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3 years ago

15

solve the equation. Justify each step. 5x - 11 = 34 Plzzz help me this needs to be explained in essay form.

1 answer:

Helga [31]3 years ago

4 0

Answer:

x = 9

Step-by-step explanation:

5x -11 (+11) = 34 (+11)

5x = 45

5x ÷ 5 = 45 ÷ 5

x = 9

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What is .13 repeating as a fraction?

Irina18 [472]

13/99 is the fraction.

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3 years ago

Which Two Numbers Add Up To Negative 26 And Multiply To 11?

Fynjy0 [20]

Xy=11
x+y=-26

x+y=-26
minus x both sides
y=-26-x

sub for y
x(-26-x)=11
-26x-x^2=11
add 26x+x^2 both sides
x^2+26x+11=0

ax^2+bx+c=0
x= $\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$

a=1
b=26
c=11

x= $\frac{-26+/-\sqrt{26^{2}-4(1)(11)} }{2(1)}$
x= $\frac{-26+/-\sqrt{676-44} }{2}$
x= $\frac{-26+/-\sqrt{632} }{2}$
x= $\frac{-26+/-2\sqrt{158} }{2}$
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x= $-13+\sqrt{158}$ or $-13-\sqrt{158}$

aprox

x=-0.420195 or -25.5698

those are the numbers

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3 years ago

The sales tax rate is 8.5%. What is the total cost, including tax, of an item priced at $40.50

Aloiza [94]

The answer for this is $43.9425

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3 years ago

The table below shows some inputs and outputs of the invertible function f etc

Snowcat [4.5K]

Answer:

$(a)\ f^{-1}(-15) = -6$

$(b)\ f^{-1}(4) + f(9)=0$

Step-by-step explanation:

Given

The attached table

$(a)\ f^{-1}(-15)$

This represents an inverse function.

So, we look into x row for its value.

i.e.

$f^{-1}(-15) = -6$

$(b)\ f^{-1}(4) + f(9)$

Just like (a)

$f^{-1}(4) = -11$ ---- by looking into the x rows

$f(9) = 11$

So:

$f^{-1}(4) + f(9)=-11 + 11$

$f^{-1}(4) + f(9)=0$

4 0

3 years ago

Let II be the tangent plane to the graph of f(x, y) = 8 – 2x^2 – 3y^2 at the point (1, 2,-6). Let S, x² + y^2 + z = 4 be another

stealth61 [152]

Let $F(x,y,z)=f(x,y)-z$ . The tangent plane to $f(x,y)$ at (1, 2, -6) has equation

$\nabla F(1,2,-6)\cdot(x-1,y-2,z+6)=0$

We have

$\nabla F(x,y,z)=(-4x,-6y,-1)\implies\nabla F(1,2,-6)=(-4,-12,-1)$

Then the tangent plane has equation

$(-4,-12,-1)\cdot(x-1,y-2,z+6)=0\implies -4(x-1)-12(y-2)-(z+6)=0\implies 4x+12y+z=22$

Let $g(x,y)=4-x^2-y^2$ , and $G(x,y,z)=g(x,y)-z$ . The tangent plane to $S$ at a point $(a,b,c)$ is

$\nabla G(a,b,c)\cdot(x-a,y-b,z-c)=0$

We have

$\nabla G(x,y,z)=(-2x,-2y,-1)\implies \nabla G(a,b,c)=(-2a,-2b,-1)$

so that this plane has equation

$(-2a,-2b,-1)\cdot(x-a,y-b,z-c)=0\implies2ax+2by+z=2a^2+2b^2+c$

In order for this plane to be parallel to the previous plane, we need to have

$\begin{cases}2a=4\\2b=12\end{cases}\implies a=2,b=6\implies g(a,b)=c=-36$

so the point we're looking for is (2, 6, -36).

6 0

3 years ago