Answer the question Pls

Answer:

1. [tex]a=b=\dfrac{3}{4}[/tex]

2. [tex]a=-3,\ b=3[/tex]

Step-by-step explanation:

1. Given:

[tex]\dfrac{3x}{(x-2)(3x+2)}=\dfrac{a}{x-2}+\dfrac{b}{3x+2}[/tex]

To find a and b, add two fractions in right side:

[tex]\dfrac{a}{x-2}+\dfrac{b}{3x+2}\\ \\=\dfrac{a(3x+2)+b(x-2)}{(x-2)(3x+2)}\\ \\=\dfrac{3ax+2a+bx-2b}{(x-2)(3x+2)}\\ \\=\dfrac{(3a+b)x+(2a-2b)}{(x-2)(3x+2)}[/tex]

So,

[tex]\dfrac{3x}{(x-2)(3x+2)}=\dfrac{(3a+b)x+(2a-2b)}{(x-2)(3x+2)}[/tex]

Two fractions with same denominators are equal when they have equal numerators, so

[tex]3x=(3a+b)x+(2a-2b)[/tex]

Equate coefficients:

[tex]At\ x:\ \ 3=3a+b\\ \\At \ 1: 0=2a-2b[/tex]

From the second equation:

[tex]a=b[/tex]

Substitute it into the first equation:

[tex]3b+b=3\\ \\4b=3\\ \\b=\dfrac{3}{4}[/tex]

Hence,

[tex]\dfrac{3x}{(x-2)(3x+2)}=\dfrac{\frac{3}{4}}{x-2}+\dfrac{\frac{3}{4}}{3x+2}[/tex]

2. Given:

[tex]\dfrac{3}{x^2-5x+6}=\dfrac{a}{x-2}+\dfrac{b}{x-3}[/tex]

Note that [tex](x-2)(x-3)=x^2-3x-2x+6=x^2-5x+6[/tex]

To find a and b, add two fractions in right side:

[tex]\dfrac{a}{x-2}+\dfrac{b}{x-3}\\ \\=\dfrac{a(x-3)+b(x-2)}{(x-2)(x-3)}\\ \\=\dfrac{ax-3a+bx-2b}{(x-2)(x-3)}\\ \\=\dfrac{(a+b)x+(-3a-2b)}{(x-2)(x-3)}[/tex]

So,

[tex]\dfrac{3}{(x-2)(x-3)}=\dfrac{(a+b)x+(-3a-2b)}{(x-2)(x-3)}[/tex]

Two fractions with same denominators are equal when they have equal numerators, so

[tex]3=(a+b)x+(-3a-2b)[/tex]

Equate coefficients:

[tex]At\ x:\ \ 0=a+b\\ \\At \ 1: 3=-3a-2b[/tex]

From the first equation:

[tex]a=-b[/tex]

Substitute it into the second equation:

[tex]-3(-b)-2b=3\\ \\3b-2b=3\\ \\b=3\\ \\a=-3[/tex]

Hence,

[tex]\dfrac{3}{x^2-5x+6}=\dfrac{-3}{x-2}+\dfrac{3}{x-3}[/tex]

To turn an equality into an identity, you would find values for 'a' and 'b' that work for all values of 'x'. The process involves equating coefficients and solving the resulting equations. Without specific equations, we must rely on general methods, such as using the quadratic formula when 'c' is known.

Finding Values of a and b

To make the equality into an identity, you'll typically want to find values of 'a' and 'b' that satisfy the given equations for all values of 'x'. It seems like part of your question is missing, as we would need the specific equations to give a precise answer. However, the process involves equating coefficients of the same powers of 'x' from both sides of the equation and solving the resulting system of equations.

For example, if you have an equation of the form ax2 + bx + c = 0 and you want to make it an identity, you can find 'a' and 'b' by applying the quadratic formula when 'c' is given.

In the case of a quadratic equation ax2 + bx + c = 0, you can determine 'a' and 'b' by solving:

-b ± √(b2 - 4ac) / (2a)

Which simplifies down when given specific constants, as shown by the example where a = 3, b = 13, and c = -10. This yields two possible solutions for 'x' which can verify the values of 'a' and 'b'.

If an equation already has set constants like a = 1.00, b = 10.0, and c = -200, then the equation is already defined, and the values are given.

Answer:

x = 3

y = 2

Step-by-step explanation:

When 2 triangles are congruent, they will have exact same 3 sides length and exact same 3 angles measure.

So we can say:

-2x + 6y = 6

and

-7x + 8y = -5

Let's multiply first equation by 7 and 2nd equation by -2, to get:

7 [-2x + 6y = 6] = -14x +42y = 42

and

-2 [-7x + 8y = -5] = 14x - 16y = 10

Now adding these 2 new equations and solving for y:

-14x +42y = 42

14x - 16y = 10

----------------------

26y = 52

y = 52/26

y = 2

Now we put y = 2 into 1st equation (or any other) and solve for x:

-2x + 6y = 6

-2x + 6(2) = 6

-2x + 12 = 6

6 = 2x

x = 6/2

x = 3

Check the picture below.

the idea being that sides of 2.5 andd 8 are fixed, what's are the possible lengths of "x"?

well, if we open the fixed sides, we'll end up with a 3rd side of 2.5 + 8 = 10.5, however if "x" is ever 10.5, the figure will become a flat-line and we'd be losing the triangle.

and if we close the fixed sizes, the longest "x" could be is 8 - 2.5 = 5.5, but the same, it can't be 5.5 exactly otherwise the figure will turn to a flat-line.

5.5 < x < 10.5.

Answer:

5.5 < x < 10.5

Step-by-step explanation:

Khan

Answer:

4 tens + 5 tenths

Step-by-step explanation:

40+5\10= 40+1/2=40.5

Answer:

X=-4

Step-by-step explanation:

In the attached file

Answer:

[tex]x=\frac{1}{4}[/tex]

Step-by-step explanation:

We can use some logarithmic rules to solve this easily.

Note: Ln means [tex]Log_e[/tex]

Now, lets start with the equation:

[tex]ln(2x) + ln(2) = 0\\ln(2x) = -ln(2)[/tex]

Writing left side with logarithmic base e, we have:

[tex]Log_{e}(2x) = -ln(2)[/tex]

We can now use the property shown below to make this into exponential form:

[tex]Log_{a}b=x\\means\\a^x=b[/tex]

So, we write:

[tex]Log_{e}(2x) = -ln(2)\\e^{-ln(2)}=2x[/tex]

We recognize another property of exponentials:

[tex]a^{bc}=(a^{b})^{c}[/tex]

So, we write:

[tex]e^{-ln(2)}=2x\\(e^{ln(2)})^{-1}=2x[/tex]

Also, another property of natural logarithms is:

[tex]e^{(ln(a))}=a[/tex]

Now, we simplify:

[tex](e^{ln(2)})^{-1}=2x\\(2)^{-1}=2x\\\frac{1}{2}=2x\\x=\frac{\frac{1}{2}}{2}\\x=\frac{1}{4}[/tex]

This is the answer.

Answer:

Your answer is 15/2 i hoped i helped

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

3×5/2

15/2

The remainder is 1

Answer:

angle sum of a triangle’Formula

Step-by-step explanation:

N stands for the number of edges, - 2 is the result after finishing, 2 has no special significance. Because the sum of outer angles is a constant n-edge shape with 360 degrees, take n flat angles 180n = inner angle and + 360, so the sum of inner angles = 180n-360 = 180 (n-2)

That formula tells you what is the sum of the interior angles of a polygon with n sides.

So, for example, a triangle has n=3 sides, and in fact the sum of its interior angles is

[tex](3-2)\cdot 180=180[/tex]

As another example, the sum of the interior angles of a polygon with 15 sides is

[tex](15-2)\cdot 180=13\cdot 180=2340[/tex]

Answer:

3.75

Step-by-step explanation:

You take your 15 feed and divide it by 4 for the four pieces she cuts the rope into giving you with each section of the cut rope being 3.75 in.

The length of each piece is 3.75 feet long.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Megan who has a rope that is 15 feet in length and she cuts the rope into 4 pieces.

Assume that the length of each piece is x ft. Then -

4x = 15

x = 15/4

x = 3.75 ft

Therefore, the length of each piece is 3.75 feet long.

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The other leg is 12cm long.

Step-by-step explanation:

Given,

Hypotenuse = c = 15cm

One leg = a = 9cm

Other leg = b

As the triangle is right angled, therefore, using Pythagoras theorem;

[tex]a^2+b^2=c^2\\(9)^2+b^2=(15)^2\\81+b^2=225\\b^2=225-81\\b^2=144\\[/tex]

Taking square root on both sides;

[tex]\sqrt{b^2} =\sqrt{144} \\b=12\ cm[/tex]

The other leg is 12cm long.

Keywords: triangle, square root

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Answer:

1.

Step-by-step explanation:

The perimeter is a length - degree 1.

The degree of the expression that represents the perimeter of this triangle is 2

The formula for calculating the perimeter of a triangle is expressed as;

P = a + b + c

Such that the parameters are denoted as;

From the diagram shown, we have that;

Perimeter = 2x²+ 2x ² + 4x + 5

collect the like terms, we get;

Perimeter = 4x²+ 4x + 5

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Answer:

[tex]\displaystyle 3 = m[/tex]

Step-by-step explanation:

2 = −7 + 3m

+ 7 + 7

__________

[tex]\displaystyle \frac{9}{3} = \frac{3m}{3} \\ \\ 3 = m[/tex]

I am joyous to assist you anytime.

Answer:

[tex]y=-30x[/tex]

Step-by-step explanation:

To simplify the expression x² + 3x + 2 / X + 1, factor the numerator and denominator expressions separately. The simplified form of the expression is (x + 2) / 1.

To simplify the expression, x² + 3x + 2 / X + 1, we can use the factoring method. First, we factor the numerator expression. The expression x² + 3x + 2 can be factored as (x + 2)(x + 1). Then, we factor the denominator expression X + 1. So, the simplified form of the expression is (x + 2) / 1.

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Answer:

He left $6 for the tip.

Step-by-step explanation:

20%=0.2

0.2*30=6

Answer:

y= -2x+31

Step-by-step explanation:

Y=-2x+B

7=-2(12)+B

7=-24+B

7+24= (-24+24)+B

31=B

Y=-2x+31

Hope it helps!!

Answer:

12(x+2)

Step-by-step explanation:

Factor a 12 out of

12x + 24

12 goes into 12 once

12 goes into 24 twice

= 12(x+2)

Answer:

HERE IS THE ANSWER 1407.5 hours

Step-by-step explanation:

Answer:

$5.24

Step-by-step explanation:

If Mom bought 4, she bought [tex]$1.19*4=$4.76[/tex] worth of pie filling. Since she paid $10, she needs [tex]$10-$4.76=$5.24[/tex] change

Answer:

x=

Step-by-step explanation:

Open parenthesis first:

2x-8x+6=6-6x

Combine like terms:

-6x+6=6-6x

Then move all like terms to one side:

6-6=-6x+6x

Simplify:

0=0

0=0 is true, so x can equal any number and the result will be true. (Like the number 4, for example. If x was 4, you would get 4=4.)

~Stay golden~ :)

Answer:

it's already in it's simplest form

Step-by-step explanation:

Answer:

the answer would still be the same as the problem because if you use prime factorization it would still be the square root of 41  

Step-by-step explanation:

[tex]\sqrt{41\\[/tex]

28 to nine means it is 8:32 ( to get this you subtract 28 from 9.) ( its saying there are 28 minutes left until it is 9)

add 8 hours

= 8+ 8 = 16

well we arent talking about military time sooo 16-12 = 4

4 : 32 and you need to add the 59 so

32+ 59 = 91

91 - 60 = 31 (dont forget to add the extra 1 hour because we subtracted 60 minutes :). )

so the correct time will be 5: 31

Answer: 5:31

Step-by-step explanation:

28 minutes to 9 is 8:32

8 hours and 59 minutes later it would be 5:31

Answer:

x=0, exactly one solution.

Step-by-step explanation:

y=3x+3

y=-2x+3

-----------

3x+3=-2x+3

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

3x+2x+3=3

5x+3=3

5x=3-3

5x=0

x=0/5

x=0

Answer:

Asha's present age is 27 years and Nisha's present age is 5 years.

Step-by-step explanation:

Let the present age of Nisha be [tex]x[/tex] years.

As per question, Asha's present age is 2 more than the square of Nisha's age.

[tex]\therefore[/tex] Asha's present age = [tex]x^2+2[/tex]

Now, Nisha will reach her mother's age after [tex]x^2+2-x[/tex] years.

Therefore, age of Asha after [tex]x^2+2-x[/tex] years will be = [tex]x^2+2+x^2+2-x=2x^2-x+4[/tex]

Now, as per question,

[tex]2x^2-x+4=10x-1\\2x^2-x-10x+4+1=0\\2x^2-11x+5=0\\2x^2-x-10x+5=0\\x(2x-1)-5(2x-1)=0\\(2x-1)(x-5)=0\\x=\frac{1}{2}\ or\ x=5[/tex]

As age can't be in fraction, we consider the present age of Nisha as 5 years. So, Asha's present age is [tex]x^2+2=5^2+2=25+2=27[/tex] years.

Therefore, Asha's present age is 27 years and Nisha's present age is 5 years.

Answer:

i believe you answer would be B. 3

Step-by-step explanation:

Without Table 14, a specific answer can't be provided. But generally you would find the y value when x is 3 for f(3), or find the x value when y is 1 for f(x)=1.

This question pertains to the evaluation of f(3) and solving for f(x)=1 within the given function f that's represented in Table 14. Unfortunately, as the Table 14 isn't provided, I can't give a specific answer. However, generally, to evaluate f(3), find the pair where the x value is 3; the corresponding y (or f(x)) value is the result of f(3). To solve f(x)=1, look for the pair in the table where the f(x) (or y) value is 1; the corresponding x value is the solution for f(x)=1.

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There are 8046.75 meters in 5 miles

Step-by-step explanation:

Method 1:

First of all we have to calculate the unit conversion.

Assuming that 3 miles is equal to 4828.05 meters

We have to find that how many meters make one mile

So,

3 miles = 4828.05 meters

[tex]1\ mile=\frac{4828.05}{3}\\=1609.35\ meters[/tex]

Now we know that:

[tex]1\ mile=1609.35\ meters\\5\ miles=1609.35*5 = 8046.74\ meters[/tex]

Method 2:

We can also use ratios to find the number of meters in 5 miles as:

3:4828.05::5:x

where x is the number of meters in 5 miles

[tex]\frac{3}{4828.05}=\frac{5}{x}\\x=\fac{5*4828.05}{3}\\=8046.75\ meters[/tex]

Hence,

There are 8046.75 meters in 5 miles

Keywords: Conversions, Units

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= 4 = x²

x = Answer: Length= 11 , Brteadth = 2

Step-by-step explanation: Let the breadth of the rectangle be x

length = 9 + x

area = 36 cm²

A.T.Q

36cm² = 9x*x

36 = 9x²

36/9 = 4 = x²

x = root of 4

x= 2

Therefore , breadth of rectangle is 3cm and length is 12 cm

verification:

l*b = 12*3 = 36cm²

She has been with her book club for 49 months.

Step-by-step explanation:

Books read = 12 books

Time period = 7 months

Therefore,

12 books = 7 months

1 book = [tex]\frac{7}{12}\ months[/tex]    

Books read so far = 84 books

Total time period = x

84 books = x months

1 book = [tex]\frac{x}{84}\ months[/tex]

Using both unit rates;

[tex]\frac{x}{84}=\frac{7}{12}\\x=\frac{7}{12}*84\\x=\frac{588}{12}\\x=49\ months[/tex]

She has been with her book club for 49 months.

Keywords: Unit rates, multiplication

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Answer:

x = 64

Step-by-step explanation:

The sum of the interior angles of a quadrilateral = 360°

Sum the given angles and equate to 360

x + 2x + 114 + x - 10 = 360, that is

4x + 104 = 360 ( subtract 104 from both sides )

4x = 256 ( divide both sides by 4 )

x = 64