What is the phase shift of y = sin(1/2 x - pi/2)?

The axis of symmetry for the parabola [tex]y = -5x^2 - 10x - 13[/tex] is the line x = -1.

To find the axis of symmetry for the parabola given by the equation [tex]y = -5x^2 - 10x - 13[/tex], we need to use the formula x = -b/(2a), where a and b are the coefficients of x² and x respectively from the standard form of a quadratic equation [tex]ax^2 + bx + c.[/tex]

In this case, a is -5 and b is -10. Plugging these values into the formula, we get:

x = -(-10)/(2*(-5))

x = 10/(-10)

x = -1

Therefore, the axis of symmetry for the parabola y = -5x² - 10x - 13 is the line x = -1.

Answer:

D' ..................> (-2,2)

C'' .................> (3,-1)

A''' ................> (4,-2)

B'' .................> (4,2)

Step-by-step explanation:

Before we begin, we should remember the rotation rules:

1- Rotation 90° clockwise:

Coordinates (x,y) become (y,-x)

2- Rotation 90° counter clockwise:

Coordinates (x,y) become (-y,x)

3- Rotation 180° clockwise:

Coordinates (x,y) become (-x,-y)

4- Rotation 270° counter clockwise:

Coordinates (x,y) become (y,-x) ...........> same as rotation 90° clockwise

Now, let's consider the given problem:

1- Coordinates of D' if polygon ABCD rotates 90° counter clockwise to create A'B'C'D'

Original coordinates of point D are (2,2)

Rotation 90° counter clockwise means that the new coordinates will be (-y,x) which is (-2,2)

2- Coordinates of C'' if polygon ABCD rotates 90° clockwise to create A''B''C''D''

Original coordinates of point C are (1,3)

Rotation 90° clockwise means that the new coordinates will be (y,x) which is (3,-1)

3- Coordinates of A''' if polygon ABCD rotates 180° clockwise to create A'''B'''C'''D'''

Original coordinates of point A are (-4,2)

Rotation 180° clockwise means that the new coordinates will be (-x,-y) which is (4,-2)

4- Coordinates of B'' if polygon ABCD rotates 270° counter clockwise to create A''B''C''D''

Original coordinates of point B are (-2,4)

Rotation 270° counter clockwise means that the new coordinates will be (y,-x) which is (4,2)

Hope this helps :)

Answer:

-6

Step-by-step explanation:

You are finding the dot product of vectors <2, 4> and <1, -2>.  Recall that the dot product is a SCALAR.  In this case  <2, 4> · <1, -2> = 2(1) + 4(-2)>, or

2 - 8, or -6.  

[tex]\bf \stackrel{\stackrel{degree}{\stackrel{2+5=7}{\downarrow }}}{-3a^2b^5}+\stackrel{\stackrel{\stackrel{degree}{1}}{\downarrow }}{2a^1}\impliedby \begin{array}{llll} \textit{highest degree of any term is 7}\\ \textit{so is a 7 degree polynomial}\\ \textit{or called a "septic"} \end{array}[/tex]

bear in mind that the degree of a polynomial comes from the highest degree of any of its terms, and the degree of a term is the sum of all exponents in the variables.

Answer:

Step-by-step explanation:

Note that the distance, along a straight line, from A:  -2 to B:  7 is 9 units.

This is found by subtracting -2 from 7, so x2 = 7 and x1 = -2.

Then x = (x2 – x1) + x1 becomes x = (7 - [-2] ) + [-2], or x = 7.  This does not make sense.  

If we ignore this x = (x2 – x1) + x1, and focus instead on finding the division point in this line segment:

4 + 3 = 7, so the longer part of this 9-unit distance will be (4/7)(9), or 36/7 units long, or 5  1/7 units long.  The shorter part will be (3/7)(9), or 27/7 units long.

To check:  determine whether the ratio 36/7 to 27/7 comes out to 4:3, as it must:

36      4*9

---- = --------- = 4/3.  YES

27       3*9

Answer:

1). a = 4

2). a + b = 7

3). x1 = -2

4). x2 = 7

Step-by-step explanation:

I just did the assignment on Edge and it's 100% correct...  Hope this helps!!

Also heart and rate if you found this answer helpful!!

Answer:

Polynomial equation is x²  - 16

Her pay if x = 12 is $128

Step-by-step explanation:

This week, Kyara worked x + 4 hours

She is paid x - 4 dollars per hour

She earned (x + 4)(x - 4) = x² - 16 dollars this week

Her pay if x - 12 is;

12² - 16 = $128

Answer:

  second difference

Step-by-step explanation:

The differences of the y-values will differ by a common amount.

Example:

  y = x^2 for x = 2, 4, 6, 8

  y-values are 4, 16, 36, 64

  differences of these are 12, 20, 28

  differences of these differences are 8 and 8, a common value.

Answer:

For reference

Step-by-step explanation:

8g fiber....12g protein

1.Crackers--->1g fiber....2g protein

2.Cookies--->1g fiber....1g protein

3.Nuts--->3g fiber....4g protein

-3 packaged of crackers

-2 packaged of cookies

-1 package of nuts

3g+2g+3g=8g fiber

6g+2g+4g=12g protein

Answer:

3 packages of crackers

, 2 packages of cookies

,  1 package of nuts  

Step-by-step explanation:

Types of packaged snacks :

Crackers

Quantity of fibre = 1 gram

Quantity of protein = 2 grams

Cookies

Quantity of fibre = 1 gram

Quantity of protein = 1 gram

Nuts

Quantity of fibre = 3 grams

Quantity of protein = 4 grams

Required quantity of fibre = 8 grams

Required quantity of protein = 12 grams

To find : Number of packages of each snack that he can eat to obtain his goal

Now 3 packages of crackers  contain 3×1=3 grams of fiber and 3×2=6 grams of proteins .

2 packages of cookies  contain 2×1=2 grams of fiber and 2×1=2 grams of proteins .

1 package of nuts  contain 3×1=3 grams of fiber and 1×4=4 grams of proteins

So, total quantity of fibres that he get from three types of packaged snacks = 3g+2g+3g = 8g fiber

Total quantity of protein that he get from three types of packaged snacks  =

6g+2g+4g = 12g proteins

Answer:

y=6sin3(x+1)

Step-by-step explanation:

Answer:

Both ladder reaches 18.1 m up the building ⇒ 3rd answer

Step-by-step explanation:

* Lets study the information to solve the problem

- There are two ladders

- The lengths of them are 22 m and 20 m

- The bottom of the longer was 4 m farther than the bottom of the

  shorter from the building

- Both of them reached the same distance up the building

* Lets solve the problem

- Let the distance between the bottom of the shorter ladder to the

 building is x

∵ The bottom of the longer ladder is farther by 4

∴ The distance between the bottom of the longer ladder and the

   building is x + 4

- Let the ladders reached the distance h up the building

* Now we have two right triangles

# Their hypotenuses are 22 and 20

# Their heights are h

# Their bases are x + 4 , x

- Lets find h in each triangle using the rule of Pythagoras

∵ (hypotenuse)² = (leg 1)² + (leg 2)²

# The longer ladder

∵ hypotenuse = 22

∵ leg 1 = x + 4

∵ leg 2 = h

∴ (22)² = (x + 4)² + h² ⇒ simplify

∴ 484 = (x + 4)² + h² ⇒ subtract (x + 4)² from both sides

∴ h² = 484 - (x + 4)² ⇒ (1)

# The shorter ladder

∵ hypotenuse = 20

∵ leg 1 = x

∵ leg 2 = h

∴ (20)² = (x )² + h² ⇒ simplify

∴ 400 = x² + h² ⇒ subtract x² from both sides

∴ h² = 400 - x² ⇒ (2)

- Equate (1) , (2) to find x

∴ 484 - (x + 4)² = 400 - x² ⇒ Add (x + 4)² and subtract 400 in both sides

∴ 84 = (x + 4)² - x² ⇒ open the bracket

∴ 84 = x² + 2(4)(x) + 4² - x² ⇒ simplify

∴ 84 = 8x + 14 ⇒ subtract 16 from both sides

∴ 68 = 8x ⇒ divide both sides by 8

∴ x = 8.5

- Substitute this value of x in (1) or (2) to find h

∵ h² = 400 - x²

∴ h² = 400 - (8.5)² = 327.75 ⇒ take √ for both sides

∴ h = 18.1

* Both ladder reaches 18.1 m up the building

Answer:

The logarithmic function modeled by the table would be

[tex]f(x)=log_{2} x[/tex]

So it would seem to be answer B.

[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi rs+\pi r^2~~ \begin{cases} r=&radius\\ s=&slant\\ &height\\ \cline{1-2} SA=&16.8\pi \\ r=&3 \end{cases}\implies 16.8\pi =\pi (3)s+\pi (3)^2 \\\\\\ 16.8\pi =3\pi s+9\pi\implies 16.8\pi -9\pi =3\pi s\implies 7.8\pi =3\pi s \\\\\\ \cfrac{7.8\pi }{3\pi }=s\implies 2.6=s[/tex]

ANSWER

(-12,8)

EXPLANATION

The equation of the parabola is given as:

[tex]y = - \frac{1}{12} {x}^{2} - 2x - 1[/tex]

We can rewrite this in the vertex form as:

[tex] {(x + 12)}^{2} = - 12(y - 11)[/tex]

This implies that

[tex]4p = 12[/tex]

p=3

The vertex of this parabola is (-12,11)

The focus is

(-12,11-3)

=(-12,8)

Answer: -12, 8

Step-by-step explanation:

Answer:

28.8π ft² ≅ 90.48 ft²

Explanation:

Use the formula area of a sector.

Answer:

≈ 28.8π ft2 ≈ 90.48 ft2

Step-by-step explanation:

It should be 40 degrees

Answer:

60 deg

Step-by-step explanation:

The measure of angle LPM is the sum of the measures of arcs LM and KN divided by 2.

m<LPM = (40 + 80)/2 = 60

Answer: m<LPM = 60 deg

The answer is d. 1/663 or about 0.0015

Answer:

(d):  0.0015

Step-by-step explanation:

Red ace:  1 chance in 52.

Red king, after that:  1 chance in 51

Joint probability:  red ace and then red king, without replacement:

 2         2

------ * ----- = 1/663, or about 0.0015 (Answer d)

52      51

(m^2 •n^3)^ -3 =m^-6 •n^ -9;

Answer is -3

The answer is -3. To make sure, you can substitute it into the equation with values for the variables, and you will get the same answer on both sides.

It is 5/3 because it going up by 5 over by 3 hope this helps.

Answer:

$22.50

Step-by-step explanation:

The cost of admission for the 5 coaches was ...

5×$27.50 = $137.50

So the cost of admission for the 12 players was ...

$407.50 -137.50 = $270.00

The cost for one player was 1/12 that amount, or ...

$270/12 = $22.50

The admission cost for each player was $22.50.

The admission cost for each player is $22.50.

To find the admission cost for each player, we need to subtract the cost of admission for the coaches from the total cost of admission for all the coaches and players. The cost for five coaches is $((5  imes 27.50) = 137.50). So, the cost for the 12 players is $(407.50 - 137.50 = 270).

Therefore, the admission cost for each player is $22.50.

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Answer:

11/2 is equal to 5.5

Take 15 and divide it by that decimal, 5.5 and I believe the answer should be 2.72.

15 is 11/2% larger than 2.72

I am 99.9% sure that is the correct answer but I could be wrong.

To represent the word problem '15 is 1 1/2% of what number?' using a proportion, we can set up the form %1 1/2/100 = 15/n. By cross multiplying and solving for 'n', we find that 15 is 1 1/2% of 1000.

To represent the word problem '15 is 1 1/2% of what number?' using a proportion, we can use the form %0/100 = is/of. Let's assign 'n' to represent the unknown number. We can set up the proportion as follows:

%1 1/2/100 = 15/n

Now, we can solve for 'n' by cross multiplying and then dividing. First, convert 1 1/2% to a decimal by dividing 1 1/2 by 100 to get 0.015. The proportion becomes:

0.015 = 15/n

To solve for 'n', we can multiply both sides of the equation by 'n':

0.015n = 15

Finally, divide both sides of the equation by 0.015 to isolate 'n':

n = 15/0.015 = 1000

Therefore, 15 is 1 1/2% of 1000.

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The complete question is here:

Create a proportion using the form %0/100 = is/of to represent the following word problem

15 is 1 (1/2)% of what number?

- =

60 100  20 78 1 (1/2)  15 42  n  30  7

Answer:

<ACD = 35 degrees

Step-by-step explanation:

An intercepted angle is an arc segment of a circle whose endpoints connect at a point on the opposite side of the circle to create an angle. In this case arc AD is the intercepted arc of <ACD.

The measure of angle is half the measure of its intercepted arc.

AD measures 70 degrees, so divide this by 2.

70/2 = 35

<ACD = 35 degrees

Answer:

combination, number of ways 10

Step-by-step explanation:

Answer:

87 million tickets are sold every year.

Step-by-step explanation:

Number of Americans attending classical music concerts:

30 million

Average number of times a spectator attends a concert in a year

2.9 times

Then the amount of tickets sold "x" for concerts of classical music in a year, will be equal to the number of people attending for the number of times they attend. So:

[tex]x= 30 * 2.9[/tex]

Where "x" is given in units of millions.

[tex]x = 87[/tex]

Answer:

The measures of the angles of the triangle are 51° , 64.5° , 64.5°

OR

The measures of the angles of the triangle are 129° , 25.5° , 25.5°

Step-by-step explanation:

* Lets explain the meaning of the inscribed triangle in a circle

- If a triangle inscribed in a circle, then the vertices of the triangle lie

 on the circumference of the circle and each vertex is an inscribed

 angle in the circle subtended by the opposite arc

- Fact in the circle the measure of the inscribed angle is 1/2 the

 measure of its subtended arc

* Now lets solve the problem

- Δ ABC is an isosceles with the base BC

∴ AB = AC

∴ m∠B = m∠C

- Δ ABC is inscribed in a circle

∴ ∠A is inscribed angle subtended by arc BC (minor or major)

# The measure of the minor arc is less than 180° and the measure of

  the major arc is greater then 180° and the sum of the two arcs

  equals the measure of the circle which is 360°

∴ ∠B subtended by arc AC

∴ ∠C subtended by arc AB

∵ The measure of the arc BC = 102°

- There is two cases in this question

(1) If the angle A subtended by the minor arc BC

(2) If the angle A subtended by the major arc BC

- Lets solve case (1)

∵ ∠A is an inscribed angle subtended by the minor arc BC

∴ m∠A = 1/2 the measure of the arc BC

∵ The measure of the arc BC is 102°

∴ m∠A = 1/2 × 102 = 51°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 51 + m∠B + m∠C = 180° ⇒ subtract 51 from both sides

∴ m∠B + m∠C = 129°

∵ m∠B = m∠C ⇒ isosceles Δ

∴ m∠B = m∠C = 129/2 = 64.5°

* The measures of the angles of the triangle are 51° , 64.5° , 64.5°

- Lets solve case (2)

∵ ∠A is an inscribed angle subtended by the major arc BC

∴ m∠A = 1/2 the measure of the arc BC

∵ The measure of the minor arc BC is 102°

∵ The measure of the circle is 360°

∴ The measure of the major arc = 360 - 102 = 258°

∴ m∠A = 1/2 × 258 = 129°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 129 + m∠B + m∠C = 180° ⇒ subtract 129 from both sides

∴ m∠B + m∠C = 51°

∵ m∠B = m∠C ⇒ isosceles Δ

∴ m∠B = m∠C = 51/2 = 25.5°

* The measures of the angles of the triangle are 129° , 25.5° , 25.5°

Answer:

x = 60°

Step-by-step explanation:

The measure of x is one- half the difference of the measures of the intercepted arcs.

The minor arc = 120°, hence

The major arc = 360° - 120° - 240°, so

x = 0.5(240 - 120) = 0.5 × 120° = 60°

The answer is:

The father's step is 80 cm

The son's step is 60 cm.

To solve the problem, we need to write equations in order to create a relation between the father's and son's steps, and the distance covered by them.

We know thay they covered 240 meters, and the father's step is 20 cm  (0.2m)greater than his son's step, so, we can write the following relation:

[tex]NumberOfSteps_{Son}=\frac{240m}{x}[/tex]

and,

[tex]NumberOfSteps_{Father}=\frac{240m}{x+0.2m}[/tex]

Now, if the know that the father made 100 fewer steps than his son, we have:

[tex]NumberOfSteps_{Son}-100=\frac{240m}{x+0.2m}[/tex]

Then, substituting the first equation into the second equation, we have:

[tex]\frac{240m}{x}-\frac{240m}{x+0.2m}=100\\\\\frac{240m(x+0.2m)-240mx}{x(x+0.2m)}=100\\\\240mx+0.2m*240m-240mx=(x)(x+0.2m)*100\\\\48m^{2}=100*(x^{2}+0.2mx)=100x^{2} +20mx\\\\48m^{2}=100x^{2}+20mx\\\\100x^{2}+20mx-48m^{2}[/tex]

We have a quadratic equation:

[tex]100x^{2}+20mx-48m^{2}=0[/tex]

Where,

[tex]a=100\\b=20\\c=-48[/tex]

So, solving it applying the quadratic formula, we have:

[tex]\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]

[tex]\frac{-20+-\sqrt{20^{2} -4*100*-48} }{2*100}=\frac{-20+-\sqrt{400+19200} }{200}\\\\\frac{-20+-\sqrt{400+19200} }{200}=\frac{-20+-\sqrt{19600} }{200}\\\\\frac{-20+-\sqrt{19600} }{200}=\frac{-20+-(140)}{200}\\\\x_{1}=\frac{-20+140}{200}=0.6\\\\x_{2}=\frac{-20-140}{200}=-0.8[/tex]

Then, since distance cannot be negative, we need to take the positive value, so, the son's step is 0.6m or 60 cm.

Now, calculating the father's step, we have:

[tex]FatherStep=SonStep+20cm\\\\FatherStep=60cm+20cm=80cm[/tex]

Hence, we have that the father's step is 80 cm.

Have a nice day!

The distance of the father and son will be 80cm and 60cm respectively.

The number of son's step will be:

= 240/x

The number or father's step will be:

= 240/x + 0.2

Solving further, we'll have 100x² - 20mx - 48m² and using quadratic formula, this will be x1 = 0.6 and x2 = -0.8.

The son's step will be:

= 0.6 × 100 = 60cm

The father's step will be:

= 60cm + 20cm = 80cm

Learn more about distance on:

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I need a more detailed question, but I think the answer is 6.

Answer:

D

Step-by-step explanation:

The roots are where the curve crosses the x-axis.  So that's x=-3 and x=4.

Answer D.

Answer:

D

Step-by-step explanation:

The roots are the points on the x- axis where the function has a value of zero. That is where the graph crosses the x- axis

The graph crosses the x- axis at x = - 3 and x = 4, hence

Roots of the quadratic function are x = -3, 4 → D

Answer:

A

Step-by-step explanation:

The geometric mean of 2 values a and b is [tex]\sqrt{ab}[/tex]

The 7 th term is the geometric mean of the 6 th and 8 th terms

Hence

[tex]a_{7}[/tex] = [tex]\sqrt{6(216)}[/tex] = 36 → A

Answer:

Eva has 24 pins

Step-by-step explanation:

D = 34 + E

E + D = 82

34 + E + E = 82

2E = 48

E = 24

D = 24 + 34

D = 58

Sure! Let's solve it step by step.

1. We know from the problem that Dulcina has 34 more pins than Eva does. This means that Dulcina's collection is Eva's collection plus 34 pins.

2. Together, Eva and Dulcina have a total of 82 pins. This means that if we add the number of pins in both collections, it should total 82.

3. If we represent the number of pins in Eva's collection as 'x', the above two steps could be represented in equation as: x + (x + 34) = 82.

4. Simplifying this equation gives us 2x + 34 = 82. To isolate the term with 'x', we subtract 34 from both sides of the equation, resulting in 2x = 48.

5. To find the value for 'x', which represents the number of pins in Eva's collection, we then divide both sides of the equation by 2, which gives us x = 24.

6. So, Eva has 24 pins in her collection.

7. Now, since Dulcina has 34 more pins than Eva, we add 34 to Eva's total to find the number of pins in Dulcina's collection. This gives us Dulcina's total as 24 + 34 = 58.

Therefore, Eva has 24 pins and Dulcina has 58 pins in their collections.