In order to find the height of a cliff, you stand at the bottom of the cliff, walk 60 feet
from the base, and place a mirror on the ground. Then you face the cliff and step back
5 feet so that can see the top of the cliff in the mirror. Assuming your eyes are 6 feet
above the ground, explain how to use this information to find the height of the cliff.
(The angles marked congruent are congruent because of the nature of the reflection of
light in a mirror.)
Q5ft
60 ft
K
Mirror

Answer:

10 weeks

Step-by-step explanation:

Answer: 26 weeks

Step-by-step explanation:

This is an example of an arithmetic sequence.

The first term = 3.5

common difference = 0.5

Using the formula for calculating the nth term of an arithmetic sequence :

[tex]t_{n}[/tex] = a + (n - 1 ) d

Therefore :

16.5 = 3.5 + ( n - 1 ) x 0.5

16. 5 = 3.5 + 0.5n - 0.5

16.5 = 3 + 0.5n

16.5 - 3 = 0.5n

13.5 = 0.5n

n = 13.5/0.5

n = 27

Therefore , it will take the cat (n-1)  weeks to weigh 16.5 ounce, which will be 27 - 1 = 26

check:

3.5 + 26 ( 0.5)

= 3.5 + 13

= 16.5

Answer:

(8, 10, 12, 14, 16) is the set which describes the set of even integers from 8 to 16

Step-by-step explanation:

To find the set of even integers from 8 to 16 as below :

There are 8,10,12,14,16 even integers in between the numbers 8 and 16

Therefore (8, 10, 12, 14, 16) is the set which describes the set of even integers from 8 to 16

using the multiplication property of equality to multiply both sides of the equation by 10

Step-by-step explanation:

Given equation is:

[tex]\frac{x+3}{2} = \frac{3x+5}{5}[/tex]

One method to solve this equation is cross-multiplication which the student has used.

One of the alternate method can be multiplying both sides by the LCM of numerators of fractions on both sides

So multiplying both sides by 10 (multiplication property of equality)

[tex]\frac{x+3}{2} * 10 = \frac{3x+5}{5} * 10\\5(x+3) = 2(3x+5)\\5x+15 = 6x+10\\5x+15-10 = 6x\\6x = 5x+5\\6x-5x = 5\\x = 5[/tex]

The alternate method of LCM produces the same answer so the correct answer is:

using the multiplication property of equality to multiply both sides of the equation by 10

Keywords: Linear equations, variables

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Answer:

using the multiplication property of equality to multiply both sides of the equation by 10

Step-by-step explanation:

Answer:

(3f - 2)²

Step-by-step explanation:

Given

9f² - 12f + 4

Consider the factors of the product of the coefficient of the f² term and the constant term which sum to give the coefficient of the f- term.

product = 9 × 4 = 36 and sum = - 12

The factors are - 6 and - 6

Use these factors to split the f- term

9f² - 6t - 6t + 4 ( factor the first/second and third/fourth terms )

= 3f(3f - 2) - 2(3f - 2) ← factor out (3f - 2) from each term

= (3f - 2)(3f - 2)

= (3f - 2)²

Answer:

9f² - 12f + 4 = (3f - 2)²

Step-by-step explanation:

9f²-12f+4 =

= (3f)²-2×(3f)×(2)+2²

= (3f-2)²

Step-by-step explanation:

All sides are congruent, therefore is an equilateral triangle.

It's also an isosceles acute triangle because two sides are congruent and all angles are acute.

It's also an isosceles triangle because two sides are congruent.

Answer:

Step-by-step explanation:

5x+2y=9.......(1)

x+y= -3.........(2)

Making y as subject bin (2)

y = -3 - x

Substituting in (1)

5x + 2(-3 - x) = 9

5x - 6 - 2x = 9

3x = 9 + 6

3x = 15

x = 15/3

x = 5

And y = -3 - x

y = -3 - 5

y = -8

Answer:

The solution for the system of linear equations is x = 5, y = -8

Step-by-step explanation:

Let's solve the system of linear equations by substitution:

5x + 2y = 9

x + y = -3

Solving for x in the 1st equation, this way:

5x + 2y = 9

5x = 9 - 2y

x = (9 - 2y)/5

Substituting x in the 2nd equation:

x + y = -3

(9 - 2y)/5 + y = -3

9 - 2y + 5y = - 15 (Multiplying by 5 at both sides)

3y = - 15 - 9

y = -24/3

y = - 8

Substituting y in the 1st equation:

5x + 2y = 9

5x + 2 * - 8 = 9

5x - 16 = 9

5x = 25

x = 25/5 = 5

The solution for the system of linear equations is x = 5, y = -8

Answer:

{-6, -5, -4, -3, -2, -1}.

Step-by-step explanation:

The set contains the integer -6  ( because of the ≤ )  but not 0 because of the < 0.

Answer:

5

Step-by-step explanation:

G=20

20÷4=5

Hope this helps!

Answer:

∠CIS.

Step-by-step explanation:

This angle is opposite from the smallest side. Therefore, according to the triangle inequality, it is the smallest angle.

The smallest angle that the angular momentum vector can make with the z-axis for an electron with quantum number l=2 is found using the magnetic quantum numbers. For m₁=+2, the angle would be the smallest, approaching 0 degrees.

The question pertains to the calculation of the smallest angle that the angular momentum vector ℓ can make with the z-axis given the quantum number l for an electron. To find this, we use the concept of quantized angular momentum in quantum mechanics.

For an electron with a quantum number l=2, it can have multiple magnetic quantum numbers m₁, ranging from -l to +l. Therefore, for l=2, m₁ can be -2, -1, 0, 1, or 2. Each of these values corresponds to a different angle with the z-axis.

The smallest angle corresponds to the maximum value of m₁, which is 2 in this case. The formula cos 0 = Lz/L uses the magnetic quantum number m₁ and the total angular momentum to calculate the cosine of the angle. For m₁=+1, the value of cos 0 would be 0.707, using the provided ratios and simplifying the formulas given. This corresponds to an angle whose cosine is 0.707, which through the inverse cosine function can be determined to be approximately 45 degrees. However, for m₁=+2, the angle would be even smaller, approaching 0 degrees as the z-component of angular momentum becomes maximally aligned with the z-axis.

Answer:

Step-by-step explanation:

3games cost38.97 so you have to divide 38.97divided by 3=12.99 so each game was 12.99 a game

To determine the cost of 1 game, set up an equation: 3n = $38.97. Divide both sides of the equation by 3 to isolate n. The cost of one game is $12.99.

To find the cost of one game, we can set up the equation 3n = $38.97based on the given information. where n represents the cost of one game. Since each game costs the same amount, we can write the equation:

3n = $38.97

Divide both sides of the equation by 3:

n = $38.97 / 3

Dividing both sides of the original equation by 3 is a way to undo the multiplication by 3 on the left side, thereby isolating the variable n.

When we perform this division, we find that n is equal to $12.99.

n = $12.99

Therefore, the cost of one game is $12.99.

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Answer:

12x^2 + 30x + 12

Step-by-step explanation:

Expand the equation using FOIL (First Outside Inside Last)

Hope this helps! :]

Answer:

To solve this inequality you need to get m by itself

3m+10<30 (First subtract 10 from each side)

3m<20 (10-10=0, 30-10=20) (Then divide each side by 3)

m< 20/3 or 6.666666

So your answer is any that is less than 6.66666

Your answer would be 5

5

Hope this helps ;)

Answer:

86,475 people live in poverty.

Step-by-step explanation:

We are given that the Total Cincinnati population is [tex]X_{TOT}=301,305[/tex] people.

We want to find the [tex]28.7[/tex]% of the Total population that lives in poverty. To do so we can use:

[tex]X_{POV}=\frac{28.7}{100}X_{TOT}[/tex]

where [tex]X_{POV}[/tex] is the amount of people that live in poperty. Plugging in values and solving we have:

[tex]X_{POV}=\frac{28.7}{100}301,305 \\X_{POV}=0.287*301,305\\X_{POV}=86,474.535[/tex]

However since here we are referring to number of people (i.e. population) we can not accept any irrational values so we need to round up our value so that

[tex]X_{POV}=86,475[/tex] people live in poverty in Cincinnati.

To find how many people live in poverty in Cincinnati, multiply the city's total population by the given percentage (expressed as a decimal). In this case, it is 301,305 * 0.287, which equals 86,574. Thus, an estimated 86,574 people live in poverty in Cincinnati.

To find out how many people live in poverty in Cincinnati, you need to calculate 28.7% of the city's total population. To calculate the percentage of a number, you can multiply that number by the percentage expressed as a decimal. The calculation will look like this:

Population x Percentage = Number of people in poverty

So, it will be:

301,305 x 0.287 = 86,574.135

Normally in population estimates, we don't count fractions of people, so we'll round this down to the nearest whole number. Therefore, the number of people living in poverty in Cincinnati is approximately 86,574.

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The quotient of 26,208 divided by 42 is 624. This is a straightforward division problem that can often be solved using a calculator or through long division by hand.

To find the quotient of 26,208 divided by 42, you need to perform a division operation. When you divide 26,208 by 42, you'll find that the answer is 624 without any remainder. This is a straightforward division problem that can often be solved using a calculator or through long division by hand.

Answer:

9 cups per bag

Step-by-step explanation:

1/12 bag = 3/4 cup

12/12 bag = ? cup

1/12 × 12 = 12/12

3/4 × 12 = 36/4

36/4 = 9

Answer: 9 cups per bag

Step-by-step explanation: Apply the division rule of fractions: multiply the numerator by the reciprocal of the denominator.

3/4

1/12

=

3/4

×

12/1

=

36/4 = 9 cups per bag

Answer: B) Tutored Alexander The Great

Step-by-step explanation: k12 test 1.12, :)

Answer:

Step-by-step explanation:

Let angle Q = x°

Angle P = (2x - 3)°

And angle P and Q are supplementary angle which implies there sum is 180°

x + 2x - 3 = 180

3x = 180 + 3

3x = 183

x = 183/3

x = 61°

Angle Q = 61°

Angle P = 2x - 3

Angle P = 2(61) - 3

Angle P = 122 - 3

Angle P = 119°

The ordered pair (-3, 1) is not a solution to system because it makes at least one of the equations false

Solution:

Given system of equations are:

x - 4y = 6 ------- eqn 1

3x + y = -8 ------------ eqn 2

Given ordered pair is (-3, 1)

We have to check if the options are true

Let us substitute (x, y) = (-3, 1) in eqn 1

[tex]-3 - 4(1) = 6\\\\-3 - 4 = 6\\\\-7\neq 6[/tex]

Thus the given ordered pair (-3, 1) did not satisfy the first equation

Substitute (x, y) = (-3, 1) in eqn 2

[tex]3(-3) + 1 = -8\\\\-9 + 1 = -8\\\\-8 = -8[/tex]

Thus the given ordered pair (-3, 1) satisfied the second equation

But for a ordered pair to be a solution to system of equations, it must satisfy both the equations

Thus the ordered pair (-3, 1) is not a solution to system because it makes at least one of the equations false

Answer:

O B. y = -2x+6

Step-by-step explanation:

The height of tree is 32 meter

Solution:

Given that,  The sun is at an angle of elevation of 58 degree

A tree casts a shadow 20 meters long on  the ground

The sun, tree and shadow forms a right angled triangle

The figure is attached below

ABC is  a right angled triangle

AC is the height of tree

AB is the length of shadow

AB = 20 meters

Angle of elevation, angle B = 58 degree

By definition of tan,

[tex]tan \theta = \frac{opposite}{adjacent}[/tex]

In this right angled triangle ABC,

opposite = AC and adjacent = AB

Therefore,

[tex]tan\ 58 = \frac{AC}{AB}\\\\tan\ 58 = \frac{AC}{20}\\\\1.6 = \frac{AC}{20}\\\\AC = 1.6 \times 20\\\\AC = 32[/tex]

Thus height of tree is 32 meter

Final answer:

To determine the height of the tree using the angle of elevation of the sun and the shadow length, apply the tangent function. With an elevation of 58º and a shadow of 20 meters, the tree’s height is calculated to be approximately 33.94 meters.

Explanation:

To find the height of the tree given the angle of elevation of the sun and the length of the shadow it casts, we can make use of trigonometry. Specifically, we will use the tangent function, which relates the angle of elevation with the opposite side (the height of the tree) and the adjacent side (the length of the shadow).

Step-by-step solution:

Thus, the height of the tree is approximately 33.94 meters.

Answer: 640

Step-by-step explanation:

You can break 16 up into 10 and 6: 40(10+6)

40(10)+40(6)

400+240

640

Final answer:

To solve 40x16, break apart the numbers into tens and use the distributive property to calculate the partial products, then sum up these products to get the final result of 640.

Explanation:

To solve 40x16 by breaking apart the numbers, you can use a strategy known as decomposing or partial products. Here's a step-by-step explanation:

Break apart the number 40 into 10s: 40 = 30 + 10.

Break apart the number 16 into 10s: 16 = 10 + 6.

Now use the distributive property to multiply each part:

(30 + 10) × (10 + 6)

Multiply each part individually: 30 x 10, 30 x 6, 10 x 10, and 10 x 6.

Calculate the partial products: 300, 180, 100, and 60.

Finally, add all the partial products: 300 + 180 + 100 + 60 = 640.

So, 40x16 equals 640 when you apply the breaking apart method.

Answer:

  24 minibites

Step-by-step explanation:

The cost of protein in the snack pack is ...

  $0.50/(4 g) = $0.125/g

The cost of protein in the minibites is ...

  $0.12/(1 g) = $0.120/g

Since the cost of protein is less for minibites, and the only criterion is the amount of protein, the lowest-cost snack mix is 24 minibites.

Answer:

24 minibites

Step-by-step explanation:hoped tt his helped

Answer:

f ( 4 ) = 18

Step-by-step explanation:

Explanation:

f ( x ) = 5 x − 2

Replace  4  instead of  x  to find  f ( 4 )

f ( 4 ) = 5 ( 4 ) − 2 = 20 − 2 = 18

The value of f(-4) for the function f(x) = x^2 - 5x + 2 is 38.

To find the value of f(-4) for the function f(x) = x^2 - 5x + 2, you substitute -4 for x in the function.

It looks like this:

f(-4) = (-4)^2 - 5(-4) + 2

First, you square -4, which is (-4)^2 = 16.

Then, you calculate -5 times -4, which is 20.

Finally, you add 2 to the result.

So, f(-4) is equal to:

f(-4) = 16 - 20 + 2 = 38

The final answer is 38.

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Answer:

The nth term of the given arithmetic sequence is [tex]a_n=-17+(n-1)9[/tex]

Step-by-step explanation:

Given sequence is -17,-8,1,...

To find the nth term of the given sequence :

Let  [tex]a_1=-17,a_2=-8,a_3=1,...[/tex]

To find the common difference d :

[tex]d=a_2-a_1[/tex]

[tex]=-8-(-17)[/tex]

[tex]=-8+17[/tex]

Therefore d=9

[tex]d=a_3-a_2[/tex]

[tex]=1-(-8)[/tex]

[tex]=1+8[/tex]

Therefore d=9

The common difference d is 9

Therefore the given sequence is an arithmetic sequence

The nth term of an arithmetic sequence is given below

[tex]a_n=a_1+(n-1)d[/tex]

Substitute [tex]a_1=-17[/tex] and d=9 in the above equation we get

[tex]a_n=-17+(n-1)9[/tex]

Therefore the nth term of the given arithmetic sequence is [tex]a_n=-17+(n-1)9[/tex]

The formula for the nth term of the sequence -17, -8, 1 is a_n = 9n - 26, where n is the position of the term in the sequence.

The sequence provided is -17, -8, 1, which suggests that there is a common difference between terms since it is an arithmetic sequence. To find the nth term of an arithmetic sequence, we use the formula a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference. In this case, the common difference is 9 (since -8 - (-17) = 9).

So, using the formula for the nth term of an arithmetic sequence:

Our formula becomes a_n = -17 + (n - 1) × 9. Simplifying this:

a_n = -17 + 9n - 9

a_n = 9n - 26

Therefore, the formula for the nth term of the given sequence is a_n = 9n - 26.

Answer:

A. 7

Step-by-step explanation:

my unit test review said the other persons answer was wrong and it said this was right so ya.

The length of one leg of the given triangle is 1 unit.

The square of the hypotenuse is equal to the sum of the squares of other two sides.

Given the following parameters;

Hypotenuse = √2

If the lengths of the other two sides are congruent, thus;

x² + x² = (√2)²

2x² = 2

x² = 2/2

x² = 1

x = 1

Hence, the length of one leg of the triangle is 1 unit.

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Answer:

U were 20% off

Ure estimate was 80%

Step-by-step explanation:

16/20 is 80%

100%-80% is 20%

The width of rectangle is [tex]2\frac{1}{4}\ cm[/tex] and length is [tex]5\frac{5}{12}\ cm[/tex]

Step-by-step explanation:

Let,

Width of rectangle = w

Length of rectangle = w+[tex]3\frac{1}{6}=w+\frac{19}{6}[/tex]

Perimeter of rectangle = [tex]15\frac{1}{3}=\frac{46}{3}\ cm[/tex]

Perimeter of rectangle = 2(Length + Width)

[tex]2(w+\frac{19}{6}+w)=\frac{46}{3}\\2(2w+\frac{19}{6})=\frac{46}{3}\\4w+\frac{19}{3}=\frac{46}{3}[/tex]

Subtracting [tex]\frac{19}{3}[/tex] from both sides

[tex]4w+\frac{19}{3}-\frac{19}{3}=\frac{46}{3}-\frac{19}{3}\\4w=\frac{46-19}{3}\\4w=\frac{27}{3}\\4w=9[/tex]

Dividing both sides by 4

[tex]\frac{4w}{4}=\frac{9}{4}\\w=\frac{9}{4}[/tex]

Therefore,

Width of rectangle = w = [tex]\frac{9}{4}=2\frac{1}{4}[/tex] cm

Length of rectangle = [tex]w+\frac{19}{6}=\frac{9}{4}+\frac{19}{6}=\frac{27+38}{12}=\frac{65}{12}=5\frac{5}{12}\ cm[/tex]

The width of rectangle is [tex]2\frac{1}{4}\ cm[/tex] and length is [tex]5\frac{5}{12}\ cm[/tex]

Keywords: perimeter, addition

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