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katrin2010 [14]

2 years ago

5

Find the greatest common factor of 14 and 33.

2 answers:

Vera_Pavlovna [14]2 years ago

6 0

Answer: 1

Step-by-step explanation: GCF is what largest number can go into both. They do not share any other number (:

Paraphin [41]2 years ago

3 0

Answer:

1

Step-by-step explanation:

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Find the missing point of the following parallelogram.

zepelin [54]

Answer:

(4,5)

Step-by-step explanation:

3 0

2 years ago

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Write an equation of a line containing (2, 1) and (3, 4) in point-slope form.

ivann1987 [24]

Answer:

$y-1=3(x-2)$

Or

$y-4=3(x-3)$

Step-by-step explanation:

The slope formula is given by:

$m=\frac{y_2-y_1}{x_2-x_1}$

The line containing (2, 1) and (3, 4) has slope;

$m=\frac{4-1}{3-2}=3$

The point-slope form is given by:

$y-y_1=m(x-x_1)$

We substitute the point and slope to get:

$y-1=3(x-2)$

Or

$y-4=3(x-3)$

8 0

3 years ago

A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

Stella [2.4K]

A parabola is a mirror-symmetrical U-shape.

The equation of the parabola is $\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$
The focus is $\mathbf{Focus = (80, -1760)}$
The directrix is $\mathbf{y = \frac{1}{640}}$
The axis of the symmetry of parabola is: $\mathbf{x = 80}$

From the question, we have:

$\mathbf{Vertex: (h,k) = (80,10)}$

$\mathbf{Origin: (x,y) = (0,0)}$

The equation of a parabola is:

$\mathbf{y = a(x - h)^2 + k}$

Substitute the values of origin and vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{0 = a(0 - 80)^2 + 10}$

$\mathbf{0 = a(- 80)^2 + 10}$

$\mathbf{0 = 6400a + 10}$

Collect like terms

$\mathbf{6400a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{640}}$

Substitute the values of a and the vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

The focus of a parabola is:

$\mathbf{Focus = (h, \frac{k+1}{4a})}$

Substitute the values of a and the vertex in $\mathbf{Focus = (h, \frac{k+1}{4a})}$

$\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}$

$\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}$

$\mathbf{Focus = (80, -11\times 160)}$

$\mathbf{Focus = (80, -1760)}$

The equation of the directrix is:

$\mathbf{y = -a}$

So, we have:

$\mathbf{y = \frac{1}{640}}$ ----- the directrix

The axis of symmetry is:

$\mathbf{x = -\frac{b}{2a}}$

We have:

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

Expand

$\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}$

Expand

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}$

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }$

A quadratic function is represented as:

$\mathbf{y = ax^2 + bx + c}$

So, we have:

$\mathbf{a = -\frac{1}{640}}$

$\mathbf{b = \frac{1}{4}}$

Recall that:

$\mathbf{x = -\frac{b}{2a}}$

So, we have:

$\mathbf{x = -\frac{1/4}{2 \times -1/640}}$

$\mathbf{x = \frac{1/4}{1/320}}$

This gives

$\mathbf{x = \frac{320}{4}}$

$\mathbf{x = 80}$

Hence, the axis of the symmetry of parabola is: $\mathbf{x = 80}$

Read more about parabola at:

brainly.com/question/21685473

6 0

2 years ago

I need help with this fast

AnnZ [28]

Answer:

l( longer side ) = 12cm

S (shorter side) =9cm

D's( distance between the shorter side). ( It is also the height. I hope you got the clue…)

Anyway,

Area=9X8=72cm^2

Distance of the longer sides is

Area/the length of the longer side

72/12=6cm…

Distance between the longer sides is 6cm

Hope this helps…

4 0

2 years ago

The density d of a substance is given by the formula d=mV, where m is its mass and V is its volume. Solve the formula for m.

NikAS [45]

Answer:m=d/V

Step-by-step explanation:

To solve for m, you must divide V from each side. Leaving you with m=d/V. Hope this helped:)

5 0

3 years ago

Read 2 more answers