Jacob was out at a restaurant for dinner when the bill came. His dinner came to $18. After adding in a tip, before tax, he paid $20.70. Find the percent tip.

Answer:

Step-by-step explanation:

(x + y)^2 = 144

x^2 + y^2 = 80

----

x + y = 12 ---> y = 12 - x

x^2 + y^2 = 80

x^2 + (12-x)^2 = 80

2x^2 - 24x + 64 = 0

x^2 - 12x + 32 = 0

x = 4, x = 8

y = 8, y = 4

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

x + y = -12 ---> y = -12 - x

x^2 + y^2 = 80

x^2 + (-12-x)^2 = 80

2x^2 + 24x + 64 = 0

x^2 + 12x + 32 = 0

x = -4, x = -8

y = -8, y = -4

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

One number is + or -4, the other is + or -8,

and the absolute value of the sum is 12.

Answer:

(4,8);(8,4);(-4,-8);(-8,-4)

Step-by-step explanation:

Ok, let's start writing down the two conditions:

[tex]\left \{ {(x+y)^2 = 144} \atop {x^2+y^2=80}} \right.[/tex]

Mumble.  The second almost look like a square, if only there was the [tex]2xy[/tex] term. Let's add (and subtract, so we aren't creating something new) term to the second:

[tex](x+y)^2-2xy = 80[/tex] But we know what the first term is, it's 144. Let's replace and do some number tricks to get:[tex]144-2xy=80 \rightarrow 72-xy=40\\72-40=xy \rightarrow xy=32[/tex]

At this point, let' stare at it for a while. You can tell that the system is simmetrical (if you replace x with y you still get a solution). Moreover, x and y have the same sign: it means that if (a,b) is a solution, then also (b,a), (-a,-b) and (-b, -a) are solutions, and since it's a 4th degree system (the degree of a system is the product of the degrees of the single equations, and they're both quadratic) there are no other solution.

Let's find one pair then. We're tasked to find two numbers that sum to [tex]\sqrt{144} = 12[/tex] and whose product is 32. that is, the root of the polynomial

[tex]z^2+12z+32= (z+4)(z+8)[/tex] (or if you can't see the factors right away, bruteforce it with quadratic formula, it's always good practice). That tells us that one of the two is -4, and the other is -8. From what we said above, the solutions are by combining them with plus or minus.

[tex](4,8);(8,4);(-4,-8);(-8,-4)[/tex]

Answer:

26s+24

Step-by-step explanation:

2(3s+9) +2(10s+3)

6s +18+20s +6

26s +24= perimeter

Answer:

(1,-2)

Step-by-step explanation:

x - 2y = 5

3x + y= 1 (1)

x - 2y = 5

x = 5 + 2y (2)

Substitute (2) into (1)

3x + y = 1

3(5 + 2y) +y = 1

15 + 6y + y = 1

15 + 7y = 1

7y = 1 - 15

7y = -14

y = -2  (3)

Plug (3) into (1) to find x

3x + y = 1

3x + (-2) = 1

3x - 2 = 1

3x = 3

x = 1

(1,-2)

Answer:

The dimension of a matrix is indicated with R × C where R is the number of rows in the matrix and C is the number of columns. When a matrix has the same number of rows as columns, then it's a square matrix. Matrices with just one row are called row matrices, and those with only one column are column matrices.

Answer:

D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

hope it can help you lovelots

Answer:

x=−3 and y=7

Step-by-step explanation Solve: 7x+2y=−7for x:

7x+2y=−7

7x+2y+−2y=−7+−2y(Add -2y to both sides)

7x=−2y−7

7x

7

=

−2y−7

7

(Divide both sides by 7)

x=

−2

7

y−1

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

−2

7

y−1forxin11x+5y=2:

11x+5y=2

11(

−2

7

y−1)+5y=2

13

7

y−11=2(Simplify both sides of the equation)

13

7

y−11+11=2+11(Add 11 to both sides)

13

7

y=13

13

7

y

13

7

=

13

13

7

(Divide both sides by 13/7)

y=7

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

Substitute7foryinx=

−2

7

y−1:

x=

−2

7

y−1

x=

−2

7

(7)−1

x=−3(Simplify both sides of the equation)

Answer:

b

Step-by-step explanation:

Answer:

16968

Step-by-step explanation:

Answer:

16,968

Hope this helps :)

Answer:

183in^2

Step-by-step explanation:

Given that the length is 15 in and the width is 26 in we can figure out the area of a full rectangle.

15x26=390in

We now want to figure out the small rectangle on the bottom of the image.

The area of a triangle is A=hb/2

A=6x15/2=45

In the image, you can see that the rectangle is incomplete and missing part of it. It's missing a triangle so in order to complete the rectangle you multiply 45x2.

45x2=90

Finally, we can solve for the remaining triangle.

A=9x26/2=117

Add up the triangles and subtract the sum from the area of the rectangle to get the shaded area.

390-(90+117)=183in^2

Hope this helps :)

Answer:

$180

Step-by-step explanation:

150 ÷ 25 = 6

6×3 = 18

18×10 = 180

The total value of the coupons that were given out is $180.

Correct option is (D).

The study and use of numbers, their relationships, and mathematical observations are topics covered by the area of mathematics known as arithmetic. The fundamental ideas in number theory, measurement, and computation are sometimes included under the umbrella word "arithmetic" (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

As per the given data:

3 out of every 25 customers receive a $10 coupon to use on their next visit.

Customers at the restaurant today = 150

For 25 customers = 3 coupons

For (25 × 6 = 150) customers = (3 × 6 = 18) coupons

Total value of the coupons = 18 × 10 = $180

Hence, the total value of the coupons that were given out is $180.

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Answer:

slope is 0

Step-by-step explanation:

it is flat on a graph

Answer:

The Answer is 28.  Please mark the brainliest! And thanks!

Step-by-step explanation:

Did with a teacher!

Answer:

This is the sample answer for plato/edmentum

Step-by-step explanation:

[tex] \: \: \: \: \: [/tex]

[tex] = \: \: \: x = - \frac{3}{2 } \\ \\ [/tex]

refer to attachment

[tex] \: \: \: \: \: [/tex]

Answer:

40...................................

Answer:

35 points because you said so O-O

5/7 of $5,404 is $3088.

Sierra earned $3088 and Gavin earned $2316

Answer:

x < 4

Step-by-step explanation:

3x - 3 < 9

3x - 3 + 3 < 9 + 3

3x < 12

[tex]\frac{3x}{3} <\frac{12}{3}[/tex]

x < 4

Answer:

the answer is x is less than 4

Step-by-step explanation:

3x-3<9

3x-3+3<9+3

-3deleted by +3

so we get 3x<12. over 3 over 3 and we got

x<4

Answer:

AAA?

Step-by-step explanation

Step-by-step explanation:

if I understand your text right, we are looking at the line going through the points (0, 2) and (5, 3).

the slope is in a line equation always the factor of x.

anyway, it is expressed as ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point on the line to another.

so, we are simply going from (0, 2) to (5, 3).

x changes by +5 (from 0 to 5).

y changes by +1 (from 2 to 3).

so, the slope is y/x = 1/5.

Answer:

B. [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Answer:

1. false

2. false

3. false

4. true

Step-by-step explanation:

a quadritilateral always has 4 sides, but it dpesnt HAVE to be a square

a parrellelogram can be any shap as long as its parrelel

a rhombus is always a square, becuase if you turn it around... VIOLA! you get a square.

Answer:

345

Step-by-step explanation:

On adding 60 to 325 and then subtracting 40 the answer will be 345.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given numbers 60, 325, and 40. The expression will be formed as below:-

E = 60 + 325 - 40
E = 385 - 40

E = 345

Therefore, on adding 60 to 325 and then subtracting 40 the answer will be 345.

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Step-by-step explanation:

that means both functions deliver the same result for the same x.

therefore

x⁵ = x⁷

one solution is of course, x = 0.

the other(s) we get for x<>0 by dividing both sides by x⁵ :

1 = x²

that means we have 2 more solutions (a quadratic equation has 2 solutions, a cubic equation has 3 solutions,...) :

x = 1

x = -1

so, the intersection points are

for x = 0, we get y = 0⁵ (or 0⁷) = 0

for x = 1, we get y = 1⁵ (or 1⁷) = 1

for x = -1, we get y = (-1)⁵ or (-1)⁷ = -1

(-1, -1)

(0, 0)

(1, 1)

The intersection points of the function y = x⁵ and y = x⁷ are (0, 0) , (1, 1) and (-1 , -1).

What is Intersection point?

The intersection point is the point at which the two lines are cuts to each other.

Given that;

The equations are,

⇒  y = x⁵

⇒ y = x⁷

Now, Solve for intersection point as;

The equations are,

⇒  y = x⁵

⇒ y = x⁷

Equate both equation to each other, we get;

⇒ x⁷ = x⁵

Subtract x⁵ both sides , we get;

⇒ x⁷ - x⁵ = x⁵ - x⁵

⇒ x⁷ - x⁵ = 0

⇒ x⁵ (x² - 1) = 0

This gives two conditions;

⇒ x⁵ = 0

or, ⇒ x² - 1  = 0

Solve both the equations as;

⇒ x⁵ = 0  

⇒ x = 0

And,  x² - 1  = 0

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

x = 1 or x = -1

Thus, The values of x are 0 , 1 and -1.

So, The intersection points are;

For x = 0; y =  x⁵ = 0

For x = 1; y =  x⁵ = 1

For x = -1; y =  x⁵ = -1

Thus, The intersection points of the function y = x⁵ and y = x⁷ are (0, 0) , (1, 1) and (-1 , -1).

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Answer:

its: 360,000,000

Step-by-step explanation:

good luck

Answer:

[tex]3.6 \times {10}^{8} [/tex]

Step-by-step explanation:

[tex]800 \times 900 \times 500 \\ = 8 \times 9 \times 5 \times {10}^{6} \\ = 360 \times {10}^{6} \\ = 3.6 \times {10}^{8} [/tex]

232 fluid ounces is equal to 1.8125 gallons.

Answer:

Exact: 1.8125

Rounded Answers:

Nearest Thousandth: 1.813

Nearest Hundredth: 1.81

Nearest Tenth: 1.8

Answer: 8

Step-by-step explanation:

plug y into the first equation:

8x+5y=24

8x+5(-4x)=24

8x-20x=24

-12x=24

x=-24/12

x=-2

then plug x to the second equation

y=-4

y=-4(-2)

y=8

x=-2

y=8

Answer:

(- 6, 24 )

Step-by-step explanation:

y = - 8x - 24 → (1)

y = - 4x → (2)

Substitute y = - 4x into (1)

- 4x = - 8x - 24 ( add 8x to both sides )

4x = - 24 ( divide both sides by 4 )

x = - 6

Substitute x = - 6 into either of the 2 equations and evaluate for y

Substituting into (2)

y = - 4(- 6) = 24

solution is (- 6, 24 )

49.85% of buyers paid between 150,000 and 154,200

The empirical rule states that for a normal distribution, 68% are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are are within three standard deviation from the mean.

Given that mean (μ) = 150000, standard deviation σ = 1400

68% are within one standard deviation = μ ± σ = 150000 ± 1400 = (148600, 151400)

95% are within two standard deviation = μ ± 2σ = 150000 ± 2 * 1400 = (147200, 152800)

99.7% are within three standard deviation = μ ± 3σ = 150000 ± 3 * 1400 = (145800, 154200)

The buyers who paid between 150,000 and 154,200 = 99.7%/2 = 49.85%

Hence 49.85% of buyers paid between 150,000 and 154,200

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Answer:

n = 3

Step-by-step explanation:

[tex]\frac{5}{15} = \frac{n}{9}[/tex]

Cross multiply

15n = 45

Divide

15n/15 = 45/15

n = 3