which expression is in simplest form?

d) 5x ≥ 15

Let's solve your inequality step-by-step.

5x≥15

Step 1: Divide both sides by 5.

[tex]\frac{5x}{5} \geq \frac{15}{5}[/tex]

[tex]x\geq 3[/tex]

(Attachment #1)

e) 3(2x + 1) ≤ 15

Let's solve your inequality step-by-step.

3(2x+1)≤15

Step 1: Simplify both sides of the inequality.

6x+3≤15

Step 2: Subtract 3 from both sides.

6x+3−3≤15−3

6x≤12

Step 3: Divide both sides by 6.

[tex]\frac{6x}{6} \leq \frac{12}{6}[/tex]

[tex]x\leq 2[/tex]

(Attachment #2)

The value of the expression 2 2/3 - (-3 2/6) is 6

The expression is given as:

2 2/3 - (-3 2/6)

Open the bracket

2 2/3 + 3 2/6

Express as improper fractions

8/3 + 20/6

Rewrite as:

16/6 +20/6

Evaluate the sum

36/6

Evaluate the quotient

6

Hence, the value of 2 2/3 - (-3 2/6) is 6

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Answer:

-5.5°C > -17.5°C

Step-by-step explanation:

Since -5.5 is larger than -17.5

The correct inequality symbol to complete the inequality statement is ">" (greater than). [tex]-5.5^{\circ}C > -17.5^{\circ}C[/tex].

To understand why this symbol is used, let's compare the two temperatures.

The temperature in Moscow is -5.5C, while the temperature in Cold Lake is [tex]-17.5^{\circ}C[/tex].

Since -5.5 is greater (warmer) than -17.5,  use the ">" symbol to indicate that [tex]-5.5^{\circ}C[/tex] is greater than [tex]-17.5^{\circ}C[/tex].

Here's a step-by-step explanation:

In summary, when comparing the temperatures of Moscow and Cold Lake, the correct inequality statement is [tex]-5.5^{\circ}C > -17.5^{\circ}C[/tex], indicating that Moscow's temperature is higher (warmer) than Cold Lake's temperature.

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Answer:

For the cost of each legging to be $12, and the shipping of $5, the expression is a straight line C = 12x + 5 where x is the number of leggings.

Step-by-step explanation:

It is given that each legging costs $12. This means that for x number of leggings, the cost will be $12x. Now there is an additional cost of shipping that is $5. So, total cost will be a linear equation and can be written as

C = 12x + 5

This equation represents a straight line like y = mx + c. Here y = C, m = 12 and c = 5.

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Answer:

  d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))

Step-by-step explanation:

The Law of Sines tells us that sides of a triangle are proportional to the sine of the opposite angle. This can be used along with a trig identity to demonstrate the required relation.

__

The law of sines applied to the top triangle is ...

  BC/sin(A) = AC/sin(θ)

Triangle ABC is isosceles, so the base angles at B and C are congruent. Then the angle at vertex A is ...

  ∠A = 180° -θ -θ = 180° -2θ

A trig identity tells us the sine of an angle is equal to the sine of its supplement. That means the sine of angle A is ...

  sin(A) = sin(180° -2θ) = sin(2θ)

and our above Law of Sines equation tells us ...

  BC = sin(A)/sin(θ)·AC = k·sin(2θ)/sin(θ)

__

The law of sines applied to the bottom triangle is ...

  DC/sin(B) = BC/sin(D)

  d/sin(α) = BC/sin(β)

Multiplying by sin(α) we have ...

  d = BC·sin(α)/sin(β)

__

Using our expression for BC gives the desired relation:

  d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))

It will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.

When two numbers can be written as p/q is called a Ratio , and when two ratios are equal they are said to be in proportion .

It is given that

Jeremy is reading a 60-page book.

The time taken to read  20 pages is 30 minutes

Then it can be written as 20:30 = 2:3

The rate of reading is same so To read the rest 40 pages is given by

40:x

40: x = 2:3

40*3/2 = x

x = 60 minutes

Therefore it will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.

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By solving a linear equation, we will see that Victor is 30 years old.

Let's say that Victor is x years old.

We know that 10 years ago, (x - 10), his age was half of what it will be in 10 years (x + 10).

Then we can write the linear equation:

(x - 10) = (x + 10)/2

Now we can solve that equation for x:

2*(x - 10) = x + 10

2x - 20 = x + 10

2x - x = 10 + 20

x = 30

So we conclude that Victor is 30 years old.

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Answer:

given - a rectangle ABCD

AB = 40

AC. = 90

BC = ?

in triangle ABC

using Pythagoras theorem

(AB) ² + (BC) ² = (AC) ²

(40)² + (BC) ² = (90)²

(BC) ² = (90)²- (40)²

(BC) ² = 8100 - 1600

(BC) ² = 6500

BC =

[tex]20 \sqrt{10} [/tex]

Answer:

4y^2

Step-by-step explanation:

least common denominator is 4y^2

Answer:

y = -3x + 1

Step-by-step explanation:

the line crosses the y-axis at (0,1) then c = 1

The points (0,1) and (1,-2) lie on the line then

m = slope = [(-2)-1]÷(1-0) = [-3]÷(1) = -3÷1 = -3

Therefore,

The equation of the line is : y = -3x + 1

Answer:

x = 114

Step-by-step explanation:

since the triangles are congruent, then corresponding angles are congruent, that is

∠ C = ∠ D

x + 18 = 132 ( subtract 18 from both sides )

x = 114

Step-by-step explanation:

log2(x) = 5.6

so,

x = 2^5.6 ≈ 48.50293013... ≈ 48.50

Answer:

  C) straight line through (1, 3) ... (-3, -7)

Step-by-step explanation:

The linear equation will describe a straight line. The slope and general location of the line on a graph can be estimated from its x- and y-intercepts.

__

The x-intercept is the value of x that satisfies the equation when y=0.

  -5x +2·0 = 1

  x = -1/5 . . . . . . divide by the coefficient of x

The y-intercept is the value of y that satisfies the equation when x=0.

  -5·0 +2y = 1

  y = 1/2 . . . . . . divide by the coefficient of y

The intercept values mean the line crosses the positive y-axis and the negative x-axis. It will have a positive slope. Points on the line that have integer x- and y-coordinates will have coordinates that have the same sign.

Of the offered answer choices, A and B are eliminated because the graph is not a curve. D is eliminated because the suggested points have coordinates with opposite signs. The correct choice is C:

  It is a straight line joining the points (1, 3), (3, 8), and (-3, -7)

The input value that produces the same output value in both charts is 2. so the correct answer is option D.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

You are given two functions  f (x) = -0.5X +2 and g(x) = 2x - 3

x      f(x)

-3     3.5

-2     3

-1     2.5

0     2

1      1.5

2     1

3     0.5

The second table is given below:-

x      g(x)

-3      

-2      

-1      

0    

1      

2      

3      

We will put the points and will find the value of functions:-

g(-3) = 2(-3) - 3 = -6 -3 = -9

g(-2) = 2 -(-2) -3 = -7

g(-1) = 2( -1) -3 = -3

g(0) = 2 - 0  - 3 = -3

g(1) = 2.1 - 3 = -1

g(2) = 2.2 -3 = 1

g(3) = 2.3 -3 = 3

Hence the second table will be

x      g(x)

-3      -9

-2      -7

-1       -5

0       -3

1        -1

2       1

3       3

The input value that produces the same output value in both charts is 2.

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the pronunciation of this question is wrong make it right first then I will answer

Step-by-step explanation:

please send this question again because I I think you want to write it fast and by mistake you are wright wrong

Answer:

[tex]y = - 2x + 4[/tex]

Step-by-step explanation:

Thank you

Answer:

39

Step-by-step explanation:

Okay so there are 52 cards in a deck and there are 4 of each card. 4 kings 4 Queens 4 Jacks 4 Ace 4 Twos 4 Threes 4 fours 4 fives 4 sixes 4 sevens 4 eights 4 nines 4 tens. One from each group is a heart there are 13 groups so therefore subtract 13 from 52.

Answer:

point A is the intersection point between XA and AC

The value of sin x in Q II is 0.86 .

This the field in Maths which deals with a right angled triangle and the other angles in the triangle.

It is given that cot = -0.59

cot x = cos x / sin x

Using online trigonometric calculator

sin x in Q II is 0.86 .

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Answer:

a. 2.25 km

Step-by-step explanation:

the scale on a map means how many units in the mapp corresponds to how many units in reality.

in this case

1 cm on the map = 75000 cm in reality =

= 75000/100 m = 750 m =

= 750/1000 km = 0.75 km

3 cm = 3×1 cm = 3 × 0.75 km = 2.25 km

Answer:

Systems of equations:

x=3

y=2

z=1

w=0

Answer:

150 yd

Step-by-step explanation:

the angle bisector divides the opposite sides into segments that are proportional to the other 2 sides .

let x be the distance from the oak tree to the hole, then

[tex]\frac{225}{x}[/tex] = [tex]\frac{375}{250}[/tex] ( cross- multiply )

375x = 56250 ( divide both sides by 375 )

x = 150 yd

The surface area is multiplied by a factor of 16

The dimensions are given as:

The factor of the surface area is calculated as:

Surface area = Factor^2

So, we have:

Surface area = 4^2

Evaluate

Surface area = 16

Hence, the surface area is multiplied by a factor of 16

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16

Step-by-step explanation:

Based on the given options, the inequality for the acceptable weights of the suitcase is 32.5 ≤ x ≤ 47.5.

You didn't include the full question but this question can be answered based on the given options.

When inequalities are written, there is no inclusion of "or" which eliminates options A and C.

It is illogical to have an inequality as 32.5 ≥ x ≥ 47.5. This is because if 32.5 is larger or equal to x, then x cannot be larger than 47.5. This is mathematically impossible.

This leaves the likely answer as 32.5 ≤ x ≤ 47.5 which means that the weight of the suitcase has to be larger than or equal to 32.5 but less than or equal to 47.5.

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Answer:

32.5 ≤ x ≤ 47.5

Step-by-step explanation:

View the answer in the Venn Diagram below.

A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a quadrilateral ABCD are A, B, C, and D. A quadrilateral has the following sides: AB, BC, CD, and DA.

A simple (non-self-intersecting) quadrilateral with two sets of parallel sides is known as a parallelogram in Euclidean geometry.

A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and breadth of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

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The correct representations are - 6x + 15 < 10 - 5x  , An open circle is at 5 and a bold line starts at 5 and is pointing to the right , Option C and E are the right answers.

Inequality are the mathematical statements where algebraic expressions are equated by another algebraic expression or a constant using an Inequality Operator.

The given statement is

–3(2x – 5) < 5(2 – x)

On simplifying can be written as

- 6x + 15 < 10 - 5x

- 6x + 15 < 10 - 5x

- 6x < -5 - 5x

- x < - 5

 x > 5

An open circle is at 5 and a bold line starts at 5 and is pointing to the right .

Therefore Option C and E are the right answers.

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The volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

We have:

The radius of the cylindrical barrel r = 30 cm

Height of the cylindrical barrel h = 110 cm

Volume:

[tex]\rm V = \pi (30)^2 (110)[/tex]

V = 311017.67 cubic cm

The volume of litres:

V = 311.017 cubic ml  (1 liter = 1000 cubic cm)

Number of bottles = 311.017 /0.73= 426 bottles

Thus, the volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.

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Answer:

y= 25/3 - x/3

Step-by-step explanation:

y= 25/3 - x/3

Answer:

No Solutions.

Step-by-step explanation:

original equation

3x+13 = 3(x+6)+1

distribute 3

3x+13 = 3x+18+1

simplify

3x+13 = 3x+19

since the slope is the same for both equations and the y-intercept is different the two equations are parallel meaning they will never intersect so there are no solutions.

Answer:

No solutions

Step-by-step explanation:

3x + 13 = 3 (x + 6) + 1

3x + 13 = 3x + 18 + 1

3x + 13 = 3x + 19

3x + 13 = 3x + 19 meaning no solution since they aren't equivalent to each other