1 The area of a triangle can be found using the formula: Area = base height 2 Find the area of the triangle pictured below, where the measurements are given in meters (m) 8 m 13 m О.

The angle of elevation of the pole from the man's eyes is about 9.2°

The angle of elevation from a point to an elevated location is the angle made by the line from the location to the point and the horizontal line from the point.

The elevation of a man's eye above the horizontal ground = 1.7 m

The (horizontal) distance of the man's eye from the vertical pole = 13 m

The height of the pole = 3.8 m

The angle of elevation of the top of the pole from the man's eye can be found as follows;

The vertical height from the man's eye to the top of the pole = 3.8 m - 1.7 m = 2.1 m

Let θ represent the angle of elevation of the top of the pole to the man's eye, from the trigonometric ratio of tangent, we get;

tan(θ) = 2.1/13

θ = arctan(2.1/13) ≈ 9.2°

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Answer is \(\frac{33}{8}\)

The width of the path, x, is 48 feet

The formula for determining the area of a rectangle is expressed as;

Area = lw

Where;

From the image shown and the information given, we can see that;

The width is given as = x

The area of the rectangle =  768 ft²

The length of the rectangle = 16

Now, substitute the values, we have;

768 = 16x

Make 'x' the subject of formula by dividing both sides by its coefficient, we have;

768/16 = 16x/16

Find the quotient

x = 48 feet

But, we have;

Width = x = 48 feet

Hence, the value is 48 feet

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Answer:

√337 or about 18.36

Step-by-step explanation:

distance formula √((y2-y1)^2+(x2-x1)^2)

√(((8-(-8))^2+(-2-7)^2)

√(16^2+9^2)

√(256+81)

√337

Answer:

A. Eva

Step-by-step explanation:

Given that

The entire school, 250 students, went to the soap box derby.2 vans went to soap box derby and each van held 6 students.

To find the total number of students from the Math Club who went to the soap box derby, we need to add the number of students in each van, the number of times equal to the number of vans.

i.e. by adding 6 (i.e. number of students in each van) 2 (number of vans )number of times, we can get the number of students from Math Club who went to the soap box derby.

Number of Math Club students who went to the soap box derby = 6 + 6 = 12

OR

Simply, multiply number of students in each van with the number of vans .

6 \(\times\) 2 = 12

Therefore, Eva is correct about the calculations.

yes the difference is calculated only with consecutive numbers and A is the form because C says that the difference is the sum between 45 and 43 an its incorrect

Answer:

37

Step-by-step explanation:

I believe you subtract the meters to the meters above the ground

Answer:

10.8 meters

Step-by-step explanation:

1.2 times 9 minutes= 10.8

Answer:

10.8 meters

Step-by-step explanation:

9 * 1.2 = 10.8

Answer:

\(a^{12} b^{4}\)

Step-by-step explanation:

To simplify we will have to use the negative exponent rule and the power rule along with some algebra.

Negative Exponent Rule

\(a^{-b} =\frac{1}{a^b}\)

Power Rule

\((a^b)^{c} =a^{bc}\)

Given

\((a^{-4}b^{-1}c )^{2} (a^2bc)^{2}\)

Rewrite \(a^{-4}\) using negative exponent rule.

\((\frac{1}{a^{4}}* b^{-1}c )^{2} (a^2bc)^{2}\)

Rewrite \(b^{-1}\) using negative exponent rule.

\((\frac{1}{a^{4}}* \frac{1}{b}*c )^{2} (a^2bc)^{2}\)

Simplify

\((\frac{c}{a^4b} )^{2} (a^2bc)^{2}\)

Rewrite the base as its reciprocal.

\((\frac{a^4b}{c} )^{2} (a^2bc)^{2}\)

Apply the power rule.

\(\frac{a^8b^2}{c^2} *(a^2bc)^{2}\)

Apply the power rule.

\(\frac{a^8b^2}{c^2} *a^4b^2c^2\)

Cancel the common factor of \(c^2\).

\(a^8b^2 a^4b^2\)

Apply the power rule.

\(a^{12} b^{4}\)

Answer:

\(a^{12}\:b^{4}\)

Step-by-step explanation:

Given expression:

\(\left(a^{-4}\:b^{-1}\:c\right)^{-2}\left(a^2\:b\:c\right)^2\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies a^{(-4 \times -2)}\:b^{(-1 \times -2)}\:c^{-2}\:a^{(2 \times 2)}\:b^2\:c^2\)

Simplify:

\(\implies a^{8}\:b^{2}\:c^{-2}\:a^{4}\:b^2\:c^2\)

Collect like terms:

\(\implies a^{8}a^{4}\:b^{2}b^2\:c^{-2}c^2\)

\(\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:\)

\(\implies a^{(8+4)}\:b^{(2+2)}\:c^{(-2+2)}\)

Simplify:

\(\implies a^{12}\:b^{4}\:c^{0}\)

\(\textsf{Apply exponent rule} \quad a^0=1:\)

\(\implies a^{12}\:b^{4}(1)\)

\(\implies a^{12}\:b^{4}\)

Answer:

No

Step-by-step explanation:

B/c trinomial has exactly 3 terms and binomial only have 2

Answer:

I think its 2nd one

HOPE IT HELPS, BE SAFE! Brainiest if possible pls! :)

Answer:

x = 8

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. First, multiply 12 and x to both sides of the equation:

(3/12)(12)(x) = (2/x)(12)(x)

3 * x = 2 * 12

3x = 24

Isolate the variable, x. Divide 3 from both sides of the equation:

(3x)/3 = (24)/3

x = 24/3

x = 8

x = 8 is your answer.

~

Step-by-step explanation:

the answer to this question is 2/8, x is 8

in order to do this proportion, you have to

1.Cross multiply:

3 * x = 12 * 2

2.

Simplifying

3 * x = 12 * 2

3.

Multiply 12 * 2

3x = 24

4.

Solving

3x = 24

5.

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

6.

Divide each side by '3'.

x = 8

7.

Simplifying

x = 8

meaning that 3/12 = 2/8

Answer:

0

Step-by-step explanation:

6-24n=3n+6

Add 24n to both sides of the equation:

6=27n+6

Subtract 6 from both sides:

27n=0

Therefore, n=0.

Hope this helps!

The centre and the radius of the circle is (-7, -1) and 6 units

The equation of the circle in standard from is expressed as:

x^2+y^2+2gx+2fy+C = 0

where;

(-g, -f) is the centre

r= √g²+f²-C

Given the equation below

x^2+y^2+14x+2y+14 = 0

2g = 14

g = 7

2f = 2

f =1

Hence the centre of the circle is (-7, -1)

Radius = √49+1-14

Radius = √36 = 6 units

Hence the centre and the radius of the circle is (-7, -1) and 6 units

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The total number of significant figures ( numerically as an integer ) in the given measurement 6.07 m is equal to 3.

Here in the measurement 6.07 m

Zero is in between two non zero digit 6 and 7.

Zero is countable.

Total number of significant figure in 6.07 m is 3.

Therefore, the number of significant figure in the 6.07 m is equal to 3.

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Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

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

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Answer:

1/9

Step-by-step explanation:

lol

Answer:

\(x = 16\)

Step-by-step explanation:

Given

\(log_{16}(x) + log_4(x) + log_2(x) = 7\)

Required

Solve for x

\(log_{16}(x) + log_4(x) + log_2(x) = 7\)

Change base of 16 and base of 4 to base 2

\(\frac{log_2(x)}{log_2(16)} + \frac{log_2(x)}{log_2(4)} + log_2(x) = 7\)

Express 16 and 4 as 2^4 and 2^2 respectively

\(\frac{log_2(x)}{log_2(2^4)} + \frac{log_2(x)}{log_2(2^2)} + log_2(x) = 7\)

The above can be rewritten as:

\(\frac{log_2(x)}{4log_22} + \frac{log_2(x)}{2log_22} + log_2(x) = 7\)

\(log_22 = 1\)

So, we have:

\(\frac{log_2(x)}{4*1} + \frac{log_2(x)}{2*1} + log_2(x) = 7\)

\(\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x) = 7\)

Multiply through by 4

\(4(\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x)) = 7 * 4\)

\(log_2(x) + 2}log_2(x) + 4log_2(x) = 28\)

\(7log_2(x) = 28\)

Divide through by 7

\(\frac{7log_2(x)}{7} = \frac{28}{7}\)

\(log_2(x) = 4\)

Apply the following law of logarithm:

If \(log_ab = c\) Then \(b = a^c\)

So, we have:

\(x = 2^4\)

\(x = 16\)

The maximum likelihood estimate of the probability of getting a green light on a single pass through the traffic signal is 0.63.

To find the maximum likelihood estimate of the probability p of a green light on a single pass, we need to consider the observed frequency of green lights in the given data.

1. We are given that the car passed through the traffic signal 100 times and got a green light 63 times.
2. To find the maximum likelihood estimate (MLE) of the probability p of a green light, we need to divide the number of successful green light events (63) by the total number of passes (100).
3. Calculate the MLE: p = 63/100 = 0.63

The maximum likelihood estimate of the probability p of a green light on a single pass is 0.63.

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The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25\(b^{2}\) + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25\(b^{2}\)  = -(5)(5) * \(b^{2}\)

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * \(b^{2}\) +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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Answer:

53

Step-by-step explanation:

Your two median numbers are 52 and 54 you add these and divide by two and get 53.

Hope this helps

Answer: 53 mark as brainlest please

Step-by-step explanation:

Answer:

a)  $497.70

b)  392.4 square feet

c)  $1,200

Step-by-step explanation:

A regular octagon has 8 sides of equal length.

Given each side of the octagon measures 9 feet in length, and one side does not have a railing, the total length of the railing is 7 times the length of one side:

\(\textsf{Total length of railing}=\sf 7 \times 9\; ft=63\;ft\)

If the railing sells for $7.90 per foot, the total cost of the railing can be calculated by multiplying the total length by the cost per foot:

\(\textsf{Total cost of railing}=\sf 63\;ft \times \dfrac{\$7.90}{ft}=\$497.70\)

Therefore, the cost of the railing is $497.70.

\(\hrulefill\)

To find the area of the regular octagonal gazebo, given the side length and apothem, we can use the area of a regular polygon formula:

\(\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\;s\;a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}\)

Substitute n = 8, s = 9, and a = 10.9 into the formula and solve for A:

\(\begin{aligned}\textsf{Area of the gazebo}&=\sf \dfrac{8 \times 9\:ft \times10.9\:ft}{2}\\\\&=\sf \dfrac{784.8\;ft^2}{2}\\\\&=\sf 392.4\; \sf ft^2\end{aligned}\)

Therefore, the area of the gazebo is 392.4 square feet.

\(\hrulefill\)

To calculate the cost of the gazebo's flooring if it costs $3 square foot, multiply the area of the gazebo found in part (b) by the cost per square foot:

\(\begin{aligned}\textsf{Total cost of flooring}&=\sf 392.4\; ft^2 \times \dfrac{\$3}{ft^2}\\&=\sf \$1177.2\\&=\sf \$1200\; (nearest\;hundred\;dollars)\end{aligned}\)

Therefore, the cost of the gazebo's flooring to the nearest hundred dollars is $1,200.

a. To find the perimeter of the gazebo, we can use the formula P = 8s, where s is the length of one side. Substituting s = 9, we get:

P = 8s = 8(9) = 72 feet

Since one side is open, we only need to find the cost of railing for 7 sides. Multiplying the perimeter by 7, we get:

Cost = 7P($7.90/foot) = 7(72 feet)($7.90/foot) = $4,939.20

Therefore, the cost of the railing is $4,939.20.

b. To find the area of the gazebo, we can use the formula A = (1/2)ap, where a is the apothem and p is the perimeter. Substituting a = 10.9 and p = 72, we get:

A = (1/2)(10.9)(72) = 394.56 square feet

Therefore, the area of the gazebo is 394.56 square feet.

c. To find the cost of the flooring, we need to multiply the area by the cost per square foot. Substituting A = 394.56 and the cost per square foot as $3, we get:

Cost = A($3/square foot) = 394.56($3/square foot) = $1,183.68

Rounding to the nearest hundred dollars, the cost of the flooring is $1,184. Therefore, the cost of the gazebo's flooring is $1,184.

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Answer:

24

Step-by-step explanation:

First: 12*10=120

Then: 12*12=144

=> Ms. Xu's old: 144-120=24

Answer:

7

Step-by-step explanation:

49 /7 = 7

Answer:

7:)

Step-by-step explanation:

group 1-ooooooo=7

group2-ooooooo

ooooooo=14

group 3-ooooooo

ooooooo               ooooooo=21

group 4-ooooooo            ooooooo=28

ooooooo               ooooooo

group 5-ooooooo            ooooooo

ooooooo               ooooooo          ooooooo=35

group 6-ooooooo            ooooooo          ooooooo

ooooooo               ooooooo          ooooooo=42

group 7-ooooooo            ooooooo          ooooooo

ooooooo               ooooooo          ooooooo

ooooooo=49

Answer:

Not similar

Step-by-step explanation:

28÷16 =1.75

7÷4=1.75

9÷15 =0.6

So, they are not similar because the don't share the same scale factor of 1.75 or 0.6.

To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:

\(f(g(x)) = f(x - 4) = (x - 4)^2 + 4\)

To simplify this expression, we can expand the square:

\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)

Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)

Next, let's find g(f(x)). We substitute f(x) into the function g(x):

\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)

Hence, g(f(x)) simplifies to 1/x^2.

In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.

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