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3 years ago

Solve for x. 3(x + 2) + 4(x - 5) = 10

Mathematics

2 answers:

____ [38]3 years ago

6 0

Step-by-step explanation:

3x+6+4x-20=10

7x-14=10

7x=24

x=24/7

Troyanec [42]3 years ago

3 0

Answer:

x=3.43

Step-by-step explanation:

3(x-2)+4(x-5)=10

3x+6+4x-20=10

7x-14=10

7x=24

x=24/7

24/7=3.428571428571429(round to nearest hundredths)

x=3.43

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At which points are the tangents drawn to the ellipse x 2 + y 2 = [ a ] x + [ a ] y parallel to

In-s [12.5K]

The given equation of the ellipse is x^2 + y^2 = 2 x + 2 y

At tangent line, the point is horizontal with the x-axis therefore slope = dy / dx = 0

<span>So we have to take the 1st derivative of the equation then equate dy / dx to zero.</span>

x^2 + y^2 = 2 x + 2 y

x^2 – 2 x = 2 y – y^2

(2x – 2) dx = (2 – 2y) dy

(2x – 2) / (2 – 2y) = 0

2x – 2 = 0

x = 1

To find for y, we go back to the original equation then substitute the value of x.

x^2 + y^2 = 2 x + 2 y

1^2 + y^2 = 2 * 1 + 2 y

y^2 – 2y + 1 – 2 = 0

y^2 – 2y – 1 = 0

Finding the roots using the quadratic formula:

y = [-(- 2) ± sqrt ( (-2)^2 – 4*1*-1)] / 2*1

y = 1 ± 2.828

y = -1.828 , 3.828

<span>Therefore the tangents are parallel to the x-axis at points (1, -1.828) and (1, 3.828).</span>

3 0

3 years ago

Need help with Math (Quadratic)

BaLLatris [955]

Answer:

f(x) = 2(x -3)² +5 or f(x) = 2x² -12x +23

Step-by-step explanation:

The equation of a quadratic is easily written in vertex form when the coordinates of the vertex are given. Here, the point one horizontal unit from the vertex is 2 vertical units higher, indicating the vertical scale factor is +2.

<h3>vertex form</h3>

The vertex form equation for a parabola is ...

f(x) = a(x -h)² +k . . . . . . vertex (h, k); vertical scale factor 'a'

<h3>equation</h3>

For vertex (h, k) = (3, 5) and vertical scale factor a=2, the vertex form equation of the parabola is ...

f(x) = 2(x -3)² +5 . . . . . vertex form equation

Expanded to standard form, this is ...

f(x) = 2(x² -6x +9) +5

f(x) = 2x² -12x +23 . . . . . standard form equation

8 0

2 years ago

A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a red face card

timama [110]

<h3>The probability of picking a red face card from the deck is $(\frac{3}{26} )$ </h3><h3>The probability of NOT picking a red face card from the deck is $(\frac{23}{26} )$ </h3>

Step-by-step explanation:

The total number of cards in the deck = 52

The total number of red( Diamond + Hearts) face cards in the given deck

= 2 Red Queens + 2 Red jacks + 2 Red kings = 6 cards

Let E : Event of picking a red face card from the deck

Now , P( any event) = $\frac{\textrm{The number of favorable observations}}{\textrm{Total number of observations}}$

So, here P(Picking a red face card) = $\frac{\textrm{The number of red face cards}}{\textrm{Total number of cards}} = (\frac{6}{52} ) = (\frac{3}{26})$

Hence, the probability of picking a red face card from the deck is $(\frac{3}{26} )$

Now, as we know P (any event NOT A) = 1 - P(any event A)

So, P(NOT Picking a red face card) = 1 - P(Picking a red face card)

$= 1 - (\frac{3}{26} ) = \frac{26-3}{26} = (\frac{23}{26})$

Hence, the probability of NOT picking a red face card from the deck is $(\frac{23}{26} )$

8 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs. Match the subtraction expressions to their correct answers. - 6 1 - 3

krek1111 [17]

Answer:

Can you give me hint

than I can answer

7 0

2 years ago

The functions f and g are graphed in the same rectangular coordinate system, shown to the right. If g is obtained from f through

german

The first thing we notice is that the function is reflected. So we can start by reflecting it with respect to the x-axis.

We do this by adding a negative sign in the function:

$\begin{gathered} f_0(x)=x^2 \\ f_1(x)=-f_0(x)=-x^2 \end{gathered}$

Now, we have the function reflected, but in the wrong position. We can track its position by the vertex. It was originally at (0,0) and remains at (0,0) after the reflection.

But the final function have its vertex at (-5,0), so we have to translate the function 5 units to the left. we do this by adding 5 to the x in the function:

$f_2(x)=f_1(x+5)=-(x+5)^2$

Now, to check if there isn't any dilatation, we can check on other point in the graph to see if it checks out.

In the blue graph, we see the point (-3,-4), so let's input x = -3 and see if it checks out:

$f_2(-3)=-(-3+5)^2=-(2)^2=-4$

We got y = -4, so it checks out.

Thus, the answer is:

$g(x)=-(x+5)^2$

3 0

1 year ago