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alexandr402 [8]
2 years ago
12

Determine the domain and the range for this relationship

Mathematics
1 answer:
ella [17]2 years ago
6 0

Answer:

domain: range: {0, 12, 24, 36, 48, 60, 72}

Step-by-step explanation:

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What is the equation of the quadratic graph with a focus of (-4,17/8) and a directrix of y=15/8
Temka [501]
So hmm notice the graph below

based on where the focus point is at, and the directrix, then, the parabola is opening upwards, meaning the squared variable is the "x"

\bf \begin{array}{llll}
(y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\
\boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})}\\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}

now, keep in mind, the vertex is at coordinates h,k
the vertex itself is half-way between the focus and directrix
the directrix is at y=15/8 and the focus is at y=17/8
so, half-way will then be \bf \cfrac{17}{8}-\cfrac{15}{8}=\cfrac{2}{8}\iff \cfrac{1}{4}

well, so is 1/4 between the focus point and the directrix, half of that is 1/8
so, if you move from the focus point 1/8 down, you'll get the y-coordinate for the vertex, or 1/8 up from the directrix, since the vertex is equidistant to either

what's the "p" distance? well, we just found it, is just 1/8

so, the x-coordinate is obviously -4, get the y-coordinate by 17/8 - 1/8   or 15/8 + 1/8

and plug your values (x-h)² = 4p(y-k)   and then solve for "y", that's the equation of the quadratic

4 0
3 years ago
Explain why the terms 4x and 4x^2 are not like like terms​
Brrunno [24]

Answer:

well for me it's because

Step-by-step explanation:

Of the raise to power

6 0
2 years ago
Here are the vertices of rectangle FROG: (-2,5),(-2,1),(6,5),(6,1). Find the perimeter of this rectangle. If you get stuck, try
ryzh [129]

Answer:

Part 1) The perimeter of rectangle is equal to 24 units

Part 2) The area of rectangle is equal to 32 square units

Step-by-step explanation:

Part 1) Find the perimeter of rectangle

we know that

The perimeter of rectangle is equal to

P=2(L+W)

where

L is the length of rectangle

W is the width of rectangle

we have

F(-2,5),R(-2,1),O(6,1),G(6,5)

Plot the figure to better understand the problem

using a graphing tool

see the attached figure

Remember that in a rectangle opposite sides are congruent and the measure of each interior angle is equal to 90 degrees

so

FG=RO=L\\RF=OG=W

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

step 1

Find the distance FG

F(-2,5),G(6,5)

substitute the values

d=\sqrt{(5-5)^{2}+(6+2)^{2}}

d=\sqrt{(0)^{2}+(8)^{2}}

FG=8\ units

step 2

Find the distance RF

R(-2,1),F(-2,5)

substitute the values

d=\sqrt{(5-1)^{2}+(-2+2)^{2}}

d=\sqrt{(4)^{2}+(0)^{2}}

RF=4\ units

step 3

Find the perimeter

P=2(L+W)

we have

FG=RO=L=8\ units\\RF=OG=W=4\ units

substitute

P=2(8+4)=24\ units

Part 2) Find the area of rectangle FROG

we know that

The area of rectangle is equal to

A=LW

we have

FG=RO=L=8\ units\\RF=OG=W=4\ units

substitute

A=(8)(4)=32\ units^2

8 0
3 years ago
What is the sum of -5 and -5?<br> -10<br> 10<br> 0
Kipish [7]

Answer:

-10

Step-by-step explanation:

5 0
3 years ago
Order the sides or angles of each triangle from least to greatest.
lubasha [3.4K]

Answer:

SU , UT , ST

Step-by-step explanation:

7 0
2 years ago
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