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solmaris [256]
3 years ago
13

What is the value of x A. 20 B. 34 C. 60 D. 69

Mathematics
1 answer:
Grace [21]3 years ago
4 0

Answer:

A

Step-by-step explanation:

The given angles are vertical and thus congruent, so

3x = x + 40 ( subtract x from both sides )

2x = 40 ( divide both sides by 2 )

x = 20 → A

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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
Which polynomial represents the sum below?
FromTheMoon [43]

Answer:          D. 8x² + x + 3

Sum means the answer to an addition problem. To find the sum of polynomials, we will add like terms.

<h2>What are like terms?</h2>

Like terms can be combined using addition or subtraction and have the same variables. Constants are also like terms with each other because they have no variables.

<h2>Solve</h2>

(4x² + 1) + (4x² + x + 2)      Starting equation from the question

= 4x² + 1 + 4x² + x + 2       Remove brackets

= 4x² + 4x² + x + 1 + 2       Rearrange to group like terms together

= 8x² + x + 1 + 2                Add like terms with the same 'x²' variables

= 8x² + x + 3                     Add like terms that are constants

Learn more about adding polynomials here:

brainly.com/question/1311115

6 0
2 years ago
Center: (-2,5), radius:7
Firlakuza [10]

Answer:

(x + 2)² + (y - 5)² = 7²

Step-by-step explanation:

Incomplete question.  I believe you meant, "write the equation of the circle with center at (-2, 5) and radius 7.

That would be:

(x + 2)² + (y - 5)² = 7²

5 0
3 years ago
20 pointss please help I appreciate it &lt;333
ivanzaharov [21]

Answer:

DE = 7.07 RS = 11.04 not congruent

Step-by-step explanation:

Formula:

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

D (5,0) E (0,-5)

DE

d=\sqrt{(0-5)^2 + ( -5 - 0)^2}

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

d=\sqrt{25+25}

d=\sqrt{50}

d= 7.07

R (-5,-5) S (6,-6)

RS

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

d=\sqrt{11^2 + (-1)^2}

d=\sqrt{121 + 1}

d=\sqrt{122}

d= 11.04

3 0
2 years ago
The ratio of rabbits to cats is 2:4 respectively. If there are
Natasha_Volkova [10]

Answer:

there are 36 cats in one house the ratio is 1:2

Step-by-step explanation:

3 0
3 years ago
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