Section
B
Determine whether the ordered pair
on the graph.
lies
1) (-3, 4): y = -2x +1
2) (2, 9): y = 6x-3
3) (4,3): 2x-5y = -7
4) (-5, 6): -8x +4y=10
5) (-1,0): -4y = 2x +3
6) (0₁-2): 6y=x+3

y= x/2 -3 , y+3x = 12 and y = x  are determined as linear equations , while y=6/x -2 and y= 3x^3  +5 are non-linear equations.  

A linear equation is a mathematical equation that forms a constant straight line on a graph.

Non-linear equations are functional equations that form different types of curves or other non-linear shapes on a graph.

According to the slope-intercept formula of the straight line : y=mx+b

1. y=6/x - 2 ,is not satisfying the above formula of straight line , having x in the denominator, hence it is a non-linear equation.

2. y=x/2-3 , here slope(m)=1/2 and intercept(b)=-3 which are real numbers and satisfy the straight line formula , hence it is a linear equation.

3. y=-3x+12, here slope(m)=-3 and intercept(b)=12 as real numbers and satisfy the straight line graph formula , hence it is a linear equation.

4. y = 3x^3+5, here slope(m)=3x^2 which is not a real number, hence not satisfying the given formula it is a non-linear equation.

5. y = x , here slope(m)=1 and intercept(b) =0 which are real numbers and satisfy the straight line graph formula ,hence it is a linear equation.

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The function's domain is (a) all real numbers.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set. A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.

The formula for the function is: f(x) = Negative 5/6. X in superscript?

The function mentioned above is exponential

There are no input value restrictions for exponential functions

Consequently, the function's domain is (a) all real numbers.

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The slopes and points are:

a) (-3/4) and the point is (4, 9)

b) (-2/3), and the point is (-4, 3)

A line with a slope a and a known point (h, k) can be written as:

y - k = a*(x - h)

So that is the slope-point form of the linear equation.

a) The first linear equation is:

y - 9 = (-3/4)*(x - 4)

Comparing this with the general line above, we can see that the slope is (-3/4) and the point is (4, 9)

b) y = 3 - 2/3 (x +4)

We can rewrite this as:

y - 3 = -(2/3)*(x + 4)

Then in this case the slope is (-2/3), and the point is (-4, 3)

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Answer: w=14

Step-by-step explanation: The way I solve it is if you take 27 and subtract 13 from it, you'll get 14. Hope this helps!

Answer:

w=14

Step-by-step explanation:

hope this helps...

The analysis of the logical statement from among the  options indicates that the inference that is not true is the option;

A logical statement is one which draws a conclusion based on an hypothesis.

The logical statement which is incorrect can be found by examining the specified statements as follows;

If p then q,

The converse statement , found by switching the positions of the hypothesis and the conclusion is therefore;

q therefore p

The inference is correct

The statement, if not p, not q . q therefore not not p

According to the law of contraposition, a conditional statement is true when the contrapositive statement is also true.

The statement if not p, not q. which is the contrapositive of the statement if q then p

The inference, q, therefore not not q is incorrect

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Answer:

Step-by-step explanation:1.08%

Interest rate required in order for Kiran to end up with $9,500 is 4.55%.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Given,

Principal amount = $6,600

Time in years = 8 years

Final amount = $9,500

The final amount is calculated in compound interest by the formula,

A = P (1 + [tex]\frac{r}{n}[/tex]) ^ (n t)

Here, P is the principal amount, r is the rate of interest, n is the number of  years.

Substituting in the formula,

9500 = 6600 (1 + [tex]\frac{r}{365}[/tex]) ^(365 × 8)

9500 / 6600 = (1 + [tex]\frac{r}{365}[/tex])²⁹²⁰

1.4394 = (1 + [tex]\frac{r}{365}[/tex])²⁹²⁰

1.000125 = 1 + [tex]\frac{r}{365}[/tex]

[tex]\frac{r}{365}[/tex] = 0.00125

r = 0.045531

r = 4.5531% ≈ 4.55%

Hence the interest rate to the nearest hundredth of a percent is 4.55%.

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Answer:

You will need to use information from (a)

False. While using the right sampling technique can increase the probability of getting sample mean values that are close to population mean values.

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics.

The sample mean is the mathematical average of values selected at random from the population. The population mean is a representation of the population's real mean.

It is impossible to ensure that the sample mean and population mean will be a perfect match. This is because sampling has intrinsic variability and randomness, which can cause discrepancies between the sample and the population even in studies that are carefully planned. Additionally, there could still be some variability or error in the estimates even if the sample mean is quite near to the population mean, which might have an impact on the accuracy of the findings.

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The percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.

According to the question,

We have the following information:

Greg evaluated his spending and found that he was spending about $50 more per month on utilities than he has budgeted. He can transfer money from other categories to increase his utilities budget to $125 per month. If his total monthly income is $2,400.

Now, let's take the percent to be x.

We have the following expression:

2400*x/100 = 125

24x = 125

x = 125/24

x = 5.21%

Hence, the percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.

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Answer:

The maximum value of a function can be found at its highest point, or vertex, on a graph

Step-by-step explanation:

Answer: x > or = to 4 (Inequality Form), [4, infinity) (Interval Notation)

Step-by-step explanation:

Isolate the equation.

Divide each side by the factors that do not contain x.

Solve for x.

The ratio of the segments formed on each transversal are equal.

  AB/CB = EF/DF

How do parallel lines work?

In terms of geometry, parallel lines are two separate lines that never cross each other and are located in the same plane. They may be vertical or horizontal.

The equation of the parallel lines are;

y = x, and y = x + 1

The point of intersection of transversal 1 and the parallel lines y, and z

(0.2, 0.2), and (0.3, 0.8)

The length of segment AB = √((0.3 - 0.2)² + (0.8 - 0.2)²) = 0.1·√(37)

The point of intersection of transversal 1 and the parallel lines x, and y

(0.3, 0.8), and (0.4, 1.4)

The length of segment CB = √((0.4 - 0.3)² + (1.4 - 0.8)²) = 0.1·√(37)

The ratio of the lengths of the line segments formed by the transversal 1, AB:CB is found as  follows;

              AB/CB = 0.1 . √37/ 0.1 . √37  = 1

The point of intersection of transversal 2 and the parallel lines y and z are;

(0.8, 0.8), and (0.7, 1.2)

The length of segment EF = √((0.7 - 0.8)² + (1.2 - 0.8)²) = 0.1·√(17)

The point of intersection of transversal 2 and the parallel lines x and y are;

(0.7, 1.2), and (0.6, 1.6)

The length of segment DE = √((0.6 - 0.7)² + (1.6 - 1.2)²) = 0.1·√17

The ratio of the lengths of the line segments formed by the transversal 2, EF:DE is found as  follows;

                EF/DF  =  0.1 . √17/ 0.1 . √17 = 1

Therefore:

The ratio of the lengths of the two line segments formed on each transversal are equal.

                AB/CB = EF/DF

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The time calculation which involve calculating the time in GMT when it is 1:31:45 PM EDT (Eastern Daylight Savings Time) is

The conversion given in the problem is

Eastern Daylight Savings Time = Greenwich mean time GMT - 4

Eastern Daylight Savings Time + 4 = Greenwich mean time GMT

Solving for the time equivalence in Greenwich mean time

Greenwich mean time GMT = Eastern Daylight Savings Time + 4

substituting known values

Greenwich mean time = 1 : 31 : 45 PM + 4

Greenwich mean time = 5 : 31 : 45 PM

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Answer: To determine the estimated age of the artifact, we can use the half-life of carbon-14 and the percentage of carbon-14 that is present in the artifact.

The half-life of carbon-14 is the amount of time it takes for half of the carbon-14 in a sample to decay. In this case, the half-life of carbon-14 is 7,730 years.

The percentage of carbon-14 that is present in the artifact is 44%. This means that the artifact contains 44% of the carbon-14 that it would have had when it was originally made.

To determine the age of the artifact, we can use the formula:

age = (half-life / log(2)) * log(percentage of carbon-14 / 100)

Substituting the values from the problem into the formula, we get:

age = (7,730 years / log(2)) * log(44% / 100)

age = (7,730 years / 0.693) * log(0.44)

age = 11,095 years * (-0.847)

age = -9,432 years

Therefore, the estimated age of the artifact is -9,432 years.

It is important to note that this is just an estimate, and the actual age of the artifact may be different. Carbon-14 dating is only accurate up to a certain point, and the accuracy of the age determination depends on several factors, including the initial concentration of carbon-14 in the sample and the presence of any contaminants.

The system of equations that to be used to calculate the number of chicken wings (x) and sliders (y) in the combination meal:

55x + 275y = 1100 and y = 8x.

A system of equations is a collection of one or more equations with multiple variables.

Let x represent each onion ring.

Allow each slider to be represented by y.

That is what we are told;

The calorie count for each onion ring is 55.

The number of calories in each slider is 275.

A combination meal of both contained 1100calories.

Thus;

The equation formed wiil be,

55x + 275y = 1100

It also shows that there are 8 more onion rings than as many sliders.

Thus;

The equation formed is,

y = 8x

Therefore the system of equations in the combination meal are as follows: 55x + 275y = 1100 and y = 8x.

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In linear equation,    x = 1  is the maximum height, in feet, reached by the pebble.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The height of the pebble over time is modeled by the equation

        y = -16x2 + 32x + 80

At the maximum height, the final velocity of the pebble is zero.

The velocity of the pebble will be obtained by taking the derivative of the given equation.

That is

                y' = dy/dx

                    = d/dx (-16x2 + 32x + 80 )

                    = -32x + 32

At the maximum height, y' = 0 .

So,

        -32x + 32 = 0

  32x = 32

    x = 32/32

    x = 1

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Answer:

1 cup of banana for 2 cups of flour

Step-by-step explanation:

Divide 4 cups of banana by 4 and 8 cups of flour by 4

Then you will get 1 cup of banana for 2 cups of flour

Equation of the line in slope intercept form is y = x - 5, when slope is 1 and a point on the line is (-12, -17).

Slope of a line is the degree of inclination of that line.

In other words, slope of a line can be calculated by taking the change in y coordinates to the change in x coordinates when x coordinate and y coordinate of two points are given.

Equation of a line in slope-intercept form is,

y = mx + c

where, m is the slope and c is the y-intercept.

y- intercept is the y-coordinate of a point where the line touches with the Y-axis. x coordinate will be zero at this point.

We have m = 1 and a point (x, y) = (-12, -17)

Substituting these values in the equation,

-17 = (1 × -12) + c

-17 + 12 = c

c = -5

Substituting m = 1 and c = -5, equation in slope intercept form can be written as,

y = x - 5

Hence, the equation of the line in slope intercept form when slope = 1 and passing through the point (-12, -17) is y = x - 5.

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Difference in miles walked between 2 teams is 2x+12.

Team A walks total of 6*x+12 miles.

let's suppose Team A walks y1 miles

y1 = 6*x+12.

Team B walks total of 4x-7 miles

let's suppose Team B walks y2 miles

y2 = 4*x-7

Let's understand what means by difference?

One of the most crucial mathematical operations, which is obtained by removing two numbers, produces difference in mathematics. It reveals how much one number deviates from another. To determine how many numbers are between the two given numbers is the goal of finding the difference in math.

Difference in miles walked between 2 teams

=  y1-y2.

=  6x+12-(4x-7)

= 6x+12-4x+7

=2x+12

So the difference in miles walked between 2 teams is 2x+12.

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Answer:

medium is 5 dollars and 39 cents

large is 6 dollars and 89 cents

Step-by-step explanation:

3m + 2l = 29.95

4m + l = 28.45

3m + 2l = 29.95

8m + 2l = 56.9

-5m = -26.95

5m = 26.95

m = 5.39

3(5.39) + 2l = 29.95

16.17 + 2l = 29.95

2l = 13.78

l = 6.89

Answer:

13/15

Step-by-step explanation:

Step 1) Convert to -5/15 - (-18/15)

Step 2) -5/15 - (-18/15)= 13/15

Answer:

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

Let the number be N.

If N is divided by 5 the remainder is 3:

Similarly:

We can observe N + 2 is divisible by both 5 and 6, then it can be represented as:

so

The left side is divisible by 3, then q = 3t:

The least m and t would be m = 5 and t = 7.

Then:

Proof:

Answer:

either h=12, b=5

or h=5, b=12

Step-by-step explanation:

We'll use a system of equations to solve this. We'll have 2 equations and 2 unknowns. Our 2 unknowns are the 2 other sides, and our 2 equations are as follows:

look for any information given. I see that the area is 30 sq.cm and the perimeter is 30cm. There are our pieces of information.

Our first equation will be the one about how the area is 30 sq.cm (we'll use b for base and h for height:

(1/2)×b×h=30

Our second equation will be the one about how the perimeter is 30cm:

13+b+h=30

These equations both have to be true at the same time, and there are a few techniques for solving a system of equations, but in this case, this way is probably the simplest. We'll get one variable on one side of an equation and then plug it into the other equation using the transitive property.

13+b+h=30

b=30-13-h

b=17-h

now we'll plug in (17-h) for all the b in the first equation:

(1/2)×(17-h)×h=30

17h-h²=60

-h²+17h-60=0

now we'll use quadratic formula (or factor) to find h:

[-17±√(289-240)]/-2

(-17±7)/-2

-24/-2 or -10/-2

12 or 5

h=12

h=5

we'll try both of them in this equation:

13+b+h=30

25+b=30

or 18+b=30

therefore;

either h=12, b=5

or h=5, b=12

5% of the students either passed all 3, or none of the tests.

What is amount ?

Mass nouns are referred to by the word amount. Count nouns are referred to as numbers.

To illustrate the process of thinking, tets assume there are no people who passed all subjects.

40% (Maths) - 10%(+sceince) - 15% (+english) = 15% only maths

45% - 10% - 20% = 15% only science

55% - 20% - 15% = 20% only english.

That gives

15+15+20 = 50% of the students passing only one course

10+20+15 = 45% of students passing only 2 courses

… that’s 95% together …

… but we need to get to 100%; obviously.

If we assume there are X% students that passed in all 3 courses, then from the first line, we substracted this person twice: (once for +science, and once for +english). Considering we only need to substract ’m once, that’s the same as substracting twice and adding once. we get:

40% (Maths) - 10%(+sceince) - 15% (+english) + X% = 15+X % only maths

and likewise

45% - 10% - 20% + X= 15 +X % only science

55% - 20% - 15% +x X= 20 +X % only english.

Now, for the students who passed exactly 2 classes, that’s

10 - X % only maths and science

20 - X %

15 - X%

And of course, the amount of students who passed all three exams: X.

This gives us

(15+X) + (15+X) + (20+X) + (10-X) + (20 - X) + (15 - X) + X = 100

95 + X = 100

X = 5

Or, 5% of students passed all 3 tests.

edit: this answer assumes all students pass at least one test. The actual summation should be: As pointed out with the first line, if that answer is

0%, the amount of students mentioned is 95%.

The actual answer is

5% of the students either passed all 3, or none of the tests.

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(2) The statements and reasons in the two-column method are presented as follows;

Statement [tex]{}[/tex]                                           Reasons

1. [tex]\overline{BD}[/tex] bisects ∠ABC [tex]{}[/tex]                          1. Given

2. ∠BAD ≅ ∠BCD   [tex]{}[/tex]                            2. Given

3. ∠ABD ≅ ∠CBD    [tex]{}[/tex]                           3. Definition of angle bisector

4. [tex]\overline{BD}[/tex] ≅ [tex]\overline{DB}[/tex]    [tex]{}[/tex]                                    4. Reflexive property

5. ΔABD ≅ ΔCBD     [tex]{}[/tex]                          5. AAS congruency postulate

(3) The two-column method used to prove the congruency of triangles ΔQRS and ΔSTU, is presented as follows;

Statement       [tex]{}[/tex]                                           Reason

1. S is the midpoint of [tex]\overline{QU}[/tex]       [tex]{}[/tex]                 1. Given

2. [tex]\overline{QR}[/tex] ≅ [tex]\overline{ST}[/tex]        [tex]{}[/tex]                                       2. Given

3.  [tex]\overline{RS}[/tex] ≅ [tex]\overline{TU}[/tex]        [tex]{}[/tex]                                       3. Given  

4.  [tex]\overline{QS}[/tex] ≅ [tex]\overline{SU}[/tex]        [tex]{}[/tex]                                  4. Definition of midpoint of [tex]\overline{QU}[/tex]

5. ΔQRS ≅ ΔSTV           [tex]{}[/tex]                            5. SSS congruency postulate

The two column method consists of statements and  the associated reasons arranged sequentially side by side in a two-column tabula format.

The reasons used to prove the above statements are as follows;

Angle bisector

An angle bisector is a segment that divides an angle into  two angles of the same measure.

Reflexive property

The reflexive property of equality states that the value of an object or the measure of a dimension is equal to itself

AAS congruency postulate

AAS which is the acronym for Angle-Angle-Side  congruency, states that  if two angles and a non included side of one triangle are congruent to two angles and the non  included side of  another triangle, then  the two triangles are congruent

Midpoint of a line

The midpoint of a line is a point that divides the line into two segments of the same measure.

SSS congruency postulate

The Side-Side-Side congruency postulate states that two triangles are congruent if three sides are congruent to three sides of the other triangle

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To calculate the total area of the cylinder, we need to use the formula for calculating surface area; SA = 2πr² + 2πrh. In this case, r is equal to 1.5 yards and h is equal to 24 yards:

SA = 2(3.14)(1.5^2) + (2)(3.14)(1.5)(24)

= 28 ft² + 144 ft²

= 172 ft²  

Therefore, we need 172/150 gallons of paint in order to cover both sides of the ilo with one coat each - approximately 1 gallon and 14 fluid ounces or about 1 3/4 gallons of paint will be needed in total

What is Surface Area?

The area is the area occupied by a flat, two-dimensional surface. It is expressed in square units. The surface area of a three-dimensional object is the space taken up by its exterior surface.

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The height of the candle after 11 hours is 20.5 if the slope is -0.5.

The ratio of "vertical change" to "horizontal change" between any two separate points on a line, or any two points, is used to compute slope. When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line. The line may be practical, as determined by a road surveyor, or in a diagram that represents a roof or a road as a description or a design.

The absolute value of the slope serves as a proxy for a line's steepness, incline, or grade.

Given, slope m= -0.5

(y-y₁)=m(x-x₁)

Also given that,

x=19, y=16.5 cm

(y-16.5)=m(x-19)

y-16.5= -0.5(x-19)

y-16.5= -0.5x+9.5

0.5x+y-26=0

After 11 hours, the height of the candle is:

x=11

0.5(11)+y-26=0

y=26-5.5

y=20.5

Therefore, the height of the candle after 11 hours is 20.5

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Inequality is 2x+178 >=2000. and Solution set is x>=911 i.e., the no: of cans that Shane should have collected

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has different meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are shared.

Lifetime Inequality (the distribution of incomes across households or individuals over a person's lifetime), Inequality of Wealth (the distribution of wealth across households or individuals at a particular point in time), and Inequality of Opportunity (the impact on income of factors that people cannot control) are all related concepts.

Let the number of cans collected by Shane = x and the number of cans collected by Abha = y.

It is given that, Abha collected 178 cans more than Shane.

So, we have, .

Since, they both have to collect cans no less than 2000 i.e. greater than or equal to 2000.

So, the equation representing the situation is,

Shane + Abha ≥ 2000

i.e. y + x ≥ 2000

Thus, by substitution we have,

Inequality for the number of cans Shane collected is .2x+178 >=2000.

Solution set of the inequality is x>=911.

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The new coordinate for point B is (0,2). Hence option B is the correct option.

What is coordinate of a point?

A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by (x,y) the x-value and y-value.

Given that the coordinate of point A and B are (3,0) and (0,4).

The line AB is dilated by 1/2.

This means the scale factor is 1/2.

The x coordinate of point B is 0.

The y coordinate of point B is 4.

Multiply 1/2 with the x coordinate and y coordinate of point B to find the new coordinate of point B:

The new  x coordinate of point B is (0 × 1/2) = 0

The new  y coordinate of point B is (4 × 1/2) = 2.

The new coordinate of point B is (0,2).

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x+y=4 is most likely the equation for line K so the set of equations has infinitely many solutions.

Equation is a declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws. also see equation system.

Given

There must be identical lines made up of the same points for there to be an endless number of solutions. This implies that when expressed in the simplest terms, their equations are also identical.

As a result, x+y Equals 4. Equation here corresponds to B.

2x + 2y = 8

Dividing equation by 2

x + y = 4

As a result, x+y Equals 4. Equation here corresponds to B.
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