Jeriel is 1.65 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 28.05 meters. He stands 23.5 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

We can actually see that the statements that are true are:

A. x = 1 is a solution.

C. x = –1 is a solution.

Rational equation is actually known as an equation that contains at least one fraction. The denominator and numerator are known to be polynomials.

We can see then that:

[tex] \frac{4}{x + 6} + \frac{1}{ {x}^{2} } = \frac{x + 10}{ {x}^{3} + 6 {x}^{2} } [/tex]

It's clear that: x ≠ 0 and x ≠ -6.

Looking for the LCM of the left hand side, we will have:

[tex] \frac{4}{x + 6} + \frac{1}{ {x}^{2} } = \frac{4 {x}^{2 } + (x + 6)}{(x + 6) {x}^{2} } [/tex]

So, we will see that left hand side and right hand side are equal.

[tex]4 {x}^{2} + x + 6 = x + 10[/tex]

[tex]4 {x}^{2} = 10 - 6[/tex]

[tex]4 {x}^{2} = 4[/tex]

[tex] {x}^{2} = 1[/tex]

[tex] x = 1[/tex]

or

[tex]x = - 1[/tex]

So, we can see that options A and C are correct.

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Answer:

-1 and 1  or A and C

Step-by-step explanation:

Answer:

It is attached

Step-by-step explanation:

Answer:

12 1/6

It wants me to add more but there's nothing to add

Answer:

Step-by-step explanation:

the 2nd and 4th answers look good.  the 1st answer is correct as well.

To solve this look at the x axis and y axis,  the x axis is in inches, the y axis is in pounds.  So you know that as the distance increase per inch,  the force in pounds is increasing too.  

so the force applied is going up,   0.73 pounds , for each inch of travel ( or stretch) of the spring.  

5 is the awsterstdysytghujfhds

1 mile = 1.6 kilometers so 24*1.6 = 38.4
24 miles = 38.4 kilometers

1 kilometer = 1000 meters so 38.4*1000 = 38,400 meters
38.4 kilometers = 38,400 meters

1 hour = 60 minutes so 2*60 = 120
2 hours = 120 minutes

To calculate meters per minute, divide.
38,400 / 120 = 320

So that means that Calvin's approximate speed is 320 meters per minute.

46204 ft³

Volume of cube: length³ ⇒ 36³ ⇒ 46656 ft³

Volume of cylinder: πr²h ⇒ π(2)²(36) ⇒ 144π ⇒ 452.39 ft³

Volume of the figure: 46656 - 452.15 = 46203.61 ft³ ≈ 46204 ft³

For cube

For cylinder

Area of base:-

Volume:-

Volume of figure:-

Answer:

-3

Step-by-step explanation:

The equation for slope is y2-y1/x2-x1 so put you numbers in and you get

-6-6/-9+5

-12/4

and then -3

Answer:

-3

Step-by-step explanation:

[tex]y=mx+b[/tex] is equation of a straight line.

Here, the slope is m.

[tex]m=\frac{y_{2}-y_{1} }{{x_{2}-x_{1}}} =\frac{-6-6}{-9-(-5)} =\frac{-12}{-4}=-3[/tex]

Answer:

1,200

Step-by-step explanation:

Divide 800 by 40

Then take that answer which is 20 and multiply it by 60

Then you get 1,200

The inequalities that Heather could have written to compare the temperatures will be:

B. 2 < -10

C. 4 >-20

E. -8 < -15

It should be noted that inequality us the relation between two expressions that aren't equal.

Therefore, the inequalities that Heather could have written to compare the temperatures will be: 2 < -10, 4 >-20,and -8 < -15.

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Answer:

See below

Step-by-step explanation:

This will create a cylinder    volume = 1/2 pi  r^2 h = 1/2  pi  4  *  12

                                                            = 24 pi = 75.398 in^3

Answer:

Step-by-step explanation:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The radius is 4.5cm.

Step-by-step explanation:

Circumference is the distance around the outside of a circle, the perimeter of the circle. Circumference formula is:

C = pi•d OR

C = 2•pi•r

Since we are looking for radius, use the second formula.

C = 2•pi•r

28.26 = 2pi•r

Divide by 2pi.

28.26/2pi = r

r = 4.5

The radius is 4.5 cm.

Answer:

2) -1, 0, 1, 2, 3, 4

3) 78, -2 , 1

Step-by-step explanation:

2) Substitute the x into the equation.

3) Substitute the 9 as the x value into the function so ([tex]9^2[/tex]) -3 = 78 etc.

The value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.

In mathematics, the summation is the addition of a sequence of any kind of numbers, called addends or summands.

Now we have a given term

[tex]\sum_{n=1}^{4} 3(4)^{n-1}[/tex]

By solving the above term;

[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^{1-1}+3(4)^{2-1}+3(4)^{3-1}+3(4)^{4-1}[/tex]

[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^0+3(4)^1+3(4)^2+3(4)^3[/tex]

[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3 + 12 +48 + 192[/tex]

Hence the value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.

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Answer:

1. 3 + 12 +48 + 192

2. 255 edge

Step-by-step explanation:

Answer:

x = 18

Step-by-step explanation:

given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 15 when x = 9 , then

15 = 9x ( divide both sides by 9 )

[tex]\frac{15}{9}[/tex] = x , that is

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

y = [tex]\frac{5}{3}[/tex] x ← equation of variation

when y = 30 , then

30 = [tex]\frac{5}{3}[/tex] x ( multiply both sides by 3 to clear the fraction )

90 = 5x ( divide both sides by 5 )

18 = x

Answer:

A=34 B=20

Step-by-step explanation:

A: y=6(5)+4 (34)

B: y=45-(9(2)+7)

y= 45-(18+7)

y=45-25 (20)

Answer:

c = -13.78.

Step-by-step explanation:

21.2x + c  ≡ 5.3(4x - 2.6)

21.2x + c  ≡ 21.2x - 13.78

Equating constant terms:

c = -13.78.

Answer:

13.78

Step-by-step explanation:

21.2x + c = 5.3(4x - 2.6)

open the bracket

21.2x + c = 21.2x - 13.78

collect like terms

c + 13.78 = 21.2x - 21.2x

c + 13.78 = 0

c = -13.78

Answer:

y-intercept = (-2,0)

Step-by-step explanation:

the "C" is the answer

Answer:

27/2 in^3 or 13.5 in^3 as a mixed fraction

Step-by-step explanation:

V=whl

Simplify the following:

(1 + 1/2) (2 + 1/4)×4

Put 1 + 1/2 over the common denominator 2. 1 + 1/2 = 2/2 + 1/2:

(2/2 + 1/2) (2 + 1/4)×4

2/2 + 1/2 = (2 + 1)/2:

((2 + 1)/2) (2 + 1/4)×4

2 + 1 = 3:

3/2 (2 + 1/4)×4

Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:

(3×4)/2 ((4×2)/4 + 1/4)

4×2 = 8:

(3 (8/4 + 1/4)×4)/2

8/4 + 1/4 = (8 + 1)/4:

(3×4)/2 ((8 + 1)/4)

8 + 1 = 9:

3/2×9/4×4

3/2×9/4×4 = (3×9×4)/(2×4):

(3×9×4)/(2×4)

(3×9×4)/(2×4) = 4/4×(3×9)/2 = (3×9)/2:

(3×9)/2

3×9 = 27:

Answer: 27/2 or 13.5 as a mixed fraction

Answer:

Area of shaded region=41 square feet

Area of non shaded region= 87 square feet

Step-by-step explanation:

As, Shaded area is made of different shapes including two rectangles and one triangle

So,

Area of shaded region,

[tex]=(8\times2)+(10\times 1)+(\frac{1}{2}\times 3\times10)\\\\ =16+10+15=41 \quad \text{square feet}[/tex]

Area of non shaded region=total area of rectangular region-Shaded region

[tex]=(16\times 8)-(41)\\=128-41\\=87 \quad \text{square feet}[/tex]

Answer:

( 16 × 8 )-40

128 -40

=87 square feet

Answer:

The surface area of cone = 54π cm²

Step-by-step explanation:

Given ;

Radius = 3 cm

slant height = 15cm

The surface area of cone = πr ( r + l )

=> π × 3 ( 3 + 15)

=> π × 3 ( 18)

=> 54 π cm²

Answer:

Option a

Explanation :

check out my attached work

Hope it helps, let me know if you have any questions !

Have a nice rest of your day :)

Answer:

Step-by-step explanation:

22000-18700=3300

3300/22000x100=15%

Answer:

It is a 15 percent decrease

Step-by-step explanation:

Divide 18700 by 22000, and your answer will be 0.85 but its asking for the decrease, 100-85=15, so 15% is the decrease.

Answer:

[tex]0 = log_{10} 1[/tex]

Step-by-step explanation:

Base for the exponent and for the logarithm are the same!

10^0 is the exponential form where 10 is the base and 0 the exponent

[tex]log_{10} 1[/tex] is the logarithm form where 10 is the base

To solve [tex]log_{10} 1 =[/tex]   ask the question :

To what power should I raise the base 10 to obtain the number 1 ?

The answer to the power 0 therefore

[tex]log_{10} 1 = 0[/tex]

[tex]1 = 10^{0} -is-the- exponential -form\\0 = log_{10} 1 - is -the -logarithmic -form[/tex]

Answer:

8a³b²c(9a²b - 4c)

Step-by-step explanation:

The GCF of 72 and 32 is 8.

72a^5b^3c - 32a^3b^2c^2 = 8a³b²c(9a²b - 4c)

Answer:

The vertex of the function is (1.333, 4.667)

Step-by-step explanation:

1. Calculate -b / 2a. This is the x-coordinate of the vertex.

2. simply plug -b / 2a into the equation for x and solve for y.

[tex]Y = 3x^{2} - 8x + 10\\Compare with the form of y = ax^{2} + bx + c\\So that means a = 3, b = -8, and c = 10.[/tex]

Calculate -b/2a:

[tex]X = -(-8)/2(3)[/tex]

[tex]X = 8/6[/tex]

This is equal to 1.33 recurring

Plug 8/6 for x and solve for y:

[tex]Y = 3x^{2} - 8x + 10[/tex]

[tex]Y = 3(\frac{8}{6})^{2} - 8(\frac{8}{6}) + 10[/tex]

[tex]Y = \frac{48}{9} - \frac{64}{6} + 10\\[/tex]

This is equal to 4.66 reccuring.