Which of the following is equivalent??

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x , y) point

vlabodo [156]

The vertex to y=x^2+8x-23 is (4,-7)

3 0

3 years ago

Read 2 more answers

Identify the vertex of the function graphed below.

77julia77 [94]

Answer: (3, -2)

Step-by-step explanation:

The vertex is the highest or lowest point of a parabola, and I found it. Hope this helps :)

7 0

3 years ago

1. How far is KFC from RCBC Savings Bank? 2. How far is BaliwagLetchon Manok from RCBC Savings Bank? 3. How far is Baliwag Lecho

umka21 [38]

Answer:

Following are the solution to the given question.

Step-by-step explanation:

Please find the graph file and its solution in the attachment.

$4x-15=3x+28\\\\4x-3x=28+15\\\\x=43\\\\$

Similarly:

$3y+5=2y+50\\\\3y-2y=-5+50\\\\y=45\\\\$

For point 1: $\to KR=4x-15= 4\times 43-15=172-15=157$

For point 2: $\to BR=2y+50= 2\times 43+50=86+50=136$

For point 3: $\to BE=KR=157$

For point 4: $\to Kf=BR=130$

For point 5: $\to ERK=KFB=180^{\circ} -\angle B-\angle ERB = 180^{\circ}-92^{\circ}-18^{\circ}=70^{\circ}$

4 0

2 years ago

Prove that the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.

sergiy2304 [10]

Answer:

See explanation

Step-by-step explanation:

a) To prove that DEFG is a rhombus, it is sufficient to prove that:

All the sides of the rhombus are congruent: $|DG|\cong |GF| \cong |EF| \cong |DE|$
The diagonals are perpendicular

Using the distance formula; $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$|DG|=\sqrt{(0-(-a-b))^2+(0-c)^2}$

$\implies |DG|=\sqrt{a^2+b^2+c^2+2ab}$

$|GF|=\sqrt{((a+b)-0)^2+(c-0)^2}$

$\implies |GF|=\sqrt{a^2+b^2+c^2+2ab}$

$|EF|=\sqrt{((a+b)-0)^2+(c-2c)^2}$

$\implies |EF|=\sqrt{a^2+b^2+c^2+2ab}$

$|DE|=\sqrt{(0-(-a-b))^2+(2c-c)^2}$

$\implies |DE|=\sqrt{a^2+b^2+c^2+2ab}$

Using the slope formula; $m=\frac{y_2-y_1}{x_2-x_1}$

The slope of EG is $m_{EG}=\frac{2c-0}{0-0}$

$\implies m_{EG}=\frac{2c}{0}$

The slope of EG is undefined hence it is a vertical line.

The slope of DF is $m_{DF}=\frac{c-c}{a+b-(-a-b)}$

$\implies m_{DF}=\frac{0}{2a+2b)}=0$

The slope of DF is zero, hence it is a horizontal line.

A horizontal line meets a vertical line at 90 degrees.

Conclusion:

Since $|DG|\cong |GF| \cong |EF| \cong |DE|$ and $DF \perp FG$ , DEFG is a rhombus

b) Using the slope formula:

The slope of DE is $m_{DE}=\frac{2c-c}{0-(-a-b)}$

$m_{DE}=\frac{c}{a+b)}$

The slope of FG is $m_{FG}=\frac{c-0}{a+b-0}$

$\implies m_{FG}=\frac{c}{a+b}$

5 0

3 years ago

Are the two ratios that make up a proportion<br> always, sometimes, or never equivalent

masya89 [10]

Answer:

Always

Step-by-step explanation:

In mathematics, when we say that two ratios form a proportion, we mean that the two ratios are equal.

Ex: Ratios and Proportions - Proportions - In Depth. A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."

A proportion is two ratios which have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 105 equals 21 .

8 0

2 years ago