MATHEMATICS HIGH SCHOOL

Solve this system of equations by using an algebraic method.Equation:
y = 3x + 5
3x - y = 5

Answers

Answer 1
Answer:

Answer:

Step-by-step explanation:

Substitute our first equation into the second equation. We are given y, so this is ideal of substitution method.

y = 3x + 5
3x - y = 5

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

There is no solution for the system because after solving, the sides of the equation are not equal. We can further check this by writing the second equation in a "y = mx + b form, or slope-intercept form. This well tell use about the graphs of the equations.

3x - y = 5
-y = -3x + 5

y = 3x -5

When comparing with the first equation, we can see that the slope is 3 for both lines, but the y-intercept is different. This means we have two parallel lines that cross the y-axis at (0, 5) and (0, -5). From this, one can conclude there is no solution because parallel lines with different y-intercepts will never cross.

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Write the product in standard form. (2p+5)(2p-5)

Answers

Answer:

4p² - 25

Step-by-step explanation:

given

(2p + 5)(2p - 5)

each term in the second factor is multiplied by each term in the first factor, that is

2p(2p - 5) + 5(2p - 5) ← distribute both parenthesis

= 4p² - 10p + 10p - 25 ← collect like terms

= 4p² - 25 ← in standard form

Final answer:

The product of the expressions (2p+5)(2p-5) in standard form, based on the difference of squares formula, is 4p² - 25.

Explanation:

The problem asked is to write the product in standard form for the expression (2p+5)(2p-5). Understanding this problem requires knowledge of the algebraic formula (a+b)(a-b) = a² - b² - this is known as the difference of squares.

By applying this formula to the given expression where a is 2p and b is 5, the product simplifies to (2p)² - (5)².

By squaring each of these terms individually, we get 4p² - 25. Hence, the product of the expressions (2p+5)(2p-5) in standard form is 4p² - 25.

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Write an expression that can be used to find 4 x 275 using mental math and properties of numbers.

Answers

Answer:

The given expression can easily be solved by using Distributive Laws of multiplication over addition.

Step-by-step explanation:

The given expression is : 4 x 275

Now, 275 can be expressed as sum of 200 + 75 + 5

So, the given expression 4 x 275 changes to 4 x (200 + 70 + 5)

The above expression can easily be solved by using the distributive law of multiplication over addition.

So, now distributing the multiplication over addition. We get,

4 x 275 = 4 x (200 + 70 + 5)

             = 4 × 200 + 4 × 70 + 4 × 5

             = 800 + 280 + 20

             = 1100

Using the distributive property, 4 multiplied by 275 can be mentally calculated as 1100.

To find the product of 4 multiplied by 275 using mental math and properties of numbers, we use the distributive property and break down the numbers into more manageable parts.

First, we split 275 into 200 and 75. Then, we apply the distributive property by multiplying 4 by each part separately:

⇒ 4 × 275 = 4 × (200 + 75),

Using the distributive property:

⇒ (4 × 200) + (4 × 75),

Calculating mentally:

⇒ 800 + 300,

⇒ 1100,

By breaking down numbers into easier-to-manage parts and applying distributive property, we can mentally calculate that 4 multiplied by 275 equals 1100.

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How many hours between 8:15 to 12:45 ?

Answers

4.5
an hour to 9:15
one to 10
one to 11
one to 12
and .5 to 1215 to 1245
Subtract:

12h   45' -
08h   15'
-----------
04h   30'

If 3t − 7 = 5t , then 6t = how do you solve this

Answers

3t-7=5t \ \ \ |\hbox{subtract 3t} \n -7=5t-3t \n -7=2t \ \ \ |\hbox{multiply by 3} \n \boxed{6t=-21}}
3t-7=5t\n5t-3t=-7\n2t=-7|\cdot3\n\boxed{6t=-21}

According to the Rational Roots Theorem, which statement about f(x) = 25x^7 – x^6 – 5x^4 + x – 49 is true?Any rational root of f(x) is a multiple of –49 divided by a multiple of 25.

Any rational root of f(x) is a multiple of 25 divided by a multiple of –49.

Any rational root of f(x) is a factor of –49 divided by a factor of 25.

Any rational root of f(x) is a factor of 25 divided by a factor of –49.

Answers

Answer:

Any rational root of f(x) is a factor of -49 divided by a factor of 25.

Step-by-step explanation:

The Rational Root Theorems states that :

If the polynomial P(x)= a _nx^n +{a_(n-1)x}^(n-1)+............{a_(2)x}^(2)+{a_(1)x}^(1)+a_0 has any rational roots, then they must be in the form of

\pm (factors of a_0)/(factors of a_n)

Consider the polynomial

f(x)=25x^7-x^6-5x^4+x-49

in this case, we have a_0=-49 and a_n=25

Any Rational root of f(x) is a factor of  a_0=-49 divided by a factor of a_n=25
According to the Rational Roots Theorem, the  statement about f(x) = 25x^7 – x^6 – 5x^4 + x – 49 which is true is:

Any rational root of f(x) is a factor of –49 divided by a factor of 25.

The key points are "factors", and "ratio between the constant term and the coefficient of the highest order (exponent) term"

The coins in the store s cash register total $12.50. The cash register contains only nickels, dimes, and quarters. There are twice as many dimes as nickels. There are also twice as many quarters as dimes. How many quarters are in the cash register?

Answers

nickels is 0,05 of dolar - n
dimes is 0,1 o dolar -d
quarters is 0,25 of dolar -q
dimes =2nickels
d=2n
quarters=2dimes
q=2d=4n
12,5=n(0,05)+2n(0,1)+4n(0,25)
12,5=0,05n+0,2n+n
12,5=1,25n
n=10
q=4n=40
There are 40 quarters
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