Using Angle Relationships to Solve Equations

Answer:

The length of legs lm, mn, and lk is 32 while that of kn is 36.

Step-by-step explanation:

The diagram is attached in the answer.

As both the angles are equal thus the two forms isosceles triangles. This is true because the converse of base angle theorem is applicable here. The theorem clearly states that when a trapezoid is divided by the diagonal, it forms two set of angles where m<1=m<2 and m<lmk=m<nmk

This leads the two set of legs such as

[tex]\dfrac{lm}{kn}=\dfrac{8}{9}[/tex]

Or this could be written as

[tex]lm=8x\\kn=9x[/tex]

Now the remaining two sides are given as

[tex]lk=lm[/tex] as this form an isosceles triangle so

[tex]lk=8x[/tex]

Similarly

[tex]mn=lm\\[/tex]

Or

[tex]mn=8x[/tex]

Now the perimeter is given as

[tex]\text{perimeter}=lm+mn+kn+lk\\[/tex]

Here perimeter is given as 132 so this gives:

[tex]\text{perimeter}=lm+mn+kn+lk\\132=8x+8x+8x+9x\\132=33x\\x=\dfrac{132}{33}\\x=4[/tex]

So the four legs are of length as given below:

[tex]lm=8x=8\times 4=32\\mn=8x=8\times 4=32\\lk=8x=8\times 4=32\\kn=9x=9\times4=36[/tex]

So the length of legs lm, mn, and lk is 32 while that of kn is 36.

Answer:

D. 140

Step-by-step explanation:

In the equation, [tex]ax^2+bx+c=0,[/tex] the discriminant can be found with [tex]b^2-4ac[/tex].

In this equation,

the discriminant would be: [tex](-10)^2-4(2)(-5)=100+40=140[/tex]

Answer:

D. 140

Step-by-step explanation:

D = b² - 4ac

So, let's identify our values.

a = 2

b = -10

c = -5

Now, we can plug in our values.

D = -10² - 4(2)(-5)

D = 100 + 40

D = 140

Answer:

75—the profit

Step-by-step explanation:

simply subtract the cost price from selling price

325-250=75

Answer:

$75

Step-by-step explanation:

Calculating profit or loss:

Selling price - Cost price

The profit or loss

= 325-250

= +$75

∴ It has a profit of $75.

Answer:

Step-by-step explanation:

4x + 3y = 9

Slope of line = -4/3

Slope of perpendicular to line = ¾

Equation of perpendicular:

y-3 = ¾(x+2)

Answer:

20

Step-by-step explanation:

Subtract the 2 from the width of 7, and then multiply the height by the width.

4x5=20

Answer:

show the options

Step-by-step explanation:

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

Answer:

The answer is 17.4.

Step-by-step explanation:

Mean is the average of all the numbers. To do this, you have to add up all the numbers then divide by how many numbers there are.

First, let's add up all the numbers.

11+14+15+16+16+18+20+20+22+22 = 174!

Next, let's divide the numbers by how many numbers there are. There are 10 numbers in total.

174÷10 = 17.4

Hope this helps! :3

Answer:

17.4

Step-by-step explanation:

To find the mean of a data set, add all numbers. Then, divide the sum by how many numbers are present.

11 + 14 + 15 + 16 + 16 + 18 + 20 + 20 + 22 + 22 = 174

There are 10 numbers, so divide 174 by 10.

174 / 10 = 17.4

Therefore, 17.4 is the mean of the data set.

Answer:

7x² - 6x + 4

Step-by-step explanation:

(4x² - x + 6) - (-3x² + 5x + 2)

4x² - x + 6 + 3x² - 5x - 2

4x² + 3x² - x - 5x + 6 - 2

7x² - 6x + 4

Answer:

edit: the answer is 1

none; I've tried all of them but they didn't work sorry

Step-by-step explanation:

211,000(1-.041/.1)^3 is the equation i used to check them

.1 because every 10 years

30*.1 is 3

decreases at a rate of .041 or 4.1%

edit: it's 1

the .1 wasn't required so it is:

211,000 (1-.041)^3

Answer:

45 is the correct answer

Answer: -15

HOPE THIS HELPS

Answer:

Step-by-step explanation:

k stands for 1000

Answer:

Solution given:

12.2k - 4.000

12.2×1000-4.000

=12196 is your answer.

Answer:

I can answer the type of angle: Acute

Step-by-step explanation:

It's less than 90 degrees, so it's [tex]acute.[/tex]

Answer:

32/24

Step-by-step explanation:

16 times 2 is 32

The value of a/b is 4/3.

The unitary method is used to find the value of a single unit from a given multiple.

One box has 16 apples.

One box has 24 lemons.

If 'a' is the weight of  box of apples and 'b' is the weight of box of lemons.

As each apples weigh 2 times the lemon

Weight of box of apples= 16*2*b=32b

Weight of lemon box = 24b

So, a/b

=32b/24b

=32/24

=4/3.

Hence, value of a/b is 4/3.

Learn more about unitary method here:

https://brainly.com/question/23423168

#SPJ2

Answer:

q te ayude tu papá o mamá ajjajajajajajajajajajajajajajaja

Answer:

Rational

Step-by-step explanation:

This can be reduced to a ratio of 1/2. Numbers that can be expressed as ratios are rational.

Answer:

Step-by-step explanation:

The white box is a rectangle with width of:

a = 2 m

and length of:

b = 7 m - 1 m = 6 m

So its area is  A = 2 m × 6 m = 12 m²

{The shaded blue area is: (5 m + 1 m)(8 m) - 12 m² = 48 m² - 12 m² = 36 m²}

Given:

The equation is:

[tex]12=5^x[/tex]

To find:

The logarithmic equation that is equivalent to the given exponential equation.

Solution:

According to the property of logarithm:

[tex]a=b^x\Leftrightarrow \log_b a=x[/tex]

We have,

[tex]12=5^x[/tex]

Here, [tex]a=12,b=5[/tex]. By using the above property of logarithm, we get

[tex]\log_{5}12=x[/tex]

[tex]x=\log_{5}12[/tex]

Therefore, the correct option is C.

Answer:

Step-by-step explanation:

7)

perimeter of a circle is d[tex]\pi[/tex]

50[tex]\pi[/tex]= 157.0796 for both of the circular ends

plus 200 for the two straights

357.07 m

8)

the triangle is 8*2.5 =20  for both sides

10*10 = 100

and 5*7=35  but that's a negative , it's subtracted

120-35=85

85 [tex]in^{2}[/tex]

Now go out side and get exercise  :)

Answer: 65in

Step-by-step explanation:

Break the trapezoid into a rectangle (8in by 10in) and the leftovers are 2 triangles. Find the area for the triangles. Because the top of the trapezoid is 10in and the bottom is 15in, then we know that 15-10 = 5 and that the triangles are 2.5in by 8in. Because the triangles are the same congruent, then just multiply 8 by 2.5 to get 20.

Find the middle part now, which is 8 times 10 to get 80. Then 80 + 20 = the area of the trapezoid.

Lastly, subtract the non shaded region (7x5=35) and then 100-35 = 65

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of calculations of bills.

The bill calculation goes as equation,

y = $250 + n*($10)

here, n = number of lines,

1.) For n = 2 , Y = cost = 250 + 20 = $270

2.) for n = 4 , Y = $290

3.) for n = 6 , Y = $310

4.) for n = x, Y = $250 + x*($10)

for lastly 12 members we get as,

Y = 250 + (12)*(10) = 250+120 = $370

The surface area of the composite solid is 165 [tex]feet^2[/tex].

We possess

4 triangles, each measuring 6 feet in height and 5 feet in base

4 rectangles, each measuring 5 feet long and 4 feet wide

1 square has side a = 5 feet.

The formula for a triangle's area is:

[tex]A_T=\frac{1}{2} bh[/tex]

Substitute:

[tex]A_T=\frac{1}{2} 5*6\\A_T=\frac{1}{2} 30\\A_T=15 ft^2[/tex]

Formula for calculating a rectangle's area:

[tex]A_R=lw[/tex]

Substitute:

[tex]A_R=5*4\\A_R=20 ft^2[/tex]

The formula for a square's area is as follows:

[tex]A_s=a^2[/tex]

Substitute:

[tex]A=s=5^2\\A_s=25 ft^2[/tex]

The composite solid's surface area is:

[tex]SA=4A_T+4A_R+A_s[/tex]

Substitute:

[tex]SA=4*15+4*20+25\\SA= 60+80+25\\SA=165 ft^2[/tex]

The composite solid has a surface area of 165 [tex]feet^2[/tex].

To learn more about surface area, refer:-

https://brainly.com/question/29298005

#SPJ1

Answer:

700 total sales

Step-by-step explanation:

The computation is shown below:

After 15% discount i.e.

= 100 - 15

= 85%

Now

85% = 595 sales of less than € 100

So,

15% = x sales of € 100 or more than € 100

After this

(595 × 15) ÷ 85 = 105 sales of € 100 or more than € 100

The number of total sales is

= 595 + 105

= 700 total sales

Answer:

square - quad with four right angles and four congruent sides

rectangle - quad with four right angles

parallelogram - quad with two pairs of parallel sides

rhombus - quad with four congruent sides

trapezoid - quad with one set of parallel sides

Answer:

75

Step-by-step explanation:

x=60

i litterly just finished this question and lesson tell me if u need help with others

Answer:

B, C, and E

Step-by-step explanation:

Answer:

98.8 cm²

Step-by-step explanation:

Hi there!

[tex]A=\frac{1}{2} Pa[/tex] where P is the perimeter of the pentagon and a is the apothem (the line going from the center of the pentagon one edge)

1) Find the perimeter

[tex]P=5l[/tex] where l is the side length

Plug in the side length 7.6 cm

[tex]P=5(7.6)\\P=38[/tex]

Therefore, the perimeter of the pentagon is 38 cm.

2) Find the area

[tex]A=\frac{1}{2} Pa[/tex]

Plug in the perimeter (38) and the apothem (5.2)

[tex]A=\frac{1}{2} (38)(5.2)\\A=\frac{1}{2} (38)(5.2)\\A=\frac{1}{2} (197.6)\\A=98.8[/tex]

Therefore, the area of the pentagon is 98.8 cm².

I hope this helps!

Answer: a,c,d

Step-by-step explanation:

Answer:

71.70

Step-by-step explanation:

Answer:

71.70 for sure