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What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer:

x = 2 or x = -5

Step-by-step explanation:

x² + 3x - 4 = 6

x² + 3x -4 - 6 = 0

x² + 3x - 10 = 0 (Here you find two numbers that have a sum of 3 and a product of -10. These two numbers would be 5 and -2. 5 - 2=3 and 5×-2 =-10.)

x² + 5x - 2x -10 = 0 (They you replace 3x by 5x and -2x)

(x² + 5x) (-2x -10) =0 - (You find common terms)

x(x + 5) -2(x + 5) = 0

(x - 2) (x + 5) = 0

So

x - 2 = 0 or x + 5 = 0

x =2               x = -5

Answer:x=2

Step-by-step explanation:

x^2+3x-4=6

2x+3x-4=6

add 2x and 3x and you get 5x

5x-4=6

add 4 to both sides 6 plus 4 is 10

5x=10

know divide 5 from both sides and you get 2

x=2

Answer: 0

============================================

Explanation:

When we multiply 0 by any number, we get 0 as a result

x*0 = 0

0*x = 0

for any number x.

The number 0 is rational since we can write it as a fraction of two integers

0 = 0/1

If Daniel were to correct his statement to say "multiply by any nonzero rational number", then his statement would be correct that the result is irrational.

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

Extra info:

Here's a proof showing why Daniel's claim is correct if we consider nonzero rational numbers

Let p be a nonzero rational number, so p = a/b for integers a,b where neither a or b are zero

Let q be an irrational number. We cannot write q as a ratio of two integers

The claim is that p*q is irrational. For now let's assume the opposite. So assume p*q is rational. This means p*q = r/s for integers r,s

This would be the same as (a/b)*q = r/s which solves to q = (r/s)*(b/a) = (rb)/(sa) making q rational, but that contradicts the fact we made q irrational earlier.

Therefore, the assumption p*q is rational cannot be the case, and p*q must be irrational.

Answer:

n = 26/45

Step-by-step explanation:

If the 9⅓ and 27⅘ are supposed to be \(9^{1/3}\)  and \(27^{4/5}\), then

\(9^{1/3}\) × \(27^{n}\) = \(27^{4/5}\)

=> \((3^{2})^{1/3}\) × \((3^3)^{n}\) = \((3^3)^{4/5}\)

=> \(3^{2/3}\) × \(3^{3n}\) = \(3^{12/5}\)

=> \(3^{3n+\frac{2}{3}}\) = \(3^{12/5}\)

=> 3n+2/3 = 12/5

=> 45n + 10 = 36

=> 45n = 26

=> n = 26/45

Answer:

  x = 124

Step-by-step explanation:

You want the value of the exterior angle x°, given that the remote interior angles are 83° and 41°.

The exterior angle of a triangle is equal to the sum of the remote interior angles:

  x° = 83° +41°

  x° = 124°

  x = 124

__

Check

The interior angle adjacent to x° is its supplement:

  180° -124° = 56°

The sum of the interior angles of the triangle is 180°:

  83° +41° +56° = 180° . . . . . true

The theorem we cite above is a consequence of the fact that the missing interior angle is supplementary to both x° and the sum of the other two interior angles. It saves having to find the measure of the missing interior angle.

The mean absolute deviation (MAD) of the data set is equal to 180.625.

The mean absolute deviation of a data set is to find the average distance of each observation of the data set and the mean of the data set.

Mean absolute deviation = 1/n ∑ absolute value of (xi - x bar)

x bar =average value of the given data set

n= total number of data set

xi = data value in a given set

According to the question,

x bar = sum of all the data set / total number of the data set

x bar = 2052/16 = 128.25

Substitute the value in the formula, we have

Mean absolute deviation = 2890/16 = 180.625

Hence, the Mean absolute deviation of the data set is equal to 180.625.

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As per the given data, the Mean absolute deviation (MAD) of the data set is equals to 17.5

The term Mean absolute deviation in math is defined as the average distance of each observation of data set  and the mean of the data set.

Here we have given the following data.

=> 13, 0 , 14 , 36, 18, 9

Then the mean of the data is calculated as,

=> (13 + 0 + 14 + 36 + 18 + 9)/6

=> 90/6

=> 15

Now, we have to the Substitute the value in the formula, we have

And then the Mean absolute deviation is calculated as,

=> (90 + 15)/6

=> 105/6

=> 17.5

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Answer:

1/30

Step-by-step explanation:

Hope you could understand.

If you have any query, feel free to ask.

Answer:

Company A's cost would be $530

Company B's cost would be $610

difference is $80

Step-by-step explanation:

Answer:

x = 99

Step-by-step explanation:

Since x is on a straight line the adjacent angle and x must equal 180. We will call this adjacent angle B. The angle to the right of B also is on a straight line.

So,

180 - 123 = the inside angle             Simplify

57

The addition of a triangles interior angles equals 180

180 = 42 + 57 + B                              Move variables to one side

180 - (42 + 57) = B                             Simplify

81 = B

Now we can solve for X

180 - 81 = x                                        Simplify

99

Answer:

540

Step-by-step explanation:

Answer:

540

Step-by-step explanation:

9 out of 10 is 90% of 10. Therefore, you have to calculate what's 90% of 600. Which is 540. Hope this helps!

The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.

To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.

The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:

-1/4 = -5/20

3/5 = 12/20

Now that the fractions have the same denominator, we can add them:

-5/20 + 12/20 = (-5 + 12)/20 = 7/20

Therefore, -1/4 + 3/5 is equal to 7/20.

To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.

Thus, the final answer is 7/20.

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Answer:

I think its C

Step-by-step explanation:

Answer:

354.330709 (depending on instructions you may need to round)

rounded to tenths - 354.3

rounded to hundredths - 354.33

Step-by-step explanation:

9 x 100 = 900

900/2.54 = 354.330709

Answer:

-38 + x = -21

Step-by-step explanation:

Since we don't know the number that -38 is being added to, we can suplement it in the equation with x.

Required value of 8x is 24.

What is equation?

The mathematical statements that contain two algebraic expressions on either side of an equal sign (=) is called Equations. It shows equality between an expression written on the left side and an expression written on the right side. In any mathematical equation, L.H.S = R.H.S (Left side = Right side). Equations can be solved to obtain the value of the unknown variable that represents the unknown values. If the statement does not have the "=" symbol that means the expression is not an equation. It is treated as an expression.

Here given equation is 5x+4 = 6x

We are Simplifying,

\(5x + 4 = 6x \\ 6x - 5x = 4 \\ x = 4\)

Therefore, value of x is 4.

Now,

\(8x = 8 \times 3 = 24\)

So, required value of 8x is 24.

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Correct question is "If 5x+4 = 6x, find 8x A) 24 C)0 B)12 D)32"

put -5 in 5 postion for the second and 5 for the first

Step-by-step explanation:

Answer:

\(2\sqrt{26} units\)

Step-by-step explanation:

1. if suppose the point M(-10;-5) and the line 5x+y+3=0, then coordinates of the point are x₀= -10 and y₀= -5, the view of the line is Ax+By+C=0, where A=5; B=1; C=3.

2. use the rule/formula:

\(d=| \frac{Ax_0+By_0+C}{\sqrt{A^2+B^2}}\)

3. if to substitute A=5; B=1; C=3; x₀= -10 and y₀= -5 into the formula, then:

\(d=| \frac{-5*10-5*1+3}{\sqrt{5^2+1} } | = \frac{52}{\sqrt{26}}=2\sqrt{26}\)

Answer:

It cost 50 cents and if you need to know it uses 500 watts.

Answer: 15

Step-by-step explanation:

Answer:80

Step-by-step explanation:

4^3+4^2=80

The length of the longer wire is 82 feet.

Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.

We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.

In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:

cos(θ) = adjacent/hypotenuse = 16/L

Given that cos(θ) = 8/41, we can substitute this value into the equation:

8/41 = 16/L

To solve for L, we can cross-multiply and solve for L:

8L = 41 * 16

L = (41 * 16)/8

L = 82

Therefore, the length of the longer wire is 82 feet.

In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.

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(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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Answer: dude take a deep breath and answer the question it’s very easy

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{1}{2}\) x + 3 ← is in slope- intercept form

with slope m = \(\frac{1}{2}\)

• Parallel lines have equal slopes , then

y = \(\frac{1}{2}\) x + c ← is the partial equation

to find c substitute (2, - 4 ) into the partial equation

- 4 = \(\frac{1}{2}\) (2) + c = 1 + c ( subtract 1 from both sides )

- 5 = c

y = \(\frac{1}{2}\) x - 5 ← equation of parallel line

Reflection across a line

A line defines points of reflection

points are ubicated at same distance with respect to line x=1

X coordinate remains equal

Y coordinate varies acording to

y - 2 (y-1 )

Then now find y coordinates

For C , y = 3- 2•(3-1) = -1

For D , y = 4 - 2•(4-1) = -2

For E, y = 5 - 2•(5-1) = -3

For F, y= 4 - 2•(4-1) = -2

Then new coordinates C',D',E',F' are

C' = ( 4,-1)

D' = ( 9,-2)

E '= ( 4,-3)

F'= ( 1, -2)

The inequality is graphed and attached

There are some points that help in interpreting inequality graphs.

the x values are also called the domain lets assume -4 0 4. this is substituted into the equation 3x - 2y > 2 to get the values in the y direction.

3x - 2 > y

y < 3x - 2

for x = -4

y < 3 * -4 - 2 = -14

for x = 0

y < 3 * 0 - 2 = -2

for x = 4

y < 3 * 4 - 2 = 10

table of values

x      y

-4   -14

0     -2

4     10

y < 3x - 2 is the equation

Then use of dashed lines of dashed lines or solid lines

dashed lines means there is no equality sign in the inequality > OR < hence used for the problem

solid line means there is equality in the inequality  ≤ OR ≥

Another part is the shaded portion

shading above the line defines greater than shading below the line defines less than. The equation has less than and the shading is below the line

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⇒Given the equation \(f(x)=-\frac{1}{2} x+3\) to get f(-6) it means that in the place of x in the given function plug in -6 and simplify

⇒\(f(-6)= -\frac{1}{2} (-6)+3\\f(-6)=3+3\\f(-6)=6\)

⇒The answer is f(-6)=6

Step-by-step explanation:

Given the equation f(x)=-\frac{1}{2} x+3f(x)=−

2

1

x+3 to get f(-6) it means that in the place of x in the given function plug in -6 and simplify

⇒\begin{gathered}f(-6)= -\frac{1}{2} (-6)+3\\f(-6)=3+3\\f(-6)=6\end{gathered}

f(−6)=−

2

1

(−6)+3

f(−6)=3+3

f(−6)=6

⇒The answer is f(-6)=6

The solution to the equation 3x = 8 - 2x is x = 1.6.

To solve the equation 3x = 8 - 2x by graphing, we can plot the two sides of the equation as functions of x and find the point(s) where they intersect. Here's a step-by-step explanation:

Express the equation in the form of y = f(x). Rearrange the equation:

3x + 2x = 8

5x = 8

x = 8/5 or 1.6

Graph the functions y = 3x and y = 8 - 2x on the same coordinate plane. The line represented by y = 3x is upward sloping, and the line represented by y = 8 - 2x is downward sloping.

Plot the points (1.6, 3(1.6)) and (1.6, 8 - 2(1.6)) on the graph.

The point of intersection represents the solution to the equation. In this case, the lines intersect at (1.6, 4.8).

Therefore, the solution to the equation 3x = 8 - 2x is x = 1.6.

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Answer:

2.2

Step-by-step explanation:

(1.85 x 2) - 1.50

...............

Answer:

14 students have to retake the test

Step-by-step explanation:

to calculate the mean mark as

sum of ( product of mark and frequency ) ÷ total

mean = \(\frac{14(2)+15(10)+16(2)+17(3)+18(13)}{30}\)

        = \(\frac{28+150+32+51+234}{30}\)

       = \(\frac{495}{30}\)

      = 16.5

students who score less than 16.5 will retake the test , that is

2 scored 16 , 10 scored 15 , 2 scored 14

number who have to retake test = 2 + 10 + 2 = 14

Answer:

  957,697,598

Step-by-step explanation:

You want a number that has 7 different prime factors.

If we choose 7 primes at random from the first 20, we might have the list ...

  {2, 11, 13, 23, 41, 53, 67}

The product of these primes will have 7 different prime factors.

  2 × 11 × 13 × 23 × 41 × 53 × 67 = 957,697,598

The number 957,697,598 has exactly 7 different prime factors.

__

Additional comment

Any of these factors might have a power greater than 1 without changing the number of different primes. We chose to keep it simple.

The second attachment shows the first 20 prime numbers.