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3 years ago

Please Help!

Mathematics

1 answer:

kipiarov [429]3 years ago

6 0

9514 1404 393

Answer:

A: -1, 3/5

B: (-1/5, -3 1/5)

2: plot the given points and draw a curve through them.

Step-by-step explanation:

The x-intercepts are most easily found from a graph of the function. I like the Desmos graphing calculator for this purpose. The x-intercepts are -1 and 3/5.

You can also find the x-intercepts by factoring the function.

f(x) = 5x^2 +5x -3x -3 = 5x(x +1) -3(x +1) = (5x -3)(x +1)

The x-intercepts are the values of x that make the factors zero:

5x -3 = 0 ⇒ x = 3/5

x +1 = 0 ⇒ x = -1

The vertex is on the axis of symmetry, which is the vertical line at the value of x halfway between the zeros. (-1 +3/5)/2 = (-2/5)/2 = -1/5

The value of f(x) there is ...

f(-1/5) = (5(-1/5) +2)(-1/5) -3 = (-1 +2)(-1/5) -3 = -1/5 -3 = -3 1/5

The vertex is (-1/5, -3 1/5).

The easiest step to take to graph the function is to type it into a graphing calculator (see attached).

If you're graphing this by hand, the three points given in parts A and B will be on the graph. The leading coefficient in the function is 3, so the x^2 parent function is vertically stretched by a factor of 3. This can make it a little more difficult to find points that lie on the graph.

Recognizing that the vertex form equation is ...

f(x) = 3(x +1/5) -3 1/5

I might choose x-values that are -1/5 ± 1/2 to get y-values that are -3 1/5 + 3/4. And, x = -1/5 ± 1 ⇒ y = -3 1/5 +3.

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Divide 3xsquared - 11x - 4 by x - 4<br><br>a. x+1<br>b. x-23<br>c. 3x+1<br>d. 3x-23

Dmitriy789 [7]

Answer:

c. $3x+1$

Step-by-step explanation:

Since the divisor is in the form of $x - c$ , use what is called Synthetic Division. Remember, in this formula, <em>-c</em> gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

4| 3 −11 −4

↓ 12 4

_______________

3 1 0 → 3x + 1

You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [3x² - 11x - 4]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 3 in your quotient can be a 3x, and the 1 follows right behind it, giving you the quotient of $3x + 1$ .

I am joyous to assist you anytime.

5 0

3 years ago

One angle of a triangle is 30° more than the smallest angle. The largest angle is the sum of the other angles. Find the measures

vladimir1956 [14]

Answer: $\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}$

Step-by-step explanation:

Let the smallest angle be x.

Then, the middle angle is x+30.

The largest angle is 2x+30.

Angles in a triangle add to 180 degrees, so:

$x+x+30+2x+30=180\\\\4x+60=180\\\\4x=120\\\\x=30$

So, the angles measure $\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}$

6 0

2 years ago

20 = -d + 6

Sphinxa [80]

ok so rearrange things so that it says 6-d=20, then subtract six from each side to get -d=20-6, then subtract 6 from 20 to get -d=-14, then multiply both sides by -1 to get rid of the negative sign in front of the d since a variable cannot be a negative thus making your answer -14 or letter D. :) ❤❤❤❤

hope this helps

3 0

3 years ago

Read 2 more answers

For which values of a, b, and c will Ax+ By=C be a horizontal line through the point (-4,2)

RUDIKE [14]

Answer:

A = 0, B = 1 and C = 2

Step-by-step explanation:

The slope of a horizonal line is zero.

y = mx + b Use the slope intercept form with m = 0 and point (-4, 2).

2 = 0(-4) + b Solve for "b"

2 = 0 + b

2 = b

The equation in slope intercept form is y = 0x + 2 ; y = 2.

The equation in standard form: Ax + By = C has the value 0x + y = 2

3 0

2 years ago

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zepelin [54]

Answer:

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Step-by-step explanation:

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