For i = √−1 , what is the sum (7 + i) + (−8 + 9i ) ? √ is the square root symbol.
A) −1 + 12i
B) −1 − 6i
C) 15 + 12i
D) 15 − 6i

Problem 1

The exterior angles sum to 360

9v+(19v-21)+45+(v+48)+7v = 360

36v+72 = 360

36v+72-72 = 360-72

36v = 288

36v/36 = 288/36

v = 8

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

Problem 2

Why is this? because TW is perpendicular to VS (the right angle marker shows this). At the same time, TW cuts VS into two equal pieces, ie VW = WS. The tickmarks indicate the segments are the same length.

Answer:

D. $340.91

Step-by-step explanation:

Answer:

3108

Step-by-step explanation:

number of 5-min segments in 1 hour

= 1 hour ÷ 5 min

= 60 min ÷ 5 min

= 12

number of 5-min segments in 7 hours

= 12 x 7

= 84

given that during each 5 min segment, jasmine decorates 37 cakes

i.e

1 (5-min) segment -----> decorates 37 cakes

84 (5-min) segments -----> decorates 37 x 84 = 3108 cakes

In this question, we're trying to find how many cakes Jasmine can decorate in 1 day.

We know that she can decorate 37 cakes everyone 5 minutes.

We also know she works 7 hours a day.

First, we need to find how much she makes it an hour.

To find this, multiply 37 by 12.

37 · 12 = 444

This means that she can decorate 444 cakes in an hour.

Now, multiply 444 by 7 to see how much she can decorate in a day.

444 · 7 = 3,108

This means that she can decorate 3,108 cakes in a day.

Answer:

3,108 cakes

Answer:

The total change in yardage of the team is by - 1 yards.

Step-by-step explanation:

Let us assume that the initial yardage of the team was x yards.

Now, the team gained 5 yards on their play of the game.

Hence, the team now has (x + 5) yards on their play of the game.

Next, the team lost 6 yards and finally, the team will have [(x + 5) - 6] = (x - 1) yards in total.

Therefore, the total change in yardage of the team is by - 1 yard. (Answer)

Answer:

The total change in yardage of the team is by - 1 yards.

Step-by-step explanation:

The total change in yardage of the team is by - 1 yards.

Answer:

150 degrees

Step-by-step explanation:

Angles FED and CEG are congruent to one another because opposite angle theorem. That makes angle CEG equal to 130. Same applies for angles DEB and AEC, making angle AEC 20 degrees.

Your variable x is a combination of these two angles, AEC + CEG. 130 + 20 = 150

Therefore x = 150 degrees.

150 degrees is the measure of the value of x from the figure.

The given diagram is a line geometry with the following parameters;

<FED = 130 degrees

<DEB = 20 degrees

Determine the measure of x

x = <FED + <DEB

Substitute the given parameters

x = 130 + 20

x = 150 degrees

Hence the measure of the value of x from the figure is 150 degrees.

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Answer:

$6900

Step-by-step explanation:

Given:

Length = 45 yards

Width = 5 yards

thickness = 1/3 yard

Volume,

= Length x Width x Thickness

= 45 x 5 x (1/3)

= 75 yards³

Costs:

1 cubic yard = $92

75 cubic yards = $92 x 75 = $6900

Surface area of cone is [tex]18 \pi[/tex] square units

Solution:

Given that cone with a slant height of 7 and a radius of 2

To find: surface area of cone

The surface area of a cone is equal to the curved surface area plus the area of the base

The surface area of cone is given by formula:

[tex]S. A=\pi r^{2}+\pi r l[/tex]

Where "r" is the radius and "l" is the slant height of cone

Substituting r = 2 and l = 7 in above formula,

[tex]\begin{array}{l}{S A=\pi\left(r^{2}+r l\right)=\pi\left(2^{2}+2(7)\right)} \\\\ {S A=\pi(4+14)=18 \pi}\end{array}[/tex]

Thus surface area of cone is [tex]18 \pi[/tex] square units

Answer:

B. [tex]\frac{1}{x^2y^7}[/tex]

Step-by-step explanation:

Given:

[tex](x^3y^{-2}z)(x^{-5}y^{-5}z^{-1})[/tex]

Hence Solving the given expression we get;

By Law of Indices which states;

[tex](a^xb^yc^z)(a^pb^qc^r) = a^{x+p}b^{y+q}c^{z+r}[/tex]

Hence we get;

[tex]x^{3+(-5)}y^{(-2)+(-5)}z^{1+(-1)}\\\\x^{3-5}y^{-2-5}z^{1-1}\\\\x^{-2}y^{-7}[/tex]

Also We know that

[tex]a^{-6} =\frac{1}{a^6}[/tex]

So,

[tex]\frac{1}{x^2y^7}[/tex]

Answer:

[tex]y=\frac{2}{3}x-\frac{16}{3}[/tex]

Step-by-step explanation:

step 1

Find the slope of the given line

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(-2,5) and (-4,8)

substitute the values in the formula

[tex]m=\frac{8-5}{-4+2}[/tex]

[tex]m=\frac{3}{-2}[/tex]

[tex]m=-\frac{3}{2}[/tex]

step 2

Find the slope of the perpendicular line to the given line

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

so

[tex]m_1*m_2=-1[/tex]

[tex]m_1=-\frac{3}{2}[/tex] ----> slope of the given line

therefore

[tex]m_2=\frac{2}{3}[/tex] ---> slope of the perpendicular line to the given line

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{2}{3}[/tex]

[tex]point\ (-1,-6)[/tex]

substitute

[tex]y+6=\frac{2}{3}(x+1)[/tex]

step 3

Convert to slope intercept form

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

isolate the variable y

[tex]y+6=\frac{2}{3}x+\frac{2}{3}[/tex]

[tex]y=\frac{2}{3}x+\frac{2}{3}-6[/tex]

[tex]y=\frac{2}{3}x-\frac{16}{3}[/tex]

The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)

Step-by-step explanation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size

Line L is mapped onto the line T by a dilation centered at the origin and  a scale factor of 3.

That means lint T is the image of line L after dilation

∵ The equation of line L is 2x - y = 7

∵ Line L is dilated by scale factor 3 and centered at origin

- That means multiply the equation of line L by 3 to find the

   equation of line t

∵ Line T is the image of line L after dilation

∴ The equation of line T is (3)(2x) - (3)(y) = (3)(7)

∴ The equation of line T is 6x - 3y = 21

Very important note:

The equation of line T is the same with equation of line L but multiplied by the scale factor 3 ⇒ L and T are coincide lines (same line)

That means the equation of lines T and L is 2x - y = 7

The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)

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The solution is Option A.

The measure of the equation A = -2xy is A = 12

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = -2xy   be equation (1)

Now , when x = -1 and y = 6

Substituting the values of x and y in the equation , we get

A = -2 ( -1 ) ( 6 )

On simplifying the equation , we get

A = 2 ( 6 )

A = 12

Therefore , the value of A is 12

Hence , the equation is A = 12

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x + (4 + x) = 20

2x + 4 = 20

2x = 16

x = 8

Proof

x + (4 + x) = 20

8 + 4 + 8 = 20

12 + 8 = 20

20 = 20

The numbers are 8 and 12.

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Answer:

For 1 is 1

For 4 is 1,2,4

Step-by-step explanation:

A fact family for 1, 4, and 4 can be created using addition and subtraction. The addition equations are 1 + 4 = 5 and 4 + 1 = 5. The subtraction equations are 4 - 1 = 3 and 4 - 3 = 1.

In mathematics, a fact family is a set of three numbers that can be used to create four different addition and subtraction equations. In this case, the numbers given are 1, 4, and 4. To create the fact family, we can use the numbers and their corresponding operations.

The addition equations would be: 1 + 4 = 5 and 4 + 1 = 5.

The subtraction equations would be: 4 - 1 = 3 and 4 - 3 = 1.

Therefore, the fact family for 1, 4, and 4 is: 1, 4, and 5 (addition) and 4, 1, and 3 (subtraction).

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Answer:

The base is 714.436.

Step-by-step explanation:

Given:

Percentage of the base = 39%

Let the base be 'x'.

39 percent of base = 278.63

We need to find the base.

We now that Percentage of the base multiplied by the base is equal to 39 percent of base.

framing in equation form we get;

[tex]39\%x= 278.63\\\\\frac{39}{100}x=278.63\\[/tex]

Now multiplying both side by 100 we get;

[tex]\frac{39}{100}\times 100 \times x=278.63\times 100\\\\39x = 27863[/tex]

Now Dividing both side by 39 we get;

[tex]\frac{39x}{39}=\frac{27863}{39}\\\\x=714.436[/tex]

Hence the base is 714.436.

Answer:

(X-10y)(x+10y)

Step-by-step explanation:

Write in exponential form , calculate the product & factor !

Answer:

Step-by-step explanation:

x² - 100y² = x² -  (10y)²

                 =(x + 10y) (x - 10y)

Hint: a² - b² = (a + b) (a - b)

Answer: 2743.2

Step-by-step explanation:

A formula to try is to multiply the length value by 30.48

Answer:

14/15  

Step-by-step explanation:

find common denomerator 15

giving you -6/15 + 20/15

add

Answer: 1

Step-by-step explanation:

It will be the smallest value for f(x).

The minimum of a sinusoidal function is the lowest point on the graph that is 1.

The minimum of a sinusoidal function is the lowest point on the graph. Looking at the image you provided, the minimum point is the lowest y-coordinate the curve reaches.

Since the graph is a sine wave, it oscillates between a maximum and a minimum value. For a standard sine function, which this graph appears to resemble, these extrema occur at points where the sine of the angle is either 1 or -1.

The minimum value of sine is -1, but the actual minimum value of the function on the graph will depend on any vertical shift and amplitude changes.

To find the exact minimum value from the graph, you'd look for the lowest point on the y-axis that the graph reaches. From the image, it's not perfectly clear, but it looks like the minimum value is around -2 on the y-axis.

This would be the case if the function has no vertical shift from the standard sine wave. If there's a vertical shift, the minimum would be the standard minimum value of sine (-1) plus the vertical shift.

Answer:

Part 3) [tex]SA=288\ cm^2[/tex]

Part 4) [tex]64\ cm^2[/tex]

Step-by-step explanation:

Part 3) Calculate the total surface area of three 4 cm cubes

we know that

The surface area of a cube is equal to the area of its six square faces

[tex]SA=6b^2[/tex]

so

The surface area of three cubes is equal to the area of its 18 square faces

[tex]SA=18b^2[/tex]

where

b is the length side of the square face

In this problem

[tex]b=4\ cm[/tex]

so

The surface area of three cubes is

[tex]SA=18b^2[/tex]

substitute the given value

[tex]SA=18(4)^2[/tex]

[tex]SA=288\ cm^2[/tex]

Part 4) How much surface area would be lost if you glued three 4-cm cubes together to make a rod that is three cubes long and one cube wide?

In this case the total surface area of the three glued 4-cm cubes is equal to the area  of  its 14 square faces

so

The surface area lost is equal to

[tex]18b^2-14b^2=4b^2[/tex]

substitute

[tex]4(4)^2=64\ cm^2[/tex]

Gluing three 4-cm cubes together to form a rod results in a loss of 64 cm²of surface area because the areas of the glued faces are no longer exposed.

Each individual cube has 6 faces, so the surface area of one cube is 6 times the area of one face. With a side length of 4 cm, the area of one face is 4 cm  imes 4 cm = 16 cm². Thus, the total surface area for one cube is 6  imes 16 cm²= 96 cm². For three separate cubes, this would be 3  imes 96 cm² = 288 cm².

When the three cubes are glued together side by side to form a rod, they share faces. Each glue contact removes two faces worth of area (one from each cube). As there are two glue contacts, a total of 4 faces are lost. Therefore, the lost surface area is 4  imes 16 cm2 = 64 cm².

The original total surface area was 288 cm², so the new surface area after gluing is 288 cm² - 64 cm² = 224 cm². Hence, gluing the cubes together results in a loss of 64 cm² of surface area.

Answer:

About the square root of 24 cubic centimeters

Answer: Its actually not. (maybe a typo)? The real bigger one is 5/8

Step-by-step explanation: So your question is "how much more is 1/8 than 5/8?" . The answer is its not. Lets do a example to help clarify. This is the butterfly method. this is by far the simplest way to compare fractions. Lets say your problem is " which is more, 5/8 or 3/4." the first thing you need to do is  line them up like so:

  5       3

  _       _

  8       4

The second thing to do is multiply the opposites.

  5       3

  _       _

  8       4

You would be multiplying 8*3 and 5*4 so like across or whatever.

put the answers on the equation like so,

20         24 <- Which ever in the top is bigger that would be 24. Which is 3/4

 5       3   ______________________________/

 _       _                                                                  

 8       4

3/4 is bigger in this problem.

Hope I helped!

:)

Answer:

3.728 cm²

90

Step-by-step explanation:

To built the envelope I am using a rectangular piece of material 28 m long and 12 m wide.  

Out of this material, I have to cut patches that are 1/12 the length and 2/15 the width of the whole material.

So, the length of the patches is [tex]28 \times \frac{1}{12} = 2.33[/tex] m and the width of the patches is [tex]12 \times \frac{2}{15} = 1.6[/tex] m.

Therefore, the area of the patches is (1.6 × 2.33) = 3.728 m² each. (Answer)

Now, the area of the rectangular piece of material is (28 × 12) = 336 m²

Hence, [tex]\frac{336}{3.728} = 90.37[/tex] ≈ 90 such patches can be made out of the whole material. (Answer)

Answer:

0.5

Step-by-step explanation:

divide 2.5 and 5 since they are equal sized bottles.

Answer:.5

Step-by-step explanation:2.5 divided by 5 = 0.5

Answer:

5 lb 11⅓ oz

Step-by-step explanation:

First, convert the weight at birth from pound and ounces to just ounces.

8 lb × 16 oz/lb + 9 oz = 137 oz

The baby doubles its weight in the first six months.  That means its weight increases by 137 oz over 6 months.  To find how much weight was gained in 4 months, write a proportion.

137 / 6 = x / 4

6x = 548

x = 91 ⅓

The baby gained 91 ⅓ oz in 4 months, or 5 lb 11⅓ oz.

Answer:

For given polynomial [tex]P(a)=a^3+2a^2-3a+5=41[/tex] and when a=3 is

[tex]P(3)=41[/tex]

Step-by-step explanation:

Given polynomial is [tex]P(x)=x^3+2x^2-3x+5[/tex]

Remainder Theorem:

To evaluate the function f(x) for a given number "a" you can divide that function by x - a and your remainder will be equal to f(a). Note that the remainder theorem only works when a function is divided by a linear polynomial, which is of the form x + number or x - number.

By using synthetic division for given polynomial [tex]P(x)=x^3+2x^2-3x+5[/tex] and factor is (x-a)    (here x-3 is a factor given)

_3|    1      2       -3         5

        0     3       15       36

      ___________________

         1      5       12      | 41

Given polynomial can be written as

[tex]P(a)=a^3+2a^2-3a+5[/tex]

To find P(a):

[tex]P(a)=a^3+2a^2-3a+5[/tex]

put a=3

[tex]P(3)=3^3+2(3)^2-3(3)+5[/tex]

[tex]P(3)=27+18-9+5[/tex]

[tex]P(3)=41[/tex]

Therefore for given polynomial [tex]P(a)=a^3+2a^2-3a+5=41[/tex] when a=3 is  [tex]P(3)=41[/tex]

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

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

Where:

m: It's the slope

b: It is the cut-off point with the y axis

By definition, if two lines are parallel then their slopes are equal.

We have the following equation of the line:

[tex]3x-2y = 8[/tex]

We manipulate algebraically:

[tex]-2y = -3x + 8\\y = \frac {3} {2} x-4[/tex]

Thus, a parallel line will have an equation of the form:

[tex]y = \frac {3} {2} x + b[/tex]

Answer:

[tex]y = \frac {3} {2} x + b[/tex]

Answer:

The total number of codes which can be assigned is, 55440 .

Step-by-step explanation:

According to the question, the home alarm system randomly assigns a five-character code for each customer.The code will not repeat a character and there are 11 distinct characters.

So, the total number of codes that can be randomly assigned is given by,

[tex]^{11}{P}_{5}[/tex]

= [tex]\frac {11!}{6!}[/tex]

= [tex]11 \times 10 \times 9 \times 8 \times 7[/tex]

= 55440

The true statement is : D. The boiling point decreases by 1.8 degrees as the altitude increases by 1000 feet. True statements are : A,D & E

Step-by-step explanation:

5.

The equation is given as : T(a)= -0.0018a +212 where T (a) is the boiling point of water measured in degrees at altitude a measured in feets.

From the equation , when the altitude is increased by 1000 feets, a=1000, the equation will be

T(1000) = -1.8 + 212, which means that the boiling point decreases by 1.8 degrees as the altitude increases by 1000 feet

6.

The values given can be taken as coordinates and plotted on a graph tool as shown in the attached figure.

Finding the slope of the graph'

m=Δy/Δx

Taking points (14,73) and (9,51.75) the slope of the linear graph will be;

Δy=73-51.75 = 21.25

Δx=14-9 =5

m= 21.25/5 = 4.25

The equation of the linear graph taking m=4.25 and point (14,73)

m=Δy/Δx

4.25 = y-73/x-14

4.25(x-14) = y-73

4.25x - 59.5 =y-73

4.25x - 59.5 + 73 =y

y=4.25x+13.5

From the graph,

The price in 2005 will be $77.25

The predicted average change in ticket price per year is $4.25

The y -intercept is the price of ticket in 1990

True statements are : A,D & E

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Answer:

$48.72

Step-by-step explanation:

5.6 liters x $8.70 per liter= $48.72 total cost

Final answer:

To determine the total cost of the olive oil, multiply the quantity of 5.6 liters by the price per liter, which is $8.70. The total cost for the restaurant owner is $48.72.

Explanation:

The question asks us to calculate the total cost for a restaurant owner who buys 5.6 liters of olive oil at a price of $8.70 per liter. To find the total cost, we multiply the quantity of olive oil by the price per liter.

Calculation: Total cost = Quantity x Price per liter

Total cost = 5.6 liters x $8.70 per liter

Total cost = $48.72

Therefore, the restaurant owner will pay $48.72 for 5.6 liters of olive oil.

Answer:

-11

Step-by-step explanation:

Given

[tex]\log_bA=3\\ \\\log_bC=2\\ \\\log_bD=5[/tex]

Use properties:

[tex]\log_b(A\cdot C)=\log_bA+\log_bC\\ \\\log_b\dfrac{A}{C}=\log_bA-\log_bC\\ \\\log_bA^k=k\log_bA[/tex]

Thus,

[tex]\log_b\dfrac{A^5\cdot C^2}{D^6}\\ \\=\log_b(A^5\cdot C^2)-\log_bD^6\\ \\=\log_bA^5+\log_bC^2-\log_bD^6\\ \\=5\log_bA+2\log_bC-6\log_bD\\ \\=5\cdot 3+2\cdot 2-6\cdot 5\\ \\=15+4-30\\ \\=-11[/tex]