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2 years ago

Marco can finish a jigsaw puzzle in 3 hours. Working together with Cliff, it takes them 1 hour. How

Mathematics

1 answer:

vovikov84 [41]2 years ago

3 0

Macro can finish the puzzle in 3 hours. We can say that her speed for working is 1/3 or 1/3 puzzle per hour.

Now if they work together, this turns into 1 puzzle per hour.

That must mean that Cliff would be doing the other 2/3 of the puzzle while Macro does his 1/3 in that hour. If Cliff has a speed of doing them 2/3 per hour. Then it would take 1 and a half hour to finish 1 whole puzzle.

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What is the slope, and what is the y-intercept of the line?

Oliga [24]

$General\ equation\ for\ line\ in\ slope\ intercept\ form:
\\\\y=ax+b\\
 a-slope\\ 
b-intercept\\\\ 
y=\frac{5}{4}x+9\\\\
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4 0

3 years ago

1<br>Determine the value of k if g(x)=4x+k is a tangent to f(x)=-x²+8x+20

tangare [24]

Answer:

k=24

Step-by-step explanation:

The tangent of the function f at x=a, can be found by differentiating f w.r.t. x and then replacing x with a.

f=-x^2+8x+20

Differentiating both sides:

f'=(-x^2+8x+20)'

By sum rule:

f'=(-x^2)'+(8x)'+(20)'

By constant multiple rule:

f'=-(x^2)'+8(x)'+(20)'

By constant rule:

f'=-(x^2)+8(x)'+0

By power rule:

f'=-2x+8

f' at x=a is -2a+8

This is the slope of any tangent line to the curve f.

The slope of g is 4 if you compare it to slope intercept form y=mx+b.

So we gave -2a+8=4.

Subtracr 8 on both sides: -2a=-4

Divide both sides by -2: a=2

The tangent line to the curve at x=2 is y=4x+k.

To tind y we must first know the y-coordinate of the point of tangency.

If x=2, then

f(2)=-(2)^2+8(2)+20=-4+16+20=12+20=32

So the point is (2,32).

g(x)=4x+k and we know g(2)=32.

This gives us:

32=4(2)+k

32=8+k

k=32-8

k=24

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2 years ago

A function's graph may include solutions that do not appear in its table of value?? True or false

Troyanec [42]

Pretty sure that’s true

4 0

3 years ago

Read 2 more answers

Which the parabola opens,

Dmitrij [34]

Table (A) represents the parabola y = x² - 6x in which the parabola opens and the y-intercept is (0, 0) table (A) is the correct choice.

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

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have the tables shown in the picture.

We know the quadratic form of a parabola is:

y = ax² + bx + c

If a > 0 the parabola opens

In the equation:

y = x² - 6x

1 > 0 the parabola opens and y-intercept is:

y = 0 (plug x = 0 in the given equation)

a = 1, b = -6, and c = 0

Thus, table (A) represents the parabola y = x² - 6x in which the parabola opens and the y-intercept is (0, 0) table (A) is the correct choice.

Learn more about the parabola here:

brainly.com/question/8708520

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2 years ago

4. The trajectory of a model rocket can be modelled by the equation h = - 3t^2 + 24t- 25, where h is the height of the rocket in

Alex Ar [27]

Answer:

It's too short. Write at least 20 characters to explain it well.

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3 years ago