A rope is cut so that one piece is three times the length
of the other. Each rope is then used to enclose an area
in the shape of an equilateral triangle. If the area
enclosed by the shorter rope is 1,000 m2, what is the
area enclosed by the longer rope?

Answer:

m<1=120

Step-by-step explanation:

A linear pair adds up to 180 degrees.

So <1+<2=180

Let <2=X, that would make <1=2X because <1 is 2 times more.

So substitute that into the equation.

2x+x=180.

Combine like terms and get 3x=180

Divide both sides by 3 and get x=60.

Substitute that into <1 and get <1=120

Answer:

x= -3

Step-by-step explanation:

12x-8x = -20+8

4x = -12

x= -12/4

x = -3

Steps:

Step 1: Subtract 8x from both sides.

12x−8−8x=8x−20−8x

4x−8=−20

Step 2: Add 8 to both sides.

4x−8+8=−20+8

4x=−12

Step 3: Divide both sides by 4.

4x/4   =    −12/4

Answer: x=−3

Please mark Brainliest

Hope this helps.

Answer:

The rate of change is "5"

which agrees with the last answer option

Step-by-step explanation:

Use the expression for the rate of change between two points on the plane:

[tex]rate\,of\,change=\frac{y_2-y_1}{x_2-x_1} \\rate\,of\,change=\frac{-5-0}{-2-(-3)}\\rate\,of\,change=\frac{-5}{1}\\rate\,of\,change=5[/tex]

Answer: is 5 I just took the test

Step-by-step explanation:

Answer:

Choice A. The shading in the Venn Diagram shown in the first attachment represents the set [tex](K \cup M) \; \cap \; (K \cup L)[/tex].

Step-by-step explanation:

Let [tex]A[/tex], [tex]B[/tex], and [tex]C[/tex] be sets. By the distributive law of sets, [tex]A \cup (B \cap C)[/tex] and [tex](A \cup B) \cap (A \cup C)[/tex] refer to the same set.

Apply this property to simplify the given expression:

[tex]\begin{aligned}(K \cup M) \; \cap\; (K \cap L) = K\cup (M \cap L)\end{aligned}[/tex]

[tex]M \cap L[/tex] refers to the intersection between the two lower circles. The union of that intersection with set [tex]K[/tex] (the upper circle) would be the shaded region seen in choice A.

Answer:

6/13

Step-by-step explanation:

There are 13 marbles total in the bag.

The chance of picking a green marble is 6/13. This fraction cannot be simplified.

Answer:

true

Step-by-step explanation:

11a - 2a

Factor out a

a(11-2)

a *9

9a

Answer:

9a is equivalent to 11a - 2a because 11a-2a=9a

Step-by-step explanation:

Answer:

hope this helps you

Explanation:

This is for contrapositive negating the converse of the conditional.

Hence,option D is correct.

Hope it helps

Good luck on your assignment

Answer:

x = 10

Step-by-step explanation:

The base angles of an isosceles triangle measure the same

The three angles of the triangle and 50 , 50 and <2

They sum to 180 degrees

50 +50 + 8x = 180

Combine like terms

100+8x = 180

Subtract 100 from each side

100-100 +8x = 180 - 100

8x= 80

Divide by 8

8x/8 = 80/8

x = 10

Answer:

x =10

Step-by-step explanation:

this is isosceles Δ so it has base ∠ that are =

sum of angles in Δ is 180 so 180 -50-50 = 80

m<2= 80

80= 8x

x =10

Answer:

6²

Step-by-step explanation:

Using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex] , thus

[tex]\frac{6^{7} }{6^{5} }[/tex] = [tex]6^{(7-5)}[/tex] = 6²

The answer is 6^2.

Division is the process of splitting a number or an amount into equal parts.

here, we have,

6^7/6^5

we know,

a^m/a^n

=a^(m-n)

so, we get,

6^7/6^5

=6^2

hence, The answer is 6^2.

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Answer:

The greatest common factor is 5.

15x+10=5(3x+2)

Answer:

A) y = 1/3x + 10/3

Step-by-step explanation:

Answer:

The truck can not safely pass under the bridge

Step-by-step explanation:

The maximum height in inches is 149in.

12 feet times 12 inches = 144 in

144 +5 = 149in

If the truck is 162 inches than it would not be safe for it to pass under the bridge.

I hope this helps you!

Answer:

5 p.m.

Step-by-step explanation:

Newton's law of cooling-

[tex]T(t)=t_a+(t_0-t_a)e^{-kt}[/tex]

where,

[tex]t_0[/tex] = the initial temp. = 98.6 F (human body temp.)

k = 0.1947,

T(t) = 66 F,

[tex]t_a[/tex] = 55 F,

Putting the values,

[tex]\Rightarrow 66=55+(98.6-55)e^{-0.1947\cdot t}\\\\\Rightarrow 66=55+(43.6)e^{-0.1947\cdot t}\\\Rightarrow (43.6)e^{-0.1947\cdot t}=11\\\Rightarrow e^{-0.1947\cdot t}=\dfrac{11}{43.6}=0.2523\Rightarrow \ln e^{-0.1947\cdot t}=\ln 0.2523\\\Rightarrow -0.1947\cdot t\times \ln e=\ln 0.2523\\\Rightarrow -0.1947\cdot t\times 1=\ln 0.2523\\\Rightarrow t=\dfrac{\ln 0.2523}{-0.1947}\\\Rightarrow t=7\ h[/tex]

Therefore, the time of death was 7 hours before midnight i.e at 5 pm.

Answer:

N=6

Step-by-step explanation:

As the answer is 6 and we already have 3 so the other half is 3. Half of 6 is three so n=6

What type of sequence does this scenario represent, and why?

✔ arithmetic; the sequence has a common difference

If the pattern of the sequence continues, how many guests will the restaurant have on its 14th night?  

✔ 360

This example doesn't accurately depict arithmetic because the succession has a common difference. The restaurant will host 360 customers on its fourteenth night if the pattern of the series holds.

Arithmetic sequences always add or subtract the same amount to go from one term to the next. Finding the difference between any AP phrase and its predecessor will reveal the common difference, indicated by the letter "d."

An arithmetic sequence's nth term is determined by, Formula an = a1 + (n - 1)d. The common difference, or d, is the difference between any two consecutive terms in an arithmetic series; it can be calculated by deducting any pair of terms starting with a and an+1.

an = 100 + (14 - 1)20.

an = 360

The restaurant will host 360 customers on its fourteenth night if the pattern of the series holds.  

To learn more about Arithmetic sequences nth term refer to:

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Answer: 192

Step-by-step explanation:

160 + (20% × 160) =

160 + 20% × 160 =

(1 + 20%) × 160 =

(100% + 20%) × 160 =

120% × 160 =

120 ÷ 100 × 160 =

120 × 160 ÷ 100 =

19,200 ÷ 100 =

Welcomeeee

Answer:

x-7>0

Straight answer: x-7

Step-by-step explanation:

Assuming that the timber is X cm long and 7cm was cut off, there remaining amount is x - 7cm. In order for 7cm to be cut off, the timber must have been > 7cm long => x > 7 => x - 7 > 0

Answer:

when both bottom numbers on a fraction are the same at the lowest form

Step-by-step explanation:

example: 2/4 + 6/8 the common denomenator is 8 as both numbers go into it and you only have to times by 2 so answer would be 10/8 which is also 1 2/8

Answer:

Fiona gets £ 174

Step-by-step explanation:

Ths problem has three unknowns: the amounts each person gets. So let's identify each amount with a letter to write them in mathematical equation form:

Amount Sushil gets is : "x"

Amount Fiona gets is : "y"

Amount Pip gets is : "z"

Now we write three equations based on the information we have:

1) the addition of all these amounts should equal the 580 total:

x + y + z = 580

2) Sushil (x) gets twice as much as Fiona (y):

x = 2 y

3) Fiona (y) gets three times as much as Pip (z):

y = 3 z

So we can write the first equation in terms of "z" only, by using the appropriate substitutions in the intermediate stes:

Replace every instance of "y" with "3 z":

Equation 2 can give then "x" in terms of "z" as well:

x = 2 y = 2 (3 z) = 6 z

Then Eq 1 becomes:

6 z + 3 z + z = 580

10 z = 580

and therefore:

z = £ 58

Now Fiona's amount (y) is "3 times z", therefore:

y = 3 * 58 = £ 174

The answer is A.) 21x/^3y

Here is proof

Answer:

The value of a is 101°, b is 79°, c is 83° and d is 97°

Answer:

x<7, The third option

Step-by-step explanation:

-1.1x+6.4>-1.3

We are trying to isolate x so we can move all the constant to one side.

-1.1x>-1.3-6.4

-1.1x>-7.7

Lastly, we need to divide both sides by -1.1.

-1.1x>-7.7/-1.1

Note that if you multiply or divide both sides of an inequality by a negative, then you need to flip the sign.

x<7

Hope this helps :)

Answer:

I believe it is the third option. It is really hard to explain. Lots of workout and I don't have enough time for it nut it is the third option...

Answer:

a) 0

b) 4.5

c) 3

d) 6

Step-by-step explanation:

Formula: 3x + 4y = 12

The questions contains the values of x. So here's an example of:

d) x = -4, y = ?

   Using the formula:   3(-4) + 4y = 12

                                     -12 + 4y = 12

                                      4y = 24

                                       y = 6

Do the same for the others!

10. tan(30) = l / 6√3

l = tan(30) x 6√3

l = 6

cos(30) = 6√3 / y

y =  6√3/cos(30)

y = 12

11. tan(30) = c/30

c = 30 x tan(30)

c = 10√3

cos(30) = 27/w

w = 27/cos(30)

w = 18√3

12.

sin(60) = 36/y

y = 36/sin(60)

y = 24√3

tan(60) = 36/x

x = 36/tan(60)

x = 12√3

Answer:

  10. (l, y) = (6, 12)

  11. (c, w) = (9√3, 18√3)

  12. (x, y) = (12√3, 24√3)

Step-by-step explanation:

Side ratios, shortest to longest, in a 30°-60°-90° triangle are ...

  1 : √3 : 2

__

10. l : 6√3 : y = 1 : √3 : 2

multiply by 6

  = 6 : 6√3 : 12

  l = 6, y = 12

__

11. c : 27 : w = 1 : √3 : 2

multiply by 27/√3 = 9√3

  = 9√3 : 27 : 18√3

  c = 9√3, w = 18√3

__

12. x : 36 : y = 1 : √3 : 2

multiply by 36/√3 = 12√3

  = 12√3 : 36 : 24√3

  x = 12√3, y = 24√3

__

This is easier when the triangle is drawn to clearly differentiate the lengths of the sides. The long leg is opposite the 60° angle; the short leg is opposite the 30° angle.

Answer:

∠AEX = 70°

Step-by-step explanation:

From the diagram

AX ≅ BX

BY ≅ CY

AZ ≅ CZ

∠XAE = 20°

A circumcenter has equal distant from vertices of the triangle since radii of circles are congruent.

For the given figure, the midpoints is at Z, X, Y

And the perpendiculars also occur at Z, X, Y

∠Z = 90°

∠X = 90°

∠Y = 90°

∠XAE ∠AXE +∠AEX= 180° (sum of angles in a triangle)

∠AXE = ∠X = 90°

20° + 90° +∠AEX= 180°

110° +∠AEX= 180°

∠AEX = 180°-110°

∠AEX = 70°

Answer:

2720 oranges were sold

Answer:

x < 6.5

y < -1.5

Step-by-step explanation:

y > x - 8

Therefore x < y + 8

y < 5 - x

Therefore x < 5 - y

2x < 13

x < 6.5

6.5 < 5 - y

y < -1.5