The altitude of an equilateral triangle is 7 units long. The length of one side of the triangle is ____ units. 7 14

The expression in the 6th term in the binomial expression is [tex]265781250y^6[/tex]

The expression is given as:

(5y + 3)^10

The above expression is a binomial expression, and the xth term can be represented using:

[tex]^nC_x (a)^x * (b)^{n-x}[/tex]

So, we have:

[tex]^{10}C_6 * (5y)^6 * (3)^4[/tex]

Evaluate the combination expression

[tex]210 * (5y)^6 * (3)^4[/tex]

Evaluate the exponents

[tex]210 * 15625y^6 * 81[/tex]

Evaluate the product

[tex]265781250y^6[/tex]

Hence, the expression in the 6th term is [tex]265781250y^6[/tex]

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[tex]\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf \!\!\!\!Wall}\put(2.8,.3){\large\bf Ground}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf$39^{\circ}$ }\end{picture}[/tex]

We need the walls height then ground distance

[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow sin39=\dfrac{P}{26}[/tex]

[tex]\\ \rm\Rrightarrow P=26sin39[/tex]

[tex]\\ \rm\Rrightarrow P=16.4in[/tex]

Distance of wall from skateboard touching point on ground:-

[tex]\\ \rm\Rrightarrow cos\theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow cos39=\dfrac{B}{26}[/tex]

[tex]\\ \rm\Rrightarrow B=26cos39[/tex]

[tex]\\ \rm\Rrightarrow B=20.2in[/tex]

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Answer:

19

Step-by-step explanation:

3(4)(2) - 5

3 * 4 = 12 * 2 = 24

24 - 5 = 19

Answer:

The surface area of this solid is:

b. 107

Step-by-step explanation:

To understand this answer we need to analyze it. First, we have different geometric figures composing the solid. A pyramid and a rectangular prism. We need to obtain the surface, not the volume so we need to obtain the area of all the figures composing the pyramid and the prism without the hidden part of the pyramid base. We need to obtain the following areas:

2 rectangles with the following measures= W=2 L= 8

1 rectangle with the following measures= W=3 L=8

1 rectangle with the following measures= W=3 L 5

2 rectangles with the following measures= W=2 L=3

4 triangles with the following measures= B=3 H=4

Following the formula for the rectangles W x L we obtain a total area for them of 83 square meters.

Following the formula for the triangles b x h / 2 we obtain the following area: 24 square meters. Then we add both and obtain 107 square meters.

Answer:

Octagon

Step-by-step explanation:

Formula for a polygon is :

Since a regular octagon has 8 sides, and a regular hexagon has 6, the octagon will have the greater area due to greater perimeter.

Answer:

Choice E.

Step-by-step explanation:

sin^2 2x = 1

sin 2x = ± 1

So 2x = 90, 270 , 450, 630  etc

x = 45, 135, 225, 315   etc

=  45 + 360n, 135 + 360n, 225 + 360n, 315 + 360n

The fraction 11/20 can not be converted to a mixed fraction since it belongs to the proper fraction, I mean that the numerator is less than the denominator.

Only improper fractions can be mixed.

[tex]\: \: \: \: \: \: \: \: \qquad\bold{\Rightarrow \dfrac{20}{11}= 1\dfrac{9}{11} }[/tex]

So no the fraction 11/20 cannot be a mixed fraction.

Answer:

Solve the set of two reals for the following exponential equation:

\Large\text{${\dfrac{27^x\:-\:3^x}{9^x\:-\:3^x} = 82}$}

The area of the pentagon, rounded to the nearest tenth will be 32.7 square cm. Then the correct option is C.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.

Then the side length of the pentagon will be

5 x Side length = 21.8 cm

     Side length = 4.36 cm

Then the area of the pentagon, rounded to the nearest tenth will be

Area of pentagon = 5 x area of triangle

Area of pentagon = 5 x 1/2 x 4.36 x 3

Area of pentagon = 32.7 square cm

Thus, the correct option is C.

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Answer:

D. is the correct option

Step-by-step explanation:

There is a total of 5 people, so we can either split the pizza cost into 5, or into 10 and multiply by 2 (since each guest ate 2 slices) We'll do the first option since it's simpler.

$17.49 ÷ 5 = 3.489 or rounded up to $3.50

Next, we'll add $1.19 to $3.59 which equals $4.69

Hope this helps!

Answer:

See below ~

Step-by-step explanation:

The three inequalities (listed below) have been plotted on a graph :

Answer:

130

Step-by-step explanation:

[tex](35*4)-(10*1)-(5*0)=130[/tex]

Answers:

=======================================================

Part (a)

Let's find the distance from point D to point E.

In other words, this will compute the length of segment DE.

[tex]D = (x_1,y_1) = (0,-6) \text{ and } E = (x_2, y_2) = (3,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-3)^2 + (-6-1)^2}\\\\d = \sqrt{(-3)^2 + (-7)^2}\\\\d = \sqrt{9 + 49}\\\\d = \sqrt{58}\\\\d \approx 7.6158\\\\[/tex]

Segment DE is roughly 7.6158 units long.

Let's repeat these steps to find the length of segment EF.

[tex]E = (x_1,y_1) = (3,1) \text{ and } F = (x_2, y_2) = (-2,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-2))^2 + (1-1)^2}\\\\d = \sqrt{(3+2)^2 + (1-1)^2}\\\\d = \sqrt{(5)^2 + (0)^2}\\\\d = \sqrt{25 + 0}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

Segment EF is exactly 5 units long.

Lastly, we'll compute the length of segment FD.

[tex](x_1,y_1) = (-2,1) \text{ and } (x_2, y_2) = (0,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-0)^2 + (1-(-6))^2}\\\\d = \sqrt{(-2-0)^2 + (1+6)^2}\\\\d = \sqrt{(-2)^2 + (7)^2}\\\\d = \sqrt{4 + 49}\\\\d = \sqrt{53}\\\\d \approx 7.2801\\\\[/tex]

Segment FD is about 7.2801 units long.

This is close to the length of DE, but not quite.

To recap, we found these segment lengths:

As you can see, all three sides are different lengths. Therefore, triangle DEF is scalene.

----------------------------------

For part (b), follow the same template as part (a).

I'll be skipping the steps.

This is what you should get for the lengths of triangle TRI

Segments TR and IT are the same length (both exactly [tex]\sqrt{37}[/tex] units long), which means triangle TRI is isosceles.

-----------------------------------

For part (c), I'll also be skipping steps.

Here are the lengths you should find

All three lengths are different, making this triangle scalene.

Answer:

the answer willl be D

Step-by-step explanation:

Answer:

Step-by-step explanation:

21/7=3

5*3=15 width

3*3=9 height

Answer:

You can choose classes of amplitude 5 , it may give you a better representation of the data :

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

h(x) = −3 |x + 1| evaluate h (-3)

h (-3) means x = -3

Plug in:

h(x) = −3 |(-3) + 1| → h(x) = −3 |-3 + 1|

h(x) = −3 |-2|       since -2 is an absolute value it becomes 2

h(x) = −3(2)

h(x) = -6

Let me know if you have anymore questions,

Good Luck studying :) YOU GOT THIS !!!

[tex]5 \frac{3}{5} \% \: of \: 750[/tex]

[tex]5 \frac{3}{5} = 5.6[/tex]

[tex] \frac{5.6\%}{100} \times \frac{x}{750} [/tex]

[tex] = 42%[/tex]

Answer:

x=80

that is because a straight angle value is 180 and that angle is already 100 sooo i guess you get the point

Answer:

Step-by-step explanation:

We know that vertical angles are congruent.

Use this property to set up equation.

Substitute the values of angles and solve for x.

The value of x is 9

Answer:

140 ounces of Vegetables

Step-by-step explanation:

23 ounces of carrots x 2 = 46 ounces

47 ounces of broccoli x 2 = 94 ounces

46 ounces of carrots + 94 Ounces of Broccoli = 140 Ounces of Vegetables

Answer:

140 oz of vetables

Step-by-step explanation:

23 x 2 = 46

47 x 2 = 94

46 + 94 = 140

There were 14 boys at Mina's disco for her birthday.

A ratio is a quantitative value that shows the number of times a certain value is in another value.

It is given that for every 2 boys at the disco, there were 3 girls. This means that the ratio of boys to girls at the disco is 2:3.

Let the proportionality constant be x.

Therefore total boys and girls are 2x and 3x respectively.

There are 35 kids at the disco. This means that the number of boys plus girls is 35. It can be written as shown below:

2x + 3x = 35

⇒ x = 35/5

⇒ x = 7

Total number of boys = 2x

= 2 * 7

= 14 boys

Therefore the total number of boys at the disco is 14.

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Answer:

45%

Step-by-step explanation:

Divide 27/60, which gives you 0.45. Multiply that by 100, you get 45 percent.

Answer:

45%

Step-by-step explanation:

27/60

At first we should calculate Monthly income by multiplying 2 then After multiplying by 12 to calculate Annual income

Answer:

[tex] {x}^{2} - 7x + 10 = 0[/tex]

Step-by-step explanation:

[tex](x -2)(x - 5) = 0[/tex]

[tex] {x}^{2} - 7x + 10 = 0[/tex]

[tex]\csc 2x+1[/tex]

Step-by-step explanation:

Answer:

M = 2

Step-by-step explanation:

3M+4/3 = 28/3 -M

3M+M +4/3-28/3 = 0

4M -8 = 0

4M = 8 ( divide 4 in both sides)

M=8/4

M=2

Answer:

Step-by-step explanation:

that should help

Answer:

I like to use Desmos when I graph parabolas. But I’m this case it would be 3 down and one to the left so the vertex should be (-1,-3) and then just graph x^2

Step-by-step explanation:

Hope this helps! ;-)

Since events a and b are independent P(a and b) = P(a) × P(b)

To answer the question, we need to know what probability is

Probability is the likelihood of an event to occur. The probability of the event P(event) = number of required outcomes/total number of outcomes

If we have two independent event sa and b that have probabilities of occuring P(a) and P(b) respectively, the probability P(a and b) = P(a) × P(b)

So, P(a and b) = P(a) × P(b)

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