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3 years ago

Nathan and his brother Zach love to play video games. Right

Mathematics

1 answer:

Monica [59]3 years ago

3 0

Answer:

$N=2Z-11$

$\begin{array}{cc}\text{Zac's score}&\text{Natan's score}\\ 6&1\\7&3\\8&5\\9&7\end{array}$

Step-by-step explanation:

Nathan's score is 11 less than 2 times Zac's score.

Let Z points be Zac's score and N points be Natan's score. then

2 times Zac's score = 2Z

11 less than 2 times Zac's score = 2Z -11

So, N = 2Z - 11

1. If Z=6, then $N=2\cdot 6-11=12-11=1$

2. If Z=7, then $N=2\cdot 7-11=14-11=3$

3. If Z=8, then $N=2\cdot 8-11=16-11=5$

4. If Z=9, then $N=2\cdot 9-11=18-11=7$

Thus, four other possibilities are

$\begin{array}{cc}\text{Zac's score}&\text{Natan's score}\\ 6&1\\7&3\\8&5\\9&7\end{array}$

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3 years ago

Suppose you need to get the dent in your car fixed. You see the ads in the newspaper above (mikes repair shop $100 service charg

Norma-Jean [14]

Answer:

Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295, so I will take the car to Amy's shop

Point of intersection: (x,y) = (4,360)

Explanation:

Part 1 )

Let x = number of hours worked

Let y = total cost to you

Determining where to take the car:

Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295

Mike's repair shop:

Service fee: $100

Per hour rate: $65

Let x is the number of hours worked on. Total cost will be equal to the service fee plus hourly charges. Charges per an hour are $65, so for x hours the charges will be 65x.

Therefore, total cost for Amy's repair shop can be written as:

y = 100 + 65x ------(1)

For 3 hours work: y = 100 + 65(3)

Cost at Mike's, y = $100 + $195 = $295

Amy's repair shop: 

Service fee: $40

Per hour rate: $80

Charges per an hour are $40, so for x hours the charges will be 80x.

Therefore, total cost for Amy's repair shop can be written as:

y = 40 + 80x ------(2)

For 3 hours work: x = 3

y = 40 + 80(3)

Cost at Amy's, y = $40 + $240 = $280

Part 2)

Find the point of intersection

Using elimination method:

y = 100 + 65 x ------1

y = 40 + 80x ------2

As the y coefficients are equal we will subtract eq1 from eq2

y - y = 40 + 80x - 100 - 65x

0 = -60 + 15x

60 = 15x

x = $\frac{60}{4}$

x = 4

put x = 4 in eq 1

we get y = 100 + 65 (4) = 100 + 260 = 360

x = 4, y = 360

Point of intersection: (x,y) = (4,360)

8 0

3 years ago

1. If x=3-√3, prove that x² +36 x² = x²

valentina_108 [34]

Answer:

we get $x^2=12-6\sqrt{3}$

Step-by-step explanation:

We are given: $x=3-\sqrt{3}$

We need to find $x^2$

Note: Since question is not clear, I am assuming that we need to find $x^2$

Solving:

$x=3-\sqrt{3} \\Taking \ square \ on \ both \ sides\\x^2=(3-\sqrt{3})^2\\$

We know that $(a-b)^2= a^2-2ab+b^2$

Using formula and simplifying

$x^2=(3)^2-2(3)(\sqrt{3})+(\sqrt{3})^2\\x^2=9-6\sqrt{3} +3\\x^2=12-6\sqrt{3} \\$

So, we get $x^2=12-6\sqrt{3}$

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2 years ago

-4x11y=15 x=24 x= y=

ira [324]

Answer:

5/352

Step-by-step explanation:

-4x11y=15

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3 years ago

What is the approximate area of the shaded region? Circumscribed square with side length 8 meters. The four regions between the

myrzilka [38]

Answer:

13.76 square meters

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The side of square is 8 meters.

So, the diameter of circle = 8 meters.

⇒ Radius = (diameter of circle) ÷ 2 = 8 ÷ 2 = 4 meters

Shaded region = Area of square - Area of circle

= (Side × Side) - π × (radius)²

= 8 × 8 - π × 4 × 4 {∵ π = 3.14 or 22÷7}

= 64 - 50.24

= 13.76 square meter

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3 years ago