bills new [porch is rectangular with an area of 50 square feet if the length of the porch is two times the width what is the perimeter of the porch

Answer:

The centroid is located at (3,3)

Step-by-step explanation:

Centroid Of A Triangle

The centroid of a triangle is the point where its three medians intersect. It is also the center of gravity of the triangle. The medians are lines that go from each vertex to the midpoint of the opposite side.

Given A(ax,by), B(bx,by), C(cx,cy) the points of the vertices, then the coordinates of the centroid [tex]P(x_c,y_c)[/tex] are

[tex]\displaystyle x_c=\frac{ax+bx+cx}{3}[/tex]

[tex]\displaystyle y_c=\frac{ay+by+cy}{3}[/tex]

The vertices are  (0,1) (2,6) (7,2), thus

[tex]\displaystyle x_c=\frac{0+2+7}{3}=3[/tex]

[tex]\displaystyle y_c=\frac{1+6+2}{3}=3[/tex]

The centroid is located at (3,3)

The coordinates of centroid are (3,3)

Step-by-step explanation:

The coordinates of centroid of a triangle are calculated by finding average of x-coordinates of vertices and the average of y-coordinates of vertices.

Given vertices are:

(0,1) (2,6) (7,2)

So,

x-coordinate of centroid:

[tex]x = \frac{0+2+7}{3}\\=\frac{9}{3}\\= 3[/tex]

y-coordinate of centroid:

[tex]y = \frac{1+6+2}{3}\\=\frac{9}{3}\\= 3[/tex]

Hence,

The coordinates of centroid are (3,3)

Keywords: Triangle, centroid

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Answer:

answer is y-5=-3(x-3)

Step-by-step explanation:

your y-coordinate is 5 s you would write y-5 and your slope is -3 with your x-coordinate as 3 so that would be written as -3(x-3).  The equation put together correctly would be y-5=-3(x-3)

Answer:

y-5=-3(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-3(x-3)

Answer:

The value of each share decreased by $8.

Step-by-step explanation:

Number of shares of a certain stock Linda owned = 4

Total value of shares went down by = $32

So find the change in value of each share.

Solution:

Let the total value of each share in dollars be = [tex]x[/tex]

Value of 4 shares in dollars will be = [tex]4x[/tex]

The total value of shares went down by $32

So, new value of 4 shares = [tex]4x-32[/tex]

New value of each share = [tex]\frac{New\ value\ of\ total\ shares}{4}[/tex]

⇒ [tex]\frac{4x-32}{4}[/tex]

Splitting the denominators.

⇒ [tex]\frac{4x{{4}-\frac{32}}{4}[/tex]

⇒ [tex]x-8[/tex]

Original value of each share in dollars was = [tex]x[/tex]

New value of each share in dollars = [tex]x-8[/tex]

Thus, we can see that the value of each share decreased by $8.

Answer:

77.78

Step-by-step explanation:

Answer:

77.78

Step-by-step explanation:

i had this ? on rsm student portal.

The y-intercept of [tex]\(12x + y^3 = 2\) is at \((0, \sqrt[3]{2})\).[/tex]

To find the y-intercept of the equation [tex]\(12x + y^3 = 2\)[/tex], we first need to understand what the y-intercept represents. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of this point is 0.

To find the y-intercept, we set [tex]\(x = 0\)[/tex] in the equation and solve for y:

[tex]\[12(0) + y^3 = 2\][/tex]

[tex]\[y^3 = 2\][/tex]

To solve for y, we take the cube root of both sides:

[tex]\[y = \sqrt[3]{2}\][/tex]

So, the y-intercept of the equation is [tex]\((0, \sqrt[3]{2})\).[/tex]

135 cubes are required to fill the prism

Solution:

Given that a rectangular prism with volume of 5 cubic units is filled with cubes with side lengths of [tex]\frac{1}{3}[/tex] units

Then the number of cubes required to fill the prism will be given by:

[tex]\text { number of cubes }=\frac{\text {volume of rectangular prism}}{\text {volume of cube}}[/tex]

Volume of rectangular prism = 5 cubic units

[tex]\text{ Volume of cube}=(\text { side })^{3}$[/tex]

[tex]\text { Volume of cube }=\left(\frac{1}{3}\right)^{3}=\frac{1}{27}[/tex]

Therefore number of cubes required to fill the prism are:

[tex]\text { number of cubes }=\frac{5}{\frac{1}{27}}=5 \times 27=135[/tex]

Therefore 135 cubes are required to fill the prism

Answer:

135

Step-by-step explanation:

Answer:

Step-by-step explanation:

an = 6n - 13

If n  = 10  ,  a10 = 6*10 - 13 = 60-13 = 47

If n  = 11 ,  a11 = 6*11 - 13 = 66-13 = 53

If n  = 12  ,  a12 = 6*12 - 13 = 72-13 =  59

The formula to find the nth term of the sequence an, is a(n) = -13 + 6n

From the question, we have the following parameters that can be used in our computation:

a(10) = 47

a(11) = 53

a(12) = 59

a(13) = 65

The nth term of an arithmetic sequence can be represented as

a(n) = a(1) + (n - 1) * d

Where,

common difference,

d = 6

So, we have

a(n) = a(1) + (n - 1) * 6

Using the 12th term, we have

a(1) + (12 - 1) * 6 = 59

a(1)  = 59 - 66

a(1)  = -7

So,, we have

a(n) = -7 + (n - 1) * 6

Expand

a(n) = -13 + 6n

Hence, the formula to find an is a(n) = -13 + 6n

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Answer:

A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.

Step-by-step explanation:

find the number line best shows how to solve −8 − (−6)

In the number line first we start with -8 . negative and negative becomes positive

from -8 move 6 units to the right. So it ends at -2

A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.

For this case we must simplify the following expression:

[tex](2a ^ 3-5a) - (7a+ 3a ^ 2) =[/tex]

By definition of the law of multiplication signs we have to:

[tex]- * + = -[/tex]

Rewriting the expression we have:

[tex]2a ^ 3-5a-7a-3a ^ 2 =[/tex]

We add similar terms taking into account that:

Equal signs are added and the same sign is placed.

[tex]2a ^ 3-3a ^ 2-12a[/tex]

ANswer:

[tex]2a ^ 3-3a ^ 2-12a[/tex]

Answer:

The area of cardboard required is 40750 cm².

Step-by-step explanation:

Given:

Length (L) = 25 cm

Width (W) = 5 m = 5 × 100 = 500 cm

Height (H) = 15 cm

Area of the cardboard is same as the total surface area of the closed rectangular box.

Total surface area of the rectangular box is given as:

[tex]SA=2(LW+WH+LH)\\\\SA=2(25\times 500+500\times 15+15\times 25)\\\\SA=2(12500+7500+375)\\\\SA=2\times 20375=40750\ cm^2[/tex]

So, the area of cardboard required is 40750 cm².

After 16 hours, the charges will be same.

Step-by-step explanation:

Given,

Janet's upfront fee = $20

Charges per hour = $7.50

Let,

x be the number of hours.

J(x) = 7.50x+20

Lisa has no upfront fee.

Charges per hour = $8.75

L(x) = 8.75x

For the charges to be equal;

J(x) = L(x)

[tex]7.50x+20=8.75x\\20=8.75x-7.50x\\20=1.25x\\1.25x=20[/tex]

Dividing both sides by 1.25

[tex]\frac{1.25x}{1.25}=\frac{20}{1.25}\\x=16[/tex]

After 16 hours, the charges will be same.

Keywords: function, division

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Answer:

16.00

Step-by-step explanation:

When you divide twenty percent(0.20) to 20.00 you will get sixteen or 4.00 dollars off

Answer:

16 serving.

Step-by-step explanation:

Given: 3/4 cup servings.

Now, computing the number of serving in 12 cups of cherries.

Using unitary method to solve.

∴ Number of serving= [tex]total\ cups \times number\ of\ serving\ per\ cup[/tex]

Number of serving in one cup is [tex]\frac{4}{3}[/tex]

Number of serving in 12 cups = [tex]12\times \frac{4}{3} = 16 \ serving[/tex]

Number of serving in 12 cups= [tex]16\ serving[/tex]

∴ There are 16 serving is possible in 12 cups of cherries.

Final answer:

To calculate the number of 3/4 cup servings in 12 cups of cherries, divide 12 by 3/4, which equals 16 servings.

Explanation:

To determine how many 3/4 cup servings are in 12 cups of cherries, we can divide the total number of cups by the size of one serving.

First, we express the serving size and the total amount in the same units: 3/4 cup and 12 cups.

Next, we divide the total amount of cherries by the serving size: 12 cups ÷ 3/4 cup.

To perform the division, we can multiply 12 by the reciprocal of 3/4, which is 4/3 (12 × 4/3 = 16).

The result is that there are 16 servings of 3/4 cup in 12 cups of cherries.

Answer:

x<=5

Step-by-step explanation:

Two things

The bearing of A from B according to the diagram is 82.86°

Using trigonometric relations ;

B = bearing of A from B

Now we have;

Tan B = 40 /5

Tan B = 8

Take the inverse value of the tangent ;

[tex]B = Tan^{-1} (8) [/tex]

B = 82.86°

Hence, the bearing of A from B is 82.86°

7/19

bc 2 5/7 = 19/7. the reciprocal is a fraction reversed. or upside down that is. So, your answer is 7/19

Answer:

7/19

Step-by-step explanation:

2 5/7=19/7

225

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Answer: 3x-x+2=4

Step-by-step explanation:

absolute value of 225 = | 225 | = 225    

Answer:

y=x/2−1/2

Step-by-step explanation:

Answer:

C. (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.

Step-by-step explanation:

The function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

The parent function is:

g(x) = IxI

And we have:

f(x) = I6x - 2I - 7

Rearranging the function:

f(x) = 6Ix - 1/3I - 7

Then, now let's define some transformations:

If we start with g(x), a translation of N units to the right is:

f(x) = g(x - N)

if we start with g(x), a translation of N units up is:

f(x) = g(x) + N

A translation down would be:

f(x) = g(x) - N

And a vertical dilation of scale factor A is written as:

f(x) = A × g(x)

Then in this case we have:

A translation to the right of 1/3 units.

A dilation of scale factor 6.

A translation down of 7 units.

And the axis of symmetry will be when the absolute value part is equal to zero, or when

6Ix - 1/3I = 0

And that is when x = 1/3.

Therefore, the function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.

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Answer:

Answer 1.) f(x)=0x-4

Answer 2.) f(x)=2/3x+4

Answer 3.) i don't really get this one so sorry

Answer 4.) f(x)= -1/5x+2

hope this helped it took me a while to figure out this but looks like the guy ahead of me beat me to it

Step-by-step explanation:

Answer:

No.

Step-by-step explanation: Assuming you mean x^3*x-7, these two equations do not produce the same line.

Answer:

Step-by-step explanation:

[tex]x^3\cdot x^{-7}=x^{3+(-7)}=x^{-4}\\\\\text{used}\ a^n\cdot a^m=a^{n+m}\\\\\text{Other way}\\\\a^{-n}=\dfrac{1}{a^n}\\\\x^3\cdot x^{-7}=x^3\cdot\dfrac{1}{x^7}=\dfrac{x^3}{x^7}=\dfrac{x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1}{x\!\!\!\!\diagup_1\cdot x\!\!\!\!\diagup_1 \cdot x\!\!\!\!\diagup_1 \cdot x\cdot x\cdot x\cdot x}=\dfrac{1}{x^4}=x^{-4}[/tex]

Answer:

See explanation

Step-by-step explanation:

1. Lines l and k are parallel. These lines are cut be transversal n. Angles 2 and 7 are corresponding angles when parallel lines l and k are cut by transversal n. By Corresponding Angles Ttheorem, angles 2 and 7 are congruent.

2. Lines m and n are parallel. These lines are cut be transversal k. Angles 2 and 10 are alternate interior angles when parallel lines m and n are cut by transversal k. By Alternate Interior Angles Theorem, angles 2 and 10 are congruent.

3. Angles 2 and 7 are congruent (see 1)

   Angles 2 and 10 are congruent (see 2)

  Hence, angles 7 and 10 are congruent by transitive property.

Answer:

x>5

Step-by-step explanation:

-3(2x+5)<-45

2x+5<-45/-3

2x+5<15

2x<15-5

2x<10

x<10/2

x<5

x>5

Answer:

No

Step-by-step explanation:

A function is a relation in which no two ordered pairs have the same first element.

A function associates each element in its domain with one and only one element in its range.

Answer:

B

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 8) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line

m = [tex]\frac{-4-8}{2+1}[/tex] = [tex]\frac{-12}{3}[/tex] = - 4 → B

Answer:

The slope of the given line is -4.

So, option (B) is correct.

Step-by-step explanation:

We know that, slope (m) of a line passing through points (x₁, y₁) and (x₂, y₂) is given by,

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Now, the given line passes through the point (-1, 8) and (2,-4).

So, (x₁, y₁) = (-1, 8) and (x₂, y₂) = (2, -4)

So, by using the above formula, we get

Slope(m) of the given line passing through (-1, 8) and (2, -4) is given by,

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-4-8}{2-(-1)}[/tex]

[tex]\implies\;m = \frac{-12}{3}=-4[/tex]

∴The slope of the given line is -4.

Hence, option (B) is correct.

Answer:

1) Expression is

[tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]

2) The standard form of the expression is

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

3) The expression is

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

Where [tex](n+1)^3[/tex] is the cube of the middle integer

Step-by-step explanation:

1) Given three consecutive integers are n. n+1, and n+2

Now multiplying the three consecutive integers

[tex](n)(n+1)(n+2)=(n^2+n)(n+2)[/tex]

[tex]=n^3+2n^2+n^2+2n[/tex]

[tex]=n^3+3n^2+2n[/tex]

Therefore [tex](n)(n+1)(n+2)=n^3+3n^2+2n[/tex]

Now adding the middle integer to the result of the multiplication.

ie, adding (n+1) to the result of the multiplication [tex]n^3+3n^2+2n[/tex]

[tex](n+1)+(n^3+3n^2+2n)=n+1+n^3+3n^2+2n[/tex]

[tex]=3n+1+n^3+3n^2[/tex]

Therefore [tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]

2) Expression is [tex]n^3+3n^2+3n+1[/tex]

Now we simplify the above expression

[tex]n^3+3n^2+3n+1=n^3+3n^2(1)+3(n)(1)^2+1^3[/tex]

[tex]=(n+1)^3[/tex]      (by using [tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]  , Here a = n and b=1)

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

3) The expression is

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

Where [tex](n+1)^3[/tex] is the cube of the middle integer.

ie, expression is equivalent to the cube of the middle integer

Answer:

[tex]x>22.5[/tex]

Step-by-step explanation:

Given linear inequality:

[tex]2x+5>50[/tex]

Solving for [tex]x[/tex]

Subtracting both sides by 5.

[tex]2x+5-5>50-5[/tex]

[tex]2x>45[/tex]

Dividing both sides by 2.

[tex]\frac{2x}{2}>\frac{45}{2}[/tex]

∴ [tex]x>22.5[/tex]

The graph of the inequality is shown below.

The line is represented by dotted line because the inequality sign is only greater than which means 22.5 is not included in the solution.  

Answer:

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

first add up the xs that gives you 5x because first 3x+4x gives you 7 then minus that with 2x that gives you five,

now add the numbers -76+96 that gives you 20 now the equation becomes

5x=20

now divide 20 by 5 that gives you 4