Of the following , which measurement is in the base units 5mg, 10kL, 2.5g, 100mm

The value of x= 4.

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

According to our question-

cos(60)= x/8

x=1/2*8

x=4

Hence, The value of x= 4.

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The perimeter of the triangle is therefore P= 45 cm.

A triangular prism is a prism composed of two triangular bases and three rectangular sides. It is a pentahedron.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.

We know that the volume of a prism is given by

V = Bh, where B is the area of the base and h is the height of the prism. In this case, we have V = 1950 cm³ and h = 20 cm.

So, we can solve for B:

B = V/h = 1950/20 = 97.5 cm².

The base of the triangular prism is a triangle with height 13 cm, so we have

B = 1/2bh = 1/2(13)(b) = 97.5.

Solving for b, we get b = 2B/h = 2(97.5)/13 = 15 cm.

Since all sides of the triangle are equal, we have b = c = 15 cm.

The perimeter of the triangle is therefore P = 3b = 3c = 3(15) = 45 cm.

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Answer:

Step-by-step explanation:

To find x + 1/x, we need to first find the value of x.

Given, x = 2-√3

To simplify x + 1/x, we need to find the value of 1/x.

1/x = 1/(2-√3)

Multiplying the numerator and denominator by the conjugate of the denominator, we get:

1/x = (2+√3)/(2-√3)(2+√3)

1/x = (2+√3)/(4-3)

1/x = 2+√3

Now, substituting the values of x and 1/x, we get:

x + 1/x = (2-√3) + (2+√3)

x + 1/x = 4

Therefore, the answer is option a) 4.

The first five terms of the recursive sequence an = an-1 + 7, where a1 = 5 can be found by applying the recursive formula multiple times.

A recursive formula is a mathematical expression that uses a sequence of previously defined terms to define each successive term. This type of formula is commonly used to define sequences and can be used to define functions as well. The recursive formula is based on the idea of self-similarity, which means that each successive term is defined in terms of the one before it.

Both equations are true when x = 1 and y = 1, so the solution is correct.

What are system of equations ?

A system of equations is a set of two or more equations that are to be solved simultaneously. The equations in the system share common variables, and the solution to the system is a set of values for those variables that satisfy all of the equations in the system.
To solve this system, we need to find the values of x and y that satisfy both equations at the same time. This means that any solution we find must work in both equations simultaneously.

According to the question:
To solve the system:

x + y = 2 ...(1)

x - y = 0 ...(2)

We can add equations (1) and (2) to eliminate y:

(x + y) + (x - y) = 2 + 0

2x = 2

x = 1

Substituting x = 1 into equation (1):

1 + y = 2

y = 1

Therefore, the solution to the system is x = 1 and y = 1. We can check the solution by substituting the values into both equations

x + y = 2

1 + 1 = 2 (true)

x - y = 0

1 - 1 = 0 (true)

Both equations are true when x = 1 and y = 1, so the solution is correct.

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We want to copy the original triangle using only two of its sides and the included angle. To do this, we'll create a new triangle with the same side lengths and angle measures as the original triangle.

To copy a triangle using two of its sides and the included angle, follow these steps:

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The Commutative Property of Addition is the mathematical principle at play here. we can see that  [tex]2 + 2 = 4[/tex]  and [tex]4 + 4 = 8[/tex]  , and this is due to the Commutative and Associative Properties of Addition.

The math property at work here is the Commutative Property of Addition. This property states that the order of the numbers being added does not affect the sum. In other words, a + b = b + a.

So, in the case of   [tex]2 + 2 = 4[/tex] and  [tex]4 + 4 = 8[/tex]  , we can apply the Commutative Property of Addition to rearrange the numbers being added:

[tex]2 + 2 = 4[/tex]

[tex]4 + 4 = 4 + (2 + 2)[/tex]

Then, we can use the Associative Property of Addition, which states that the grouping of the numbers being added does not affect the sum. In other words, ([tex]a + b) + c = a + (b + c).[/tex]

Applying this property to  [tex]4 + (2 + 2)[/tex] , we get:

[tex]4 + (2 + 2) = (4 + 2) + 2 = 6 + 2 = 8[/tex]

Therefore, we can see that  [tex]2 + 2 = 4[/tex]  and [tex]4 + 4 = 8[/tex]  , and this is due to the Commutative and Associative Properties of Addition.

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Answer:

ти можеш загуглити в інтернеті, і все

Answer:

A (-6, -4),(-3,-3)

Step-by-step explanation:

Formula for slope of a line is y2-y1/x2-x1

If you plug each equation in:

-3-(-4)/-3-(-6)=1/3

1/3 is the perpendicular slope of -3

Answer:

they have equal shape calculate the number

Answer:

7a^2(a^4 + 4)(a^4 - 4)

Step-by-step explanation:

To simplify 7a^10 - 112a^2, we need to find the greatest common factor (GCF) of the two terms and factor it out.

The GCF of 7a^10 and 112a^2 is 7a^2.

So, we can factor out 7a^2 from both terms, which gives:

7a^2(a^8 - 16)

Now, we can further simplify the expression by noticing that a^8 - 16 is a difference of squares. We can write it as:

a^8 - 16 = (a^4)^2 - 4^2 = (a^4 + 4)(a^4 - 4)

Therefore, the fully simplified expression is:

7a^2(a^4 + 4)(a^4 - 4)

Answer:

-6x + 6y = 6 (Equation 1)

-6x + 3y = -12 (Equation 2)

We can use the method of elimination, which involves adding or subtracting the equations to eliminate one of the variables.

In this case, we can start by multiplying Equation 2 by 2 to eliminate the x variable:

-6x + 6y = 6 (Equation 1)

-12x + 6y = -24 (Equation 2 multiplied by 2)

Now we can subtract Equation 1 from Equation 2:

-12x + 6y = -24 (Equation 2 multiplied by 2)

-(-6x + 6y = 6) (Equation 1, with the opposite sign)

-6x = -30

Simplifying this expression, we get:

x = 5

Now we can substitute this value of x into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:

-6x + 6y = 6

-6(5) + 6y = 6

-30 + 6y = 6

6y = 36

y = 6

Therefore, the solution to the system of equations is x = 5 and y = 6, or (5, 6) in coordinate form.

Step-by-step explanation:

Answer:

It's y = 3x + 1 :)

Answer:

6/20 and 9/30

Step-by-step explanation:

The length and width of the new poster are 240 cm and 288 cm, respectively.

To find the length and breadth of the enlarged poster, we need to multiply the original dimensions by the enlargement ratio.

Let's first find the common ratio between the original poster and the enlarged poster:

Common ratio = Enlarged size / Original size

Common ratio = 5/3

Now, we can find the dimensions of the enlarged/New poster:

Length of enlarged poster = Length of original poster x Common ratio

Length of enlarged poster = 150 cm × 5/3

Length of enlarged poster = 250 cm

Breadth of enlarged poster = Breadth of original poster x Common ratio

Breadth of enlarged poster = 180 cm × 5/3

Breadth of enlarged poster = 300 cm

Therefore, the the dimensions of the new poster is 250cm by 300cm.

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The expected number of students who classify the crown shapes as medium is approximately 38.3.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To find the expected number of students who classify the crown shapes as medium, we need to use the assumption that the distributions of responses from the professionals and the students are the same. We can use the row and column totals to calculate the expected counts.

First, let's calculate the marginal totals for the students:

The total number of students is 91.

The total number of students who classified the crown shapes as low is 43.

The total number of students who classified the crown shapes as medium is 39.

The total number of students who classified the crown shapes as high is 9.

Now let's calculate the expected counts for the students who classified the crown shapes as medium:

The total number of classifications for the medium category is 87 (from the table).

The proportion of classifications in the medium category made by the professionals is 48/109.

The expected number of classifications in the medium category made by the students can be calculated as (proportion from professionals) x (total number of student classifications) = (48/109) x 87 = 38.3 (rounded to one decimal place).

Therefore, the expected number of students who classify the crown shapes as medium is approximately 38.3.

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Answer: a

Step-by-step explanation:

Answer:

[tex]( - 28 \infty )[/tex]

Step-by-step explanation:

We have already found the solution to the inequality, but since we want to represent the solution in interval notation, we have changed it.

hopefully this helps! :)

The answer is 140m squared

The WETHIC score of 79 into a z-score is 0.33.

A WETHIC score of 62 into a z-score is 0.80.

The proportion of workers that will have a WETHIC score that is below 79 is 63%.

The proportion of workers that will have a WETHIC score that is below 62 is 21%.

1) Z score = (79-74)/15 = 0.33 , it means score is 0.33 standard deviations above the mean

2) Z score = (62-74)/15 = -0.80 , it means score is 0.80 standard deviations below the mean

3) P(X<79)

= P(Z<0.33)

= 0.6293

d) P(X<62)

= P(Z<-0.80)

= 0.2119

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The probability that a given person drank between 40 and 45 glasses of water is 13.5%.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number outcomes.

between 40 and 45 glasses of water.

First, we need to standardize the values of 40 and 45 using the z-score formula:

z1 = (40 - 50) / 5 = -2

z2 = (45 - 50) / 5 = -1

Next, we look up the area under the standard normal distribution curve between z = -2 and z = -1. We can use a standard normal distribution table or a calculator to find this area, which is approximately 0.135.

Therefore, the probability that a given person drank between 40 and 45 glasses of water is 13.5%.

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Answer:

BC = 62

Step-by-step explanation:

There are 3 triangles total in the figure shown, one large triangle, and two smaller triangles created by the segment BC. Now, look at triangle ACD and see that is a scaled version of common right triangle.

Some common right triangles are 3-4-5, 5-12-13, and 7-24-25. You may be able to see a pattern here where the square of the smallest side length is equal to the sum of the other two side lengths. Triangle ACD happens to be a scaled form of a 5-12-13 triangle. The triangle is scaled by a factor of 3. So the respective side length of AD is 12 * 3 = 36.

Now look at triangle ABD. We have two of the three side lengths.

AD = 36

AB = 85

We want to find BC, so we will use the pythagorean theorem, with (x + 15) to represent the length of BD.

35² + (x + 15)² = 85²

1225 + (x + 15)² = 7225

(x + 15)² = 6000

x + 15 = ±√6000

x = -15 ± √6000

Our equation provides two answers, but the negative value doesn't make sense because length can't be negative, so use the positive length for this application.

x = -15 + √6000

x = 62.4596

Rounded to the nearest whole number, the length of BC is 62.

To find the average rate of change of the function f(x) = x² - 4x + 1 from x=3 to x = 5, we need to find the difference in f(x) between these two values and divide by the difference in x:

f(5) - f(3) / (5 - 3)

= (5² - 4(5) + 1) - (3² - 4(3) + 1) / 2

= (25 - 20 + 1) - (9 - 12 + 1) / 2

= (6) / 2

= 3

Therefore, the average rate of change of f(x) from x=3 to x=5 is 3.

Step-by-step explanation:

Given a interval x=a to x=b, the average rate of change is equal to

[tex] \frac{f(b) - f(a)}{b - a} [/tex]

where [a,b] is the interval.

Here

a is 3

b is 5 so

[tex] \frac{f(5) - f(3)}{5 - 3} [/tex]

Using the function

[tex]f(5) = 25 - 20 + 1 = 6[/tex]

[tex]f(3) = 9 - 12 + 1 = - 2[/tex]

So

[tex] \frac{6 - ( - 2)}{5 - 3} = 4[/tex]

The average rate of change of f from x=3 to x=5 is 4

The value of the unknown sides and angles are;

<B = 65 degrees

b = 27

c= 13

In the triangle, Using the SOHCAHTOA rule,

such that

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have that;

sin C = c/30

sin 25 = c/30

find the value and cross multiply, we get;

c = 12. 67

< B = 180 - sum of angle A and C

<B = 180 - 115

subtract the values

<B = 65 degrees

The value of side b

sin B = b/30

sin 65 = b/30

b = 27. 19

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Answer:

140inch^2

Step-by-step explanation:

5×8=40inch^2

4^2×π= 16π

4^2×π=16π

16π+16π=32π

40+32π=140.53096491487

rounded to the nearest 10th= 140inch^2

To enable Riley to save up to buy a new television priced $1,200.17, and since he already has $200.34 saved and earns $76.91 per week at her job, she needs to work for 13 more weeks.

To determine the number of weeks Riley has to work to earn enough to buy the new television, we apply the mathematical operations of subtraction and division.

Subtraction and division are two of the four basic mathematical operations, including addition and multiplication.

The total amount that Riley requires = $1,200.17

The amount of savings Riley already has = $200.34

The remaining amount that Riley needs to earn = $999.83 ($1,200.17 - $200.34)

Riley's earnings per week = $76.91

The number of weeks Riley needs to work to save enough money = 13 weeks ($999.83 ÷ $76.91)

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Questions:

1. 6 is not more than z.

2. The value of w is at least 12

3. Josiah plans to complete his 50 minutes of Mappers practice in 5 days and split the practice up evenly. Which inequality can he use to decide how many minutes he must complete each day?

4. Amy has $35.75 for her visit to the zoo. She must pay $7.25 for admission and wants to feed as many animals as she can. Food for the animals costs $1.25 each. What inequality represents the largest number of animal food that Amy can buy?

5. Jacob spent $40 on supplies to make 100 shirts for a baseball team fundraiser. Solve the inequality to help him decode how much to charge for each shirt to make a profit of more than $350.

100t-40 is greater than 350

Answers:

1. 6 is less than or equal to z (2nd option)

2. w is greater than or equal to 12 (1st option)

3. 5x is greater than or equal to 50 (1st option)

4. 1.25x + 7.25 is less than or equal to 35.75 (4th option)

5. t is great than 39 (3rd option)

The solution of the given problem of unitary method comes out to be beam's maximum bending moment is 180 Nm.

Here,

=> RA - wL = 0

=> wL = 40 N/m x 2 m = 80 N, where RA =

=> RBv - RA = 0 (sum of forces in the vertical direction)

=> RBh = 0 (sum of forces in the horizontal direction) (sum of forces in the horizontal direction)

To solve for RBv, we obtain:

=> 80 N = RBv = RA

Hence, the responses at support points A and B are as follows:

=> RA = 80 N (vertical response at A) (vertical reaction at A)

=> RBv = 80 N (vertical response at B) (vertical reaction at B)

=> RBh = 0 N (horizontal reaction at B) (horizontal reaction at B)

=> M = 80 N x 2 m - 40 N/m x (2 m)2/2 - 500 Nm

=> -180 Nm, where MB = RA x L - wL2/2 -

Keep in mind that the bending moment is opposite the applied moment, as shown by the negative sign.

Thus, at point B, the beam's maximum bending moment is 180 Nm.

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Answer:

-x - 12

Step-by-step explanation:

x- (-12) = x+12. The opposite of x+12 = -x-12. The answer is therefore -x -12, NOT x + 12.

Answer:

the equation's intervals are (0;+∞)

Step-by-step explanation:

Replace x with -12:

-12 - (-12) = -12 + 12 = 0

With -12 this equation is equal to zero, but since x > -12, that means we have to replace x with numbers that are greater that -12 (-11; -10; etc.)

And since there are open intervals ( > ), we do not count the zero.