Igor, whose eye height is 4. 5 ft. , wishes to find the height of an oak tree out in front of his castle. He places a mirror on the ground between himself and the tree. He is now 5. 5 feet away from the center of the mirror and the mirrors is 70 feet from the tree. What is the height of the oak tree in front of Igor´s castle?

Answer:

11 :)

Step-by-step explanation:

Answer:

\(p=132cm^2\)

Step-by-step explanation:

Given the following question:

Formula for perimeter:

\(2(s+b)\)

We are given a base and a length for this parallelogram. So, to find the perimeter we simply have to substitute the values into the formula and solve.

\(2(s+b)\)
\(2(34+32)\)
\(34+32=66\)
\(2(66)\)
\(2(66)=2\times66=132\)
\(p=132cm^2\)

Hope this helps.

The steps to construct a parallelogram using a ruler and a compass are;

1. Draw a starting line segment l linger than 8 cm.

2. Mark point K on the line segment.

3. Widen the compass to a radius of 8 cm using the ruler.

4. Place the compass at point K and with the 8 cm radius mark point L on the line l.

5. At point L construct a 45° angle as follows;

The above steps bisects the 90° angle of the perpendicular lines.

6. Adjust the radius of the compass to give an opening of 6 cm and from point L draw an arc to intersect XL at M.

7. At point M construct a line YM at 45° angle to the line l.

8. From point M draw an arc to intersect YM and label the point as point N.

9. Join point M and N to complete the construction of the parallelogram KLMN.

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Answer:

14 189,40 United States Dollar

Answer:

this is K12 approved

I hope you have a fantastic day

Answer: -3x + 6

Step-by-step explanation:

Multiply using the disturbutive property.

Answer:

-3x + 6

Step-by-step explanation:

-3x - 3x (-2)

multiply it

-3x+6

The mathematical equation in the statement is (c) -10(r  + 12.5) = 60.5

From the question, we have the following statement that can be used in our computation:

Negative ten times the sum of a number and 12.5 is 60.5.

Represent the number with r

So, we have the following representation

Negative ten times the sum of r and 12.5 is 60.5.

Mathematically, this statement can be expressed as

-10 * (r  + 12.5) = 60.5

Hence, the expression is -10(r  + 12.5) = 60.5

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Answer:

V = pi x radius x 2 x height OR pi x diameter x height

Hope that helps!

Answer:

the formula for the volume of a cylinder is V=πr²h

Answer:

sry u dont have the table

Step-by-step explanation:

To determine the number of smaller boxes that would contain the same amount of cereal as a larger box, we set the expressions representing the cereal content equal to each other. Solving the equation, we find that 15 smaller boxes are required to match the cereal quantity in the larger box.

To find the number of smaller boxes that equal the same amount of cereal in a larger box, we need to equate the two expressions and solve for n.

Setting the expressions equal to each other:

10 + 6.3n = 7 + 6.5n

Simplifying the equation:

6.3n - 6.5n = 7 - 10

-0.2n = -3

Dividing both sides by -0.2:

n = -3 / -0.2

n = 15

Therefore, 15 smaller boxes would equal the same amount of cereal as the larger box.

The problem states that the expressions 10 + 6.3n and 7 + 6.5n represent the amount of cereal in the new larger box. The variable n represents the number of smaller boxes.

To find how many smaller boxes are equivalent to the larger box, we need to set the two expressions equal to each other and solve for n. This equation represents the balance between the amount of cereal in the larger box and the combined amount of cereal in the smaller boxes.

By simplifying the equation and solving for n, we find that 15 smaller boxes are needed to equal the same amount of cereal as the larger box.

This means that if the cereal manufacturer wants to package the same amount of cereal as the larger box, they would need to use 15 smaller boxes instead. This calculation helps the manufacturer determine the number of smaller boxes needed to maintain the same quantity of cereal while changing the box size.

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Answer:

x = 240°, x = 300°

Step-by-step explanation:

Using the identity

sin x = \(\frac{1}{cosecx}\) = \(\frac{1}{-\frac{2}{\sqrt{3} } }\) = - \(\frac{\sqrt{3} }{2}\) , then

x = \(sin^{-1}\) ( \(\frac{\sqrt{3} }{2}\) ) = 60° ← related acute angle

Since sin x < 0 then x is in 3rd / 4th quadrants

x = 180° + 60° = 240°

x = 360° - 60° = 300°

Step-by-step explanation:

6x=2x+5

6x-2x=5

4x=5

4x/4=5/4

X=1.25

A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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Answer:

  9 cm²

Step-by-step explanation:

Sometimes these inscribed polygon problems respond nicely to a little geometrical thinking. The figure is symmetrical about the vertical line through the center of the square(s).

__

That line of symmetry divides the figure into halves that are twice as tall as wide. That same ratio applies to both the outer square and the inner (blue shaded) square.

In other words, a line from the center of the top segment through either bottom corner of the figure will pass through the corners of both squares. That line will have a slope of ±2, making it easy to find the coordinates of one of the lower corners of the shaded square.

__

Analytically, we can write the equation of the right circle shown in the attachment as ...

  x² +y² = 5²

and the equation of the line as ...

  y = 2x +5

__

Then the x-value of the lower left corner will be found where these intersect.

  x² +(2x +5)² = 25 . . . . . . substitute for y

  x² +4x² +20x +25 25 . . . . eliminate parentheses

  5x² +20x = 0 . . . . . . . . . . . . subtract 25

  5x(x +4) = 0 . . . . . . factor

  x = -4 or 0 . . . . . the x-coordinates of the points of intersection

The y-coordinate of the lower left point is ...

  y = 2(-4) +5 = -3

__

Since the top edge of the blue square has a y-coordinate of 0, this means the square is 3 cm on a side. Its area is ...

  A = s² = (3 cm)² = 9 cm² . . . . area of the blue shaded square

Answer:

27 cm

Step-by-step explanation:

Multply each side. 4cm×4cm, 2cm×2cm and 3cm×3cm. After that, add them together.

Answer:

is

this the right picture??

Answer:

1). x = 14

2). y = 2.4 cm

Step-by-step explanation:

In the diagram ΔNPQ ~ ΔNLM and NL = 3,

1). ∠P ≅ ∠L [All angles of similar triangle are equal in measure]

   (3x + 18)° = 60°

   3x = 60 - 18

   x = 14

2). Since, both the triangles are similar, corresponding sides will be proportional.

   \(\frac{PN}{NL}=\frac{NQ}{NM}\)

   \(\frac{y}{3}=\frac{3.2}{4}\)

   y \(=\frac{3.2\times 3}{4}\)

   y = 2.4 cm

Answer: £6.80

Step-by-step explanation:

Kara bought 5 jumpers for the price of 4.  Thus, multiply 4.8*5 = 24.  Then divide 24/4 to get 6.

Hope it helps <3

Answer:

222222:#&&&#+17265262

The value of x at which the minimum value of y occurs in [0, 1] is B) 1/8

Given y = 3x^(4/3) - 2x

We are asked to determine the value of x at which the minimum value of y occurs in [0, 1].

                                    Now, dy/dx = 0

                                     4x^(1/3) - 2 = 0

                                             x^(1/3) = 1/2

                                                     x = 1/8

Here, dy/dx = 0 when x = 1/8

So calculating y at x = 0, 1/8, 1

y(x = 0) = 0

y(x = 1/8) =3 (1/8)^(4/3) - 2/8 =  -1/16

y(x = 1) = 1

Hence, y has a minimum value of -1/16 at x = 1/8

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The question is asking for the probability of the chain failing under the given load. The strength of the links is independent of each other. We can use Bernoulli's trial to solve this problem.

Let's define the probability of any one link not failing under the given load as `p = 1 - q`. Here, q is the probability that any one link will fail under the given load.

The probability that all n links will not fail under the load can be calculated as `P(success) = p^n`. Here, we multiply the probability of success of one link by the probability of success of another link and so on until the nth link.

The probability of the chain failing is the complement of the probability that all the links will not fail. Hence, `P(failure) = 1 - P(success) = 1 - p^n`.

Therefore, the probability of the chain failing under the given load is `1 - p^n` or `1 - (1 - q)^n`.

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The number of meters ahead is Sunny when Sunny finishes the second race is d meters.

Given data:

In the first race, Sunny is d meters ahead of Windy when Sunny finishes the race. This means that Sunny runs the entire h meters, while Windy runs h−d meters.

In the second race, Sunny starts d meters behind Windy, who is at the starting line. Since both runners run at the same constant speed as they did in the first race, they will finish the same h meters in the second race.

On analyzing the second race:

Windy starts at the starting line and runs the entire h meters.

Sunny starts d meters behind Windy and also runs the entire h meters.

On simplifying the expression:

Since both runners run the same distance, but Sunny starts d meters behind Windy, Sunny will finish d meters ahead of Windy in the second race.

Therefore, when Sunny finishes the second race, Sunny will be d meters ahead.

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The value of the highlighted interior angle is 130 degrees.

What are interior angles ?

In geometry, interior angles are angles that are formed inside a polygon. For a polygon with n sides, there are n-2 interior angles. The sum of the interior angles of a polygon depends on the number of sides it has.

For example, in a triangle (a polygon with 3 sides), there are 3 interior angles. The sum of these angles is always 180 degrees.

In a quadrilateral (a polygon with 4 sides), there are 4 interior angles. The sum of these angles is always 360 degrees.

In a pentagon (a polygon with 5 sides), there are 5 interior angles. The sum of these angles is always 540 degrees.

According to the question:

When two parallel lines are intersected by a transversal, the alternate interior angles are congruent.

Therefore, we can write:

angle A = angle B

Substituting the given expressions for angle A and angle B, we get:

19x - 3 = 18x + 4

Solving for x, we get:

x = 7

Substituting x = 7 into the expression for angle B, we get:

angle B = 18x + 4 = 18(7) + 4 = 130

Therefore, the value of the highlighted angle is 130 degrees.

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Tablespoons is an English unit for volume. This problem asks us to convert the given quantity into liters, a metric unit.  the correct order of conversions is explained below.

The correct order for the conversions to convert tablespoons to liters is as follows:

1 tablespoons -> 1/2 fluid ounce(fl oz)

1 fluid ounce->1/128 US gallon

1 US gallon -> 3.78541 liters

Therefore, to convert tablespoons to liters, we need to first convert tablespoons to fluid ounces, then fluid ounces to US gallons, and finally US gallons to liters. using these conversion factors, we can convert any given quantity in tablespoons to liters.

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Answer: I Think it's 20%

The reflected points for A and B over the x-axis are (0, -3) and (2, -1), respectively.

What is reflection?

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

It is given that the point A is (0,3) and B is (2,1).

To reflect a point over the x-axis, we keep the x-coordinate the same and negate the y-coordinate.

For point A, the x-coordinate is 0 and the y-coordinate is 3. Reflecting over the x-axis negates the y-coordinate, so the reflected point is (0, -3).

For point B, the x-coordinate is 2 and the y-coordinate is 1. Reflecting over the x-axis negates the y-coordinate, so the reflected point is (2, -1).

The graph is plotted for the points.

Therefore, the points are (0,-3) and (2,-1).

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The distance of the top of the square pyramid will be 10.5 unit.

It should be noted that based on the information, the hypotenuse theorem will be illustrated. This will be:

AC² = AB² + BC²

AB = length of the segment

BC and AC are the other two sides

This will be illustrated as:

AC² = 10² + (6/2)²

AC² = 100 + 9

AC² = 109

AC = ✓109

AC = 10.5

Therefore, the distance is 10.5 units.

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There are 2520 ways to divide the 10 distinct books among the three students with the given distribution.

To find the number of ways to divide 10 distinct books among three students with the given distribution (5 books for the first student, 3 books for the second, and 2 books for the third), you can use the combination formula:

C(n, r) = n! / (r! * (n - r)!)

Where "C" represents the number of combinations, "n" is the total number of items, and "r" is the number of items to choose. We'll apply this formula to each student's distribution, and then multiply the results to find the total number of ways.

1. First student (5 books from 10):
C(10, 5) = 10! / (5! * (10 - 5)!) = 252

2. Second student (3 books from the remaining 5):
C(5, 3) = 5! / (3! * (5 - 3)!) = 10

3. Third student (2 books from the remaining 2):
C(2, 2) = 2! / (2! * (2 - 2)!) = 1

Now multiply the results for each student:
Total number of ways = 252 * 10 * 1 = 2520

So, there are 2520 ways to divide the 10 distinct books among the three students with the given distribution.

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The exact value of sin(2θ) is calculated to be -√11/11.

This question can be solved by concepts of trigonometry.

To find the exact value of sin(2θ) if tan θ = 21/20 and π < θ < 3π/2:

Rearrange the equation tan θ = 21/20 to find the value of θ.
Substitute the value of θ into the equation sin(2θ).
Simplify the equation to find the exact value of sin(2θ).

The exact value of sin(2θ) is -√11/11.

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Answer:

The first option. "If lines on a coordinate plane have opposite reciprocal slopes, then they are perpendicular."

Step-by-step explanation:

It is the only one that makes sense, tbh. But, it includes the proper "if-then" form like the question requests it have. It also incorporates all aspects of the original statement-

a.) lines on a coordinate plane

b.) perpendicular

c.) opposite reciprocal slopes.

You're welcome. :D

Answer:

Its A

Step-by-step explanation:

edge 2021

Answer:

see answers below

Step-by-step explanation:

B = 180 -90 - 40 = 50° (angles in triangle add up to 180). so, 50 + 40 + 90 = 180.

Sine rule:   a/SIN A  =  b/SIN B  =   c/SIN C

b/sin 50 = 25/sin 40

b = (25 sin 50) / sin 40

= 29.8.

In a right-angled triangle, a ² + b ² = c ²

c ² = 25² + b²

= 1512.67

c = √1512.67

= 38.9