The length of the shadow of a pole on level ground increase 90m, when the angle of elevation of the sum changes from 58-38.calculate the height of the pole, correct to 3sf

Answer:

28.49

Step-by-step explanation:

2.99 + 25.5 = 28.49

To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

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Answer:

The proportion that can be used is  

2 inches           30 inches

15 miles                   x

Step-by-step explanation:

If 15 miles is 2 inches and 30 divided by 2 is 15, you have to multiply 15 by 15 to figure out how many miles 30 inches is. Because 15 x 15 = 225, 30 inches is 225 miles. Therefore, x = 225.

Hello !

Answer:

\( \boxed{h = 6}\)

Step-by-step explanation:

He has grown :

We also know that in total, he has grown 11 vegetables.

We will have to solve an equation !

\(h + 2h + 5 = 11\)

\( \iff3h + 5 = 11\)

We want to isolate h.

\(3h + 5 - 5= 11 - 5 \\ \iff3h = 6 \\ \iff \frac{3h}{3} = \frac{6}{3} = 2\)

The value of h is 2.

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Answer:

20.

Step-by-step explanation:

60 - 40 = 20

Answer:

There are 5 prime numbers between 40 and 60.

Step-by-step explanation:

A prime number is a number that is ONLY divisible by itself and 1 with no remainder. For example 3 can only be divided by 1 or 3 without a remainder left.

Between 40 and 60 there are 5 prime numbers: 41, 43, 47, 53, and 59.

Answer: It is a scalene triangle.

Step-by-step explanation:

It is scalene because the length between T and V are not equal,the length between T and S is not equal and the length between V and S is also not equal. All the side lengths of the triangle have different measures.

Step-by-step explanation:

\( \frac{4}{ \sqrt{5} + \sqrt{2}} - \frac{3}{ \sqrt{5} - \sqrt{2} } = \\ = \frac{4( \sqrt{5} - \sqrt{2} ) - 3( \sqrt{5} + \sqrt{2} ) }{( \sqrt{5} + \sqrt{2} )\times ( \sqrt{5} - \sqrt{2} )} = \\ = \frac{4 \sqrt{5} - 4 \sqrt{2} - 3 \sqrt{5} - 3 \sqrt{2} }{5 - \sqrt{10} + \sqrt{10} - 2 } = \\ = \frac{ \sqrt{5} - 7 \sqrt{2} }{3} \)

Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

Answer:

no, 6a x 4 and 24a are not equal

Step-by-step explanation:

in 6a x 4 your multiplying 6a 4 times  so the a is multiplied 4 times

in 24a it's 24 times a, a is not being muliplied so this is not equal

Answer:

yes

Step-by-step explanation:

Answer:

I think the second one. I'm not quite sure tho. Hope this helps:)

Answer: The length of the prism is 8 yards

Step-by-step explanation:

First, take the volume of the prism, divide it by the width (2 1/2). Once you get that divide that answer by height (5 3/4) getting you the length of the prism (8 yards)

Answer:

28p + 14q + 21r

Step-by-step explanation:

7(4p + 2q + 3r) ← multiply each term in the parenthesis by the 7 outside

= 28p + 14q + 21r

Answer:

the correct answer is d :)

Step-by-step explanation:

Answer:

4ti + 5tj + k

Step-by-step explanation:

Initial condition V(0) = k

at t = 0

general equation for v(t )

V(0) = 0i + 0j + c = k

when we compare V(0) and solve for c ,     c = k

back to general equation

V(t) = 4ti + 5tj + c = 4ti + 5tj + k

The functions and its domain are a representation of their dependance on one another.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). In the given question, we have two functions and we are required to find the composite of which ever form of the functions as well as the domain of the said function.

\(f(x) = \frac{3}{x}, g(x) = 2x + 8;\\(f.g)(x) = \frac{3}{2x + 8}\)

The domain of the function is given as

\(domain = (-\infty , -4) U (-4, \infty)\\\)

In the second composition of the function,

\((g.f) = \frac{6}{x} + 8\\domain = (-\infty, 0) U (0, \infty)\)

The third composition of function

\((f.f) = x\\domain = (-\infty, \infty)\)

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Answer:

A, 616 cm^2

Step-by-step explanation:

Area- πr^2

A- 3.14(14^2)

A- 3.14(196)

A- 615.44 cm^2 or ≈ 616 cm^2

Answer:

A.

Step-by-step explanation:

Answer: 2 dolls

Step-by-step explanation: got it right

Answer:

1/3 foot longer

Step-by-step explanation:

2/3-1/3=1/3

Answer:

\(=8x^6y^6z^7\)

Step-by-step explanation:

\((4x^3*y^2*z^4)(2x^3*y^4*z^3)\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\\:a^c=a^{b+c}\\=4y^2z^4\cdot \:2x^{3+3}y^4z^3\\\mathrm{Add\:the\:numbers:}\:3+3=6\\=4y^2z^4\cdot \:2x^6y^4z^3\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\y^2y^4=\:y^{2+4}\\=4z^4\cdot \:2x^6y^{2+4}z^3\)

\(\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\z^4z^3=\:z^{4+3}\\=4\cdot \:2x^6y^6z^{4+3}\\\mathrm{Add\:the\:numbers:}\:4+3=7\\=4\cdot \:2x^6y^6z^7\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:2=8\\=8x^6y^6z^7\)

Step-by-step explanation:

54^2 + a^2 = 90^2

2916 + a^2 = 8100

a^2 = 8100 - 2916

a^2 = 5184

take the square root of 5184

a = 72

you could have also guessed that its a 3 4 5 right triangle

all the sides are multiples of 3 4 or 5

Approximately 34.658 Hispanic females out of 26,000 to have this particular disease.

A woman or girl who identifies as Hispanic or Latino, which usually refers to persons of Spanish-speaking origin or lineage from Latin America or Spain, is referred to as a "Hispanic female."

The proportion of Hispanic females with the disease is 1 in 750, which can be expressed as:

1 / 750 = 0.001333

This means that for every 750 Hispanic females, one is expected to have the disease.

To calculate the expected number of Hispanic females with the disease in a group of 26,000, we can multiply the proportion by the total number of Hispanic females:

0.001333 * 26,000 = 34.658

So we would expect approximately 34.658 Hispanic females out of 26,000 to have this particular disease.

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Answer:

An equation contains an equal sign so -20 is not an equation, I think it's a typing error

Answer:

∠ W = 53°

Step-by-step explanation:

the measure of the secant- secant angle W is half the difference of the measures of the intercepted arcs , that is

∠ W = \(\frac{1}{2}\) (YC - GT) = \(\frac{1}{2}\) (160 - 54)° = \(\frac{1}{2}\) × 106° = 53°

Answer: -11/7

Step-by-step explanation: Got it right

The slope of the given relation 2x³ - 3xy + y³ = -1 is -11/7. Option (A) is correct option.

The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.

the slope of any funtion y = f(x) can be given as dy/dx.

The given relation is,

2x³ - 3xy + y³ = -1

To find the slope of the graph of the given relation,

Differentiate relation with respect to x,

d/dx(2x³ - 3xy + y³) = d/dx(-1)

6x² - 3x dy/dx - 3y + 3y²dy/dx = 0

6x² - 3y = 3x dy/dx -3y² (dy/dx)

dy / dx =(6x² - 3y)/3x - 3y²

dy / dx = 2x²  - y / x -y²

The slope at point (2, -3)

dy / dx = 2(2)²  - (-3) / 2 - (-3)²  

= 8 + 3 / 2 - 9

= 11/ -7

= -11/7

The slope of the given relation is -11/7.

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The term refers to a thorough count, often known as a comprehensive enumeration.

Every unit, whether it be an individual or the entire population, is studied during a census. A comprehensive enumeration, which refers to an exhaustive count, is what is meant by the term.

A census is a survey that is carried out on the entire collection of observational objects that are a part of a certain population or universe. A census is a thorough count of a population or groups at a particular period in relation to clearly specified qualities, such as population, production, or traffic on specific roadways.

The population of a nation is counted during a census. It also provides information about those individuals, including their histories, possessions, and way of life. Censuses are a key decision-making tool for both governments and enterprises.

The correct answer is option C. A study of the durability of earthquake-proof building materials.

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Answer:

5/3

Step-by-step explanation:

Answer:

to torture people

Step-by-step explanation:

but real anwser is to help children learn more about their ecosystem and to give more knowledge and learn new things

Answer:

\(x=-\frac{3\sqrt{2}}{2},\frac{3}{4},\frac{3\sqrt{2} }{2}\)

Step-by-step explanation:

Given expression is,

f(x) = 8x³ - 6x² - 36x + 27

For zeros of the function,

f(x) = 0

8x³ - 6x² - 36x + 27 = 0

2x²(4x - 3) - 9(4x - 3) = 0

(2x² - 9)(4x - 3) = 0

(2x² - 9) = 0

x² = \(\frac{9}{2}\)

x = \(\pm\frac{3}{\sqrt{2}}\)

x = \(\pm \frac{3\sqrt{2}}{2}\)

Or (4x - 3) = 0

x = \(\frac{3}{4}\)

Therefore, all zeros of the given functions are  \(x=-\frac{3\sqrt{2}}{2},\frac{3}{4},\frac{3\sqrt{2} }{2}\).