If Carla runs across the park along the diagonal instead of along the streets, how many yards of running will she save?

2 people share 4/3 feet of rope. What length of rope should each friend get?

melisa1 [442]

2 x $\frac{4}{3}$ = $\frac{6}{3} * \frac{2}{3} = \frac{12}{9} = \frac{4}{3}$

5 0

3 years ago

A biology test is worth 100 points and has 36 questions.

Ad libitum [116K]

Answer:

(a) 7 essays and 29 multiple questions

(b) Your friend is incorrect

Step-by-step explanation:

Represent multiple choice with M and essay with E.

So:

$M + E= 36$ --- Number of questions

$2M + 6E = 100$ --- Points

Solving (a): Number of question of each type.

Make E the subject of formula in $M + E= 36$

$E = 36 - M$

Substitute 36 - M for E in $2M + 6E = 100$

$2M + 6(36 - M) = 100$

$2M + 216 - 6M = 100$

Collect Like Terms

$2M - 6M = 100 - 216$

$-4M = - 116$

Divide both sides by -4

$M = \frac{-116}{-4}$

$M = 29$

Substitute 29 for M in $E = 36 - M$

$E = 36 - 29$

$E = 7$

Solving (b): Can the multiple questions worth 4 points each?

It is not possible.

See explanation.

If multiple question worth 4 points each, then

$2M + 6E = 100$ would be:

$4M + xE = 100$

Where x represents the number of points for essay questions.

Substitute 7 for E and 29 for M.

$4 * 29 + x * 7 = 100$

$116 + 7x = 100$

Subtract 116 from both sides

$116-116 + 7x = 100 -116$

$7x = 100-116$

$7x = -16$

Make x the subject

$x = -\frac{16}{7}$

Since the essay question can not have worth negative points.

Then, it is impossible to have the multiple questions worth 4 points

<em>Your friend is incorrect.</em>

6 0

2 years ago

13. Find the surface area of each figure to the nearest tenth. Show your work.

stiv31 [10]

A. The figure is a triangular pyramid. You can findits surface area by adding up the area of the three faces of the triangle and the area of the base. A derived formula also is used where the SA is equal to 12 times the perimeter of base times the slant height, added to that is the area of the base. The area of the square base is s^2. Its perimeter is 4s.

SA of Pyramid = 12*P*l + s^2
SA of Pyramid = 12*4s*l + 16^2
SA of Pyramid = 12*4(16)*(17) + (16)^2
SA of Pyramid = 11,008 square inches

b.) The formula for the SA of a cone is:

SA of cone = πr[r+√(h^2+r^2)]
SA of cone = π(3)[(3+√(8^2+3^2)]
SA of cone = 108.8 square inches

7 0

3 years ago

Read 2 more answers

ABC and CBD form a linear pair and have equal measures. Tell if ABC is acute, right, or obtuse

Murrr4er [49]

To form a linear pair means that when added, they equal 180 degrees.
but if they have equal measures....180/2 = 90...then they would both equal 90 degrees.....and 90 degrees is a right angle.
So ABC and CBD are both right angles

6 0

3 years ago

Read 2 more answers

Alfred works for a graphic design firm. He is making a poster to raise awareness for global warming. Which type of poster is he

12345 [234]

Answer: The answer is A

Step-by-step explanation: The answer is A because he is try to spread awareness for global warming which is informative.

6 0

3 years ago