Find the product of 4√6 and √10 in simplest form. Also, determine whether the
result is rational or irrational and explain your answer.

The graph of the function y = -2 can be described as Horizontal.

Given, a function y = -2.

As, we can see that the given function is an one variable function.

And the functions in one variable have straight line graph.

Now, the function y = -2 has a graph that will be parallel to the x-axis.

So, the function y = -2 has a graph that will be horizontal as the x-axis is horizontal in cartesian plane.

Hence, the graph of the function y = -2 can be described as Horizontal.

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The solution to the equation are 5 or -1 after applying the quadratic formula.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

It is given that:

x² - 4x² - 5 = 0

The above equation is a quadratic equation:

Using the quadratic formula:

[tex]\rm $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

Plug the values in the formula:

[tex]\rm $x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(-5)}}{2(1)}$[/tex]

After solving:

x = 5 or -1

Thus, the solution to the equation is 5 or -1 after applying the quadratic formula.

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If you can choose a prize of either a $25,000 car or one penny on the first day. The number of days you receive more than the value of the car is 15 days.

Let x represent the number of days

Convert $25,000 to cents by multiplying it by 100

 $25,000 × 100 = 2,500,000 cents

Hence:

3^x-1 > 2,500,000

(x-1) log3/log 3 > log 2500000/log 3

x-1 > 13.409

x = 13.409+1

x =14.409

x = 15 days (Approximately)

Therefore the number of days is 15.

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Answer:

[tex]28\frac{4}{7}[/tex] miles

Step-by-step explanation:

mileage = m

Primo: cost = 0.3m + 20

Ultimo: cost = 0.95m + 30

Ultimo = twice Primo

0.95m + 30 = 0.6m + 40

subtract 0.60m and 30 from each side and simplify to get

0.35m = 10

divide by 0.35 into both sides to get

m = [tex]28\frac{4}{7}[/tex]

therefore, the daily mileage would be [tex]28\frac{4}{7}[/tex] miles

Answer:

y = - [tex]\frac{3}{4}[/tex] x + 5

Step-by-step explanation:

the hypotenuse is the line AB

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (0, 5 ) and (x₂, y₂ ) = B (4, 2 )

m = [tex]\frac{2-5}{4-0}[/tex] = [tex]\frac{-3}{4}[/tex] = - [tex]\frac{3}{4}[/tex]

the line AB crosses the y- axis at A (0, 5 ) ⇒ c = 5

y = - [tex]\frac{3}{4}[/tex] x + 5 ← equation of hypotenuse

Answer: 32

Step-by-step explanation: you have to count by 7 everytime

Answer:

7w ≤ -25

Step-by-step explanation:

If 7 x W is at most -25 then it cant be greater than -25 but can be equal to it.

Hope this helped!

The expression for the other number is (n-1) when n is the greater of two consecutive numbers.

Given that,

We have to write an expression for the other number if n is the greater of two successive numbers.

We know that,

One is equal to the difference between any two consecutive numbers.

Let us take

x be the smaller of two consecutive number

n be the larger of two consecutive numbers

We have that

n-x=1

Solve for x

x=n-1

Therefore, The expression for the other number is (n-1) when n is the greater of two consecutive numbers.

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Answer:

area increases by a factor of 4

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = lw ( l is length and w is width )

doubling the length and width , that is

l = 2l and w = 2w , then

A = 2l × 2w = 4lw

that is the area is increased by a factor of 4

The Determinant of the equation is 17

What is the determinant of the equation?

The determinant is a scalar variable in mathematics that is a function of the elements of a square matrix. It enables the characterization of some characteristics of the matrix as well as the linear map expressed by the array. The determinant is nonzero, in particular, if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a matrices product is the product of their determinants (the preceding property is a corollary of this one). The determinant is a scalar variable in mathematics that is a function of the elements of a square matrix. It enables the characterization of some attributes of the matrix as well as the vertical map presented by that of the array.

Given equation is 2x² + 7x - 4 = 0

Therefore, determinant = (7)² - 4x2x(-4)

                                        = 49 - 32

                                        = 17

Hence, the determinant of the given equation is 17

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The values of the function are 1/9, 1/3, 1, 3 and 9.

A function is defined as a relation between a set of inputs having one output each.

Given a function, f(x) = [tex]3^{x}[/tex]

When x = -2

y = [tex]3^{-2}[/tex] = 1/3² = 1/9

When x = -1

y = [tex]3^{-1}[/tex]

y = 1/3

When x = 0

y = [tex]3^{0}[/tex]

y = 1

When x = 1

y = 3

When x = 2

y = 3² = 9

Hence, The values of the function are 1/9, 1/3, 1, 3 and 9.

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If wall-to-wall carpeting is installed in a room 21 ft long and 17 ft wide and the edges of the carpet are held down by tack strips, the feet of tack-strip material needed are 76 ft calculated by determining the perimeter of the rectangle room.

Tack strips are thin pieces of wood studded with nails or tacks in the installation of carpets. These thin strips are placed along all the edges of the carpet. In order to determine the length of the tack strips needed to hold the wall to wall carpeting installed in a rectangular room of 21 ft by 17 ft. The formula of the perimeter of a rectangle is:

P = 2 (length + width)

P = 2 (21 + 17)

P = 2 (38)

P = 76 ft

Hence, the feet of tack-strip material needed are 76 ft.

Note: The question is incomplete. The complete question is Wall-to-wall carpeting is to be installed in a rectangular room that is 21 ft long and 17 ft wide. The edges of the carpet are to be held down by tack strips. How many feet of tack-strip material is needed?

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The number of grains on square 59 will be 5.7646075230342 x 10^17grains.

No. of grains on the first square = 1 = 2^0

No. of grains on the second square = 2 = 1*2 = 2¹

No. of grains on the third square = 4 = 2*2 = 2²

No. of grains on the fourth square = 8 = 2*4 = 2³

From the pattern it could be seen that amount of wheat is doubled for every next square

So, the number of grains in the nth square = 2^n-1

Therefore, No. of grains on 59th square

= 2^59 -1 =

= 5.7646075230342 x 10^17

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a. [tex]a^{3}[/tex].

b. [tex]\frac{1}{2c^{6}}[/tex].

[tex]\frac{a^{4} }{a}[/tex]

[tex]\frac{a^{4-1} }{a^{1-1} }=\\ \\\frac{a^{3} }{a^{0} }=\\\\ \frac{a^{3} }{1 }=\\ \\a^{3}[/tex]

[tex]a^{3}[/tex]

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

[tex]\frac{2c^{-4} }{c^{2}}[/tex]

[tex]\frac{1}{c^{2}*2c^{4} }[/tex]

[tex]\frac{1}{2c^{6}}[/tex]

Answer: 8 days

Step-by-step explanation: 138-42 = 96 then you divide that by daily fee of 12 to get 8 days

The number of discs that can be filled in the box is 17.

length of box , l =26 cm , breadth , b =15 cm , height = 20 cm

So,the volume of the box = l × b × h

= 26 × 15 ×20 cm³

= 7800 cm³

Now length of a disc case, l= 1.6 cm

breadth ,b =14.2 cm

height, h =19.3 cm

So the volume of a disc case = 1.6×14.2×19.3 cm³

= 438.496 cm³

No of disc cases can be stacked inside the box

= 7800 ÷ 438.496

=7800000÷438.496

= 17.8

Hence 17 disc cases can be fitted into the box.

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There are 204 possible methods to choose a chief executive officer, a director, a treasurer, and a secretary, if there are 18 members on the board of directors.

Combinations are mathematical procedures that count how many different ways a collection of items might be arranged when the order in which they are chosen is immaterial. Regardless of the order in which the things are chosen, a combination is the choice of all or part of a collection of objects. A combination is "an arrangement of items where the order of the components is unimportant," according to the definition. When these two terms are combined, "Selection of things" is meant, where the order of the items is not important.

Here,

If the order doesn't matter then we have a combination, if the order do matter then we have a permutation.

18C4=18!/(18-4)!(4)!

=18!/14!4!

=18*17*16*15/4*3*2*1

=3*17*4

=204 ways

A chief executive officer, a director, a treasurer, and a secretary be  can be selected in 204 ways If a board of directors consists of 18 people.

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Answer:

Length: 42, width: 24

Step-by-step explanation:

Perimeter: 132

L: W = 7:4

7u+7u+4u+4u= 22u (Length + length + width + width)

132/22= 6 (1u)

6x4= 24 (Width/ 4u)

6x7=42 (length/7u)

recheck:

42+42+24+24= 132cm

perimeter= 132

Answer: Yes

Step-by-step explanation: To show that the percentage has increased we would need to prove that 416/1015 with a 99% level of confidence or a 1% margin of error to do this we divide 416 by 1015

This equals 0.40985221674

Which can be rounded to 0.41 or 41% since there is a one percent margin of  error we can assume that this is enough evidence, because if 1% of the poll's recipients mistakenly voted for a option they did not really think was true it would not be enough to change 41% to 33%

Hope this helps!

Applying the trigonometry ratio, SOH, the height, h = 6.2172 cm.

Area of the region that is shaded in the circle = 47.1784 cm²

Recall the formulas for the trigonometric ratios, which are given as SOHCAHTOA, where:

Find the height, h, of the triangle using the sine ratio of trigonometry:

∅ = 51°

Opposite length = h

Hypotenuse = 8 cm

sin 51 = h/8

h = 8(sin 51)

h = 6.2172 cm

Area of the triangle = 1/2(base)(height) = 1/2(8)(6.2172)

Area of the triangle = 24.8688 cm²

Area of the sector =  /360 × r² = 129/360 × (8²)

Area of the sector = 72.0472 cm²

Area of the shaded region = area of the sector - area of the triangle

= 72.0472 - 24.8688

= 47.1784 cm²

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Answer:

Pete ate 2, Joe ate two, and Blake ate 1

2 + 2 + 1 = 5

They ate 5 out of 8 slices. The boys ate 5/8 of the pizza

The overall speedup of such a system that spends 40% of its time performing calculations is 1.25 when a processor upgrade results in 100% more throughput.

The overall speedup of a machine that spends 40% of its time processing data with a processor upgrade that offers 100% more throughput answers the issue.

Thus, with a CPU upgrade that results in 100% more throughput, a system that spends 40% of its time performing calculations sees an overall speedup of 1.25.

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Answer:

72.52

Step-by-step explanation:

circumference of a circle formula = [tex]2\pi r[/tex]

where r is the radius

the radius is half of diameter, and the diameters for all semicircles are given.

so the radius for the smaller semicircles is 10/2 which is 5

so [tex]2\pi 5[/tex] = 2(3.14)(5) = 31.4

31.4 is the circumference of the whole circle, since we have 2 semicircles with the same radius, we don't need to divide this by 2, we will simply use 31.4 for instead of doing this exact calculation again for the other small semicircle.

for the larger cemicircle, the diameter is 16 so the radius will be 16/2 which is 8

[tex]2\pi 8[/tex] = 2(3.14)(8) = 50.24

since 50.24 is the circumference of an entire circle, we will have to divide this by 2 to d=find the circumference of the semicircle.

50.24/2 = 25.12

Now we will simply add up the lengths of the borders,

31.4 + 25.12 + 16 = 72.52

Answer:

57.7 meters total perimeter for the object.

Step-by-step explanation:

See the attached worksheet. Break up the object into three circles and one rectangle. Label them to keep track of the work. The object's perimeter is coprised of:

- One side of rectangle R (16 m)

- 1/2 the circumference of circles b and c, each with a radius of 5 m

- 1/2 the circumference of circle a, with a circumference of 8 m.

The perimeter of a circle is 2πr. The perimeter of circles b and c is 31.4 meters in total, which is reduced to (1/2) or 15.7 m total. Circle a contributes 26 meters to the object's perimeter.

The sum of these measurements is (16m) + (15.7m) + (26m) = 57.7 meters total perimeter for the object.

Answer:

81,-247, 729

Step-by-step explanation:

each time its multiplying it by -3

so -27x-3=81

Answer: 729

Step-by-step explanation: The thing that happens every time is -3 is multiplied: 1, -3, 9, -27,  81, -243, 729

hope this helps!

please give brainliest!

The value of length of pen should always be greater than 5 feet.

Rectangle:

                Rectangle is a special kind of parallelogram in which opposite sides are equal and adjacent sides are perpendicular to each other.It contains of length and breadth,The area of rectangle is given by,

                  Area = length x breadth

Now as per question,

A family wants to build a pen for their new puppy.

They want's the area of the pen to be more than 225 square feet.

width of the pen is = 25 feet

let,

     The length of the pen is [tex]x[/tex] feet.

Area of pen = length * width

                    = [tex]x[/tex] * 25

                    = 25x

According to the question,

                        Area of pen > 225 square feet

                         25x > 225

                            x >225/25

                             x > 5 feet

Thus,

        The value of length should always be greater than 5 feet.

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Answer:

3y+4=22
3y+4-4=22-4
3y=18
(3y)/3=18/3
y=6

Step-by-step explanation:

pls mark brainliest

The amount of zinc in the jar is 160 grams.

According to the question,

We have the following information:

In a certain chemical the of zinc to copper is 4 to 15 and a jar contains 600 grams of copper.

Let's take the amount of zinc in a chemical to be 4x and that of copper to be 15x.

So, we have the following expression:

15x = 600

Dividing both the sides by 15 will give us the value of x:

x = 600/15

x = 40 grams

Now, we will put this value of x in the amount of zinc:

4x grams

4*40

160 grams

Hence, the amount of zinc in the given jar is 160 grams.

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There is only 1 real zero of the function.

What are Zeros of a Function?

The zeros of a function are the values of the function's variables that fulfil the equation and yield the function's value of 0. The zeros of a function can be represented graphically as the x-coordinates (x-intercepts) where the graph intersects the x-axis.

Solution:

As mentioned above,

The zeros of a function can be represented graphically as the x-coordinates (x-intercepts) where the graph intersects the x-axis.

So,

We can see that there is only one point where the graph intersects the x-axis.

Therefore, it can be said that there is only 1 real zero of the function.

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The value of x is 22.37 and y is 20

What is Interior angle?

An angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon.

What is Exterior angle?

An exterior angle (also called an external angle or turning angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.

We know, the sum of interior angle is 180 degree

The given interior angles is ,

3y + 5 and 5y + 15

So, equate to 180°

3y + 5 + 5y + 15 = 180°

Solve for 'y'

8y + 20 = 180

4(2y + 5) = 180

2y + 5 = 45

2y = 45 - 5

2y = 40

y = 20

Now, we know the sum of exterior angle is 360 degree

The given exterior angle is,

17x - 70 and 2x + 5

So, equate to 360°

17x - 70 + 2x + 5 = 360°

Now, solve for 'x'

19x - 65 = 360

19x = 360 + 65

19x = 425

x = 22.368 or 22.37

Hence, the value of x is 22.37 and y is 20

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