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3 years ago

Write each equation in standard form using integers? y = 3x + 1 y = 4x - 7

Mathematics

1 answer:

Maru [420]3 years ago

3 0

Answer:

The standard form of y = 3 x + 1 is -3x + y = 1 .

The standard form of y = 4x - 7 is -4x + y = -7.

Step-by-step explanation:

Here the given equation are:

y = 3 x + 1

and y = 4x - 7

The above equations are of the form: y = m x + C

Now, the STANDARD FORM of the equation is Ax + By = C

Consider equation 1:

y = 3 x + 1

or, y - 3x = 1

or. -3x + y = 1

⇒ The equation -3x + y = 1 is in STANDARD FORM.

Consider equation 2:

y = 4 x - 7

or, y - 4x = -7

or. -4x + y = -7

⇒ The equation -4x + y = -7 is in STANDARD FORM.

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3 years ago

Which congruent theorem can be used to prove..

hjlf

Answer:

Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent? Two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle.

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3 years ago

Evaluate -1-3-(-9)+(-5)

babunello [35]

To evaluate this expression, we need to remember that subtracting a negative number is the same as adding a positive number, and that adding a negative number is the same as subtracting a positive number. Using this knowledge, let's begin to simplify the expression below:

-1 - 3 - (-9) + (-5)

Because addition of a negative number is the same as subtraction of a positive number, we can change + (-5) to -5, as shown below:

-1 - 3 - (-9) - 5

Next, because we know that subtracting a negative number is the same as adding a positive number, we can change - (-9) to + 9, as shown below:

-1 - 3 + 9 - 5

Now, we can subtract the first two terms and begin to evaluate our expression:

-4 + 9 - 5

Next, we can add the first two numbers of the expression:

5 - 5

Now, we can subtract our last two numbers, which gives us our answer:

Therefore, your answer is 0.

Hope this helps!

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3 years ago

1) Determine the discriminant of the 2nd degree equation below:

Aleksandr-060686 [28]

$\LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}$

We have, Discriminant formula for finding roots:

$\large{ \boxed{ \rm{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }}}$

Here,

x is the root of the equation.
a is the coefficient of x^2
b is the coefficient of x
c is the constant term

1) Given,

3x^2 - 2x - 1

Finding the discriminant,

➝ D = b^2 - 4ac

➝ D = (-2)^2 - 4 × 3 × (-1)

➝ D = 4 - (-12)

➝ D = 4 + 12

➝ D = 16

2) Solving by using Bhaskar formula,

❒ p(x) = x^2 + 5x + 6 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5\pm \sqrt{( - 5) {}^{2} - 4 \times 1 \times 6 }} {2 \times 1}}}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm \sqrt{25 - 24} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm 1}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 2 \: or - 3}}}$

❒ p(x) = x^2 + 2x + 1 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times 1} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{4 - 4} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm 0}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 1 \: or \: - 1}}}$

❒ p(x) = x^2 - x - 20 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 1) \pm \sqrt{( - 1) {}^{2} - 4 \times 1 \times ( - 20) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ 1 \pm \sqrt{1 + 80} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{1 \pm 9}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 5 \: or \: - 4}}}$

❒ p(x) = x^2 - 3x - 4 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 3) \pm \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 4) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm \sqrt{9 + 16} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm 5}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 4 \: or \: - 1}}}$

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5 0

3 years ago

Read 2 more answers

X-Y=5, 6X-6Y =?

denis-greek [22]

Answer:

Yes, it is 30

Step-by-step explanation:

And yes, you thought it through correctly. 6(X-Y) = 6*5

6(X-Y) = 30

3 0

3 years ago

Read 2 more answers