1. Using the right triangle above, fill in the correct ratios for each trigonometric function. (do not simplify)

Sav [38]

Answer: con que cariño?

Step-by-step explanation:

3 0

2 years ago

Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.

sattari [20]

Answer:

Solutions: (2,10), (4,5)

Not solutions: (1,12), (6,10), (12,8), (18,6)

Step-by-step explanation:

Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.

1. Tyler has $36, then

$x+3y\le 36.$

2. Tyler can carry up to 20 pounds of food in his backpack, then

$x+1.5y\le 20.$

You get the following system of inequalities:

$\left\{\begin{array}{l}x+3y\le 36\\ x+1.5y\le 20\end{array}\right.$

Now substitute the coordinates of each point:

(1,12):

$\left\{\begin{array}{l}1+3\cdot 12=37> 36\\ 1+1.5\cdot 12=19\le 20\end{array}\right.$

False, because first inequality doesn't hold.

(2,10):

$\left\{\begin{array}{l}2+3\cdot 10=32\le 36\\ 2+1.5\cdot 10=17\le 20\end{array}\right.$

True, both inequalities hold.

(4,5):

$\left\{\begin{array}{l}4+3\cdot 5=19\le 36\\ 4+1.5\cdot 5=11.5\le 20\end{array}\right.$

True, both inequalities hold.

(6,10):

$\left\{\begin{array}{l}6+3\cdot 10=36\le 36\\ 6+1.5\cdot 10=21> 20\end{array}\right.$

False, because secondt inequality doesn't hold.

(12,8):

$\left\{\begin{array}{l}12+3\cdot 8=36\le 36\\ 12+1.5\cdot 8=24> 20\end{array}\right.$

False, because second inequality doesn't hold.

(18,6):

$\left\{\begin{array}{l}18+3\cdot 6=36\le 36\\ 18+1.5\cdot 6=27> 20\end{array}\right.$

False, because second inequality doesn't hold.

7 0

3 years ago

The population in the city is 4000 people. The population decreased by 42%. What is the new population?

soldi70 [24.7K]

2,320 people is the new population amount.

8 0

3 years ago

Read 2 more answers

Which graph shows the solution to the system of linear inequalities?

Korvikt [17]

Answer:

Send q picture of the graphs so I can help

Step-by-step explanation:

need pictures of graph

4 0

3 years ago

You are going to mow your neighbor's lawn for some extra money. Below is a scale drawing of their lawn, where each square repres

Colt1911 [192]

9514 1404 393

Answer:

rectangle; parallelogram with 90° angle
150 feet
$40 flat rate

Step-by-step explanation:

1. The slope of AB is ...

mAB = (yB-yA)/(xB-xA) = (4-0)/(6-3) = 4/3

The slope of AD is ...

mAD = (yD-yA)/(xD-xA) = (6-0)/(-5-3) = 6/-8 = -3/4

The product of these slopes is (4/3)(-3/4) = -1, so the segments AB and AD are perpendicular.

The midpoints of AC and BD will be the same if the sum of their coordinates is the same:

A+C = (3, 0) +(-2, 10) = (1, 10)

B+D = (6, 4) +(-5, 6) = (1, 10)

The midpoints of the diagonals of ABCD are the same, so the figure is a parallelogram. One corner angle is 90°, so the parallelogram is a rectangle. The quadrilateral ABCD is a rectangle.

__

2. Using the coordinate differences found in part 1, we know the length AB is the hypotenuse of a 3-4-5 triangle, so is 5 grid squares. Similarly, the length of AD is twice that length, so is 10 grid squares. The perimeter in grid squares is ...

P = 2(L+W) = 2(10+5) = 30 . . . . grid squares

Each grid square represents 5 ft, so the perimeter is ...

(30 squares)(5 ft/square) = 150 ft . . . perimeter

__

3. The rectangle is 5 × 10 grid squares, or 25 × 50 ft. Then its area is ...

A = LW = (50 ft)(25 ft) = 1250 ft²

At $0.03/ft², the payment for mowing would be ...

($0.03/ft²)(1250 ft²) = $37.50

The $40 flat rate would make you the most money.

5 0

2 years ago