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The equation of line passes through the points (2, -1) and (5, -10) will be;

⇒ y = - 3x + 5

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (2, -1) and (5, -10)

Now,

Since, The equation of line passes through the points (2, -1) and (5, -10)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 10 - (-1)) / (5 - 2)

m = - 9 / 3

m = - 3

Thus, The equation of line with slope - 3 is,

⇒ y - (-1)= - 3 (x - 2)

⇒ y + 1 = - 3x + 6

⇒ y = - 3x + 6 - 1

⇒ y = - 3x + 5

Therefore, The equation of line passes through the points (2, -1) and

(5, -10) will be;

⇒ y = - 3x + 5

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For the given case the pair of angles are consecutive angles, corresponding angles, consecutive interior angles and alternate interior angles respectively and ∠8 = 105°. The correct option is (1).

The parallel lines are a group of straight lines that never intersect with one another. The distance between two parallel is always the same.

The given problem can be solved as follows,

(4) The pair of angles can be named as below,

(1) The angles ∠1 and ∠6 are called consecutive angles.

(2) The angles ∠2 and ∠6 are called corresponding angles.

(3) The angles ∠3 and ∠5 are called consecutive interior angles.

(4)  The angles ∠4 and ∠5 are called alternate interior angles.

(5) The measure of ∠8 is given as below,

Since ∠4 and ∠8 are corresponding angles.

∠4 = ∠8 = 105°.

Hence, the names of the pair of angles are consecutive angles, corresponding angles, consecutive interior angles and alternate interior angles respectively and ∠8 = 105°.

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Answer:

The correct options are A, C and D.

Step-by-step explanation:

The quadratic parent function is

[tex]f(x)=x^2[/tex]

The properties of quadratic parent function are:

1. It has one intercept, i.e, x- and y-intercept are at origin.

2. It has a vertex at (0, 0).

3. It is U-shaped.

4. Each image y has two preimage, except 0.

5. It opens up.

From the given option one the option B is incorrect because the quadratic parent function opens upward.

Therefore the correct options are A, C and D.

Answer:

x³y³ is monomial.

Step-by-step explanation:

Given :Polynomial  x³y³ .

To find : Identify monomial binomial trinomial.

Solution : We have given that

Polynomial  x³y³ .

Monomial : A polynomial with just one term.

Examples : 1) 3xy

2) 5y²x³  Both are monmial .

x³y³ is also a monomial because it has only one term.

Therefore,  x³y³ is monomial.

a) 116 ways to select seven people.

b) ways to select 7 women.

c) The probability is 0.004662

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

a) Number of ways can seven people be selected from this group of thirteen

C( 13, 7)

= 13! /6! 7!

= ​1716

b) Number of ways seven women selected from  Eight women

C(8 ,7)

= 8!/ 7! 1!

= 8

c) The probability that the selected group will consist of all women

= 8 / 1716

= 0.004662

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Answer:

The ladder reaches 142 inches and the base of ladder is 25 inches far from the base of the wall.

Step-by-step explanation:

Let us draw a diagram for the given situation.

In the attached figure,

AB = the height of wall where the ladder reaches

AC = ladder

BC = distance of base of ladder from the base of the wall

In triangle ABC,

[tex]\sin C=\frac{AB}{AC}\\\\\sin80=\frac{AB}{12}\\\\AB=12\sin80\\\\AB=11.82[/tex]

And

[tex]\cos C=\frac{BC}{AC}\\\\\cos80=\frac{BC}{12}\\\\BC=12\cos80\\\\BC=2.08[/tex]

Now, 1 feet = 12 inches

Hence, 11.82 ft = 141.84 inches

and 2.08 feet = 24.96 inches

Therefore, in the nearest inches, we have

The ladder reaches 142 inches and the base of ladder is 25 inches far from the base of the wall.

Answer:

a

Step-by-step explanation:

The next number in pattern 1/324, 1/108, 1/36, 1/12 would be 1/4

Firstly , let us learn about types of sequence in mathematics.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

[tex]\boxed{T_n = a + (n-1)d}[/tex]

[tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

d = common difference between adjacent numbers

Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.

[tex]\boxed{T_n = a ~ r^{n-1}}[/tex]

[tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

r = common ratio between adjacent numbers

Let us now tackle the problem!

Given:

This problem is about Geometric Sequence. Let's see why.

[tex]\frac{1}{324} , \frac{1}{108} , \frac{1}{36} , \frac{1}{12} , . . .[/tex]

T₁ = [tex]\frac{1}{324}[/tex]

T₂ = [tex]\frac{1}{108}[/tex]

T₃ = [tex]\frac{1}{36}[/tex]

T₄ = [tex]\frac{1}{12}[/tex]

[tex]\large {\boxed {\frac{T_2}{T_1} = \frac{T_3}{T_2} = \frac{T_4}{T_3} = r = 3} }[/tex]

From the above results it can be concluded that this is Geometric Sequence.

The next number will be the fifth term and can be calculated as following.

[tex]T_n = a ~ r^{n-1}[/tex]

[tex]T_5 = \frac{1}{324} \times 3^{5 - 1}[/tex]

[tex]T_5 = \frac{1}{324} \times 3^4[/tex]

[tex]T_5 = \frac{1}{324} \times 81[/tex]

[tex]\large {\boxed {T_5 = \frac{1}{4} } }[/tex]

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

It will take at least 12 years for Sarah's $600 deposit at a 2.5% annual interest rate to grow to more than $800, assuming the interest is compounded annually.

To determine how long it will take for Sarah's $600 deposit at a 2.5% annual interest rate to grow to over $800, we can use the formula for compound interest: [tex]A = P(1 + r/n)^{(nt)[/tex], where:

Since the problem doesn't specify the compounding frequency, let's assume it's compounded annually for simplicity:
[tex]A = 600(1 + 0.025)^t[/tex]. We need A to be greater than $800.

To find the minimum number of years (t), we solve for t:

[tex]800 < 600(1 + 0.025)^t[/tex]

Solving for t gives us: t > ln(800/600) / ln(1.025).

Using a calculator, we find that t > 11.89.

Therefore, it will take at least 12 years for the amount in Sarah's account to exceed $800.

Answer:

Let's consider this right triangle described in the picture.

∠ABD = ∠CBD, since BD is a bisector.

Angles ∠ADB and ∠BDC are neighbor angles and their sum is equal to 180°.

∠BDC is an exterior angle and ∠BDC=∠ABD+∠ADB.

Similarly, ∠ADB is an exterior angle and ∠ADB=∠CBD+∠BCD

Step-by-step explanation:

Final answer:

The two numbers that multiply to -90 and add up to -8 are -10 and 2. This is found by factoring -90 and checking different factor pairs until the correct one is identified.

Explanation:

The student is asking for two numbers that when multiplied result in -90, and when added result in -8. This is a factorization problem that can be addressed by setting up a system of equations or by using intuition to guess and check pairs of factors. We are looking for a pair of numbers that have one positive and one negative number, because the product is negative (-90), and the sum is also negative (-8).

By listing out the factors of 90, we can test which pair of numbers, with one being negative, would multiply to -90 and add up to -8. After some trial and error, we find the pair that works are -10 and 9. -10 × 9 = -90 and -10 + 9 = -1. However, since the sum needs to be -8, then the correct pair is -10 and 2, because -10 × 2 = -20 and -10 + 2 = -8.

Answer:

The density of the wood is, 0.64 [tex]g/cm^3[/tex]

Step-by-step explanation:

Using the density formula:

[tex]\text{density} = \frac{\text{mass}}{\text{Volume}}[/tex]         .....[1]

As per the statement:

If the volume of a cube of wood is 15.625 cm3 and its mass is 10.00 grams.

⇒Volume = 15.625 cubic cm and mass = 10 gram

Substitute the given values in [1] we have;

[tex]\text{density} = \frac{10}{15.625}[/tex]

Simplify:

density = 0.64 [tex]g/cm^3[/tex]

Therefore, the density of the wood is, 0.64 [tex]g/cm^3[/tex]

Final answer:

A recursive definition for the set of odd positive integers starts with a base case of 1 and uses a recursive step where each subsequent odd integer is obtained by adding 2 to the current odd integer.

Explanation:

To write a recursive definition for the set of odd positive integers, you can define a base case and a recursive step. The base case is the smallest odd positive integer, which is 1. The recursive step will then generate the next odd integer by adding 2 to the current odd integer. Here's how you can express it:

Base case: Let O1 = 1, which establishes that 1 is the first odd positive integer.

Recursive step: For every odd positive integer On, there exists an On+1 = On + 2. This means that if you have an odd positive integer, the next one in the set can be found by adding 2 to the current one.

This definition ensures that every number generated by the recursive step will be odd since adding 2 to an odd number always results in another odd number, and starting from 1, guarantees that all numbers will be positive.

Answer:

∠C = 107°

Step-by-step explanation:

Quadrilateral ABCD is inscribed in a circle, and a quadrilateral inscribed in a circle is known as cyclic quadrilateral.

So, ABCD is cyclic quadrilateral.

∠A = 2x + 3

∠B = 2x - 4

∠D = 3x + 9

Also. the sum of opposite angles of the cyclic quadrilateral is supplementary.

⇒ ∠B + ∠D = 180

⇒ 2x - 4 + 3x + 9 = 180

⇒ 5x = 175

⇒ x = 35

Now, ∠A = 73

Also, ∠A + ∠C = 180

⇒ ∠C = 180 - 73

⇒ ∠C = 107°

Answer: The median is the only appropriate measure of center.

Step-by-step explanation:

The statement is ''Both the median and mode are appropriate measures of center''. Actually, the three, that is, the mean, media and mode can be used to measure the central of tendency. But the MEAN has a problem, it can be Skewed by large values in the distribution/data. Assuming, the days of the week when patients visiting a dentist's office are;

Monday: 8, Tuesday: 41, Wednesday: 35, Thursday: 39, Friday: 36, and Saturday: 42.

And the mean of the distribution = 33.5. Most patients visit the dentist Tuesday to Saturday, where Saturday is the highest. The data is skewed. So, the MEDIAN will do the job perfectly.

For the mode; since we do not have; (1). two highest mode with the same value in the data provided and, (2). the highest value and the second to the highest values are not too far from each other. We can use the MODE here for measuring the central tendency.

===> CONCLUSION: (1). Assuming the data fails the two condition for mode, the most correct statement will be ''The median is the only appropriate measure of center".

===> (2). Also, for this data, the MEDIAN will be the only appropriate measure of center.