How many toothpicks make a triangle? Two triangles? Write
an expression that represents the number of toothpicks
needed to make x triangles that appear side-by-side in a
single row, as shown. Explain your reasoning,

Given:

The pair of expressions in the options.

To find:

The pairs which show a pair of equivalent expressions.

Solution:

Property of exponent:

[tex](\sqrt[n]{x})^m=x^{\frac{m}{n}}[/tex]

In option A,

[tex](\sqrt[4]{81})^5=81^{\frac{5}{4}}[/tex]

So, option A is correct.

In option B,

[tex]6^{\frac{7}{2}}=(\sqrt[2]{6})^7[/tex]

[tex]6^{\frac{7}{2}}=(\sqrt{6})^7[/tex]

So, option B is correct.

In option C,

[tex]5^{\frac{2}{3}}=(\sqrt[3]{5})^2[/tex]

[tex]5^{\frac{2}{3}}\neq (\sqrt{5})^3[/tex]

So, option C is incorrect.

In option D,

[tex]7^{\frac{5}{7}}=(\sqrt[7]{7})^5[/tex]

[tex]7^{\frac{5}{7}}\neq (\sqrt{7})^5[/tex]

So, option D is incorrect.

Answer:it’s a and b

Step-by-step explanation:

did the test

Answer:

Answer below

Step-by-step explanation:

right

acute

i believe this is correct :)

Answer:   512m³

Step-by-step explanation:

v = whl

The volume for left building:

v = w x h x l

v = 4 x 10 x 8

v = 320 m³

The volume for right and lower building:

v = w x h x l

v = 8 x 4 x 6

v = 192 m³

The total volume for the entire Charter School is: 320m³ + 192m³ = 512m³

Answer:

Slope = -1/2

Y-Intercept = 2

Equation: Y=-1/2x+2

Step-by-step explanation:

Graph goes 2 units up at y=2, that's your y-intercept. From there, plot your second point by moving 1 down and 2 to the right from the y-intercept, landing on the point (2,1) to get your slope, written as -1/2.

Answer: x = -7

Step-by-step explanation:

7 (x + 4) = -21

7x + 28 = -21

Subtract 28 from both sides

7x = -49

Divide both sides by 7

x = -7

Answer:

x = -7

Step-by-step explanation:

first distribute he 7 to get 7x + 28 = -21

then subtract 28 from both sides to get 7x = -49

lastly divide 7 from both sides to get x = -7

Answer: 7

Step-by-step explanation: because 45 divided by 6 is 7.5

Answer:

nudaw HAHABSASASNA

Step-by-step explanation:[tex]x^{2} g[/tex]

hggggguuuuugs berte bhu jira yuwa

your answer would be 33.

step 1

2(+14)−1(2−5)

2+28−1(2−5)

step 2 distribute

2+28−1(2−5)

2+28−2+5

step 3 then add the numbers

2+28−2+5

2+33−2

combine

2+33−2

ANSWER IS

33

Answer:

100/ 651 , or 0.15361

Step-by-step explanation:

this took so long

Answer:

0.15360983102

.......

Answer:

there are not solutions because they never cross each other

Answer:

x=30

Step-by-step explanation:

180-55=125

5x-25=125

125+25=150

5x=150

5/150=30

x=30

Answer:

64

Step-by-step explanation:

Given :

h α 1 / sqrtk

h = k/sqrt(d)

Obtain the value of k, when. d = 4 and h = 20

20 = k / sqrt(4)

20 = k / 2

20 * 2 = k

k = 40

Therefore, the value of d when h = 5

h = k/sqrt(d)

5 = 40 / sqrt(d)

Square both sides

25 = 1600/d

25d = 1600

d = 1600 / 25

d = 64

d = 64

Answer:

9(2x-1)

Step-by-step explanation:

common factor of both 9 and 18 is 9

thus, you can take a 9 out

9(2x-1)

(to check if it is correct, you can expand it, and if it is the same as original then it is correct )

Answer:

9 (2x-1)

Step-by-step explanation:

Grouping

1. Common factor:

18x-9

Solution:

9 (2x-1)

Answer:

p,q,r

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

these are vertical angles, so they equal eachother!

12x-3=105

move three to the other side of the equals sign

12x=108

divide both sides by 108

x=9

Answer: x=9

Step-by-step explanation:

These angles are equal, so you can set 105 equal to 12x-3. Add 3 and divide by 12 to get x=9.

Answer:

The points that fits the equation would be option D.

Answer:

1 simple

Step-by-step explanation:

Answer:

the graph on the bottom left

Step-by-step explanation:

outliers are points that are away from the cluster of points in the bottom left graph all of the points are grouped up therefor the bottom left graph is the correct answer

Answer:

8

Step-by-step explanation:

Given that

19 + 7 divided by 2 - 5

So if we solve this we have to apply proper brackets

= (19 + 7) ÷ 2 - 5

= 26 ÷ 2 - 5

= 13 - 5

= 8

After solving this the answer is 8

Answer: 5040

Step-by-step explanation: There are 4 sides which is equal to 1260, 1260 x 4 = 5040

The characteristics of the sinusoidal function can be found from the given

graph of the function.

The sinusoidal function is the sine function that has the following general equation;

a = The amplitude

b = Angular frequency

h = The horizontal shift

k = The vertical shift

The minimum value of the sinusoidal function.

From the given graph, we have;

The amplitude, a = 2

The period, T = 10 = 2·π/b

b = π/5

The vertical shift, k = 3

The horizontal shift = 0

The minimum value of the function = k - a

Therefore;

Learn more about sinusoidal functions here:

https://brainly.com/question/6666829

Answer:

[tex]\displaystyle 1[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{y = 2cos\:(\frac{\pi}{5}x - \frac{\pi}{2}) + 3} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{2\frac{1}{2}} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{\pi}{5}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{10} \hookrightarrow \frac{2}{\frac{\pi}{5}}\pi \\ Amplitude \hookrightarrow 2[/tex]

OR

[tex]\displaystyle \boxed{y = 2sin\:\frac{\pi}{5}x + 3} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{10} \hookrightarrow \frac{2}{\frac{\pi}{5}}\pi \\ Amplitude \hookrightarrow 2[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2cos\:\frac{\pi}{5}x + 3,[/tex] in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle 2\frac{1}{2}\:units[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle 2\frac{1}{2}\:units,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{2\frac{1}{2}} = \frac{\frac{\pi}{2}}{\frac{\pi}{5}}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2cos\:(\frac{\pi}{5}x - \frac{\pi}{2}) + 3.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph approximately hits [tex]\displaystyle [-10, 3],[/tex]from there to the y-intercept of [tex]\displaystyle [0, 3],[/tex]they are obviously approximately [tex]\displaystyle 10\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 10.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 3,[/tex]in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

**Now, the minimum value is the lowest possible value the graph touches, and in this case, the graph's lowest peaks cycle around [tex]\displaystyle y = 1,[/tex]therefore the minimum of his sinusoidal function is [tex]\displaystyle 1.[/tex]

I am delighted to assist you at any time.

Answer:

118

Step-by-step explanation:

a triangle is 180 degrease and two sides that are equal to each other which means the angles across from them have the same thing.

so. 180-31-31=118

Answer:

-8y° -7y

Step-by-step explanation:

Like terms:

13y-11y-9y= -7y

-8y°= -8y°

Simplified Expression:

-8y°-7y

Answer:

100 miles

Step-by-step explanation:

7.50-2.50=5.00

100x0.05=5.00

Answer:

2.9 miles or 3 miles

Step-by-step explanation:

1. Add 2.50 & 0.05 (dont forget to line up the decimals!)

2. Divide 7.50 & 2.55

3. You then get your final answer. ( round to the nearest tenths-)

A- im sorry if this is wrong T-T