The magnitude and direction of two vectors are shown in the diagram. What is the magnitude of their
sum?
A) 5 squared
B) 8
C) 20
D) 6

By applying the PEMDAS rule, the solution to the given expression is equal to 24.

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.

Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical expression:

20 + 2(3y - 4x)

20 + 2(3(6) - 4(4))

20 + 2(18 - 16)

20 + 2(2)

20 + 4 = 24

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Answer:

A. Steve

Step-by-step explanation:

Steve has to pay $50. So he has more debt than John

Answer:

Perimeter and area of drawing

Perimeter= 10 In

Area = 6.25 In²

Perimeter and area of object

Perimeter = 51.836 mm

Area = 167.936 mm²

Step-by-step explanation:

We are dealing with a square object, so let's talk about the drawing first.

The length of one side = 2.5 In

Perimeter of square= 4L

Perimeter = 4*2.5

Perimeter= 10 In

Area = L*L

Area = 2.5*2.5

Area = 6.25 In²

Letd note that 1 inch =

25.4 millimetres

So 2.5 Inch = 2.5 * 25.4

2.5 In = 63.5 mm.

25.4 mm is to 5mm

63.5 mm is to (63.5*5)/24.5

63.5mm is to 12.959 mm

So the length of actual object is 12.959mm

The perimeter = 4*12.959

Perimeter = 51.836 mm

Area = 12.959²

Area = 167.936 mm²

Answer:

The perimeter of the actual object  is 50 mm.

The area of the actual object is 156.25 mm square

Step-by-step explanation:

Given

Shape: Square

Scale: 1 in : 5 mm

Length of Scale Drawing = 2.5 in

Required:

- Perimeter of Actual Object

- Area of Actual Object

Calculating the perimeter of the actual object

Provided that the shape is a square;

The perimeter of the actual object is calculated by

Perimeter = 4 * Length

Recall that the scale is 1 in : 5 mm

This means 1 in on the scale represents 5 mm of the actual measurements of the object.

So, if 1 in ≈ 5 mm, then

2.5 in ≈ 2.5 * 5 mm

2.5 in = 12.5 mm

So, Length = 12.5mm

Now, the perimeter of the actual object can be calculated.

P = 4 * 12.5mm

P = 50mm

Hence, the perimeter of the actual measurements is 50 mm.

Calculating the area of the actual object

The area of the actual object is calculated by

Area = Length * Length

Recall that Length = 12.5 mm as calculated above

So,

Area = 12.5 * 12.5

Area = 156.25 mm square

Hence, the area of the actual object is 156.25 mm square

Answer:

1/4 or 25%

Step-by-step explanation:

So there are 1/4 of the students wearing each of the items. 1/4=25% if you are asked for it. I hope this helps.

Answer:

The 6 above 960 is incorrect.

It should be 60.

4240/16 = 265

Answer:

1/4

Step-by-step explanation:

There are 4 slot, he/she need 1 slot to win, so 1/4

Answer:

36.5 miles

Step-by-step explanation:

Answer:

write out the first three terms (ex. the first term was 8 miles for the first week)

find out the arithmetic sequence or d. (d= 1.5)

plug into explicit formula.

answer: 35

Answer:

simple just subtract and you get-74.85

Step-by-step explanation:

Answer:

x = 2

y = -1

Step-by-step explanation:

Since it gives you the value of y already, just plug that into the equation, like so:

y = 4x - 9

x - 3 = 4x - 9

Subtract the x from both sides:

x - 3 = 4x - 9

-x       - x

__________

-3 = 3x - 9

Then, add 9 to both sides:

-3 = 3x - 9

+9        + 9

________

6 = 3x

Divide both sides by 3:

2 = x

Now plug in x for y:

y = x - 3

y = 2 - 3

y = -1

Answer:

25 hours

Step-by-step explanation:

5/.2=25

Answer:

25 hours

Step-by-step explanation:

If it travels 1/5 of an inch in an hour, then it travels 1 inch every 5 hours. We want 5 inches, so 5 hours x 5 is 25 hours. :)

Answer:

4

Step-by-step explanation:

The bottom half needs to be equal due to it's symmetrical sides.

Answer:

3

Step-by-step explanation:

^^

Final answer:

The center of the given circle is at (13, 1), and the radius of the circle is 2.

Explanation:

The equation of a circle is generally given in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Looking at the given equation (x - 13)^2 + (y - 1)^2 = 4, we can see that it is already in this standard form.

To answer the questions:

The center of the circle is (13, 1), which comes from the terms within the parentheses being subtracted from x and y.

The radius of the circle is not simply 4, as one might surmise by a quick glance. Instead, the equation gives us the radius squared, r^2 = 4. Taking the square root of both sides, we find that the radius, r, is 2.

Answer:

y = 3 (x+8)^2  -7

Step-by-step explanation:

The vertex form of the equation is

y = a(x-h)^2 +k

where (h,k) is the vertex

y = a (x- -8)^2 + -7

y = a (x+8)^2  -7

Now substitute the point into the equation to determine a

-4 = a (-7+8)^2  -7

-4 = a (1^2) -7

-4 = a -7

Add 7 to each side

-4+7 = a-7+7

3 =a

y = 3 (x+8)^2  -7

Answer:

y = 3(x + 8)² - 7

Step-by-step explanation:

y = a(x - -8)² - 7

y = a(x + 8)² - 7

-4 = a(-7 + 8)² - 7

3 = a

y = 3(x + 8)² - 7

Step-by-step explanation:

f(n) = - 29 - f( n - 1 )

f(1) = - 16

Now

f(2) = - 29 - f ( 2 - 1 )

= - 29 - f ( 1)

= -29 - ( - 16)

= - 29 + 16

= - 13

Answer: A, C, E

Step-by-step explanation:

Since it was only translated and reflected, nothing changed except for its location.

Therefore, I chose answers A, C, and E.

Hope this helps! :)

If the radius was 1, the angle θ is the arc length.  Here we have an arc length of 5 and a radius of 2, so an angle

θ = 5/2 radians

Not sure if they expect a fraction or a decimal.

Answer: 2.5 radians

Answer:

Step-by-step explanation:

No; the graph for the path of a ball must be a parabola that opens downward, so if the equation is in the form y = ax2 + bx + c, a must be negative.

Answer:

Susan invested some money (M) at 6% annual interest and 800 dollars at 7%. The money earned 128 dollars interest in a year. Then we have:

M x 6/100 + 800 x 7/100 = 128

=> M*0.06 = 128 - 800*0.07 =  128 - 56 = 72

=> M = 72/0.06 = 1200 dollar

Hope this helps!

:)

Answer:

[tex]\sqrt{697}[/tex]

Step-by-step explanation:

If the base of the square pyramid has an area of 576 units, then the side length must have a length of [tex]\sqrt{576}=24[/tex]. 24/2=12, and using the pythagorean theorem you can find that the height of the pyramid is [tex]\sqrt{29^2-12^2}=\sqrt{697}[/tex]. Hope this helps!

Answer:

[tex]\sqrt{72}[/tex] = 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{72}\\\sqrt{(4)(18)}\\[/tex]

2[tex]\sqrt{(2)(9)}[/tex]

(2)(3)[tex]\sqrt{2}[/tex]

6[tex]\sqrt{2}[/tex]

Answer:

6√2

Step-by-step explanation:

hello :

√72 = √(36×2) =√36×√2 =6√2  because :√36=6

Answer:

Easy! X is going to be 58° degree's as well, because of the Vertical Angles Theorem!

Answer:

58 degrees

Step-by-step explanation:

It is symmetrical to the other side, which is 58 degrees.

Answer:

Area = 54.1 ft²

Perimeter = 25.5 ft

Step-by-step explanation:

Area:

The formula for the area of a circle is (A = πr²). The radius is r, and r is half of the diameter, or d. So, it would be:
A = (3)(4.25)²

A = (3)18.0625

A = 54.1

Perimeter:

The perimeter, of circumference, formula for a circle is (C = πd), where C is the circumference and d is the diameter.

C = (3)(8.5)

C = 25.5

Hope this helps! Sorry it is a bit late! Have a great day! :)

Answer:

Step-by-step explanation:

hello :

x2+y2+16y−30x=0  means : (x²-30x)+(y²+16y) =0

(x²-30x+15²)-15²+(y²+16y+8²) -8²=0

(x-15)²-225+(y+8)²-64=0

(x-15)²+(y+8)²=289=17²......standard form when the center is (15,- 8)

and radius 17

Final answer:

To transform x^2+y^2+16y-30x=0 into the standard form of a circle equation, we must complete the square to obtain (x-15)^2+(y+8)^2=289. The circle's center is at (15, -8) and has a radius of 17 units.

Explanation:

To rewrite the given equation of the circle x^2+y^2+16y−30x=0 into standard form, we must complete the square for both x and y terms. First, rearrange the equation to group x and y terms together: x^2−30x + y^2+16y = 0. To complete the square, take half of the coefficient of x, which is −15, square it to get 225, and add it to both sides. Similarly, take half of the coefficient of y, which is 8, square it to get 64, and add it to both sides as well.

After adding these values, the equation becomes x^2−30x+225 + y^2+16y+64 = 225+64. Now it can be written as (x−15)^2 + (y+8)^2 = 289.

The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center of the circle and r is the radius. Thus, from our equation (x−15)^2 + (y+8)^2 = 289, the center is at (15, −8) and the radius is √289 which is 17 units.

Therefore, the correct statement is: 'The equation of the circle is (x−15)^2+ (y+8)^2=289; the center is at (15, −8), and the radius is 17 units.'

Answer:

6/12=1/2

Step-by-step explanation:

6/12_1/12

Reduce 6/12 into lowest form

6/12=1/2

We get,

1/2_1/2

Both are equal,therefore

6/12=1/2

Step-by-step explanation:

6. and 1

12. 2

=1. = 1

2. 2

i simplified 6 and 12

which gave me

1 over 2

Answer:

175

Step-by-step explanation:

Since the mean is 158

(121+189+147+x)/4=158

121+189+147+x=632

x=175

Answer:

[tex]175[/tex] (thousand dollars)                                   - written in [tex]2/22/2021[/tex]

Step-by-step explanation

In order to know the answer in the question, we should need to solve for the [tex]x[/tex] (Granton). It is other way around in solving for the mean because in here the mean is given. After using this formula, [tex]\frac{121+189+147+x}{4}=158[/tex] we derived at our answer that Granton has a revenue of [tex]175[/tex] (thousand dollars).

The circle moves down

the circle moves left

the circle's radius increases

I took the test

The circle radius increases , the circle moves down and the circle moves left.

A circle is special kind of "ellipse in which eccentricity is zero and the two foci are coincident".

According to the question,

The circle x² + (y-7)² = 49. When the given circle changes (x+5)² + (y-4)² = 64

Equation of the circle = (x-a)² + (y-b)² = r²

x² + (y-7)² = 49

(x-0)² + (y-7)² = (7)²

The circle has center (0,7) and radius is 7.

Circle changes (x+5)² + (y-4)² = 64

(x+5)² + (y-4)²  = (8)²

The circle has center (5,4) and the radius 8.

Below diagram clearly shows the circle radius increases , the circle moves down and the circle moves left.

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Answer:

- ∠3 & ∠5

- ∠2 & ∠8

----------------------------------------------------------------------

Interior Angles - Angles that appear INSIDE the transversal

Transversal - The shape you see with two parallel lines intersecting it.

Alternate - Opposite of each other, on the other side as well.

The alternate interior angles are the pair of ∠2,∠8 and ∠3,∠5.

Alternate interior angles are the angles which are formed when two parallel lines cut by a transversal line.

Hence, the pair ∠2,∠8 and ∠3,∠5 are alternating interior angle.

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