The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 36°.Calcule the height of the pole

Answer:

Step-by-step explanation:

[tex]\sqrt{x-3} +5=x\\\sqrt{x-3} =x-5\\squaring ~both~sides\\x-3=x^2-10x+25\\x^2-10x-x+25+3=0\\x^2-11x+28=0\\x^2-7x-4x+28=0\\x(x-7)-4(x-7)=0\\(x-7)(x-4)=0\\x=7,4[/tex]

put x=7 in the given equation

[tex]\sqrt{7-3} +5=7\\\sqrt{4} +5=7\\2+5=7\\7=7[/tex]

which is true .

∴ x=7 is a solution of the given eq.

now put x=4 in the given eq.

[tex]\sqrt{4-3} +5=7\\1+5=7\\6=7\\[/tex]

which is not true.

∴x=4 is an extraneous solution.

Answer:

the answer is 60.7

Step-by-step explanation:

60 to has a between numbers like given in the picture

so as number line it's

60.1 . 60.2 60.3 60.4 60.5 60.6 60.7 60.8 and continue

if u get any 3 digit number like 600 to 650 in number line

u do it like it the same 600.1 600.2.... and go on

Answer:

63½ or 63.5

Step-by-step explanation:

65-60=5

10points=5

1point=?

1×5/10= ½

that means the sequence continues after adding ½ i.e

60..60½...61...61½...62...62½...63...63½...64..64½...65

you have been asked the 8th number which is 63½

Answer:

[tex]1296x^3y^4[/tex]

Step-by-step explanation:

Given the terms:

[tex]144x^3y^2[/tex]

and [tex]81xy^4[/tex]

To find:

Greatest Common Divisor of the two terms or Least Common Multiple (LCM) of two numbers = ?

Solution:

First of all, let us find the HCF (Highest Common Factor) for both the terms.

i.e. the terms which are common to both.

Let us factorize them.

[tex]144x^3y^2 = \underline{3 \times 3} \times 16\times \underline x \times x^{2}\times \underline{y^{2} }[/tex]

[tex]81xy^4= \underline {3\times 3}\times 9 \times \underline{x} \times \underline{y^2}\times y^2[/tex]

Common terms are underlined.

So, HCF of the terms = [tex]9xy^2[/tex]

Now, we know the property that product of two numbers is equal to the product of the numbers themselves.

HCF [tex]\times[/tex] LCM = [tex]144x^3y^2[/tex] [tex]\times[/tex] [tex]81xy^4[/tex]

[tex]LCM = \dfrac{144x^3y^2 \times 81xy^4}{9xy^2}\\\Rightarrow LCM = 144x^3y^2 \times 9x^{1-1}y^{4-2}\\\Rightarrow LCM = 144x^3y^2 \times 9x^{0}y^{2}\\\Rightarrow LCM = \bold{1296x^3y^4 }[/tex]

Answer:

Step-by-step explanation:

[tex]A=s^2\cdot \sin\alpha\\\\s=10\\\alpha=120^o\\\\A=10^2\cdot\sin(120^o)=100\sin(180^o-60^o)=100\sin(60^o)=100\cdot\frac{\sqrt3}2=50\sqrt3[/tex]

Answer:

Step-by-step explanation:

Given this expression 2(b+3c), its equivalent expression is derived by simply opening up the bracket as shown below;

Open the parenthesis by multiplying the constant outside the bracket with all the variables in parenthesis.

= 2(b+3c)

=  2(b)+ 2(3c)

= 2b +2*3*c

= 2b +6c

It can also be written as sum of b+3c in 2 places i.e (b+3c)+(b+3c) because multiplying the function b+3c by 2 means we are to add the function by itself in two places.

Hence the equivalent expression are (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c

Answer:

y = 5x + 3

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 )

Here m = 5, thus

y = 5x + c ← is the partial equation

To find c substitute (2, 13) into the partial equation

13 = 10 + c ⇒ c = 13 - 10 = 3

y = 5x + 3 ← equation of line

Answer:

358 and remainder of 3

Step-by-step explanation:

1. Divide it like any other problem

Hope this helps

1 mile = 5,280 feet

1 hour = 3600 seconds

3600/5280 = 0.681818 feet per second

25 ft per second x 0.681818 = 17.045 miles per hour

Round the answer as needed.

Answer:

The correct answer is 17.045 miles per hour.

Step-by-step explanation:

L*b=1800m^2

L=2b

2b*b=1800

2b^2=1800

b^2=900

b=30m

L=2*30

=60m

Perimeter=2(l+b)

=2(60+30)

=2*90

=180m

Answer: x=-22

Step-by-step explanation:

    6x-4=-26+5x

6x-4-5x=-26+5x-5x ⇔ subtraction property of equality

       x-4=-26

  x-4+4=-26+4 ⇔ addition property of equality

         x=-22

Answer:

Step-by-step explanation:

6x - 4 = - 26 + 5x

First of all group like terms

Send the constants to the right side of the equation and those with variables to the left

That's

6x - 5x = 4 - 26

Simplify

We have the final answer as

Hope this helps you

Part A

Her steps were

[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{6}{17} \times \frac{3}{4}\\\\-\frac{6\times 3}{17\times4}\\\\-\frac{18}{68}\\\\-\frac{9}{34}\\\\[/tex]

Kelsey made a mistake on line 3. Note how the 17/6 flips to 6/17. This is not correct. You keep the first fraction the same, but you do flip the second fraction. This only applies when you divide two fractions.

The third step should look like [tex]-\frac{17}{6}\times \frac{3}{4}[/tex]

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

Part B

Here's what she should have written

[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{17}{6} \times \frac{3}{4}\\\\-\frac{17\times 3}{6\times 4}\\\\-\frac{51}{24}\\\\-\frac{17}{8}\\\\[/tex]

If you want to convert that improper fraction to a mixed number, then you could do something like this

[tex]-\frac{17}{8} = -\frac{16+1}{8}\\\\-\frac{17}{8} = -\frac{16}{8}-\frac{1}{8}\\\\-\frac{17}{8} = -2 \frac{1}{8}\\\\[/tex]

Or you could divide 17 over 8 using long division to get 2 remainder 1. The 2 is the quotient that goes to the left of the 1/8. The remainder of 1 is the numerator of 1/8.

Answer:

Step-by-step explanation:

Using the equation A(t) = 400e-.032t

a) replace t with 4 so A(4) = 400e((-.032)(4))

The hardest part about this is making sure to use order of operations. Be certain it works like this:

A(4) = 400e-.128

A(4) = 400(.8799)

A(4) = 351.9 grams

b) A(8) = 400e((-.032)(8)) = 309.7 grams

c) A(20) = 400e((-.032)(20)) = 210.9 grams

Note here that even after 20 years, not quite half of the original amount is gone. So, we can anticipate that in finding the half life, that our answer should be slightly greater than 20 years.

d) 200 = 400e(-.032t)

Divide both sides of the equation by 400.

.5 = e(-.032t)

Change this to logarithmic form.

Ln .5 = -.032t

-.6931≈ -.032t

t ≈ 21.7 years

Hope this helps!

The amount of radioactive lead,

(a).After 3 years is 454.23 grams

(b).After 8 years is 387.07 grams

(c).After 10 years is 363.07 grams.

(d). half life is 21.66 years.

The decay of radioactive lead is given by function,

                          [tex]A(t)=500e^{-0.032t}[/tex]

The amount of radioactive lead After 3 years is,

             [tex]A(3)=500e^{-0.032*3}=0.908*500=454.23g[/tex]

The amount of radioactive lead After 8 years is,

            [tex]A(8)=500e^{-0.032*8}=500*0.774=387.07g[/tex]

The amount of radioactive lead After 10 years is,

            [tex]A(10)=500e^{-0.032*10}=500*0.726=363.07g[/tex]

Half life is defined as the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.

So,       [tex]250=500e^{-0.032t}[/tex]

            [tex]e^{-0.032t}=0.5\\\\-0.032t=ln(0.5)\\\\-0.032t=-0.693\\\\t=0.693/0.032=21.66 years[/tex]

Learn more:

https://brainly.com/question/158534

Answer:

A. R=0.86; strong correlation

Step-by-step explanation:

The correlation coefficient of 0.29 indicates that the correlation is a weak positive correlation. Thus option (D) is the correct answer.

"Correlation is a statistical tool that studies the relationship between two variables. Data sets have a positive correlation when they increase together, and a negative correlation when one set increases as the other decreases".

For the given situation,

Correlation coefficient = 0.29

Positive correlation: the two variables change in the same direction.

Negative correlation: the two variables change in opposite directions.

No correlation: there is no association or relevant relationship between the two variables.

The correlation coefficient lies between 0 to 0.3 indicating that the correlation is a weak positive correlation.

Hence we can conclude that option (D) weak positive correlation is the correct answer.

Learn more about correlation here

https://brainly.com/question/10721912

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A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width.

The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower

:

Let x = the width of flower bed

:

Then the overall dimensions (flower bed & lawn) will be:

(2x + 8) by (2x + 4)

:

Overall area

(2x+8)*(2x+4) = 165

FOIL

4x^2 + 8x + 16x + 32 = 165

A quadratic equation

4x^2 + 24x + 32 - 165 = 0

4x^2 + 24x - 132 = 0

Simplify, divide by 4, results:

x^2 + 6x - 33 = 0

Use the quadratic formula to solve this

Answer:

Hey there!

A simple way to think about slope is rise over run. Between any two points on this line, the rise is 3, and the run is -1.

3/-1=-3, so  the slope is -3.

Let me know if this helps :)

Step-by-step explanation:

Hello, there!!!

I hope you mean the question is like the above problem in picture.

so, let's simply work with it.

here, we may use cosine rule,

so, according to cosine rule,

[tex] {c}^{2} = {a}^{2} + {b}^{2} - 2ab.cosc[/tex]

so, just put value of formulae here,

we get;

5^2 = 3^2 + 4^2 - (2×3×4) . cos thita

or, 25 = 9 + 16 -24 cos thita.

or, 24 cos thita = 0

or, cos thita = 0/25

or, cos thita = 0

now, taking cos to right side we get,

[tex] {cos}^{ - 1 } (0)[/tex]

now, after typing cos ^-1 (0) we get angle as 90°.

(note: in step {cos thita = 0} you couold directly write like; cos thita = cos 90°. and cos would be cancelled in it as cos 90°=0. but it is only applied in particular angle like 0°,30°,60°,..... which are identified or if you don't know you must use the method above using calculator and remember to put inverse {cos^-1}).

so, In this way we find angle.

I hope it helps....

Answer:

first answer

Step-by-step explanation:

(8x³ - 22x² - 4) / (4x - 3)

when you do long division you get the first answer

Answer:

[tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}=\dfrac{-13}{8}[/tex]

Step-by-step explanation:

We need to find the value of expression [tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}[/tex].

Firstly solving the second term as :

[tex](2-\dfrac{3}{8})=\dfrac{16-3}{8}=\dfrac{13}{8}[/tex]

Now the above expression becomes,

[tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}\\=\dfrac{-3}{2}-\dfrac{13}{8}+\dfrac{3}{2}[/tex]

-3/2 and +3/2 equals 0.

It means that, [tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}=\dfrac{-13}{8}[/tex]

Answer:

128

Step-by-step explanation:

Answer:

a. €1200;$1667.70

Step-by-step explanation:

a. Number of euros

[tex]\text{euros} = \$1962 \times \dfrac{\text{1 euro}}{\text{\$1.635}} = \textbf{1200 euros}[/tex]

b. Dollars remaining

Dollars on hand                        = $1962.00

Less 15 % spent = 0.15 × 1962 =   -294.30

Balance remaining                   =  $1667.70

Answer: x=1/9

Step-by-step explanation:

[tex]2\left(\frac{1}{9}\right)x=\frac{2}{81}[/tex]

[tex]\frac{2}{9}x=\frac{2}{81}[/tex]

multiply both sides by 9

[tex]9\cdot \frac{2}{9}x=\frac{2\cdot \:9}{81}[/tex]

[tex]2x=\frac{2}{9}[/tex]

divide 2 on both sides

[tex]x=\frac{1}{9}[/tex]

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question the equation is

y = 2x + 3

Comparing this equation with the general equation above

Slope / m = 2

Hope this helps you

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Answer:

C.) 7.14 in²

Step-by-step explanation:

The figure is made up of a square and a circle. The circle is divided in half and each piece is set on one side of the square. This means that the diameter of the circle is equal to the length of the sides of the square, 2 inches.

The area of the square can be found by multiplying length times the width:

[tex]2*2=4[/tex]

The area of the square is 4 inches, and since we multiplied two lengths, we square the value:

A=4in²

Now find the area of the circle using the formula:

[tex]A=\pi r^2[/tex]

The radius is half of the diameter, so the radius is 1. Insert values and solve:

[tex]A=\pi *1^2\\\\A=\pi *1\\\\A=\pi[/tex]

The area of the circle is equal to π. Add the values together:

[tex]4+\pi =7.14[/tex]

The area of the figure is 7.14 in²

:Done

Answer:

>

Step-by-step explanation:

Even though its 0 its still greater than any negative number.

Answer:

Step-by-step explanation:

Answer:

P(A∩B) = 7/80

P(A∩B) = 0.0875

Step-by-step explanation:

Given

P(B)=7/20

P(A|B)=¼

Required

P(A∩B)=?

The given probability shows conditional probability and the relationship between the given parameters is as follows.

P(A∩B) = P(B) * P(A|B)

Substitute ¼ for P(A|B) and 7/20 for P(B)

The expression

P(A∩B) = P(B) * P(A|B) becomes

P(A∩B) = 7/20 * ¼

P(A∩B) = 7/80

P(A∩B) = 0.0875

Hence, the calculated P(A∩B) is 7/80 or 0.0875

Answer:

The correct option is;

(Choice C) Both angle measures and segment lengths

Step-by-step explanation:

The given transformations are;

The reflection over the line, [tex]\overleftrightarrow{PQ}[/tex], with, A rotation about the point P. Another reflection over [tex]\overleftrightarrow{PQ}[/tex]. A rotation about the point Q, we have;

The transformations involve changes only in the orientation and location of the pre-image, which remain rigid, therefore, there are no changes in the segment lengths or angle dimensions

Therefore, the correct option is,  both angle measures and segment lengths.

(Choice C) C Both angle measures and segment lengths

Answer:

A

Step-by-step explanation:

Hi!

An exponent is the same thing as just multiplying the expression by itself the number of times the exponent says. So we need to multiply 1/3 by itself three times.

1/3 * 1/3 * 1/3 = 1/27

Answer:

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Step-by-step explanation:

Let suppose that [tex]g(x) = \frac{1}{x^{2}}[/tex], then [tex]f(g(x))[/tex] is:

[tex]f(g(x)) = 7\cdot \left(\frac{1}{x^{2}} \right) + 10[/tex]

[tex]f(g(x)) = 7\cdot g(x) + 10[/tex]

Thus,

[tex]f(x) = 7\cdot x + 10[/tex]

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Answer:

D) 11 13 15 19 23 23 24 26.5 28 33​

Step-by-step explanation:

The box-and-whisker plot displayed above has the following key values that we can use to identify which of the given data set it matches. It has:

Minimum value = 11

Q1 = 15

Median = 23

Q3 = 26

Maximum value = 33

From the options given, using just the max and min value, we can conclude that the data set in option D matches the box plot.

The data set in option D has a minimum value of 11, and a maximum value of 33.