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3 years ago

Which set of side lengths form a right triangle?

1 answer:

8 0

If you have a right triangle, you can use the Pythagorean theorem, which is a²+b²=c². (c is the longest side or the hypotenuse)

You plug in the shorter sides for a and b, then you square root the answer.

A 14m, 20m, 25m

14² + 20² = 25²

196 + 400 = 625

596 = 625 X

B 10cm, 6cm, 8cm

6²+8²=10²

36+64=100

100=100 So your answer is B

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The price of oil, in dollars per barrel, declined last week by 3.5%. If it started the week at 102.00 per barrel, at what per ba

scoray [572]

Answer:

98.57

Step-by-step explanation:

3.5% over 100% X 102=3.43

102-3.43= 98.57

6 0

3 years ago

Chemistry is an experimental science in which a consistent system of measurements is used. Scientists throughout the world use t

Elena L [17]

Answer:

(a) 142 km trip requires 15.16 Liters of Gasoline

(b) The money spent is 69.34 euros or $87.37.

(d) 4 lb of candy contains 0.559 kg of dietary fat.

Step-by-step explanation:

(a)

Given that;

Mileage = 22 mi/gal

Converting it to km/L

Mileage = (22 mi/gal)(1 gal/3.78 L)(1 km/0.6214 mi)

Mileage = 9.36 km/L

Now, the gasoline required for 142 km trip:

Gasoline Required = (Length of trip)/(Mileage)

Gasoline Required = (142 km)/(9.36 km/L)

Gasoline Required = 15.16 L

(b)

Given that;

Mileage = 30 mi/gal

Converting it to km/L

Mileage = (30 mi/gal)(1 gal/3.78 L)(1 km/0.6214 mi)

Mileage = 12.77 km/L

Now, the gasoline required for 142 km trip:

Gasoline Required = (Length of trip)/(Mileage)

Gasoline Required = (115 km/day)(7 days/week)/(12.77 km/L)

Gasoline Required = 63 L/week

Now, we find the cost:

Weekly Cost = (Gasoline Required)(Unit Cost)

Weekly Cost = (63 L/week)(1.1 euros/L)

Weekly Cost = 69.34 euros/week = $87.37

since, 1 euro = $1.26

(c)

Average Speed = (Distance Travelled)/(Time Taken)

Average Speed = 200 m/20.9 s

Average Speed = (9.57 m/s)(3600 s/1 h)(1 km/ 1000 m)

Average Speed = 34.45 km/h

(d)

22.7 g piece contains = 7 g dietary fat

(22.7 g)(1 lb/453.592 g) piece contains = (7 g)(1 kg/1000 g) dietary fat

0.05 lb piece contains = 0.007 kg dietary fat

1 lb piece contains = (0.007/0.05) kg dietary fat

4 lb piece contains = 4(0.007/0.05) kg dietary fat

4 lb piece contains = 0.559 kg dietary fat

8 0

3 years ago

What is half way between -5 degrees F and postive 15 degrees F?

andre [41]

To find the halfway points between two numbers, add the numbers and divide the quantity by 2. -5+15 equals 10 and 10/2=5 therefore 5 is halfway between -5 and 15.

3 0

3 years ago

The value of y varies directly with x.

Usimov [2.4K]

Answer:

Step-by-step explanation:

Hello. Y/x = a constant k because y and x are by definition always in the same ratio. (y varies directly as x so if x is doubled y is also doubled etc.)

4 0

2 years ago

Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each

Basile [38]

Answer:

Part 1) The inequality that describes the relationship between the number of cookies each one of them has is $x^{2} -30x+224\geq 0$

Part 2) Jessica has at least 2 cookies more than Martha

Step-by-step explanation:

Part 1) Find the inequality that describes the relationship between the number of cookies each one of them has

Let

x----> the number of cookies when Jessica started

30-x ----> the number of cookies when Martha started

we know that

Each of them ate 6 cookies from their bag

The cookies left in each bag are

(x-6) ----> Jessica

and (30-x-6)=(24-x) ---> Martha

The product is equal to (x-6)(24-x)

The product of the number of cookies left in each bag is not more than 80.

$(x-6)(24-x)\leq 80\\ \\24x-x^{2}-144+6x\leq 80\\ \\-x^{2} +30x-144-80\leq 0\\ \\-x^{2} +30x-224\leq 0$

Multiply by -1 both sides

$x^{2} -30x+224\geq 0$

Part 2) Solve the quadratic equation

$x^{2} -30x+224\geq 0$

Solve by graphing

The solution is x=16 cookies

(30-x)=30-16=14 cookies

therefore

The number of cookies when Jessica started was 16 cookies

The number of cookies when Martha started was 14 cookies

The number of cookies left in each bag is equal to

Jessica

16-6=10 cookies

Martha

14-6=8 cookies

Jessica has at least 2 cookies more than Martha

7 0

2 years ago

Read 2 more answers