Given: -3(4x + 1) = 21
Prove: x = -2

The equation to represent the cost of each drink is 3(x + 2.5) + 3x = 25.50. The cost of each drink will be $3.

In the given question, it is stated that the family spent a total of $25.50 and they bought 3 Popcorn and 3 Drinks. Each popcorn costs $2.5 more than the drink. Now, suppose the cost of one drink is 'x' then we get:

Cost of 3 Drinks = 3x

Cost of 3 Popcorn = 3(x + 2.5)

The equation to represent this will be:

=>  3(x + 2.5) + 3x = 25.50

=>  3x + 7.5 + 3x = 25.50

=>  6x = 18

=>  x = 3

We get x = 3, Cost of one drink will be $3

Hence,  equation representing it will be 3(x + 2.5) + 3x = 25.50, and the cost of each drink will be $3

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Answer:

Step-by-step explanation: do 193.75 divided by 15

Answer:

6/10

Step-by-step explanation:

first, use your calculator to convert them to decimals

8/12 = 0.66

6/10 = 0.60

5/8 = 0.625

2/3 = 0.66

then see which one is the smallest

6/10 =0.60

done!!!! your answer

Take 1 cm of 5th, 6th and 7th shelves, it comes out to be = 210

Now,

5 - 2 = 3 book in the shelves

6 - 3 = 3 book in the shelves

7 - 4 = 3 book in the shelves

3 books are in common, so, 210 - 3 = 207 book Lizzie have.

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   First, we need to know the units they used. For every hectare, there are 2.47105 acres.

   Next, we can set up a proportion to solve.

        [tex]\displaystyle \frac{\text{\$8,963}}{1 \;acre} =\frac{\text{\$x}}{2.47105 \;acres}[/tex]

   Now, we will cross-multiply:

       $8,963 * 2.47105 = x

       x ≈ $22,148

   I was $10 from the answer they ended up with, so I most likely used a different conversion unit factor than they did. However, the steps are still the same.

the coodrinates of JKLM is,

J(1,3) , K(3,1), L(-1,-3) and M(-3,-1)

the length JK is ,

length KL is,

Length LM is,

length MJ

so, the perimeter = sum of sides,

= JK + KL + LM + MJ

= 2 root 2 + 4root2 + 2root2 + 4root2

= 12 root 2

thus, the perimeter is 12 root 2

The arity typically assumed to be limited. The "typical" operations of finite dimensionality are referred to as the finiteary operations when infinitary operations are taken into consideration. The mean of the five numbers is 8.2, four of numbers are 8, 10, 12 and 10. The fifth number is 1.025.

An operation, often known as a "operand" or "argument," is the function in mathematics that converts zero or more input values into a clearly defined output value. The operation's arity is determined by number of operands.

Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are operations that are most frequently studied. A constant is operation with arity zero, often known as a nullary operation. An example of operation of arity 3, sometimes known as a ternary operation, is the mixed product.

The arity typically assumed to be limited. The "typical" operations of finite dimensionality are referred to as the finiteary operations when infinitary operations are taken into consideration.

Similar to an operation, but with partial function in place of a function, is the definition of a partial operation.

The mean of five numbers is 8.2. Four numbers are 8, 10, 12 and 10.

Let the number be x,

[tex]\frac{8+10+12+10+x}{5} = 8.2[/tex]

x= 1.025

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1. The slope of the line on the graph is: 6

2. The graph of the line with a slope of 4/3 is shown in the image below.

Slope of a line = change in y / change in x = rise/run.

The equation that can be used to represent a linear graph can be written in slope-intercept form as y = mx + b, where the value of b is the y-intercept of the line and the value of m is the slope of the line.

1. Using two points on the line, (0, -1) and (1, 5):

Slope of the line = change in y / change in x = (-1 - 5)/(0 - 1)

Slope of the line = -6/-1

Slope of the line = 6

2. Slope (m) = 4/3

A point on the line is given as (1, 3)

Write the equation of the line by substituting (a, b) = (1, 3) and m = 4/3 into y - b = m(x - a):

y - 3 = 4/3(x - 1)

y - 3 = 4/3x - 4/3

y = 4/3x - 4/3 + 3

y = 4/3x + 5/3

The graph of y = 4/3x + 5/3 is shown in the image below.

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The probability of randomly selecting an order and getting the order that is used in the spelling bee is 1/6

Here we have 6 possible arrangements:

3!=3*2*1

3!= 6

Hence, the probability of selecting an order and getting the order = 1/6.

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Answer:

[tex]-2 < a < 1[/tex]

Step-by-step explanation:

-15 < 9a + 3 < 12 (Combine like terms)

-18 < 9a < 9 (Subtraction Property)

-2 < a < 1 (Division Property)

Note that just like solving a linear equation, instead of having two sides, you have three. And, whatever you carry out on one side, you have to carry out on all three.

Although, unlike linear equations, if you are dividing/multiplying all sides with a negative integer, then you have to flip the signs.

The Number system from least to greatest of the given number 8.116, 8.119, 8.18, 8.03, 8.14, 8.1 is 8.03 ,  8.1,  8.116, 8.119, 8.14, 8.11.

We were given the number 8.116, 8.119, 8.18, 8.03, 8.14, 8.1 so that we can arrange them from the smallest number to the highest number.

The first number will be 8.03 , then follow by 8.1, the after that we can see that the next number will be 8.116, which will be followed by the number 8.14, then this will be followed by 8.119 then followed by the number 8.18.

Therefore, the arrangement will be  8.03 ,  8.1,  8.116, 8.119, 8.14, 8.11.

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Answer: 6a³ + a² - 7

Step-by-step explanation:

(5a³ + 4a² − 3a + 2) + (a³ − 3a² + 3a − 9)=

5a³ + a³ + 4a² − 3a² - 3a + 3a + 2 - 9=

6a³ + a² - 0 - 7 = 6a³ + a² - 7

Answer:

6a³ + a²-7

Step-by-step explanation:

1. Get rid of the parentheses by distributing them.

(5a³ + 4a² − 3a + 2) + (a³ − 3a² + 3a − 9) = 5a³ + 4a² − 3a + 2 + a³ − 3a² + 3a − 9

2. Add like-terms.

5a³ + 4a² − 3a + 2 + a³ − 3a² + 3a − 9 = 6a³ + a²-7

Answer:Company b

Step-by-step explanation: 41.10/15=2.74

48.96/18=2.72

35.92/12=2.99

The method that can not be used to prove that lines i and k are parallel is the statement "shows that both lines are perpendicular to a third line".

and the measures of the other three angles are 60°, 60°, and 120°

Interior angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles

The method that can not be used to prove that lines i and k are parallel is the statement "shows that both lines are perpendicular to a third line".

Lines l and k intersect forming two pairs of vertical angles. If one of these angles measures 120°,

As per the given question,

Let angle ∠1 is 120°

here angles ∠1 and ∠2 are supplementary

So  ∠2 = 180° - 120° = 60°

However, if a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.

∠2 = ∠4 = 60°

∠1 = ∠3 = 120°

Therefore, the measures of the other three angles are 60°, 60°, and 120°.

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The required equation of slope intercept the line parallel to the given line and passing through (4,5) is  y = -1/4x + 6.

What exactly does slope intercept mean?

1)   5x + y = 3

   y = - 5x + 3

compare equation y = mx + c

        m = -5  

2) 7x - 5y = 20

      5y = 7x - 20

   y = 7/5x - 4

compare equation y = mx + c

      m = 7/5

3) y = -1/3x - 4

 compare equation y = mx + c

         m = -1/3

4) points ( 4,5) parallel to y = 1/4x - 4

               m₁  = m₂

  compare equation y = mx + c

             m₁ = 1/4  c = -4

now lets put the value

                  1/4 = m₂

So the equation of the line parallel to the given line assuming that its y-intercept is b will be

 y = 1/4x + b

the equation of the parallel line which passes through

(4,5, it should satisfy these points.

So let's substitute these points

5 = -4/4 + b

5 = -1 + b

b =  6

Hence the required equation of the line parallel to the given line and passing through (4,5) is

            y = -1/4x + 6

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the values of both angles are

2x - 8 = 2*25 - 8

          = 42 degree

x -7 = 25 - 7

      = 18 degree

Both internal and external angles make up a triangle. The angle that forms between two of a triangle's adjacent sides is known as the interior angle. The angle created between a triangle's side and its next-to-furthest side extending outward is known as the exterior angle. Triangle Angle sum feature of triangle states for ABC that 180 degrees is the sum of the triangle's internal angles.

2x - 8 + x - 7 + 90 = 180

3x - 15 = 90

x = 25

therefore the values of both angles are

2x - 8 = 2*25 - 8

          = 42 degree

x -7 = 25 - 7

      = 18 degree

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The evaluation of the expression, if m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5 , and t = − 2 | 16 + 4 ( 3 q + p ) is 46.

the given expression is  t = − 2 | 16 + 4 ( 3 q + p )

Then since we are given  m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5

Then, we can substitute all the given values of the terms into the given expression as :

t = − 2 | 16 + 4 ( 3 q + p )

t= -2 I 16+4(-18+2)

t= -2 I 16+4(-16)

t= -2 I 16 -64

t= -2 I -48

t =46

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The number of gigabytes that Sydney can use while staying within her budget is less than 2.9 gigabytes.

From the information, Sydney pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month.

The inequality that can be used to determine x x, the number of gigabytes Sydney can use while staying within her budget will be:

35.50 + 5x < 50

Collect like terms

5x < 50 - 35.50

5x < 14.50

x < 14.50 / 5

x < 2.9

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9^(2-x) = 3 -> 2-x = 1/2

into details about why it is 1/2 (ill call 2-x as y for easier demonstration)

9^y = 3
(3^2)^y = 3

And we have : (x^m)^n = x^mn
-> (3^2)^y = 3^2y = 3
-> 2y = 1
y = 1/2, therefore 2-x = 1/2.

So, x = 2 - 1/2 = 3/2.

Answer:

61

Step-by-step explanation:

Answer:

Step-by-step explanation:

TRUE

5 is a non-negative number

Conjecture : - 5 is a negative number

Answer: R1=0

Step-by-step explanation:

R1 = 200 divide R1 = 200 by 2 = R1 = 0

Note that the rational numbers represented on points- P, Q, R, and S are given as follows:  7/3, 8/3, -4/3, -5/3 respectively. See the explanation below.

A rational number is defined in mathematics as the proportion or fraction p/q of two integers, a numerator p, and a non-zero denominator q. 3/7, for example, is a rational number, as is every integer.

For the solution above:
Each section in between two numbers is broken into three sections.

Thus, we have a = (6/3), P = (7/3), Q = (8/3) and B = (9/3)

In the same way,

T = = -3/3,

R = -4/3

S = -5/3 and

U = -6/3

Therefore, the rational numbers represented - P, Q, R, and S are given as follows:  7/3, 8/3, -4/3, -5/3.

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a) Because it is an equilateral triangle, all the sides must have equal lengths.

The perimeter = 24cm -> Each side = 8.
Area = 1/2 b.h = 8.8.1/2 = 32 cm2.

b) A square has all of its sides of equal lengths just like an equilateral triangle.

The perimeter = 24cm -> Each side = 6.
Area = side.side = 6.6 = 36 cm2.

c) Since they have equal perimeters and the same properties (all sides equal) BUT they have different number of sides and lengths, they won't have the same areas.

d) A rectangle. E.g :
A set of lengths of 5cm and 7cm makes a rectangle with a perimeter of 24cm : (5+7).2

But, its area equals 5 x 7 = 35cm2, which is greater than the triangle.

Answer:

a) 27.71 cm²

b) 36 cm²

Step-by-step explanation:

a) Perimeter of equilateral triangle = 3a

Here, a is the side of equilateral triangle.

Perimeter of equilateral triangle = 24 cm

                   3a = 24 cm

                    a = 24 ÷ 3

                    a = 8 cm

[tex]\sf Area \ of \ equilateral \ traingle = \dfrac{\sqrt{3}}{4}a^2[/tex]

                                         [tex]\sf = \dfrac{\sqrt{3}}{4}*8*8\\\\ = 1.732*2*8\\\\ = 27.71 \ cm^2[/tex]

b)   Perimeter of square = 4s

Here, s is the side of square.

Perimeter of square = 24 cm

                         4s = 24

                           s = 24 ÷ 4

                           s = 6 cm

Area of square = s*s

                         = 6 * 6

                         = 36 cm²

c)  When the dimensions (length, width, height) of the shape changes, the area and volume changes.

d) Length of the rectangle is 10 cm and width is 2 cm.

Perimeter of rectangle = 2*length + 2* width

                                      = 2*10 + 2*2

                                       = 20 + 4

                                       = 24 cm

Area of perimeter of rectangle = length *width

                                                   = 10 * 2

                                                   = 20 cm²

Answer:

As a fraction, it would be 10/7 or as a number, 1 and 3/7.

A force of 85 N is applied over an area of 530 cm2. Then the pressure on it is equal to 1603.8 [tex]\frac{N}{m^{2} }[/tex].

Force(F) = 85 N

Area(A) = 530 [tex]cm^{2}[/tex]

Pressure(P) = ?

Calculating as per the above amount

Area = 530/100 × 100

= 0.053 [tex]m^{2}[/tex]

The definition of pressure is "force applied per unit area." The equation P = FA, where F is the force acting perpendicular to surface area A, provides the answer. The pascal (Pa), or one newton per square meter, is the accepted unit of pressure [tex]\frac{N}{m^{2} }[/tex].

Pressure is the physical amount of force exerted on a particular area. The definition of pressure is "force per unit of area." The pressure being applied to a body can be calculated by taking the amount of force being applied and dividing it by the area of contact.

Pressure = force/area

= 85/0.053

= 1603.8 [tex]\frac{N}{m^{2} }[/tex]

Pressure on the body is 1603.8 [tex]\frac{N}{m^{2} }[/tex]

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Answer:

oh k

Step-by-step explanation:

sure, I will!