Distance between -1.75 and 1.5 on a number line

Answer:

C)

Step-by-step explanation:

Trigonometry ratio:

         \(\sf Cos \ \theta = \dfrac{Adjacent \ side}{hypotenuse}=\dfrac{-3}{10}\)

We need to find the opposite side using Pythagorean theorem.

 opposite side² = hypotenuse² - adjacent side²

                           = 10² - (-3)²

                            = 100 - 9

                           = 91

opposite side    = √91

                 \(\sf tan \ \theta = \dfrac{opposite \ side}{adjacent \ side}\)

                           \(\sf = \dfrac{\sqrt{91}}{3}\)

In quadrant II, value of tan \(\theta\) is negative.

              \(\sf tan \ \theta = -\dfrac{\sqrt{91}}{3}\)

Answer:

You can divide fractions in one of two ways: the cross multiplication method or the inverse multiplication method.

Step-by-step explanation:

The other factor of the polynomial x² - 8x + 15 is (x - 3)

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

A binomial is a polynomial with two terms.

Given the polynomial:

x² - 8x + 15

= x² - 5x - 3x + 15

= x(x - 5) - 3(x - 5)

= (x - 3)(x + 5)

The other factor of the polynomial x² - 8x + 15 is (x - 3)

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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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The quadrilaterals with exactly one pair of parallel sides are: Trapezoid and Isosceles Trapezoid.

1. Trapezoid: A trapezoid has exactly one pair of parallel sides. The other two sides are non-parallel. The parallel sides are called the bases, and the non-parallel sides are called the legs.

2. Isosceles Trapezoid: An isosceles trapezoid is a special type of trapezoid where the legs are congruent (equal in length). It has exactly one pair of parallel sides, which are the bases.

Note: In some sources, the term "parallelogram" is also included in this list because a parallelogram technically has one pair of parallel sides. However, a parallelogram is commonly defined separately as a quadrilateral with both pairs of opposite sides parallel. So, depending on the definition being used, a parallelogram may or may not be included in this list.

The quadrilaterals with exactly one pair of parallel sides are: Trapezoid and Isosceles Trapezoid.

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c₁₆ - a₁₆ = 12 - 10 = 2₁₆

7 < c = 12 in base 16, so borrow 1 from the next place value:

17₁₆ - c₁₆ = 23 - 12 = 11 = b₁₆

In the next place, we replace 5 with 4, but 4 < 6, so borrow 1 from the next place value again:

14₁₆ - 6₁₆ = 20 - 6 = 14 = e₁₆

Replace d with c, so that

c₁₆ - 7₁₆ = 12 - 7 = 5₁₆

and this gives

d57c₁₆ - 76ca₁₆ = 5eb2₁₆

No, not all square numbers have an odd number of factors. In fact, square numbers can have either an odd or an even number of factors, depending on their prime factorization.

A square number is a number that can be expressed as the product of an integer multiplied by itself. For example, 4 is a square number because it can be written as 2 * 2.

When we analyze the factors of a square number, we find that each factor has a corresponding pair that multiplies to give the square number. For instance, the factors of 4 are 1, 2, and 4. We can see that the pairs are (1, 4) and (2, 2). Thus, 4 has an even number of factors.

However, there are square numbers that have an odd number of factors. Consider the square number 9, which is equal to 3 * 3. The factors of 9 are 1, 3, and 9. In this case, 9 has an odd number of factors.

In conclusion, while some square numbers have an odd number of factors (like 9), others have an even number of factors (like 4). The determining factor is the prime factorization of the square number.

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Answer:

M=112

N=180-112=68

V=E

E=180-88=92

R=G

G=88(opposite angle)

There were 16 ounces of oil in the lantern at noon.

Let's start by defining the variables we know. We'll call the amount of oil in the lantern at noon "x," the rate at which the oil burns "r," and the time elapsed from noon to 2 pm "t." We know that the amount of oil in the lantern at 2 pm is 12 ounces, and at 4 pm, it's 8 ounces.

We can use the rate of oil burning to create an equation relating the amount of oil in the lantern to the time elapsed. The equation is:

x - rt = y

where "y" is the amount of oil in the lantern at any given time after noon. We can solve for "x" by plugging in the values we know at 2 pm:

x - 2r = 12

And at 4 pm:

x - 4r = 8

Now we have two equations with two variables. We can solve for "r" by subtracting the second equation from the first:

2r = 4

r = 2

Now we can plug in "r" to one of the equations to solve for "x." Let's use the first equation:

x - 2(2) = 12

x - 4 = 12

x = 16

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Answer:

D

Step-by-step explanation:

250/9.99=25.0250... Round it to 25.03

The required converted value is $25.03, which is 250 pesos to U. S. dollars.

As we all know, unit conversion is the process of multiplying a provided quantity by a conversion factor that combines the two interconnected units.

To convert 250 pesos to U.S. dollars, we divide the amount of pesos by the exchange rate.

Here, the exchange rate is given as 9.99 pesos per U.S. dollar.

It is the process of assigning a quantity from one unit of measurement to another.

250 pesos / 9.99 pesos per U.S. dollar = 25.025 U.S. dollars

Rounding this to two decimal places, the conversion is approximately $25.03.

Therefore, the correct option is (d) $25.03.

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Answer:

2 hours, 4 hours

Step-by-step explanation:

So lets go over what we know.

There are already 10 worksheets created.

Every 1 hour 3 more are made.

27 worksheets need to be made.

Ok, the first thing we can do is subtract the amount of worksheets needed by the amount we laready have:

27-10

=

17

Now, lets divide the amount of worksheets we still need, by how many we make each hour:

17/3

=

Well, 3 goes into 15, 5 times. Then 2 is left. So we know it takes 5 2/3 hours to create all 27 worksheets.

Looking at the answers, 6 hours, 8 hours, and 10 hours would work. However 2 hours and 4 hours would not work.

Hope this helps! ;)

\(c = \pi \: d = 6 \times 3.14 = 18.84 \: yd\)

\(radius = \frac{diameter}{2} = \frac{6}{2} = 3\)

\(area = \pi \: r {}^{2} = 3.14 \times 3 {}^{2} = 3.14 \times 9 = 28.26 \: yd {}^{2} \)

Hey there!

Radius ⇒ d/2 = 6/2 = 3

Radius = 3 yd

Circumference = 2πr

⇒ 2 × 3.14 × 3

⇒18.84 yd

Area = πr²

⇒3.14 × 3²

⇒3.14 × 3 × 3

⇒28.26 yd²

Dodie's triangular plot with 160 rose plants will have 12 rows.

To solve it,

Assigning a variable to the number of rows we want to find. Assume that this variable is "n".

Since there are 5 more plants in each row than in the previous row,

We can use an arithmetic sequence to represent the number of plants in each row.

Specifically, the first row will have 1 plant, and the second row will have

1 + 5 = 6 plants, the third row will have 1 + 5 + 5 = 11 plants, and so on.

The formula for an arithmetic sequence is,

an = a1 + (n-1)d

Where an is the nth term of the sequence,

a1 is the first term,

And d is a common difference.

Using this formula, we can write an expression for the total number of plants in all n rows,

160 = n/2 (2 + (n-1)5)

Simplifying this equation, we get,

160 = 2.5n² + 2.5n - 5

Now we can solve for n using the quadratic formula,

n = (-2.5 ± √(2.5²+ 4(2.5)(165)))/(2(2.5))

After simplifying this equation, we get two solutions,

n = -13.2 and n = 12.2.

Since we can't have a negative number of rows, we'll take the positive solution, n = 12.2.

Now, since we can't have a fraction of a row, we'll round down to the nearest integer.

Therefore, Dodie's plot will have 12 rows.

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A vector orthogonal to (2, -7, 0) is (7, 2, z), where z can be any real number. A basis for the orthogonal complement L¹ of L is {(7, 2, z)}, where z can be any real number.

To find a basis for the orthogonal complement of a line L in R³, we need to find vectors that are orthogonal (perpendicular) to all vectors in L. In this case, L is the line spanned by a basis vector (2, -7, 0).

To find a vector orthogonal to (2, -7, 0), we can find the null space of the matrix [2, -7, 0] by solving the equation:

2x - 7y + 0z = 0

This equation represents the condition for a vector (x, y, z) to be orthogonal to (2, -7, 0).

Simplifying the equation, we have:

2x - 7y = 0

We can choose a value for x and solve for y to get a vector orthogonal to (2, -7, 0). Let's choose x = 7, then:

2(7) - 7y = 0

14 - 7y = 0

-7y = -14

y = 2

So, a vector orthogonal to (2, -7, 0) is (7, 2, z), where z can be any real number.

Therefore, a basis for the orthogonal complement L¹ of L is {(7, 2, z)}, where z can be any real number.

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Solution given:

left hand limit

f(0)=5×0-9=-9

right hand limit

f(0)=|2-0|=2

functional value

f(0)=|2-0|=2

since left hand limit≠right hand limit.so

d. The limit does not exist

Answer: The team's time on the final run can be found by successively multiplying their first time by (1 - 0.512) twice:

First run time: 4.85 minutes

Second run time: 4.85 * (1 - 0.512) = 2.37 minutes

Third run time: 2.37 * (1 - 0.512) = 1.15 minutes (rounded to the nearest hundredth)

So the team's time on their final run was 1.15 minutes.

Step-by-step explanation:

Answer:

4x-5=17

4x-5+5=17+5

4x=22

4x÷4=22÷4

2x=11

2x÷2=11÷2

x=5and1/2

The committee can best catalog the data so it can be used to make meaningful changes by using a database management system (DBMS).

A database management system (DBMS) is a system that enables users to create, read, update, and delete data in a database. The DBMS is a tool that handles all data-related tasks. Organizations employ a DBMS to keep data organized and easy to access and manage.

DBMS provides a set of computerized tools for managing all types of data. A DBMS allows end-users to extract and analyze data from a database.

The committee can use a database management system to ensure that data is organized and easily retrievable. They can employ a DBMS to streamline data entry and report production for high-quality output.

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The volume of the cone is 58.875 cubic inches. The volume of the cylinder is 176.625 cubic inches. The volume of the cylinder is three (3) times the volume of the cone.

The volume of a cone is equal to one-third (1/3) of the area of the circular base as well as the height product.

Mathematically, the volume of a cone can be expressed as:

\(\mathbf{V_{cone} = \pi r ^2 \dfrac{h}{3} }\)

where;

\(\mathbf{V_{cone} = 3.14 \times (2.5 ^2)\times \dfrac{9}{3} }\)

\(\mathbf{V_{cone} = 3.14 (2.5 ^2)\times 3 }\)

\(\mathbf{V_{cone} =58.875\ inches ^3}\)

The volume of a cylinder implies the amount of quantity of material being carried in the cylinder. The volume of the cylinder can be expressed as:

V = πr²h

V = π(2.5)² × 9

V = 3.14 × (2.5)² × 9

V = 176.625 inches³

The volume of the cylinder is three times the volume of the cone because:
\(\mathbf{=\dfrac{176.625 \ in^3}{ 58.875\ in^3}}\)

=  3

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Answer: 23 + 9 = 32

Step-by-step explanation:

Answer:

(6,3)

Step-by-step explanation:

It will make a weird diamond shape.

Answer:

(6,3)

Step-by-step explanation:

A rhombus lis like a diamond shape so we know its going to be opposite if point B.

Point B is located 3 units above the invisible line that connects A and C.

Count down 3 units from that line and you will get your answer.

:)

Answer:

32 Is Eight More Than 3 Times A Number

Explanation:

32 Is Eight More Than: + 8 = 32

3 Times A Number: 3y

Put Everything Together: 3y + 8 = 32

Step-by-step explanation:

Hey there!

3y+8 = 32 --> The sum of thrice of a number and 8 is 32.

Reason:

So, the word problem for this equation is " The sum of thrice of a number and 8 is 32.

Hope it helps...

Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

Answer:

1. Area of a circle = 452.2 m²

2. Area of a circle = 1,017.4 ft²

Step-by-step explanation:

Area of a circle = πr²

1.

When radius, r = 12 m

π = 3.14

Area of a circle = πr²

= 3.14 * (12m)²

= 3.14 * 144 m²

= 452.16 m²

Approximately to the nearest tenth,

Area of a circle = 452.2 m²

2.

When radius, r = 18 ft

π = 3.14

Area of a circle = πr²

= 3.14 * (18 ft)²

= 3.14 * 324 ft²

= 1,017.36 ft²

Approximately to the nearest tenth,

Area of a circle = 1,017.4 ft²

The value of dy/dt is -52/x².

The process of finding the derivative of a dependent variable in an implicit function by differentiating each term separately, by expressing the derivative of the dependent variable as a symbol, and by solving the resulting expression for the symbol.

From the given expression, the value of dy/dx is calculated as follows;

xy = 4

y = 4/x

y = 4x⁻¹

dy/dx = -4x⁻² = -4/x²

dx/dt = 13

dy/dt = dy/dx .  dx/dt

dy/dt = -4/x²(13) = -52/x²

Thus, the value of dy/dt is -52/x².

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Answer:

π(x+2)^2

Step-by-step explanation:

The formula for the area of a circle is π*radius squared.

2x + 4 is the length across the entire circle, which would make it the diameter.

The radius is half the diameter.

So, to find out the radius, simply divide the diameter by 2.

2x+4/2

x+2

Now, plug the newly found radius into the formula.

Area=π*(x+2)^2