Help me on this inequality please!

Newton's Law of Gravitation:

Statement: According to this law, when two mass bodies are separated at finite distance then there must be an attractive force experience by them which is directly proportional to the product of their masses and inversely proportional to the square of their separation.

Consider two mass bodies m1 & m2 be kept at distance d. Then the force of attraction F is given as

                            [tex]Fam_{1}.m_{2}[/tex]

                                 [tex]Fa1/d^2[/tex]

Now, from above equations, we have

                          [tex]Fa\frac{m_{1}m_{2}}{d^2}[/tex]

or,                           [tex]F=G\frac{m_{1}m_{2}}{d^2}[/tex]

Here         [tex]G=6.67*10^{-11}Mm^2kg^{-2}[/tex]   is the universal gravitational constant.

Answer:

-125

Step-by-step explanation:

Twice a number is x*2

x*2 = 500 + x*6

=> x = -125

The number or amount of ounces of the 75% tangy mustard sauce must the chef have used is: 20 ounces .

First step

Since 5 ounce sauce containing 50% tangy

Hence:

5 oz×.50 tangy

=2.50 oz-tangy

Second step

(5+x)×0.7=3.5+0.7x

Third step

2.50+0.75x=3.5+0.7x

Collect like term

0.75x-0.7x=3.5-2.50

0.05x=1

Divide both side by 0.05

x=1/0.05

x=20 ounces

Therefore the number of ounces of the 75% tangy mustard sauce must the chef have used is: 20 ounces .

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Answer:

Circumference = 25.14 cm

Area = 50.28 cm²

Step-by-step explanation:

∴ Circumference = 2πr

⇒C = (2) (22/7) (4)

⇒C = 25.14 cm

∴ Area = πr²

⇒A = (22/7) (4)²

⇒A = 50.28 cm²

Hope that helps...

The length of the hypotenuse AB is equal to the sum of the square of other two sides AC and BC. The measure of the curve DE is 10.5 units

The theorem states that the length of the hypotenuse AB is equal to the sum of the square of other two sides AC and BC.

According to the theorem;

AB^2 = AC^2 + BC^2

AB^2 = 6^2 + 8^2

AB^2 = 36 + 64

AB = 10

If the curve DE is 5% longer than line segment АВ, the measure of curve DE is given as;

DE = 1.05 * 10
DE = 10.5

Hence the measure of the curve DE is 10.5 units

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Answer:

D

Step-by-step explanation:

It goes 2 down. The ' mark shows that it is the new one

Answer:

x = 12.5

Step-by-step explanation:

17 = 2(x - 4)

17 = 2x - 8

17 + 8 = 2x - 8 + 8

25 = 2x

12.5 = x

Answer:

Step-by-step explanation:

Given:

Isolate the term of y from one side of the equation.

(3y+2)(y-1)

Use the foil method.

[tex]\underline{\text{FOIL METHOD:}}[/tex]

[tex]\Longrightarrow: \sf{\left(A+B\right)\left(C+D\right)=AC+AD+BC+BD}[/tex]

(3y+2)(y-1)=3yy+3y(-1)+2y+2(-1)

Solve.

[tex]\sf{3yy=3y^2}\\\\\\\sf{3y(-1)=-3y}\\\\\\\sf{2(-1)=-2}[/tex]

[tex]\sf{3y^2-3y+2y-2}[/tex]

Add or subtract the numbers from left to right.

Solutions:

[tex]\sf{-3y+2y=-y}[/tex]

[tex]\Longrightarrow: \boxed{\sf{3y^2-y-2}}[/tex]

I hope this helps. Let me know if you have any questions.

Answer:

3y^2-y-2

Step-by-step explanation:

(3y+2)(y–1)

Use the FOIL method

First 3y * y = 3y^2

outer  3y * -1 = -3y

inner  2 * y = 2y

last  2 * -1 = -2

Add them together

3y^2 -3y +2y -2

Combine like term

3y^2-y-2

Answer:

40 so C would be your answer.

The third quartile of the data set is 38.

Quartiles are statistical measures that divide a dataset into four equal parts, each representing 25% of the data. They are used to analyze the distribution and spread of data.

There are three quartiles: the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3).

To find the third quartile of a data set, we need to arrange the data in ascending order and then locate the value that divides the upper 25% of the data from the lower 75%.

Arranging the data set in ascending order:

14, 18, 20, 21, 25, 32, 38, 42, 48

The data set has 9 values, so the third quartile will be the value at the

(9 0.75)th position

= 6.75th position.

Since we can't have a fractional position, we round up to the nearest whole number, which is 7.

The value at the 7th position is 38. Therefore, the third quartile of the data set is 38.

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Answer:

Shown in the photo

Step-by-step explanation:

I just followed the steps. If you need more help let me know :)

Answer: 3.6

Step-by-step explanation:

Answer:

Sum of diagonals = 20 units

Step-by-step explanation:

[tex]A(rectangle)=25\sqrt 3\: units^2\\w(rectangle) =5\: units[/tex]

To find: Sum of diagonals

[tex]A(rectangle)=l(rectangle)\times w(rectangle) [/tex]

[tex]\implies l(rectangle)=\frac{A(rectangle)}{w(rectangle)}[/tex]

[tex]\implies l(rectangle)=\frac{25\sqrt 3}{5}[/tex]

[tex]\implies l(rectangle)={5\sqrt 3}\: units[/tex]

Let the diagonals of the rectangle be [tex]d_1\:\&\:d_2\: units[/tex]

Diagonals of a rectangle are equal in measure.

[tex]\implies d_1=d_2=\sqrt{l(rectangle)^2+w(rectangle)^2}[/tex]

(By Pythagoras Theorem)

[tex]\implies d_1=d_2=\sqrt{(5\sqrt 3)^2+(5)^2}[/tex]

[tex]\implies d_1=d_2=\sqrt{75+25}[/tex]

[tex]\implies d_1=d_2=\sqrt{100}[/tex]

[tex]\implies d_1=d_2=10\: units[/tex]

[tex]Sum \:of \:diagonals = d_1+d_2[/tex]

[tex]\implies Sum \:of \:diagonals = 10+10[/tex]

[tex]\implies Sum \:of \:diagonals = 20\: units[/tex]

Answer:

Step-by-step explanation:

Total number of days

The number of days she bought a banana or orange

The probability of buying a banana or an orange is

Answer:

[tex]\sf \dfrac{7}{10}=0.7=70\%[/tex]

Step-by-step explanation:

Given information:

Total number of days = 30

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Probability of buying a banana:

[tex]\implies \sf P(Banana)=\dfrac{12}{30}[/tex]

Probability of buying an orange:

[tex]\implies \sf P(Orange)=\dfrac{9}{30}[/tex]

Therefore,

[tex]\implies \sf P(Banana) \: or \: P(Orange)=\sf \dfrac{12}{30}+\dfrac{9}{30}=\dfrac{21}{30}=\dfrac{7}{10}[/tex]

So the probability of buying either a banana or an orange is:

  [tex]\sf \dfrac{7}{10}=0.7=70\%[/tex]

Answer:

Step-by-step explanation:

44/2 is 22

84/3 is 28

Patrick Mahomes can throw more yards/sec

Answer:

Hello there! 10 square of 3

Answer:

(2x + y)(2x - y)

Step-by-step explanation:

1. Simplify the square 4x²:

(2x)² - y²

2. Apple the difference of two squares formula x² - y² = (x + y)(x - y):

(2x + y)(2x - y)

hope this helps!

5m long ladder placed against 4.3m up the wall.

the angle between the ladder and the ground.

Based on the given conditions, formulate: 

sin⁡x=4.3÷5

Evaluate the equation/expression:

x= 1.03527 or 2.10632

x= 1.03527°

or x= 2.10632°

Answer:

The answer is B.

Step-by-step explanation:

4x-7 = 2x+9

2x = 16

x = 8

And then we put x into the equations.

y = 32 - 7

y = 25

We then check it with the other equation just to make sure we are correct.

y = 16 +9

y = 25

Therefore, the answer is (8,25).

Answer:

3

Step-by-step explanation:

0.1 rounds to 0 and 0.04 also rounds to zero. Therefore, the answer is 3.

Answer:

3,000 numbers.

Step-by-step explanation:

First digit: 2, 3, 5, or 7 (primes)

Second digit: 0, 1, 2, 3, or 4 (less than 5)

Third digit: 0-9

Fourth digit: 0, 1, or 8 (cubic numbers)

Fifth digit: 1, 3, 5, 7, or 9 (odd numbers)

So we have 4 * 5 * 10 * 3 * 5 = 3,000 possible numbers.

Answer:

It depends on how many students there are in Mr. Edwards class

Step-by-step explanation:

Answer: according to my calculator, the answer is 8.5714285714286 i hope this is correct lol,

Step-by-step explanation: Hope this helps ^_^

Answer:

See below

Step-by-step explanation:

Inscribed angles encompass twice as many degrees of arc as their angle measure

 soo    2* {   6x-5   +  x+17 } = 360

             shows x = 24      then ROP = x+17 = 41 degrees

Explanation:

The arc markings for each angle show that we have two pairs of congruent angles (angle O = angle Q, angle M = angle R). This takes care of the two "A"s in "ASA". The tickmarks show us that the sides MO and RQ are the same length, so this takes care of the "S" of "ASA". Note the congruent sides are between the angles mentioned. The order is important.