At a restaurant your bill is $32. You have a coupon for 15% off. You are in Idaho and they charge you 7% tax. (Discount before tax) What is the final cost of your meal after your discount and with tax included? Round to the nearest cent.

Questions:

(a) What is a simplified expression for (x + y) – (x – y)?

(b) Carlotta thinks that [tex]3y + 5y^3[/tex] is the same as [tex]8y^4[/tex]. Which statement shows that it is NOT the same?

Answer:

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

[tex]3y + 5y^3 \ne 8y^4[/tex]

Step-by-step explanation:

Solving (a):

Given

[tex](x + y) - (x - y)[/tex]

Required

Simplify

[tex](x + y) - (x - y)[/tex]

Open brackets

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

Collect Like Terms

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

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

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

Solving (b):

Given

[tex]3y + 5y^3[/tex] and [tex]8y^4[/tex]

Required

Which expression shows they are not the same

The expression that shows this is:

[tex]3y + 5y^3 \ne 8y^4[/tex]

Take for instance; y=2

Substitute 2 for y in [tex]3y + 5y^3 \ne 8y^4[/tex]

[tex]3*2 + 5*2^3 \ne 8*2^4[/tex]

Evaluate all exponents

[tex]9 + 5*8 \ne 8*16[/tex]

[tex]9 + 40 \ne 128[/tex]

[tex]49 \ne 128[/tex]

The above expression supports [tex]3y + 5y^3 \ne 8y^4[/tex]

Answer:

[tex]1\frac{5}{12}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3} + \frac{9}{12}[/tex]   <-- let's change 2/3 into a fraction that has 12 as the denominator

[tex]\frac{2}{3}[/tex] × 4   <-- multiply both the numerator and the denominator by 4

2 × 4 = 8   <-- new numerator

3 × 4 = 12   <-- new denominator

now we have [tex]\frac{8}{12}[/tex] + [tex]\frac{9}{12}[/tex]

[tex]\frac{8}{12}[/tex] + [tex]\frac{9}{12}[/tex] = [tex]\frac{17}{12}[/tex]    <-- let's change it into a mixed number

17 ÷ 12 = [tex]1\frac{5}{12}[/tex]

Answer: its 17/12

Step-by-step explanation:

Answer:

112/126 = 8/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

yur gay

Answer: From the conditions given, the total number of the problems should be 29. This means that the sum of x and y should be 29. With this and the point-system, the best system of equation that is useful for this problem is,

                                     x + y = 29

                                     5x + 2y = 100

Your first answer choice is the correct answer.

Fact: I suggest looking up the question before asking it because  sometimes others have asked the questions and it will be answered. Just letting you know to help you save points.

Answer:

x + y = 29, 5x + 2y = 100

Step-by-step explanation:

just did it

Answer:

cx

Step-by-step explanation:

g

Answer:

Step-by-step explanation:

Given triangle ACD

Perimeter is sum of the side lengths:

AD = CD because D is vertex and the triangle is isosceles

AC = AB + BC because B is midpoint of AC

Then P is:

Find the value of x from the AB = BC:

Then find the value of P:

Answer:

2,250 + 95n

Step-by-step explanation:

Cost of a food booth = 100 + 2n

Cost of 10 food booth = 10(100 + 2n)

= 1,000 + 20n

Cost of a game booth = 50 + 3n

Cost of 25 game booth = 25(50 + 3n)

= 1,250 + 75n

Total amount earned by the company = Cost of 10 food booth + Cost of 25 game booth

= (1,000 + 20n) + (1,250 + 75n)

= 1,000 + 20n + 1,250 + 75n

= 1,000 + 1,250 + 20n + 75n

= 2,250 + 95n

Total amount earned by the company = 2,250 + 95n

Answer: x=7

Step-by-step explanation:

2x=17-3

2x=14

X=7

Answer:

x=6,-4

Step-by-step explanation:

solve for x by cross multiplying

Answer:

6c^5+4c−301, assuming that you meant 6c^5  

Answer:

Step-by-step explanation:

first question is -1

and i think the sec option is  13/3+y/3 i think im wrong on the sec option

Answer:

Solving the inequality: [tex]x - 2 > 2x + 12[/tex] we found the value of x: [tex]\mathbf{x<-14}[/tex]

Option D is correct option.

Step-by-step explanation:

We need to solve the inequality: [tex]x - 2 > 2x + 12[/tex] and find value of x

Solving the inequality

[tex]x - 2 > 2x + 12[/tex]

First of all, we will add 2 on both sides

[tex]x - 2+2 > 2x +12 +2\\x>2x+14[/tex]

Now, add -2x on both sides of inequality

[tex]x-2x>2x+14-2x\\-x>14[/tex]

Now, multiply both sides by -1, when multiplying by negative number, the inequality is reversed i.e. > will become <

[tex]-1*-x<14*-1\\x<-14[/tex]

So, solving the inequality: [tex]x - 2 > 2x + 12[/tex] we found the value of x: [tex]\mathbf{x<-14}[/tex]

Option D is correct option.

Step-by-step explanation:

[tex]for1 \\ x =8 \\ y = x \sqrt{2} = 8 \sqrt{2 } = 11.31[/tex]

[tex]for2 \\ x =25 \sqrt{2} = 35.36 \\ y = 25[/tex]

[tex]for3 \\ 19 = x \sqrt{2} \\ x = \frac{19}{ \sqrt{2} } = 13.44 \\ y = 13.44 \\ [/tex]

Answer:

True.

Step-by-step explanation:

We have to tell about the statement true or false

Two triangles that have the same side length will always be congruent

The SSS congruency rule states that if all three sides of one triangle are equal to corresponding three sides of another triangle, then the triangles are congruent.

∴ we say that when the sides are the same then the triangles are congruent.

Hence, the statement is true.

Because the definition of a congruent triangle is a triangle with every side of same length.

Answer:

C . 16 miles in 3/6 hour. Because 3/6 is 1/2. So, the answer would basically be 16 miles in 1/2.

Answer:

y= 3 /4 x−11

Step-by-step explanation:

3x - 4y = 44

Add -3x to both sides.

3x−4y+−3x=44+−3x

−4y=−3x+44

Divide both sides by -4.

−4y /−4 = (−3x+44 )/−4

y= 3 /4 x−11

Answer:

hypotenuse=6.4

Step-by-step explanation:

One side is 4 units and the other is 5 units.

Hypotenuse= c^2

a^2+b^2=c^2

5^2+4^2=c^2

25+16=c^2

41=c^2

√41=c

c=6.4

Answer:

3 I believe

Step-by-step explanation:

The factors of 3 are: 1, 3

The factors of 6 are: 1, 2, 3, 6

Then the greatest common factor is 3.

Answer:

3 is the great common factor

Step-by-step explanation:

factors:

3- 1,3

6- 1,2,3,6

hope it helps:))

Answer:

Commutative and multiplicative identity

Step-by-step explanation:

mark brainlyist

Answer: 4.3

Step-by-step explanation: To find the range you have to subtract the highest number by the lowest number. So you'd subtract 2.6 by -1.7. And since -1.7 is already a negative number, it would get turned into a positive.

Answer:

y-10=2/3(x-8)

Step-by-step explanation:

(y2-y1)/(x2-x1) is the equation for slope so put your points in you get 2/3 once simplified then its just a matter of putting points in the equation y-y1= m(x-x1)

Answer:

Sum: 21 + 9 = 30

Difference: 21 - 9 = 12

Step-by-step explanation:

Let the number is a and b

The sum of two numbers =30

so,a+b=30 ............(1)

The difference of two number =12

so,a-b=12 .................(2)

If we add two equation (1) and (2)

we get,

a+b+a-b=30+12

2a=42

[tex]\tt{ a=\dfrac{42}{2} }[/tex]

[tex]\tt{ a=21 }[/tex]

so,one number is a=21

if we put the value a in (2) equation

we get,

a-b=12

21-b=12

b=21-12

b=9

so,the another number is=b=9

[tex]\tt{ the~two~ number~ are~ 21 ~and~ 9 }[/tex]

Answer:

The answer is 6x² - 21x.

Step-by-step explanation:

You have to substitute the expressions inro the formula :

[tex]A = length \times width[/tex]

[tex]let \: l = 2x - 7,w = 3x[/tex]

[tex]A = (2x - 7) \times 3x[/tex]

[tex]A = 3x(2x - 7)[/tex]

[tex]A = 6 {x}^{2} - 21x[/tex]

The area of the rectangular garden is 6x² - 21x.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know, The area of a rectangle is (length×width).

Given, The rectangular garden has a length of (2x - 7) and a width of 3x.

Therefore, The area of the garden is,

= (2x - 7)×3x.

= 6x² - 21x.

= x(6x - 21).

learn more about rectangles here :

https://brainly.com/question/28993977

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Answer:

1196cm^3

Step-by-step explanation:

The height of the box with the smaller base is 4 times larger than that of the box with the larger base.

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism=Length X Width X Height

The volume of a box is the product of the base area and the height of the box,

Volume = base area × height

For the smaller base box,

base = 5 cm by 5 cm,

Therefore, the base area of the smaller base box

= 5 cm × 5 cm

= 25 cm².

Let the height of the smaller base box be h

The volume of the small box = 25 cm² × h

For the larger base box,

The base of 10 cm by 10 cm

Therefore, the base area of the larger base box

= 10 cm × 10 cm  

= 100 cm².

Let the height of the large base box be H.

The volume of the larger base box = 100 cm² × H

Since both boxes have the same volume so,

100 cm² × H  = 25 cm² × h

h / H = 4

h = 4H

Hence, The height of the box with the smaller base is 4 times larger than that of the box with the larger base.

Learn more about a rectangular prism;

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Answer:

Step-by-step explanation:

We start at (-7, 7).  A translation of 1 unit to the right results in (-6, 7).  A translation down from there results in (-6, 4).  This is the desired image point.

Answer:

[tex]\sqrt{27x^2y^2}=3xy\:\sqrt{3}[/tex]

Hence, option C is correct.

Step-by-step explanation:

Given the expression

[tex]\sqrt{27x^2y^2}[/tex]

simplifying the expression

[tex]\sqrt{27x^2y^2}=\sqrt{27}\sqrt{x^2}\sqrt{y^2}[/tex]

Apply radical rule: [tex]\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]

               [tex]=\sqrt{27}x\sqrt{y^2}[/tex]

Apply radical rule: [tex]\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]

                [tex]=\sqrt{27}xy[/tex]

                [tex]=xy\sqrt{3^3}[/tex]

                 [tex]=xy\sqrt{3^2\cdot \:\:3}[/tex]

Apply radical rule: [tex]\sqrt{a^2}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]

                  [tex]=3xy\:\sqrt{3}[/tex]

Therefore,

[tex]\sqrt{27x^2y^2}=3xy\:\sqrt{3}[/tex]

Hence, option C is correct.

Answer:

FE=√210=14.49.

Step-by-step explanation:

In right triangle EFH,angle EFH is 90°and FG is perpendicular to EH.

Therefore,

FE²= EG.EH

FE²=10×(10+11)

=10×21

FE²=210

FE= √210