has infinitely many solutions
3x + 2 = 7(x-2)
open the parenthesis
3x + 2 = 7x - 14
collect like term
7x -3x = 2 + 14
4x = 16
Divide both-side by 4
x = 4
It has exactly one solution
How do I get the answers to thisQuestion 1 - 4
Answers
Answer:
Lines d and e are parallel and lines s and t are also parallel
1. Alternate Exterior Angles Theorem
2. Corresponding Angles Postulate
3. Alternate Angles Postulate
4. Co-interior Angles Theorem
Explanation:
Given the below;
1. Given that;
[tex]\angle1\cong\angle4[/tex]The theorem that justifies the above is the Alternate Exterior Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
2. Given that;
[tex]\angle2\cong\angle3[/tex]The theorem that justifies the above is the Corresponding Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the corresponding angles are congruent.
3. Given that;
[tex]\angle6\cong\angle7[/tex]The theorem that justifies the above is the Alternate Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the alternate angles are congruent.
4. Given that;
[tex]m\angle5+m\angle8=180[/tex]The theorem that justifies the above is the Co-interior Angles Theorem which states that if a pair of parallel lines are cut by a transversal, angles that are in the same similar position are supplementary, that is, they add up to 180 degrees.