Find two positive numbers whose product is 36 and whose sum is a minimum.

The expression sin(2x) − sinx is equivalent to 2sin (3x/2) sin(x/2) therefore option (D) is correct.

Recall the formula of sine

[tex]\sin x-\sin y=2 \sin (\frac{x+y}{2}) \sin (\frac{x-y}{2})[/tex]

The given expression is sin (2x) − sin x.

Apply the formula

[tex]\sin (2x) - \sin x =2 \sin (\frac{2x+x}{2}) \sin (\frac{2x-x}{2})[/tex]

                      [tex]=2 \sin (\frac{3x}{2}) \sin (\frac{x}{2})[/tex]

Hence the expression is equivalent to 2sin (3x/2) sin(x/2)

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He needs 15 weeks to pay back his brother completely.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Hugo decided to pay $2 a week to his brother to buy a bicycle.

The equation y - 10 = - 2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.

To pay back to the brother he must owe no money which is y = 0.

∴ The weeks needed is,

0 - 10 = -2(x - 10).

- 10 = -2x + 20.

2x = 30.

x = 15.

He needs 15 weeks to pay back completely.

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To solve the linear system given by -14x + 11y = 23 and 7x - 3y = 37, we used the elimination method, which resulted in finding the solution x = 13.6 and y = 19.4.

To solve the system of linear equations given by -14x + 11y = 23 and 7x - 3y = 37, you can use the method of substitution or elimination. Here, I'll demonstrate the elimination method:

Therefore, the solution to the system of equations is x = 13.6 and y = 19.4.

The area of rectangle is 60 yd²

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The length of a rectangle is 4 yd longer than its width.

Let, the length = x

And, width = y

Now,

Perimeter of rectangle = 2(x+y)

the area of rectangle = xy

x = y+ 4

2(x+y) = 32

Subtract x by equation (1) in (2), we get;

2(y+4+y) = 32

2y+8 +2y = 32

4y = 24

y= 24\4

y  =6yd

And, x = 6+4

x  = 10yd

Thus, Area of rectangle = xy

                                   = 10 × 6

                                   = 60yd²

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After testing each given point by substituting them into the inequality y > -2x + 5, only the point (1, 4) satisfies the condition, making it the correct answer.

The question is asking to find which point among the options given satisfies the inequality y > -2x + 5. To solve this, we will substitute the x and y values from each option into the inequality and check whether the inequality holds.

For (1, 4), if we substitute x = 1 and y = 4 we get 4 > -2(1) + 5, which simplifies to 4 > 3. Since this is true, this point is a solution.

For (0, 5), if we substitute x = 0 and y = 5 we get 5 > -2(0) + 5, which simplifies to 5 > 5. Since this is not true (it should be strictly greater), this point is not a solution.

For (-2, 8), if we substitute x = -2 and y = 8 we get 8 > -2(-2) + 5, which simplifies to 8 > 9. Since this is not true, this point is not a solution.

For (1, -2), if we substitute x = 1 and y = -2 we get -2 > -2(1) + 5, which simplifies to -2 > 3. Since this is not true, this point is not a solution.

Therefore, the correct answer is the point (1, 4) as it is the only one that satisfies the given inequality.

Answer: b. 300 feet

Step-by-step explanation:

We know that 1 yard = 3 feet

Given : The length of a football playing field is 100 yards between the opposing goal lines.

Then, the length of the football field in feet will be :-

[tex]100\times3=300[/tex]

Therefore, the length of the football field in feet = 300 feet

Hence b is the correct option.

Answer:

Option D. 4 or more times

Step-by-step explanation:

we have

[tex]3t+10\geq 22[/tex]

Solve for t

Subtract 10 both sides

[tex]3t+10-10\geq 22-10[/tex]

[tex]3t\geq 12[/tex]

Divide by 3 both sides

[tex]t\geq 4\ times[/tex]

The solution is all real numbers greater than or equal to 4

therefore

4 or more times

Answer:

Option D is the correct answer.

Step-by-step explanation:

The inequality is given by 3t + 10 ≥ 22, where t is the number of loops Elena rides in the park.

Solving we will get

                            3t + 10 ≥ 22                            

                            3t  ≥ 22 - 10

                              3t ≥ 12

                                t ≥ 4

That is t is 4 or more times,

Number of times Elena need to ride around the loop is 4 or more times.

Option D is the correct answer.

The woman's average speed is 49 miles per hour, so in 7 hours she will travel 343 miles.

To solve how far a woman will drive in 7 hours at the same rate as she did for 245 miles in 5 hours, we need to calculate her average speed and then use that to find the distance for 7 hours. The average speed is calculated by dividing the total distance by the total time of travel. So in this case, the average speed is 245 miles divided by 5 hours, which is 49 miles per hour.

Next, to find out how far she will travel in 7 hours, we multiply her average speed by the total time of travel. Therefore, 49 miles per hour multiplied by 7 hours equals 343 miles.

Answer:the awnser is c 76

Step-by-step explanation:

Answer:

[tex]2h+20[/tex]

Step-by-step explanation:

It is given that there are two trees in Jon yard, where one tree is 20 feet taller than the other.

We need to find the algebraic expression for the sum of the two trees' heights.

So, in order to solve that we first need to find the height of individual trees then we have to add.

Also, It is given that the height of the smaller tree is h.

So, height of the larger tree is [tex]h+20[/tex]

Now, the total height of both the trees [tex]=h+h+20[/tex]

[tex]=2h+20[/tex]

Hence, the total height of both the trees is [tex]2h+20[/tex].

Answer:

600

Step-by-step explanation:

145% can be written as 145/100.

"of" is another word for multiplication in math

"x" will be the variable for the number

The equation:

145/100x=870

Here, we simplify the equation:

Step 1 (write the equation): 145/100x=870

Step 2 (multiply both sides by 100): 145x = 87000

Step 3 (divide both sides by 145): x=600

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Answer:

Thus, she has enough pizza left for the meeting.

Step-by-step explanation:

It is given that, Cyndi cut pizza in 12 pieces.

Also, She ate 1/6 of pizza yesterday afternoon.

⇒ She ate = [tex]12\times\frac{1}{6} = 2\ \text{pieces}[/tex]

Her Brother ate 1/5 of left pizza

⇒ Her Brother ate = [tex]10\times\frac{1}{5} = 2\ \text{pieces}[/tex]

Then she has left pieces of pizza = 12 - (2 + 2) = 8 pieces

And also that much pieces she wants for the club meeting.

Thus, she has enough pizza left for the meeting.

 all the coordinates of the original triangle have been multiplied by 1/2

A (-4,-6) x 1/2 = -2,-3

B (-8,2) * 1/2 = -4,1

C (-2,4)  *1/2 = -1,2

 so the scale factor is 1/2

 Answer is B

An equation is formed of two equal expressions. The number is 1,011.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the unknown number be represented by x.

Given that if you add one-third of a number to itself, you get 1348. Therefore, we can write the given statement in the form of an equation as,

(1/3)x + x = 1348

(x/3) + (3x/3) = 1348

(x + 3x)/3 = 1348

4x / 3 = 1348

4x = 1348 × 3

x = (1348×3)/4

x = 1011

Hence, the number is 1,011.

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Answer:

3

Step-by-step explanation:

Similar problem to a previous one that I solved