Lesson 13 Practice Pro Lesson 13 Practice Problems 1. a. How can you find 50% of a number quickly in your head? b. Andre lives 1.6 km from school. What is 50% of 1.6 km? c. Diego lives mile from school. What is 50% of mile? ​

Solution to the given system of equations is (6, -9).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are y=x-15 -----(I) and y=-2x+3 -----(II).

Substitute x=y+15 in equation (II), we get

y=-2(y+15)+3

y=-2y-30+3

3y=-27

y=-9

Substitute y=-9 in equation (II), we get

-9=-2x+3

-12=-2x

x=6

So, solution is (6, -9)

Therefore, solution to the given system of equations is (6, -9).

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The ratio of rubies to diamonds is 4:1.

The ratio is the relative size of one value compared to another.

The ratio shows the quantity of a variable or number contained in another.

We depict ratios as fractional values, like proportions.

Fractional values can be represented as fractions, decimals, or percentages.

The number of rubies = 4x

The number of diamonds = x

The sum of ratios = 5x (4x + x)

The ratio of rubies to diamonds = 4:1

Thus, on this other ring, we can conclude that the ratio of rubies to diamonds is 4:1, meaning that rubies outnumber diamonds by 4 times.

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Answer:

Truth is being honest and not lie and get them upset.

Step-by-step explanation:

The time that Mrs James have her eyes open than closed will be 13 19/20 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

From the information, the average person spends about 1/10 of their walking hours with their eyes closed. If Mrs. James was awake for 15 1/2 hours today.

The more time that she have her eyes open than closed will be:

= 15 1/2 - (1/10 × 15 1/2)

= 15 1/2 - 1 11/20

= 13 19/20

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Answer:

the correct answer is -1/16 i believe

This unit has provided me with a greater understanding of the different aspects of communication.

A unit is a standard measurement of a particular quantity. It is used to quantify or compare the amount or size of something. For example, the international system of units (SI) is a standard system of units that uses meters, kilograms, and seconds as its base units of measurement. Other examples of units include miles, pounds, inches, and Celsius.

It has enabled me to recognize the importance of active listening, being mindful of non-verbal cues and tailoring messages to the audience. I have gained insight into the various methods of communication, both verbal and non-verbal, and how to effectively use them for successful communication. I have also learned about the importance of setting clear expectations and maintaining a positive attitude to help ensure successful interactions.

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Answer:

Water is the only molecule because of which life is possible on Earth. In outer space, the conditions are so hostile that Water cannot be found in its natural form- liquid. This liquid Water has been giving us sustenance throughout billions of years.

Step-by-step explanation:

mark me brainleit plss

Line T crosses the x-axis at point R, with coordinates (k,0). Suppose that w is increasing at the constant rate of 5 units per second.

In the figure above, line T is tangent to the graph of

y=1/x2

at point

P

, with coordinates

(w,1/ w2 )

​, where

w>0

. Point

Q

has coordinates

(w,0)

. Line

T

crosses the

x

-axis at point

R

, with coordinates

(k,0)

. Suppose that

w

is increasing at the constant rate of 5 units per second. When

w=2

, what is the rate of change of the area of triangle PQR with respect to time? Determine whether the area is increasing or decreasing at this instant. Round to three decimal places.

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The function f(x) = x² - 2x - 3 / x² + 3x + 2 have holes at coordinate (-1, -4)

Function holes are areas of a function that are not defined. They can be caused by a lack of data, a lack of understanding of the problem, or a lack of knowledge of the domain. Function holes can lead to errors in the output of a function, as the function will not be able to produce a result for the undefined area. A hole is a location on the graph where the function's value is not known. When a rational function is simplified, its numerator and denominator will cancel if they have a common factor. The cancelled value creates a hole in the graph.

In the given question, we need to plot the function on a graph to determine it's holes.

f(x) = x² - 2x - 3 / x² + 3x + 2

Using a graphing calculator to plot this;

The holes in this function is located at a coordinate (-1, -4)

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The probability that you will win at least one prize if you buy one ticket each month for three months is 0.314 or 31.4%.

The probability of not winning a prize in one drawing is 1 - 0.11 = 0.89.

If we assume that the draws are independent events, the probability of not winning a prize in three consecutive months is 0.89^3 = 0.686.

Therefore, the probability of winning at least one prize in three months is 1 - 0.686

= 0.314 or 31.4%.

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Answer:2.600

Step-by-step explanation:

2.599 rounded to nearest tenth will be 2.60 .

Given,

2.599

Here,

The concept of rounding states that if a decimal number is present and the digits after decimal is greater than 5 or less than 5 then the number can be rounded off .

For example:

Decimal number : 10.7

Estimated whole number : 11

Thus here the rounding off is required at tens place ,

So,

Number = 2.599

After round to nearest tenth = 2.60

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Answer:

125

Step-by-step explanation:

The values of (f+g)(0) , (f-g)(0) , (fg)(0) are -5 , 7,-6 respectively for the given functions f(x) = 3x^2 - 4x + 1 and g(x) = x-6

What is function ?

Function can be defined in which it relates an input the output.

Given functions ,

f(x) = 3x^2 - 4x + 1 and g(x) = x-6

(f+g) (x)  =  3x^2 - 4x + 1 + x-6

(f+g) (x) = 3x^2 - 3x - 5

(f+g)(0) = 3(0) - 3(0) - 5

(f+g)(0) = -5

(f-g) x  = 3x^2 - 4x + 1 -( x-6)

(f-g)x = 3x^2 - 5x +7

(f-g)(0) = 3(0)-5(0) + 7

(f-g) (0) = 7

(fg)(x) = (3x^2 - 4x + 1) *( x-6)

(fg) (x) = 3x^3 - 4x^2 + x -18x^2+24x -6

(fg) (x) = 3x^3 - 22x^2 + 25x - 6

(fg) (0) = 3(0) - 22(0) + 25(0) - 6

(fg) (0) = -6

Hence, The values of (f+g)(0) , (f-g)(0) , (fg)(0) are -5 , 7,-6 respectively for the given functions f(x) = 3x^2 - 4x + 1 and g(x) = x-6

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The place value of the digit 6 in the given number is 0.006

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number. For example, the place value of 7 in 3,743 is 7 hundreds or 700. However, the place value of 7 in 7,432 is 7 thousands or 7,000.

Given that, California receives average rainfall of 0.476 m per year, we need to find the place value of 6 in the number given,

The number is 0.476

We know that, the first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredths place. The remaining digits continue to fill in the place values until there are no digits left.

Here, the place of 6 is after 2 digits after the decimal,

Therefore, the place of 6 is thousandths place,

Therefore, the digit 6 has value = 6 × 1/1000 = 0.006

Hence, the place value of the digit 6 in the given number is 0.006

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The three decimal numbers are 0.5, 2.25 and 3.25 as Exactly one of the numbers is less than .

What is an average ?

average can be defined as ratio of the sum of the observations and total number of observations

From the information given,

we have to get three decimal numbers that have their sum as 6.0

Therefore, the three decimal numbers are 0.5, 2.25 and 3.25.

In order to confirm this, we can add the numbers together and check. This will be:

= 0.5 + 2.25 + 3.25 = 6.0

Also, from the numbers, 0.5 is less than 1.

Hence , The three decimal numbers are 0.5, 2.25 and 3.25.

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A triangle's x value is 120°. Using a triangle angle characteristics, an unknown angle can be found.

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When lines a and b overlap, angle 1 equals angle 3.

The intersection of two lines in Euclidean geometry might be the empty set, a point, or another line. Distinguishing these circumstances and locating the intersection have applications in computer graphics, motion planning, and collision detection, among others. When two or more lines intersect on a plane, they are referred to as intersecting lines. The crossing lines have a common point, which exists on all of them and is known as the point of intersection. The intersecting lines are two lines that have precisely one common point. The crossing lines have a point in common. The point of intersection is the common point that exists on all intersecting lines.

Here,

To prove ∠1 ≅ ∠ 3, we can use the congruent supplements theorem. According to the congruent supplements theorem, If two angles are supplements of the same angle then two angles are congruent.

Line a and line b intersect                                         (given)

∠3 is supplementary to ∠2 because of linear pair theorem (given)

So, if we take ∠2 as the common angle

And  ∠1 is supplementary to ∠2  by linear pair theorem     ( option D)

Then, ∠1 is supplementary to ∠2 which is supplementary to ∠3

Therefore, ∠1 ≅ ∠3 (according to the congruent supplements theorem)

This is proved when line a and line b intersect, angle 1=angle 3.

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The range of the function is {0.16, 0.4, 1, 2.5, 6.25}. With an increase in the value of the domain, the range of the function is increasing.

What is a function?

A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

The given function is

f(x) = 2.5^x.

Given domain is {-2, -1, 0, 1, 2}.

Now putting x = -2, -1, 0, 1, 2 in the function f(x) = 2.5^x.

When x = -2:

f(-2) = 2.5^(-2)

f(-2) = 0.16.

When x = -1:

f(-1) = 2.5^(-1)

f(-1) = 0.4

When x = 0:

f(0) = 2.5^(0)

f(0) = 1.

When x = 1:

f(1) = 2.5^(1)

f(1) = 2.5

When x = 2:

f(2) = 2.5^(2)

f(2) = 6.25

The range of the function is {0.16, 0.4, 1, 2.5, 6.25}

The values of the range increase with the increase of domain.

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25% percent of Amanda's day was spent on either meals or homework.

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(-4,-3)

x=-4,y=-3

Step-by-step explanation:

solve for the first variable in one of the equations, then substitute the results into the other equation. point form:

Find out the perimeter of an Ellipse (oval,egg) we can use the by using the formula, perimeter = π × (a + b)[1 + (3 × h/(10 + √(4 - 3h)))]

The length of an ellipse's boundary is its perimeter. It is sometimes referred to as the ellipse's circumference (recall that perimeter is also known as the circumference for the curved shapes).

The length of an ellipse's boundary is its perimeter. It is sometimes referred to as the ellipse's circumference (recall that perimeter is also known as the circumference for the curved shapes). The orbits of the planets in our solar system, as well as 2D illustrations of objects like eggs and watermelons, are some instances of ellipses in nature. The collection of all points whose distance from two fixed points (referred to as foci) is always constant is known mathematically as an ellipse.

The circumference of the ellipse can be calculated using one of three approximate formulas. When the ellipse is nearly circular, or when the values of a and b are roughly equal, the first one is employed. When one of the values of "a" and "b" is noticeably larger than the other value, the second (or third) formulas are employed.

We can use either formula 2 or 3 to determine the perimeter when the values of "a" and "b" are not exactly identical. Formula 3 provides a value that is smaller than the actual value, but formula 2 provides a bigger value. By averaging the results from formulas 2 and 3, we can therefore reach a result that is reasonably close.

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Answer:

x = 3 ; y = 2

Step-by-step explanation

3x - y = 7

= 3x - y - 7 = 0

= 3x - 7 = y — (equation i)

Substitute (equation i) into the second equation:

3x + (3x - 7) = 11

Expand the brackets by applying the Distributive Law and bring all the like terms together:

3x + 3x - 7 = 11

= 6x - 7 = 11

= 6x = 11 + 7

= 6x = 18

= x = [tex]\frac{18}{6}[/tex]

= x = 3

Substitute the calculated value of x into (equation i) to determine the value of y:

3 x - 7 = y

= 3(3) - 7 = y

= 9 - 7 = y

= y = 2

On solving the provided question, we can say that we have the equations as  y = 3x - 7 where x > 0. so let us assume x = 4 = > y = 5

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

we have the equations as

y = 3x - 7 where x > 0

so let us assume x = 4

y = 5

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Answer:

x = 108

Step-by-step explanation:

78-(x-60)=30

Solving for x,

x = 78-30+60

x = 108

The measure of angle RSN is obtained as follows:

m < RSN = 31º.

First we must consider that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angles of triangle RST, along with their measures, are given as follows:

The sum of these three measures is of 180º, hence the value of x is obtained as follows:

3x + 17 + 8x - 32 + 2x = 180

13x = 195

x = 195/13

x = 15.

Then the measure of angle RST is given as follows:

m < RST = 3(15) + 17

m < RST = 62º.

Angle RSN is a bisection of the angle RST, meaning that it has the measure half that of RST, hence:

m < RSN = 0.5 m < RST

m < RSN = 0.5 x 62

m < RSN = 31º.

The diagram is given by the image presented at the end of the answer.

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Answer:ok

Step-by-step explanation:kk

The two sides are x and 2x.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

Given here: In a triangle ABC,point D divides side DC in the ratio AD:DC is 1:2

Thus the two sides are x and 2x respectively.

and x+2x=DC

Hence, The two sides are x and 2x.

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The following are the solutions for the student data:

a. 25 students like exactly two of the composers

b. 31 students like exactly one these composers

c. 10 students like only Mozart

d. 19 students like haydn and exactly one of the other two composers

e. Only one student like none of these composers.

Venn diagrams are commonly used in mathematics, statistics, and logic to illustrate relationships between sets of data. It consists of circles that overlap to show the similarities and differences between the sets like in the case of students data.

Students who like:

All three composers = 8

Only Mozart and Beethoven = 14 - 8 = 6

Only Mozart and Haydn = 20 - 8 = 12

Only Beethoven and Haydn = 15 - 8 = 7

Only Mozart = 36 - (6 + 12 + 8) = 10

Only Beethoven = 37 - (6 + 7 + 8) = 16

Only Haydn = 32 - (12 + 7 + 8) = 5

Students who like none of the composers:

65 - (10 + 16 + 5 + 12 + 6 + 7 + 8)

65 - 64 = 1

Therefore, students who like:

exactly two of the composers = 12 + 6 7 = 25 students

exactly one these composers = 10 + 16 + 5 = 31 students

only Mozart = 10 students

Haydn and exactly one of the other two composers = 12 + 7 = 19 students

none of the composers = 1 student

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"And Miss Brill's eyes filled with tears and she looked smiling at all the other members of the company. Yes, we understand, we understand, she thought though what they understood she didn't know." Option B

Generally, When academics discuss the idea of a social connection, they are referring to the sensation of being a part of a community and having a general sense of proximity to the members of that community. It is clear from the information that science has gathered that this is a fundamental psychological need that must be met in order to experience contentment with one's life.

A human connection is a profound link that develops between individuals as a result of their shared experience of being noticed and loved. People are able to trust one another and share good energy with one another when they are having genuine human connections.

Human connection enables one to experience being heard and understood, as well as a feeling of belonging to a group.

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