What is the following difference?

Answer:

A. 22.5° AND D. 22°30’

Step-by-step explanation:

First of all, it's the correct answer on ap*x

To convert π/8 to degrees, replace π with 180°.

π/8 = 180°/8 = 22.5° (A)

Convert 22.5° to degrees minutes seconds

22.5° = 22°30’ (D)

To convert an angle from radians to degrees, multiply by 180/π. The angle measuring π/8 radians is equal to 22.5°.

To convert an angle from radians to degrees, we use the conversion factor 180/π. So, an angle of π/8 radians is equal to:

Therefore, the angle measuring π/8 radians is equal to 22.5°.

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Step-by-step answer:

Step 1:

find out the amount and direction of the vertical translation.

+3 means translating 3 units up, and -6 means translating 6 units down.

Step 2:

to each of the coordinate pairs, add the value of the translation to the y-coordinate (i.e. the second number of the pair).

For example, if the translation is +3, and if one of the vertices is (4,1), then the image of the vertex is (4,1+3) = (4,4).

Repeat for the rest of the vertices.

Step 3:

Check by graphing both image and preimage to see if the shapes are identical.  If not, look for a mistake in the translation process.

To translate a figure vertically, add the translation value to the y-coordinates of each vertex. For a translation of 'k' units, the new vertices will be (x, y + k). This keeps the shape the same and only changes its position vertically.

To find the coordinates of the image vertices when a figure is translated vertically,

you need to follow these simple steps:

This method ensures that the shape of the figure remains unchanged and it is only shifted up or down vertically.

Answer:

124

Step-by-step explanation:

Answer:

124

Step-by-step explanation:

32 goes into 39 one time, 39-32= 7

bring down the 6

32 goes into 76 two times, 76 - 64= 12

bring down the 8

32 goes into 128 four times, 128 - 128 = 0

So 3968/32 = 124

Answer:

Option D [tex]x^{2} -x-6=0[/tex]

Step-by-step explanation:

Verify each quadratic equation

case A) we have

[tex]x^{2} +x+6=0[/tex]

This quadratic equation has a leading coefficient of 1

Substitute the value of x=3 and x=-2 in the equation

For x=3

[tex](3)^{2} +(3)+6=0[/tex]

[tex]18=0[/tex] ----> is not true

therefore

x=3 is not a solution of the quadratic equation

case B) we have

[tex]x^{2} -x-5=0[/tex]

This quadratic equation has a leading coefficient of 1

Substitute the value of x=3 and x=-2 in the equation

For x=3

[tex](3)^{2} -(3)-5=0[/tex]

[tex]1=0[/tex] ----> is not true

therefore

x=3 is not a solution of the quadratic equation

case C) we have

[tex]x^{2} +x+5=0[/tex]

This quadratic equation has a leading coefficient of 1

Substitute the value of x=3 and x=-2 in the equation

For x=3

[tex](3)^{2} +(3)+5=0[/tex]

[tex]17=0[/tex] ----> is not true

therefore

x=3 is not a solution of the quadratic equation

case D) we have

[tex]x^{2} -x-6=0[/tex]

This quadratic equation has a leading coefficient of 1

Substitute the value of x=3 and x=-2 in the equation

For x=3

[tex](3)^{2} -(3)-6=0[/tex]

[tex]0=0[/tex] ----> is true

therefore

x=3 is a solution of the quadratic equation

For x=-2

[tex](-2)^{2} -(-2)-6=0[/tex]

[tex]4+2-6=0[/tex]

[tex]0=0[/tex] ----> is true

therefore

x=-2 is a solution of the quadratic equation

Answer: 6x + 4

6x represents 6 times the quantity x.

+ 4 represents plus 4.

Put 6x and + 4 together to get 6x + 4.

Answer:

54 is x

Step-by-step explanation:

Sounds like you describing vertical angles. Vertical angles are congruent so that means 2x+2=3x-52

2=1x-52. Subtracted 2x on both sides

54=1x. Added 52 on both sides

54=x. Since 1 times x is x

Answer:

1/6

Step-by-step explanation:

[tex]\frac{1}{3}x=\frac{1}{18}\\3(\frac{1}{3}x=\frac{1}{18} )\\[/tex]

[tex]x=3/18\\x=1/6[/tex]

Answer:

(2, 2), (3, 1), (4, 2)

Step-by-step explanation:

y ≥-1/3 x + 2

y < 2x + 3

(2, 2), (3, 1), (4, 2)

(2, 2), (3, –1), (4, 1)

(2, 2), (1, –2), (0, 2)

(2, 2), (1, 2), (2, 0)

I will assume which we determining which set of points is a solution

(2,2) is in all the sets, so we ignore it

Looking at the graph, we do not have negative solutions for y when x >0 so (3,-1) cannot be a solution and (1,-2) cannot be a solution

(2, 2), (3, 1), (4, 2)

(2, 2), (3, –1), (4, 1)   x

(2, 2), (1, –2), (0, 2)   x

(2, 2), (1, 2), (2, 0)

Again looking at the graph (2,0) is not a solution

(2, 2), (3, 1), (4, 2)

(2, 2), (3, –1), (4, 1)   x

(2, 2), (1, –2), (0, 2)   x

(2, 2), (1, 2), (2, 0)  x

Answer:

(2, 2), (3, 1), (4, 2)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The y-intercept is the number or constant at the end of the equation.

D sets both of their y-intercepts to -6, so it's correct.

=============================================

Explanation:

Plug x = 0 into f(x)

f(x) = 4x + 1

f(0) = 4(0) + 1

f(0) = 1

The y intercept of f(x) is 1

----------

Now plug x = 0 into g(x)

g(x) = 3^x - 2

g(0) = 3^0 - 2

g(0) = -1

The y intercept of g(x) is -1

----------

Note how the y intercepts are 2 units apart.

Each of the answer choices are in the form of f(x) + M and g(x) + N. The goal is to see which M and N values will be 2 units apart. In this case, that would be choice C where M = -1 and N = 1

We see that f(x) - 1 = f(0) - 1 = 1 - 1 = 0 and g(x) + 1 = g(0) + 1 = -1 + 1 = 0

Therefore, f(x) - 1 and g(x) + 1 have the same y intercept of 0.

Answer:

Step-by-step explanation:

a

Answer:

4/x14y8     -    Last Option

Answer:

50%

Step-by-step explanation:

The total number of marbles is 7 + 3 + 2 + 8 = 20

Blue or red means that the total on any one draw is 7 + 3 = 10

You would expect to draw blue or red 1/2 the time.

Out of 150 throws, you would get 1/2 * 150 which is 75 but that is not what you are asked.

% = (1/2 ) * 100  = 50% of the time

Answer:

15.79%

Step-by-step explanation:

do 95-80 which is 15

then do 15/95 as a fraction then multiply that number by 100 to get 15 15/19 then turn that into a decimal and you get 15.79%

Jillian's percent error in estimating the time it would take her to run 7 miles is 15.79%.

Jillian's percent error in her run can be calculated by taking the absolute value of the difference between her estimated time and actual time, divided by the estimated time, and then multiplied by 100 to get the percentage. Here is the calculation step-by-step:

Therefore, Jillian's percent error in her estimation is 15.79%.

Answer:

AC ≈ 10.5 cm (1 dec. place )

Step-by-step explanation:

Given

tan55° = [tex]\frac{15}{b}[/tex]

Multiply both sides by b

b × tan55° = 15 ( divide both sides by tan55° )

AC = b = [tex]\frac{15}{tan55}[/tex] ≈ 10.5 cm

Answer:

Heya mate here's the answer

let the 4th angle be x

so 75°+ 75°+75° +x= 360°

=> x= 360 - 225

=> x = 135°  

therefore the 4th angle= 135°

hope this helps

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The easiest way to determine this is to realize that time is the independent variable (n) and temperature is the dependent variable (a).

From the table, we can plug in the two points (n) into n of each equation and see if that equals the temperature values (a).

A little thinking would get us to plug the numbers in C first.

[tex]a(n)=46-(n-1)*4\\46-(5-1)*4=30[/tex]

Works!!

Now, second number:

[tex]a(n)=46-(n-1)*4\\46-(6-1)*4=26[/tex]

Works!!

Hence, C is the correct answer.

Answer:

[tex]a(n)=46-(n-1) \times 4[/tex]

Step-by-step explanation:

It's important to know that the graph is showing a linear function, which means its equation cannot be exponential. So, choices A and B are not correct here.

To find the correct equation, we could find the slope first with the following formula and the two given points

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\ m=\frac{26-30}{6-5}=4[/tex]

Now, we use the point-slope formula to find the equation

[tex]y-y_{1} =m(x-x_{1} )\\y-30=4(x-5)\\y=4x-20+30\\y=4x+10[/tex]

Notice that choice C has the same coefficient of 4, which is the slope of the line. Therefore, that's the right answer.

Let's prove it for [tex]n=6[/tex]

[tex]a(n)=46-(n-1) \times 4\\a(6)=46-(6-1) \times 4=46-20=26[/tex]

As the table shows.

Therefore, choice C is correct.

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (1, 5) and (1, -3).

Substitute:

[tex]m=\dfrav{-3-5}{1-1}=\dfrac{-8}{0}\ \bold{!}[/tex]

Dividing by zero is not possible.

The slope does not exist.

Conclusion: this is a vertical line with the equation x = a

From the points

(1, 5) → x = 1, y = 5

(1, -3) → x = 1, y = -3

we have the equation x = 1.

Answer:

a

Step-by-step explanation:

Answer:

8,000-24x

Step-by-step explanation:

there's 24 months in 2 years. If it's value decreased from 8,000 at a constant rate over a 2 year period, the equation would be 8,000-24x

Answer:

B. [tex]8,000-24x[/tex].

Step-by-step explanation:

We have been given that Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period.

Since the value of car depreciates at a constant rate each month, so the value of car depreciated in 2 years would be [tex]2\times 12=24[/tex].

There are 24 months in two years, so value of car depreciated in 2 years would be 24x.

The initial value of car is $8,000, so value of car after 2 years would be [tex]8,000-24x[/tex].

Therefore, option B is the correct choice.

Answer:

TRUE

Step-by-step explanation:

The well known trigonometry identity states that cot^2(x) + 1 = csc^2(x), rearrangin the equation we have that cot^2(x) - csc^2(x) = -1, which is exactly the expression in the statement. Therefore, the expression is TRUE.

Answer:

-316

Step-by-step explanation:

Each operation shown in bold is done on the next line.

(-5+1)(((3+6)*2-2)(5)-1) =

= (-4)((9*2-2)(5)-1)

= (-4)((18-2)(5)-1)

= (-4)(16(5)-1)

= (-4)(80-1)

= (-4)(79)

= -316

Answer:

28 i think.

Step-by-step explanation:

Answer:

The actual distance between the two cities is 28 kilometers

Step-by-step explanation:

A map has a scale of 3.5 inches = 20 kilometers

Distance between two cities on the map = 4.9 inches

We can use the unitary method in this question to get the actual distance between two cities

∵ 3.5 inches on the map = 20 kilometers

∴ 1 inch distance on the map = [tex]\frac{20}{3.5}[/tex] kilometers

∴ 4.9 inches on the map = [tex]\frac{20}{3.5}\times 4.9[/tex]

                                         = 28 kilometers

Therefore, the actual distance between the two cities is 28 kilometers.

A. and C. are fractions. this is because they are only proportions of a whole unless they are a mixed number. but in this case, these numbers do not go over 1 (a whole).

Answer: Option A and Option C

[tex]\frac{3}{7}[/tex] and [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The numbers in the form of fraction have the following form:

[tex]\frac{b}{c}[/tex]

Where b is known as numerator and c is known as denominator.

To know which of the numbers shown has a fraction form, identify all those with the form [tex]\frac{b}{c}[/tex]

Then you can see that the answer is option A and option C

[tex]\frac{3}{7}[/tex] and [tex]\frac{1}{2}[/tex]

Answer:

A 30

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

100 = 70+x

Subtract 70 from each side

100-70 = 70-70 +x

30 =x

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = (x - h)² + k (h, k) are the coordinates of the vertex

Given y = x² + 7x - 5

To express in vertex form use the method of completing the square

add/subtract ( half the coefficient of the x- term )²

y = x² + 2( [tex]\frac{7}{2}[/tex] )x +[tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] - 5

y = (x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] - [tex]\frac{20}{4}[/tex]

y = (x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{69}{4}[/tex]

Hence

a = [tex]\frac{7}{2}[/tex] and b = - [tex]\frac{69}{4}[/tex]

Answer:

[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)=\dfrac{27}{8}=3\dfrac{3}{8}}[/tex]

Step-by-step explanation:

[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)\qquad\text{the quotient of two negative numbers is positive}\\\\=2\dfrac{1}{4}\div\dfrac{2}{3}\qquad\text{convert the mixed number to the improper fraction}\\\\=\dfrac{2\cdot4+1}{4}\div\dfrac{2}{3}=\dfrac{9}{4}\div\dfrac{2}{3}\\\\\text{dividing by a fraction is the same as multiplying by its reciprocal.}\\\\=\dfrac{9}{4}\cdot\dfrac{3}{2}=\dfrac{9\cdot3}{4\cdot2}=\dfrac{27}{8}\qquad\text{convert to the mixed number}\\\\=3\dfrac{3}{8}[/tex]

So I simplify the expression and it is..

8x^3  +  14x^2  +  5x  −  15

____

I hope this helps, as always. I wish you the best of luck and have a nice day, friend..

Answer:

total cost = 150 + 25n

Step-by-step explanation:

total cost = flat fee + cost per person* number of people

total cost = 150 + 25n

Answer:

A. 10i and -10i

Step-by-step explanation:

We are given our equation as

[tex]x^2+101=1\\[/tex]

Let us subtract 101 from both hand sides

[tex]x^2+101-101=1-101\\[/tex]

[tex]x^2=-100[/tex]

Now taking square roots on both hand sides

[tex]\sqrt{x^{2}}} = \sqrt{-100}[/tex]

[tex]x=\sqrt{100} * \sqrt{-1}[/tex]

[tex]x=10 * (+i) \\x=10*(-i)\\[/tex]

[tex]x=+10i \\x=-10i\\[/tex]

Answer:

Step-by-step explanation:

a - number of lawn that Tim needs to mow

310 < 120 + 30a

190 < 30a

6.333 < a

a > 6.333

Tim needs to mow at least 7 lawns to earn more than $310

Answer: 120 different ways. It is a permutation.

Step-by-step explanation:

Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).

The number of ways to award the medals in 120 different ways.

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

Given

Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has a first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).

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