3(x + 7) + 2(-x + 4) + 5x

Is a supplement of a acute angle always obtuse? What if one angle is 30 and the other is 170?

worty [1.4K]

Yes because if an acute angle is less than 90, then its supplement (the angle that when added to another angle equals to 180°) has to be greater than 90° but less than 180° ( which is basically the definition of an obtuse angle)

A 30° angle is an acute angle and a 170° angle is obtuse but they are not supplementary angles because they do not add up to 180°

I hope this helps you :)

3 0

4 years ago

the weight of abes dog can be found using the expression 2(x+3), where x is the number of weeks. the weight of karens dog can be

ivanzaharov [21]

To find this out we can set the expressions equal to each other:

$\sf 2(x+3)=3(x+1)$

Solve for 'x', first distribute:

$\sf 2x+6=3x+3$

Subtract 3 to both sides:

$\sf 2x+3=3x$

Subtract 2x to both sides:

$\boxed{\sf x=3}$

So the answer is yes, after 3 weeks the dogs will be the same weight(because 'x' represents # of weeks).

7 0

3 years ago

1. The figure shows the regular triangular pyramid SABC. The base of the pyramid has an edge AB = 6 cm and the side wall has an

Musya8 [376]

Given:

• AB = 6 cm

,

• SM = √15 cm

Let's solve for the following:

• 1) the base elevation AM.

Given that we have a regular triangular pyramid, the length of the three bases are equal.

AB = BC = AC

BM = BC/2 = 6/2 = 3 cm

To solve for AM, which is the height of the base, apply Pythagorean Theorem:

$\begin{gathered} AM=\sqrt{AB^2-BM^2} \\ \\ AM=\sqrt{6^2-3^2} \\ \\ AM=\sqrt{36-9} \\ \\ AM=\sqrt{27} \\ \\ AM=5.2\text{ cm} \end{gathered}$

The base elevation of the pyramid is 5.2 cm.

• (2)., The elevation SO.

To find the elevation of the pyramid, apply Pythagorean Theorem:

$SO=\sqrt{SM^2-MO^2}$

Where:

SM = √15 cm

MO = AM/2 = 5.2/2 = 2.6 cm

Thus, we have:

$\begin{gathered} SO=\sqrt{(\sqrt{15})^2-2.6^2} \\ \\ SO=\sqrt{15-6.76} \\ \\ SO=2.9\text{ cm} \end{gathered}$

Length of SO = 2.9 cm

• (3). Area of the base:

To find the area of the triangular base, apply the formula:

$A=\frac{1}{2}*BC*AM$

Thus, we have:

$\begin{gathered} A=\frac{1}{2}*6^*5.2 \\ \\ A=15.6\text{ cm}^2 \end{gathered}$

The area of the base is 15.6 square cm.

• (4). Area of the side surface.

Apply the formula:

$SA=\frac{1}{2}*p*h$

Where:

p is the perimeter

h is the slant height, SM = √15 cm

Thus, we have:

$\begin{gathered} A=\frac{1}{2}*(6*3)*\sqrt{15} \\ \\ A=34.86\text{ cm}^2 \end{gathered}$

• (5). Total surface area:

To find the total surface area, apply the formula:

$TSA=base\text{ area + area of side surface}$

Where:

Area of base = 15.6 cm²

Area of side surface = 34.86 cm²

TSA = 15.6 + 34.86 = 50.46 cm²

The total surface area is 50.46 cm²

• (6). Volume:

To find the volume, apply the formula:

$V=\frac{1}{3}*area\text{ of base *height}$

Where:

Area of base = 15.6 cm²

Height, SO = 2.9 cm

Thus, we have:

$\begin{gathered} V=\frac{1}{3}*15.6*2.9 \\ \\ V=15.08\text{ cm}^3 \end{gathered}$

The volume is 15.08 cm³.

ANSWER:

• 1.) 5.2 cm

,

• 2.) 2.9 cm

,

• 3.) 15.6 cm²

,

• 4.) 34.86 cm²

,

• (5). 50.46 cm²

,

• 6). 15.08 cm³.

7 0

1 year ago

Can Someone please answer this ?

Anna11 [10]

(2,0)
(-3,6)
(4, -20)

3 0

3 years ago

Which of the following point-slope form equations could be produced with the points (4, 5) and (-3, -5)?

NikAS [45]

Answer:

Equation; y = 1 3 / 7x - 5 / 7

Step-by-step explanation:

First consider the slope of this equation we must derive;

Slope Formula = Rise / Run,

y2 - y1 / x2 - x1 ⇒

5 - ( - 5 ) / 4 - ( - 3 ) ⇒

10 / 7 ⇒ Slope : 1 3 / 7

So far we can formulate an equation as such;

y = 1 3 / 7 * x + b, where b ⇒ y - intercept

Given one of the points, substitute into this equation solving for b;

5 = 1 3 / 7 * ( 4 ) + b,

5 = 40 / 7 + b,

b = - 5 / 7

From this we can derive one point - slope from equation to be :

Equation; y = 1 3 / 7x - 5 / 7

3 0

3 years ago