Select all true statements.

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Work Shown:

Let x = 5i-3

That allows us to go from (5i-3)(2i+1) to x(2i+1)

Distribute the x through: x*(2i) + x*(1) = 2i*x + x = 2i(x) + 1(x)

Now we replace every x in 2i(x) + 1(x) with 5i-3, and then we distribute a second time

2i(x) + 1(x) = 2i(5i-3) + 1(5i-3)

2i(x) + 1(x) = 2i(5i)+2i(-3) + 1(5i)+1(-3)

2i(x) + 1(x) = 10i^2 - 6i + 5i - 3

2i(x) + 1(x) = 10(-1) - i - 3

2i(x) + 1(x) = -10 - i - 3

2i(x) + 1(x) = -13 - i

Therefore, (5i-3)(2i+1) = -13 - i

The result is in a+bi form where a = -13 and b = -1.

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An alternative method is to use the box method. This is where you set up a grid that helps you multiply out (5i-3)(2i+1)

See the diagram below.

Each of the 4 red terms in the boxes represents the result of multiplying the outer blue and green terms. Example: 5i times 2i = 10i^2 in row1, column1.

Answer:

Please check the attached figure a for a complete visual.

Step-by-step explanation:

Considering the triangle ΔABC with vertices

When a figure is multiplied by a scale factor greater than 1, the figure is enlarged.

As the center of enlargement is (4, 4).

So, Draw a straight line from vertex A to the point (4, 4). Count how many units it needed in two dimensions to reach the center of enlargement (4, 4).

In case of vertex A, it was 6 units right and 4 units up. So, multiply them with 1.5 and locate the resulting position as A' which is the image of A after the scale factor of 1.5 using the center of enlargement as (4, 4).

So, when we multiply '6 units right' with 1.5, it becomes 9 units. So, move 9 units right from the center of enlargement (4, 4).

Similarly, when we multiply '4 units up' with 1.5, it becomes 6 units. So, move 6 units up from the center of enlargement (4, 4).

So, new the position of A' is shown in figure a.

Similarly, the vertex B and C are enlarged and the positions of B' and C' are shown in figure a.

The complete enlargement of triangle ΔABC is done as ΔA'B'C'. Please check the attached figure a for a complete visual.

Keywords: enlargement, scale factor, transformation

Learn more about transformation from brainly.com/question/9930004

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Answer:

40ft^2

Step-by-step explanation:

multiply :

2(2*3)

2(2*2.8)        

2(3*2.8)

Each value in the parenthesis are the areas of 3 different sides. You then multiply by two because there is another side opposite to the side that is the same.

then add all of those up

you get 40

Eric is wrong because even square numbers do not always have more factors than odd square numbers for example square of 785.

Given :

Even square numbers always have more factors than odd square numbers.

The following steps can be used in order to show that Eric is wrong:

Step 1 - According to the given data, even square numbers always have more factors than odd square numbers.

Step 2 - So, to prove this statement wrong there are some examples given in the below steps.

Step 3 - The square of 61 gives 3721 whose total number of factors are 4 similar number of factors as 4.

Step 4 - The square of 785 gives 616225 whose total number of factors are more than 16.

For more information, refer to the link given below:

https://brainly.com/question/18832008

Answer:

Step-by-step explanation:

emily : 16 + 22x....with x being the number of days

Lily : 24 + 18x

16 + 22x = 24 + 18x

22x - 18x = 24 - 16

4x = 8

x = 8/4

x = 2 <==== they will be on the same page in 2 days

16 + 22x = 16 + 22(2) = 16 + 44 = 60

24 + 18x = 24 + 18(2) = 24 + 36 = 60

and they will both be on page 60 <===

They are both in page 60

Let the number of days that they used in reading till they are on the same page be represented by x.

Since Emily has already read 16 pages. Emily reads 22 pages per day until the book is finished. This can be represented as:

Emily = 16 + (22 × x) = 16 + 22x

Lily has already read 24 pages and she reads 18 pages per day until the book is finished. This can be represented as:

Lily = 24 + (18 × x) = 24 + 18x

Then, we will equate the two equations and this will be:

16 + 22x = 24 + 18x

Collect like terms

22x - 18x = 24 - 16

4x = 8

Divide both side by 4

4x/4 = 8/4

x = 2

Therefore, the number of days will be in 2 days time.

Then the page number will be gotten by choosing any of the equations and this will be:

= 16 + 22x

= 16 + 22(2)

= 16 + 44.

= 60

Also, 24 + 18x will be:

= 24 + 18(2)

= 24 + 36

= 60

They are both in page 60

You can read related question on:

https://brainly.com/question/17210525

Answer:

The total surface are is 252 sq. units.

Step-by-step explanation:

The right triangular sides have legs 8 units and 6 units and hypotenuse 10 units.

So, their area will be [tex]2(\frac{1}{2} \times 8 \times 6) = 48[/tex] sq. units.

Now, the length of the prism is 8.5 units.

So, the area along the length will be = (8.5 × 6 + 8.5 × 8 + 8.5 × 10) = 204 sq. units.

Therefore, the total surface area is (48 + 204) = 252 sq. units. (Answer)

Answer:

78

Step-by-step explanation:

hope this helps fucas

The equations that can be graphed are;

y₁=log(2x+1)  and y₂=3x-2

Step-by-step explanation:

The equation given  is: log (2 x + 1) = 3x-2

The solution to this equation can be found by graphing the separate equations;

(i)y₁= log(2x+1)

(ii)y₂=3x-2

From the graph, the solution is : x= -0.4998 or x= 0.8056

Learn More

Solving logarithmic functions by graphs:https://brainly.com/question/11096185

Keywords: equations,graphed,solve

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Answer:

The short answer is B.

Answer:

28+4v

Step-by-step explanation:

multiply each term in parenthesis by 4.

multiply the numbers 4×7+4v

= the solution 28+4v

Answer:

V = -7 or 28 + 4V

Step-by-step explanation:

distribute the 4 to the 7 and V ---> 28 + 4v = 0

subtract 28 from both sides ---> 4V = -28

divide 4 by both sides --> V = -7

Answer:

11x+3

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

The eqn. of a circle with centre (h,k)and radius ris given by,

Answer:

y is going back by 3's x is going back one

Step-by-step explanation:

The number of sections made is [tex]\frac{3}{4}[/tex]

Solution:

Given that, Sarah paints a straight line

The line is [tex]13\frac{1}{2}[/tex] feet

She wants to divide the line into sections that are each 18 ft long

To find: Number of sections

From given,

[tex]\text{Length of line } = 13\frac{1}{2} = 13.5 \text{ feet }[/tex]

[tex]\text{Length of 1 section } = 18 \text{ feet }[/tex]

Number of sections can be found by dividing the total length of line by length of 1 section

[tex]\text{Number of sections } = \frac{\text{Total length of line}}{\text{length of 1 section}}[/tex]

Substituting the values, we get,

[tex]\text{Number of sections } = \frac{13.5}{18} = 0.75 = \frac{3}{4}[/tex]

Thus number of sections made is [tex]\frac{3}{4}[/tex]

Answer:

15x + 9y= 36

Step-by-step explanation:

To find such an equation, it would simply have to be a multiple of the given equation. So, multiply the whole equation by any integer (to make life easy):

[tex]3(5x+3y)=3(12)[/tex]

[tex]15x+9y=36[/tex]

Answer:

Center

Minor segment.

Step-by-step explanation:

See the attached diagram of the circle.

Here, two blanks are there and we have to fill up with the correct circle vocabulary.

The blank with an arrow can be filled up by the Center of the circle about which the circle is drawn.

And the other blank should be the Minor segment of the circle.  

A chord divides the circle into two areas, major and minor segments. (Answer)

Answer:

The integers are 13, 14, and 15.

Step-by-step explanation:

Let the smallest one be x.

Then, the other two integers are x + 1 and x + 2.

x + x + 1 + x + 2 = 42

3x + 3 = 42

3x = 39

x = 13

x + 1 = 14

x + 2 = 15

The integers are 13, 14, and 15.

Answer:

B: Reflection

That's the answer.

Final answer:

A circle graph is the optimal choice for the doctor to represent the patient age percentages.

Explanation:

The best graph for the doctor to represent the percentages of her patients across different age groups is a circle graph. Circle graphs, also known as pie charts, are specifically designed to showcase proportions or percentages of a whole, making them ideal in this scenario.

Answer:

  y = 8x -25

Step-by-step explanation:

The two-point form of the equation of a line can be used.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (7-(-1))/(4-3)(x -3) +(-1)

  y = 8(x -3) -1

  y = 8x -25 . . . . slope-intercept form of the equation

_____

We don't know what you're starting with, so we don't know how to "complete the equation." Perhaps the above equation is sufficient for the task.

Answer:

1.2

sorry if its not the right problem

Step-by-step explanation:

To express the difference in means as a multiple of the larger MAD, divide the difference by the larger MAD.

To express the difference in means as a multiple of the larger MAD, we first need to determine which MAD is larger. The MAD for the fall data is 2.8 cookies, and the MAD for the spring data is 2.6 cookies. Since the MAD for fall is larger, we will use it as the denominator in our calculation.

The difference in means is 24 - 23 = 1 cookie.

To express this difference as a multiple of the larger MAD, we divide the difference by the larger MAD:

1 / 2.8 = 0.3571

Therefore, the difference in means is approximately 0.3571 times the larger MAD.

Answer:

The mode is 6.

Step-by-step explanation:

6 is the answer because it is the only number Twice.

Hope this helps!

We are UNIQUE!!!

Answer:

  w = V/(ℓh)

Step-by-step explanation:

Divide the given equation by the coefficient of w:

  V/(ℓh) = ℓwh/(ℓh)

  w = V/(ℓh)

Answer:

The metalworker should use 60 kg of metal alloy that is 70% copper and 40 kg of metal alloy that is 20% copper.

Step-by-step explanation:

System of Equations

Let's call  

x=amount of metal alloy that is 20% copper

y=amount of metal alloy that is 70% copper

The metalworker wants to create 100 Kg of 50% copper alloy. This gives us the first relation

x+y=100

The combination of 20% of x and 70% of y will produce 50% of the sum of both, thus

20x+70y=50(x+y)

Operating

20x+70y=50x+50y

Reducing and dividing by 10

2y=3x

The system of equations is easily solved by isolating x in the first equation

x=100-y

And replacing into the last equation

2y=3(100-y)

Operating

2y=300-3y

5y=300

y=60

Thus

x=100-60=40

The metalworker should use 60 kg of metal alloy that is 70% copper and 40 kg of metal alloy that is 20% copper.

The radius of ferris wheel is 124 feet

Solution:

Given that, Sabrina rode on a ferris wheel at the state fair

In one rotation she traveled 778.72 ft

To find: Radius of ferris wheel

The distance traveled in one rotation is equal to circumference of circle

Thus circumference of circle is equal to 778.72 feet

The circumference of circle is given as:

[tex]C = 2 \pi r[/tex]

Where, "r" is the radius and [tex]\pi[/tex] is a constant equal to 3.14

Substituting, C = 778.72

[tex]778.72 = 2 \times 3.14 \times r\\\\778.72 = 6.28r\\\\r = \frac{778.72}{6.28}\\\\r = 124[/tex]

Thus radius of ferris wheel is 124 feet

Answer:D:$218,000

Step-by-step explanation:he owns 1300 monthly on the 30 year mortgage

So for a year he owes

1300*12= 15600 a year

Which will multiply by 30 years

15600*30= $468000 will be all he need to paid to cover is mortgage

To know the interest the needs to pay

Subtract the total amount from the real amount of the house

$468000-$250000= $218,000

Final answer:

Dave will have paid $218,000 in interest on his $250,000 home after making $1300 monthly payments for 30 years. The interest paid is determined by subtracting the original loan amount from the total amount paid over the mortgage term.So,option  D. $218,000 is correct.

Explanation:

The question asks, once Dave has paid off his mortgage, how much will he have paid in interest for a $250,000 home with a 30-year mortgage at $1300 a month. To solve this, first, we calculate the total amount paid over the 30 years, then subtract the principal to find the interest paid.

First, multiply the monthly mortgage payment by the number of months in 30 years: $1300 × (30 × 12) = $468,000.

Next, subtract the original home value (or the principal of the loan) from the total amount paid: $468,000 - $250,000 = $218,000.

Therefore, over the course of 30 years, Dave will have paid $218,000 in interest on his mortgage.

Answer:

[tex]4[/tex] ounces of nuts are there per cake.

Step-by-step explanation:

Given Isaac used [tex]\frac{1}{4}[/tex] of an ounce of nuts to make [tex]\frac{1}{16}[/tex] of a pound cake.

We need to find ounces of nuts per cake.

We can see that  [tex]\frac{1}{16}[/tex] pound of the cake made by [tex]\frac{1}{4}[/tex] ounce of nuts.

We will multiply both side by [tex]16[/tex].

So, [tex]\frac{16\times 1}{16}=1[/tex] pound of cake will be made by [tex]\frac{1}{4}\times 16=4[/tex] ounces of nuts.

So, there are [tex]4[/tex] ounces of nuts there per cake.

Answer:

The answer is 1w+7

Step-by-step explanation:

you first combine 8w and -7w to get 1w then you combine 9 and -2 to get 7

Answer:

2x2+4xy+2y+x+y−6

Step-by-step explanation:

Hope this helps!

Please Mark Brainliest!

Final answer:

The question is best addressed by describing the behavior and characteristics of lions as carnivorous animals and the species they typically prey upon in the wild. Highlighting the lion's status as an apex predator and protected species emphasizes the importance of conservation.

Explanation:

The question posed seems to be about the dietary habits of lions, which are large carnivorous mammals known for their hunting prowess. Discussing the consumption of lion meat by humans is ethically controversial and in many regions illegal, as lions are a protected species. Instead, we can focus on the nature of lions as carnivores and their role in the ecosystem as apex predators. Lions primarily hunt and feed on a variety of herbivorous wildlife, including zebras, giraffes, pigs, antelope, and wildebeests. Hunting is a critical skill for lions, utilizing their keen sense of smell and powerful physique. The appearance of lions, including their distinctive mane, is not just for show but also serves to intimidate rivals and prey.

Lions are indeed among the largest of the big cat species and hold a historical significance across various cultures. Due to their size and nature, lions may pose a threat to humans if disturbed or threatened. It is important to remember that they are a protected species vital to the ecosystem and should be respected in their natural habitats.

Serving lion meat is illegal in many places and ethically controversial. It's important to respect wildlife conservation and choose sustainable, legal options.

Serving lion meat is fraught with ethical, legal, and conservation concerns. Lions are apex predators and vital to their ecosystems; their populations are already under significant threat due to habitat loss, human-wildlife conflict, and poaching. Consuming lion meat can exacerbate these issues by promoting illegal wildlife trade and threatening already vulnerable populations.

From a legal standpoint, many countries have strict regulations against hunting and consuming lions due to their endangered or protected status. Additionally, there are ethical considerations surrounding the killing of such majestic animals for human consumption. Lions are often viewed with awe and respect, and the idea of slaughtering them for food can be deeply unsettling for many people.

In summary, the best way to serve lion meat is not to serve it at all. Instead, it's crucial to prioritize wildlife conservation efforts and support sustainable, legal alternatives that do not harm endangered species or their habitats.