The graph is supposed to show f(x)=3sin(x/4+1)-1/2. Which of the following are correctly represented in the graph? Select all that apply. (2 answers)
a. the amplitude
b. the vertical shift
c. the horizontal shift
d. the period
e. the horizontal expansion or compression
Answers
The vertical shift is correct
and the horizontal shift is correct
Answer:
a , b, c are only applicable in graph.
Step-by-step explanation:
Given : The function [tex]f(x)=3sin(\frac{x}{4}+1)-\frac{1}{2}[/tex]
To find : Which of the following are correctly represented in the graph?
Solution :
General form of sin function is [tex]y=A sin(B(x-C)+D[/tex]
Where A is the amplitude
[tex]B=\frac{2\pi}{\text{Period}}[/tex]
D is the vertical shift.
C is the horizontal shift or phase shift.
Comparing with the general form:
[tex]f(x)=3sin(\frac{x}{4}+1)-\frac{1}{2}[/tex]
Transform little bit we get,
[tex]f(x)=3sin(\frac{1}{4}(x-(-4)))-\frac{1}{2}[/tex]
a. Amplitude is [tex]A=3[/tex]
It is correct.
b. Vertical shift is [tex]D= -\frac{1}{2}[/tex]
it is correct.
c. Horizontal shift [tex]C=-4[/tex]
It is correct.
d. Period is [tex]P=\frac{2\pi}{B}[/tex]
[tex]P=\frac{2\pi}{\frac{1}{4}}[/tex]
[tex]P=8\pi[/tex]
It is not correct .
Actual period in graph is [tex]2\pi[/tex]
e. The horizontal expansion or compression
It also not correct because period is not correct.
The expansion and compression depends on the period.
Therefore, a , b, c are only applicable in the graph.
Related Questions
12pts BRAINLIEST, THX, AND RATE AVAILABLE TO CORRECT ANSWER.
PLEASE HELP ME ON THIS
****RANDOM ANSWERS WILL BE REPORTED****
Answers
someone please help :(
Answers
Because 5/4 = 1.25
tan (51) = 1.235
tan (45) = 1
tan (60) = 1.732
tan (57) = 1.5399
The closest to 1.25 is tan (51)
Hope this helps :)
find the perimeter of the quadrilateral. if x = 2 the perimeter is ___ inched.
Answers
3(2^2) -5(2)+20 = 12 - 10 + 20 = 22
4(2^2) +8(2) = 16 + 16 = 32
P = 31 + 44 + 22 + 32 = 129
answer
129 inches
Answer:
Perimeter is 129 inches.
Step-by-step explanation:
We are given,
A quadrilateral with sides lengths [tex](4x^2+8x),(3x^2-5x+20),(7x+30),31[/tex] inches.
Now, the values of the side lengths when x = 2 are,
[tex](4x^2+8x)=(4\times 2^2+8\times 2)=(4\times 4+16)=16+16=32\ inch\\\\(3x^2-5x+20)=(3\times 2^2-5\times 2+20)=(3\times 4-10+20)=12+10=22\ inch\\\\(7x+30)=(7\times 2+30)=14+30=44\ inch[/tex]
Since, Perimeter of a quadrilateral = Sum of its sides.Then, Perimeter of given quadrilateral = 32 + 22 + 44 + 31 = 129 inches.
Hence, the perimeter is 129 inches.30 POINTS + BRAINLIEST! SHOW YOUR WORK FOR BRAINLIEST PLEASE!
Answers
2x + 3 + 4x + 3 = 180o
6x + 6 = 180
6x = 174
x = 174 / 6
x = 29
C = 2x + 1
C = 2*29 + 1
C = 59o
2x+3+4x+3= 180o 6x+6=180 6x=174 174/6 29
2x+1 (2)29+1 59o
Step-by-step explanation:
helppppppppppppppppppppp
Answers
1.796
Explanation:
log base 6 of 25 can be rewritten as:
log base 6 of (5^2) = 2 * log base 6 of 5
= 2 *0.8982
= 1.7965
Hope this helps :)
Im learning Polynomials and we are learning the strategy grouping, can anyone please explain how to group polynomials and maybe give an example :) greatly appreciated
Answers
Ex
5(4x+1)10(4x+1)
(5+10)(4x+1)
Example
x^2 +2x +3x +6
(x^2 +2x) +(3x +6) . . . . parentheses added to group pairs of terms
x(x +2) +3(x +2) . . . . . . common factor pulled from the terms of each group
(x +3)(x +2) . . . . . . . . . common factor removed to give factored result
what is the sum of
2(5a-4a)+6a
Answers
5a - 4a = a
Then you would multiply 2 by a, which would equal 2a.
Finally, combine all like terms (all terms with a), to get 8a. (2a + 6a = 8a)
Hope this helps!
We need to open the brackets and distribute the 2
However, we can see that both the terms within the parenthesis are like terms
5a - 4a = 1a or a
2(1a) + 6a
2a + 6a We can combine the like terms
= 8a
A tessellation is a (blank) patterns of figures?
reflecting
repeating
symmetrical,
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Find the value of z.
Answers
3. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35. To the nearest hundredth, find the search area. 2.08 mi²
2.97 mi²
1.49 mi²
1.04 mi²
Answers
Answer:
2.08 mi²
Step-by-step explanation:
Since, the area of the triangle is,
[tex]A=s_1\times s_2\times sin \theta[/tex]
Where, [tex]s_1[/tex] and [tex]s_2[/tex] are adjacent sides and [tex]\theta[/tex] is the included angle of these sides,
Here, [tex]s_1[/tex] = 2.75 miles,
[tex]s_2[/tex] = 1.32 miles,
And, [tex]\theta[/tex] = 35°,
hence, the area of the given triangle is,
[tex]A=2.75\times 1.32\times sin 35^{\circ}[/tex]
[tex]= 3.63\times 0.57357643635[/tex]
[tex]= 2.08208246395\approx 2.08\text{ square miles}[/tex]
What are the values of a and b in the equation (4x^a)^b = 256/x^8
Answers
(4x^-2)^4
= 4^4 x^-8
= 4^4 / x^8
= 256/x^8
Answer:
The value of a is -2 and the value of b is 4.
Step-by-step explanation:
Given expression is,
[tex](4x^a)^b = \frac{256}{x^8}[/tex]
Using [tex](ab)^m=a^m.b^n[/tex] on left side,
[tex]4^b(x)^{ab}=\frac{4^4}{x^8}[/tex] ( [tex]4^4 = 256[/tex] )
Using [tex]a^m=\frac{1}{a^{-m}}[/tex],
[tex]4^b(x)^{ab}=4^4 (x)^{-8}[/tex]
By comparing both sides,
We get,
b = 4 and ab = -8
⇒ a = -2
Hence, the value of a is -2 and the value of b is 4.
If the intquantity and decprice variables contain the numbers 3 and 15.75, respectively, the condition if intquantity > 0 andalso intquantity < 10 orelse decprice > 20 will evaluate to
Answers
expression evaluates to
(3>0 and 15.75<10 or 15.75>20)
which, using priority of operations, "and" has a higher precedence than "or",
=>
( (3>0 and 15.75<10) or 15.75>20)
=>
( false or false )
=>
false
Find the lengths of x and y.
Answers
we know that
in the triangle ABD
applying the Pythagorean theorem
y²=3³+4²---------> y²=25------------> y=5 units
tan alfa=4/3-----------> equation 1
in the triangle BDC
tan alfa=DC/BD----------> tan alfa=(x-3)/4------------> equation 2
matching equations 1 and 2
4/3=(x-3)/4---------> 4*4=3*(x-3)--------> 16=3x-9---------> 3x=25----> x=25/3 units
the answer is
x=25/3 units
y=5 units
Maria plans to fill pots in her garden with soil and plant food. Maria has 8 1/2 quarts of soil as 1 1/2 quarts of plant food. Each pot requires 3/4 quart of soil. For how many pots does Maria have enough soil?
Answers
- Maria has 8 1/2 quarts of soil.
- Each pot requires 3/4 quart of soil.
2. Keeping this on mind, you can convert the mixed number 8 1/2 and the fracion 3/4 to decimals, as below:
8 1/2=8.5 quarts
3/4=0.75 quarts
3. Therefore, you have:
1 pot-----0.75 quarts
x-----8.5 quarts
x=(8.5x1)/0.75
x=11 pots
For how many pots does Maria have enough soil?
The answer is: 11 pots
please help.
solve the inequality |6 - v| < 9
write the inequality as two inequalities with the absolute value and give a solution set.
Answers
-15 < -v < 3 . . . . . subtract 6
-3 < v < 15 . . . . . . multiply by -1
2. Which is equal to log6?
log26
log62
log610
log106,
Answers
The mean of 10,12,16,20,p,26 is 17.Find the value of p.
Answers
17 * 6 = 102
10 + 12 + 16 + 20 + 26 = 84
p = 102-84 = 18
p = 18
__________________________________________________
Explanation:
__________________________________________________
The [arithmetic] mean =
{the sum of all the values in the data set}
divided by {the number of values in the number set} ;
__________________________________________________
→ 17 = (10 + 12 + 16 + 20 + 26 + p) / 6 ;
__________________________________________________
→ (10 + 12 + 16 + 20 + 26 + p) = 17 * 6 ;
→ (p + 84) = 102
Subtract "84" from each side of the equation;
to isolate "p" on one side of the equation; & to solve for "p" ;
→ p + 84 – 84 = 102 – 84 ;
→ p = 18 .
_________________________________________________
The answer is: " p = 18 " .
_________________________________________________
Farmer Fran has some cows and some hens. Between them, they have 52 legs and 38 eyes. How many hens does Farmer Fran have? How many cows does Farmer Fran have?
Answers
Number of hens: h=?
Total number of legs: 4c+2h=52 (1)
Total number of eyes: 2c+2h=38 (2)
Subtracting equations (1) and (2)
4c+2h-(2c+2h)=52-38
4c+2h-2c-2h=14
2c=14
2c/2=14/2
c=7
Replacing c=7 in equation (2)
2(7)+2h=38
14+2h=38
14+2h-14=38-14
2h=24
2h/2=24/2
h=12
Answers:
Farmer Fran has 12 hens
Farmer Fran has 7 cows
1. _____ is exchanging one good for another without using money.
Credit
Barter
Negotiating
Brokering
2. A _____ has to be paid in full on the due date. (1 point)
Charge card
Credit card
Debit card
Check card
3. The _____ is the original amount owed on a loan. (1 point)
Loan due
Interest
Available balance
Principal
4. APR is used to calculate the _____. (1 point)
Loan amount
Interest accrued
Principal
Future earnings,
Answers
The answers are:
1. Barter
2. charge card
3. principal
4. interest accured
You buy 3 grapefruits for $1.50, a pound of apples for $.79, some grapes for $2.50, and some bananas for $1.21. Find the total cost of the fruit.
Answers
Happy studying!
El lote de la familia lópez tiene un lote de 16m*10m y se desea construir una casa de base rectangular en el centro de el.¿que dimensiones debe tener el rectángulo del piso de la casa si tiene un área de 91m2?
Answers
If the house is to be centered, we will take the same amount from the width as we do from the length of the lot for the dimensions. This gives us (10-x) and (16-x) as the dimensions.
The area of a rectangle is found by multiplying the length and width:
(10-x)(16-x) = 91
Multiplying the binomials we have:
10*16 - x*10 - x*16 -x*(-x) = 91
160 - 10x - 16x --x² = 91
160-10x-16x+x² =91
Combine like terms:
160-26x+x²=91
Rewrite this in standard form:
x²-26x+160=91
Subtract 91 from both sides:
x²-26x+160-91 = 91-91
x²-26x+69 = 0
Factoring this, we look for factors of 69 that sum to -26. -23*-3 = 69 and -23+-3 = -26, so:
(x-23)(x-3) = 0
Using the zero product property we know that either x-23=0 or x-3=0, so x=23 or x=3.
x was the amount we take off of the width and length of the lot; if we took 23m off of it, 10-23 gives us a negative amount, which is not realistic. This means both the width and length are subtracted by 3.
10-3 = 7 and 16-3 = 13.
These are the dimensions of the house.
△ABC is similar to △RST . In addition, m∠C=76° and m∠S=3(m∠A) . What is m∠A ? Enter your answer in the box.
Answers
Answer:
∠A = 26°
Explanation:
If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. In case of similar triangle, corresponding angles are congruent.
Angle ∠C = 76
So, ∠T = 76 because of corresponding angle.
Given that,
m∠S=3(m∠A)
We know that,
∠S ≅ ∠B
That means ∠B = 3 (∠A)
Sum of angles in a triangle = 180°
∠A + ∠B + ∠C = 180°
∠A + 3∠A + 76° = 180°
4∠A = 180° - 76°
4∠A = 104°
∠A = [tex] \frac{104}{4} [/tex]
∠A = 26°
Final answer.
Joes is 10 years older than james. in 8 years joe will be three times older than james. how old are they now
Answers
Find the equation for the line that passes through the point (−1,2), and that is parallel to the line with the equation 3/2x−2y=2.
Answers
.. (3/2)(x +1) -2(y -2) = 0 . . . . . the given line translated to the point (-1, 2)
.. 3(x +1) -4(y -2) = 0 . . . . . . . . multiply by 2
.. 3x +3 -4y +8 = 0 . . . . . . . . . eliminate parentheses
.. 3x -4y = -11 . . . . . . . . . . . . . . put in standard form (not necessary, but prettier)
a building in san francisco is shaped like a square pyramid it has a slant height og 856.1 feet and each side of its base is 145 feel long find the lateral area of the building
Answers
for a Square Pyramid
[lateral area]=4*[a*s/2]--------> 2aS
where
a is the length side of the square base
S is the slant height
a=145 ft
S=856.1 ft
[lateral area]=2*145*856.1---------> 248269 ft²
the answer is 248269 ft²
What is the term for a Wage and Tax statement and what is it’s purpose?
Answers
Sara is 8 years old and her mom is 34 years old. In how many years will Sara be twice as young as her mom will be?
If x is the number of years, then the equation is ______
The answer is _____
Answers
Mom = 34 years old
Let the number of years be x when Sara will be twice as young as her mom will be.
2(8 + x) = 34 + x
16 + 2x = 34 + x
2x - x = 34 - 16
x = 18
Answer:
If x is the number of years, then the equation is 2(8 + x) = 34 + x
The answer is 18
Which statements correctly use the properties of exponents to simplify? Check all that apply.
(xy2)2 = x2y4
x3x3 = x6
3y–2 =
2(x2)3 = 8x6
–x2(–x3) = –x6
Answers
Answer:
1 2 and 3
Step-by-step explanation:
How many solutions does the system have?
{y = −2x + 2
y = x^2 − 3x
Enter your answer in the box.
________
Answers
Answer:
The system has two solution
Step-by-step explanation:
we have
[tex]y=-2x+2[/tex] ----> equation A
[tex]y=x^{2}-3x[/tex] ----> equation B
Solve the system of equations by graphing
Remember that
The solution of the system of equations is the intersection point both graphs
There are two point of intersection between the two graphs
see the attached figure
therefore
The system has two solution
ASAP Plz what is the value of x? Plz no joking around this is from quiz 4.09: Special Right Triangles 2
Answers
Firstly, let's find RT so that we can solve the top triangle.
We could actually use 3 methods to find this side: 1) trig to find RT
2) trig to find ST, then Pythagorean Theorem to determine RT
3) use the special 30-60-90 right triangle rule ... hmm, I'm going with the last because it's easiest ;)
For 30-60-90 triangles, the sides are always as follows: smallest side (opposite the 30) is s, the middle side is sSR3, and the hypotenuse is 2×s
Thus, since we have the side opposite 60, it is = sSR3, so:
[tex]s \sqrt{3} = 2 \sqrt{3} \\ s \sqrt{3} \div \sqrt{3} = 2 \sqrt{3} \div \sqrt{3} \\ s = 2[/tex]
So now, the hypotenuse (RT) = 2s = 2(2) = 4
Secondly, we are looking at the other type of special right triangle, the 45-45-90:
The side opposite the 45s are s (remember side lengths are equal whose opposite angles are equal); and the hypotenuse is always
[tex]s \sqrt{2} [/tex]
we only need QR, which is s, which is also = RT
So the answer is:
QR = x = 4
x = 4 IS THE FINAL ANSWER!!!
[ i hope by my explanations you understand how better to do special right triangles in the future] :-D
Answer: The correct answer is 4
Step-by-step explanation:
Here is proof from the quiz