A right triangle has side lengths that are consecutive interest and a perimeter of 12 feet what are the angles of the triangle

Answer:

JL = 12.5

Step-by-step explanation:

[tex] In\: \triangle JKL, KM\perp JL[/tex]

Therefore, by geometric mean property:

[tex] KM^2 = JM\times ML[/tex]

[tex] 6^2 = 8\times ML[/tex]

[tex] 36 = 8\times ML[/tex]

[tex] \frac{36}{8} = ML[/tex]

[tex]ML= 4.5 [/tex]

JL = JM +ML

JL = 8 + 4.5

JL = 12.5

Answer:

142 cm^2

Step-by-step explanation:

2(L*H)+2(L*W)+2(W*H)=SA

7*3=21

21*2=42

7*5=35

35*2=70

5*3=15*2=30

30+70+42=142

Answer:

y=-3/2x+6

Step-by-step explanation:

Answer:

B, D, and E

Step-by-step explanation:

8 oz = 1 cup

1 qt = 32 oz

1 pint = 16 oz

14 cups = 8 x 14 = 112 oz

A)  64 + 64 = 128            no

B)  96 + 16 = 112             yes

C)  32 + 96 + 16 = 144     no

D) 32 + 80 = 112              yes

E)  64 + 32 + 16 = 112       yes

Answer:

x = - 5, x = 2

Step-by-step explanation:

Given

x(x + 7) = 4x + 10 ← distribute left side

x² + 7x = 4x + 10 ( subtract 4x + 10 from both sides )

x² + 3x - 10 = 0 ← in standard form

(x + 5)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 2 = 0 ⇒ x = 2

Answer:

x = 1

y = -2

Step-by-step explanation:

We have the system of equations:

-7*x - 8*y = 9

-4*x + 9*y = -22

To solve this type of system, we need to start by isolating one of the variables in one of the equations.

I will isolate the variable x in the first equation to get:

-7*x - 8*y = 9

-7*x = 9 + 8*y

x = (9 + 8*y)/(-7)

x = -(9 + 8*y)/7

Now we can replace this in the other equation to get:

-4*(-(9 + 8*y)/7) + 9*y = -22

And now we can solve this for y, we will get:

(4/7)*(9 + 8*y) + 9*y = -22

(4/7)*9 + y*(9 + 8*(4/7)) = -22

y*(63/7 + 32/7) = -22 - (36/7)

y*(95/7) = -(22*7/7) - (36/7)

y = (7/95)*(-(22*7/7) - (36/7)) = (-22*7 - 36)/95 = -2

y = - 2

Now we can replace this in the equation x = (9 + 8*y)/(-7) to find the value of x:

x = (9 +8*(-2))/(-7) = 1

Then the solution for the system is the pair (1, -2)

That means:

x = 1

y = -2

Answer:

-24k - 12

Step-by-step explanation:

6(-4k - 2)

-24k - 12

Answer: 36k

Step-by-step explanation: 6(-4k-2) The u disrtube the 6 into ach number in teh perenteces making 6x-4= -24 and 6x2=12 whichs changes the problem to -24-12 which is equal to 36k. Hope this helps :)

Answer:

31.5

Step-by-step explanation:

Ok.

2/3x - 9 = 12

2/3x = 21

x = 21*(3/2)

x = 63/2 = 31.5

Answer:

[tex]x=\frac{63}{2}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3} \times x-9=12[/tex]

Add 9 to both sides:

[tex]\frac{2}{3}x-9+9=12+9\\\frac{2}{3}x=21[/tex]

Multiply both sides by 3/2:

[tex](\frac{3}{2} )\times(\frac{2}{3}x)=(\frac{3}{2} )*(21)\\x=\frac{63}{2}[/tex]

x = 63/2 is your answer.

Answer:

x = 111

Step-by-step explanation:

x + x - 42  = 180     {Lines are parallel. So, they are supplementary}

2x - 42 = 180  

Add 42 to both sides

2x - 42 + 42 = 180 + 42

               2x = 222          {Divide both sides by 2}

                 x = 222/2

x = 111

Answer:

positive and negative or c1

Answer:

1 in 5

Step-by-step explanation:

Multiples of 3 from 1 to 15:

3, 6, 9, 12, 15

Find the lowest multiple of 3.

Formula for probability:

Probability number is drawn/total

3/15

Convert it to simplest form.

1/5

I am not so sure about this, but I have seen people do this, hope I'm not wrong.

Answer:

11.4

Step-by-step explanation:

Since this triangle is a right triangle, we can solve using SOHCAHTOA.

Our angle is 25 degrees and the given hypotenuse length is 27. So, the best trigonometry equation to use would be sine, since it includes the hypotenuse and the opposite side, which is the r length that we are looking for.

Through SOHCAHTOA, sin 25° = [tex]\frac{opp}{hyp}[/tex]

sin 25° = [tex]\frac{r}{27}[/tex]

r = 27 (sin 25°)

Using a calculator, 27 (sin 25°) ≈ 11.4

Answer:

The sides of a right triangle form an arithmetic sequence with the difference is described below in detail.

Step-by-step explanation:

Let's denominate the first term aa and the obvious difference dd. Therefore, your course enhances:

a, a+d, a+2da, a+d, a+2d

Now, these three terms form the sides of a right triangle. Since a+2da+2d is the highest (considering d > 0), we can state that it is the hypothenuse.

applying the Pythagorean Theorem:

a2+(a+d)2=(a+2d)2a2+(a+d)2=(a+2d)2

a2+a2+2ad+d2=a2+4ad+4d2a2+a2+2ad+d2=a2+4ad+4d2

3d2−a2+2ad=03d2−a2+2ad=0

(3d−a)(d+a)=0(3d−a)(d+a)=0

Therefore, your solutions are

3d=a3d=a

andd=−ad=−a

So if a = 3, d = 1. Therfore, one potential  sequence is 3, 4, 5.

Similarly, if a = 6, then d = 2, so another potential sequence is 6, 8, and 10

Answer:

41.472 m²

8.449m²

Step-by-step explanation:

c) scale facot is 7.2/5 = 1.44

the square scale factor is 1.44^2 = 2.0736

times 20 by this to get the area

2.0737x 20 = 41.472 m²

d) 2.8/6 = SF = 0.467

0.2178 x 38.8 = 8.449m²

Answer:

32.5

Step-by-step explanation:

We can set this problem up as a proportion:

[tex]\frac{10}{25} = \frac{13}{x}[/tex] In doing this, we find the exact distance from Boomtown to Dayville. Another way to do it is by dividing 25 by 10, to get 2.5, then multiplying 2.5 by 13 to get 32.5

Answer:

8/49

Step-by-step explanation:

Given data

Sample space

4 red marbles

8 blue marbles

2 green

Sample size

4+8+2 = 14

Pr(picking a red)

Pr(red)= 4/14= 2/7

With replacement

Pr(picking a blue)

Pr(blue)= 8/14= 4/7

Hence the probability of picking a red marble, replacing the item, and then picking a blue marble

= 2/7*4/7

= 8/49

Answer: 40

Step-by-step explanation: 60/3= 20    20x3= 60    20x2=40

Answer:

Step-by-step explanation:

(-1,1) and (0,-2) are points on the line

slope of line = (-2-1)/(0-(-1)) = -3

y-intercept = -2

y = -3x - 2

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

Explanation:

Refer to the diagram below.

If we focus on triangle ACD, then we can use the pythagorean theorem to say

d^2 + m^2 = 2050^2

d^2 = 2050^2 - m^2

Now if we focus on triangle DCB, we can also use the pythagorean theorem to say

d^2 + n^2 = 1420^2

2050^2 - m^2 + n^2 = 1420^2 ...... replace d^2 with 2050^2 - m^2

n^2 - m^2 = 1420^2 - 2050^2

n^2 - m^2 = -2,186,100

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

In the diagram, I set up m and n such that m+n = 3000. This solves to n = 3000-m

We can then say

n^2 - m^2 = -2,186,100

(3000-m)^2 - m^2 = -2,186,100

m^2 - 6000m + 9,000,000 - m^2 = -2,186,100

-6000m + 9,000,000 = -2,186,100

-6000m = -2,186,100 - 9,000,000

-6000m = -11,186,100

m = (-11,186,100)/(-6000)

m = 1864.35

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

We now have enough to find angle theta, which is the angle between segments AC and AD (the line of sight to the first tower and the highway lines respectively)

We'll focus entirely on triangle ACD

cos(angle) = adjacent/hypotenuse

cos(A) = AD/AC

cos(theta) = m/2050

cos(theta) = 1864.35/2050

cos(theta) = 0.90943902439024 which is approximate

theta = arccos(0.90943902439024)

theta = 24.572056388088

theta = 24.6 degrees

Make sure your calculator is in degree mode. One way to check is that cos(60) should evaluate to 0.5

Answer:

35.19

Step-by-step explanation:

equation is : C=2πr

[tex] \Large \underline{\tt Given} :[/tex]

[tex] \\ [/tex]

[tex] \Large \underline{\tt To \: Find} :[/tex]

[tex] \\ [/tex]

[tex] \Large \underline{\tt Solution} :[/tex]

As, we have diameter of circle is 5.6 cm and radius is half of diameter.

[tex] \tt : \implies Radius, r = \dfrac{d}{2}[/tex]

[tex] \tt : \implies Radius, r = \dfrac{5.6 \: cm}{2}[/tex]

[tex] \tt : \implies Radius, r = \dfrac{\cancel{56} \: cm}{10\times \cancel{2}}[/tex]

[tex] \tt : \implies Radius, r = \dfrac{28 \: cm}{10}[/tex]

[tex] \tt : \implies Radius, r = 2.8 \: cm[/tex]

[tex] \\ [/tex]

Now, for Circumference :

[tex] \Large \underline{\boxed{\bf{Circumference = 2\pi r}}}[/tex]

[tex] \tt : \implies Circumference = 2 \times \dfrac{22}{7} \times 2.8 \: cm[/tex]

[tex] \tt : \implies Circumference = \dfrac{44}{\cancel{7}} \times \dfrac{\cancel{28}}{10} \: cm[/tex]

[tex] \tt : \implies Circumference = 44 \times \dfrac{4}{10} \: cm[/tex]

[tex] \tt : \implies Circumference = \dfrac{176}{10}\: cm[/tex]

[tex] \tt : \implies Circumference = 17.6\: cm[/tex]

[tex] \\ [/tex]

Hence, circumference is 17.6 cm.

Answer:

375g

Step-by-step explanation:

250g = 4

X = 10

Cross Multiply

2500=4x

Divide both sides by x

x=625

1000-625

375g left