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3 years ago

Is (4, 1) a solution to this system of inequalities? x ≥ 4 x + 7y ≤ 11

Mathematics

2 answers:

Naya [18.7K]3 years ago

6 0

Yess!!!!!!!!!!!!!!!!!!!!

My name is Ann [436]3 years ago

4 0

<h3>Answer: Yes (4,1) is a solution</h3>

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

Explanation:

Plug (x,y) = (4,1) into the first inequality

We replace x with 4. There is no y value to worry about here.

After doing so, x ≥ 4 turns into 4 ≥ 4 which is a true statement.

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Plug (x,y) = (4,1) into the second inequality

x + 7y ≤ 11 turns into 4 + 7(1) ≤ 11 which simplifies to 11 ≤ 11

This is also a true statement.

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

Both inequalities result in true statements after plugging in (x,y) = (4,1). Therefore, (4,1) is a solution.

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Eric, Cam, and Brooke are playing a game of mini golf on a computer. The computer program for the game stores

andrew-mc [135]

Answer:

Eric

Step-by-step explanation:

First, we determine the distance of each player to the hole using the distance formula.

Given points $(x_1,y_1)$ and (x_2,y_2)$

Distance $=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Eric

The hole is at (3,2)

Eric's golf ball is at point (-6,6)

Distance= $\sqrt{(-6-3)^2+(6-2)^2}$

$=\sqrt{(-9)^2+(4)^2}\\=\sqrt{97} \\\approx 9.85$

Cam

The hole is at (3,2)

Cam's golf ball is at point (8,-6)

Distance= $\sqrt{(8-3)^2+(-6-2)^2}$

$=\sqrt{(5)^2+(-8)^2}\\=\sqrt{89} \approx9.43$

Brooke

The hole is at (3,2)

Brooke's golf ball is at point (10,8)

$Distance=\sqrt{(10-3)^2+(8-2)^2}\\=\sqrt{(7)^2+(6)^2}\\=\sqrt{85} \approx 9.22$

Since Eric's ball is the farthest from the hole, Eric should shoot next.

7 0

3 years ago

forrest has pennies, nickels, dimes, and quarters in a cookie jar- a total of 201 coins. He has twice as many nickels as dimes a

Digiron [165]

We use letters to represent the unknown coins.
P for pennies that worth 1 cents
N for nickels that worth 5 cents
D for dimes that worth 10 cents
Q for quarters that worth 25 cents.

"He has twice as many nickels (N) as dimes (D)" So D=2N
"and four times as many pennies (P) as quarters (Q)." So Q=4P

Number of coins equals P+N+D+Q=P+N+2N+4P (Dimes and quarters are written in terms of nickels and pennies, respectively)

So, number of coins is equal to 5P+3N=201. Thats is the first equation (I)
To write the second equation, use cents of coins. 12.10 $ in coins can be shown as

5P. 1 cent + 3N. 5 cent=1210 cents or simply 5P + 15N=1210 (Second equation)

We have two equations and two unknowns so it is soluble.
number of coins: 5P+3N=201 (I)
cents of coins: 5P+15N=1210 (II)
Use the substitution method. (II) - (I)=12N=1009
N=1009/12=84 ( Actually it is 84.08)
D=2N=168
P= -10
Q=-40
Number of pennies and quarters are meaningless. They can't be negative. So they should be something wrong in the question.

3 0

3 years ago

Find the length indicated Find EG

Oksi-84 [34.3K]

Answer:

hope you don't mind but im using this for points

6 0

3 years ago

Every week,Mr.Kirkson uses 3/16 gallon of water to every 1/3 square foot of his garden hiw many gallons of water does mr.Kirkson

nadezda [96]

Answer:

9/16 gallons

Step-by-step explanation:

We can use a ratio to solve

3 /16 gallon x gallons

------------------ = --------------

1/3 ft^2 1 ft^2

Using cross products

3/16 * 1 = 1/3 x

Multiply each side by 3

3/16 * 3 = 1/3x *3

9/16 = x

9/16 gallons

5 0

3 years ago

Solve the inequality d – 6 < –0.5 and graph the solutions.

joja [24]

Answer:

Hope it will help you :)

Step-by-step explanation:

d-6<-0.5

Adding 6in both sides to find out the value of d

d-6+6<-0.5+6

d<5.5

Solution set={d/d<5.5}

7 0

3 years ago