MATHEMATICS
COLLEGE

Answer:

Answer:: To solve problems for the area of a reduced or enlarged figure, first square the scale factor. Then use the given dimensions to find the area of the original figure. Multiply the square of the scale factor by the area of the original to get the reduced or enlarged figure.

Step-by-step explanation:

Answer: Find the area of the original figure and multiply that by the square of the scale factor.

MIDDLE SCHOOL

Show work for this problem 3(x+5)=2(3x+12)

I can help!!

Let's solve your equation step-by-step.

3(x+5)=2(3x+12)

Step 1: Simplify both sides of the equation.3(x+5)=2(3x+12)

(3)(x)+(3)(5)=(2)(3x)+(2)(12)(Distribute)

3x+15=6x+24

Step 2: Subtract 6x from both sides.3x+15−6x=6x+24−6x

−3x+15=24

Step 3: Subtract 15 from both sides.

−3x+15−15=24−15

−3x=9

Step 4: Divide both sides by -3.

−3x−3=9−3

x=−3

Answer:x=−3

Hope this helps!!

Let's solve your equation step-by-step.

3(x+5)=2(3x+12)

Step 1: Simplify both sides of the equation.3(x+5)=2(3x+12)

(3)(x)+(3)(5)=(2)(3x)+(2)(12)(Distribute)

3x+15=6x+24

Step 2: Subtract 6x from both sides.3x+15−6x=6x+24−6x

−3x+15=24

Step 3: Subtract 15 from both sides.

−3x+15−15=24−15

−3x=9

Step 4: Divide both sides by -3.

−3x−3=9−3

x=−3

Answer:x=−3

Hope this helps!!

Expand 3(x + 5): 3x + 15

Expand 2(3x + 12): 6x + 24

3x+ 15=6x + 24

then, subtract 15 from both sides

Simplify,

3x= 6x + 9

subtract 6x from both sides

3x - 6x= 6x + 9 - 6x

Simplify,

-3x=9

divide both sides by -3

-3x/-3 = 9/-3

Simplify,

x= -3, which is the final answer

Expand 2(3x + 12): 6x + 24

3x+ 15=6x + 24

then, subtract 15 from both sides

Simplify,

3x= 6x + 9

subtract 6x from both sides

3x - 6x= 6x + 9 - 6x

Simplify,

-3x=9

divide both sides by -3

-3x/-3 = 9/-3

Simplify,

x= -3, which is the final answer

HIGH SCHOOL

Circle A is inscribed in a quadrilateral. What is the perimeter of the quadrilateral?

AB + CD = BC + DA

Where A, B, C, and D are points on the quad, and AB is the length of the line A to B, etc.

Since you know three sides, you can easily solve for the fourth.

Where A, B, C, and D are points on the quad, and AB is the length of the line A to B, etc.

Since you know three sides, you can easily solve for the fourth.

COLLEGE

f. The student is conducting a nutrition experiment using lab rats. One group (control group) is fed a normal diet, while the other group (experimental group) is fed a diet high in protein. There were 30 rats total used in the experiment. At the end of the experiment, the average mass (weight) of a rat in the control group was 60.4 g while the average mass (weight) of a rat in the experimental group was 0.0689 kg. What is the average difference in weight between the two groups in grams

Answer: 4.25g

Step-by-step explanation:

If a student is conducting a nutrition experiment using lab rats and one group (control group) is fed a normal diet, while the other group (experimental group) is fed a diet high in protein, and at the end of the experiment, the average mass of a rat in the control group was 60.4g while the average mass of a rat in the experimental group was 0.0689 kg (68.9g), the average difference in weight between the two groups in grams would be as follows:

68.9 minus 60.4 = 8.5

8.5; divided by 2 = 4.25g

Question says find the average difference in weight between two groups in grams but first we should know that unit of weight cannot be the gram because it is the unit of force while gram is the unit of mass of a body.

Here due to confusion between, I am going to explain basic difference between mass and weight. Also, I find both average difference in weight as well as mass.

Answer:

Average difference in Weight=41.65units

Average difference in Mass=4.25g

Step-by-step explanation:

Mass:

- Quantity of matter contained in a body is called mass.

- it's unit is kilogram/gram

Weight:

- Force exerted on a body due to gravity.

- it's unit newton/lbf (pound force)

Given:

The average mass of a rate in control group is =m1= 60.4g

The average mass of a rat in experimental group is =m2= 0.0689kg

Required:

A) Average difference in mass=?

B) Average difference in weight=?

Solution:

To find the difference first we need to make the units same as grams.

m1=60.4g

m2=0.0689kg=0.0689*1000=68.9g (1kg=1000g)

A) Average difference in mass=?

Average difference in mass= the difference in average masses of two groups.

Average difference in mass= =

B) Average difference in weight=?

As we know

weight=w=mg (g=gravitational force=9.8)

w1=m1g=60.4*9.8=591.92

w2=m2g=68.9*9.8=675.22

Thus, Average difference in weight of two groups=

MIDDLE SCHOOL

Write an expression for the product of 4 and the sum of five and a number

Product of 4 and the sum of 5 and a number

Call the number x

4(5+x)

Hope this helps :)

Call the number x

4(5+x)

Hope this helps :)