The numbers are (-8, 3) or (3, -8).
Step-by-step explanation:
- Step 1: Given the product of the numbers are -24 and their sum are -5. Let the numbers be a and b. Form equations out of these details.
⇒ a + b = -5 ⇒ b = -5 - a
⇒ a × b = -24 -------- (1)
- Step 2: Substitute the value of b in eq(1)
⇒ a × (-5 - a) = - 24
⇒ -5a - a² = -24
⇒ a² + 5a - 24 = 0
- Step 3: Solve the quadratic equation for a.
a = (-5 ± √25 - 4 × 1 × -24)/2
= (-5 ± √121)/2
= - 16/2, 6/2 = -8 or 3
- Step 4: For each value of a, find b.
When a = -8, b = -5 +8 = 3
When a = 3, b = -5 - 3 = -8.
Answer:
The measure of angle A is 53 degrees
The measure of angle B is 37 degrees
Step-by-step explanation:
Here in this question, we are interested in calculating the measure of the two angle.
When how angles are complementary, it means the sum of both equals 90 degrees
mathematically ;
(7x + 4) + (4x + 9) = 90
7x + 4x + 4 + 9 = 90
11x + 13 = 90
11x = 90-13
11x = 77
x = 77/11 = 7
The measure of angle A = 7x + 4 = 7(7) + 4 = 49 + 4 = 53 degrees
The measure of B = 4x + 9 = 4(7) + 9 = 28 + 9 = 37 degrees
A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 3 weeks, the sheet is only 1.25 meters thick. Let y represent the ice sheet's thickness ( in meters) after x weeks. Complete the equation for the relationship between the thickness and number of weeks.
Answer:
y = 2 - 0.25x
Step-by-step explanation:
From the question, the initial thickness of the ice sheet = 2 meters,
After 3 weeks, the thickness of ice sheet reduced to 1.25 meters
Hence, the difference in the thickness in 3 weeks is calculated as:
2m - 1.25m = 0.75m
The amount of changes that occurred in 3 weeks is given as:
= 0.75/3 = 0.25 meters,
We are told that, the ice is melting with the constant rate.
Therefore, the equation for the relationship between the thickness and number of weeks is given as:
y = 2 - 0.25x
Answer:
the answer is two groups. six times two is 12, 12 is one less than 13 but six cannot go into one
Each bus was filled with 54 students
