In a 1-dimensional space Identify the points x = 3, y = - 5/2, and z = 2.25. How does the fact that you need only one number to identify a particular point relate to the dimension of the space?

The value of (AB)² + (BC)² = 130

The value of (AC)² = 130.

Therefore the triangle is a right angled triangle

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).

AB)² = 5-(-2)²+7-11)²

= 7² + 4²

= 49+16

AB)² = 65

BC)² = 1-5)² + 0-7)²

BC)² = 4² + 7²

= 16 +49

BC) ² = 65

BC)² + AB)² = 65+65 = 130

AC)² = 1-(-2)² +0-11)²

AC)² = 3²+ 11²

AC)² = 9+121

AC)² = 130

therefore the value of BC)² + AB)² = AC)²

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The expression [tex]\frac{3x^2 + 6x + 3}{x + 1}[/tex] , where x ≠ -1, is equivalent to Option (D) 3x + 3. We can factor the numerator of the expression by first factoring out the greatest common factor of 3.

What is numerator ?

In a fraction, the numerator is the top number that represents the quantity being considered.

Take 3 common from expression:

[tex]3(x^2 + 2x + 1)[/tex]

We can further factor the expression inside the parentheses using the identity [tex](x + 1)^2 = x^2 + 2x + 1[/tex] , giving:

[tex]3(x + 1)^2[/tex]

Therefore, the original expression can be written as:

[tex]\frac{3(x + 1)^2}{x + 1}[/tex]

We can simplify this expression by canceling out the (x + 1) term in the numerator and denominator, leaving us with:

[tex]3(x + 1)[/tex]

So the expression [tex]\frac{3x^2 + 6x + 3}{x + 1}[/tex] , where x ≠ -1, is equivalent to 3(x + 1). This expression represents a straight line with a slope of 3 and a y-intercept of 3.

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The figure has rotational symmetry of order 2 and to achieve rotational symmetry of order 4, three plates need to added.

Explain about symmetry?

Symmetry is a property of an object that describes how it appears identical after some transformation, such as reflection, rotation, or translation. It is an essential concept in mathematics, science, art, and many other fields.

There are several types of symmetry, including:

Reflectional symmetry (also called bilateral symmetry).
Rotational symmetry.

Translational symmetry.

According to the question:

a. The figure has rotational symmetry of order 2. This means that if we rotate the figure 180 degrees around its center, the figure will look exactly the same as it did before the rotation.

b. To achieve rotational symmetry of order 4, we need to add plates in such a way that the figure looks the same after a rotation of 90 degrees, 180 degrees, and 270 degrees around its center.
To achieve this, we can add three more plates to the figure, one in between each pair of existing plates, After adding these plates, the figure has rotational symmetry of order 4. We can see this by rotating the figure 90 degrees, 180 degrees, and 270 degrees around its center

so the figure has rotational symmetry of order 4. Therefore, we only needed to add three plates to the figure to achieve rotational symmetry of order 4 around its center.

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Answer: 40

Step-by-step explanation: Because jasmine is enlarging the drawing, we can divide 60 and 3.75 to get how much she is enlarging. 60 divided by 3.75 is 16 meaning she is enlarging by 16. So now we multiply 16 times 2.5 to find the top and we get 40.

The scale factor of the dilation will be 1/4.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The blue figure is a dilation image of the black figure.

And, The origin is the center of dilation.

Now,

Since, The blue figure is a dilation image of the black figure.

And, The origin is the center of dilation.

Here, The length of black figure = 8 units

And, The length of blue figure = 2 units

So, The scale factor of the dilation = 2/8

                                                         = 1/4

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Answer:

look in the comments and have a good day

If the original triangle has an area equal to 729 small dotty triangles. The original triangle has an area of 8 square units.

Let's first find the pattern of the number of small triangles in each row. The first row has 1 small triangle. The second row has 3 small triangles. The third row has 5 small triangles, and the fourth row has 7 small triangles. We can see that the pattern is that each row has 2 more small triangles than the previous row.

To find how many small triangles are in the third row, we add 2 to the number of small triangles in the second row:

3 + 2 = 5

So there are 5 small triangles in the third row.

To find how many small triangles are in the fourth row, we add 2 to the number of small triangles in the third row:

5 + 2 = 7

So there are 7 small triangles in the fourth row.

To find the total number of rows, we can count the number of rows from the top of the triangle to the bottom. Alternatively, we can use the formula for the sum of an arithmetic series to find the number of terms in the sequence. In this case, the first term is 1, the common difference is 2, and the last term is 7. Using the formula:

n = (last term - first term) / common difference + 1

n = (7 - 1) / 2 + 1

n = 4

So there are 4 rows in the triangle.

Finally, we can use the formula for the sum of an arithmetic series to find the total number of small triangles in the original triangle. In this case, the first term is 1, the common difference is 2, and the number of terms is 4. Using the formula:

sum = (n / 2) * (first term + last term)

sum = (4 / 2) * (1 + 7)

sum = 4 * 4

sum = 16

So there are 16 small triangles in the original triangle. Since each small triangle has an area of 1/2, the total area of the original triangle is:

area = 16 * (1/2)

area = 8

Therefore, the original triangle has an area of 8 square units.

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The correct inequality that represents the allowable measurements the bar can bend is | x - 4.5 | ≤ 0.1 , So correct option is E.

n mathematics, an inequality is a statement that indicates that two values are not equal. It is a relationship between two expressions that can be compared using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

For example, 5 < 10 is an inequality that indicates that 5 is less than 10. Similarly, x + 3 ≤ 8 is an inequality that indicates that the sum of x and 3 is less than or equal to 8.

Inequalities are used to express relationships between quantities that are not necessarily equal. They can be used to represent constraints, limits, or ranges of values. Inequality statements can be combined with other mathematical expressions, such as equations or inequalities, to create more complex mathematical models.

The correct inequality that represents the allowable measurements the bar can bend is:

| x - 4.5 | ≤ 0.1

This is because the average allowable bend is 4.5 cm with a margin of error of 0.1 cm, which means that the actual allowable bend can range from 4.4 cm to 4.6 cm. The absolute value inequality represents this range of values, with the center of the range being 4.5 cm.

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One mistake Quinn made was in setting up the equation.

An equation is a mathematical statement that expresses the relationship between two or more quantities, using symbols such as +, -, =, and so on. It can be used to solve problems involving unknowns, such as the number of solutions to an equation or the value of a certain variable. In addition, equations can help to predict future outcomes based on current data.

Quinn set up the equation incorrectly by subtracting 3/2 from both sides instead of subtracting 3/1 from both sides. This caused the equation to become unbalanced, resulting in an incorrect solution. To solve the equation correctly, Quinn should have subtracted 3/1 from both sides to get the correct equation: 2/3 = q.

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she made the mistake of calculating

Step-by-step explanation:

Answer:

D or B

Step-by-step explanation:

from my perspective, that doesn't look like a or b, and it looks like it's 90 degrees. But it could also be "We need more information to solve this problem, due to it all being x. i hope I'm correct, sorry if I'm not, and Goodluck!!!!!

We proved that ΔPQR congruent to ΔSTR and  ΔJKL is congruent to ΔNKM using the given conditions.

What are congruent traingles?

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form. It is necessary for both triangles to be superimposed on one another.

1) Consider triangles ΔPQR and ΔSTR

PQ ≅ ST     -   Given

QR ≅ TR     - Given

R is the midpoint of PS  - Given

PR ≅ SR  - Since R is the midpoint it cuts line PS equally

ΔPQR  ≅ ΔSTR - Since the corresponding sides of the triangles are equal, they are congruent triangles.

2) Consider triangles ΔJKL and ΔNKM

JL ≅ NM     -   Given

K is the midpoint of JN and LM  - Given

JK ≅ NK  - Since K is the midpoint it cuts line JN equally

LK ≅ MK  - Since K is the midpoint it cuts the line LM  equally

ΔJKL  ≅ ΔNKM - Since the corresponding sides of the triangles are equal, they are congruent triangles.

Therefore we proved that ΔPQR congruent to ΔSTR and  ΔJKL is congruent to ΔNKM using the given conditions.

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The final answer is 1/10, which is a reduced fraction in lowest terms.

What is the fraction?

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity by another.

To perform the operation described, we first need to multiply the two fractions together using cross multiplication:

(3/5) x (1/6) = (3 x 1) / (5 x 6) = 3/30

The resulting fraction 3/30 is an improper fraction, meaning that the numerator is larger than the denominator. To convert this to a mixed fraction, we need to divide the numerator by the denominator, and express the remainder as a fraction. In this case:

3/30 = 1/10

Hence, the final answer is 1/10, which is a reduced fraction in lowest terms.

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2k + 5 = 2(8) + 5 = 16 + 5 = 21

k is substituted into the expression

Answer:

The correct answer you're looking for is either 85, or 68.07 (rounded)
The correct answer is if x is the hypotenuse or the most extensive length than its 85.
If x is one of the legs then 68.07 (rounded) is the correct answer.

Recommendation:

When trying to solve for a missing length you need to be sure whether it's just a leg or the hypotenuse, usually would be obvious in a picture as the sides attached to the 90º angle are usually legs and the one opposite of it is the hypotenuse.
Anywho below are the two different ways to get the answer.

Disclaimer:

There will be two answers that I will have given and I would suggest looking at the question to see which one it is, I am not only giving one possible answer. (Also very long answer, sorry!)

Note:

If messaged or commented on which numbers go on which side I'll be more than happy to confirm one answer.

Step-by-step explanation:

Figuring out only if X is Hypotenuse:

To solve for a hypotenuse you need to use the equation for the Pythagorean Theorem which states: [tex]a^{2} +b^{2}= c^{2}[/tex].

In this case, 36, and 77 are the two legs that make up this triangle.

We would insert these two numbers to replace a and b for when solving the equation.

Now you have [tex]36^{2}+ 77^{2}= c^{2}[/tex].

You then do the exponent operations for the terms that we know the values of and also add them up together to get this equation:
1296 + 5929 = 7725 or [tex]c^{2}[/tex].

After that, we'll make sure to add the terms on the first side and keep [tex]c^{2}[/tex] on the other and to also square root them giving this equation: [tex]\sqrt{7725} = \sqrt{c^{2}[/tex].

With that, your answer is 85 = X


Figuring out only if X is a Leg:

Figuring out only if X is Hypotenuse:
To solve for a leg you need to use the equation for the Pythagorean Theorem which states: [tex]c^{2}- b^{2}= a^{2}[/tex]

In this case, 36, is one of the two legs that make up this triangle while 77 is the Hypotenuse.

We would insert these two numbers to replace b and c when solving the equation.

Now you have [tex]72^{2} -36^{2} =a^{2}[/tex]

You then do the exponent operations for the terms that we know the values of and also add them up together to get this equation:
5929 - 1296 = 4633 or [tex]a^{2}[/tex]

After that, we'll make sure to subtract the terms on the first side and keep [tex]a^{2}[/tex] them on the other and also to square root them giving this equation:  
[tex]\sqrt{4633} =\sqrt{a^{2} }[/tex]

With that, your answer is 68.07 (rounded) = X

I hope this was helpful!

Answer:

3hours and 40 mins

Step-by-step explanation:

Answer:

I speak english so this might be wrong...

Step-by-step explanation:

Build the distribution table

of frequencies and histogram of the height (in cm) of 80 third-secondary students.

(Construir la tabla de distribución

de frecuencias e histograma de la altura (en cm) de 80 estudiantes de tercero medio.)

I think this is what you sayed?

For the following:

a) To determine the range of the heights, find the difference between the highest and lowest values.

Range = Highest value - Lowest value

The highest value is 188 cm, and the lowest value is 162 cm.

Range = 188 - 162 = 26 cm

b) The amplitude is the interval width of each class in the frequency table. To determine the amplitude, Know the number of classes. Assume to create 10 classes for the height data.

Amplitude = Range / Number of classes

Amplitude = 26 cm / 10 = 2.6 cm

c) To build the frequency table, to create the class intervals for the height data. Since the amplitude is 2.6 cm, choose the class intervals accordingly.

Set up the frequency table with 10 classes:

Class Intervals: (160 - 162.6], (162.6 - 165.2], (165.2 - 167.8], ..., (185 - 187.6], (187.6 - 190]

Next, count the number of data points falling into each class interval and calculate the absolute frequency (frequency), cumulative frequency, relative frequency, and percentage relative frequency.

The frequency table for the height data is attached.

In the frequency table, the "Cumulative Frequency" column shows the running total of frequencies, the "Relative Frequency" column shows the proportion of each class frequency to the total number of data points (80), and the "Percentage Relative Frequency" column shows the relative frequency expressed as a percentage.

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[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=23\pi \end{cases}\implies 23\pi =2\pi r\implies \cfrac{23\pi }{2\pi }=r\implies \cfrac{23}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{23}{2} \end{cases}\implies A=\pi \left( \cfrac{23}{2} \right)^2\implies A=132.25\pi[/tex]

Answer:

32 ft

Step-by-step explanation:

pls make me brainleist

The savings plan balance after 2 years with an APR of 6% and monthly payments of $150 is approximately $3,814.79.

What are payments?

In compensation for products or services received or to fulfill a legal duty, payment is the voluntarily given exchange of money, its equivalent, or other valuables from one person to another. Frequently, the individual giving the money is referred to as the payer, while the person receiving it is referred to as the payee.

Assuming that the payments are made at the end of each month, we can use the formula -

[tex]A = PMT\Bigg[\frac{\big(1+\frac{APR}{n}\big)^{nY}-1}{\frac{APR}{n}}\Bigg][/tex]

where -

A = the savings plan balance after 2 years

PMT = the monthly payment ($150)

APR = the annual percentage rate (6%)

n = the number of compounding periods per year (12, since the payments are made monthly)

Y = the number of years (2)

Plugging in the values, we get -

[tex]A = 150\Bigg[\frac{\big(1+\frac{0.06}{12}\big)^{12 \times 2}-1}{\frac{0.06}{12}}\Bigg][/tex]

A ≈ $3,814.79

Therefore, value is obtained as $3,814.79.

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The probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as 0.5.

The probability of an event is a number that indicates how likely the event is to occur.

It is expressed as a number in the range from 0 and 1 or it can be expressed using percentage notation, in the range from 0% to 100%

Given is that the probability of a randomely selected fertilized egg will take 21 days to hatch is 0.028.

We can write the probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as -

P{E} = {0.028 + (1 - 0.028)}/2

P{E} =  1/2

P{E} = 0.5

Therefore, the probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as 0.5.

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The triangle can be classified as follows:

NUMBER 4: obtuse

NUMBER 5: obtuse

NUMBER 6: obtuse

NUMBER 7: right

NUMBER 8: right

NUMBER 9: acute

NUMBER 10: right

To classify the triangle as Right, Obtuse, or Acute, follow the following steps:

1. Calculate the sum of squares of the two smaller sides.

2. Compare it to the square of the longest side.

3. If the sum is greater, your triangle is acute. If they are equal, your triangle is right. If the sum is less, your triangle is obtuse.

NUMBER 4

6² + 7² = 58

9² = 81

58 < 81 (obtuse)

NUMBER 5

10² + 12² = 244

16² = 256

244 < 256 (obtuse)

NUMBER 6

8² + 16² = 320

(8√6)² = 384

320 < 384 (obtuse)

NUMBER 7

20² + 21² = 841

29² = 841

841 = 841 (right)

NUMBER 8

8² + 3² = 73

(√73)² = 73

73 = 73 (right)

NUMBER 9

8² + 10² = 164

12² = 144

164 > 144 (acute)

NUMBER 10

9² + 15² = 306

(3√34)² = 306

306 = 36 (right)

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Answer: The length of one fairy fly is 1.39×10−4 meter. To find the total length of two fairy flies placed end to end, we need to add their lengths.

1 fairy fly = 1.39×10−4 meter

2 fairy flies = 2 × 1.39×10−4 meter (adding the lengths of two fairy flies)

= 2.78×10−4 meter

Therefore, the total length of two fairy flies placed end to end is 2.78×10−4 meter.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the measure of the central angle for the group that likes the student government program in a circle graph, we need to determine what proportion of the total number of students surveyed this group represents. We can do this by adding up the number of students who like the program and the number of students who think it is unnecessary, since these two groups represent the total number of students surveyed. Then we can divide the number of students who like the program by the total number of students surveyed and multiply by 360, which is the total number of degrees in a circle.

Total number of students surveyed = 190 + 135 + 220 = 545

Proportion of students who like the program = 190 / 545 ≈ 0.3486

So the measure of the central angle for the group that likes the program would be:

0.3486 x 360 ≈ 125

Therefore, the measure of the central angle for the group that likes the student government program would be approximately 125 degrees in a circle graph.

Therefore , the solution of the given problem of trigonometry comes out to be csc θ - csc(90° - θ) is equal to -√(13) / 6.

Mathematics and cubic splines relationships It is believed that astrophysics was created with in third century BC, when the various fields were merged. Many geometric equations can be solved or the results of computations involving them can be determined using precise mathematical methods. Trigonometry is the analysis of the six basic trigonometric formulas. They are known by a variety of titles and acronyms, including sine, dispersion, angle, angle, etc (csc).

Here,

=> h² = 2² + 3²

=> h² = 4 + 9

=> h² = 13

=> h = √(13)

Using the specification of csc, we can now determine the value of csc:

csc θ = hypotenuse / opposite

csc θ = sqrt(13) / 3

csc(θ) - csc(90° - θ) must be calculated using the identity:

csc(90° - θ) = sec θ

As a result, we have:

csc θ - csc(90° - θ) = csc θ - sec θ

= (hypotenuse / opposite) - (hypotenuse / adjacent)

= (√(13) / 3) - (√(13) / 2)

= √(13) / 6 * (2 - 3)

= -√(13) / 6

Therefore, in its simplest radical version, csc θ - csc(90° - θ) is equal to -√(13) / 6.

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The inverse of the function will be f⁻¹(y) = y + 1.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.

The given function is y = x - 1.

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

y = x - 1

Adding 1 to both sides, we get:

y + 1 = x

Therefore, the inverse function is:

x = y + 1

f⁻¹(y) = y + 1

Note that the inverse function represents the reflection of the original function across the line y = x.

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The value of x is given as follows:

x = 4.8.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

In the context of this problem, the parameters are given as follows:

Applying the Pythagorean Theorem, the value of x is obtained as follows:

x² + 14² = (x + 10)²

x² + 196 = x² + 20x + 100

20x = 96

x = 96/20

x = 4.8.

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Answer:

Below

Step-by-step explanation:

The wedge shaped area is ABOVE (greater than)  and INCLUDES  y = 5x+2    AND  ABOVE (greater than ) y= -3x-2

See image below: