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2 months ago

Guest #5082

2 months ago

Grandfather is 57 and Miguel is 11 .Therefore, 57 + 11 =68 Miguel was 10 last year. In 3 years grandfather will be 60. 10 x 6= 60

Question

How can you prove a triangle is a right triangle? select one:a. use the distance formula to see if at least two sides are congruent.b. use the slope formula to see if any sides are perpendicular.c. use the distance formula to see if all three sides are congruent.d. use the slope formula to see if any sides are parallel?

Solution 1

B.

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Question

How many arrangements are possible using the letters in the word fuzzy if each letter "z" is distinctly different than the other? how many arrangements are possible if the letter "z" is interchangeable with the other? explain your reasoning?

Solution 1

Case 1: If the letter z is distinctly different

If we have the letter z which is distinctly different than the other "z", then we have five letters in the word F U Z Z Y and the number of arrangements would be = 5*4*3*2*1 =5! = **120 different arrangements**

Case 2: If the letter Z is interchangeable

If the letter "Z" is interchangeable with the other "z" then we have 2 letters which cancel out each other that would be represented by 2*1 = 2! = 2

So, the number of arrangements in this case would be 5!/2! = 5*4*3*2*1/2*1 = **60 arrangements**

Solution 2

120, 60

First answer is 5!, second answer is 5!/2 because swapping two z's does not generate a new permutation.

First answer is 5!, second answer is 5!/2 because swapping two z's does not generate a new permutation.

Question

The U-Drive Rent-A-Truck company plans to spend $15 million on 310 new vehicles. Each commercial van will cost $35 comma 000 , each small truck $70 comma 000 , and each large truck $60 comma 000 . Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?

Solution 1

Let x, y, and z be number of vans, small trucks and large trucks respectively. Therefore,

x+y+z = 310 ----- (1)

But, the company will spend $15 million. Then,

35000x+ 70000y +60000z = 15,000,000

35x + 70y + 60z = 15000 ---- (2)

Additionally, twice as many van as small trucks will be required. Then,

x = 2y ---- (3).

Substituting for x in (1) and (2);

2y +y +z = 310 => 3y +z =310 ---- (4)

35(2y) + 70y + 60z = 15000 => 70y+70y+60z = 15000 => 140y + 60z = 15000 ---- (5)

Solving (4) and (5)

From (4), z = 310 -3y

Then, using (5)

140y +60(310-3y) = 15000

140y + 18600 - 180y = 15000

-40y = -3600

y = 3600/40= 90

Then, z= 310 -3y = 310 -3(90) = 310 -270 = 40

And, x = 2y = 2(90) = 180

Therefore, the number will be:

Vans (x) = 180

Small trucks (y) = 90

Large trucks (z) = 40

x+y+z = 310 ----- (1)

But, the company will spend $15 million. Then,

35000x+ 70000y +60000z = 15,000,000

35x + 70y + 60z = 15000 ---- (2)

Additionally, twice as many van as small trucks will be required. Then,

x = 2y ---- (3).

Substituting for x in (1) and (2);

2y +y +z = 310 => 3y +z =310 ---- (4)

35(2y) + 70y + 60z = 15000 => 70y+70y+60z = 15000 => 140y + 60z = 15000 ---- (5)

Solving (4) and (5)

From (4), z = 310 -3y

Then, using (5)

140y +60(310-3y) = 15000

140y + 18600 - 180y = 15000

-40y = -3600

y = 3600/40= 90

Then, z= 310 -3y = 310 -3(90) = 310 -270 = 40

And, x = 2y = 2(90) = 180

Therefore, the number will be:

Vans (x) = 180

Small trucks (y) = 90

Large trucks (z) = 40

Question

How to solve when sally went bowling her scores were 108, 72, and 95. if she bowls a 4th game, what will her score need to be to give her an average of 91?

Solution 1

I love weed. it is great.

Question

If a recipe calls for 3 servings calls for 2 grams of saffron . how many mililgrams of saffron are needed for 6 servings

Solution 1

If 3 servings needs 2 grams then 6 servings needs twice as much. So 6 servings needs 4 grams which equals 4000 milligrams.

Question

Eliminate the parameter to find a cartesian equation of the curve. x = 3sin(t), y = 4cos(t)

Solution 1

Question

A 10ft pole is to be erected and held in the ground by four wires attached at the top. The guy wires are attached to the ground at a distance of 15 ft from the base poke. What is the exact length of each guy wire? how much wire should be purchased if it cannot be purchased in franctions of foot

Solution 1

The pole, guy wire and ground forms a right angled triangle with the guy wire being the hypotenuse.

Legs = 10 ft and 15 ft.

The length of guys wire = Sqrt (10^2+15^2) = ≈18.03 ft

A total of 4 guy wires.

Te total length required = 4* ≈ 72.11 ft.

Since wire cannot be bought in fractions of foot, the length is rounded to the next whole number. That is,

Length required = 73 ft.

Legs = 10 ft and 15 ft.

The length of guys wire = Sqrt (10^2+15^2) = ≈18.03 ft

A total of 4 guy wires.

Te total length required = 4* ≈ 72.11 ft.

Since wire cannot be bought in fractions of foot, the length is rounded to the next whole number. That is,

Length required = 73 ft.

Question

James has 16 balloons.1/4 of his balloons are red.How many red balloons does he have?

Solution 1

Hello!

First you have to convert the fraction to a decimal

1/4 = 0.25

Multiply the amount of balloons by the amount that are red

16 * 0.25 = 4

The answer is 4

Hope this helps!

First you have to convert the fraction to a decimal

1/4 = 0.25

Multiply the amount of balloons by the amount that are red

16 * 0.25 = 4

The answer is 4

Hope this helps!

Question

Find all solutions of the equation in the interval [0, 2π). (enter your answers as a comma-separated list. if there is no solution, enter no solution.) 6 cos3 x = 6 cos x

Solution 1

0, π/2, π, 3π/2

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Question

-7(8 + k)
-56 + 7k
-7k - 56
-7k + 56

Solution 1

I believe you want me to distribute?

-7(8+k)

= -56 -7k

-7(8+k)

= -56 -7k

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