the titanic had about half as many plates as they did pieces of silverware . About how many plates did they have ?

The number that has to fill the blank to make the trinomial a perfect square is 72x

From the question, we are to determine the number that makes the given trinomial a perfect square

The given trinomial is

9x² + ___+ 144

For any given trinomial ax² + bx + c, the trinomial is a perfect square if

b² = 4ac

In given trinomial,

a = 9, c = 144, b = ?

Now, we will determine the value of b

Putting the values into the equation,

b² = 4ac

b² = 4×9×144

b² = 5184

b = √5184

b = 72

Thus,

The trinomial will become 9x² + 72x+ 144

Hence, the number that has to fill the blank to make the trinomial a perfect square is 72x

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[tex]a=3x^3\hspace{5em}b=4x^4 \\\\[-0.35em] ~\dotfill\\\\ c=ab^2\implies c=(\underset{a}{3x^3})(\underset{b}{4x^4})^2\implies c=(3x^3)(4^2x^{4\cdot 2}) \\\\\\ c=3x^3\cdot 16x^8\implies c=(3\cdot 16)x^{3+8}\implies c=48x^{11} \\\\[-0.35em] ~\dotfill\\\\ \boxed{bc}\implies (\underset{b}{4x^4})(\underset{c}{48x^{11}})\implies (4\cdot 48)x^{4+11}\implies \boxed{192x^{15}}[/tex]

Answer:

  bc = 192x^15

Step-by-step explanation:

Perform substitution as required, then simplify.

  bc = b(ab^2) = ab^3 = (3x^3)(4x^4)^3 = (3·4^3)(x^3)(x^(4·3))

  = 192x^(3+12)

  bc = 192x^15

__

Additional comment

The relevant rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

Answer:

x =  45 degrees.

Step-by-step explanation:

The arc of 90 degrees  an angle of 1/2 its value on  the circumference.

1/2 * 90

= 45 degrees.

The correct equation that has been shown by the graph is y<-2x+1. Option D

The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.

Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D

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Answer: The correct equation that has been shown by the graph is y<-2x+1. Option D

What is inequality?

The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.

Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D

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Step-by-step explanation:

Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Tyler can run 1 mile in 8 minutes and 20 seconds.

Time taken = 8 mins + 20 sec (0.33 min) = 8.33 minutes

Speed = distance / time = 1 mile / 8.33 = 0.12 mile per min

In 10 minutes, distance = 0.12 mile per min * 10 min = 1.2 mile

Haler is given by:

y = 8x; where y is time and x is distance.

In 10 minutes, distance = y/8 = 10/8 = 1.25 miles

Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.

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Answer:

f = 78 , g = 32 , h = 74

Step-by-step explanation:

f and 78° are alternate angles and are congruent , then

f = 78

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

h and 74° are alternate angles and are congruent , so

h = 74

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

the sum of the 3 angles in the triangle = 180°

sum the 3 angles and equate to 180

78 + g + h = 180

78 + g + 74 = 180

152 + g = 180 ( subtract 152 from both sides )

g = 28

The correct option is (A) P(X) × P(Y) = P(X ∩ Y)

What is probability and example?

 We are given to consider a situation in which X and Y are two events such that

P(X) = 4/5, P(Y) = 1/4, P(X ∩ Y) = 1/5

We are to select the statement that best describes the events X and Y

We know that

any two events A and B are said to be independent if

P(A) × P(B) = P (A ∩ B)

We have, for events X and Y,

P(X) × P(Y) = 4/5 × 1/4 = 1/5 = P (X ∩ Y)

P(X) × P(Y) = P(X ∩ Y)

Thus, X and Y are independent because P(X) × P(Y) = P(X ∩ Y)

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The complete question is -

Consider a situation in which P(X) = 4/5 and P(Y) = 1/4. If P(X and Y) is = 1/5, which best describes the events?

They are independent because P(X) x P(Y) = P(X and Y).

They are independent because P(X) + P(Y) = P(X and Y).

They are dependent because P(X) x P(Y) = P(X and Y).

They are dependent because P(X) + P(Y) = P(X and Y).

Answer: a

Step-by-step explanation:

just took the test

The cost of new product on the website is $309.375.

Given that, the cost of product = $412.50 and discount percentage = 25%.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Discount = 25% of 412.50

= 25/100 × 412.50

= 0.25 × 412.50

= 103.125

So, cost = 412.50-103.125

= $309.375

Therefore, the cost of new product on the website is $309.375.

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The factored form of the expression is (2x-1)(2x+5) and the x-intercept of the function is 1/4 and -5/2 respectively

Quadratic equations are equations that has a leading degree of 2. Given the quadratic equation below;

y = 4x^2 + 8x -5

The x-intercept is the point where the value of y is zero.

Factorize the resulting expression

y = 4x^2 + 8x -5

y = 4x^2 - 2x + 10x -5

y = 2x(2x-1)+5(2x -1)

y = (2x-1)(2x+5)

The factored form of the expression is (2x-1)(2x+5)

Equate the given factors to zero

(2x-1)(2x+5) = 0

Equate the factors to zero

2x - 1 = 0

2x = 1

x = 1/4

Similarly

2x + 5 = 0

2x = -5

x = -5/2

Hence the x-intercept of the function is 1/4 and -5/2 respectively

C) For the end behavior, as the value of x tends to infinity, hence the y-values tends to infinity

D) In order to plot the graph, the x-intercepts of the will be plotted on the graph and then curve will be created.

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The simplified expression of (x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6 is x^(12) y^(10/9) z^(-1/3)

The algebraic statement is given as:

(x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6

Rewrite the algebraic statement as:

[(x^0 y^2/3 z^-2y)^2/3]/[(x^2 z^1/2)^-6]

Evaluate the like factors

[(x^0 y^(2/3+1) z^-2)^2/3]/[(x^2 z^1/2)^-6]

Evaluate the sum

[(x^0 y^5/3 z^-2)^2/3]/[(x^2 z^1/2)^-6]

Expand the exponents

[(x^(0*2/3) y^(5/3 * 2/3)z^(-2*2/3)]/[(x^(2*-6) z^(1/2*-6)]

Evaluate the products

[(x^0 y^(10/9) z^(-4/3)]/[(x^(-12) z^(-3)]

Apply the quotient law of indices

x^(0+12) y^(10/9) z^(-4/3+3)

Evaluate the sum of exponents

x^(12) y^(10/9) z^(-1/3)

Hence, the simplified expression of (x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6 is x^(12) y^(10/9) z^(-1/3)

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Answer:[tex]x^3-x^2-17x+20[/tex]

Step-by-step explanation:

The pairs of angles that fit the description are

1. alternate exterior angles            S and Z; T and Y

2. alternate interior angles            U and X; V and W

3. consecutive interior angles       U and W; V and X

4. corresponding angles               S and W; T and X; U and Y; V and Z

5. vertical angles                           S and V; U and T; W and Z; Y and X

6. adjacent angles                         S and T; Y and Z

From the question, we are to list the angles that fit the given descriptions

1. alternate exterior angles            S and Z; T and Y

2. alternate interior angles            U and X; V and W;

3. consecutive interior angles       U and W; V and X

4. corresponding angles               S and W; T and X; U and Y; V and Z

5. vertical angles                           S and V; U and T; W and Z; Y and X

6. adjacent angles                         S and T; Y and Z

Hence, the pairs of angles that fit the description are

1. alternate exterior angles            S and Z; T and Y

2. alternate interior angles            U and X; V and W

3. consecutive interior angles       U and W; V and X

4. corresponding angles               S and W; T and X; U and Y; V and Z

5. vertical angles                           S and V; U and T; W and Z; Y and X

6. adjacent angles                         S and T; Y and Z

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Answer:

if you end up landing on a heads you should walk away with a $1.46

standard form of the given equation are

-f(*) = (x + 2)(x - 6) = x² - 4x - 12

f(x) = (x - 4)(x + 3) = x² - x - 12

f(x) = (x - 12)(x + 1) = x² - 11x - 12

f(x) = (x -3)(x + 4) = x² + x - 12

A polynomial function with one or more variables in which the second-degree term is the highest degree is known as a quadratic function, quadratic polynomial, polynomial of degree 2, or simply a quadratic, in algebra.

As long as an is not equal to zero, the quadratic function f(x) = a(x - h)2 + k is considered to be in standard form. The graph starts out in either an upward or a downward direction depending on the value of a. The point at the vertex of the symmetry is represented by the vertical line x = h. (h,k).

The standard form list.

1 .   (x + 2)(x - 6)

= x² - 6x + 2x - 12

=  x² - 4x -12

2.  (x - 4)(x + 3)

    = x² + 3x - 4x - 12

   =   x² - x - 12

3. (x - 12)(x + 1)

    = x² + 1x - 12x - 12

    =  x² - 11x - 12

4.  (x -3)(x + 4)

    =   x² + 4x - 3x - 12

     = x² + x - 12

So the equivalent standard form  of the give values are :

-f(*) = (x + 2)(x - 6) = x² - 4x - 12

f(x) = (x - 4)(x + 3) = x² - x - 12

f(x) = (x - 12)(x + 1) =  x² - 11x - 12

f(x) = (x -3)(x + 4) = x² + x - 12

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I understand that the question you are looking for is:

Match each quadratic function given in factored form

with its equivalent standard form listed on the left.

f(x) = (x + 2)(x – 6)

f(x) = (x – 4)(x+3)

f(x) = (x – 12)(x+1)

f(x) = (x – 3)(x +4)

Answer:

Step-by-step explanation:

true

Answer:

False because the account isn't full

Answer:

C (Third option)

Step-by-step explanation:

The prime factorization of 675 is 5*5*3*3*3 or 5^2*3^3. With the square root, we take out all square integers, leaving (5*3)(sqrt3). The answer is 15(sqrt3) or C.

Break

Option C

Answer:

Step-by-step explanation:

The steps to constructing either circle start with finding the relevant center and radius. The required construction techniques are ...

The incenter (center of the inscribed circle) is located at the coincidence of the angle bisectors. The radius is the perpendicular distance to any side, so will lie on the line through the incenter and perpendicular to one side.

Reference the first attachment. We have elected to bisect the largest two angles of triangle ABC. In each case, we used these steps:

After this process is repeated for another angle, the point of intersection of the two angle bisectors is the incenter (R).

Finding the radius requires finding the perpendicular distance to one side of the triangle. That is done by constructing a perpendicular to the side through the incenter.

The inscribed circle is centered at R and has radius RX.

__

The circumcenter (center of the circumscribed circle) is located at the coincidence of the bisectors of the sides of the triangle. The radius is the distance from the circumcenter to any vertex.

Reference the second attachment. We have elected to bisect the longest and shortest of the triangle's sides. The purpose of this choice is to make the perpendicular bisectors intersect at a large angle, so the point is as accurately located as possible.

Repeat this process for another side (BC to create bisector JK). The intersection of the two bisectors (L) is the circumcenter.

The circumscribed circle is centered at L and has radius LA.

__

Additional comments

In general, arcs that are required to intersect each other will be drawn with the same radius. An arc that is required to intersect two lines, or one line in two places, may have any convenient radius.

As with any geometric construction, the tools required are a marking tool, a compass, and a straightedge. Usually, the preferred marking tool is a sharp pencil.

If the triangle is obtuse, the circumcenter will be outside the triangle (adjacent to the long side). If the triangle is a right triangle, the circumcenter is the midpoint of the hypotenuse.

Answer:

16 pi/ 9 inches should be the right one.

Answer:

153 in²

Step-by-step explanation:

[tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]

[tex]\sf \boxed{\text{\bf Area of square = side *side}}[/tex]

Figure I:

   length = 12 in

   width = 6 in

Area of figure I = 12 * 6

                         = 72 in²

Figure II:

      length = 13 in

      width = 5 in

Area of figure II = 13 * 5

                          = 65 in²

Figure III:

       side = 4 in

Area of figure III = 4 * 4

                           = 16 in²

Area of irregular shape = 72 + 65 + 16

                                      = 153 in²

Answer:

12.5< × < 18.9

Step-by-step explanation:

because you would use the pythagoras theorem which a² + b² = c² in this case c is the third side the unknown so to work this out do square root of ( 10² + 16²) which is 100 + 256 = 356 and the square root of 356 is 18.86 which rounds to 18.9 so the second answer is correct :)

i hope this helps pls ask if you need any more help :)

The minimum number of bricks Salah will have to buy is 4050 bricks

Given that the

So, the length of walkway plus garden, L = 40 ft + 18 ft = 58 ft. The width of walkway plus garden, W = 17 ft + 18 ft = 35 ft.

We now need to find the area of the walkway.

Area of walkway, A" = area of walkway plus garden - area of garden

= LW - lw

= 58 ft × 35 ft - 40 ft × 17 ft

= 2030 ft² - 680 ft²

= 1350 ft²

Now, since each brick is 6 inches wide and 8 inches long, the area of each brick is A' = 6 in × 8 in  = 48 in²

So, the number of bricks required, n = area of walkway/area of brick

= 1350 ft²/48 in²

= 1350 × 144 in²/48 in²

= 194400 in²/48 in²

= 4050 bricks

So, the minimum number of bricks Salah will have to buy is 4050 bricks

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Answer:

y=[4]x + [12]

Step-by-step explanation:

Remember that parallel lines have identical slopes; and to make a line which passes through a point we will use point-slope form.

Familiarize yourself with point-slope form:

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

If the line is parallel to [tex]y=4x+11[/tex] the slope must be 4.

[tex]y-y1=4(x-x1)[/tex]

And we know the point it must pass through is (-2,4), so we can fill those values in too.

[tex]y-4=4(x+2)[/tex]

Now all we have to do is solve for y:
[tex]y-4=4(x+2)\\y-4=4x+8\\y=4x+12[/tex]

Answer:

[tex]y = 4x + 12[/tex]

Step-by-step explanation:

The solution is in the attached image

The trigonometry illustrates that the four angles whose cosine is the same as cos pi/3 will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3

From the information, given cos (x), the value that is similar to cos x will be the sum of the angle and multiple of 360.

Therefore, for the angle cos(∏/3), the angles that are similar to this angle will be expressed as Cos(2∏n + ∏/3) where n is any positive integer.

Then the other four angles will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3. Also, the statement that all angles that have the same cosine will have the same sine is false. The sine of an angle is simply equal to the cosine of the complementary angle.

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The length of the smaller leg is 3.79

Represent the smaller leg with x.

So, we have:

[tex]x^2 + x^2 = ((12\sqrt5)/5)^2[/tex] -- Pythagoras theorem

This gives

2x^2 = 144/5

Divide by 2

x^2 = 72/5

This gives

x^2 = 14.4

Take the square root

x = 3.79

Hence, the length of the smaller leg is 3.79

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Answer:

1/2^6 = 1/64

Step-by-step explanation:

Half life = 10 years

Time = 60 years

No of half life = T/t

= 60 / 10 = 6

Remaining fraction = 1/2^(no of half life)

= 1/2^6

= 1/64

Answer:

23.6

Step-by-step explanation:

→ Identify length not given

Opposite

→ Find a formula without opposite

Cos = Adjacent ÷ Hypotenuse

→ Rearrange

Adjacent = Cos × Hypotenuse

→ Substitute

cos 38 × 30 = 23.6

Answer:

[tex]x = 23.6[/tex]

Step-by-step explanation:

To find the missing side of a right-angled triangle, first look at the given angle, and notice its relationships with the given and required sides.

In this case:

• The side adjacent to the given 38° angle is [tex]x[/tex] (required).

• The hypotenuse is 30 units.

The trigonometric ratio that relates the adjacent side and hypotenuse of a triangle is cosine (cos), where:

[tex]\boxed{cos \space\ \theta = \frac{adjacent}{hypotenuse}}[/tex].

Substituting into the formula:

[tex]cos (38^{\circ}) = \frac{x}{30}[/tex]

⇒ [tex]x = cos(38^{\circ}) \times 30[/tex]

⇒ [tex]x = 23.6[/tex]

By working with percentages, we will see that they served 56 salmon filets.

Here we know that the restaurant served 70 specials in total, such that 80% of these were salmon filets.

So we just need to calculate what is the 80% of 70.

This is just given by:

70*(80%/100%) = 70*0.8 = 56

This means that they served 56 salmons filet.

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Answer:

10

Step-by-step explanation:

f(x) = 3x + 1

f^-1 = x-1/3 , it is known as inverse function.

f(3)= 3*3 +1

=9+1

=10

To find inverse,

x=3x + 1

y=3x+1

Exchanging the position or x and y

x=3y+1

x-1=3y

.•. y=x-1/3

Answer:

The answer is option A SAS.We have a side,an angle and the last side.If this helps please mark me BRAINLIEST