The sum of the measures of two angles of a scalene triangle is calculated, and the result is the same as the measure of one of the external angles of a triangle. Which pair of angle measures was calculated?

To convert 2x + 4y = 12 into slope-intercept form, we must put it into y = mx + b form, where m represents the slope of the line and b is the y intercept of the equation. To begin, we should subtract 2x from both sides so that we can get the variable y alone on the left side of the equation.

2x + 4y = 12

4y = -2x + 12

Next, because there cannot be a coefficient on the variable y in this form, we must divide both sides of the equation by 4.

y = -2/4x + 3

Because 2 and 4 are both divisible by 2, we can divide both the numerator and the denominator by 2 to further simplify the equation.

y = -1/2x + 3

Therefore, the answer is y = -1/2x + 3.

Hope this helps!

To convert the equation 2x + 4y = 12 into slope-intercept form (y=mx+b), you subtract 2x from both sides and then divide by 4 to isolate y, resulting in y = -1/2x + 3, where the slope (m) is -1/2 and the y-intercept (b) is 3.

To convert the equation 2x + 4y = 12 into slope-intercept form (y=mx+b), we need to solve for y. Here's how you can do it step by step:

Now the equation is in slope-intercept form where m (the slope) is -1/2 and b (the y-intercept) is 3. The slope m is defined as the rise over the run of the straight line, and the y-intercept b is the point where the line crosses the vertical axis, which in this case is when x=0 and y=3.

Final answer:

The tree's maximum height is not limited to 30 ft but approaches 301 ft. Initially, the tree is 30 ft tall, not 2 ft. To verify the growth between the 5th and 7th years, one must calculate f(5) and f(7). The rate of growth indeed decreases over time.

Explanation:

When analyzing the function f(x) = 301 + 29e^{-0.5x} to understand the growth pattern of a tree, it is apparent that some statements about the tree's growth can be identified as true or false.

Answer:

the answer is c.

Step-by-step explanation:

Answer:

Option d - [tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4=-\frac{9}{2}+\frac{9\sqrt3}{2}i[/tex]      

Step-by-step explanation:

Given : [tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4[/tex]

To find : Use DeMoivre's theorem to evaluate the expression?

Solution :

DeMoivre's theorem state that, for complex number

If [tex]z = r(\cos\theta+ i\sin \theta)[/tex] then [tex]z^n = r^n(\cos n\theta+ i\sin n\theta)[/tex]

We have given,

[tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4[/tex]

On comparing [tex]r=\sqrt3[/tex] and n=4

Applying DeMoivre's theorem,

[tex]=(\sqrt3)^4(\cos 4(\frac{5\pi}{3})+i\sin4(\frac{5\pi}{3}))[/tex]

[tex]=9(\cos (\frac{20\pi}{3})+i\sin(\frac{20\pi}{3}))[/tex]

[tex]=9(\cos (6\pi+\frac{2\pi}{3})+i\sin(6\pi+\frac{2\pi}{3}))[/tex]

[tex]=9(\cos (\frac{2\pi}{3})+i\sin(\frac{2\pi}{3}))[/tex]

We know, the value of

[tex]\cos (\frac{2\pi}{3})=-\frac{1}{2},\sin (\frac{2\pi}{3})=\frac{\sqrt3}{2}[/tex]

[tex]=9(-\frac{1}{2}+i\frac{\sqrt3}{2})[/tex]

[tex]=-\frac{9}{2}+i\frac{9\sqrt3}{2}[/tex]    

Therefore, Option d is correct.

[tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4=-\frac{9}{2}+\frac{9\sqrt3}{2}i[/tex]      

To begin this problem, we need to use the two points that we are given to find the slope of the line. Slope is defined as the change in y values divided by the change in x values, or rise/run, and is represented by the variable m.

m = (y1-y2)/(x1-x2) = (8-0)/(3-6) = 8/(-3) = -8/3

Now, we can use the slope and one of the points from our given values to create an equation of the line in point-slope form.

y = m(x-h) + k, where a point on the line is (h,k)

y = -8/3(x - 3) + 8

Now, we can distribute our slope and simplify through addition.

y = -8/3x + 8 + 8

y = -8/3x + 16

Therefore, your answer is y = -8/3x + 16.

Hope this helps!

The box plot that represents the data is option B.

A box plot is known to be a method that is employed to demonstrate the locality and skewness of numerical data. This is carried out graphically and done through the quartiles of the given numerical data.

Rearranging the given data, we have:

112,116, 134, 134, 135, 141, 149, 154, 156, 156

The minimum value after rearranging = 112.

First Quartile, Q1 = 134.

Second Quartile, Q2 or Median = 135+141/2 = 276/2 = 138

Third Quartile, Q3 = 154

Largest figure = 156

The answer is the second figure.

Learn more about box plot on https://brainly.com/question/14277132

The trinomial "10[tex]x^2[/tex] + 7x - 12" is factored by finding two numbers that multiply to -120 and add up to 7, which are 15 and -8. Split the middle term, group, and factor by grouping to get (2x + 3)(5x - 4), which is option A.

To factor the trinomial "10x2 + 7x − 12" completely, you want to find two binomials that, when multiplied together, will give you the original trinomial. To do this, you will need two numbers that multiply to give you the product of the coefficient of the x2 term (which is 10) and the constant term (which is −12), which equals −120, and also add up to the coefficient of the x term (which is 7).

The two numbers that meet these criteria are 15 and −8, since (15)(−8) = −120 and 15 + (−8) = 7. Next, split the middle term of the trinomial using these two numbers:

10x2 + 15x − 8x − 12

Now, group the terms:

(10x2 + 15x) − (8x + 12)

Factor out the greatest common factor from each group:

5x(2x + 3) − 4(2x + 3)

Finally, factor out the common binomial factor:

(2x + 3)(5x − 4)

Therefore, the correct factorization of the trinomial 10x2 + 7x − 12 is (2x + 3)(5x − 4), which corresponds to option A.

Answer:

answer is 1 & 3 on edg

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

It is D

Answer:

The value of lesser root is:

                         x=2

Step-by-step explanation:

We are given  a quadratic equation in terms of variable " x " as:

[tex]x^2-6x+8=0[/tex]

We know that for any quadratic equation of the type:

              [tex]ax^2+bx+c=0[/tex]

The roots of x are calculated as:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here we have:

      a=1 , b=-6 and c=8

Hence, on solving for roots:

[tex]x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4\times 1\times 8}}{2\times 1}\\\\\\x=\dfrac{6\pm \sqrt{36-32}}{2}\\\\\\x=\dfrac{6\pm \sqrt{4}}{2}\\\\\\x=\dfrac{6\pm 2}{2}[/tex]

Hence, we have:

[tex]x=\dfrac{6+2}{2}\ or\ x=\dfrac{6-2}{2}\\\\x=\dfrac{8}{2}\ or\ x=\dfrac{4}{2}\\\\\\x=4\ or\ x=2[/tex]

Hence, the value of lesser root is:

                             x=2

Answer:

The correct option is c.

Step-by-step explanation:

Given information: The measure of arc AXC is 235°. Let the center of the circle be O.

The sum of all disjoint arcs is 360°. So,

[tex]Arc(AXC)+Arc(AC)=360^{\circ}[/tex]

[tex]235^{\circ}+Arc(AC)=360^{\circ}[/tex]

[tex]Arc(AC)=360^{\circ}-235^{\circ}[/tex]

[tex]Arc(AC)=125^{\circ}[/tex]

[tex]\angle AOC=125^{\circ}[/tex]

The measure of arc AC is 125°.

Line BA and BC are tangent on the circle O from the same point, so the sum of opposite angles of the quadrilateral is 180°.

[tex]\angle AOC+\angle ABC=180^{\circ}[/tex]

[tex]125^{\circ}+\angle ABC=180^{\circ}[/tex]

[tex]\angle ABC=180^{\circ}-125^{\circ}[/tex]

[tex]\angle ABC=55^{\circ}[/tex]

The measure of angle ABC is 55°. Therefore the correct option is c.

The radius of the circle with the equation (x−2)^2+(y−16)^2=169 is 13 units.

The equation of the circle provided is (x−2)2+(y−16)2=169. In the standard form of a circle's equation, (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is the radius, we see that 169 represents r2. Hence, to find the radius of the circle, we take the square root of 169.

The radius r is calculated as r = √169 = 13 units. Therefore, the circle's radius is 13 units.