In the figure, ABCDEF is a regular hexagon. △ BDF is drawn by joining the
alternate vertices. Show that △ BDF is equilateral

Answer: 42

Step-by-step explanation:

angle t is 42 degrees

Answer:

  ∠T = 42°

  PT = 14.4

  QT = 19.4

Step-by-step explanation:

An angle and its adjacent side are given in the right triangle. The other two sides can be found using trig relations. The third angle can be found using the angle sum theorem.

The mnemonic SOH CAH TOA is intended to remind you of the relations between sides of a right triangle and the trig functions of its angles. The relations relevant to this triangle are ...

  Cos = Adjacent/Hypotenuse   ⇒   Hypotenuse = Adjacent/Cos

  Tan = Opposite/Adjacent   ⇒   Opposite = Adjacent×Tan

Then the missing side lengths are ...

  QT = QP/cos(Q) = 13/cos(48°) ≈ 19.4282 ≈ 19.4

  PT = PQ×tan(Q) = 13×tan(48°) ≈ 14.43796 ≈ 14.4

The angle sum theorem tells you the sum of angles in a triangle is 180°. This means the acute angles in a right triangle are complementary.

  ∠T = 90° -48° = 42°

The solution to the triangle is ...

  ∠T = 42°

  PT = 14.4

  QT = 19.4

__

Additional comment

The attachment shows the solution from one of many available triangle solvers. Some calculators have triangle solver functions built in.

The probability that the last marble removed is non-red is 2/3.

According to the given question.

Total number of marbles in a bucket = 3

And, a person arbitary pulls out each marble one at a time.

So, there are 6 possible sequences of removing 3 marbles.

Let R be the red marble, B be the blue marble and G be the green marble.

The possible sequences or sample space for removing marbles are: {RBG, RGB, BGR, BRG, GRB and GBR}.

Let A denotes the event of removing the non-red marbles at the last.

The favorable cases for event A are: RBG, RGB, BRG and GRB.

As, we know that probability of any event is calculated as by taking the ratio of total number of favorable outcomes to the total number of outcomes.

Thereofre,

The probability that the last marble removed is non-red

= 4/6

= 2/3

The probability that the last marble removed is non-red is 2/3.

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Using the Pythagorean Theorem, it is found that the unknown side length of the triangle is of 7.9 cm.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Researching this problem on the internet, we have that:

Hence:

x² + 9² = 12²

x = sqrt(12² - 9²)

x = 7.9 cm.

The unknown side length of the triangle is of 7.9 cm.

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The radius of the table can be either 13 inches or 73 inches.

Let the radius of the table be r inches and the corner be the origin.

The coordinates of the center of the table exist (r, r).

The equation for the circumference of the table exists (x−r)²+(y−r)²=r².

The mark at the edge of the table exists 18 inches from one wall and 25 inches from the other wall. Therefore, the coordinates of this point exist (18, 25). It could also be (25, 18) but it does not make any difference to our estimations.

As the mark exists on the edge, it meets the requirements of the equation of the circumference of the table.

(18−r)² + (25−r)² = r²

324−36r+r²+625−50r+r² = r²

r²−86r+949 = 0

(r − 13)(r − 73) = 0

r = 13 inches and r = 73 inches

Therefore, the radius of the table can be either 13 inches or 73 inches.

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Answer:

4

Step-by-step explanation:

h(x) = -1/3x+2 where we need to find -4h(9)

h(9): x = 9

h(x) = -1/3(9) + 2

h(x) = -3 + 2

h(x) = -1

-4h(9) is -4h(x):

-4(-1) = 4

The value of a = 11

What is complex numbers ?

Let  a + i b = (a,b)

       c + i d = (c , d)

the distance between two points = [tex]\sqrt{( a - c)^{2} + (b -d )^{2} }[/tex]

put values in the formula -

[tex]\sqrt{(a- (-9))^{2} + (3 - 24 )^{2} }[/tex] = 29

square both sides

[tex]{(a + 9)^{2} + (21)^{2} } = 29^{2}[/tex]

(a + 9)² = 841 - 441 ⇒ 400

(a + 9) = √400 = + 20

a =  +20 -9

So,  a = -29  or 11

Therefore, the value of a = 11

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Mass is the amount of matter that a body possesses and its unit in the international system of units is the kilogram.

Answer: In 2 pounds there are 0.907 kilograms.

Answer:

-15 would be the answer because if it's below sea level it would have a negative sign in front of 15

Step-by-step explanation:

Answer:

y = [tex]\frac{1}{2}[/tex] x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 1) ← 2 points on the line

m = [tex]\frac{1-0}{0-(-2)}[/tex] = [tex]\frac{1}{0+2}[/tex] = [tex]\frac{1}{2}[/tex]

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = [tex]\frac{1}{2}[/tex] x + 1 ← equation of line

The straight line equation is :

[tex]\boxed {y = mx + c}[/tex]

Here, c = 1 as it intersects (0, 1) on the y-axis.

The slope is :

Hence, the equation will be :

y = 0.5x + 1

I hope it helped you solve the problem.

Good luck in your studies!

Answer:

$525

Step-by-step explanation:

We can find the original price by using the formula x - 0.36x = 336, where x is the original price, 0.36 is the discount percentage (converted to decimal form), and 336 is the total amount paid after the discount is applied:

[tex]x-0.36x=336\\0.64x=336\\x=525[/tex]

To check and further understand why the formula works, we can simply apply the discount to the original price and subtract the number from the original price:

525 * 0.36 = 189

525 - 189 = 336

Modeling the first formula gives us:

525 - (0.36 * 525) = 336

525 - 189 = 336

Answer:

E

Step-by-step explanation:

We can find the volume either by finding the scale factor between the two figures and multiplying the first cylinder's volume by it or simply finding the diameter of the second cylinder and doing the equation for volume of a cylinder.

I chose the second way to work out.

Since the two cylinders are similar, we can simply set up a proportion to find the diameter, d, of the second cylinder:

[tex]\frac{6}{d}=\frac{4.5}{6}\\ \\ 4.5d=36\\ d=8[/tex]

The formula for volume of a cylinder is [tex]V=\pi r^2h[/tex]

The radius is simply d/2 so the radius of the second cylinder is 8/2 or 4.

Thus, we have

[tex]V=\pi *4^2*6\\V=\pi *16*6\\V=96\pi \\V=301.59[/tex]

Part A

Using the Pythagorean on the right triangle PQR, with PQ and QR as the legs and PR as the hypotenuse,

[tex]14^2 +6^2 =(PR)^2\\\\(PR)=\sqrt{14^2 +6^2}\\\\PR \approx \boxed{15.23 \text{ ft}}[/tex]

Part B

[tex](QR)^2 +6^2 =16^2\\\\(QR)^2 =16^2 -6^2\\\\QR=\sqrt{16^2 -6^2}\\\\QR \approx \boxed{14.83 \text{ ft}}[/tex]

The length of edge FC in the triangular prism is: 12 cm.

Volume of a right triangular prism = 1/2(Length of triangular base × height of triangular base × height of the prism).

Considering the image given showing a right triangular prism, we have the following:

Volume of triangular prism = 900 cubic centimeters

Length of triangular base = FC = ?

Height of triangular base = 10 centimeters

Height of the prism = 15 centimeters

Plugin the values

900 = 1/2(FC × 10 × 15)

900 = 1/2(FC × 150)

Multiply both sides by 2

2(900) = 2(1/2(FC × 150))

1,800 = FC × 150

Divide both sides by 150

1,800/150 = FC × 150/150

12 = FC

FC = 12 cm

The length of edge FC is: 12 cm.

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Answer: 12

Step-by-step explanation:

Answer:

6.becuase after the decimal or "." it goes 00.tenth, hundredth, thousandth, and so on

Step-by-step explanation:

PLEASE GIVE BRAINLIEST OR 5 ⭐

[tex]f(1)[/tex] is [tex]81.[/tex]

To find  f(1):

f(n 1) = one-half(n).

f(3) = 9.

[tex]f(3) = 9If n = 1,f(2) = 9×3f(2) = 27If n = 0,f(1) = 27 ×3f(1) = 81[/tex]

A sequence is defined by the recursive function [tex]f(1)[/tex] is [tex]81.[/tex]

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Answer:

36

Step-by-step explanation:

Assuming I understand the question correctly

[tex]\text{one-halff(n)} = \frac{1}{2} f(n)[/tex]

We have the recursive relationship

[tex]f(n+1) = \frac{1}{2} f(n)[/tex]

[tex]f(3) = 9[/tex]

[tex]f(3) = \frac{1}{2} f(2)[/tex]

[tex]f(2) = \frac{1}{2} f(1)[/tex]

So

[tex]f(3) = \frac{1}{2} (\frac{1}{2} f(1) = \frac{1}{4} f(1) \\[/tex]

So [tex]f(1) = 4f(3) = 4(9) = 36[/tex]

Verifying

If f(1) = 36 then f(2) = (1/2)f(1) = (1/2)36 = 18

f(3) = (1/2) f(2) = (1/2)(18) = 9

we conclude that the correct option is A, the slope is:

"the average number of pounds per foot tall"

The linear equation:

y = 48.3*x - 127

Relates the height, x, and the weight, y of an adult.

Then the slope, which is 48.3, should have units of mass over height.

Now, if x is in feet and y is in pounds, then the slope has units of pounds/feet.

Then it represents the mean number of pounds per feet. So we conclude that the correct option is A:

"the average number of pounds per foot tall"

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The system of equations to find the value of x, the first number, and y, the second number are;

y = -x + 84

y = x² + 6

The system of equation are equations that contains more than two equation and unknown.

Let the two unknown numbers x and y

If the sum of two numbers is 84, hence;

x +y = 84

y = -x + 84

If the square of the first number is 6 more than the second number, hence;

x² = y + 6

Substitute equation 2 into 2 to have:

x² = y + 6

x² = (-x+84) + 6

x² = -x+84 + 6

x² +x+84 + 6  = 0

x² +x + 90 = 0

Hence the system of equations to find the value of x, the first number, and y, the second number are;

y = -x + 84

y = x² + 6

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Considering the given function in the problem, it is found that:

a. 9.6 offspring survive to maturity when there are 12 female rabbits in the population.

b. At least 18 female rabbits are required for there to be 13 offspring.

The function gives the relationship between the number of adult female rabbits F and the number of offspring R as follows:

[tex]R = 3 + \frac{350F}{F + 625}[/tex]

When there are 12 female rabbits, we have that F = 12, hence:

[tex]R = 3 + \frac{350 \times 12}{12 + 625} = 9.6[/tex]

9.6 offspring survive to maturity when there are 12 female rabbits in the population.

For at least 13 offspring, we have that the number of rabbits needed is given as follows:

[tex]R \geq 13[/tex]

[tex]3 + \frac{350F}{F + 625} \geq 13[/tex]

[tex]\frac{350F}{F + 625} \geq 10[/tex]

[tex]350F \geq 10F + 6250[/tex]

[tex]F \geq \frac{6250}{340}[/tex]

[tex]F \geq 18[/tex]

At least 18 female rabbits are required for there to be 13 offspring.

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According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7

Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.

Given,

n = 66

We know that,

According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:

[tex]k=1+log_{2} n[/tex]

Here, n is equal to 66 and by substituting the value to the equation we get:

[tex]k=1+log_{2} (66)[/tex]

k = 7.0444

k ≈ 7

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Recall that for [tex]|x|<1[/tex], we have the convergent geometric series

[tex]\displaystyle \sum_{n=0}^\infty x^n = \frac1{1-x}[/tex]

Now, for [tex]\left|\frac x5\right| < 1[/tex], we have

[tex]\dfrac1{5 - x} = \dfrac15 \cdot \dfrac1{1 - \frac x5} = \dfrac15 \displaystyle \sum_{n=0}^\infty \left(\frac x5\right)^n = \sum_{n=0}^\infty \frac{x^n}{5^{n+1}}[/tex]

Integrating both sides gives

[tex]\displaystyle \int \frac{dx}{5-x} = C + \int \sum_{n=0}^\infty \frac{x^n}{5^{n+1}} \, dx[/tex]

[tex]\displaystyle -\ln(5-x) = C + \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}[/tex]

If we let [tex]x=0[/tex], the sum on the right side drops out and we're left with [tex]C=-\ln(5)[/tex].

It follows that

[tex]\displaystyle \ln(5-x) = \ln(5) - \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}[/tex]

or

[tex]\displaystyle \ln(5-x) = \boxed{\ln(5) - \sum_{n=1}^\infty \frac{x^n}{5^n n}}[/tex]

The surface area of the pyramid is 34.8 in²

Since the figure is a square pyramid, its surface area, A = 4 × area of triangular face + area of square base.

Area of triangular face A' = 1/2bh where

So, A' = 1/2 × 4.3 in × 3 in

A' = 1/2 × 12.9 in²

A' = 6.45 in²

Area of square base A" = L² where L = length of base = 3 in

So, A" = (3 in)²

= 9 in²

Surface area of pyramid, A = 4A' + A"

= 4 × 6.45 in² + 9 in²

= 25.8 in² + 9 in²  

= 34.8 in²

So, the surface area of the pyramid is 34.8 in²

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Answer:

-7

Step-by-step explanation:

[tex]f(10) = 5-g(10)\\=5-(2(10)-8)\\=5-(20-8)\\=5-(12)\\=-7[/tex]

Answer:

The third one as they have no links really

Answer:

2/5 or 0.4

Step-by-step explanation:

First we have to make equation into the gradient slope form :

y=mx+c    m is gradient and c is y-intercept

15y-6x=8

First we add 6x to both sides :

15y = 6x+8

Now we divide both sides by 15 :

y = 6x+8 / 15

Split the fraction on the right :

y = 6x/15 + 8/15

6x/15 = 6/15x

Our gradient will be 6/15 = 2/5 or 0.4

Hope this helped and have a good day

she should use 2 by 6

Step-by-step explanation:

2 divided by 6 will give 0.3 in 1d.p

Answer:

25%

Step-by-step explanation:

Each flip has a 50% probability of landing heads.  Two in a row would be (50%)*(50%) = 25%

[Note:  25% of $40 is $10].  Don't waste your time.

Look at the attached image above ☝️for explanation

Hope it helps! and if it's not pls tell me on the comment.

Answer:

the second option L = 0.05F + 10

Step-by-step explanation:

the first one

F = 0.05L + 10

does not make any sense, as for length = 10 the force has to be 0. but this function here gives us

0.05×10 + 10 = 0.5 + 10 = 10.5

which is clearly not 0. so, this is wrong.

the second one is correct.

L = 0.05F + 10

it is not perfect, but it is the only one describing the first data points well. like, when F = 0, then L = 10.

the third

L = 0.05F

fails already at the beginning F = 0, as it gives us L = 0 instead of 10. this is wrong.

the fourth

F = 0.05L

fails also already at the beginning. for L = 10 we need to have F = 0. but instead we get F = 0.5. this is wrong.

Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 2 ) and (x₂, y₂ ) = (- 18, 2 )

m = [tex]\frac{2-2}{-18-6}[/tex] = [tex]\frac{0}{-24}[/tex] = 0

The slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

m = ( y₂ - y₁) / (x₂ - x₁)

It is given that the two points are (6, 2) and (-18, 2).

The two-point can be represented as,

(x₁, y₁  ) = (6, 2)

(x₂, y₂ ) =(-18, 2)

The slope of the line can be obtained as,

m = ( y₂ - y₁) / (x₂ - x₁)

m = (2-2) / (-18-6)

m =0 / -24

m =0

Thus, the slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.

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