f(x) =
4 if x≤3
-4 if x>3
What is the functions range ?

Example of The Transitivity Property that follows

Premise:  If x = 3 and y = x + 2, then y = 5.

Premise: If y = 5 and z = y - 1, then z = 4.

Conclusion: If x = 3, then z = 4.

The transitivity property is a logical property that states that if a=b and b=c, then a=c. This property is commonly used in mathematics to make deductions and draw conclusions.

Example:

Premise: If x = 3 and y = x + 2, then y = 5.

Premise: If y = 5 and z = y - 1, then z = 4.

Conclusion: If x = 3, then z = 4.

Explanation: By the transitivity property, we can substitute the value of y in the second premise with the value of x + 2 from the first premise to get z = (x + 2) - 1, which simplifies to z = x + 1. Then, we can substitute x = 3 to get z = 4.

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The angles measures are m∠1 is 103, m∠2  is 38, m∠3 is 77.

In geometry, an angle is a measure of the amount of turn between two lines or line segments that meet at a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians.

A degree is a unit of measure for angles, where one full circle contains 360 degrees. A right angle, which forms a quarter of a circle, is 90 degrees. Angles that are smaller than a right angle are called acute angles, while angles that are larger than a right angle are called obtuse angles. Angles that add up to a straight line, which forms half of a circle, are called supplementary angles, while angles that add up to a full circle are called explementary angles.

A radian is another unit of measure for angles, where one full circle contains 2π radians. A right angle, which forms a quarter of a circle, is π/2 radians.

Here, m∠5 + m∠2 = 180   [ Supplementary Angles ]

142 + m∠2 = 180

m∠2 = 180 - 142 = 38

Now, m∠2 + m∠3 + m∠4 = 180   [ Angles in a Triangle ]

38 + m∠3 + 65 = 180

m∠3 = 180 - 103

m∠3 = 77

Again, m∠3 + m∠1 = 180   [ Supplementary Angles ]

m∠1 + 77 = 180

m∠1 = 180 - 77 = 103

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The complete question is:

Answer:

C: 54-x^2

Step-by-step explanation:

54(decreased=minus)-number^2

Answer:

A, B, and D

Step-by-step explanation:

The inequality n + 15 less-than 22 can be simplified by subtracting 15 from both sides:

n + 15 - 15 < 22 - 15

This simplifies to:

n < 7

So, any inequality of the form n < 7 is equivalent to n + 15 less-than 22.

Out of the given options:

A: n + 15 minus 15 less-than 22 minus 15

This simplifies to n < 7, which is equivalent to the original inequality.

B: n + 15 less-than 22 minus 15

This simplifies to n < 7, which is equivalent to the original inequality.

C: n + 15 minus 22 less-than 22 minus 22

This simplifies to n - 7 < 0, which is not equivalent to the original inequality.

D: n + 15 + 6 less-than 22 + 6

This simplifies to n + 21 less-than 28, which simplifies further to n < 7, which is equivalent to the original inequality.

E: n + 15 minus 22 less-than 22

This simplifies to n - 7 less-than 0, which is not equivalent to the original inequality.

Therefore, options A, B, and D are equivalent to the inequality n + 15 less-than 22.

Answer:

its A C D

Step-by-step explanation:i took the test the answer i used was wrong

The values of angles A , B, C are 140 , 40 , 140 respectively if other angle

is 40 degrees.

What are parallel lines ?

Parallel lines can be defined as lines which are equidistant from each other and which never intersect .

from the given figure ,

the angle b and 40 degrees are vertically opposite angles ,

vertically opposite angles are always equal

so,

b = 40

and sum of angles A and 40 is 180 degrees

so,

A + 40 = 180

A = 180 - 40

A = 140

And here similarly ,

angles A and C are vertically opposite angles ,

so,

C = 140 degrees.

Therefore, The values of angles A , B, C are 140 , 40 , 140 respectively  if other angle is 40 degrees.

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Assuming Sanford paid no sales tax, he received $10.15 in change.

What are basic arithmetic operations?

Basic arithmetic calculations are the fundamental operations used in mathematics to perform numerical computations. These operations include addition, subtraction, multiplication, and division of numbers. In addition, arithmetic calculations may also involve other concepts, such as fractions, decimals, percentages, and ratios.

The total cost of the two shirts is 2 x $24.95 = $49.90.

The total cost of the two shirts and the pair of pants is $49.90 + $39.95 = $89.85.

Sanford paid with a $100 bill, so his change would be:

$100 - $89.85 = $10.15

Therefore, Sanford received $10.15 in change.

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Answer:

let video game be x

let DVDs be y

2x+3y=148.85

3x +5y=230.75

make x the subject of the formula

x=148.85-3y/2

3(148.85-3y/2)+5y =230.75

446.55-3y/2=230.75

461.5=446.55-3y

461.5-446.55 =-3y

-3y = 14.95

y=-4.987

x=

The length would decrease at first to AB - BC then it would increase to the maximum of B + BC

From the diagram we have that two triangles are formed when we have AB = 3 cm and when we have BC = 1.5cm

This would happen when at point AC we have C moving in a counterclockwise direction around A

As AC goes towards A, then we would have AC decrease at first to AB - BC. Then it would increase. The maximum length would be AB + BC

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Answer:

It decreases

Step-by-step explanation:

Answer:

A'(4,-3) B'(6,11) C'(-7,-2)

Step-by-step explanation:

X-axis is (x,y) --> (x,-y)

A(4,3) --> (4,-3)

B(6,-11) --> (6,11)

C(-7,2) --> (-7,-2)

♡♡♡

Answer:

10 miles

the first option

Work Shown:

[tex]17600 \text{ yards} = 17600 \text{ yards}\times\frac{3 \text{ feet}}{1 \text{ yard}}\times\frac{1 \text{ mile}}{5280 \text{ feet}}\\\\= \frac{17600 \times 3\times 1}{1 \times 5280\times 1} \text{ miles}\\\\= \frac{52800}{5280} \text{ miles}\\\\= 10 \text{ miles}\\\\[/tex]

Take notice in the jump from the 1st to 2nd lines, we have the "yards" and "feet" units cancel out.

Answer:33.34

Step-by-step explanation:

we'll use sinuses theorem for this which is,

[tex]\frac{x}{sina}=\frac{y}{sinb}\\\frac{27}{sin39} =\frac{x}{sin(90-39)} \\\frac{27}{sin39} =\frac{x}{sin51} \\x=\frac{sin51*27}{sin39}\\x=33.34[/tex]

The exponential growth of bacteria gives the growth percentage to be 4.05%.

What is an exponential function?

The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

Let N(t) be the number of bacteria in the population at time t.

According to the continuous exponential growth model, we have -

[tex]N(t) = N0 \times e^{(rt)}[/tex]

where N0 is the initial number of bacteria, r is the hourly growth rate parameter, and t is the time elapsed in hours.

We know that a sample of 1800 bacteria reached the size of 2204 bacteria in five hours, so we can use this information to find the hourly growth rate parameter.

First, we can set up a ratio of the final size to the initial size -

[tex]\frac{2204}{1800} = e^{5r}[/tex]

Simplifying, we get -

[tex]e^{5r} = 1.2244[/tex]

Taking the natural logarithm of both sides, we get -

5r = ln(1.2244)

Solving for r, we get -

r = ln(1.2244) / 5

On further simplifying, we get -

r = 0.20245 / 5

r ≈ 0.04049

To express the growth rate as a percentage, we can multiply by 100 -

r percentage = 100 × r ≈ 4.049

Rounding to the nearest hundredth, we get -

r percentage ≈ 4.05%

Therefore, the hourly growth rate parameter is approximately 4.05%.

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a) The total interest that Angelica must pay on the loan during the period that payments are not being made is $2,998.58.

b) Angelica's monthly payment on the loan is $204.07.

The total interest when there were no repayments is determined using an online finance calculator.

The same calculator is used to determine the monthly payments after her graduation.

The total interest and the monthly payments are computed based on monthly compounding interest.

The amount of the non-subsidized student loan = $13,000

Annual compound interest rate = 5.2%

Loan period = 12 years

Non-repayment period = 4 years

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 5.2%

PV (Present Value) = $13,000

PMT (Periodic Payment) = $-0

Results:

FV = $-15,998.58

Total Interest = $2,998.58

N (# of periods) = 96 months (8 years x 12)

I/Y (Interest per year) = 5.2%

PV (Present Value) = $15,998.58

FV (Future Value) = $0

Results:

Monthly Payments (PMT) = $-204.07

Sum of all periodic payments = $-19,590.49

Total Interest = $3,591.91

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The equation of the axis of symmetry is [tex]x = 1/2.[/tex]

The definition of the an equation in algebra is a logical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical equation, such as 6 × 4 = 12 x 2, states that two quantities or values are equal. A noun that counts. When two or more components must be taken into account together in order to comprehend or describe the whole situation, this is known as an equations.

To find the equation of the axis of symmetry for the parabola[tex]y = x^2 - x - 6,[/tex]  we first need to find the x-coordinate of the vertex.

We can use the formula [tex]x = -b/2a[/tex] to find the x-coordinate of the vertex. In this case, a = 1 and b = -1, so:

[tex]x = -(-1) / 2(1) = 1/2[/tex]

So the x-coordinate of the vertex is [tex]1/2[/tex].

To find the y-coordinate of the vertex,

x = 1/2

[tex]y = (1/2)^2 - (1/2) - 6 = -25/4[/tex]

So the coordinates of the vertex are [tex](1/2, -25/4).[/tex]

[tex]x = 1/2[/tex]

Therefore, the equation of the axis of symmetry is [tex]x = 1/2.[/tex]

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Answer: Recall that E ∩ F ∩ G denotes the intersection of the three sets E, F, and G, and the superscript "c" denotes the complement of this set (i.e., everything outside of this intersection).

First, let's find E ∩ F ∩ G:

E ∩ F ∩ G = {24, 29}

Now, let's find the complement of this set:

(E ∩ F ∩ G)c = S - {24, 29}

This means that we take the set S and remove the elements 24 and 29.

So,

(E ∩ F ∩ G)c = {4, 9, 14, 19}

Step-by-step explanation:

Answer:

The value of "c" is 4.

Here's the solution:

2^-4 • 2² = a = c

2^-4 = 1/2^4 = 1/16

2² = 4

a = c = 1/16 • 4 = 1/4

Therefore, c = 1/4 = 0.25

Answer: 48.3

Step-by-step explanation:

Answer:

48.3

Step-by-step explanation:

Histogram would be the best for the data representation of the girls by dietitian.

Histogram, it is an approximate representation of the distribution of numerical data. The most popular graph for showing frequency distributions is a histogram. Though it also closely resembles a bar chart, there are significant differences. One of the seven basic quality tools is this useful gathering and analysing information tool.

Variable = the height of 13-year-olds in the state of Texas.

Where the height of each bar represents the frequency of observations.

[tex](2 - 2.5) feet\\\\(2.6 - 3) feet\\(3.1 - 3.5) feet\\(4.1 - 4.5) feet[/tex]

So, The best graphical representation of the dietitian's data would be a histogram.

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Answer:

the answer is 19/20

Step-by-step explanation:

the explanation is 3/4 x 5/5=15/20+ 4/20=1/5 x 4/4

Answer:B

Step-by-step explanation:

we can show this as,

[tex]x^{y^{z} } =x^{yz} \\18^{21} *5^{27} /18^{3} =18^{18}*5^{27}[/tex]

The correct option is (d) i.e. by grouping x²(x + 11) -3(x +11).

What are Factors?

Factors are numbers or algebraic expressions that can be multiplied together to obtain a given product.

In algebra, factors are often used to factorize polynomials or other expressions, which involves expressing them as a product of simpler expressions.

One way to determine the factors of x³ + 11x² - 3x - 33 by grouping is:

x²(x + 11) - 3(x + 11)

We can see that the two terms have a common factor of (x + 11), so we can factor it out as follows:

 = x³ + 11x² - 3x - 33

 =x²(x + 11) -3(x +11)

 = (x² - 3) (x+11).

The quadratic factor can be factored further using the difference of squares formula:

(x + 11)(x - √3)(x + √3)

So the factors of x³ + 11x² - 3x - 33 are (x + 11)(x - √3)(x + √3).

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The statements that are true are: Option c) Kelsey spent more on the pencils than she spent on the markers.

Option e) Kelsey spent $24 in all.

The problem provides us with some information about the cost and quantity of packages of pencils and markers, as well as the quantities of pencils and markers that Kelsey bought. We need to use this information to determine which statements are true.

We know that a package of pencils has 10 pencils and costs $2, and a package of markers has 8 markers and costs $4.

Kelsey bought 40 pencils and 24 markers. We can use this information to determine the number of packages of each item that Kelsey bought:

Pencils: Kelsey bought 40 pencils, and each package has 10 pencils, so she must have bought 4 packages of pencils.

Markers: Kelsey bought 24 markers, and each package has 8 markers, so she must have bought 3 packages of markers.

Now we can use this information to evaluate the statements:

a) Kelsey bought 4 packages and 3 packages of markers - This statement is false. Kelsey actually bought 4 packages of pencils and 3 packages of markers.

b) Kelsey spent $4 in pencils - This statement is false. Kelsey bought 4 packages of pencils, and each package costs $2, so she spent a total of $8 on pencils.

c) Kelsey spent more on the pencils than she spent on the markers - This statement is true. Kelsey bought 4 packages of pencils, which cost a total of $8, and 3 packages of markers, which cost a total of $12. Therefore, she spent more on markers than on pencils.

d) Kelsey spent $20 dollars in all - This statement is false. Kelsey spent $8 on pencils and $12 on markers, so she spent a total of $20.

e) Kelsey spent $24 in all - This statement is true. Kelsey spent $8 on pencils (4 packages x $2 per package) and $12 on markers (3 packages x $4 per package), so she spent a total of $20.

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Yοu wοuld need apprοximately $274,394.92 in yοur accοunt at the beginning tο be able tο withdraw $20,000 each year fοr 30 years at an 8% interest rate.

Tο calculate the amοunt needed in the accοunt at the beginning tο withdraw $20,000 each year fοr 30 years, we can use the fοrmula fοr the present value οf an annuity: [tex]PV = PMT * ((1 - (1 / (1 + r)^n)) / r)[/tex]

Where:

PV = present value (amοunt needed in the accοunt at the beginning)

PMT = payment per periοd (annual withdrawal amοunt = $20,000)

r = interest rate per periοd (8% per year = 0.08)

n = tοtal number οf periοds (30 years)

Plugging in the given values, we get:

[tex]PV = 20,000 * ((1 - (1 / (1 + 0.08)^{30})) / 0.08)[/tex]

PV ≈ $274,394.92

Therefοre, yοu wοuld need apprοximately $274,394.92 in yοur accοunt at the beginning tο be able tο withdraw $20,000 each year fοr 30 years at an 8% interest rate.

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The peaches cost $2.50 per pound.

Conversion rate is the percentage of website visitors or potential customers who take a desired action, such as making a purchase, signing up for a newsletter, or filling out a form. In other words, it is the rate at which website visitors are converted into customers or subscribers.

To find the cost per pound of peaches, we need to divide the total cost by the weight in pounds.

Cost of 3.1 pounds of peaches = $7.75

Cost of 1 pound of peaches = $7.75 / 3.1

Cost of 1 pound of peaches = $2.50 (rounded to the nearest cent)

Therefore, the peaches cost $2.50 per pound.

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Answer:

[tex]x = \frac{40\sqrt{3}}{3}\\\\y = \frac{20\sqrt{3}}{3}[/tex]

===================================================

Explanation:

The short leg is y because it is opposite the 30 degree angle.

The connection between the long leg and short leg is through this formula

[tex]\text{long leg} = (\text{short leg})*\sqrt{3}[/tex]

which applies to 30-60-90 triangles only.

Let's use that template to solve for y.

[tex]\text{long leg} = (\text{short leg})*\sqrt{3}\\\\20 = y\sqrt{3}\\\\y = \frac{20}{\sqrt{3}}\\\\y = \frac{20\sqrt{3}}{\sqrt{3}\sqrt{3}}\\\\y = \frac{20\sqrt{3}}{\sqrt{3*3}}\\\\y = \frac{20\sqrt{3}}{\sqrt{9}}\\\\y = \frac{20\sqrt{3}}{3}\\\\[/tex]

Then to find the hypotenuse x, we double the short leg.

[tex]x = 2y\\\\x = 2*\frac{20\sqrt{3}}{3}\\\\x = \frac{2*20\sqrt{3}}{3}\\\\x = \frac{40\sqrt{3}}{3}\\\\[/tex]

This formula works for 30-60-90 triangles only.

-----------

Side notes:

[tex]\frac{20\sqrt{3}}{3} \approx 11.54701\\\\\frac{40\sqrt{3}}{3} \approx 23.09401\\\\[/tex]

Answer:

x = 23.09 (2 d.p.)

y = 11.55 (2 d.p.)

Step-by-step explanation:

The interior angles of a triangle sum to 180°.  Therefore, from inspection of the given diagram, the interior angles of the given right triangle are:

This means the triangle is a special right triangle and that the 30-60-90 theorem can be applied to quickly find the measures of the missing sides.

A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio  1 : √3 : 2.

Therefore, the formula for the ratio of the sides is b : b√3 : 2b where:

From inspection of the given triangle, the side opposite the 60° angle is 20.  Therefore:

[tex]\implies b\sqrt{3}=20[/tex]

[tex]\implies b=\dfrac{20}{\sqrt{3}}[/tex]

[tex]\implies b=\dfrac{20\sqrt{3}}{3}[/tex]

Substitute the found value of b into the expressions for the other two sides to find the values of x and y.

x is the side opposite the right angle. Therefore:

[tex]\implies x=2b[/tex]

[tex]\implies x=2\cdot \dfrac{20\sqrt{3}}{3}[/tex]

[tex]\implies x=\dfrac{40\sqrt{3}}{3}[/tex]

[tex]\implies x=23.09\; \sf units\;(2\;d.p.)[/tex]

y is the side opposite the 30° angle. Therefore:

[tex]\implies y=b[/tex]

[tex]\implies y=\dfrac{20\sqrt{3}}{3}[/tex]

[tex]\implies y=11.55\; \sf units\;(2\;d.p.)[/tex]

Answer: We are given a right triangle where the two legs have lengths 2 and 4, and we need to find the length of the hypotenuse (which is denoted by x in the question). We can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. That is,

hypotenuse^2 = leg1^2 + leg2^2

Plugging in the values we know, we get:

x^2 = 2^2 + 4^2

Simplifying the right-hand side, we get:

x^2 = 4 + 16

x^2 = 20

Taking the square root of both sides (and noting that x must be positive since it is a length), we get:

x = sqrt(20) = 2sqrt(5)

Therefore, the length of the hypotenuse is 2sqrt(5).

Step-by-step explanation:

Answer:

175

Step-by-step explanation:

To find the median of a set of numbers, we must first arrange them numerically.

Arranging the given set in ascending order, we get:

125, 150, 150, 150, 175, 175, 200, 225, 250

The median is the middle number when the set is ordered this way. If the set has an odd number of values, the median is the middle value. If the set has an even number of values, the median is the average of the two middle values.

In this case, the set has nine values, so it is odd. The middle value is the fifth number, which is 175. Therefore, the median of the set is 175.

Answer:

The quote "Elie sees the death of the boy as the death of the God within" illustrates that Elie has learned from Moishe the Beadle that one's spirituality and relationship with God is a personal experience that resides within oneself. Moishe's teachings suggest that God is not necessarily an external force that determines the fate of individuals or the world, but rather a presence within oneself that must be nurtured and maintained. Elie's interpretation of the boy's death as the death of God within himself shows that he has internalized this lesson and is searching for meaning and understanding within his own experiences. This reflects Moishe's teachings that the "real answers lie in oneself," rather than in external sources of authority or dogma.

Step-by-step explanation:

The lateral surface area is 84 square centimeters and the total surface area is 96 square centimeters. The solution has been obtained by using the triangular prism.

What is a triangular prism?

A pentahedron with nine different nets, the triangular prism. Through their three rectangular sides, the bases' vertices and edges are connected. The rectangular sides of the triangular prism are joined side by side to one another. A triangle is represented by any cross-section that is parallel to the base faces.

We know that lateral surface area of prism is given by

A = (a + b + c) * h

Here, we are given

a = 4

b = 3

c = 5

h = 7

On substituting this, we get

⇒ A = (4 + 3 + 5) * 7

⇒ A = (12) * 7

⇒ A = 84 square centimeters

The formula for total surface area is

A = 2 * (area of base) + lateral surface area

Area of base = 0.5 * 3 * 4

Area of base = 6 square centimeters

So, we get

⇒ Total surface area = 2 * 6 + 84

⇒ Total surface area = 12 + 84

⇒ Total surface area = 96 square centimeters

Hence, the lateral and total surface area of the prism are obtained.

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