solve each linear equation 7+2x=4x-3

Answer:

Sometimes people think negative numbers are irrational.

They aren't. They are actually rational because they can be divided and multiplied to make 0.

The fractions are often mistaken as irrational as well.

The only irrational numbers are π, terminating decimals, and non-perfect squares.

Step-by-step explanation:

Btw, Brainliest? Thanks!

Answer:

Step-by-step explanation:

R=X(A+B)

distribute the x to get:

R=AX+BX

subtract BX from both sides

R-BX=AX

divide both sides by X

A=(R-BX)/X

The plant is 8 inches above the ground

The height of the seed below the ground is 2 1/4

9/4

After one month, the tomatoes has grown 10 1/2

10 1/2

= 21/2

The height of the plant above the ground is

21/2 - 9/4

= 8

Hence the height of the plant above the ground is 8 inches

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Answer:

Step-by-step explanation:

In order to convert 109/100 to mixed number, you follow these steps :

Divide the numerator by the denominator

109 ÷ 100 = 1 with a remainder of 9

Write down the whole number 1 and then write down the remainder as new numerator (9) above the denominator (100), As below :

1

9

100

Answer:

109/100 or 1.09

Take into account that the figure at the center is a square. Its area is given by:

A1 = (8 ft)² = 64 ft²

To the area of the other two triangles, first determine the length of the below side of the triangle, as follow:

20 ft - 8 ft = 12 ft

12 ft is the length of the two sides. Due to both triangles are equal, the length of their sides is:

12 ft/2 = 6 ft

Then, the area of the triangles is:

A2 = (6 ft)(8 ft)/2 = 48 ft/2 = 24 ft

Hence, the total area of the figure is:

AT = A1 + A2 + A2

AT = 64 ft² + 24 ft² + 24 ft² = 112 ft²

The toal area of the figure is 112 ft²

The probability that a randomly selected patient is 0-12 years old given that the patient suffers from ankle pain is 4/7.

Probability is used to determine the likelihood that a random event would happen. The odds that the random event happens has a probability value that lies between 0 and 1. The more likely it is that the event would occur, the closer to one, the probability value would be.

The probability that a randomly selected patient is 0-12 years old given that the patient suffers from ankle pain = number of 0 - 12 that suffer from ankle pain / total number of people that suffer from ankle pain

= 4 / (4 + 3) = 4 / 7

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Given:

Total members in the committee = 19

Let's find the number of ways a president, vice president, secretary and treasurer can be chosen.

Here, we are to use permutation formula:

Where:

n = 19

r = 4

Thus, we have:

Solving further:

Therefore, the number of ways they can be chosen is 93024 ways.

ANSWER:

93024 ways

The result by using long division method for the given polynomial equation is: 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]

What is long division method?

In mathematics, the long division method can be performed on the polynomial equations. Basically, in this big equation can be solved by making smaller group of equations to make the calculation simple. It divide the dividend with divisor.

According to the question, the given polynomial equation is 3x³ +19x² + 23x + 15. Using long division method, divide it by 25

Therefore, the expression can be written as:

Required expression: [tex]\frac{3x^{3} +19x^{2} + 23x + 15 }{25}[/tex]

Dividing it by 25, we get:

(25/3x³) +(25/19x²) + (25/23x) + (25/15)

⇒ 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]

Hence, the result by using long division method for the given polynomial equation is: 25[(1/3x³) +(1/19x²) + (1/23x) + (1/15)]

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A table of data for two different linear functions using the same values of x for both functions is shown below:

x | y=2x+7 y=-x+4 -3 | 2(-3)+7=-6+7=1| -(-3)+4=3+4=7 -2 | 2(-2)+7=-4+7=3|-(-2)+4=2+4=6 -1 | 2(-1)+7=-2+7=5|-(-1)+4=1+4=5 0 | 2(0)+7=0+7=7 |-(0)+4=0+4=4 1 | 2(1)+7=2+7+9 |-(1)+4=-1+4=3 2 | 2(2)+7=4+7=11|-(2)+4=-2+4=2 3 | 2(3)+7=6+7=13|-(3)+4=-3+4=1 From the table, it can be seen that when x = -1, the function y = 2x + 7 has a value of 5 and the function y = -x + 4 has a value of 5. Therefore, the graph of the two functions will intersect at (1, 5)

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The quadratic function to model the values in the table will be,

y = 3x² + 3x - 3

Option 1 is true.

What is Quadratic equation?

An algebraic equation of the second degree in x is called Quadratic equation.

Given that;

The values of x and y are,

x = -1, 0, 3

y = -3, -3, 33

Let a quadratic function is,

y = ax² + bx + c     ... (i)

Then, It satisfy all the values given in table.

So, Substitute point (x, y) = (-1, -3) in equation (i) we get;

- 3 = a - b + c  ... (ii)

And, Substitute point (x, y) = (0, -3) in equation (i) we get;

-3 = c  .. (iii)

And, Substitute point (x, y) = (3, 33) in equation (i) we get;

33 = 9a + 3b + c ... (iv)

Now, Substitute c = -3 from (iii) in equations (ii) and (iv) we get;

From (ii);

- 3 = a - b - 3

a - b = 0      ... (v)

From (iv);

33 = 9a + 3b - 3

Divide by 3;

11 = 3a + b - 1

3a + b = 12   .... (vi)

Solve equations (v) nd (vi) we get;

a = 3 and b = 3

Thus, Substitute the values a = 3, b = 3 and c = -3 in quadratic equation we get;

y = ax² + bx + c

y = 3x² + 3x - 3

So, The quadratic function to model the values in the table will be,

y = 3x² + 3x - 3

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Answer:

Step-by-step explanation:

The solution of the system with two lines is the x-coordinate of their intersection point.

a. there is only a solution if the lines are identical

b. both the x–coordinate and the y–coordinate of the intersection point,

c. the y–coordinate of the intersection point

d. the x–coordinate of the intersection point

Answer:10

Step-by-step explanation:

found area

Answer: It's 35

Step-by-step explanation:5 and 7 both go into 35

Alice spend a total of $10.50, and the 30% of total was spent on snacks.

So, if we call x the money spent on snacks we have that the ratio between x and total spent money is 30%:

Answer:

x= 19

Step-by-step explanation:

I believe you would put both expressions equal to each other. So,

3x-11= x+27

3x-x=27+11

2x=38

x= 38/2

x=19

An sample mean can be thought to be the worth from populace having a typical dissemination when both or both of these circumstances is met:

1) The populace from which the example is being taken is Regularly circulated. So for this situation, if the number of inhabitants in grade-point midpoints is regularly circulated, the example mean would be treated as a worth from a populace having a typical dissemination

2) The example size is more prominent than 30. On the off chance that we don't know about the populace, yet the example size is more prominent than 30, the example mean can be considered as a worth from a populace having a typical conveyance.

If the matching sides and angles of two triangles are proportional, then the triangles are said to be similar.

Triangles that share the same form but differ in size are said to be similar.

Hence from the above properties we can find if any two triangles are similar.

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i hope that this helps

goodluck :)

The range of the function is for the population of the deer in the salt lake if found as  [P, ∞).

The number of deer is proportional to t, the number of years since 1990.

As a result, time t becomes the independent variable as well as the number of deer becomes the dependent variable; the number of deer DEPENDS upon the year.

A function's range is the set of values that the dependent variable can take.

The values in the range in this example represent the number of deer throughout  salt lake in specific years.

Let 'P' be the population of the deer in salt lake.

Range: [P, ∞)

Then, the range of the function is for the population of the deer in the salt lake if found as  [P, ∞).

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The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3.

What is Algebraic expression?

The Algebraic expression in this case is:

x + y = 8

which traverses points (8,-5)

Let's start by utilizing the point-intercept equation of line, which is provided by: to determine the slope of line m, that is parallel towards the line x + y = 8.

y = mx + c →(1)

x + y = 8

y = -x + 8

Comparing the aforementioned Algebraic expression to equation (1), we obtain

m = -1

The slope of the line parallel to the line x + y = 8 will now be the same, and it will be m = -1.

Let's use the point-slope equations of line to determine the linear equation now:

(y-y₁) = m(x-x₁)

Changing every value in the equation above to obtain the Algebraic expression for a line

(y-(-5)) = -1(x-8) (x-8)

(y+5) = -x+8

y + 5 = -x +8

y = -x +3

The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3.

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Step-by-step explanation:

Thus {u, v} is linearly independent if and only if {u v, u − v} is linearly independent

It is given that {u,v} be a linearly independent set of a set S.

This means that there exist constant a,b such that if:

                               au+bv=0

                            then a=b=0

Now we are asked to prove that:

{u+v,u-v} is a linearly independent set.

Let us consider there exists constant c,d such that:

                           c(u+v)+d(u-v)=0

To show:   c=d=0

The expression could also be written as:

cu+cv+du-dv=0

( Since, using the distributive property)

Now on combining the like terms that is the terms with same vectors.

cu+du+cv-dv=0

i.e.

(c+d)u+(c-d)v=0

Since, we are given that u and v are linearly independent vectors this means that:

c+d=0------------(1)

and c-d=0 i.e c=d-----------(2)

and from equation (1) using equation (2) we have:

2c=0

i.e. c=0

and similarly by equation (2) we have:

        d=0

Hence, we are proved with the result.

We get that the vectors {u+v,u-v} is linearly independent.

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Answer:

127°

Step-by-step explanation:

Angles f and d are supplementary because they are consecutive interior angles. This means that d is 123°.

a and d are vertical angles, which are congruent, meaning angle a is 127°.

Answer:

see below

Step-by-step explanation:

-4/5 using long division gives -0.8

-5/6 using long division gives -0.8333333 => repeats forever

the 3 is repeating

IN THE PLACE OF X PLUG IN 3 AND SIMPLIFY

[tex]f(3) = ({3})^{3} + 2( {3})^{2} - (3) - 1 \\ f(3) = 27 + 2(9) - 3 - 1 \\ f(3) = 27 + 18 - 4 \\ f(3) = 45 - 4 \\ f(3) = 41[/tex]

ATTACHED IS THE SOLUTION.

Answer:

[tex]\frac{x+1}{x-1}[/tex]

Step-by-step explanation:

given

x = [tex]\frac{a}{b}[/tex] ( multiply both sides by b )

bx = a

substitute a = bx into the expression

[tex]\frac{a+b}{a-b}[/tex]

= [tex]\frac{bx+b}{bx-b}[/tex] ← factor out b from each term on the numerator and denominator

= [tex]\frac{b(x+1)}{b(x-1)}[/tex] ← cancel b on numerator / denominator

= [tex]\frac{x+1}{x-1}[/tex]