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1 year ago

Solve the system of equations below using the substitution method. x = y + 7 / 2 4x − 2y = 8

Mathematics

1 answer:

Verdich [7]1 year ago

3 0

Answer:

y = -3

x = $\frac{1}{2}$

Step-by-step explanation:

4(y + $\frac{7}{2}$ ) - 2y = 8 Distribute the 4. Multiply everything in the parentheses by 4

4y + 14 - 2y = 8 4 $(\frac{7}{2})$ = $\frac{28}{2}$ = 14 Combine the like terms 4y and -2y

2y + 14 = 8 Subtract 14 from both sides

2y = -6 Divide both sides by 2

y = -3

Plug -3 in for y in either original equation.

4x - 2y = 8

4x -2(-3) = 8

4x + 6 = 8 Subtract 6 from both sides

4x = 2 Divide both sides by 4

x = $\frac{2}{4}$ = $\frac{1}{2}$

Check:

x = y + $\frac{7}{2}$

$\frac{1}{2}$ = -3+ $\frac{7}{2}$

$\frac{1}{2}$ = $\frac{-6}{2}$ + $\frac{7}{2}$

$\frac{1}{2}$ = $\frac{1}{2}$

4x - 2y = 8

4( $\frac{1}{2}$ ) - 2(-3) = 8

2 + 6 = 8

8 = 8

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Write a quadratic equation with the given roots. Write the equation in the form of ax^2+bx+c=0 where a b and c are integers

Bas_tet [7]

You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the $x^2$ coefficient is 1, i.e. the equation is written like $x^2+bx+c=0$ , then you can say the following about the coefficients b and c:

$b$ is the opposite of the sum of the roots
$c$ is the multiplication of the roots.

So, for example, if we want an equation whose roots are 4 and -2, we have:

$4+(-2) = 4-2 = 2 \implies b = -2$
$4 \cdot (-2) = -8 \implies c = -8$

So, the equation is $x^2-2x-8=0$

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

$\dfrac{3}{4}+\dfrac{1}{2} = \dfrac{3}{4}+\dfrac{2}{4} = \dfrac{5}{4} \implies b = -\dfrac{5}{4}$
$\dfrac{3}{4} \cdot \dfrac{1}{2} = \dfrac{3}{8} \implies c = \dfrac{3}{8}$

And so the equation is

$x^2 - \dfrac{5}{4} + \dfrac{3}{8} = 0$

In order to have integer coefficients, you can multiply both sides of the equation by 8:

$8x^2 - 10 + 3 = 0$

5 0

3 years ago

Rsm question please explain<br> The question is in the picture

strojnjashka [21]

A triangle is a three-edged polygon with three vertices. ΔAKE and ΔCKP are congruent.

<h3>What is a triangle?</h3>

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.

In ΔABC, since AB≅BC, therefore, the triangle will be an isosceles triangle, and the measure of ∠A ≅ ∠C, using the base angle theorem.

Now In ΔAKE and ΔCKP,

∠A ≅ ∠C {Proved above}

∠AKE ≅ ∠CKP {Given}

AK ≅ KC {Given }

Since two angles and a side of the triangle are equal, therefore, we can write the two triangle are congruent using the Side-angle-side or Angle-Side-Angle congruence.

Hence, ΔAKE and ΔCKP are congruent.

Learn more about Triangle:

brainly.com/question/2773823

#SPJ1

7 0

2 years ago

Can you help me with the last four? Thanks!!!

Lina20 [59]

When you have -(-2) it equals +2 and the same goes for any other number. When you have +(-2) it equals -2 and the same goes for any other number. Hope this helps!

4 0

3 years ago

I need to know the answer to the second one.

Debora [2.8K]

Travis got 43 dollars

Robin collected 35 percent more so we can model this with

Travis + (Travis x .35)

43 + 15.05 =58.05

Jessica colelcted 20 percent less so

Travis - (Travis x .20)

43 - 8.6 = 34.3

34.4 + 58.05 + 43 = 135.45

C is the closest

7 0

3 years ago

Read 2 more answers

What is the slope of the line that is parallel to the line y = -2x + 5?<br> slope =

11111nata11111 [884]

Answer:

-2

Step-by-step explanation:

Slope intercept form is

y = mx + b

Where m is the slope

Parallel lines have the same slope

----------------------------

y = -2x + 5

is in slope intercept form

the slope, m = -2

The slope of the parallel ine will be the same

m = -2

4 0

3 years ago