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1) Q.1 Find the equation of a line that passes through (1, 2) and (5, 4).

Hate to have to tell you this but we need to see the homework to be able to help

The original price of the blender before the discount is $49.41.

We shall represent the original price of the blender with the letter x so that we use $x to evaluate for the original price before the discount price as follows:

x - 15x/100 = $42 {simply the left hand expression to a single fraction}

(100x - 15x)/100 = $42 {simply the terms in the bracket}

$85x/100 = $42

$85x = $4200 {cross multiplication}

$85x/$85 = $4200/$85 {divide through by $85}

x = $49.41

Therefore, the original price of the blender before the discount is $49.41

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The mantissa of scientific notation is between 1 and 10 in absolute value, or 1 ≤ |a| < 10.  It can be 1, hence, it does not have to be greater than 1.

A scientific notation has the form:

a x 10ᵇ

Where b is an integer and is called exponent.

a is a real number between 1 and 10 (in absolute value), it includes 1 but not 10, or we can write a should satisfy 1 ≤ |a| < 10.

Usually, a is called mantissa.

Example:

2567 can be written in scientific notation as:

2567 = 2.567 x 10³

0.0045 can be written in scientific notation as:

0.0045  = 4.5 x 10⁻³

250 x 10² can be written in scientific notation as:

250 x 10² = 2.5 x 10⁴

-0.032 can be written in scientific notation as:

-0.032 = -3.2 x 10⁻²

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Answer:

Refer to the step-by-step

Step-by-step explanation:

Since ∠1 and ∠2 are alternate exterior angles, m∠2=108°

The polynomial 3x³ 2x² +3 can be written as 3x³ + 2x² + 3. In order to get the polynomial 3x² + 4, we need to add a polynomial which is equal to -3x³ + 5x² + 1.

Therefore, the correct answer is (3) - 3x3 + 5x2 +1.

We can confirm this by performing the following calculation:

3x³ + 2x² + 3 + (-3x³ + 5x² + 1) = 3x² + 4

3x³ + (-3x³) = 0

2x² + 5x² = 7x²

3 + 1 = 4

Therefore, 0 + 7x² + 4 = 3x² + 4, which confirms that the correct answer is  3x3 + 5x2 +1.

3x3 + 5x2 +1 is the polynomial should be added in 3x³ 2x² +3 to get the polynomial 3x² +4.

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The statement that describes a relationship that has a negative slope: "Greg pays $25 each time he goes rock climbing".

A negative slope indicates that two variables are adversely connected; that is, when x rises, y falls, and when x falls, y rises. A negative slope on a line graph signifies that the line falls as it travels from left to right. For example, when the number of individuals that quit smoking (x) grows, the number of persons developing lung cancer (y) drops. This relationship's graph has a negative slope. Positive slopes are predicated on the fact that when x grows, so does y, hence the change in y/change in x is positive. Negative slopes are based on the fact that when x grows, y decreases, resulting in a negative change in y/positive change in x, yielding a negative response.

Here,

"Greg pays $25 every time he goes rock climbing," says the statement describing a connection with a negative slope.

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The given fraction converted to a decimal fraction is 1.4

The given fraction converted to a mixed fraction in its lowest terms is 1 2/5

From the question, we are to convert the given fraction.

The given fraction is

14/10

Converting to a decimal fraction

14/10 = 1.4

Converting to a mixed fraction

14/10 = 1 4/10

Reducing the fraction

14/10 = 1 2/5

Hence,

The fraction converted is 1.4 and 1 2/5

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The value of the missing angle m<JKL is; 46º

Since we are told that the angle KN bisects ∠LKM then to get m<LKN, we just multiply 26° by 2 to get;

m<LKM =  26° * 2

= 52º

Now, since JKM is the total of all angle measurements, then we can say that;

88 - 52 = 36 degrees

Thus; m<JKL = 46º

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Answer:

The scale factor is 3. Step-by-step

Step-by-step explanation:

The line of the best fit of the scatter plot is line 2

From the question, we have the following parameters that can be used in our computation:

The graph

A good line of best fit would have equal number of points on either sides

On the graph, we can see that the lines 1 and 3 divide the points on the line unevenly

Where as, the line 2 divides the scatter points approximately evenly

Hence, the line of the best fit is line 2

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Answer:

The exponential form of 5184 is 5184

In simple words, the exponents can said to be the powers of the base. For example, in 2³, the exponent will be 3. If a number is given without any power then its power is 5184. The exponential form is simply the number with exponents.

The range of this graph (see attachment) include the following: {8, -6}.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following:

Domain = -6 < x < 11 or [-6, 11].

Range = -6 < y < 8 or [-6, 8].

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The ratio of carp to salmon for each lake is given as follows:

Then the ascending order on the proportion of fish that are salmon is given as follows:

Lake b, Lake c, Lake c.

The ratio of an amount A over an amount B is obtained applying the proportion of these amounts, that is, the division of A by B.

The ratios of carp to salmon, in the form 1:n, are obtained considering that n is the division of the number of salmon by the number of carp, hence:

The higher rates of salmon have the higher values of n, thus the ascending order of the proportion of fish that are salmon is given as follows:

Lake b, Lake c, Lake c.

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Answer:

Step-by-step explanation:

y = x + 8

x + y = 2

using substitution, since y is equal to x + 8 we substitute it for the y in x + y = 2

so we get: x + (x+8) =2

then we simplify, getting 2x + 8 = 2

We make the x on its own on one side of the equation by subtracting 8 on both sides.

2x = -6

divide

x = -3

y = 5

(if x = -3, y = 5 because -3 + 8 =5)

test answer

5 = -3 + 8 works and -3 + 5 = 2 works as well

Answer:

4 feet per hour

Step-by-step explanation:

48 inches is 4 feet in total

4 x 12 =48

The line that has the constant of proportionality between y and x of 1 / 2 , is C. Line C.

The ratio used to compare changes in one variable to those in another is known as the constant of proportionality. The dependent variable fluctuates more with the independent variable when the proportionality constant increases.

The formula for the constant of proportionality is:

= Value of y / Value of x

For Line A we have point ( 1, 7 ) so the constant of proportionality is:

= 7 / 1

= 7

For line B, we have point (2, 3 ) so the constant of proportionality is:

= 3 / 2

= 1 . 5

For line C, we have point ( 4, 2 ) so the constant of proportionality is:

= 2 / 4

= 1 / 2

Line C is the line with a constant of proportionality of  1 / 2.

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Log2 of 0 is undefined. Log values can be defined for only real numbers which is greater than 0.

It is not defined because log values is defined only for numbers greater than zero but not zero and negative numbers. It's not a real number, because you can never get zero by raising anything to the power of anything else. You can never reach zero.

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The paragraph proof is a proof written in the form of a paragraph. In other words, it is a logical argument written as a paragraph, giving evidence and details to arrive at a conclusion.

Paragraph proofs are comprehensive paragraphs that explain the process of each proof. Like two-column proofs, they have multiple steps and justifications. But instead of columns, the given information is formatted like a word problem — written out in long-hand format.

Since vertical angles are congruent, it is known that angle DCB is congruent to angle ACE. It can now be concluded that triangle DCB is congruent to triangle ACE according to the Side-Angle-Side (SAS) theorem.

There are two different types of proofs: informal and formal. Formal proof is often introduced using a two-column format, as favored by many geometry teachers.

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Complete question:

What is a Paragraph prove statement?

Answer:

-------------------------------

Patrick has spent:

Oscar has spent:

Since they both spent same amount of money, we have:

They both spent 2 hours and $(2 + 11) = $13.

Step-by-step explanation:

PLEASEEEE GIVE BRANLIEST

Answer:

60+15+20+21+20+30+45= *212*

Yes, Number 512 represents it is a multiple of 8 is a true statement.

As given in the question,

Given number is equal to 8,

Given multiple is equal to 512 :

Multiple of any number is the representation of any number multiply by some integer.

When we multiply 8 by different integers we get its multiple as follow:

8, 16, 24, 32, 40, 48, 56, 64, 72,..... and so on.

When we multiply 64 by 8 we get 512.

Yes , the given statement is true.

Therefore, 512 represents a multiple of 8 which we get when we multiply 8 by 64 represents that the given statement is true.

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Answer:

IF tan(theta) = -8/7 = opposite side/adjacent side, then that means that sin(theta) = -8/(sqr(64+49) = -8/sqr113 = about -0.7526

Step-by-step explanation:

the tangents are negative in the quadrant II or IV

and sines are negative in the quadrant III or IV

so i think that this angle is in quadrant IV to satisfy for the of the both requirements.

but angle 0 seems to try and mean something other than 0 degrees or 0 radians. so It probably just means theta, which is a 0 probably with a line through it

IF tan(theta) = -8/7 = opposite side/adjacent side, then sin(theta) = -8/(sqr(64+49) = -8/sqr113 = about -0.7526

I hope this helps

The graph for each equation and inequality is shown below.

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

a)  2y – 4x < 8

The graph area is shaded with red region.

b)  -4y > -x + 12

The graph area is shaded with blue region.

c) | x + 3 |= y

The graph has the vertex at (-3, 0).

d) |2x – 6| + 2 = y

The graph has the vertex at (3, 2).

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Answer:

23

Step-by-step explanation:

Given Information:

If we have to evaluate f(-2), we can consider that f(x) = f(-2) = 6x²- 2x - 5.

Now, we can substitute the solution into the quadratic equation and simplify it to its simplest possible form using the solution (x = -2).

Therefore, the evaluated form for f(-2) is 23.

The situation regarding the experimental probability is described as follows:

The probability that she makes a shot is of 62.5% = 5/8. Use whole numbers from 1 to 8, with 1-5 representing shots that she makes, and 6-8 representing the shots that she misses. For each trial, generate 10 random numbers. Count the number of trials in which the numbers 1 - 5 appears 3 or more times. Divide the number of trials in which she made at least 3 shots by the total number of trials.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The theoretical probability of making a shot in this problem is given as follows:

62.5%.

The equivalent fraction is given as follows:

5/8.

Hence, to obtain the experimental probability, we need to design an experiment for which there are eight possibilites, with five of them composing a success and three of them composing a failure.

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The value of A when x - 5 is a factor of x³ - 3x² + ax - 10 is -8.

A polynomial factor is a polynomial that divides another polynomial exactly, with no remainder.

For example, if we have a polynomial P(x) = x³ - 3x² + ax - 10, and we have a polynomial factor F(x) = x - 5, we can say that P(x) is divisible by F(x) with no remainder.

In general, a polynomial of degree n has n roots (or zeroes) and the factorization of polynomial can be expressed as a product of its roots and its corresponding multiplicity.

To find the value of A, set x = 5 in the equation x³ - 3x² + ax - 10 and solve for A that will make the equation equal to zero..

So when x = 5, we have:

x³ - 3x² + ax - 10 = 0

(5)³ - 3(5)² + a(5) - 10 = 0

125 - 75 + 5a - 10 = 0

5a = -40

a = -8

Hence, if x - 5 is a factor of x³ - 3x² + ax - 10, then A is equal to -8.

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The statements that relate each function are given as follows:

1. At 3 seconds, the toy rocket is higher than the drone: f(3) > g(3).

2. At the start, the toy rocket is 25ft above the drone: f(0) - g(0) = 25.

The four inequality symbols, along with their meaning, are presented as follows:

The functions for this problem are given as follows:

At 3 seconds, we have that the toy rocket is higher than the drone, that is, f(3) is greater than g(3), hence the inequality is given as follows:

f(3) > g(3).

At the start, the heights are given as follows:

The difference is of 25 ft, hence the expression is given as follows:

f(0) - g(0) = 25.

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