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2 years ago

Number 11 please , someone? Thank you .

Mathematics

1 answer:

KIM [24]2 years ago

8 0

In a triangle, the measure of an angle is in the same order of size as the length of the opposite side. The smallest angle is opposite the shortest side. The largest angle is opposite the longest side. The middle-sized angle is opposite the middle-sized side.

Also, in a triangle, the sum of the measures of the interior angles is 180.

We can now calculate the measures of the three angles by writing and solving an equation.

m<A + m<B + m<C = 180

9x - 7 + 7x - 9 + 28 - 2x = 180

Collect like terms on the left side.

9x + 7x - 2x - 7 - 9 + 28 = 180

14x + 12 = 180

Subtract 12 from both sides.

14x = 168

x = 12

Now that we know x, we can find the measure of each angle.

m<A = 9x - 7 = 9(12) - 7 = 108 - 7 = 101
m<B = 7x - 9 = 7(12) - 9 = 84 - 9 = 75
m<C = 28 - 2x = 28 - 2(12) = 28 - 24 = 4

(Quick check: Add the angles measures: 101 + 75 + 4 = 180. The sum is 180 as it should be.)

Now that we know the angle measures, the opposite sides are in the same order of size.

AB < AC < BC

The sides are, in increasing order of length:

AB, AC, BC

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A park is 4.6 miles long and 2.7 miles wide.What is the total distance around the park

levacccp [35]

The distance around the park is the perimeter.

To find the perimeter add two lengths plus two widths:

Perimeter = 4.6 +4.6 + 2.7 +2.7 = 14.6 miles

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2 years ago

Graph the data in the table below. Which kind of function best models the data? write an equation to model the data.

harina [27]

Answer:

A quadratic function.

$y=2.5x^{2}$

Step-by-step explanation:

If you plot the points given in the table, you obtain the graph shown in the figure attached.

As you can see, it is a parabola, therefore, the function that best models the data is a quadratic function.

By definition, the parent function of a quadratic function is:

$y=x^{2}$

You can compress or stretch it in the y-direction by multiplying the function by a constant $C$ :

$y=Cx^{2}$

If $0$ , then the function is compressed.

If $C>1$ , then the function is stretched.

You can find the constant of the function asked as following:

- Substitute x=1 into the parent function to obtain the y-coordinate:

$y=(1)^{2}=1$

Then the point is (1,1)

- As you can see, with x=1 you obtain y=1 in the parent function, and in the function given in the table when x=1, y=2.5, therefore, the function is multiplied by 2.5. Therefore the constant is:

$C=2.5$

Then the function is:

$y=2.5x^{2}$

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2 years ago

Find the vertex of the parabola. Is the vertex a maximum or minimum? What is the equation for the axis of symmetry?

Phoenix [80]

Answer:

(2,45) ; x = 2

Step-by-step explanation:

The method for solving for the vertex of a parabola from standard form involves converting to vertex form by forming a squared term. First, we need to actually put this equation into standard form, which dictates that the x^2 must never have a number in front of it (including -1). This means factoring out a negative 5 from the whole left side:

-5 (x^2 - 4x - 5) = y.

The next step is to pull the -5 out of the parentheses,

-5 (x^2 - 4x) + 25 = y,

which means multiplying it by the term on the outside to result in a positive 25. From here, we form the squardo term from what is inside the parentheses. We do this by changing the form of the equation, similar to how one changes the form of a fraction (multiplying by a number over the same number so that you are effectively multiplying by one). Inside of the parentheses, we a going to add a number and on the outside of the parentheses, we are going to subtract that number multiplied by what is in front of the parentheses (effectively adding zero to the equation):

-5 (x^2 - 4x + __) +25 - (-5*__) = y.

Now, the number that goes in the blank is the coefficient of the x divided by two and then squared:

__= (-4/2)^2,

__= 4.

From there, we just plug in the __ , simplify, and factor:

-5 (x^2 - 4x + (4)) + 25 - (-5*(4)) = y,

-5 (x^2 - 4x + 4) + 25 - (-20) = y,

-5 (x^2 - 4x + 4) + 45 = y,

-5 (x - 2) (x - 2) + 45 = y,

-5 (x - 2)^2 + 45 = y.

Now the equation is in vertex form, and from it, we can determe the vertex. The general equation for vertex form is

m (x - $x_{1}$ ) + $y_{1}$ = y,

where ( $x_{1}$ , $y_{1}$ ) is the vertex. *Notice that there is a negative sign built in to the equation, so when you pull out $x_{1}$ , make sure that you leave behind a negative sign. In our case, we pull out a positive two, leaving behind the negative sign. *If it were a ( x + 2 ), we would change it into ( x - (-2)) and pull out the -2, leaving behind a negative sign.*

This gives us a vertex of (2,45).

Now, the second part of the question asks for the equation of the axis of symmetry. The general equation for the axis of symmetry is

x = $x_{1}$ ,

since the axis of symmetry is just a vertical line that goes through the vertex. Plugging in $x_{1}$ then gives us

x = 2,

our axis of symmetry.

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2 years ago

For 15 points Select the correct answer. What is |-14|?

cestrela7 [59]

Answer:

D. Positive 14.

Step-by-step explanation:

The absolute value is the distance between a number and zero. The distance between -14 and 0 is 14. Therefore, the answer is positive and not negative.

Hope this helps! :D

Edit: Thank you so much for brainliest! One away from Ace rank!

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2 years ago