MATHEMATICS HIGH SCHOOL

Which choice is equivalent to the expression below?2√2 + √18 + √8

A.7√2
B.8√2
C.6√2
D.4√2

Answers

Answer 1
Answer: 2\sqrt2+√(18)+\sqrt8=2\sqrt2+√(9\cdot2)+√(4\cdot2)\n\n=2\sqrt2+\sqrt9\cdot\sqrt2+\sqrt4\cdot\sqrt2=2\sqrt2+3\sqrt2+2\sqrt2=7\sqrt2\n\nAnswer:A.\ 7\sqrt2
Answer 2
Answer: √(18) = √(3*3*2) = 3√(2) \n √(8) = √(2*2*2) =2 √(2) \n 2 √(2) + 3 √(2) + 2√(2) = 7 √(2)

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What causal link can be inferred from this statement? As weather conditions change, birds migrate from one region to another for breeding.Weather changes cause birds to breed.
Weather changes cause bird migration.
Migrating birds cause weather changes.
Breeding birds cause weather changes.
Bird breeding causes bird migration.

Answers

Weather changes cause bird migration.

B weather changes cause bird migration


Solve 2cos x+2cos 2x=0 on the interval [0,2pi)

Answers

2cosx+2cos2x=0 \n -2sin^2x+2cos^2x+2cosx=0 \n -2(1-cos^2x)+2cos^2x+2cosx=0 \n -2+2cos^2x+2cos^2x+2cosx=0 \n 4cos^2x+2cosx-2=0 \n t=cos x \n 4t^2+2t-2=0 \n \Delta=4+32=36 \n t_1= (-2-6)/(8)=-1 \n t_2= (-2+6)/(8)= (1)/(2) \n cos x=-1 \lor cos x= (1)/(2) \n x=-\pi \lor x= (5\pi)/(3)

Which fraction is equivalent to 7/15?
A. 14/28
B. 14/17
C. 21/45
D. 21/35

Answers

C. 21/45

If you multiply both the 7 and 15 by 3, you get 21 and 45.

(7)/(15) × (3)/(3) = (21)/(45)
THe answer is C since you multiply the numerator and denominator by 3

Simplify the polynomial.

1. 4a²b + 5 - 6a³b - 3a²b + 2a³b

Answers

1.\n \n 4a^2b + 5 - 6a^3b - 3a^2b + 2a^3b = \n \n = - 6a^3b + 2a^3b +4a^2b - 3a^2b+ 5=\n \n= - 4a^3b + a^2b + 5
4a²b + 5 - 6a³b - 3a²b + 2a³b

We first simplify similar expressions,

4a²b - 3a²b + 5 -6a³b + 2a³b

= a²b + 5 - 4a³b

PLZZZZ HELP WILL MARK BRAINLIEST IF CORRECT8. While doing bicep curls, Tamara applies 155 Newtons of force to lift the dumbbell. Her forearm is 0.366 meters long and
she begins the bicep curl with her elbow bent at a 15° angle below the horizontal, in the direction of the positive x-axis.
Determine the magnitude of the torque about her elbow.
(Show work)

Answers

Answer:

54.8 Nm

Step-by-step explanation:

Torque is the cross product of the radius vector and force vector:

τ = r × F

Another way to write it is the product of the radius and force magnitudes times the sine of the angle between the vectors.

τ = rF sin θ

Here, r = 0.366 meters and F = 155 Newtons.  F is in the +y direction, and r is 15° below the +x axis, so the angle between the vectors is 90° − 15° = 75°.

τ = (0.366 m) (155 N) (sin 75°)

τ = 54.8 Nm

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26 students in a hostel have provisions for 60 days if 10 more student are admitted to the hostel for how many days would the provisions be enough?​

Answers

Answer:

About 43 days

Step-by-step explanation:

Let's assume that the provisions in the hostel are consumed at a constant rate by each student per day. To find out how long the provisions would last with an additional 10 students, we need to consider the total number of students after the new admissions.

Initially, there are 26 students, and the provisions last for 60 days. Therefore, the total provision "student-days" is 26 students multiplied by 60 days, which equals 1560 student-days.

If 10 more students are admitted, the total number of students becomes 26 + 10 = 36 students.

To calculate how many days the provisions would last for 36 students, we divide the total provision "student-days" by the new total number of students:

1560 student-days / 36 students = 43.33 days (approximately)

Therefore, with 10 more students admitted, the provisions would be enough for approximately 43 days.

Answer:

44 days for the 36 students.

Step-by-step explanation:

Let's break down the information given:

Initially, there are 26 students in the hostel and provisions for 60 days. This means that the total "student-days" that the provisions can support is 26 students * 60 days = 1560 student-days.

Now, 10 more students are admitted to the hostel. So, the total number of students becomes 26 + 10 = 36 students.

We want to find out for how many days the provisions will be enough for these 36 students.

We can set up a proportion to solve this:

Initial student-days = New student-days

1560 student-days = 36 students * x days

Now solve for x:

x = 1560 student-days / 36 students

x = 43.33 days

Since you can't have a fraction of a day, we'll round up to the nearest whole day. Therefore, the provisions would be enough for approximately 44 days for the 36 students.
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