when a 6ft tall fence pole casts a 10 ft shadow, a pine tree casts a 45 ft shadow. How tall is the tree?

Answer:56

Step-by-step explanation:

Let ttt be the initial number of trees.

Hint #22 / 5

MacDonald now has t-5t−5t, minus, 5 trees and each one produced 210210210 oranges this harvest.

The total number of oranges produced is 210(t-5)210(t−5)210, left parenthesis, t, minus, 5, right parenthesis.

Hint #33 / 5

Since the trees produced a total of 417904179041790 oranges, let's set this equal to 417904179041790:

\qquad210(t-5)=41{,}790210(t−5)=41,790210, left parenthesis, t, minus, 5, right parenthesis, equals, 41, comma, 790

Now, let's solve the equation to find the initial number of trees (t)(t)left parenthesis, t, right parenthesis.

Hint #44 / 5

\begin{aligned}210(t-5)&=41790\\&\\ \dfrac{210(t-5)}{\blue{210}}&=\dfrac{41790}{\blue{210}}&&\text{divide both sides by $\blue{210}$}\\ \\ t-5&=199\\ \\ t-{5}\pink{+5}&=199\pink{+5}&&\pink{\text{add }} \pink{5} \text{ to both sides}\\ \\ t&=204\end{aligned}

210(t−5)

210

210(t−5)

​

t−5

t−5+5

t

​

=41790

=

210

41790

​

=199

=199+5

=204

​

​

divide both sides by 210

add 5 to both sides

​

Hint #55 / 5

The equation is 210(t-5)=41790.210(t−5)=41790.210, left parenthesis, t, minus, 5, right parenthesis, equals, 41790, point

MacDonald's farm initially had 204204204 orange trees.

Related content

The population of the city grew from 2010 to 2020 by 13.37%.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

We have to given that;

In 2010, the population of a city was 237,000.

And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.

We know that;

Where, A = P (1+r)ⁿ

A = final population.

P = Initial population.

r = rate

n = time

Hence, The population in 2015 is, =

A = 237,000(1 + 0.076)⁵

A = 341829.629

And, The population in 2020 =

A = P (1 - r)ⁿ

A = 341829.629 (1 - 0.047)⁵

A = 268704.047

So, Percent grow = (268704.047 - 237,000) / 237,000 × 100

                           = 31704.047 / 237,000 × 100

                            = 13.37 %

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Answer:

x=-3, y=1. (-3, 1).

Step-by-step explanation:

-x+5y=8

3x+7y=-2

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

3(-x+5y)=3(8)

3x+7y=-2

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

-3x+15y=24

3x+7y=-2

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

22y=22

y=22/22

y=1

-x+5(1)=8

-x+5=8

-x=8-5

-x=3

x=-3

Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population.

The null and alternative hypotheses are two opposing ideas that researchers use a statistical test to analyze evidence for and against: The null hypothesis (H0) states that there is no influence in the population. Alternative hypothesis (Ha or H1): There is a population effect.

Identify the null and alternative hypotheses.

As well as the sample size, specify.

Choose a suitable statistical test.

Gather information (note that the previous steps should be done prior to collecting data)

Based on the sample data, compute the test statistic.

Examine the null hypothesis, usually indicated by H0.

Always write the alternative hypothesis, which is usually marked by Ha or H1, with less than, greater than, or not equals symbols, i.e., (,>,or).

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Answer:

x=

y=31

Step-by-step explanation:

hope this helps

Answer:

16 ounces = 1 pint, 8 times 2 = 16

Step-by-step explanation:

Answer in explanation:

1 pint is 16 ounces so he could make 2 batches of lemonade with 1 pint of lemon juice.

(8 x 2 = 16

your answer is 2

Hope this helps!

Answer:

x = 11 and x = -1

Step-by-step explanation:

We have x^2−10x = 11 and want to make a perfect square out of x^2−10x.

To do this, take half of the coefficient of x, square this half, and then add and then subtract the square immediately following x^2−10x:

Half of -10 is -5, and the square of -5 is 25.

x^2−10x = 11 becomes x^2 - 10x + 25 - 25 = 11

Rewrite x^2−10x + 25 as the square of a binomial:  (x - 5)^2.

Then we have (x - 5)^2 - 25 = 11.  Solve this for x -5:

(x - 5)^2 = 36.  Taking the square root of both sides, we get

x - 5 = ±6

Then x = 11 and x = -1

The equation y = 5x - 8 and y = 9x - 8 have one solution at

(0, -8)

The equation is solved simultaneously by elimination method as follows

y = 5x - 8

y = 9x - 8

subtraction the equations

0 = -4x - 0

-4x = 0

x = 0

substituting x = 0 into y = 5x - 8

y = 5x - 8

y = 5 * 0 - 8

y =0 - 8

y = -8

The solution of the equation is at the point (0, -8)

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If the pickup charge for taxi is $3.50 and additional charge of $0.75 per mile , then the cost for riding 5 miles is $7.25  and cost for riding m miles is $[tex]3.50+0.75m[/tex]   .

The pickup charge that taxi service charges is = $3.50  ;

the additional charge for per miles driven is = $0.75  ;

we have to find the cost for riding 5 miles ;

So , the total cost for riding 5 miles is = [tex]Pickup Charge + (Additional Charge)\times(Number Of Miles Driven)[/tex] ;

substituting the values , the total cost equation becomes ;

[tex]Total Cost = 3.50 + 0.75\times5[/tex]

= [tex]3.50+3.75[/tex]

= 7.25

So , the cost for 5 miles is = $7.25  ;

to find cost for driving "m" miles ,we substitute the number of miles = m;

[tex]Total Cost = 3.50+0.75\times m[/tex]

= [tex]3.50+0.75m[/tex]

Therefore , the cost for riding m miles is $ [tex]3.50+0.75m[/tex] .

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Answer:

Average Rate = -14/7

Step-by-step explanation:

f(3) = 3^2 - 3 - 8 = -2

f(-4) = (-4)^2 - (-4) - 8 = 12

interval: [-4, 3]

Average Rate = [f(b) - f(a)]/(b - a) interval: [a, b]

= [(-2) - 12] / [3 - (-4)]

= -14/7

The required two numbers are 9 and 41.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

Let x be the lesser number, and y be the greater number.

From the question, we know that:

x + y = 50 (Equation 1: The sum of the two numbers is 50)

y = 5x - 4 (Equation 2: The greater number is four less than five times the lesser number.)

The equation is to solve for one of the variables, and then substitute that value into the other equation to find the other variable.

Then, two numbers are x = 9 and y = 41.

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Answer:

8.8

Step-by-step explanation:

Normally, to find the distance between two points, you would use the distance formula, but these two points have the same x-coordinate, meaning they will form a vertical line when connected. To find the length of a vertical line you find the distance between the y-coordinates, in this case -4.7 and 4.1. Finding the distance is the same as finding the absolute value of the difference:

|4.1 -(-4.7)|

|4.1 + 4.7|

|8.8|

8.8

Answer:

23.88 feets

Step-by-step explanation:

C=2π2

=2×3.142×3.8

=23.8792 feets

rounded to the nearest TENTH

=23.88 feets

Answer:

Step-by-step explanation:

Answer is 6 units

Answer:

6 units fs

Step-by-step explanation:

so for given expression x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

we can start by squaring the equation x²+(1/x)=3

so we have x⁴ + 2x² + (1/x)² = 9

x⁴ + 2x² + 1 = 9x²

x⁴ - 7x² + 1 = 0

Now we can factor it

(x²-1)(x²-1) = 0

so x² = 1

now we can substitute x² = 1 in the equation x⁴-2x³-x²-2x+1

x⁴-2x³-x²-2x+1 = x⁴-2x³-1-2x+1

= x⁴-2x³-2x-1

= (x⁴-2x³) - (2x+1)

= x⁴-2x³-2x-1

= (x²-x)² - (2x+1)

= (x-1)² - (2x+1)

so x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)

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The best answer from the choices provided is a = plus-or-minus 16 . Option C

A quadratic equation can be defined as an equation that can be rearranged in a standard form

Such that;

These quadratic equation are also described as polynomial equation having its highest degree as 2.

From the information given, we have that;

3a² - 21 = 27

collect like terms

3a² = 27 + 21

Add the values

3a² = 48

Divide both sides by 3

a² = 48/3

a² = 16

Hence, the value is a² = 16

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Answer:

x=5, y=3

Step-by-step explanation:

y=x−2;4x+y=23

Step: Solve y=x−2 for y:

Step: Substitute x−2 for y in 4x+y=23:

4x+y=23

4x+x−2=23

5x−2=23(Simplify both sides of the equation)

5x−2+2=23+2(Add 2 to both sides)

5x=25

5x/5 = 25/5(Divide both sides by 5)

x=5

Step: Substitute 5 for x in y=x−2:

y=x−2

y=5−2

y=3(Simplify both sides of the equation)

Here's link[tex]^{}[/tex] to the answer:

bit.[tex]^{}[/tex]ly/3gVQKw3

Carman buy the video game in the cost of $45.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Carman has saved 80% of the money she needs to buy a new video game.

And, she saved the cost $36.

Let total cost of the video game = x

So, We can formulate;

⇒ 80% of x = $36

⇒ 80/100 × x = 36

⇒ 8x = 360

⇒ x = $45

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Yes, 6/8 and 9/12 are equal. After simplifying both the fractions we got that both are equal and their value is 3/4.

Let's first try to understand what is a fraction.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

A fraction would be 5/10, for instance.

Here, the numerator is 5 and the denominator is 10.

6/8 is a fraction.

6/8 can be simplified further.

6/8 = 3/4

9/12 is also a fraction.

9/12 can be simplified further.

9/12 = 3/4

To compare 2 fractions first we try to make the same denominator.

we have the same value. so they are equivalent.

Given question is incomplete complete the question here:

Are 6/8 and 9/12 equivalent?

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Answer:

[tex]\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}[/tex]

Step-by-step explanation:

Inverse of a matrix is given by,

[tex]\begin{bmatrix}a & b\\ c & d\end{bmatrix}=\frac{1}{ad-bc}\begin{bmatrix}d & -b\\ -c & a\end{bmatrix}[/tex]

By using this property,

[tex]\begin{bmatrix}5 & 4\\ 3 & 2\end{bmatrix}^{-1}=\frac{1}{(5\times 2-4\times 3)}\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}[/tex]

              [tex]=-\frac{1}{2}\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}[/tex]

              [tex]=\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}[/tex]

Therefore, inverse of the given matrix will be [tex]\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}[/tex]

There are  17/36 pounds of trail mix in each bag.

you need to first add the weight of the peanuts and M&M's together.

1[tex]\frac{17}{18}[/tex] + 1 [tex]\frac{5}{6}[/tex] =([tex]\frac{35}{18}[/tex]) +([tex]\frac{11}{6}[/tex]) =  [tex]\frac{35+33}{18}[/tex]    =[tex]\frac{68}{18}[/tex]

which can be simplified to 3 [tex]\frac{14}{18}[/tex]

So there are 3 [tex]\frac{14}{18}[/tex]pounds of trail mix altogether.

3 [tex]\frac{14}{18}[/tex]÷ [tex]\frac{8}{1}[/tex] =

[tex]\frac{68}{18}[/tex]  ÷  [tex]\frac{8}{1}[/tex]=[tex]\frac{68}{144}[/tex]

which can be simplified to [tex]\frac{17}{36}[/tex]

So there are [tex]\frac{17}{36}[/tex]pounds of trail mix in each bag.

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Answer:  First, let's consider the rotation of 180 degrees clockwise. This can be thought of as a reflection over the x-axis, followed by a reflection over the y-axis.

The reflection over the x-axis will negate the y-coordinate, while the reflection over the y-axis will negate the x-coordinate. So after the rotation, the coordinates of point C will become (-5,-5)

Next, we'll consider the translation 5 units up. Translating a point up means that we'll add 5 to its y-coordinate. So the coordinates of point C'' will become (-5,-5) + (0, 5) = (-5, 0)

So the coordinates of C'' are (-5,0)

Therefore the answer is B.

Step-by-step explanation:

Answer:

C = 31

Step-by-step explanation:

always do the parenthesis first so (2+4) = 6

3² + 4(6) x 6 ÷ 8 + 4 (Use PEMDAS)

9 + 4(6) x 6 ÷ 8 + 4, multiply 4 and 6

9 + 24 x 6 ÷ 8 + 4, multiply 24 and 6

9 + 144 ÷ 8 + 4, divide 144 and 8

9 + 18 + 4, now just add

31.

Answer:

c) 31

Step-by-step explanation:

9 + 4(6) * 6 / 8 + 4

9 + 24 * 6 /8 + 4

9 + 144 / 8 + 4

9 + 18 + 4

= 31

angle ADC equals 74 degrees