Find the remaining sides of a 45°-45°-90° triangle if the longest side is 4. Answer exactly.

Archimedes went to sleep about 9.24 meters away from the rock where its shadow should end when it was 7 AM.

Trigonometric ratios are ratios of the sides of a right triangle to its angles. The three primary trigonometric ratios are

Sine = opposite/hypotenuse.

Cosine = adjacent/hypotenuse.

Tangent = opposite/adjacent.  

Here we have

Archimedes wanted to get up at 7. AM, but the alarm clock was yet to be invented. Archimedes knew that at 7.AM, the sunlight reaches the ground at an angle of 31°.

The rock beside which he slept was 5.55 meters tall.

Let's assume that the distance from the rock where Archimedes went to sleep is "x".  

Form a right triangle where the height of the triangle is the height of the rock (5.55 meters) and the angle between the ground and the sunlight at 7 AM is 31° and the opposite side to that angle is x.

Using trigonometry, we can solve for x as follows

tan(31°) = 5.55 / x

x = 5.55 / tan(31°)

x = 5.55/0.60086

x = 9.24 meters    

Therefore,

Archimedes went to sleep about 9.24 meters away from the rock where its shadow should end when it was 7 AM.

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Answer:

200.904

Step-by-step explanation:

200904 is the same as 200904.0

On dividing by 1000, the point moves three steps to the left, 20090.4 , 2009.04 then finally 200.904.

Answer: As a fraction: 1/2

              As a decimal: 0.005

Step-by-step explanation:

FRACTION:

To figure out how to write 0.5% as a fraction, all you need to know is that 0.5 = to a half, or 1/2 because 0.5 is half of 1.

DECIMAL:

0.5% as a decimal form is 0.005 because it is 1000 times less than 1, so you move the 0 3 times right.

The total number of cars that will fit in the spaces at school is less than or equal to 155, which means that the combined number of parking spaces in the parking lot and on the side of the building cannot exceed 155.

What is expression ?

In mathematics, an expression is a combination of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that represents a quantity or a relationship between quantities. Expressions can be as simple as a single number or variable, or they can be complex, involving multiple variables and operations.

Let x be the number of parking spaces in each row of the school parking lot. Then, the total number of parking spaces in the parking lot is 6x.

The total number of parking spaces in the school is the sum of parking spaces in the parking lot and parking spaces on the side of the building, which is 6x + 35.

Since the total number of cars that will fit in the spaces at school is at most 155, we can write the inequality:

6x + 35 ≤ 155

Simplifying this inequality, we get:

6x ≤ 120

x ≤ 20

Therefore, the total number of cars that will fit in the spaces at school is less than or equal to 155, which means that the combined number of parking spaces in the parking lot and on the side of the building cannot exceed 155.

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Answer:

x = ± √((y + 2)/4)

Step-by-step explanation:

To find the inverse of a function, we need to solve for x in terms of y.

Steps to find the inverse of y = 4x^2 - 2:

Replace y with x and x with y:

x = 4y^2 - 2

Solve for y:

x + 2 = 4y^2

(x + 2)/4 = y^2

± √((x + 2)/4) = y

Note that we have a ± sign because the square root of a positive number can have two values, one positive and one negative.

Therefore, the inverse of y = 4x^2 - 2 is:

x = ± √((y + 2)/4)

Answer:

y=±([tex]\sqrt{x+2}/2[/tex])

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's use the following variables:

Let F be the number of sections of Finite Math

Let A be the number of sections of Applied Calculus

Let C be the number of sections of Computer Methods

We can create a system of equations based on the given information:

F + A + C = 7 (the college wishes to offer a total of seven sections)

40F + 60A + 290C = 298000 (the college wishes to bring in $298,000 in revenues)

40F + 40A + 10C = 220 (the college wishes to accommodate 220 students)

We can solve this system of equations using any method we prefer. Here's one possible way:

Multiply the third equation by 10 to get:

400F + 400A + 100C = 2200

Subtract the third equation from the second equation to eliminate C:

20A + 280C = 76000

Multiply the first equation by 40 and subtract it from the previous equation to eliminate A:

240C = 76000 - 1600

Solve for C:

C = 290

Substitute C = 290 into the third equation to solve for F:

40F + 40A + 10(290) = 220

40F + 40A = -2680

F + A = -67

Substitute C = 290 and F + A = -67 into the first equation to solve for A:

A = 10

Substitute A = 10 and C = 290 into the first equation to solve for F:

F = -3

We have a problem here: we obtained a negative number of sections for Finite Math, which is impossible. This means that the original system of equations is inconsistent, and there is no solution that satisfies all the requirements.

Therefore, the college cannot offer the desired number of sections while accommodating the desired number of students and revenue. Some adjustments need to be made, such as changing the number of students per section or the tuition fees.

The total area is given as 160 sq feet. The total yard that is to be purchased is 18 yards

To get the area of the room we would first have to find the area of the sides.

We can call 1 of the areas S1.

The length l1 = 13

The width w1 = 16

area =

s1 = 13 * 16

We have

s2 with

l2 = 6

w2 = 8

then the area

s2 = 6 * 8

S1 - s2

= 208 - 48 =

160

1 square yard = 9 square foot

17.7778 = 160 square feet

Juan has to purchase approximately 18 yards

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A solution to the given system of linear equations is (2, 6).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x - y = 0     ......equation 1.

5x + 2y = 7  ......equation 2.

In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (1, 1).

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Answer: We can start by evaluating g(2):

g(2) = 2 + 9 = 11

Now we can use the definition of function composition to evaluate (f ∙ g)(2):

(f ∙ g)(2) = f(g(2)) = f(11)

To find f(11), we need to substitute 11 for x in the expression for f(x):

f(11) = (11 - 3)^2 + 1 = 8^2 + 1 = 65

Therefore, (f ∙ g)(2) = f(g(2)) = f(11) = 65.

Step-by-step explanation:

Because of the isosceles triangle.

The triangle whose two sides are equal length is called an isosceles triangle. The third side, known as the base, may or may not be a different length from the other two sides. An isosceles triangle also has two angles that are equal in measure, which are opposite the two equal sides.

Given that in ΔMQN: MQ=MN,

therefore, ∠MQP=60°=∠MNO (isosceles triangle )

also given in ΔMPO: MP=MO,

therefore, ∠MPO=80°=∠MOP (isosceles triangle )

For the straight line PON,

∠POM + ∠MON = 180° (straight line angle)

80° + ∠MON = 180°

∠MON = 100°

In ΔNMO,

∠NMO +∠MON + ∠MNO = 180° ()

∠NMO + 100° + 60° = 180°

∠NMO = 20°

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Answer:

C = 2 x 4.5 x π

Step-by-step explanation:

The equation to find the circumference of the circle is

C = 2π · r

r = 4.5 in

Looking at the options, the answer is C = 2 x 4.5 x π

Answer:

Below

Step-by-step explanation:

radius = 4.5       diameter = 2 x 4.5  in

the circumference of a circle is given by the formula   p * d

  substitute in the underlined equation for 'diameter')

          circumference = 2 * 4.5 * pi    inches

Answer:-3p

Step-by-step explanation: less = subtract -3+p=-3p

Answer:

x + 118 = 180

Step-by-step explanation:

Because the angle x added with 118 must be 180 degree for this to be true. So, the answer is x + 118 = 180

Answer:

2.) x + 118 = 180 degrees

Step-by-step explanation:

x + 118 = 180 can be solved as taking 118 on both sides, 118 and 180.

118=0 and 180-118= 62. The other equations in the 4 options do not work.

I hope this helps : )

the product will be 35/3.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

product of 5 x 2 1/3

=5*7/3

=35/3

Hence the product will be 35/3.

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27-2=25

25:5=5

4(5)+2=20+2=22

the shorter piece = 5

the longer piece = 22

Answer:

4 cookies

Step-by-step explanation:

If you can get 6 cookies for $1.50, then the cost of each cookie is:

$1.50 ÷ 6 = $0.25

This means that for $1.00, you can get:

$1.00 ÷ $0.25 per cookie = 4 cookies

Therefore, you can get 4 cookies for $1.00 at the Math munch cafe.

Answer:

Cindy's time was 5 2/5 minutes, or 5.4 minutes to the nearest tenth.

Step-by-step explanation:

To find Cindy's time, we need to use the information given about the total time and the times of the other three runners.

Let's first convert all the times to fractions of a minute:

Barbara: 3 3/10 = 3 + 3/10 = 3.3 minutes

Donna: 2 4/5 = 2 + 4/5 = 2.8 minutes

Cindy: x minutes

Nicole: 2 1/10 = 2 + 1/10 = 2.1 minutes

Now, we can set up an equation to represent the total time of the team:

Barbara's time + Donna's time + Cindy's time + Nicole's time = 11 3/5 minutes

Substituting the values we know:

3.3 + 2.8 + x + 2.1 = 11 3/5

Simplifying and converting mixed numbers to fractions:

8/5 + 14/5 + x + 11/5 = 116/10 + 3/5

Multiplying both sides by 10 to eliminate the denominators:

16 + 28 + 10x + 22 = 116 + 6

Simplifying:

10x = 54

Dividing by 10:

x = 5.4

Therefore, Cindy's time was 5 2/5 minutes, or 5.4 minutes to the nearest tenth.

Correct order of steps for constructing an angle bisector of ∠DEF using only a straightedge and compass is option C.

A angle bisector is a line that bisects an angle into two equal angles. A bisector means dividing a shape or object into two equal parts. When we draw a ray that bisects an angle into two equal parts of equal magnitude, it is called a bisector.

Given,

Compass and straightedge to draw angle bisector of ∠DEF

Steps to draw angle bisector are:

1. Draw a circle with a radius less than DE and center E, and label

the points of intersection G and H.

2. Draw a line from point G to point H.

3. Draw a circle with radius GH and center G and another circle

with radius GH and center H, and then draw an equilateral triangle.

4. Use a straightedge to connect E to the rightmost vertex of the

equilateral triangle.

Hence, option C describes correct order of constructing an angle bisector of ∠DEF using only a straightedge and compass.

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When the radius is 4 inches, the circle's circumference measures roughly 25.1 inches.

No matter what size circle you drew, you will obtain roughly 3.14 when you divide the circumference by the diameter. The ratio will never change even though a larger circle will have a higher radius and circumference. Circumference to diameter ratio (C/d) is always constant at. As a result, the diameter (D) and circumference (C) are always approximately 3.14 times each other (d).

C = 2r is the formula for calculating a circle's circumference.

C = 2π(4)

C = 8π

Using the approximation of π = 3.14, we can evaluate this expression:

C ≈ 8(3.14)

C ≈ 25.12

Rounding this answer to the nearest tenth gives:

C ≈ 25.1 inches.

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Therefore, the scale factor used in the drawing is 4000/3.

In mathematics, a factor refers to a number or algebraic expression that divides another number or expression without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because each of these numbers can be multiplied by another whole number to produce 12 (1 × 12, 2 × 6, 3 × 4). Factors play an important role in many areas of mathematics, including algebra, number theory, and geometry, and are used to simplify expressions, solve equations, and factorize polynomials.

Given by the question.

The scale factor is the ratio of the length of an object on the drawing to the actual length of the object.

Since 6 millimeters on the drawing represents 8 meters in reality, the scale factor can be expressed as:

Scale factor = Actual length / Length on drawing

Scale factor = 8 meters / (6 millimeters)

To simplify this fraction, we need to convert meters to millimeters by multiplying by 1000:

Scale factor = (8 meters * 1000) / 6 millimeters

Scale factor = 8000 / 6

The fraction cannot be simplified further, so the scale factor is:

Scale factor = 4000/3

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Answer:

The researcher used a ratio scale of measurement for the number of people using their cell phone.

Mean: (3+4+4+5+6+8)/6 = 30/6 = 5

Median: arrange the data in ascending order: 3, 4, 4, 5, 6, 8. The median is the middle value which is 5.

Mode: there is no mode as no value occurs more than once.

Range: 8-3 = 5

Variance:

s^2 = Σ(x-ȳ)^2 / (n-1)

s^2 = [(3-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (6-5)^2 + (8-5)^2] / (6-1)

s^2 = 5.6

Standard deviation: s = sqrt(s^2) = sqrt(5.6) ≈ 2.37

To find the number of people using their cell phone associated with +1 SD, we add one standard deviation to the mean:

Mean + 1 SD = 5 + 2.37 ≈ 7.37

Therefore, approximately 7 people using their cell phone are associated with +1 SD.

To find the number of people using their cell phone that reflects 96% of the sample, we need to find the z-score that corresponds to the 96th percentile. From a standard normal distribution table, we find that the z-score is approximately 1.75. We can use this z-score to find the corresponding value in our data set using the formula:

z = (x - ȳ) / s

Rearranging, we get:

x = z * s + ȳ

x = 1.75 * 2.37 + 5

x ≈ 9.3

Therefore, approximately 9 people using their cell phone reflect 96% of the sample.

Step-by-step explanation:

The theorem that justifies the similarity of the two triangles is given as follows:

A: AA.

The Angle-Angle (AA) Congruence Theorem states that if two pairs of corresponding angles are congruent, then the triangles are similar.

In other words, if two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle must also be equal in measure, and the two triangles are therefore congruent.

The two pairs of corresponding angles that are congruent in this problem are given as follows:

Hence the third angle will also have the same measure for both triangles.

Hence the AA theorem can be used and the correct option is given by option A.

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Answer:

The two ride-sharing companies will have the same price after 40 miles have been driven. At that point, both companies will have charged $10 in pickup fees and $10 in total for miles driven, meaning the cost of taking either service will be the same

Step-by-step explanation:

Answer: see bellow

Step-by-step explanation: Z is 80   Y is 90 and    x is 90

This works because each measure is the same arcoss!!!

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Answer:

Step-by-step explanation:

We are interested in finding out the missing angles of the rhombus . Some properties of rhombus that needs to be kept in mind are ,

[tex]\implies z = 80^o \\[/tex]

[tex]\implies x = y \\[/tex]

Now since the opposite sides are parallel, the sum of co interior angles would be 180° .

Here x and 80° are co interior angles. So their sum would be 180° . Hence,

[tex]\implies x + 80^o = 180^o \\[/tex]

[tex]\implies x = 180^o - 80^o \\[/tex]

[tex]\implies x = 100^o\\[/tex]

Now since x and y were equal , therefore,

[tex]\implies y = 100^o \\[/tex]

Therefore the value of x is 100° , z is 80° and y is 100° .

Answer:

1 term (monomial).

Step-by-step explanation:

A term includes at least either a number, a variable, or both together, and can have more than one.

In this case, there is 1 term, which denotes that a variable, has an exponent of 9.

[tex]b^9[/tex] is one term.

Examples of more than 1 term can include:

[tex]b^9 + 1[/tex] , which is two terms (Binomial).

[tex]a^2 + b + 3[/tex] is three terms (Trinomial).

* One thing to note is to always simplify when possible.

~

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The minimum clearance required for safety of fitting 95% of men is approximately 18.7 inches.

What is percentage ?

Percentage is a way of expressing a proportion or a ratio as a fraction of 100. It is often represented by the symbol % and is used to compare values, make comparisons, and analyze data. For example, if there are 25 red marbles and 75 green marbles in a jar, the percentage of red marbles is 25% (25/100), while the percentage of green marbles is 75% (75/100). Percentages are commonly used in many fields, including finance, business, statistics, and science.

To determine the minimum clearance required for safety of fitting 95% of men, we need to find the value of the sitting knee height at the 95th percentile for men.

Using the formula for a normal distribution, we can calculate that the sitting knee height at the 95th percentile for men is approximately 23.2 inches.

Therefore, the minimum clearance required for safety of fitting 95% of men would be the difference between the sitting knee height at the 95th percentile for men (23.2 inches) and the height of the work table.

Therefore, the minimum clearance required for safety of fitting 95% of men is approximately 18.7 inches.

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Answer:

look in the comments give me a minute please and thank you

The angles of the triangle will be 5 °, 45 °, and 130 °.

The triangle is a two-dimensional geometric object with three straight sides and three angles. The lengths of the triangle's three sides can differ from the third side (isosceles triangle), be equal (equilateral triangle), or be any combination of the three (scalene triangle).

The sum of the angles in a triangle is always 180 degrees; the opposite angle of the longest side is the largest, and the opposite angle of the shortest side is the smallest.

Now,

Let x be the common factor that multiplies the ratio of 1:9:26. Then, the measures of the angles can be expressed as x, 9x, and 26x.

Since the sum of the angles in a triangle is always 180 degrees, we can set up an equation:

x + 9x + 26x = 180°

Simplifying the equation, we get:

36x = 180

Dividing both sides by 36, we get:

x = 5

Therefore, the measures of the angles are:

x = 5 degrees (the smallest angle)

9x = 45 degrees

26x = 130 degrees (the largest angle)

So the angles of the triangle are 5 degrees, 45 degrees, and 130 degrees.

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