All categories

4 years ago

Consider the system of equations shown below.

Mathematics

2 answers:

enyata [817]4 years ago

6 0

Answer:

The linear equations have the same slope but different y-intercepts.

Step-by-step explanation:

A linear equation has the general form

$y=mx+b$

where $m$ is the slope and $b$ is the y-intercept.

In the case of the first line $y=-5x+1$

$m=-5$

and $b=1$

for the second line $y=-5x+10$

$m=-5$

and $b=10$

Thus, the lines have the same slope but a different y-intercept.

This is why they are parallel, because they increase at the same rate always (hence the same slope) and the cross the y-axis at different point (hence the different y-intecept)

Rina8888 [55]4 years ago

4 0

The linear equations have the same slope but different y-intercepts. This is the right answer because you can see the x coefficient for both equations is -5 but 1 and 10 are not the same and they are y-intercepts. These two are parallel so they will never meet.

You might be interested in

The diameter of Joe's large pizza is 19 inches. Approximately how many inches are there in the circumference of the large pizza?

Burka [1]

Answer:

There are 59.66 inches in the circumference of the large pizza.

Step-by-step explanation:

It is given that:

Diameter of Joe's large pizza = 19 inches

Diameter = 2r

2r = 19

Circumference of large pizza = 2πr = 2r * π

Circumference of large pizza = 19*3.14

Circumference = 59.66 inches

Therefore,

There are 59.66 inches in the circumference of the large pizza.

6 0

3 years ago

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1

VikaD [51]

Answer:

Step-by-step explanation:

If you plot the focus and the directrix you see that the focus is above the directrix. Since a parabola always wraps itself around the focus, this parabola opens upwards and has the standard form equation:

$(x-h)^2=4p(y-k)$ where h and k are the coordinates of the vertex and p is the number of units between the vertex and the focus, or the vertex and the directrix. This number of units will be the same for both since the vertex is smack dab inbetween the focus and the directrix. The focus is also on the axis of symmetry, which means that it shares the x coordinate with the vertex (which is actually the h coordinate) of -5. Halfway between the y value of 5 and the y value of -1 is 2. So the vertex is located at (-5, 2). The number of units between the vertex and the focus is 3, so the equation is:

$(x+5)^2=4(3)(y-2)$ and simplify a bit to

$(x+5)^2=12(y-2)$

I'm not sure how far down you need to simplify that. Taking it a few steps further gives you:

$\frac{1}{12}(x+5)^2=y-2$ and then to

$\frac{1}{12}(x+5)^2+2=y$

It all depends upon the form you're being asked for.

3 0

3 years ago

PLS BRANLIEST

Neko [114]

Dilation is the process in which the dimensions of a given shape is increased or decreased by a scale factor. Therefore the answers to the questions are:

A. Since the dilation of triangle XYZ do not affect the measure of its internal angles, then the trigonometric ratios of respective internal angles are the same.

B. segment CB = 10

ii. segment AB = 11.18

From the given information in the question, triangle XYZ is an image of triangle ACB. In triangle XYZ, given that Sin X = ; it implies that its hypotenuse is 5.59, and the opposite side as 5. So that;

Sin X =

X = 0.8945

X =

Thus,

<X + <Y + <Z =

+ + <Z =

<Z = -

<Z =

So then, the third side can be determined by applying the Pythagoras theorem.

= +

= -

= 6.2481

x =

= 2.49962

x = 2.5

Thus,

Cos X =

Tan X =

Therefore:

A. Considering triangles XYZ and ACB, the measure of their respective internal angles are the same.

i.e <X ≅ <A

<B ≅ <Z

<C ≅ <Y

So that the trigonometric ratios of respective internal angles are the same.

B. Given that triangle XYZ was dilated by a scale factor of 2, then the respective length of each sides of triangle ACB is twice that of XYZ.

Then,

i. segment CB = 2 x segment YZ

= 2 x 5

segment CB = 10

ii. segment AB = 2 x segment XZ

= 2 x 5.59

segment AB = 11.18

8 0

3 years ago

Segment & Angle Addition Test

Westkost [7]

Hope it is correct!!

5 0

3 years ago

A bowl has a radius of 3 inches. What is the circumference of the bowl?

madreJ [45]

Answer:

9.42 (sorry if im late)

Step-by-step explanation:

I believe that if you take the radius and multiply it by pi (3.14), you get the circumfrence

3.14 x 3 = 9.42

6 0

2 years ago