What is the product of these numbers?
(1 + 2i)(2 + i)


1 − 5i


1 + 5i


0 − 5i


0 + 5i

Answer:

UT

Step-by-step explanation:

The projection of ST on QT is found by locating the points on QT that are nearest the endpoints S and T of the original segment. On QT, U is the point closest to S, and T is the point closest to T. Then the projection is the segment between those identified points: UT.

Answer:

UT

Step-by-step explanation:

Answer:

B.The area of the base of the pyramid is 24cm^2.

C.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 3 times volume of this pyramid.

E.The volume of this pyramid is 72cm3.

Step-by-step explanation:

Area of base of the pyramid = l × w = 4 × 6 = 24 cm^2

Volume of rectangular pyramid = (l × w × h)/3 = (4 × 6 × 9)/3 = 72 cm^3

Volume of rectangular prism = w × h × l = 9 × 4 × 6 = 216 cm^3

So according to these calculations, the correct answer options are:

B.The area of the base of the pyramid is 24cm^2.

C.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 3 times volume of this pyramid.

E.The volume of this pyramid is 72cm3.

Final answer:

The true statements about the rectangular pyramid are B, C, and E.

The base area is 24 cm² (Statement B), the volume of the pyramid is 72 cm³ (Statement E), and the volume of a similarly dimensioned rectangular prism is three times that of the pyramid (Statement C).

Explanation:

To determine which statements are true about the rectangular pyramid with given dimensions, we need to calculate the base area and the volume of both the pyramid and the rectangular prism and compare them.

The base area of the pyramid, denoted as B, is the area of the rectangle formed by the base's dimensions.

Therefore, B = length x width = 4 cm x 6 cm = 24 cm².

Thus, statement B is true.

For the volume of the pyramid (V), we use the formula V = (1/3) x B x height.

Plugging the values, we get V = (1/3) x 24 cm² x 9 cm, which equals 72 cm³.

So, statement E is true.

The volume of a rectangular prism with the same height and base dimensions is volume of the prism = length x width x height = 4 cm x 6 cm x 9 cm = 216 cm³.

Since the volume of the prism is three times the volume of the pyramid, statement C is true.

Statements A, D, and F are not true based on the above calculations and explanations.

bart has a choice of twelve different movies at 5 different times each so you just multiply twelve and five to get 60 choices

Answer:

Step-by-step explanation:

Givens

To find the total number of choices of movies and showtime that Bart have, we just need to multiply. Because, if each movie is shown at five different times, and there are 12 movies, then the total number of choices are

[tex]12 \times 5 = 60[/tex]

Therefore, Bart has 60 choices to watch a movie.

Answer:

The answer is B. 0.04

Step-by-step explanation:

too lazy to write

There are 2 ways that you and your friend can both be chosen as contestants.

The question is on the concept of probability. There are 8 people in the front row, including you and your friend.

The host randomly chooses 3 people to be contestants.

The order in which they are chosen does not matter.

Since you and your friend are both in the front row, there are 2 cases where you both can be chosen: either you are chosen and your friend is chosen, or your friend is chosen and you are chosen.

So the total number of ways you and your friend can both be chosen is 2.

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Answer:

  (d)  $1120.70

Step-by-step explanation:

You want the total of deposited checks as shown on the deposit slip.

The total value of checks is shown on the line "Subtotal." This is amount of the deposited checks. The same deposit slip shows a withdrawal of $80 cash, so the net deposit is $80 less than that subtotal.

Vera deposited $1120.70 in checks, choice D.

The correct total amount of all checks Vera deposited is $664.30, and the deposit ticket reflects a subtotal of $1040.70, which includes both checks and cash. Therefore, option (b) $664.30 is the accurate representation of the total amount of all checks.

To determine the total amount of all checks Vera deposited, we need to add the amounts of the individual checks listed on the deposit ticket.

1. Check #184: $138.09

2. Check #308: $312.15

3. Check #298: $214.14

Adding these amounts: $138.09 + $312.15 + $214.14 = $664.38

Therefore, the correct answer is option (b) $664.30. This represents the total amount of all checks Vera deposited. The deposit ticket indicates the subtotal of checks as $1120.70, but this includes the cash amount received as well. To find the total amount of all checks, we subtract the cash amount received, which is $80.00, from the subtotal: $1120.70 - $80.00 = $1040.70.

Answer:

See below

Step-by-step explanation:

a.  here you are to multiply the two functions together:

[tex](3x-1)(2x^{2} )=6x^{3}-2x^{2}[/tex]

b.  here you are to subtract g from f:

[tex](3x-1)-(2x^{2})=-2x^{2}+3x-1[/tex]

c.  here you are to compose g into f.  In other words, pick up the whole g function and plug it into f wherever you see an x:

[tex]3(2x^{2} )-1=6x^{2} -1[/tex]

d.  here you are compose f into g.  In other words, pick up the whole f function and plug it into g wherever you see an x:

[tex]2(3x-1)^2[/tex]

You now have to FOIL out the (3x-1) like so:

[tex]2[(3x-1)(3x-1)][/tex]

which gives you

[tex]2(9x^{2} -6x+1)[/tex]

Distribute in the 2 and you'll end up with the answer:

[tex]18x^{2} -12x+2[/tex]

[tex]\vec u[/tex] starts at (1, 1) and ends at (-4, 3), so it's pointing in the same direction as the vector

[tex](-4, 3)-(1,1)=(-5,2)[/tex]

This vector terminates in the second quadrant, so its direction is

[tex]\pi+\tan^{-1}\left(-\dfrac25\right)\,\mathrm{rad}\approx158.2^\circ=(180-158.2)^\circ\,\text{N of W}=21.8^\circ\text{N of W}[/tex]

Answer:

C. 21.8 degrees N of W

Step-by-step explanation:

got it right on edge :)

It is so jard for me .

so by drawing construction i have done it.Value of x i haven't done.due to no perfect angle

Answer:

The correct answer would be (8,2.40).

Step-by-step explanation:

Option one(-3, -0.9) and two (-2.5, -0.75) Would not be a viable solution because the value of number of days can not be negative and in option one and two, value of days -3 and -2.5 is negative.

Option three(4.5, 1.35) can not be correct because library charges fee for a full day so the number for days would be a whole number. Library would not charge for 4.5 days, they would either charge of 4 days or 5 days because 4.5 is not an whole number.

Option four(8, 2.40) is the correct answer because it satisfies our equation;

Y= 0.30 * X

2.40= 0.30 * 8

2.40 = 2.40

hope this helps :)

D is the right answer

Answer:

See below in bold.

Step-by-step explanation:

Here is 1 grain on square 1 , 2 on square 2, 4 on square 3  and so on. This is a geometric sequence with the nth term = a1r^(n - 1) where a1 = first term , r = common ratio.

So the 20th term  (the number of grains on square 20) would be

 1*2^(20-1)  = 524,288.

Total =   a1 * (r^n - 1) / (r - 1)

=  (2^20 - 1)  / 2-1 =  1.048,575

By comparing the perimeters, we can deduce the scaling factor:

[tex]k = \dfrac{34}{20} = 1.7[/tex]

The areas scale with the square of the scaling factor, so the new area is

[tex]19.6 \cdot 1.7^2 = 56.644[/tex]

Answer:

12x - 15 dollars

Step-by-step explanation:

Sunny earns $12 per hour for delivering cakes.

She worked for x hours this week.

Unfortunately, she was charged $15 for a late delivery on Tuesday

She was supposed to earn $12 × x = $12x this week

But she was charged $15 for late delivery on Tuesday

So her net earning this week is; $12x - $15

Answer:

12x-15

Step-by-step explanation:

Answer: [tex]x=\frac{8}{3}[/tex]

Step-by-step explanation:

By the Intersecting secants theorem, we know that:

[tex]EC*ED=EB*EA[/tex]

Then, substituting, we get:

[tex](x+4)(x+4+1)=(x+1)(x+1+11)\\\\(x+4)(x+5)=(x+1)(x+12)[/tex]

Now we need to expand the expression:

[tex]x^2+5x+4x+20=x^2+12x+x+12[/tex]

Simplifying, we get that the value  of "x" is:

[tex]x^2+9x+20=x^2+12x+12\\\\9x+20=12x+12\\\\20-12=12x-9x\\\\8=3x\\\\x=\frac{8}{3}[/tex]

Answer:

2/10 simplify into 1/5

Step-by-step explanation:

Since there is a total of 10 cards in the deck, the denominator would be 10. As there is only two 'I's in the deck it would be the numerator.

Hope this will help :)

Answer:

2/130 = 1/65

Step-by-step explanation:

There are  4 kings out of 52  cards total.  Your chances of drawing a king are 4/52

Incredible has 10 letters 2 of which are 'i's' So your chances of picking 2  eyes   is 2/10

Combined  you have

4/52 * 2/10 = 2/ 130 = 1/65

Answer:

78.9  degrees to the nearest tenth.

Step-by-step explanation:

This equals the angle whose tangent is 320/62.5 ( opposite side / adjacent side).

The angle of elevation from the coin to the top of the tower

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

Given that:

The coin  lands 62.5m away from the center of the base of the 320m- high structure.

Height= 320 m

Base= 62.5 m

Now, tan [tex]\theta[/tex] = [tex]\frac{P}{B}[/tex]

                  =[tex]\frac{320}{62.5}[/tex]

                  = 5.12

               [tex]\theta[/tex]= [tex]tan^{-1} (5.12)[/tex]

               [tex]\theta[/tex]= [tex]78.94^{0}[/tex]

The angle of elevation is: 78.94 degrees.

Learn more about angle of elevation here:

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3x^3 and 2x^3 should be combined because if numbers have an exponent combine only if they both have matching exponents and variables as well

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

131 m³

Step-by-step explanation:

The volume (V) of a cone is

V = [tex]\frac{1}{3}[/tex] area of base × height

  = [tex]\frac{1}{3}[/tex] × π × 5² × 5

  = [tex]\frac{1}{3}[/tex] π × 125 ≈ 131

Answer:

$38.00

Step-by-step explanation:

You purchase 4 large pizzas.

Each one costs $9.50

Total expenditure on pizza = $9.50 × 4 = $38.00

4 times 9.50 would be 38. So you will have to spend $38.00

Answer:8 meters

z^2=x^2+y^2

10^2=x^2+6^2

100-36=x^2

x=swrt(64)=8

By applying the Pythagorean Theorem, we find out that the width of Blake's living room is 8 meters. This theorem helps to calculate the unknown side of a right triangle when the other two sides are known.

To answer this question, we can apply the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the diagonal across the rectangular room is the hypotenuse of a right triangle, with the length and width of the room as the remaining sides.

Given that the length of the room is 6 meters and the hypotenuse is 10 meters, we can substitute these values into the formula of the Pythagorean Theorem:

Width² = Hypotenuse² - Length²

Substituting the known values gives:

Width² = 10² - 6²

Width² = 100 - 36

Width² = 64

Then, taking the square root of both sides:

Width = 8 meters

Therefore, the width of Blake's living room is 8 meters.

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answer: right

reason: because you are talking about the x axis so if you go left that would be a negative and you cant go up and down bc that's the y axis so the only way to go is right

hope this helped

Answer:

The answer is R0, 90° and (x , y) → (-y , x) ⇒1st and 4th

Step-by-step explanation:

* Lets revise the rotation rules

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

 (+90° or -270°)

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

 (-90° or +270°)

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

 (+180° or -180°)

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or  

  anti-clockwise around the origin

* Lets solve the problem

∵ Δ XYZ has vertices⇒ X (0 , 0) , Y (0 , -2) , Z (-2 , -2)

∵ Δ X'Y'Z' has vertices X' (0 , 0) , Y' (2 , 0) , Z' (2 , -2)

* From them

# Y = (0 , -2) and Y' = (2 , 0), that means the image is (-y , x)

# Z = (-2 , -2) and Z' = (2 , -2), that means the image is (-y , x)

∴ The rotation is around the origin with angle 90° anti-clockwise

V.I.N: Anti-clock wise means positive angle , clockwise means

negative angle (90° means anti-clockwise , -90° means clockwise)

∴ The answer is: R0, 90° and (x , y) → (-y , x)

Given:

Problem-solving:

Let us prepare the leading terms, constant terms, and the coefficients of the polynomial are being asked.

[tex]\boxed{ \ 7x^5 + bx^4 + cx^3 + dx^2 + ex + 6 \ }[/tex]

Now we make the first polynomial, for example:

Thus, the result is [tex]\boxed{\boxed{ \ 7x^5 + 3x^4 - 2x^3 + 2x^2 - 5x + 6 \ }}[/tex]

Then we make the second polynomial as an alternative. For example:

Thus, the polynomial is [tex]\boxed{\boxed{ \ 7x^5 - 6x^4 + 4x^2 + 6 \ }}[/tex]

Of course, you can form another polynomial using the procedure above. Try to vary the coefficients.

Notes:

Let us rephrase the following definitions.

For example, consider the polynomial [tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex]

A polynomial is said to be in standard form if the terms are written in descending order of degree. For example:

Keywords: a polynomial of the 5th degree, a leading coefficient of 7, a constant term of 6, a monomial, terms, the leading coefficient, constant, in a standard form, rational function, whole number power, integer

A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 could take the form of 'f(x) = 7x^5 + 6'. The other coefficients (b, c, d, e) can be any real numbers, but for simplicity, they can be set to zero in this instance.

The student's question relates to constructing a polynomial of the 5th degree with specific characteristics in the field of Mathematics, specifically in algebra. One can present such a polynomial with the general form:

f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f

Where the leading coefficient a is 7 and the constant term f is 6. In this case, since the only information provided is the leading coefficient and the constant term, and not any constraints on the other coefficients (b, c, d, e), they can be any real numbers, including zero. Thus, one example of a polynomial fitting these constraints is:

f(x) = 7x^5 + 0x^4 + 0x^3 + 0x^2 + 0x + 6

To simplify the algebra and make calculations easier, one can eliminate terms wherever possible, which in this example has been executed by setting the coefficients of x^4, x^3, x^2, and x to zero. After forming any polynomial, it is also important to check the answer to ensure that it matches the given criteria, which in this case it does.

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Answer:

[tex]\frac{8}{81}[/tex]

Step-by-step explanation:

Since the sequence is geometric there is a common ratio r between consecutive terms.

r = [tex]\frac{1}{3}[/tex] ÷ [tex]\frac{1}{2}[/tex]

  = [tex]\frac{1}{3}[/tex] × [tex]\frac{2}{1}[/tex] = [tex]\frac{2}{3}[/tex]

Multiplying [tex]\frac{4}{27}[/tex] by r gives the next term in the sequence

[tex]\frac{4}{27}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{8}{81}[/tex]

Answer:

-560a^4b^3

Step-by-step explanation:

Given:

(2a - b)^7

By using Binomial theorem:

128a^7 - 448a^6b + 672a^5b^2 - 560a^4b^3 + 280a^3b^4 - 84a^2b^5 + 14ab^6-b^7

Here the fourth term is -560a^4b^3 !

Answer:

-560a^4 b^3.

Step-by-step explanation:

The (r + 1)th term of (a + x)^n = nCr a^(n-r) x^r.

So, the 4th term of (2a - b)^7 =  7C3 (2a)(7-3)x^3

=  35*16a^4(-b)^3

= -560a^4 b^3.

Answer:

A. 5x^2 − 2x − 24 = 0

Step-by-step explanation:

height = 5b-2

b =x

We can rewrite the height as

h = 5x-2

We know the formula for area of a triangle

A = 1/2 bh

A =1/2 x * (5x-2)

Distributing the x

A=    1/2 (5x^2 - 2x)

We know A =12

12 = 1/2 (5x^2 - 2x)

Multiply each side by 2

12*2 = 2*1/2 (5x^2 - 2x)

24 = 5x^2 - 2x

Subtract 24 from each side

24-24 = 5x^2 - 2x-24

0 = 5x^2 - 2x-24

Answer:

43 is the smaller angle

Step-by-step explanation:

greater angle is 47

43+47=90

43 is 4 less than 47

Answer:

  5/11 amperes ≈ 0.455 amperes

Step-by-step explanation:

The applicable formula for the current (I) is ...

  I = P/V . . . . where P is power in watts, and V is voltage in volts

  I = (50 watts)/(110 volts) = 5/11 amperes

Answer:

c

Step-by-step explanation:

Using Pascal's triangle, the expansion, although EXTREMELY lengthy, will help you find the 7th term.  I am going to type out the expansion only up til the 7th term (although there are actually 10 terms because we are raised to the power of 9).  If you would like to learn how to use Pascal's Triangle for binomial expansion, you will need to visit a good website that explains it because it's just too difficult to do it via this website.

The expasion is as follows (up to the 7th term):

[tex]1(3c)^{9} +9(3c)^{8}(2d)^{1} +36(3c)^{7}(2d)^{2} +84(3c)^6(2d)^3+126(3c)^5(2d)^4+126(3c)^4(2d)^5+84(3c)^3(2d)^6[/tex]

That last term is the 7th term.  You find out its value by multiplying all the numbers together and adding on the c^3d^6.  Again those come from Pascal's triangle, and it's one of the coolest math things ever.  I encourage you to take the time to explore how it works.

Answer:

3:20

Step-by-step explanation:

The 360 degrees clockwise rotation of the minute hand corresponds to 60 minutes.

The 90 degrees clockwise rotation is one-fourth of the 360 degrees, and hence will corresponds to 15 minutes.

The time is now 3:05.

After 15 minutes the time will be 3:20

Therefore the teacher dismisses the class at 3:20