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3 years ago

Find the midpoint of the line segment whose endpoints are (7, 5) and (7, 11).

2 answers:

5 0

The midpoint of two points can be obtained by taking the average between the two abscissas or two ordinates. In this case ,the x-value of the midpoint is equal to (7+7)/2 equal to 7 while the y-value of the midpoint is equalto (5+11)/2 equal to 8. Hence the midpoint is t (7,8)

ElenaW [278]3 years ago

4 0

The midpoint of AB where $A(x_A;\ y_A)$ and $B(x_B;\ y_B)$

$\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)$

$A(7;\ 5);\ B(7;\ 11)$

The midpoint of AB: $\left(\dfrac{7+7}{2};\ \dfrac{5+11}{2}\right)=\left(\dfrac{14}{2};\ \dfrac{16}{2}\right)=(7;\ 8)$

Answer: (7, 8)

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Use any method to solve the equation. If necessary, round to the nearest hundredth.

vlada-n [284]

Here, in order to find the solutions to the quadratic equation - x² + x - 30 = 0, we will use factorization method.

In the method, we will split 30, in such factors, which when added or subtracted gives us 1, and when multiplied gives us -30.

So, we will use, -5 and 6. When they are added they will give us 1 and when multiplied they will give us -30 as answer.

Now, the equation will be written as -

x² - 5x + 6x - 30 = 0

Taking common, we get

x(x - 5) +6(x-5) = 0

(x-5)(x+6) = 0

So, x - 5 = 0 and x +6 = 0, we will get, x = 5 and x = - 6

<u>Thus, the correct option is C). x = 5 and -6</u>

4 0

4 years ago

Y=(x-3)^2-4

Ne4ueva [31]

<h2>Steps:</h2>

Vertex Form: y = a(x - h)² + k with (h,k) as the vertex

So firstly, let's start with the vertex. Since this is in vertex form, we can find the vertex easily. Since 3 is in the h variable and -4 is in the k variable, <u>the vertex is (3,-4).</u>

Next, the axis of symmetry. Remember that the vertex's x-coordinate and the axis of symmetry are the same. In this case, since the vertex's x-coordinate is 3, this means that <u>the axis of symmetry is x = 3.</u>

Next, whether the vertex is a minimum or a maximum. To determine whether it's a minimum or a maximum, we look towards the a variable of the vertex form. If a is negative, then the parabola opens down and the vertex is a maximum. However, if a is positive, then the parabola opens up and the vertex is a minimum. In this case, a = 1 and since 1 is positive, <u>this makes the vertex a minimum.</u>

Next, to find the y-intercept plug 0 into the x-variable and solve:

$y=(0-3)^2-4\\y=(-3)^2-4\\y=9-4\\y=5$

<u>The y-intercept is (0,5).</u>

Next, to find the x-intercepts plug 0 into the y-variable to solve. Since it's a bit less straightforward than finding the y-intercept, I will walk through the steps:

$0=(x-3)^2-4$

Firstly, add 4 to both sides:

$4=(x-3)^2$

Next, square root both sides:

$\pm\ 2=x-3$

Next, add 3 to both sides:

$3\pm2=x$

Lastly, solve the left side twice: once with the plus sign, once with the minus sign:

$3+2=x\\5=x\\\\3-2=x\\1=x$

<u>Your x-intercepts are (5,0) and (1,0).</u>

<h2>Answers:</h2>

In short:

Vertex: (3,-4)
x-intercept(s): (5,0) and (1,0)
y-intercept(s): (0,5)
Axis of symmetry: x = 3
Minimum or Maximum? Minimum.

5 0

3 years ago

Round 0.0564 to 1 significant figure

OleMash [197]

Answer:

0.1

Step-by-step explanation:

anything after the decimal (.) becomes a sogfig

6 0

3 years ago

Read 2 more answers

If the ratio of star shaped cookies to circular cookies is 5: 6 and the ratio of circular cookies to triangular cookies is 3: 10

SCORPION-xisa [38]

Answer:

$1:4$

Step-by-step explanation:

Without loss of generality, let there be 5 star shaped cookies. Following the proportions given, there will be 6 circular cookies. We can set up the following proportion to find out how many triangular cookies there would be:

$\frac{3}{10}=\frac{6}{x},\\3x=60,\\x=20$ .