whats the set of all prime numbers

Answer: x[tex]\geq[/tex]9

Step-by-step explanation:

5x+3 [tex]\geq[/tex] 48

5x[tex]\geq[/tex]45

x[tex]\geq[/tex]9

Treat inequalities like normal equations. Only when the right side of the equation is introduced to a negative sign via multiplication or division should you flip the inequality sign

Hope this helps!

Answer is

(a) She can buy 7 packages of plain coffee or 5 packages of coffee.

(b) f = [tex]\frac{T- 5.50 p}{7}[/tex]

(c) she can buy 3 packages of  flavoured coffee

(a) she spent on coffee is $ 40

amount of money she spends on coffee is 5.50

then, packages of plain coffee = [tex]\frac{40}{5.50}[/tex] ≈ 7.2

      so she buy 7 packages of plain coffee.

she spent on coffee is $ 40  and amount spends on flavoured coffee is 7

then , packages of flavoured coffee = [tex]\frac{40}{7}[/tex] ≈ 5.7

so she can buy 5 packages of flavoured coffee.

(b)According to question ,

T = 5.50 + 7f

so 7f = T - 5.50

then , f = [tex]\frac{T - 5.50}{7}[/tex]

(c) we get the value of f = [tex]\frac{T - 5.50}{7}[/tex]

given that , f is equal to 3

then,  f = [tex]\frac{T - 5.50}{7}[/tex]

           =   [tex]\frac{T - 5.50}{7}[/tex]×3

we get   =  [tex]\frac{T - 16.5}{7}[/tex]

when T is equal to 40

then , f = [tex]\frac{40 - 16.5}{7}[/tex] ≈ 3.35

so she can buy 3 packages of flavoured coffee.

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Answer:

An angle measures 26° more than the measure of its complementary angle.

Step-by-step explanation:

The distance between the center of the circle to any point in the circle is called the radius of the circle. The student staying in the lounge connected to the said wifi will be in the range of the wifi.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

The distance between the center of the circle to any point in the circle is called the radius of the circle, while the diameter is twice this distance.

Given that the range of the router, which services the wifi connection of the school has a diameter of 3.5 meters. Therefore, the radius of the wifi will be,

Radius = Diameter/2 = 3.5 meters / 2 = 1.75 meters

Now, it is also given that a router is located in the school library which is 1.5 meters away from the student lounge. Therefore, the distance between the school library and the lounge is less than the radius of the range of the wifi.

Thus, the student staying in the lounge connected to the said wifi will be in the range of the wifi.

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Answer:

2 1/2 x 1/3 x 3 = 5/2 or 2 1/2

Quadilateral ABCD is reflected over the x-axis. ---> (2, -4)

ABCD is translated 2 units right and 1 unit down. ---> (4, -5)

ABCD is dilated about the origin by a scale factor of 3. ---> (6, 12)

ABCD is rotated 180° clockwise about the origin. ---> (-2, 4)

Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional shape. Concave and convex are the two most common forms. Additionally, there are numerous subgroups of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombus, and squares.

quadrilaterals come in a variety of forms.

Trapezium.

Parallelogram.

Rectangle.

Rhombus.

Square.

Kite.

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Answer:

3t (t²-7t-4t)

Step-by-step explanation:

The highest common factor was 3t

Answer: it is .

Step-by-step explanation:

Rita and Tina each make $11 an hour -> 11r for Rita and 11t for Tina in the week

Rita also worked overtime hours and got paid an extra $32 -> Rita and Tina's total weekly wages can be represented as 11r + 11t + $32 (or 11(r+t) + 32)

Answer: -8

Step-by-step explanation:

-2(2)-4 -> -4-4 = -8

Answer:

<

Step-by-step explanation:

Negative numbers are always smaller than positive numbers, and "<" is the smaller than symbol, so < is the correct choice. We can eliminate = immediately because a negative number can't equal a positive number (excluding the weird number 0)

The amount of Lemon's commission is $4.7

According to the question we have been given that

     Commission earned by Lemon = 3.2%

     Selling price of drone which is sold by Lemon  = $146.97

We need to find the amount of commission she earned by selling the drone.

The formula to be used to find the amount of commission is

                =  percentage of commission * selling price

putting the required value we get

               = 3.2% of $146.97

here 'of' is denoted as multiplication

thus,        =0.032 * 146.97

               = $4.7

Hence the amount of Lemon's commission is $4.7

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The simplified form of √84 is 2√21.

To simplify the given value, first, we need to write down the prime factorization of 84.

The prime factorization of 84 = 2² × 3 × 7

Therefore,

√84 = √(2² × 3 × 7)

Applying the radical rule: √ab = √a × √b, we get

√84 = √2² × √(3 × 7)

Applying the radical rule: √a² = a, for a ≥ 0, we get

√84 = 2 × √(3 × 7)

Multiply the numbers 3 and 7 we get 3 × 7 = 21

√84 = 2 × √21

√84 = 2√21

Therefore, the simplified form of √84 is 2√21.

Refer to the attached image for the above steps.

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The value of x is 4 and the value of ∠ABC is 68°.

To solve this problem we first have to understand the concept of an angle bisector. Angle bisector is a straight line passes through the vertex of an angle dividing the angle in two equal angles.

According to the condition BD bisects ∠ABC

Therefore the two angles formed by the angle bisector are ∠ABD and ∠CBD.

The angle value of these two angles are equal.

Given:

m∠ABD=11x-10

m∠CBD=8x+2

Therefore from the above condition:

m∠ABD=m∠CBD

Substituting the values we get:

11x-10=8x+2

Solving the linear equation to find the value of x.

[tex]or,11x-10=8x+2\\or,11x-8x=2+10\\or,3x=12\\or,x=4[/tex]

Now let us find the value of ∠ABC

m∠ABC=m∠ABD+m∠CBD

or,∠ABC=11x-10+8x+2

or,∠ABC=19x-8

Substituting the value x=4 in the equation we get:

m∠ABC=19×4-8

or,m∠ABC=68°

Therefore we can conclude that the value of xis 4 and the value of ∠ABC is 68°.

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Answer:

1. -2/3        3. -5/4         5. 3/2          FOR THE REST OF THE PARTS LOOK THROUGH THE EXPLANATIONS

Step-by-step explanation:

Before I start the workings, I'll give a little explanation on this topic.

So, the equation of a straight line is

y = mx + c

where x and y are any coordinates of any point on the line.

m is the gradient or slope

m can be calculated using 2 formulas,

formula 1: Rise/Run

where rise is the how much a graph goes upwards or downwards, if its upwards use positive integer and if its downwards use negative integer.

Run is how much a graph moves to the right or to the left, if it moves to the right is is positive, if it moves to the left it is negative.

Formula 2: (y2-y1)/(x2-x1)

the values of these are taken through any 2 coordinates on the line.

and c is the y-intercept(the point where the line crosses the y-axis.

MOVING TO ANSWERING NOW

1. Dotted points on the line are (1,0) and (4,-2)

Formula of slope,

U can use any of the 2 formulas given above

I'll show both for this question

m = (y2-y1)/(x2-x1) = (-2-0)/(4-1) = -2/3

OR

m = rise/run = where rise is -2 and run is 3 so -2/3

2. TRY DOING THIS ONE YOURSELF

For the next part I'll do 3 and 5 for your understanding, try doing 2 and 4 on your own to understand.

3. Coordinates given (13,1) and (1,16)

m = (y2-y1)/(x2-x1) = (16-1)/(1-13) = 15/-12  simplify this and it becomes -5/4

5.  (-8,-14) and (-10,-17)

m =  (y2-y1)/(x2-x1) = (-17-(-14))/(-10-(-8)) = -3/-2 = 3/2

FOR THE NEXT PART I'LL DO 7,8 AND 10 FOR YOU, TRY DOING 9 ON YOUR OWN FOR PRACTICE.

I WILL ALSO ATTACH FILES FOR THE NEXT PARTS IN ORDER OF QUESTIONS SO SEE THEM.

7. y = x + 3 this means y = 1x +3 which means:

1 is the gradient

3 is the y-intercept

so 1 as a fraction is 1/1 which means rise is one upwards and run is 1 to the right.

Now go to the graph on the y-axis and plot the point 3, (0,3) is your y-intercept. From their rise by one and run by one this will lead u to point (1,4)

Mark both these points and make a line through them.

8. x = -5

now look at this equation in the form of y = mx + c

0 = 1x + 5 the means y is 0 and it is already told in the question that x = -5

if u rearrange 0 = 1x + 5 it will give you x = -5

now when y is  0 x = -5 put a point on the coordinate (-5,0) and draw a vertical straight line.

10. y = (1/4)x - 1

slope is 1/4 which means rise is 1 and run is 4

y-intercept is -1

now go to y=-1 which is the coordinate (0,-1) and rise by one and run by 4, this will take u to the coordinate (4,0) now put a dot on both coordinates, connect them and put a line through them.

Answer:

b = 3

Step-by-step explanation:

We already know that x = 2, so just plug it back into the equation to solve for the variable b.

[tex]b(2(2)+6)=30[/tex]

[tex]b(4+6)=30[/tex]

[tex]10b=30[/tex]

[tex]b=3[/tex]

We can check this by plugging it back in:

[tex]3(2(2)+6)=30[/tex]

[tex]3(10)=30[/tex]

[tex]30=30[/tex]

This is the correct solution :)

The answer will be  : x = -- 3y -- 9

⇒ -2 (x + 3y) = 18

⇒ -(2x + 2 * 3y) = 18

⇒ -(2x + 6y) = 18

⇒ (-2x -6y) + 6y = 18 + 6y

⇒ -2x -6y + 6y = 6y + 18

⇒ -2x = 6y + 18

⇒ [tex]\frac{2x}{2} = \frac{-6y + 18}{2}[/tex]

⇒ [tex]x = \frac{-(2*3)y + (2*3)^{2} }{2}[/tex]

⇒ [tex]\frac{-2*3\frac{2*3y}{2*3} + \frac{(2*3)^{2} }{2*3} }{2}[/tex]

⇒ [tex]x = \frac {2*3(y + (3)^{2 - 1}) }{2}[/tex]

⇒ [tex]x = \frac{-2*3(y + 3)}{2}[/tex]

⇒ x = -[3(y + 3)]

⇒ x = (3y + 3*3)

⇒ x = -(3y + 9)

⇒ x = - 3y - 9

WORKING NOTES :

-2 (x + 3y) = 18

[We must multiply a term and an expression in order to enlarge this word.

We'll utilize the following product distributive property:

A(B + C) = AB + AC

⇒ -(2x + 2 * 3y) = 18

The final expression, in this case, will have two terms:

The first term is a product of '2' and 'x'

the second term is a product of '2' and '3y'.]

In this term, numerical components have been multiplied.

⇒ -(2x + 6y) = 18

We must group all the variable terms on one side of the equation and all the constant terms on the other in order to solve this linear equation.

⇒ (-2x -6y) + 6y = 18 + 6y

Here, the '-' (minus)  term, -6y will be moved to the right side.

When a term "moves" from one side of the equation to the other, you'll notice that its sign changes.

Parentheses around expressions must be eliminated.

Each term in the expression changes sign if a negative sign is placed in front of it. Otherwise, the expression stays the same.

There is no negative sign in the situation.

⇒ -2x -6y + 6y = 6y + 18

In order to join like terms in this expression, we must first sum all of the numerical coefficients and, if necessary, replicate the literal section.

Nothing in a number suggests a value of 1.

There is just one set of related terms: -6y, 6y.

⇒ -2x = 6y + 18

We must eliminate the coefficient that multiplies the variable in this linear equation in order to isolate it.

If both sides are divided, then the coefficient must be removed (-2)

⇒ [tex]\frac{2x}{2} = \frac{-6y + 18}{2}[/tex]

We must simplify this fraction to its simplest form.

To do this, divide the variables that occur in both the numerator and the denominator.

The common factor, in this case, is 2.

⇒ [tex]x = \frac{-(2*3)y + (2*3)^{2} }{2}[/tex]

We must consider the GCF (Greatest Common Factor).

The GCF and the original expression, split by the GCF, provide the final term.

⇒ [tex]\frac{-2*3\frac{2*3y}{2*3} + \frac{(2*3)^{2} }{2*3} }{2}[/tex]

GCF in this case is 2*3.

The fraction [tex]\frac{2*3y}{2*3}[/tex] must be lowered to its simplest form. To do this, divide the variables that occur in both the numerator and the denominator.

Here, the common factor is 2*3.

⇒ [tex]x = \frac {2*3(y + (3)^{2 - 1}) }{2}[/tex]

The expression must be lowered to its simplest form.

Driving out the components that exist in both the numerator and the denominator will accomplish this.

2*3 is a common factor.

⇒ [tex]x = \frac{-2*3(y + 3)}{2}[/tex]

Numerical terms in the factor {y + (3²⁻¹)} is added which makes it (y + 3)

The fraction will then be broken down into its smallest terms next.

To do this, divide the variables that occur in both the numerator and the denominator.

2 is the common factor.

⇒ x = -[3(y + 3)]

⇒ x = -(3y + 3*3)

We must multiply a term and an expression in order to expand this term.

We'll utilize the following product distributive property:

A=AB+AC = A(B + C)

The final expression, in this case, will have two terms:

"3" and "y" are the product in the first term.

The second term is the result of the numbers 3 and 3.

⇒ x = -(3y + 9)

This term's numerical terms have been multiplied by three (3*3 = 9).

⇒ x = - 3y - 9

The parenthesis around expressions must be eliminated.

Each term in the expression changes sign if a negative sign is placed in front of it.

Otherwise, the expression stays the same.

The signs of the following two terms will now change. -(3y + 9) = - 3y - 9

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Answer: See explanation

Step-by-step explanation:

f=First car seat. s=Second car seat. t=Third car seat

f<=28

15<s<45     ==> Second car seat can hold between 15 and 45 pounds noninclusive.

28<=t<=90   ==> Third car seat can hold between 28 and 90 pounds inclusive.

Answer:

0 + 47 = 47

Step-by-step explanation:

➟ 0 + __ = 47

Let's Change __ to x

➟ 0 + x = 47

Calculate 0 + x = x

➟ x = 47

∴ 0 + 47 = 47

Property used is Identity property of addition

The measure of the corresponding central angle for XY in radians is; 229.1°

We know that an arc is a part of the entire perimeter of a circle.

Radian is defined as a unit of plane angular measurement that is equal to the angle subtended by the circle at the center by an arc that is of the length equal to the radius.

We also know that the circle as a whole contains 2π radians. Now, at first we are required to find the perimeter of the circle.

Perimeter of the circle is given by the formula 2πr.

Thus, perimeter of the circle = 2πr = 2π * 10 =20π = 62.851cm

Hence value of arc in radians = 40/62.851 * 2π = 0.636 x 2 π = 1.272π

Radian can be converted to degree by multiplying the radian measure by 180/π

Therefore, angle subtended by arc in degrees =1.272 π * 180 /π =229.1 °

Hence the angle subtended by arc is 229.1°

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The graph of the given piecewise function is plotted at the end of the answer.

A piecewise function is a function that has different definitions, depending on the input.

From the definition in the problem, we have that:

Considering these three definitions, the graph is given at the end of the answer, with the legend of the closed interval given in the text.

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Answer:

Dot plots are hard to construct when dealing with larger, more precise data sets. This makes it difficult to read multiple data points, and it gets very confusing after a while. Therefore, it would not be a good choice for graphing due to its inaccuracy.

Answer:

Dot plot aren't too good for large sets of datas. If you also got many data that are close together, the more you got the harder it will be might to read the data that your doing

answer is -1 < x < 5

-|x - 2|+ 9 > 6

Rearrange the terms

-|x - 2| > 6 - 9

-|x - 2| > - 3

then divide both sides of the inequality by the co- efficient of variable

|x - 2| < 3

convert the absolute inequality to standard inequality

-3 <x - 2 < 3

separate compound inequalities into system of inequality

{x - 2}> -3

{x - 2 < 3}

Rearrange variable to the left side of the equation

x > -3 + 2                    

calculate the sum or difference

x > -1

x -2 < 3

Rearrange variable to the left side of the equation

x < 3 + 2

calculate the sum or difference

x < 5

x > -1 and x < 5

Find intersection

-1 < x < 5

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

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Answer: The equation is true

Step-by-step explanation:

Since x=3 and y= 5

Substitute the values for x and y

y=2x-1

5=2(3)-1

5=6-1

5=5

⇒The equation is true

Answer:

X=3

Step-by-step explanation:

Remember to get all your variables on one side by doing the "Reverse function" etc...

Once youve got your variables on one side (and only 1 is remaining) you should get rid of whats BESIDE the variable by dividing it by *whatever it is thats beside the variable!* AND REMEMBER TO DO THIS ON BOTH SIDES OF THE EQUATION SO THAT THEYRE EQUAL!!

Answer:

[tex]f(x) = 12 + \frac34x[/tex]

Step-by-step explanation:

Hello!

Function notation simply means replacing the term y with f(x).

Given the equation: y = 3/4x + 12

The equation in function notation is [tex]f(x) = \frac34 x + 12[/tex].

The meaning of f is just the name of the function. x is the variable being used in the function. Therefore, it can also be written as g(y), s(d), or e(f), as long as the variable inside the parenthesis exists in the equation.

Suppose you see a number in the spot for the variable. In that case, you are replacing the variable in that equation to evaluate when the x-value is that number.

Interpreting this will tell you the value of y when x is 1. The y-value is 2.

Answer:

I think it's C.

Step-by-step explanation:

hope you get it right

Answer:

fdsjfgdndgnxhñgjxgjxgjx

The value of both the interior angles of the triangle is calculated as 70° and 35°.

If a triangle side is formed, the exterior angle made is equal to the sum of a 2 interior opposite angles.

Now, as per the given question;

The exterior angle of a triangle is 105°.

Let one of the interior angle is 'x'.

Then, the other interior angle is 35 degree less; x - 35°.

By the exterior angle property.

Sum of interior angles = exterior angle

x + x - 35° = 105°

2x = 105° + 35°

2x = 140°

x = 70°

The other interior angle is; x - 35°

= 70° - 35°

= 35°

Therefore, the two interior angles of the triangles are estimated as 70° and 35°.

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Answer:

37/30

Step-by-step explanation:

In the given statement is:

Gravitational Force between two bodies at a distance x is given by:-

F = GmM/ x2 ; If a body of mass ' m' is revolving around the body of mass M and it's orbit is stationary then centrifugal force must be equal to the Gravitational Force i.e. Fg = mv2/x therefore FG = Fg i.e. GmM/ x2 =mv2/x; where v is the orbit motion of the orbiting body of mass.

Now, Let us understand the :

In mechanics, gravity, often known as gravitation, is the constant force of attraction occurring on all matter. It plays no part in shaping the interior features of common stuff because it is easily the weakest force known to exist in nature.

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