Lines k and n are perpendicular. If the slope of line k is -6, what is the slope of line n?
A. -6
B.-1/6
C.6
D.1/6

Answer: [tex]x^4[/tex]

Step-by-step explanation:

Here, the given expressions are,

[tex]x^4[/tex]

[tex]x^5[/tex]

The factors of [tex]x^4[/tex] = x × x × x × x

While, the factors of [tex]x^5[/tex] = x × x × x × x × x

Hence, the common factors = x × x × x × x = [tex]x^4[/tex]  

So, the greatest common factor of the given expression is [tex]x^4[/tex]          

Answer:

A. x4

Step-by-step explanation:

Answer:

Evaluate from left to right

Evaluate using order of operations

Step-by-step explanation:

To evaluate any complex expression that contains addition, subtraction , multiply or divide, exponents , parenthesis etc we use order of operation.

Order of operation is PEMDAS

To evaluate , first we simplify the parenthesis part and then exponents

Then do the multiplication and division from left to right.

Finally we do addition and subtraction from left to right

So the rules for evaluating a complex expression is

Evaluate from left to right

Evaluate using order of operations

Tony because he spent $19 while Mario spent $18. To explain, you would multiply 3 by $4 because Tony bought 3 of the $4 packs of pencils. Therefore, he would have spent $12. In addition, add $7 to $12, you get $19. On the other hand, Mario bout 4 of the $6 binders. That would mean he spent $24 on binders However, he had a $6 coupon which means he can take $6 off the total price of $24. That would mean subtracting $6 from $24. That would get Mario $18

View the image to see how I solved this problem.

There is an obvious factor of x², so we can reduce this to the problem of finding zeros of a quadratic by factoring that out. Then, we can determine the zeros of the quadratic factor to complete the finding of zeros for the function.

A factor of x² can be factored out, leaving ...

... f(x) = x²(x² +x +4)

The latter factor has only complex zeros. It can be rewritten by completing the square.

... x² +x +4 = (x² +x +1/4) +(3 3/4) = (x +1/2)² +(3 3/4)

So, the real zeros are where x² = 0, at x = 0. The complex zeros are where the above expression is zero, ...

... (x +0.5)² +3.75 = 0

... (x +0.5)² = -3.75

... x + 0.5 = √-3.75 = ±0.5i√15

... x = -0.5(1 ±i√15)

The function zeros are 0 (multiplicity 2) and -0.5±0.5i√15.

A plot of the points shows you the triangle is an acute triangle.

_____

All angles are less than 90°.

C.) Dilation changes the size

Distributive property: ⇒ a(b+c)=ab+ac

First you had to rewrite down as the nine and its should be three times three is equal to nine. Then you rewrite down as the twenty-seven and its should be nine times three is equal to twenty-seven. Next, you rewrite down as fifteen and its should be five times three is equal to fifteen.

And it gave us ⇒ [tex]=5*3y+9*3-3*3x[/tex].

Then you had to factor out by the common term of three.

And it gave us ⇒ [tex]3(5y+9-3x)[/tex]

Final answer ⇒ [tex]\boxed{=3(5y+9-3x)}[/tex]

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

All 3 terms have a common factor 3 which we can take out

=3 ( 9 - 3x + 5y )

Line segment of length k is divided into 3 equal parts.

so first segment is 0-k/3 and third segment is 2/3k-k

so mid-pt of 1st = k/6 and 3rd = 5/6k

so the distance in between = 5/6k-k/6 = 4/6k = 2/3k

ans is A

The distance between the midpoints of the first segment and the third segment is 2k/3. Hence, option A is the right choice.

The mid-point of a line segment is the point from which the distance to both ends of the line segment is equal.

In the question, we are given a line segment of length k units, which is divided into 3 equal parts.

We are asked to find the distance between the midpoints of the first and third segments.

Firstly, we divide the line segment at points k/3 and 2k/3, to get three equal parts of lengths k/3 each.

Now, the mid-point of the first segment = (0 + k/3)/2 = k/6.

The mid-point of the third segment = (2k/3 + k)/2 = 5k/6

Therefore, the distance between the midpoints of the first segment and the third segment is (5k/6 - k/6) = 4k/6 = 2k/3. Hence, option A is the right choice.

Learn more about midpoints at

https://brainly.com/question/5566419

#SPJ2

Your answer is C.The relation passed the vertical line test.

340 miles because you do 123-21 divided by 0.30.

I'm so smart!! :D

Final answer:

The function y=2x+13 takes on a positive value for x > -6.5 and a negative value for x < -6.5.

Explanation:

The function y=2x+13 represents a linear equation. To find the values of x for which the function takes on a positive value, we need to solve the inequality 2x+13 > 0.

Subtracting 13 from both sides gives 2x > -13.

Dividing both sides by 2, we get x > -6.5.

Therefore, for x values greater than -6.5, the function will be positive.

To find the values of x for which the function takes on a negative value, we need to solve the inequality 2x+13 < 0. Subtracting 13 from both sides gives 2x < -13.

Dividing both sides by 2 and flipping the inequality sign, we get x < -6.5.

Therefore, for x values less than -6.5, the function will be negative.

Answer: First option. y-15=5(x-3)

Solution:

We can take any pair of points of the table. For example:

P1=(3, 15)=(x1, y1)→x1=3, y1=15

P2=(5, 25)=(x2,y2)→x2=5, y2=25

And we can find the slope m using the following formula:

m=(y2-y1)/(x2-x1)

m=(25-15)/(5-3)

m=(10)/(2)

m=5

Now we can apply the point-slope formula to find the equation of the right line:

y-y1=m(x-x1)

Replacing y1=15, m=5, and x1=3

y-15=5(x-3)

The equation in point-slope form that represents the plant's growth over time would be 'y - 9 = 3x', given that the y-intercept is 9 and the slope is 3.

Based on the information given, it is clear that the y-intercept where the line intersects the y-axis is 9 and the slope of the line is 3. We know that y stands for the height of the plant and x for time in months. Using these values, the equation in point-slope form, which is normally written as y - y1 = m(x - x1) where m is the slope and (x1, y1) is a given point on the line, can be simplified assuming that x1=0 and y1 is our y-intercept which is 9.

Therefore, the equation of the line that represents the growth of the plant over time in point-slope form would be y - 9 = 3x.

https://brainly.com/question/29054476

#SPJ3

Answer:

Your answer is 16√3 units2

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

The notation (f∘g)(1) means f(g(1)). We can first find g(1), then use that value as the argument to the f function.

g(1) = 2·1-6 = -4

f(-4) = -4(-4)+7 = 16+7 = 23

Answer:

2

Step-by-step explanation:

Try this solution (see the attachment, there is not the only way).

The short explanation: the target - to prove, PN≠OM; PN⊥OM; point S is midpoint of OM&PN, - the properties of rhombus.

x = 5 or x = - 1

equate f(x) and g(x)

x² - 7x + 3 = - 3x + 8 ( subtract (- 3x + 8 ) from both sides )

x² - 4x - 5 = 0 ← in standard form

(x - 5)(x + 1) = 0

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 1 = 0 ⇒ x = - 1

EXPLANATION

The nth term of the sequence is given by

[tex]U_n=a+(n-1)d [/tex]

Where

[tex]a[/tex]

is the first term and

[tex]d[/tex]

is the constant difference.

We were given that,

[tex]a=6[/tex]

S we just need the common difference to write the nth term.

We can get that from another information given to us.

We were also given that the 4th term is 6. This gives the equation.

[tex]a+3d=-6[/tex]

We substitute

[tex]a=6[/tex]

to obtain

[tex]6+3d=-6[/tex]

Or

[tex]2+d=-2[/tex]

This implies,

[tex]d=-2-2[/tex]

[tex]d=-4[/tex]

We substitute these values into the general formula to obtain,

[tex]U_n=6+(n-1)\times-4[/tex]

This gives us,

[tex]U_n=6+-4n+4[/tex]

[tex]U_n=10-4n[/tex]

Hence the nth term of the sequence is,

[tex]10-4n[/tex]

[tex]a_{n}[/tex] = 10 - 4n

this is an arithmetic sequence with n th term

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d

where [tex]a_{1}[/tex] is the first term and d the common difference

given [tex]a_{4}[/tex] = - 6, then

6 + 3d = - 6 ( subtract 6 from both sides )

3d = - 12 ( divide both sides by 3 )

d = - 4 ← common difference hence

[tex]a_{n}[/tex] = 6 - 4 (n - 1 ) = 6 - 4n + 4 = 10 - 4n

21.6 units

Calculate the length of the 2 inclined sides using the distance formula

d = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (3, 4 )

d = √(3 + 3 )² + (4 - 3)² = √(36 + 1 ) = √37

repeat for (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (3, - 3 )

d = √(3 + 3 )² + (- 3 - 3 )² = √(36 + 36 ) = √72

the vertical side has a length of 7 units

perimeter = √37 + √72 + 7 = 21.6 ( nearest tenth of a unit )

The perimeter of the triangle shown on the coordinate plane is 15.5 units

The perimeter of the triangle is the sum of the lengths of its three sides. To find the lengths of the sides, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

The coordinates of the three points are:

A = (0, 0)

B = (10, 0)

C = (5, 10)

The length of side AB is:

distance from A to B = sqrt((10 - 0)^2 + (0 - 0)^2) = sqrt(10^2) = 10

The length of side BC is:

distance from B to C = sqrt((5 - 10)^2 + (10 - 0)^2) = sqrt((-5)^2 + 10^2) = sqrt(125) = 5 \sqrt{5}

The length of side AC is:

distance from A to C = sqrt((5 - 0)^2 + (10 - 0)^2) = sqrt(5^2 + 10^2) = sqrt(125) = 5 \sqrt{5}

Therefore, the perimeter of the triangle is:

perimeter = AB + BC + AC = 10 + 5 \sqrt{5} + 5 \sqrt{5} = 10 + 10 \sqrt{5}

To the nearest tenth of a unit, the perimeter of the triangle is 15.5 units.

Therefore, the answer is 15.5 units.

For such more question on perimeter

https://brainly.com/question/397857

#SPJ2

The length of fence she will need to divide the garden is 9.22 m.

Rectangle is a quadrilateral (has four sides and four angles) in which both sides are parallel and opposite to each other.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.

From the diagram, let x represent the length of the fence, hence using Pythagoras:

The length of fence she will need to divide the garden is 9.22 m.

Find out more on rectangle at: https://brainly.com/question/2687959

Yes.  Notice that the Pythagorean Theorem applies here.  3^2 + 4^2 = 5^2, so this triangle is a right triangle.

Substitute the value of the variable into the expression and simplify.

1. 24

2. 17

(A) Subtracting the right side from both sides, we get ...

... (20 -4x) -(12 -x +8 -3x) = 0

... (20 -12 -8) +x(-4 +1 +3) = 0

... 0 = 0 . . . . . true for all values of x (infinite solutions)

(B) Subtracting the right side from both sides, we get ...

... (5x +4x -3) -(24 +8x) = 0

... x(5 +4 -8) +(-3 -24) = 0

... x -27 = 0

... x = 27 . . . . . . (one solution)

(C) Subtracting the right side from both sides, we get ...

... (5x +6) -(2x +6 +3x -15) = 0

... x(5 -2 -3) +(6 -6 +15) = 0

... 15 = 0 . . . . . . . not true for any value of x (no solutions)

A) The price elasticity of demand is given by

... Ed = (dx/dp)·(p/x)

... = -250·(15/(9500-250·15)) ≈ -0.652

B) This value has a magnitude less than 1, so price can be increased to increase revenue.

_____

The price at which Ed has a magnitude of 1 is ...

... 250p/(9500 -250p) = 1

... 250p = 9500 -250p

... 500p = 9500

... p = 9500/500 = 19

Revenue will increase as price increases up to $19 per pair.

DC = [tex]\frac{5}{2}[/tex] = 2.5

since the triangles are similar then the ratios of corresponding sides are equal

[tex]\frac{AC}{AD}[/tex] = [tex]\frac{BC}{DE}[/tex]

[tex]\frac{7.5+DC}{7.5}[/tex] = [tex]\frac{8}{6}[/tex] (cross-multiply )

45 + 6DC = 60

6DC = 60 - 45 = 15 ( divide both sides by 6 )

DC = [tex]\frac{5}{2}[/tex]

Initial amount: $210,000

Setting aside: $50,000

Remaining: $160,000

3/4 of remaining amount: 160,000 times 0.75 = $120,000

1/4 of remaining amount: 160,000 times 0.25 = $40,000

28/33 × 100% = 0.84848... × 100% ≈ 85%

Michael got about 85% of the available points.

_____

Since we're not told the number of points per question, we don't actually have enough information to answer the question.

To find out the percentage of correct answers, divide the number of correct answers by the total number of questions and multiply by 100. Michael got 85% of the questions correct on his math test.

To find out what percent of the questions Michael answered correctly, we need to divide the number of correct answers by the total number of questions and multiply by 100.

Here's the step-by-step calculation:

So, Michael got 85% of the questions correct on his math test.

Learn more about Percentage Calculation here:

https://brainly.com/question/329987

#SPJ2