What is the first step that should be taken to solve the equation 5 - 2 (1x +3) = 12.

(A) Divide both sides of the equation by 5

(B) Add 1x + 3 inside the parenthesis

(C) Distribute -2 to (1x +3)

(D) Rewrite 5 - 2 as 3​

The pair of ratios that will make a proportion include:

A. 1/3 and 12/36

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.

In this case, it should be noted that 12 over 36 can be reduced to the lowest term. This will be:

12 / 36

= 1/3

Therefore, the correct option is A.

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There were total 11 birds and 7 cats on Thursday.

Make the cats = 'x'

and the birds = 'y'

x + y = 18.......(1)

500x + 650y = 10000......(20

Multiply (1) by 50

500x + 500y = 9000.....(1)

500x + 650y = 10050.....(2)

Subtract (2) from (1)

.......150y = 1050

y = 1050/150

y=7

Substitute y =7 into (1)

x + 7 = 18.......(1)

x = 18 - 7

x = 11

11 birds and 7 cats were in on Thursday.

Hence we get the required answer.

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Answer: 12

Step-by-step explanation:

x/6 = 2

you have to divide x equally into 6 two times to find x you have to

Times the Denominator and the answer (6·2)

which results in being 12

and to check you plug 12 into x and get this 12/6 = 2

6*2 = 12

so 12 was divided 2 times into 6 and you get 2 = 2  

I know the way I summed it up was lengthy sorry about that.

The height of the box is 2.15 inches.

Let the height be 'h'

Given, length is 5 inches more than height, l = h + 5

Width is 2 times the height, b = 2h

Total Volume of rectangular box = 66 in³

⇒ l×b×h = 66

⇒ (h+5)(2h)h = 66

⇒ 2h³ + 10h² = 66

⇒ 2(h³ + 5h²) = 2×33

⇒ h³ + 5h² - 33 = 0

Using, graphing calculator and by plotting the above equation, we can get h = 2.149 in ≈ 2.15 in

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The perimeter and area of the rectangle are 13 / 6 yards and  1 / 4 yard² respectively

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

The perimeter of a rectangle is the sum of the whole 4 sides of the rectangle.

Therefore,

perimeter of a rectangle = 2(l + w)

where

Therefore,

perimeter of the rectangle = 2(3 / 4 + 1 / 3)

perimeter of the rectangle = 2 ( 9 + 4/ 12)

perimeter of the rectangle = 2(13 / 12)

perimeter of the rectangle  = 26 / 12

perimeter of the rectangle  = 13 / 6 yards

Area of the rectangle = lw

Therefore,

Area of the rectangle = 3 / 4 × 1 / 3

Area of the rectangle = 3 / 12

Area of the rectangle = 1 / 4 yard²

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The surface area of the regular pyramid is 131.15 cm.

The surface area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. The whole area of the surface of the specified solid item is referred to as surface area. We should add the areas of the surfaces to determine the object's surface area because the faces of three-dimensional objects are essentially 2D shapes.

Given,

Surface area = 1/2(a× b) + 3/2(b ×s)

Where b is a pyramid's side, a is a triangle's base height, and s is a pyramid's slant height.

Side = 6.1

Base = 7

Slant height = 12

Equating in formula:

1/2(6.1 × 7) + 3/2(6.1 × 12)

1/2(42.7) + 3/2(73.2)

21.35 + 109.8

131.15

The surface area of the regular pyramid is 131.15 cm.

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The error Noa made is:

Step 4: 44 32/24 - 37 15/24= 8 17/24

Here we can finally find out the mistake done by Noa. The result is 7 17/24 and not 8 17/24.

1. Let's review carefully all the steps taken by Noa to calculate the difference of the circumferences of the two trees.

Circumference Tree 1 = 37 5/8 inches around

Circumference Tree 2 =  45 1/3 inches around

Step 1: 45 1/3- 37 5/8

The measures are correct, no issues copying them.

Step 2: 45 8/24 - 37 15/24

Noa looked for common denominators

1/3 * 8/8 = 8 /24 is correct; 5/8 * 3/3 = 15/24 is also correct.

Step 3: 44 32/24 - 37 15/24

Noa looked for making the fraction part higher on the left side:

45 8/24 = 44 32/24 is correct because 24/24 = 1

Step 4: 44 32/24 - 37 15/24= 8 17/24

Here we can finally find out the mistake done by Noa. The result is 7 17/24 and not 8 17/24.

Hence Noa made a mistake in step 4.

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Subtraction Property of Equality

Properties of equality can help manipulate literal equations to solve for specific variables.

Subtraction Property of Equality

The subtraction PoE states:

This means if an equivalent quality is subtracted from both sides of an equation, then the equation is still true. In the equation above, 3x is subtracted from both sides of the equation. The subtraction PoE tells us that we are allowed to do this and maintain equality.

Other Properties of Equality

There is a multitude of PoEs including Addition, Multiplication, and Division. All of the properties also state that if an equal operation is done on both sides of an equation, then it is still equal. So, the subtraction PoE applies to all operations. There are also other properties of equality like Reflexive and Transitive that also help to solve literal equations.

Answer:

(-5,4) and (5,-8) are our points

as slope formula is [tex]\frac{y2-y1}{x2-x1}[/tex]

we can say the slope is

-8-4/ 5-(-5)

-12/10

-6/5 is our slope

so for slope intercept form it should be,

[tex]y=\frac{-6}{5} x-2[/tex]

good luck! <3

Using the Sales tax rate formula ,

The sales tax rate of an item is 8% (in percentage).

Sales tax : Sales Tax is defined as a tax on the sale, transfer, or exchange of a taxable item or service. Sales tax generally applies on the sale to the end user or ultimate consumer. Sales tax is generally added to the sales price and is charged to the purchaser.

formula :

When written out, the equation,

Sales tax rate = Sales tax percent / 100.

Sales tax = List price x Sales tax rate

We have given that,

An item cost price before tax = $460

sales tax = $36.80

we have to calculate sales tax rate in percentage form .

Using the above formula of sales tax rate,

Sales tax rate= sales tax /list price

=> Sales tax rate =$36.80/$460

=> Sales tax rate = $0.08

=>Sales tax rate = 8%

Hence, sales tax rate is 8% .

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The Probability is 0.5 or 50% so the option is (A)

What is probability?

Total puppies are = 8

The different breed  of puppies are = 4

Probability = Number of favourable outcomes / Number of Total outcomes

Probability  = 4 / 8

                  = 1 / 2 = 0.5 or 50%

Therefore, The Probability is 0.5 or 50% so the option is (A)

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Answer:

(10x - 2)° = 180°

Step-by-step explanation:

Since the sum of a triangle is always 180°,

∴ (5x - 5)° + (3x + 3)° + (5x)° = 180°

           5x - 5 + 3x + 3 + 5x = 180

                             ∴ 10x - 2 = 180

Answer:

13x - 2

Step-by-step explanation:

(5x - 5) + (3x + 3) + (5x)

5x - 5 + 3x + 3 + 5x

5x + 3x + 5x - 5 + 3

13x - 2

This question can be done using simple BODMAS rule, the answer according to which is in main body.

What is BODMAS?

BODMAS stands for Bracket Of Division Multiplication Addition Subtraction.

Main Body:

according to question=

6-4x = 6x -8x +2

solving the like terms on right side

6 - 4x = -2x +2

-2x is the answer to first blank

solving further,

6 = -2x +4x +2

6 = 2x +2

so 2x is the answer to second blank.

now taking 2 to left side ,

4 = 2x

x= 2

Hence the value to blanks are found.

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Answer:

35

Step-by-step explanation:

if x/y is 70

then x/2y is half 70

so it's. 70÷2

x/2y=35

The value for x/2y is 1/140.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

x/y= 70

So, for x/2y we have multiply the quantity y by 2.

Then x/2y= 1/70 x 1/2

x/2y = 1/140

Hence, the value for x/2y is 1/140.

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Answer:

Step-by-step explanation:

Answer:

96%

Step-by-step explanation:

48 ÷ 50 × 100

The average of the positive numbers from 1 to 100= 50.5

According to our question-

the median of all positive values between 1 and 100.

Since there are 100 whole numbers in this range, we know that adding up all of the whole numbers in this range equals 5050.

The sum of all whole numbers from 1 to 100 divided by 100 is the average of all whole numbers from 1 to 100.

Hence, 50.5 is the average of all whole numbers between 1 and 100.

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Answer:true

Step-by-step explanation:

Answer:

2,-3,-1

Step-by-step explanation:

f(x)=2x³+4x²-10x-12

f(x)=2(x-2)(x+1)(x+3)

F.theo: if f(a)=0, (x-a) is a factor of f(x)

Therefore, (x-2)=0 (x+1)=0 (x+3)=0

The other zeros are x=2, x=-1 and x=-3

Answer: y= 2/5x - 5

Step-by-step explanation:

To use this we will put the equation in point slope form

y-y1 = m (x-x1)     (y1 and x1 and points where the line passes through)

y + 3 = 2/5(x - 5)

y + 3 = 2/5x - 2

y = 2/5x - 5

The domain of the table is: set of values under weight not over.

The range of the table is: set of values under price.

Given a table that represents a relation, there is usually a set of input values (x-values) which represents the domain elements, and the output values (y-values) which represents the range elements.

In the table given, we have the values for weight not over that ranges from 0, 1, 2, up to 10. This set of values is the domain of the table.

The set of values that is under price is the output of the table, which represents the range of the table.

Domain of the table is the weight not over, while the range is the set of values under price.

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The mean of the sample is affected by the outlier. The mean is non-resistant. That means, it's affected by outliers.

More specifically, the mean will want to move towards the outlier.

Say we have some information

1\s,2 \s, \s3 \s. This has a mean of 2 in it. However, if we include a 94-point outlier in the data set, the mean will change to 25. The mean shifted toward the outlier, as you can see.

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

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The slope(m) of the equation is 1 and the y intercept(b) is  -4 , the graph of the line is shown below .

In the question ,

it is given that ,

the equation of the line is given as

y = x - 4 ,

we need to find the slope(m) and y intercept(b) of the given line ,

We know that the general equation of the line is y = mx + b

where m is slope and b is  y intercept .

On comparing both the equations , we can conclude that

the slope is 1 and the y intercept is -4 .

to graph the line , we need two points

put x = 0 , we get y = -4

the first point is (0,-4)

for second point put y = 0, we get x = 4 ,

the second point is (4 , 0)

the graph of the line described by the equation is shown below .

Therefore , The slope(m) of the equation is 1 and the y intercept(b) is  -4 .

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The number of cubes made from the given cuboid is 9.

From the given figure, height =6 units, width =4 units and length =3 units.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

a) Now, volume of cuboid = Length × Width × Height

= 3×4×6

= 72 cubic units

From the figure, edge of cube is 2 units

b) Volume of cube =a³, where a is edge

= 2³

= 8 cubic units

Number of cubes = Volume of cuboid/Volume of cube

= 72/8

= 9

Therefore, the number of cubes made from the given cuboid is 9.

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Answer: 117.2

Step-by-step explanation:

c² = a² + b² - 2ab cos C

b²= a² + c² - 2ac cosB

x² = 61² + 63² - 2(61)(63) cos142

x²= 13746.65065

x ≈ 117.2  

Answer: A≈451.93

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

So, for long division we have 38.5/0.5

     60+16+1 =77

0.5/38.5

     -30= (0.5/8.5)

                     -8.0=(.5/.5)

                               -.5=0

The measure of angle h is  19° angle measure of angle c is 132°

In this question, we need to find the value of h and c.

We can observe that the opposite angle to angle (h + g) measures 48 degrees.

So, angle (h + g) = 48°                ..........(1)

We know that sum of linear angles is 180°

So, 151° + e = 180°

e = 180 - 151

e = 29°

As angle d and angle e are opposite angles, angle d = 29°

Consider given parallel lines and a transversal passing through points a and f

then angle g and angle d are alternate interior angles.

So, angle g = angle d = 29°

from (1),

∠h + ∠g = 48°

∠h = 48° - 29°

∠h = 19°

Consider a triangle with angles h, c and d.

∠h + ∠c + ∠d = 180°

19° + ∠c + 29° = 180°

∠c = 180° - (19 + 29)°

∠c = 132°

Therefore, the measure of angle h is  19° angle measure of angle c is 132°

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