William and
Debra
Pierce are celebrating their
20th anniversary by having a reception at a local reception hall. They have budgeted
$2,000 for their reception. If the reception hall charges a
$50 cleanup fee plus
$36 per​ person, find the greatest number of people that they may invite and still stay within their budget.

Answer:

B 2x - 31 = -2x - 31 have exactly one solution

Step-by-step explanation:

Which of the following equations have exactly one solution?

Choose all answers that apply:

A 2x - 31 = 2x - 31

B 2x - 31 = -2x - 31

C 2x + 31 = 2x - 31

D 2x - 2 = 2x - 31

A. 2x - 31 = 2x - 31

2x-31=2x-31

Collect like terms

2x-2x= -31+31

0=0

Infinite number of solutions

B 2x - 31 = -2x - 31

2x - 31 = -2x - 31

Collect like terms

2x+2x=-31+31

4x=0

x=0

One solution

C 2x + 31 = 2x - 31

2x + 31 = 2x - 31

Collect like terms

2x-2x= -31-31

0= -62

No solution

D 2x - 2 = 2x - 31

2x - 2 = 2x - 31

Collect like terms

2x-2x= -31+2

0= -29

No solution

Answer:

The expression in factored form is (3x - 7)(3x + 7)

Step-by-step explanation:

Here in this question, we are interested in using the difference of two squares to factor the given expression.

Mathematically, supposed we have two squares a^2 and b^2, and we are told to factorize a^2-b^2.

By using the difference of two squares;

a^2-b^2 can thus be written as;

(a-b)(a + b)

Now, we can apply same approach to the problem at hand.

9x^2 - 49

kindly note that 9x^2 can be written as ((3x)^2 and 49 can be written as 7^2

So applying what we have said earlier about difference of two squares;

9x^2 - 49 will be ;

(3x-7)(3x + 7)

Answer:

The answer is (3x - 7) (3x +7)

Step-by-step explanation:

Answer:

Line S

Step-by-step explanation:

Answer:

line s

Step-by-step explanation:

coz if you extend both the line (line r and line s )

they will not intersect at any point...

plz let me know if it was helpful to you dude!

Answer:

Stick 2: [tex] \frac{1}{2} [/tex]

Stick 3: [tex] \frac{4}{10} [/tex]

Step-by-step explanation:

To determine which of the lengths are less than ⅗ meters, you would compare each given length with ⅗ meters.

Stick 1: Comparing ⁹/10 and ⅗

Find The common denominator of both fractions. 10 is the common denominator. Multiply the numerator and denominator of ⅗ by 2 to create a fraction equivalent to ⁹/10.

Thus,

[tex] \frac{3*2}{5*2} = \frac{6}{10} [/tex]

Compare the numerator of [tex] \frac{9}{10} [/tex] and [tex] \frac{6}{10} [/tex].

9 is greater than 6. This means [tex] \frac{9}{10} [/tex] > [tex] \frac{6}{10} [/tex].

Therefore, [tex] \frac{9}{10} [/tex] > [tex] \frac{3}{5} [/tex]

Stick 2: comparing ½ and ⅗

Common denominator = 10

Make both fractions equivalent to each other as follows,

[tex] \frac{1*5}{2*5} = \frac{5}{10} [/tex]

[tex] \frac{3*2}{5*2} = \frac{6}{10} [/tex]

5 < 6. This means, [tex] \frac{5}{10} [/tex] < [tex] \frac{6}{10} [/tex].

Therefore, [tex] \frac{1}{2} [/tex] < [tex] \frac{3}{5} [/tex]

Stick 3: comparing ⁴/10 and ⅗

Common denominator = 10

Make the fractions equivalent as follows,

[tex] \frac{4*1}{10*1} = \frac{4}{10} [/tex]

[tex] \frac{3*2}{5*2} = \frac{6}{10} [/tex]

4 < 6. This means, [tex] \frac{4}{10} [/tex] < [tex] \frac{6}{10} [/tex].

Therefore, [tex] \frac{4}{10} [/tex] < [tex] \frac{3}{5} [/tex]

Stick 4: comparing ⅘ and ⅗

Common denominator = 5

Since both denominators are already the same, both fractions are equivalent. Comparing their numerator, 4 > 3. Therefore, ⅘ > ⅗.

Answer:

  swap the middle two steps to put them in order

Step-by-step explanation:

The steps in order would be ...

Answer:

6

Step-by-step explanation:

are=A=πr2

28.26/3.14=9

√9=3

3•2=6

Answer:

6

Step-by-step explanation:

Area = πr^2

r = √(area/π)

r = √(28.26/3.14)

r = 3

and we know that,

d = 2r,

d = 2 x 3 = 6

Answer:

1001.66 in²

Step-by-step explanation:

radius=r=diameter/2

r=22/2=11

l is the slant =18

surface area of a cone= area of circle + area of the curved part of cone

SA=πr²+πrl

SA=3.14(11)²+3.14(11)(18)=1001.66 in²

Answer:

Probability of people order a salad or an appetizer P(A∪B) = 62%

Step-by-step explanation:

Given:

Probability of appetizer P(A) = 55%

Probability of salad P(B) = 25%

Probability of choose both P(A∩B) = 18%

Find:

Probability of people order a salad or an appetizer P(A∪B)

Computation:

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 55% + 25% - 18%

P(A∪B) = 62%

Probability of people order a salad or an appetizer P(A∪B) = 62%

Answer:

19.45

Step-by-step explanation:

The median is the middle number.  Put the data in order from smallest to largest

16.3, 17.8,17.8  ,18.0, 18.7,19.3, 19.6,20.1,20.5, 21.9, 25.2 ,25.4

There are 12 pieces of data,

16.3, 17.8,17.8  ,18.0, 18.7,19.3,         19.6,20.1,20.5, 21.9, 25.2 ,25.4

The median lies between the 6th and 7th piece

Add the 6th and 7th together and divide by 2

(19.3+19.6)/2 =19.45

Answer:

[tex]\large \boxed{\mathrm{19.45}}[/tex]

Step-by-step explanation:

Median of a data set is the middle value.

The data is to be arranged from smallest to largest.

16.3, 17.8, 17.8, 18.0, 18.7, 19.3, 19.6, 20.1, 20.5, 21.9, 25.2, 25.4

Find the middle value.

16.3, 17.8, 17.8, 18.0, 18.7, 19.3, 19.6, 20.1, 20.5, 21.9, 25.2, 25.4

Average the two middle numbers.

(19.3+19.6)/2 = 19.45

The median of the data set is 19.45.

Answer:

13.6

Step-by-step explanation:

tan(45)=x÷8.5

1.6=x/8.5

x=13.6

Use the law of sines

x/sin(45) = 8.4/sin(85)

x = sin(45)*8.4/sin(85)

x = 5.96238563941842

x = 6.0

Answer:

C. [tex]x[/tex] and $(x-6)$

Step-by-step explanation:

The roots of the quadratic equation are $0$ and $6$.

Hence the equation is $(x-0)(x-6)=x(x-6)$

Answer:

See below

Step-by-step explanation:

Answer:

54

Step-by-step explanation

You can't find the other sides, it may seem impossible, but you have to look at this problem in a different way. To find the perimeter of any figure you just need to know the top base, bottom base, right side, and left side.

We see that the top base equals to the bottom base as it is a rectilinear figure. You have to treat the side with 8 and side with 5 as one base. So they equal 13. Now do the same for the bottom.

So, 13 + 13 = 26

The right side is equal to the left side as it is a rectilinear figure, so the right side is 4 + 10 = 14. The left side is also 14.

So 14 + 14 = 28

26 + 28 = 54 units

Sorry, if I couldn't explain properly. I tried my best. As it is hard for me to explain in words. If I could draw it out, I could do better.

Answer:

45

Step-by-step explanation:

I broke the sections apart and then added:

14+14=28

13+13=26

26+28=54

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

Explanation:

Let's find the area of the hexagon. It's composed of two identical (aka congruent) trapezoids.

Each trapezoid has two parallel bases of 4+4 = 8 and 5 units. The height is 3. The area of one trapezoid is

area = height(base1+base2)/2

area = 3*(8+5)/2

area = 19.5

which doubles to 2*19.5 = 39 to represent the area of the entire hexagon

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

The volume of any prism is found through this formula

volume = (area of base)*(height of prism)

We just found the area of the base to be 39. The height is unknown, so we'll call it h. The volume is given to be 234.

We end up with this equation

234 = 39h

which solves to h = 6 after dividing both sides by 39. This prism has a height of 6 units.

The height of the prism is 6 units

The hexagonal prism is a prism with hexagonal base.

An isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Given,

Each hexagon is made from two congruent isosceles trapezoids

Therefore

Area of one isosceles trapezoids = [tex](a+b).(\frac{h}{2} )[/tex]

where,

a =4+4 = 8 units

b = 5 units

h = 3 units

Area of one isosceles trapezoids =[tex](8+5)(\frac{3}{2} )[/tex] =19.5 unit square

Area of  the hexagon = Area of two isosceles trapezoids

Area of hexagon = 2× 19.5 = 39 unit square

We know that,

Volume = Base area × Height

Volume = 234 cubic units

234 = 39 × h

h = [tex]\frac{234}{39}[/tex] = 6 units

Hence, the height of the prism is 6 units

Learn more about Hexagonal prism, Isosceles trapezoids and Volume here

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Answer:

Quadrilateral ABCD is a parallelogram, quadrilateral with opposite sides parallel

Step-by-step explanation:

Statement,                                       Reason

∠A = ∠C,                                          Given

∠B = ∠D,                                          Given

Therefore, we have

∠A + ∠B + ∠C + ∠D = 360°,            Sum of interior angles of a quadrilateral

2×∠A + 2×∠B = 360°,                         Substitution property of equality

∴ ∠A + ∠B = 360°/2 = 180°

∠A + ∠B, are supplementary  angles,   Angles that sum up to 180°

Similarly,

∠C + ∠D, are supplementary  angles,   Angles that sum up to 180°

Therefore, segment DA is parallel to segment BC, (Lines with supplementary angles on the same side of the transversal)

Similarly, given ∠A = ∠C and ∠B = ∠D, we have;

∠A + ∠D and ∠C + ∠B are supplementary  angles,   Angles that sum up to 180°

Therefore, segment AB is parallel to segment DC, (Lines with supplementary angles on the same side of the transversal)

Therefore;

Quadrilateral ABCD is a parallelogram, quadrilateral with parallel opposite sides.

Answer:

the horizontal distance is the x-intercept, and the vertical distance is the y-intercept

1) x-int=1, y-int=1

2) x-int=6, y-int=5

Answer:  1) D      2) B

Step-by-step explanation:

1) The denominator cannot equal zero, Factor the denominator to find the zeros.  n³ - 4n² + 3n = 0

           n(n - 3)(n - 1) = 0

       n=0  n-3=0   n-1=0

       n=0    n=3      n=1

2) In order to be a rational expression, it must be in the form [tex]\dfrac{a}{b}[/tex] where both a and b are integers.

Since [tex]\sqrtb[/tex][tex]\sqrt b[/tex] is irrational and not an integer, then the expressions containing an irrational term after simplified cannot result in an integer.

Therefore, options (i) and (iv) are not rational expressions.

Option (iii) contains b as an exponent.  Since there is no information about b, it could be a fraction, which means it could be an irrational number.

Answer:

x= 7/4 =1.750

Step-by-step explanation:

Answer:

196

Step-by-step explanation:

Surface area of a cuboid:

2 ( lw + wh + hl)

L = Length

W = Width

H = Height

Area of the base = 30 = lw; So we could take the length as 15 cm and width as 2 cm.

Volume = lwh; 15 x 2 x (4); So 4 is the height

So, 2 ( lw + wh + hl)

= 2 (15 x 2 + 2 x 4 + 4 x 15)

= 2 (30 + 8 + 60)

= 2 (98)

= 196 is the surface area of cuboid

Answer:

Step-by-step explanation:

Given one side and diagonal of rectangle we can use Pythagorean theorem to calculate the other side of it.

[tex]L=40\, cm\\D=41\,cm\\W=\ ?\\\\W^2+L^2=D^2\\\\W^2+40^2=41^2\\\\W^2+1600=1681\\\\W^2=81\\\\W=9[/tex]

Perimeter:

P = 2W + 2L = 2•40 + 2•9 = 80 + 18 = 98

Answer:

[tex]\large \boxed{\sf \bf \ \ a^2+b^2=20 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

[tex]a^b=b^a\\\\\text{ We can replace a by 2b.}\\\\(2b)^b=2^b\cdot b^b=b^{2a}=b^2\cdot b^b\\\\\text{ Let's assume that b is different from 0 and we can divide by }b^b \\ \\ \text{ both sides of the equation, and it come.}\\\\2^b=b^2\\\\\text{ We find b = 2 and then a = 4, So}\\\\a^2+b^2=4^2+2^2=16+4=20[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

c. 5.333...

Step-by-step explanation:

When converting fractions into decimals, all you have to do is that you have to divide the numerator by the denominator. In this case, we will get 16 divided by 3. If we do this, we will get 5 and 1/3. One third in decimals is 0.3333... so the answer is 5.333...

The decimal 5.33 will be equivalent to 16/3 so option (A) will be correct.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given the fraction of 16/3

So divide 16 by 3

16/3 = (15 + 1 )3

⇒ 15/3 + 1/3

⇒ 5 + 0.333

⇒5.3

Hence "The decimal 5.33 will be equivalent to 16/3".

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Answer:

....the answer is 682.5

Answer:

The answer is 702. Hope it helped! :D

Step-by-step explanation:

Answer:

(C) [tex]y = 2x+5[/tex]

Step-by-step explanation:

Looking at this graph, we can see that the slope of it is 2. We know this because for every time x increases by 1, y increases by 2.

We also know that the y-intercept of this graph is 5, since it intercepts the y-axis at the value 5.

We can easily create an equation with this info.

[tex]y = 2x + 5[/tex].

Hope this helped!

Answer:

C. y= 2x+5

Step-by-step explanation:

y=mx+b

(+b) is y- intercept

(mx) is the slope.

plot the y- intercept first which the line starts at (0,5)

since the slope isn't a fraction you turn it into one which would be

[tex] \frac{2}{1} [/tex]

Answer:

122

Step-by-step explanation:

5!=5 x 4 x 3 x 2 x 1 = 120

2!=2 x 1 = 2

120+2=122

Answer:

484 meters

Step-by-step explanation:

diameter of a circular Garden = 140 metre

we know diameter = 2*radius

140 = 2*radius

radius = 140/2 = 70 meter

thus, radius of garden is 70 meter

Given that

On its outside there is a road of 7 metre wide

Thus, radius of garden along-with road will increase by 7 meters

Total radius of garden and road = 70 meter + 7 meter = 77 meter

 outer circumference of the road can be calculated using radius 77 meter.

we know that circumference = [tex]2\pi r[/tex]

we will use value of [tex]\pi = 22/7[/tex]

Thus, outer circumference of the road ​ with radius 77 m

= [tex]2\pi r \\=>2*22/7 *77\\=> 44*11 = 484[/tex]

Thus,

The outer circumference of the road ​is 484 meters.

Answer:

P(t)=25000(1.12)^t

Step-by-step explanation:

only answering so i can go back to not watching ads :/ but hope u dont get it wrong even tho i gave right answer

Answer:

P(t) = 25000 x 1.12^t

Step-by-step explanation:

25000 times 1.12 because it is increasing by a factor of 1.12.

Step-by-step explanation:

let the function be $y=mx+c$ since it is linear.

1=3m+c

and

5=2m+c

solve c to get the y intercept

Answer:

(-3,6) (1,8) (2,10) and so on.

Answer:

( 4,7)    ( -1,2)

Step-by-step explanation:

y = x + 3

y = x^2 - 2x - 1

Set the equations equal to each other

x + 3  = x^2 - 2x - 1

Subtract x from each side

3 = x^2 -3x -1

Subtract 3 from each side

0 = x^2 -3x -4

Factor

0 = ( x-4) ( x+1)

Using the zero product property

x-4 =0   x+1 =0

x = 4     x=-1

Find y for each x

x=4    y =x+3  y = 4+2  y=7

x = -1  y = x+3   y = -1+3 y = 2

( 4,7)    ( -1,2)

Answer:

D.  (-1, 2) and (4, 7).

Step-by-step explanation:

Eliminating y:

x^2 - 2x - 1 = x + 3

x^2 - 3x - 4 = 0

(x - 4)(x + 1) = 0

x = -1, 4.

When x = -1, y = -1 + 3 = 2.

When x = 4, y =  4 + 3 = 7.

So the answer is (-1, 2) and (4, 7).

Answer:

Malcom's maximum speed = 200 km/h

Ravi's maximum speed = 320 km/h

Step-by-step explanation:

Let m = Malcom's maximum speed

Let r = Ravi's maximum speed

Average of their maximum speed would be represented as [tex] \frac{m + r}{2} = 260 [/tex]

[tex] m + r = 520 [/tex].

Make m the subject of the formula by subtracting r from both sides:

[tex] m = 520 - r [/tex]. Let this be equation 1.

Given that Malcom's speed (m), when doubled is 80 km/h more than that of Ravi (r). This can be expressed as: [tex] 2m = r + 80 [/tex]. This is equation 2.

Plug in (520 - r) into equation 2 to replace m:

[tex] 2(520 - r) = r + 80 [/tex]

[tex] 1040 - 2r = r + 80 [/tex]

Solve for r. Subtract 1040 from both sides:

[tex] 1040 - 2r - 1040 = r + 80 - 1040 [/tex]

[tex] - 2r = r - 960 [/tex]

Subtract r from both sides

[tex] - 2r - r = r - 960 - r [/tex]

[tex] - 3r = - 960 [/tex]

Divide both sides by -3

[tex] \frac{-3r}{-3} = \frac{-960}{-3} [/tex]

[tex] r = 320 [/tex]

To find m, plug in the value of r into equation 1.

[tex] m = 520 - r [/tex]. =>Equation 1

[tex] m = 520 - 320 [/tex]

[tex] m = 200 [/tex].

Malcom's maximum speed = m = 200 km/h

Ravi's maximum speed = r = 320 km/h