Tamara said the Distributive Property was used to write 21x + 56xy as an equivalent expression, 7(3x + 8y). Is she correct? Explain. And what is the correct expression.

Answer: 1:3

Step-by-step explanation:

I'd say 1:3 but I could be wrong

The amount of GI is $35,468.

The amount of taxable income is $23,068.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Gross income = $35,468

Exemption = $12,400

Deduction = 0

Adjustment = 0

Taxable income.

= Gross income - Exemption

= 35,468 - 12,400

= $23068

Thus,

GI and taxable income are $35,468 and $23,068

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On interchanging the logical AND operator with logical OR operator and zeroes with ones,

(B'+C).A = (B'.C) + A

Now, According to the question:

Concept:

Duality theorem states that the dual of the Boolean function is obtained by interchanging the logical AND operator with logical OR operator and zeroes with ones. For every Boolean function, there will be a corresponding Dual function.

Calculation:

On interchanging the logical AND operator with logical OR operator and zeroes with ones,

(B'+C).A = (B'.C) + A

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The complete question is this:

Calculate the dual of the Boolean expression (B' + C).A

To ride a bike to school Torrin takes 15.75 min to ride to school and 3.54 km is the distance from his house to school.

Let  v₁ = 13.5 km/h the speed to school

v₂ = 10.5 km the speed returning home

t = the time of the ride to school in minutes

36 - t = the time of the ride from school in minutes

Since, distance = speed × time

⇒v₁ × t/60 = v₂ × (36 - t)/60

⇒13.5 × t/60 = 10.5 × (36 - t)/60

⇒t = 15.75 min

Now, the distance = v₁ × t/60 = 13.5 × 15.75/60 = 3.54 km.

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24 cars lacked power steering but did have air conditioning and an automatic gearbox.

According to the question,

No. of cars with Air conditioning = 88

No. of cars with Automatic transmission = 96

No. of cars with power steering = 76

All three = 4

None of these extras = 19

Only air conditioning = 23

Only automatic transmissions = 61

Only power steering = 28

Power steering and automatic transmission both = 11

The calculation for missing values:

11 - 4 = 7

96-61-4-7 = 24

88-24-4-23=37

It is obvious that 24 cars lacked power steering but did have air conditioning and an automatic gearbox.

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The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 does not have any solution for any value of k.

We can rewrite the equations as:

3x + 5y = 3

6x + ky = 8

To solve this system, we need to eliminate one of the variables. To do this, we can multiply the first equation by 2 and the second equation by -3. This will give us:

6x + 10y = 6

-18x - 3ky = -24

Now we can add the two equations together and get:

-12x - 3ky = -18

Since the coefficient of x is 0, this equation does not have any solution for any value of k.

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On solving the provided question we can say that  by linear equation number of, Red Balls = 6x 18; Blue Balls = 3;  Yellow Balls = 6

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

A bag contains 27 balls

• The ratio of red to blue to yellow balls is 6:1:2

To Find : The number of red,blue and yellow balls present in the bag

Let us take the variable as 'x' to represent the number of balls in the bag

When we Put the values in a equation,

6X+X+2x = 27

9x = 27

x = 3

Hence the number of,

Red Balls = 6x 18

Blue Balls = 3

Yellow Balls = 6

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Answer:

b

Step-by-step explanation:

Answer:

B. Students of the high school

Step-by-step explanation:

It is high school because you just want to ask that area.

yes it  is the same as that of all students at Faber GPAs as 2.32 and lower will mean that a track team athlete will be recommended for extra tutoring and population is 2.3* student number

What is the definition of a population?

In ordinary usage, a population is a distinct group of individuals with shared citizenship, identity, or characteristics. In statistics, a population is a representative sample of a larger group of people (or even things) with one or more characteristics in common.

When the distribution is normal, we use the z-score formula.

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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The area of a right-angled triangle is represented by the expression

x(x + 2) = 24 having area 24 square feet.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the area of a right-angled triangle is (1/2)×base×height.

Given, The area of a triangle is 24 square feet whose height is 2 more than it's base.

Let, The base of the triangle be 'x', Therefore the measure of the height is (x + 2).

Therefore, The area of the triangle is,

(1/2)×x(x + 2) = 24.

x(x + 2) = 24.

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Check the picture below.

As per the concept of graph, the name of the point where the two axes cross is origin.

Graph in math is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Here we have to identify the name of the point where the two axes cross.

As we all know that the horizontal axis in the coordinate plane is called the x-axis and the vertical axis is called the y-axis.

Here we have also know that the point at which the two axes intersect is called the origin.

Where the origin is at 0 on the x-axis and 0 on the y-axis.

And these intersecting x- and y-axes divide the coordinate plane into four sections

Finally all these four sections are called quadrants.

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The missing measures, using the Pythagorean Theorem, are given as follows:

3. Leg x = 21.75.

4. Hypotenuse x = 13.85.

The Pythagorean Theorem states that length of the hypotenuse squared is equals to the sum of each of the sides of the triangle squared.

For item 3, we have that the leg x is missing, while another leg and the hypotenuse are given, meaning that the relation is of:

x² + 16² = 27²

Hence:

x² = 27² - 16²

[tex]x = \sqrt{27^2 - 16^2}[/tex]

x = 21.75.

For item 4, we are given two legs and want to find the hypotenuse, hence the relation is given as follows:

x² = 12.8² + 5.3²

[tex]x = \sqrt{12.8^2 + 5.3^2}[/tex]

x = 13.85.

As for item 5, there is not enough information to answer, but the procedure should be the same.

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The provided schematic must be followed in order to answer these diamond problems. You must multiply the values on the left (x) and right (y) cells in order to find the value that belongs in the top cell.

we have,

For Diamond Problems a

x+y=1.2

xy=.32

so value of x= .8 and y = .4.

for Diamond Problems b

x= 11

x+y=25.

so y= 14 and xy=11*14=154.

for Diamond Problems c

x=-7

y=-9

so x+y=-16 and xy= 63.

for Diamond Problems d

x+y=31

xy=234

x=13 and y=18

Because puzzles engage both the left and right sides of your brain, solving them aids in the development of your problem-solving abilities. Solving puzzles with others is a terrific method to improve your communication and cooperation skills in addition to your problem-solving and critical thinking abilities.

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The two posters will cover 776 square inches of Melody's bedroom wall.

To find this, you add the area of the two posters together. Poster A has an area of 450 square inches, and poster B has an area of 326 square inches. By adding these two values together, we get 450 + 326 = 776 square inches. This is the total area that the two posters will cover on Melody's bedroom wall. It is important to note that this is assuming that the posters do not overlap each other and that they are placed next to each other, covering an equal area of the wall.

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The values of x and y could be 25 and 113

What are parallel lines ?

parallel lines can be stated as , they both are equi distant from each other and which never intersect.

From the given figure,

y+12 = 3x + 50

as both are parallel to each other.

y-3x = 38

and 5x  = y + 12

as vertically opposites are always equal .

y = 3x + 38

y = 5x - 12

hence,

5x - 12 = 3x +38

2x = 50

x = 25

put x = 25 in y = 3x + 38

y = 3 * 25 + 38

y = 113

hence the values of x and y are 25 and 113 respectively.

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Answer:

y = 90°

Step-by-step explanation:

Answer:

80 ducks (16+64)

Step-by-step explanation:

So if there were 32 brown ducks in the pond at first, then twice the amount of brown ducks (32).

32x2=64 white ducks

So now their are 64 white ducks at the pond. We still have to add how many brown ducks their were so…

64+32=96 ducks in total

But then as the white ducks came in half of the brown ducks flew away.

32/2=16 brown ducks left in the pond.

Lastly add the remaining brown ducks with the white ducks and that is you answer!
16+64=80 total amount of ducks

Final Answer:

80 ducks

I hope this helps! I am sorry if I got it wrong!

On solving the provided question we can say that *629 = n - 99 is an equation. The textbook contains 728 pages*.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

In other words, the geometry book is 99 pages LONGER than the algebra book, which is 99 pages SHORTER. The solution can be obtained using this equation. I'm sorry, but 530 is not the solution.

629 = n - 99 is an equation. The textbook contains 728 pages*.

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We can conclude from answering the above question that the first two patterns of the matrix  form a sequence in the third from top with the numbers 4-2-6.

A matrix is a set of numbers arranged in rows and columns. learns about the elements and dimensions of matrices and introduces them for the first time. A rectangular grid of numbers in rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. Its single row and 1 n row matrix order are the reasons behind its name. A = [1 2 4 5] is a row matrix of order 1 by 4, for instance. P = [-4 -21 -17] of order 1-by-cubic is another illustration of a row matrix.

We can conclude from answering the above question that the first two patterns of the matrix  form a sequence in the third from top with the numbers 4-2-6.

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Answer:

x = 4

y = 28

Step-by-step explanation:

1) y = 7x

2) y = 2x + 20

substitute y = 7x into equation 2:

7x = 2x + 20   now you can solve for x:

7x - 2x = 20

5x = 20

x = 20/5 = 4

Plug x = 4 into either equation 1 or 2 to solve for y:

y = 7x = 7(4) = 28

The coefficient of the variable x  in the expression 4a+3x +a is 3

Given that,

The expression is 4a+3x +a which can be simplified as 4a+3x +a

To find : The coefficient of the variable x in the expression

The coefficient of x in 4a+3x +a is 3

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6

Coefficient is the number that is beside the variable in the equation.

As we can see that the term that is in multiplication with x is 3

Hence, the coefficient of x in the equation  is 3

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 As per Given data,

The month in which the balance of two bank accounts A is become equal to the balance of account B is 30thmonths,

Unknown variables are used to find the unknown values of the problem using the algebraic expressions.

Month       Account A        Account B

 0                    $ 100                 $ 250  

  1                    $ 125                 $ 270

  2                   $ 150                 $ 290

Clearly

The amount in account A is growing with $25 each month. Thus, the amount in this account in nth month is,

100+25[tex]n[/tex]

The amount in account B is just growing with $20. Thus, the amount in this account in nth month is,

250+20[tex]n[/tex]

x month

balances of two

account becomes equal,

then

100 + 25x =250 + 20x

25x - 20x = 250 - 100

5x = 150

x =30

Therefore, in 30th month balance of account A equal to balance of account B

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Q. The table shows the balances of two bank accounts for 3 months. In 30th month will the balance of account A be equal to the balance of account B?

Month       Account A      Account B

   0               $100                $250

    1               $125                 $270

    2              $150                 $290

The degree of the polynomial  [tex]2xA^2 5xA^2A^37[/tex] is 9

A polynomial's degree is the sum of the degrees of its monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer.

The degree of a polynomial is the highest or largest power of a variable in a polynomial equation. The degree denotes the polynomial with the maximum exponential power (ignoring the coefficients).

Consider the following polynomial expression with two variables: [tex]x^3 + 6x^2y^4 + 3y^2+5[/tex]

The polynomial has a degree of 6.

This is because the exponent values of x and y in the second term of the algebraic formula, [tex]6x^2y^4[/tex], are 2 and 4, respectively. We get 6 when we sum the exponent values. As a result, the multivariable polynomial expression has a degree of 6.

As per question, polynomial is: [tex]2xA^2 5xA^2A^37[/tex]

The total sum of power is: 1+2+1+2+3=9

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The perimeter of the possible larger triangle with possible side lengths of 24, 32 and 40 is 96 units

The perimeter of a figure is the length of the boundary surrounding the figure.

Two triangles that have proportional dimensions are similar triangles

The dimensions (arranged in the order of corresponding sides) of the possible similar right triangles in the question, obtained from a related question, having two similar right triangles, posted online are;

The similarity of the triangles (proportional corresponding sides, indicates that we get;

[tex]\dfrac{24}{9} = \dfrac{32}{12} = \dfrac{x}{15}[/tex]

Therefore, by cross multiplication, we get;

32 × 15 = 12 × x

x = 32 × 15 ÷ 12 = 40

The perimeter of the larger triangle is; 24 + 32 + 40 = 96

Please find attached the possible diagram of proportional right triangles, created with MS Word, obtained from a question with regards to proportional right triangles online.

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When a calcium atom forms an ion, it loses two electrons. The electrical charge of the calcium ion is +2

Calcium ions are net positive two charges. In calcium, when it has assumed its most stable state, the relationship between the quantity of protons (20) and the quantity of electrons (18) is represented by the +2 charge.

In the event that calcium (Z = 20) picks up two electrons, the resultant ion will have 18 electrons and 20 protons, giving it a charge of +2. (two more positive protons than negative electrons). It's a cation, this ion. Using the Ca2+ symbol, we can identify a calcium ion.

Atoms that lose electrons acquire a positive charge as there are fewer electrons left with negative charges to balance the positive charges of the protons in the nucleus. Positively charged ions are known as cations.

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Answer: nswer ; x , we can find ; y with the first equation :.

1 answer

·

We know that y=5x−7 so we are just going to replace the y in the other equation : −3x−

Step-by-step explanation:

The number of hours after which the cars will be 350 miles apart is 34 hours.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Vehicle 1.

Speed = 55.5 mph

Distance(1) = 55.5 x Time

Vehicle 2.

Speed = 45(1/4) mph

Distance(2) = 45(1/4) x Time

The difference in the distance = 350 miles.

Distance(1) - Distance(2) = 350

55.5 x Time - 45(1/4) x Time = 350

55.5 x Time - (181/4) x Time = 350

(55.5 - 181/4) x Time = 350

Time = 350 / (55.5 - 45.25)

Time = 350 / 10.25

Time = 34 hours.

Thus,

The car will be 350 miles apart after 34 hours.

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