expand and simplify 7(x-2)-2(x-3)

[tex](2x + 3x + 4x) = 180 \\ 9x = 18 \\ \frac{9x}{9} = \frac{180}{9} \\ x = 20[/tex]

ATTACHED IS THE SOLUTION with the steps.

The law of mathematical logic that was used to derive the given conclusion is; Law of Syllogism

The law of syllogism is defined as a type of logical argument using deductive reasoning.

Now, In mathematical logic, the Law of Syllogism states that if the following two statements are true:

(1) If d , then e .

(2) If e , then f .

Then we can derive a third true statement:

(3) If d , then f .

Now, applying that law to our question, we see that;

1) If you have a cat, then it will chase mice.

2) You have a cat.

Then we can derive a third true statement:

3)  Your cat will chase mice.

Read more about Law of Syllogism at; https://brainly.com/question/28560796

#SPJ1

The numbers in the rational form ( in there lowest form) of p/q are

(a) 0.75 = 3/4

(b) 0.12 = 3/25

(c) 0.80 = 4/5

(d) 1.25 = 5/4

In the question ,

number in the decimal form are given , and we have to express them in the rational form that is p/q .

So ,the expressions in rational form and lowest form are

(a) 0.75 [tex]=[/tex] 75/100 = 3/4

(b) 0.12 [tex]=[/tex] 12/100 = 6/50 = 3/25

(c) 0.80 [tex]=[/tex] 80/100 = 8/10 = 4/5

(d) 1.25 [tex]=[/tex] 125/100 = 5/4

Therefore , The numbers in the form of p/q are  (a) 0.75 = 3/4 , (b) 0.12 = 3/25 , (c) 0.80 = 4/5  , (d) 1.25 = 5/4   .

Learn more about Rational Numbers here

https://brainly.com/question/20459207

#SPJ1

Simplify both sides of the inequality.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{3x+6 < 3x-21 } \end{gathered}$} }[/tex]

Subtract 3x from both sides.

Subtract 6 from both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{0 < -27} \end{gathered}$} }[/tex]

Answer:

0 < - 27

Step-by-step explanation:

1. Distribute

3x + 6 < 3(x-7)

3x + 6 < 3x - 21

2. Subtract 6 from both sides

3x + 6 <  3x - 21

3x + 6 - 6 < 3x - 21 - 6

3. Simplify

   subtract

    3x + 6 - 6 < 3x - 21 - 6

    3x <  3x - 21 - 6

   subtract

     3x < 3x - 21 - 6

     3x < 3x - 27

4. Subtract 3x from both sides

3x < 3x - 27

3x - 3x < 3x - 27 - 3x

5. Simplify

    combine like terms

     3x - 3x < 3x - 27 - 3x

     0 < 3x - 27 - 3x

     0 < 3x - 27 - 3x

      0 < -  27

And that is how you get your answer

The equations with same value of x as (3/5)(30x - 15) = 72 is 18x - 9 = 72, 3(6x - 3) = 72 and x = 4.5

An equation shows the relationship between two or more numbers and variables.

Given the equation:

(3/5)(30x - 15) = 72

Opening the parenthesis:

18x - 9 = 72

Factorizing the equation:

3(6x - 3) = 72

Dividing through by 3:

6x - 3 = 24

6x = 27

Dividing through by 6:

x = 4.5

The solution to the equation (3/5)(30x - 15) = 72 yields x = 4.5

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

x = 4 , x = 2.4

Step-by-step explanation:

[tex]\frac{4}{x-2}[/tex] + [tex]\frac{3}{x-3}[/tex] = 5

multiply through by (x - 2)(x - 3)

4(x - 3) + 3(x - 2) = 5(x - 2)(x - 3)

4x - 12 + 3x - 6 = 5(x² - 5x + 6)

7x - 18 = 5x² - 25x + 30 ( subtract 7x - 18 from both sides )

0 = 5x²  - 32x + 48

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 5 × 48 = 240 and sum = - 32

the factors are - 20 and - 12

use these factors to split the x- term

0 = 5x² - 20x - 12x + 48 ( factor the first/second and third/fourth terms )

0 = 5x(x - 4) - 12(x - 4) ← factor out (x - 4) from each term

0 = (x - 4)(5x - 12)

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

5x - 12 = 0 ⇒ 5x = 12 ⇒ x = 2.4

Answer: It is obtuse

Step-by-step explanation: the angle looks greater than 90 degrees :)

A linear relationship between the distance that a car drives and the amount of gas left in the tank of the car is negative, and the value of r is -0.99

A linear relationship between the distance that a car drives and the amount of gas left in the tank of the car are negative because when a car travels a distance, it consumes fuel, and so fuel decrease with distance

Calculating the value of r

Given, r^2=98.01%

r^2=0.9801

r=±√0.9801

r=±0.99

Since r should be negative, so we pick the negative value and reject the positive value

r=-0.99

Learn more about linear relationships here:

https://brainly.com/question/13828699

#SPJ4

Mean of the number of adults (out of the sample of 38) with blood type b- positive (x) is 3.04

Let x be the number of adults out of 38 with blood type b-positive

Probability, p of adults with blood type b-positive=8%=0.08

Sample size, n=38

Using binomial random variable x binomial(n=38, p=0.08)

p(X=x)=[tex]\left \ ({{n} \atop {x}}) \right. p^{x} q^{n-x}[/tex], where x=0,1,2,3,.....n

Mean of x:

Mean of x=(probability of adults with blood type b-positive*sample size)

So, mean of x=p*n, where n=38, p=0.08

                    =0.08*38

                    =3.04

Learn more about binomial random variable here:

https://brainly.com/question/23780714

#SPJ4

Answer: y-intercept (0,−2) and the slope is 1/3

Firstly, congruent angles are equal

The three statements are

1. Triangle PTW = Triangle HGD

2. Triangle WPT = Triangle DHG

3. Triangle TWP = Triangle GDH

From the figures, it was observed that they are similar

When you look at the figures very well

You will observed that Triangle PTW is Similar to triangle HGD

They both have similar properties

Answer: 16

Step-by-step explanation: Solve for x

by simplifying both sides of the equation, then isolating the variable.

Answer:

x= 1/3

Step-by-step explanation:

1. Combine multiplied terms into a single fraction

2. Multiply all terms by the same value to eliminate fraction denominators

3. Cancel multiplied terms that are in the denominator

4. Divide both sides by the same factor

5. Simplify

Answer: 2

Step-by-step explanation: 12 divided by 3 is 4 so 6 divided by 3 would be 2

⇒I will use the similarity theorem which works by proportion of sides in similar shapes.

⇒The side with magnitude 12 in the bigger triangle is proportional with the  side with magnitude 4 in the  smaller triangle

⇒The side with magnitude 6 in the bigger triangle is proportional with the side with magnitude x in the smaller triangle. The proportionality theorem allows us to equalize the proportions of the sides

⇒HOW? HERE it is the solution

⇒[tex]\frac{12}{4} =\frac{6}{x} \\[/tex]

⇒[tex]12(x)=4(6)\\12x=24\\\frac{1x}{12} =\frac{24}{12} \\x=2[/tex]

⇒I used cross multiplication

Answer: B, the middle graph - "On a graph, points are grouped together and decrease."

Step-by-step explanation:

         A negative slope means the x-value is going down as the y-value increases. The only option that consistently meets this criteria is B, "On a graph, points are grouped together and decrease."

Answer:

The 2nd Graph aka B

Step-by-step explanation:

got it right on edge

Outward journey Speed = 20 km/hr , James stopped for  45  Mins  ,Average speed homewars 15 km/hr

What is speed, for instance?

From graph  Journey Started at 2PM

on 3PM  James covered 20 km

Hence Speed =  (20 - 0)/(3 -2) = 20 km/hr

outward journey Speed = 20 km/hr

Now outward Distance = 45 km

Time taken = 45/20 = 2 hr 15 min

Hence reached at 4 : 15 PM

Started home at 5 PM

James stopped for  45  Mins  (3/4 hrs)

Reached back at 8PM

time taken = 8 - 5 = 3 Hrs

Distance = 45 km

Average speed homeward = 45/3 = 15 km/hr

Average speed homeward =  15 km/hr

Learn more about speed

brainly.com/question/28224010

#SPJ13

MFM (option A)

Outcome could be male or female

At least two male means the minimum of number of men that we would have in the sample space outcome is 2.

The outcome that satisfies this are:

MMM, MMF, MFM, FMM

From the above, the one in the options is MFM (option A)

Answer:Rotation then a translation

Step-by-step explanation: rotate 90 degrees clockwise around center J. Then translate 3 to the right, 2 down

The roots of a function are the points where the graph crosses the x-axis.

Thus, in the following graph, we can see that the function has 2 roots. These are in:

Answer:

x = -2

x = 2

Answer:

step 1 is correct

Step-by-step explanation:

when you find the absolute value of a number i.e | | the result is always positive

eg |-20| = 20

step 1 is correct

Answer:

A: Common multiple of 4 and 6 is 24

B: They would both be common multiples but they are two different multiples of 4 and 6.

C: 3/4= 18/24    1/6= 4/24

Step-by-step explanation:

A common multiple is a number that two numbers can be multiplied to. Something that both 4 and 6 can be multiplied to is 24, but there are many other multiples of 4 and 6  as well.

Answer:

1

5

Step-by-step explanation:

y = mx + b

b = -5 (the y-intercept)

m = 1/1 = 1

y = x - 5

The slope of the line is represented by the word m which is obtained as 0.5.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

To determine a line's inclination or steepness, use the slope formula. Calculating the ratio of the change in the y-axis to the change in the x-axis may be used to calculate the slope of any line.

From the graph, the data is observed as,

(x₁,y₁)=(0,1)

(x₂,y₂) = (-2,0)

The slope of the line is found as,

[tex]\rm m =\dfrac{0-1}{-2-0} \\\\ m = 0.5[/tex]

Thus, the slope of the line is represented by the word m which is obtained as 0.5.

Learn more about the slope here:

brainly.com/question/3605446

#SPJ1

Similarity Theorems

Triangles ABG and DCB are similar by the AA similarity postulate

"If two angles in one triangle are congruent to two angles in another triangle, then the two triangles are similar"

The steps previous to statement 7 prove angles C and B are congruent because they are formed by two parallel lines that intersect a common line.

On the other side, angles DBC and AGB are congruent also because they are both right angles.

With two corresponding congruent angles, the AA similarity postulate is satisfied and the triangles are similar.

The integer is x>-2

5 x+12>2 x+6

Subtract 12 from both sides

5 x+12-12>2 x+6-12

Simplify

5 x>2 x-6

Subtract 2x from both sides

5 x-2 x>2 x-6-2 x

Simplify

3 x>-6

Divide both sides by 3

[tex]\frac{3 x}{3} > \frac{-6}{3}$$[/tex]

Simplify

x>-2

Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043.

To learn more about integer visit:https://brainly.com/question/15276410

#SPJ1

The power reducing formula for the fourth power of the cosine function is:

Replace θ=3x to find the expression for cos⁴(3x) in terms of the first power of the cosine function:

Therefore, the answer is:

Use the second option to write this expression as input.

The answer to the function as provided that f(n) = 3 to the power of n can thus, solving the linear function as n for -1 we get the answer.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

A statement, rule, or law that establishes a relationship between an independent variable and a dependent variable in mathematics (the dependent variable) is said as a function.

f[n]= [tex]3^n[/tex]

And find f(-1)

So put -1 in place of n

thus f[-1] = [tex]3^{-1[/tex]

=1/3

=0.33

In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

To know more about function, visit:

https://brainly.com/question/28028288

#SPJ13

Answer:

51.06 degree

Step-by-step explanation:

x=sin^(-1)(7/9)

= 51.06 degree