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3 years ago

What two integers have a sum of -31 and a difference of -55?

Mathematics

1 answer:

nekit [7.7K]3 years ago

3 0

Answer:

Integer 1 is x

Integer 2 is y

x + y = -31

x - y = -55

Add:

2x = -86

x = -43

Substitute:

-43 + y = -31

y = 12

Therefore, the two integers are: 12 and -43

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Every day going to school, June has to go by boat (point A) over a 217m-wide river to point B (the other bank), and then from B

Anit [1.1K]

Answer:

647m

Explanation:

The distance traveled by June, from A to D, is the sum of the distance from A to C plus the distance from C to D:

Travel from A to D = Distance AC + Distance DC.

1) Find the distance AC

Triangle ABC is a right triangle, from which you have to calculate the hypotenuse (AC), knowing angle A (50º), and its adjacent leg (217 m).

cos (50º) = 217m / AC

AC = 217m / cos (50º) = 337.59m

2) Find the distance DC

First, you need to calculate the side BC which is a common side of both triangles ABC and DBC.

You can use Pythagora's or a trigonometric function (tangent or sine).

tan (50º) = BC / 217 m ⇒ BC = 217 m × tan (50º) = 258.61 m

Now you can use Pythagora's theorem to find the distance DC, which is the hypotenuse of the triangle DBC:

DC² = (170m)² + (258.62)² = 95,779.41m²

DC = 309.48m

3) Find the total distance traveled from A to D

Travel from A to D = Distance AC + Distance DC = 337.59m + 309.48m = 647.07 m ≈ 647m.

4 0

3 years ago

Which triangle correctly shows that the side opposite the larger angle is the larger side?

user100 [1]

Answer:

A triangle has side lengths of 13, 5, 10 and angle measures of 30 degrees, 100 degrees, and 50 degrees.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A reporter collects a random sample of 50 runners from all the runners who finished the Cherry Blossom Ten Mile Run in 2009 and

goldenfox [79]

Answer:

Option D

Step-by-step explanation:

A reporter collects a random sample of 50 runners from all the runners who finished the Cherry Blossom Ten Mile Run in 2009 and constructs a 99% confidence interval for the true mean finish time to be (86.05, 99.38) minutes.

Assuming the reporter performed the calculations correctly, which of the following statements are appropriate interpretations of this confidence interval?

We can expect that 99% of confidence intervals created using the same method the reporter used will contain the true mean run time for runners of this race.

4 0

3 years ago

4. Parking fees at IIUM are RM 5.00 for IIUM students and RM 7.50 for non-IIUM students. At the

professor190 [17]

Answer:

(a) 780 students and 960 non-students

(b) No. The maximum revenue is RM9000 from 1200 non-students.

(c). Revenue is maximum of RM9000 at 1200 non-students, decreasing by RM2.50 per student to a minimum of RM6000 at 1200 students

Step-by-step explanation:

Let x = IIUM students and

and y = non-IIUM students

You have two conditions

(a) x + y = total vehicles parked

(b) 5.00x + 7.50y = total gross receipts

(a) Wednesday

From your table,

x + y = 1740

5.00x + 7.70y = RM11 100

Solve the simultaneous equations

$\begin{array}{rrcrl}(1) & x + y & = &1740&\\(2) & 5.00x + 7.50y & = & 11 100\\(3)& 5.00x + 5.00y & = & 8700 & \text{Multiplied (1) by 5}\\&2.50 y & = &2400 &\text{Subtracted (3) from (2)}\\(4)&y& = &\mathbf{960} &\text{Divided each side by 2.50}\\& x +960& = &1740& \text{Substituted (4) into (1)}\\& x& = &\mathbf{780}& \\\end{array}\\\text{There are $\large \boxed{\textbf{780 students and 960 non-students}}$}$

(b) Can 1200 vehicles bring in RM10000?

No. Even if all the cars were from non-students, the most you could get is

1200 × 7.50 = RM9000

(c) Possible combinations for 1200 vehicles

Revenue = 5.00x + 7.50y = 5.00x + 7.50(1200 -x) = 5.00x + 9000 - 7.50x =

Revenue = 9000 - 2.50x

The maximum revenue of RM9000 occurs when there are no student cars and 1200 non-student cars.

For each student car that enters and displaces a non-student, the revenue drops by RM2.50.

Finally. when there are 1200 student cars and no non-students, the revenue has dropped to a minimum of RM6000.

3 0

3 years ago

Can someone tell me what 8 x 1 1/2 equals

Lady_Fox [76]

8 x 1 = 8
8 x 1/2 = 4
8+4 =12
therefore, 8 x 1 1/2 = 12

7 0

4 years ago

Read 2 more answers