What is 10.4 in a mixed number in simplest form

3) x2+ y2 - x + 3y - 42 = 0<br> X+y=4

REY [17]

The solution is $(-1,5)$ and $(7,-3)$

Step-by-step explanation:

The expression is $x^{2} +y^{2} -x+3y-42=0$ and $x+y=4$

Using substitution method we can solve the expression.

Let us substitute $x=4-y$ in $x^{2} +y^{2} -x+3y-42=0$

$(4-y)^{2} +y^{2} -(4-y)+3y-42=0$

Expanding and simplifying the expression, we get,

$\begin{array}{r}{16-8 y+y^{2}+y^{2}-4+y+3 y-42=0} \\{2 y^{2}-4 y-30=0}\end{array}$

Let us use the quadratic equation formula to solve this equation,

$\begin{aligned}y &=\frac{4 \pm \sqrt{16-4(2)(-30)}}{2(2)} \\&=\frac{4 \pm \sqrt{16+240}}{4} \\&=\frac{4 \pm 16}{4} \\y &=1 \pm 4\end{aligned}$

Thus, $y=5$ and $y=-3$

Substituting y-values in the equation $x+y=4$ , we get the value of x.

For $y=5$ ⇒ $x=4-5=-1$

For $y=-3$ ⇒ $x=4+3=7$

Thus, the solution set is $(-1,5)$ and $(7,-3)$

7 0

3 years ago

pedro has 6 packs of gum with p pieces in each pack he had a total of 72 pieces of gum decide whether each equation represents t

Serga [27]

Answer:

$6p = 72$ --- The equation

The solution is 12 packs i.e. p = 12

Step-by-step explanation:

No options given. So, I will solve generally.

Given

$Packs = 6$

$Quantity = p$ per pack

$Total = 72$

Required

Determine the equation

This is calculated using:

$Packs * Quantity = Total$

$6 * p = 72$

$6p = 72$

Divide both sides by 6

$p = 12$

4 0

3 years ago

How do i solve (3c^2d^4) ^3 x (2c^5d^8)^3?

vredina [299]

Answer:

$216c^{21}d^{36}$

Step-by-step explanation:

$(3c^2d^4)^3 * (2x^5d^8)^3$

$(3c^2)^3 (d^4)^3 * (2c^5)^3 (d^8)^3$

$27c^6 d^{12} * 8c^{15} d^{24}$

$216c^{21}d^{36}$

Hope this helps!

7 0

2 years ago

Match the following reasons with the statement givem

ANEK [815]

Answer:

AAS(Angle-Angle-Side) postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent

In triangle RAS and triangle QAT

$\angle R =\angle Q$ [Angle]

$AS =AT$ [Side] [Given]

By Base Angle Theorem states that in an isosceles triangle(i.e, AST), the angles opposite the congruent sides(AS =AT) are congruent.

⇒ $\angle 5= \angle 6$ [By base ∠'s of isosceles triangle are equal]

By definition of supplementary angles, if two Angles are Supplementary when they add up to 180 degrees.

$\angle 4$ , $\angle 5$ are supplementary and $\angle 6$ , $\angle 7$ are supplementary.

⇒ $\angle 4+ \angle 5 =180^{\circ}$ and

$\angle 6+ \angle 7 =180^{\circ}$

Two $\angle 's$ supplementary to equal $\angle 's$

$\angle 4+ \angle 5 =\angle 6+ \angle 7$

Since, $\angle 5 =\angle 6$

then, we get;

$\angle 4 =\angle 7$ [Angle]

then, by AAS postulates,

$\triangle RAS \cong \triangle QAT$

By CPCT[Corresponding Part of Congruent Triangles are equal]

$RS = QT$ Hence Proved!

7 0

3 years ago

A person standing on level ground is 2000 feet away from the foot of a 420-foot-tall building, as shown in the accompanying diag

antoniya [11.8K]

Answer:

12

Step-by-step explanation:

The formula for the tangent of an angle is the length of the opposite side divided by the length of the adjacent side. Therefore, the tangent of angle x is 420/2000=0.21. Taking the arctangent of that to get the angle, you get about 12 degrees. Hope this helps!

7 0

3 years ago