Bob ran for president of the chess club, and he received 48 votes. There were 64 members in the club. What percentage of the club members voted for Bob?

The sum of the two complex numbers will give:

(-4 + i) + (10 - 5i) = 6 - 4i

So the correct option is the third one.

Let's assume we have two complex numbers which are:

A = a + bi

B = c + di

The sum between these two complex numbers is:

A + B = (a + bi) + (c + di)

Taking i as a common factor we can rewrite:

(a + bi) + (c + di) = a + c + (b + d)i

And that is the general sum.

Here we want to solve:

(-4 + i) + (10 - 5i)

Again, if we take i as a common factor we can rewrite:

-4 + 10 + (1 - 5)*i

6 - 4i

So the correct option is the third one.

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The non-real roots of the polynomial x³ - 10x² + 29x - 30  are; x = 2 + i or 2 - i

We are given the polynomial as;

x³ - 10x² + 29x - 30

We are told that the real root of the polynomial is -6. Thus, (x + 6) is a factor of the polynomial.

Now, we can use polynomial long division to get;

x³  -  10x²  +  29x  -  30

- divisor  * x²     x³  -  6x²        

remainder      -  4x²  +  29x  -  30

- divisor  * -4x¹     -  4x²  +  24x    

remainder             5x  -  30

- divisor  * 5x⁰             5x  -  30

remainder                0

Quotient :  x² - 4x + 5  Remainder:  0

          x²    -    4x   +   5_______

(x + 6) | x³  -  10x²  +  29x  -  30

         -  x³  -  6x²

                     -4x²  +  29x  -  30

                   -  - 4x²  +  24x

                                    5x  -  30

                                 -  5x -   30

                                             0

Now, using quadratic calculator to find the roots of the quotient, we get;

x = 2 + i or 2 - i

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the area of the generic rectangle will be x²-2x-15.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

Area of rectangle is A = a*b

(x + 3)(x - 5) in a generic rectangle

The product will give the area

x²-2x-15

hence the area of the generic rectangle will be x²-2x-15.

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Answer:

It is a good idea to choose a breakfast that includes a variety of healthy and nutritious foods to fuel your body and mind.

Step-by-step explanation:

It is important to eat a healthy and balanced breakfast to start your day off on the right foot. Some good options for breakfast include whole grain toast with eggs and avocado, oatmeal with fruit and nuts, or a smoothie with yogurt and berries. It is also a good idea to include a source of protein in your breakfast, such as eggs, Greek yogurt, or nuts, to help keep you feeling full and satisfied. Ultimately, the best breakfast for you will depend on your personal preferences and dietary needs. It is a good idea to choose a breakfast that includes a variety of healthy and nutritious foods to fuel your body and mind.

Answer: Eggs

Extra: Bacon

Drink : Milk/OJ

Answer:

the A' is 2,-1

b'is 1,-1

c' is 4,-2

The expression that is equivalent to the perimeter of the rectangle in the image shown is, 6x + 8.

To find the perimeter of a rectangle, add all the four sides of the rectangle. The following formula can be used:

Perimeter (P) = 2(length + width).

In the rectangle shown below, the dimensions are:

Length of rectangle = 2x + 3

Width of rectangle = x + 1

Substitute into the perimeter each expression of the dimensions:

Perimeter = 2[(2x + 3) + (x + 1)]

Open the parentheses by applying the distributive property of equality:

Perimeter = 2(2x + 3 + x + 1)

= 2(3x + 4)

= 2(3x) +2(4)

= 6x + 8

Therefore, the expression is, 6x + 8.

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Answer:

-2

Step-by-step explanation:

Given,

g(x) = f(4)

or, 2 - 4x = 3*4 - 2

or, 2 - 4x = 10

or, 2 - 10 = 4x

or, -8 = 4x

or, x = -2

Dimensions of the Rectangle are : 16 feet by 13 feet .

A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal . A rectangle has two dimensions. we can measure its length and, perpendicular to that, its width.

Rectangle is 3 feet longer than it is wide and its area is 208 sq-feet .

Area of Rectangle = l×b  ( Where l = length , b = breadth )

Therefore , Let X be the the width of rectangle . then from given it's length is (X+3).

∴ X × (X+3) = 208

∴ [tex]x^{2}[/tex]+3X-208 = 0

(X+16)(X-13) = 0

X = -16 & X = 13

Distance can't be negative so Width = X = 13 feet.

∴ Length = X+3 = 16 feet.

Thus the Dimensions are 16 feet by 13 feet .

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Answer:

D

Step-by-step explanation:

base= y2-y1

height = x3-x1

so (1/2)×(y2-y1)×(x3-x1)

The square root of 15 is approximately 4.

To approximate the square root of 15, we can find the perfect squares that are closest to 15. The perfect squares that are closest to 15 are 9 and 16. Since 15 is closer to 16, we can say that the square root of 15 is slightly less than 4.

Another approach could be:

The square root of 15 is approximately 3.87. Rounding to the nearest integer gives us 4. To round a number, we look at the number following the place value we are rounding to. If it is greater than or equal to 5, we round up. If it is less than 5, we round down. In this case, the digit following the ones place is 8, which is greater than 5, so we round up to 4.

After solving the equation the length of AB is [tex]2\sqrt{3}[/tex]

What do you mean by trigonometry?

Trigonometry  “triangle” and  “measure”) is a branch of mathematics that studies the relationship between the side lengths and angles of triangles.

A trigonometric ratio is the ratio between the edges of a right triangle.

The sine function (sin) defined as the ratio of the opposite side of the angle to the hypotenuse.

In the given triangle ABC , use sin ratio to find AB.

tan θ = P/B

tan 30 = AB/6

[tex]\frac{1}{\sqrt{3} } =AB/6[/tex]

AB = [tex]\frac{6}{\sqrt{3} }[/tex] = [tex]\frac{6}{\sqrt{3} }\times \frac{\sqrt{3}}{\sqrt{3}}= \frac{6\sqrt{3}}{3}=2\sqrt{3}[/tex]

Therefore, length of AB is [tex]2\sqrt{3}[/tex]

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Answer:

The mistake was made when we rewrote the equation wrong after dividing 2 to both sides

Step-by-step explanation:

After we divide two on both sides the equation should have been rewriting as   [tex]2x-20=-6[/tex]     not       [tex]6x-20=-12[/tex]

(-20, 19) is a solution to the following system of inequalities: y<-x-1, g ≥ 0.5 – 7 is false.

What is  inequalities?

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different individuals, it is prone to misunderstanding in public discourse. However, certain differences are shared. In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality.

y<-x-1

Move x to the left side

y+x<-1

Move y to the right sid

x<-1-y

[tex]g \geq 0.5-7[/tex]

Subtract the numbers: 0.5-7=-6.5

[tex]g \geq-6.5[/tex]

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By evaluating a revenue equation, we will see that she earned $139 last week.

We know that Isha is a pet sitter, and she earns $5 for each cat and $12 for each dog.

So, if she pet sats for x cats and y dogs, the revenue will be:

R(x, y) = $5*x + $12*y

In this case we know that she pet sat for 11 cats and 7 dogs, then we have:

x = 11

y = 7

So we need to evaluate the above revenue function, we will get:

R(11, 7) = $5*11 + $12*7

R(11, 7) = $55 + $84

R(11, 7) = $139

Isha earned $139 last week.

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Answer: Therefore, the correct formula is {a}_{21}  = 2000 * 0.5^{20}.

Step-by-step explanation:

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant factor called the common ratio. In this case, the common ratio is 0.5, since each term is found by dividing the previous term by 2.

To find the nth term in a geometric sequence, we can use the formula:

a_n = a_1 * r^(n-1)

where a_1 is the first term in the sequence, a_n is the nth term, and r is the common ratio. In our case, the first term is 2000, the nth term is the 21st term, and the common ratio is 0.5. Therefore, the formula we need to use is:

a_21 = 2000 * 0.5^(21-1)

    = 2000 * 0.5^20

Therefore, the correct formula is {a}_{21}  = 2000 * 0.5^{20}.

Answer:

Step-by-step explanation:

1. A

2. C

3. B

Answer: 4. ?=18

5. x = 6

Step-by-step explanation:

First put the length in ratio form:

4. 54:? and 24:8 ==> 54:?=24:8

Now put the ratios in division form:

54/? = 24/8

54/? = 3  ==> simplify

? * 54/? = 3*?  ==> multiply by ? on both sides to remove denominator

54 = 3?

54/3 = 3?/3  ==> divide by 3 on each sides to solve for ?

?=18  ==> simplify

5. (6x-1):14 and 15:6

(6x-1)/14 = 15/6

14*(6x-1)/14 = 14 * 15/6  ==> multiply by 14 on both sides to isolate x

6x-1 = 210/6

6x-1 = 35 ==> simplify

6x-1+1 = 35+1 ==> add 1 on both sides to isolate x

6x = 36

6x/6 = 36/6  ==> divide by 6 on both sides to isolate x

x = 6 ==> simplify

Answer:

3(4) - 2 is 10 the value is 10

5(2) + 6 is 16 the value is 16

I hope this helps have a good day or night!

Answer:

x + x - x = x

explanation:

give us the actual formula lol

Answer:

x ≥ 72/5

8.6 ≤ x -5 4/5= 8.6 ≤ x -29/5

8.6 ≤ x -29/5= x ≥ 72/5

The equation that represents the situation in which case the percent of successful free throws is 75% during the game is; ( 8 + x ) = 0.75 ( 15 + x ).

It follows from the task content that the equation which represents the situation in which case the percent of successful free throws rises to 75% is to be determined.

As evident in the task content; Initially, Shaq made 8 out of 15 free throws he attempted.

Therefore, let the number of consecutive free throws he has to make to raise the success rate to 75% be; x.

Therefore, it follows from percent proportion that;

( 8 + x ) / ( 15 + x ) = 75 / 100

The simplified equation which represents the required situation is therefore;

( 8 + x ) = 0.75 ( 15 + x ).

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The number of volunteers recruited for the first 5 weeks is; 486 people

A geometric sequence is defined as a sequence in which the result of the division of consecutive terms is always the same, called common ratio r.

The nth term of a geometric sequence is given by:

aₙ = a₁rⁿ⁻¹

where;

a₁ is the first term

r is the common ratio

In this question, on the first week there are 6 people, and since each new people involve three more, the common ratio is 3, hence the parameters for the geometric sequence are:

a₁ = 6

r = 3

Hence the number of people after n weeks is:

aₙ = 6(3)ⁿ⁻¹

Thus, the number of volunteers recruited for the first 5 weeks is;

a₅ = 6(3)⁵⁻¹

a₅ = 6 * 3⁴

a₅ = 486

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Answer:

$0.10 (nearest cent)

10.5¢

Step-by-step explanation:

Given:

To find the approximate unit price per ounce, divide the cost of the can by the number of ounces in the can:

[tex]\implies \dfrac{0.89}{8.5}=0.104705882...[/tex]

Therefore, the approximate unit price per ounce is $0.10 (nearest cent) or 10.5¢ (nearest half cent).

The volume of this shape is 628 cm³.

What is a volume?

It is given that,

r=5

h=8

Then volume=π(5²)×8

                     =3.14×25×8

                     =628 cm³

Hence, The volume of this shape is 628 cm³.

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Answer:

Step-by-step explanation:

Let's call the four integers x, y, z, and w. We know that the mean of these four integers is 8, so:

x + y + z + w = 8 * 4 = 32

We also know that the median of these four integers is 6, which means that two of the integers are less than 6 and two are greater than 6. The mode of 6 means that one of the integers is 6.

Let's assume that x and y are the two integers that are less than 6. This means that z and w are the two integers that are greater than 6. We can then set up the following system of equations to represent this information:

x + y + z + w = 32

x + y < 12

z + w > 12

We also know that the range of these four integers is 14, which is the difference between the largest and smallest integers. Since z and w are the two largest integers, the range is equal to w - x. We can set up another equation to represent this information:

w - x = 14

We can solve this system of equations using substitution. First, we can solve the second equation for x:

x = 12 - y

We can then substitute this expression for x in the third equation to get:

w - (12 - y) = 14

w = 14 + y

Finally, we can substitute this expression for w in the first equation to get:

x + y + z + (14 + y) = 32

x + 2y + z = 18

We can then substitute the expression for x in the third equation to get:

(12 - y) + 2y + z = 18

-y + 2y + z = 18

z = 18 - y

We can then substitute this expression for z in the third equation to get:

w = 14 + y = 14 + (18 - z) = 14 + 18 - y = 32 - y

Substituting this expression for w in the first equation gives us:

x + y + z + (32 - y) = 32

x + 2y + z = 32

We can then substitute the expressions for x and z in the third equation to get:

(12 - y) + 2y + (18 - y) = 32

-y + 2y + 18 - y = 32

18 = 32

This equation is clearly not true, so the original assumptions we made about which integers were less than 6 and which were greater than 6 must be incorrect.

However, we can use a similar process to solve for the other possibility: that x and z are the two integers that are less than 6, and y and w are the two integers that are greater than 6.

In this case, we can set up the following system of equations:

x + y + z + w = 32

x + z < 12

y + w > 12

w - x = 14

Solving this system of equations using substitution gives us the solution x = 4, y = 10, z = 6, and w = 8.

Therefore, the four integers are 4, 6, 8, and 10.

Answer: $71.53

Step-by-step explanation:

77.76 = 100%

Answer: <D, < E, <C

Step-by-step explanation:

Answer:

(46+42)÷2

Step-by-step explanation:

Answer:

I assume you meant (-1/3)(6x + 15) - 3 = ?

(-1/3)(6x + 15) - 3 = (-1/3)(6x) + (-1/3)(15) - 3 = -2x - 5 - 3 = -2x - 8

Step-by-step explanation: