A piece of rope 60 meters long is cut into two
pieces so that the longer piece is twice the
length of the shorter. How long are the two
pieces?

Simplify both sides of the inequality.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{3x+6 < 3x-21 } \end{gathered}$} }[/tex]

Subtract 3x from both sides.

Subtract 6 from both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{0 < -27} \end{gathered}$} }[/tex]

Answer:

0 < - 27

Step-by-step explanation:

1. Distribute

3x + 6 < 3(x-7)

3x + 6 < 3x - 21

2. Subtract 6 from both sides

3x + 6 <  3x - 21

3x + 6 - 6 < 3x - 21 - 6

3. Simplify

   subtract

    3x + 6 - 6 < 3x - 21 - 6

    3x <  3x - 21 - 6

   subtract

     3x < 3x - 21 - 6

     3x < 3x - 27

4. Subtract 3x from both sides

3x < 3x - 27

3x - 3x < 3x - 27 - 3x

5. Simplify

    combine like terms

     3x - 3x < 3x - 27 - 3x

     0 < 3x - 27 - 3x

     0 < 3x - 27 - 3x

      0 < -  27

And that is how you get your answer

Step-by-step explanation:

Since area = 27cm²

area = 3 × (x + 4)

27 = 3(x + 4)

expand the right side

27 = 3x + 12

move 12 to the left side and subtract it with 27

15=3x

then divide both sides with 3

x=5

Answer: y-intercept (0,−2) and the slope is 1/3

a) From the exercise we can identify 3 unknowns from the 3 funds

• Large Growth = ,LG

• Small Growth = ,SG

• Large Value = ,LV

b)

Assuming the question is : How much does x liters/milimeters of oil weigh?

First, we calculate how much mass did the bottle of oil lose : 590 - 400 = 190 (grams)

Since it loses 190 grams after Sophia uses 200 milimeters of oil, 200 milimeters of oil weighs 190 grams (yes.)

-> 1 milimeter of oil weighs : 190/200 = 0.95(grams)

So, to calculate the mass of x *liters* of oil, we take 0,95 x 1000 times x.

For example : To calculate the mass of 22,5 liters of oil, we take 0,95 x 1000 x 22,5 = 21375 (g) or 21.35(kg).

The given equation is

5(x - 3) = x + 13

We want to test if x = 6 is a solution. We would substitute x = 6 into the equation. We have

5(6 - 3) = 6 + 13?

5(3) = 6 + 13?

15 = 19?

Since both sides of the equation is not equal, then

x = 6 is not a solution of the equation

900km is less than the perimeter of the of Bhutan about 1075km.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The surface of a shape's area is measured.

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It takes Phindi to run almost 22 tracks to cover 12kms

Given that,

First you have to figure out the length of the track whihc is circumference of circle ,

r is the radius  of circular track which is 88m

The athlete has to run 12km on the track

Circumference of circle = 2πr

Solving circumference will give length of the circular track which is,

Circumference of circle = 2(3.14)(88)

                                          =552.6 meters

If she covers 552.6 m whe runs one circular track then,

1 circular track -------- 552.6 meters

? circular track -------- 12000 meters or 12 kilometers

No of circular tracks = 12000/552.6 = 21.7 tracks

Therefore, It takes Phindi to run almost 22 tracks to cover 12kms

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Answer:

x = 1 or x =3

Step-by-step explanation:

2x² + 4x = 3 + 3x²

2x²-3x²+4x -3 = 0

-x² + 4x -3 = 0

by calculator:

x = 1 or x =3

Answer:

  -8k -2

Step-by-step explanation:

You want the simplified form of -2(k+1)-6k.

The process of simplifying an algebraic expression includes ...

Parentheses are removed using the distributive property. The factor outside parentheses multiplies each term inside.

  -2(k +1) -6k

  = (-2)(k) +(-2)(1) -6k = -2k -2 -6k

Terms with the same variable content can be combined by adding their coefficients. (The distributive property is involved here, too.)

  = (-2 -6)k -2 = -8k -2

The simplified expression is -8k -2.

Answer:Rotation then a translation

Step-by-step explanation: rotate 90 degrees clockwise around center J. Then translate 3 to the right, 2 down

The law of mathematical logic that was used to derive the given conclusion is; Law of Syllogism

The law of syllogism is defined as a type of logical argument using deductive reasoning.

Now, In mathematical logic, the Law of Syllogism states that if the following two statements are true:

(1) If d , then e .

(2) If e , then f .

Then we can derive a third true statement:

(3) If d , then f .

Now, applying that law to our question, we see that;

1) If you have a cat, then it will chase mice.

2) You have a cat.

Then we can derive a third true statement:

3)  Your cat will chase mice.

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The equation is 10x=2x+60

 x=15/2

∠CFH=75

∠CBD= 75

We are dealing with parallel lines, which are the lines that are equidistant to each other and never meet,  will never meet, when such lines are crossed by another line called the transversal creates many angles such as corresponding angles, vertical angles, alternate interior angles, alternate exterior angles, consecutive angles.

Since, angle CBD and angle CFH are the corresponding angles and they are equal to each other, we are given CBD=2x+60 and CFH = 10x

therefore , 10x=2x+60

=>10x-2x=60

=>8x=60

x=15/2

So, the angle CBD= 2x+60= 2(15/2)+60=  75

and the angle CFH = 10x= 10(15/2)= 75

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Answer:

step 1 is correct

Step-by-step explanation:

when you find the absolute value of a number i.e | | the result is always positive

eg |-20| = 20

step 1 is correct

The probability of drawing a consonant from the given set of cards is 0.66.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The given letters are  M, A, T, H, I, S, F, U and N.

Total number of letters are 9.

The number of vowels is 3.

Then, the number of consonants is 9 - 3 =6.

Now, the probability for choosing consonant is given as follows,

P(Consonant) = Number of Consonants ÷ Total letters

⇒ 6/9 = 0.66

Hence,  the probability of randomly drawing a consonant is given as 0.66.

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Answer: 6/10 is answer

Step-by-step explanation:

Just trust please

Answer:

x = 4 , x = 2.4

Step-by-step explanation:

[tex]\frac{4}{x-2}[/tex] + [tex]\frac{3}{x-3}[/tex] = 5

multiply through by (x - 2)(x - 3)

4(x - 3) + 3(x - 2) = 5(x - 2)(x - 3)

4x - 12 + 3x - 6 = 5(x² - 5x + 6)

7x - 18 = 5x² - 25x + 30 ( subtract 7x - 18 from both sides )

0 = 5x²  - 32x + 48

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 5 × 48 = 240 and sum = - 32

the factors are - 20 and - 12

use these factors to split the x- term

0 = 5x² - 20x - 12x + 48 ( factor the first/second and third/fourth terms )

0 = 5x(x - 4) - 12(x - 4) ← factor out (x - 4) from each term

0 = (x - 4)(5x - 12)

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

5x - 12 = 0 ⇒ 5x = 12 ⇒ x = 2.4

Answer:

1

5

Step-by-step explanation:

y = mx + b

b = -5 (the y-intercept)

m = 1/1 = 1

y = x - 5

[tex](2x + 3x + 4x) = 180 \\ 9x = 18 \\ \frac{9x}{9} = \frac{180}{9} \\ x = 20[/tex]

ATTACHED IS THE SOLUTION with the steps.

MFM (option A)

Outcome could be male or female

At least two male means the minimum of number of men that we would have in the sample space outcome is 2.

The outcome that satisfies this are:

MMM, MMF, MFM, FMM

From the above, the one in the options is MFM (option A)

The equation of S in terms of N is S(N) = 2200 + 40N

From the question, the given parameters are

Monthly salary = $2200

Additional earnings = $40 per copy of Math fun sold

The equation that relates S to N is then calculated as

Total = Monthly salary + Additional earnings x Number of copy of Math fun sold

Substitute the known values in the above equation

So, we have

S(N) = 2200 + 40N

So, the equation is S(N) = 2200 + 40N

See attachment for the graph

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According to the solving the space between Arthur and Jamie are 39.1 meters.

A coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.

The length of the line segment bridging two locations in a plane is known as the distance between them. d=√((x2 – x1)² + (y2 – y1)²).  is a typical formula for determining the separation between two places. Any two sites on an x-y plane or coordinate plane can have their distance between them calculated using this equation.

location of Arthur is (20, 30)

location of Jamie is (45, 60)

Let's apply the rule of distance to determine how far away they are because we know that :

d = √((X₂ - X₁)² + (Y₂ - Y₁)²)

let substituting the value we get:

d = √((X₂ - X₁)² + (Y₂ - Y₁)²)

d = √((45 - 20)² + (60 - 30)²)

=   √(25)² + (30)²)

= 39.1

According to the solving the space between Arthur and Jamie are 39.1 meters.

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Answer: It is obtuse

Step-by-step explanation: the angle looks greater than 90 degrees :)

Anwser is 18

I used a website

Answer: x = 18

Isolating a variable: rearranging the equation to make the variable on side of the equation and the others on the other side

1. Collect like terms

2. Inverse operations to isolate

3. simplify if necessary

Calculations:

[tex]3x -14 +3x +9= 103[/tex]

Collect like terms: [tex]6x -5 =103[/tex]

Inverse operations:

[tex]6x = 103 +5[/tex]

[tex]6x= 108[/tex]

[tex]\frac{6x}{6}=\frac{108}{6}[/tex]

∴ [tex]x= 18[/tex]

Answer: 28.75 cm

Step-by-step explanation:

           Using the formula for the area of a rectangle, we can plug in our known values and solve for the height.

A = B * H

(345 cm²) = (12cm) * H

28.75 cm = H

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Firstly, congruent angles are equal

The three statements are

1. Triangle PTW = Triangle HGD

2. Triangle WPT = Triangle DHG

3. Triangle TWP = Triangle GDH

From the figures, it was observed that they are similar

When you look at the figures very well

You will observed that Triangle PTW is Similar to triangle HGD

They both have similar properties

Answer:

17 * 2= 34

therefore, 17 and 2 are the factors of 34

Step-by-step explanation:

Answer:

11.4 m

Step-by-step explanation:

2m / 5 cm   * 28.5 cm = 11.4 m