if the perimeter of an equilateral triangle is 24cm, find the length of it's side​

The length is 25 feet and the width is 135 feet

What are consecutive odd integers?

Consecutive odd integers differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers.

How to find the perimeter of the rectangle?

⇒Perimeter of rectangle = 2(l+w)

The perimeter of a rectangle is 320 feet

let the length of a rectangle is x

The next consecutive odd integer is x+2

width = 5(x+2)

=5x+10

2(length + width) = 320

l+w=160

x+5x+10=160

6x=150

x=25

length = 25 feet

width = 5(25+2)=135 feet

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The solution to the system of equations is (-2, 3)

The plane we want and the plane we're given are parallel, so they share the same normal vector. The normal to [tex]2x+3y-z=0[/tex] is the vector (2, 3, -1), since [tex](2,3,-1)\cdot(x,y,z)=0[/tex].

Then the plane we want has equation

[tex](2,3,-1) \cdot (x-3, y-2, z-5) = 0 \\\\ \implies 2(x-3) + 3(y-2) - (z-5) = 0 \\\\ \implies \boxed{2x + 3y - z = 7}[/tex]

Using proportions, it is found that the difference between the two salary options each year is of $5,545.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

For the first option, $115 per week plus 9.5% commission on the associate’s total sales, the yearly salary is:

115 x 52 + 0.095 x 125000 = $17,855.

For the second option, $450 per week with no commission, the yearly salary is:

450 x 52 = $23,400.

Hence the difference is given as follows:

23400 - 17855 = $5,545.

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The ordered pairs (0,13) and (10, 0) are joined to best draw the line of best fit for the given scatter plot. So, option 4 is correct.

For the given scatter plot, to draw a line of best fit, the slope is to be calculated. The slope of the required line is calculated by

m = [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]

Where,

∑xy = sum of the product of x and y values

∑x = sum of x values

∑y = sum of y values

∑x² = sum of square values of x

n = total number of scatter points

And the y-intercept is calculated by

b = [∑y - m(∑x)]/n

Where m is the slope obtained above

The given scatter plot has the coordinate points:

(0,14), (1, 11), (2, 9), (3, 10),(4, 7), (5, 7), (6, 5), (7, 5), (8, 3), (9, 1), (10, 0)

Such that n = 11

Then the required components are calculated as follows:

∑x = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

∑y = 14 + 11 + 9 + 10 + 7 + 7 + 5 + 5 + 3 + 1 + 0 = 72

∑xy = (0 × 14) + (1 × 11) + (2 × 9) + (3 × 10) + (4 × 7) + (5 × 7) + (6 × 5) + (7 × 5) + (8 × 3) + (9 × 1) + (10 × 0) = 220

∑x² = 0² + 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9² + 10² = 385

Then the slope is calculated as follows:

slope m =  [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]

On substituting,

m = [11(220) - (55)(72)]/[11(385) - (55)²]

⇒ m = -14/11 = -1.2727273 ≅ -1.3

∴ m = -1.3

Then calculating the y-intercept:

we have b = [∑y - m(∑x)]/n

On substituting,

b = [72 - -1.3(55)]/11

∴ b = 13

Then the slope-intercept form of the required line is

y = -1.3x + 13

When x = 0,

y = -1.3(0) + 13 = 13

When y = 0,

0 = -1.3x + 13

⇒ 1.3x = 13

⇒ x = 13/1.3 = 10

Therefore, the coordinates (0, 13) and (10, 0) give the best draw for the line of best fit.

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Volume=80cubic feet

Length×Width×Height =80cubic feet

Base area×Height =80cubic feet

25square feet×Height =80cubic feet

Height =80÷25

=3.2feet

The height of the rectangular prism is 3.2 feet.

To determine the height of a rectangular prism with a volume of 80 cubic feet and a base area of 25 square feet,

The volume of a rectangular prism, that is V = lwh, where l is the length, w is the width, and h is the height of the prism.

Given:

Volume (V) = 80 cubic feet

Base area (A) = 25 square feet

We know that the base area is equal to the product of the length and width:

A = lw.

Calculate the length (l) and width (w) from the given base area:

We know that A = lw, and A = 25 square feet.

If we assume the length to be greater than the width, we can express the base area as lw = 25.

We need to find two factors of 25 that have a difference as small as possible. The factors of 25 are 1, 5, and 25.

We can choose l = 5 feet and w = 5 feet.

V = lwh.

80 = 5 * 5 * h

Divide both sides of the equation by 25:

80/25 = h.

h = 16/5 = 3.2 feet.

Therefore, the height of the rectangular prism is 3.2 feet.

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The value of the polynomial difference when the value of x is 2.1 is -3.51

Polynomials are functions that has a leading degree of 3 and above. Given the following polynomial expression below;

g(x)= 2x^2+3x-9 and;

h(x)=x^2+2x-6

Take the difference

(h-g)(x) = h(x) - g(x)

Substitute

(h-g)(x) = x^2+2x-6 - (2x^2+3x-9)

(h-g)(x) = x^2+2x-6-2x^2-3x+9
(h-g)(x) = -x^2-x+3

Substitute the value of x to have;

(h-g)(2.1) = -(2.1)^2 - 2.1 + 3

(h-g)(2.1) = -4.41 + 0.9

(h-g)(2.1) = -3.51

Hence the value of the polynomial difference when the value of x is 2.1 is -3.51

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Answer:

dean = 10

franco = 50

helen = 2

steps

you want to get the age of one of the people first

'is' means equal

'older than' means plus

'sum' means total by adding

d

f = 5d

d = 8 + h

d + f + h = 62

make sure there is 1 letter to solve for

d = 8 + h -> h = d - 8

f = 5d

d = d

d + f + h = 62

d + (5d) + (d-8)

7d - 8 = 62

7d = 70

d = 10

f = 50

h = 2

The correct option is (d)

He wrote commutative instead of associative in step 2.

According to the commutative property, a mathematical principle, the product of a multiplication does not depend on the order in which the numbers are multiplied.

Commutative property:  a+b = b+a

Associative property: (a+b) + = a+(b+c)

Now consider the provided expression.

(6.2 − 1.6) − 4.4 + 7.8

Step 1:

(6.2 − 1.6) − 4.4 + 7.8

Step 2 Use Associative property

6.2 + (−1.6 − 4.4) + 7.8

Step 3: Simplify

6.2 − 6 + 7.8

Step 4: Use commutative property

14 − 6

Step 5: Simplify

14 − 6 = 8

Hence, the wrong step is step 2.

He wrote commutative instead of associative in Step 2.

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I understand that the question you are looking for is:

Matt is showing his work in simplifying (6.2 − 1.6) − 4.4 + 7.8. Identify any error in his work or reasoning. Step 1: (6.2 − 1.6) − 4.4 + 7.8 Step 2: 6.2 + (− 1.6 − 4.4) + 7.8 (commutative property) Step 3: 6.2 − 6 + 7.8 Step 4: −14 − 6 = 8 (commutative property) Step 5: 14 − 6 = 8

(a)-He wrote commutative instead of distributive in Step 4.

(b)-He wrote commutative instead of distributive in Step 2.

(c)-He wrote commutative instead of associative in Step 4.

(d)-He wrote commutative instead of associative in Step 2.

Answer:

i think answer is 5

Step-by-step explanation:

since you could think what are factors of 36
1x36
2x18
3x12
4x9 and
6x6

Samantha and Mia are 13 km apart from each other.

A right triangle's squared sides add up to the hypotenuse's squared length, according to the Pythagorean Theorem.

Mia is 7 kilometers north of Julia's home as she walked at a speed of 7 kilometers per hour.

Samantha walked at an average speed of 11 km/h, and she is now 11 kilometers west of Julia's home.

A right-angled triangle is formed by Julia's house, Mia and Samantha's locations after one hour, and the figure's points.

Hypotenuse of the triangle, which measures distance between the females

the Pythagorean theorem,

H² = P² + B²

H² = 7² + 11²

H² = 49 + 121

H = √170

H = 13.038

H = 13km

Between them, there is a 13 kilometer distance.

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Answer: 18

Step-by-step explanation:

4 I-2I + (8+2)=

4(2) + 8+2=

8+8+2=

18

Answer:

c if lsrt lstr name two congruent segments

Answer:

a) 7000

b) 20000

c) 300000

Rounding is the act of replacing a number with values that are an approximation.

Basic rounding rules:

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 68 rounded to 1 significant figure would be 70.

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 13 rounded to 1 significant fugue is 10.

3. Zero digits that come after a non zero digit are non significant. Example: 10000 only has 1 significant figure

Calculations:

A) 78 x 92 = 7176

The answer for A is 7000

B) 615 x 38 = 23370

Answer for B is 20000

C) 423 x 764 = 323172

Answer for C is 300000

Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Given solution of a question done by two people.

Jenna's method

5(30+4)

(5)(30)+(5)(4)

150+20=170

Mia's method

5(30+4)

5(34)=170

We are required to find why they have achieved at the same answer.

Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.

Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

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Answer:  C

Step-by-step explanation: the other two options are both wrong, 0.13 is larger than 0.125 and she did order by volume per fish.

Answer:

8 types of sandwiches.

Step-by-step explanation:

she has choices of :

1 turkey sandwich

1 roast beef sandwich

1 ham sandwich

1 white sandwich

1 white bread sandwich

1 American sandwich

1 swiss sandwich

1 colby cheese sandwich.

Answer:

8 types

Step-by-step explanation:

she had alot of choice like :

Turkey, roast beef, ham, swiss, corby cheese, wheat or whitebread and american sandwhich .

The situation described by the distance from Town A is the first graph.

Given that cities A,B and C are on straight line.

We are required to find the graph appropriate the given situation.

Distance is basically the measurement of how far two things,places are located.It can be measurement from one point to another .

On the first hour,they leave town B to town C moving farther from Town A,hence the distance is increasing on the first hour.

On the second hour they stop for lunch,meaning that the distance remains constant at the point, it was at the end of the first hour.

Hence if towns A,B C lie on a straight line and Jack and Arthur start at town B and drive for an hour from Town B to Town C then the distance shown from Town A during these two hours is first graph.

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Answer: 35.7 feet per second.

Step-by-step explanation: The scientist starts at -86 feet. Then she goes to -193 feet. The difference here is 193-86 =  107 feet. That means she traveled 107 ft in 3 seconds. 107/3 = 35 with a remainder of 2. 2/3 approximately equals 0.6666667. We need to round to the nearest tenth which is 0.7. So, we are left with  35.7.

Answer:

255,000,000m^2

Step-by-step explanation:

Let 5:12:17:25 be 5x, 12x, 17 x, 25x respectively

So

Perimeter of quadrilateral=5x+12x+17x+25x

590m=59x

590m/59=x

10m=x

So now value

5x= 5*10 =50

12x= 12*10 =120

17x= 17*10 =170

25x= 25*10 =250

Now

Area of quadrilateral=50m*120m* 170m* 250m

=255,000,000m^2

Step-by-step explanation:

if I understand you correctly the sides are in a

5 : 12 : 17 : 25 ratio.

a ratio is basically a fraction. but instead of the denominator telling us the structure of the whole (e.g. 2/5 tells us that the whole is split into 5 equal parts), a ratio tells us this by the sum of its elements :

5 : 12 : 17 : 25

means that the whole perimeter of the quadrilateral has

5 + 12 + 17 + 25 = 59 equal parts.

since the perimeter is 590 m, we know with 59 equal parts, that one part is 590/59 = 10 m.

so, the sides are

50 m, 120 m, 170 m, 250 m

but for the area of the quadrilateral there is at least the information of one angle missing.

to have just the 4 side lengths is not enough. these sides can still have all kinds of angles between them, which creates different areas.

Answer:

I don't understand the formatting after the first two equations.

Step-by-step explanation:

See attached graph.

The reliability of two components in series is 0.996.

To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.

Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.

We can find this probability multiplying all the ten reliabilities:

P = 0.998^2 = 0.996004

Rounding to three decimal places, we have P = 0.996

The reliability of the engine is 0.996.

Hence,

The reliability of two components in series is 0.996.

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The system of inequalities represented on the graph is:

A linear function is modeled by:

y = mx + b

In which:

The linear function in this problem has y-intercept of b = 3, and also goes through the point (1,5), hence the slope is of 2. The line is dashed, hence it is not included in the solution, hence only the part greater than the line is, hence:

y > 2x + 3

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this graph, the vertex of the parabola is of (-1,-4), hence h = -1, k = -4, and the equation is:

y = a(x + 1)² - 4

When x = 0, y = -3, hence the leading coefficient is found as follows:

-3 = a - 4

a = 1.

Hence:

y = (x + 1)² - 4.

And the inequality is:

y > (x + 1)² - 4.

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To do content analysis on the characteristics people seek in a partner by examining the personals section of three newspapers the unit of analysis will be objective of the section.

Given that we are interested in doing content analysis on the characteristis people seek in a partner by examining the personals section of three newspaper.

Content analysis is basically a research tool used to determine the presence of certain words, themes,or concepts within some given qualitative data. Using content analysis, a researchers can quantify and analye the presence meanings and relationships of such certain words, themes and concepts.

When we are required to do content analysis by examining the personals section of three newspapers, its units can be objective of section. Some part is related to matrimonials, some are for rent,etc.and some are for commercial advertisements.

Hence the unit of analysis is objective of the section.

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Answer:

rotate 180° about origin

The preimage and image of the figure are given below. The transformation rule that is applied is (x, y) → (-x, y).

Given a triangle with vertices A(—3, 2), B(—l, —l), and C(—4, —2), which is preimage. Further, an image is created of this triangle that has vertices at A'(3, 2), B'(l, —l), and C'(4, —2). As shown in the given figure.

Now, as per the image and preimage in the given graph. The image is the reflection of the preimage about the y-axis. This can be verified as when the image and preimage are reflected about the y-axis the vertices change as:

(x, y) → (-x, y)

A(-3, 2) → A'(3,2)

B(-1, -1) → B'(1, -1)

C(-4, -2) → C'(4,-2)

Hence, the transformation rule is (x, y) → (-x, y).

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Radius of smaller circle = 25 in

Radius of larger circle = 25 + 13 = 38 in

Area of ring : Area of larger circle - Area of smaller circle

[tex]\qquad❖ \: \sf \:\pi {(38)}^{2} - \pi {(25)}^{2} [/tex]

[tex]\qquad❖ \: \sf \:\pi( {38}^{2} - 25 {}^{2} )[/tex]

[tex]\qquad❖ \: \sf \:3.14(1444 - 625)[/tex]

[tex]\qquad❖ \: \sf \:3.14(819)[/tex]

[tex]\qquad❖ \: \sf \:2571.66 \: \: in {}^{2} [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer: A, C, and D

Step-by-step explanation:

          A terminating decimal is a decimal that has an end. In other words, [tex]\frac{1}{4} =0.25[/tex] is one, but [tex]\frac{1}{3} =0.3333...[/tex] is not.

✓ A. 0.032

✗ B. 0.999...

✓ C. 0.525

✓ D. 0.75

Answer:

[tex]f(x)=-2(x-3)^2+2[/tex]

Step-by-step explanation:

To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute 0 for x and solve for y.

x-intercept(s): (2,0),(4,0)

y-intercept(s): (0,−16)

Answer:

D     f(x) = -2(x - 3)² + 2

Step-by-step explanation:

The y-intercept occurs at x = 0.

A

f(x) = 2x(x + 14) - 64

f(0) = -64     Not -16

B

f(x) = (x + 4)² + 2x

f(0) = 16     Not -16

C

f(x) = (x - 16)² + 4

f(0) = 260      Not -16

D

f(x) = -2(x - 3)² + 2

f(0) = -18 + 2 = -16   <-------------------- this is it

Correct option for solving the system of two equation is ([tex]y\times z =6[/tex])[tex]\times -8[/tex] .

What is simultaneous linear equation?

A system of simultaneous linear equations is any set of two or more linear equations that share the same unknown variables. Finding values for the unknown variables that simultaneously satisfy all of the equations is required to solve such a system.

Simultaneous linear equations are two linear equations in two variables put together.

The ordered pair (x, y) that satisfies both linear equations is the system of simultaneous linear equations' solution.

Given,

Equation p: [tex]y+z=6[/tex]

Equation q: [tex]8y+7z=1[/tex]

To solve the above simultaneous linear equation multiply the equation p with (-8)

[tex](y+z=6)\times -8[/tex]     ...................................................... Equation (1)

Now add Equation (1) with Equation (q)

[tex]-8y-8z=-48[/tex]

+ [tex]8y+7z=1[/tex]

⇒ [tex]-z=-47[/tex]

⇒ [tex]z=47[/tex]

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Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's consider the shape given to us:

 ⇒ a rectangle with two semicircles cutout on the edges

     ⇒ perimeter/circumference of the two semicircles can count as one

         circle

Let's solve:

               [tex]\hookrightarrow \text{Total circumference} =\frac{1}{2} *\pi *\text{ diameter} +\frac{1}{2} *\pi * \text{diameter}\\= \pi *\text{diameter}=10\pi =10 * 3.14 = 31.4[/tex]

Answer: 59.4 square units

Hope that helps!

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