Find the smaller of two
consecutive integers, x, if the
sum of the smaller and the
larger is 15. Write an equation
and solve.

The graph would replicate itself starting at (0,0) if we wanted to start there (4,0).

A sine function, a periodic function that oscillates smoothly between high and low values, serves as the foundation for a sinusoidal function. Cosine functions can also be used as the foundation for sinusoidal functions because they are essentially a horizontal shift of sine functions.

We must establish the amplitude, period, and vertical shift of the periodic phenomenon in order to establish a sinusoidal function that models it. Determining whether to utilize a sine or a cosine function and the ensuing phase shift is also necessary.

The interval over which the graph repeats itself can be inferred from the graph. The graph would replicate itself starting at (0,0) if we wanted to start there (4,0). So, four is the era.

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a) The possible rational zeroes of the function are: ±1, ±2, ±3, ±6

b) The possible number of positive, negative, and imaginary roots of the function are: 0 to 2 positive roots, 0 to 2 negative roots, An odd number of imaginary roots.

What is Descartes' Rule?

The number of real zeros in a polynomial function is determined using Descartes' rule of sign. It states that the number of positive real zeros in a polynomial function f(x) is equal to or fewer than the number of changes in the sign of the coefficients.

a) To find the possible rational zeroes of the function, we can use the Rational Root Theorem, which states that if p/q is a rational zero of a polynomial with integer coefficients, then p must divide the constant term (in this case, -6) and q must divide the leading coefficient (in this case, 2).

The possible rational zeroes of the function are: ±1, ±2, ±3, ±6

b) To use Descartes' Rule of Signs to determine the number of positive, negative, and imaginary roots of the function, we count the number of sign changes in the coefficients of the polynomial. In this case, the signs are +, +, -, +, +, so we have two sign changes. Descartes' Rule of Signs states that a polynomial with n sign changes will have either n or n-2 positive roots. Since n=2 in this case, the polynomial can have either 0 or 2 positive roots. The same is true for negative roots. Additionally, if the degree of the polynomial is odd and the leading coefficient is positive, the polynomial will have an odd number of imaginary roots.

Therefore, The possible number of positive, negative, and imaginary roots of the function are:

0 to 2 positive roots

0 to 2 negative roots

An odd number of imaginary roots.

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Answer:

3/8

Step-by-step explanation:

Two triangles = one square

Since there are 4 squares, then there are 8 triangles

We see one triangle is shaded.

We also see one square is shaded, which means 2 triangles are shaded.

2 + 1 = 3 triangles shaded. Since there are a total of 8 triangles, then the fraction would be 3/8

Answer:

16.7%

Step-by-step explanation:

84 - 70 = 14

14 divided by 84, times 100 = 16.7%

So, it increase by 16.7%

Answer:

Step-by-step explanation:

The graph of y = 2x + c is a straight line with a slope of 2 and a y-intercept of c. The value of k cannot be determined from the equation alone, as it depends on the value of the constant c. To find the value of k, you would need additional information such as the coordinates of a point on the line or the x and y values that correspond to a specific k.

Number of packs of cups to be purchased = 5 packs and Number of cups remaining if 80% lemonade is sold = 85 cups.

The volume of cone is calculated using the formula (1/3)r2h, where "h" stands for the cone's height and "r" for the base radius. As a result, (1/3)r2 is the cone's volume in terms of the slant height "L." (L2 - r2).

Volume of a cone is given by the expression,

V = 1/3πr²h

Here,

r = radius of the cone

h = Height of the cone

Radius of the cone =  = 4 cm

Height of the cone = 11 cm

Amount of lemonade = 10 gallons

Volume of one cone = 1/3π(4)²× 11

 = 184.307 cm³

Covert the gallons into cubic cm,

  ∵ 1 gallon = 3785 cm³

  ∴ 10 gallons = 37850 cm³

  ∵1 cones are represented by a volume of 184.307 cm3.

∴ 1 cm³ will represent the volume = 1/184.307 cup

∴ 37850 cm³ will represent the volume = 37850/184.307 cups

                                                                  = 205.36 cups

                                                                   = 205 cups

Therefore, number of packs of cups to be bought = 205/50

                                                                                    = 5 packs

b). If 80% of the lemonade are sold, amount of lemonade sold = 10 × 80/100

= 8 gallons

Volume of 8 gallons lemonade in cm³ = 8 × 3785

                                                                    = 30280 cm³

Therefore, number of cups to be used = 30280/184.307 cups

= 164.29 cups

≈ 164 cups

Number of cups purchased = 250

And there are 250 cups left after subtracting 164.

                                                                = 86 cups

Therefore, number of cups remaining are 86 cups.

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The total cost of Mr.Bhavsar's order after the coupon for 25% off, a 6% tax, and $7 shipping will be $72.19.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The cost of the new Star Wars after a coupon for 25% off and a 6% tax will be given as,

⇒ $82 x (1 - 0.25) x (1 + 0.06)

⇒ $82 x 0.75 x 1.06

⇒ $65.19

The total cost after shipping will be given as,

Total cost = $65.19 + $7

Total cost = $72.19

The total cost of Mr.Bhavsar's order after the coupon for 25% off, a 6% tax, and $7 shipping will be $72.19.

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The number -4 as an exponent of 2 is is (√-4)^2

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

-4

Express the exponent of teh expression as 1

So, we have the following representation

-4^1

Express 1 as 2/2

-4^2/2

So, we have

(√-4)^2

Hence, the solution is (√-4)^2

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The expression "15 more than a number" can be represented using the variable n as n + 15.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
The variable mentioned in the question is n.
To write an expression for 15 more than a number, we have to add the number with 15.
So,
Expression = 15 + n

Thus, the expression "15 more than a number" can be represented using the variable n as n + 15.

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On solving the provided question, we can say that A Equation is[tex]y=100/3 e^{(ln3/2) t}[/tex]

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.

[tex]Y= ce^{kt}[/tex]

Sub in [tex]300= ce^{4k}[/tex]

[tex]100= ce^{2k}[/tex]

Divide to get[tex]3= e^{2k[/tex]

Take log of both sides    ln3= 2k lne

So k=ln3/2

We now have y=ce^(ln3/2)t

Sub in to solve for t

100= ce^ln3

c=100/3

A Equation is[tex]y=100/3 e^{(ln3/2) t}[/tex]

B At t=0 there were approx 100/3 or 33 filies.

C After 10 days there will be 100/3 e^(ln3)/2 *10 or approx  8100 flies.

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The value of DC is of 80, hence the statement is false.

Similar triangles share these two features listed as follows:

The similar triangles for this problem are given as follows:

AOB and COD.

Hence the proportional relationship established between the side lengths is given as follows:

OA/OC = OB/OD = 1/4 = AB/DC.

Taking the last two terms, considering that AB = 20 cm, the length of DC is given as follows:

DC = 4 x AB

DC = 4 x 20 cm

DC = 80 cm.

Hence the statement is false, as the length is of 80 cm and not of 120 cm.

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Answer:y = 4x-5.

Step-by-step explanation:

222222222222222222222

Check the picture below.

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-5}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{5}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-5) ~~ )^2 ~~ + ~~ ( ~~ y-5 ~~ )^2~~ = ~~5^2\implies \boxed{(x+5)^2 +(y-5)^2 = 25}[/tex]

Answer:

SP-CP=PROFIT

210-190=20

the profit is 20

Step-by-step explanation:

Answer:

Rs 20

Step-by-step explanation:

S.P. (Selling Price) is the price at which a product is sold. C.P. (Cost Price) is the price at which a product is purchased. When S.P. is greater than C.P., it results in a profit. To calculate profit, the formula is simple:

Profit = S.P. - C.P.

In this case, S.P. is Rs. 210 and C.P. is Rs. 190. So, the profit would be calculated as:

Profit = Rs. 210 - Rs. 190 = Rs. 20.

<NOM = 59° (vertically opposite angles)

<STU = 96°(Exterior angle of a triangle)

There are mathematical statement that can be used to show the relationships between the sides of the triangle this is what we call the theorems of the triangle.

In question 1; Angle NOM = 59° because it is vertically opposite angle POQ

In question 2; Angle UVT = Angle VUT = 42°

Angle UTV = 180 - 2(42)

= 96°

Then;

Angle STU = 96° (This is because the angle STU is the sum of the interior  opposite angles.).

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The value of the expression is -3.

Integer tiles are one way of using a material representation to introduce the concept of adding and subtracting integers.

This model can be useful for working on the type of problem that many students find harder, that is, problems like -4 + -5.

Given that, Allison is evaluating the expression Negative 5 minus (negative 2) using integer tiles.

Allison has 5 negative tiles

So,

she  needs to remove 2 negative tiles,

then, subtract -2 to 5 to get left  3 negative tiles.

(-5) -(-2)  =   (-5+2)  

= -3

Hence, The value of the expression is -3.

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Answer:

its actually remove 2 negative tiles

Step-by-step explanation:

i did it on my exam

The average rate of change of g(x) = -x3 + 2 is therefore -51/5 from x = -1 to x = 4.

The slope of the secant line connecting two points on a function across an interval represents the average rate of change of that function over that interval. We must determine the slope of the secant line that connects the points (-1, g(-1)) and (4, g(4)) in order to calculate the average rate of change of g(x) = -x³ + 2 from x = -1 to x = 4.

g(-1) = -(-1) (-1)

4³ + 2 = -1 + 2 = 1 \sg(4) = -4^3 + 2 = -52 + 2 = -50

The secant line's slope is therefore ((-50) - 1) / (4 - (-1)) = -51 / 5

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Answer: 4

Step-by-step explanation:

3x4+12

------------ (over)

6

12+12

---------

6

24

----- = 4

6

The expression can be written as: a * b + 5.

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

The product of a and b increased by 5.

The product of a and b is represented as

a * b

Increased by 5 means

a * b + 5

So, the expression is a * b + 5

The expression "a * b + 5" represents the mathematical operation of first multiplying two values, 'a' and 'b', and then adding 5 to the result.

The '*' symbol is used for multiplication, and the '+' symbol is used for addition.

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Answer:A. 315,000 ÷ 900 = 350

Step-by-step explanation:

A. 315,000 ÷ 900 = 350

The percentage of the tip at the restaurant will be 15%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Kim and sam went to a Mexican restaurant for lunch the total bill including tip was 25.46. They left 3.82 for a tip.

The percentage of the tip will be calculated as:-

Percentage = 3.82 / 25.46

Percentage = 0.15 x 100
Percentage - 15%

Hence, the percentage of the tip at the restaurant will be 15%.

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The solution of the matrix product is:

[tex]\left[\begin{array}{ccc}4&0\\-16&-7\\\end{array}\right][/tex]

Remember that the general product between two 2by2 matrices can be written as:

[tex]\left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\\\end{array}\right] *\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\\end{array}\right] = \left[\begin{array}{ccc}a_{11}*b_{11} + a_{12}*b_{21}&a_{11}*b_{12} + a_{12}*b_{22}\\...&...\\\end{array}\right][/tex]

So we multiply the the rows of the first matrix by the columns of the second one, then our product will be:

[tex]\left[\begin{array}{ccc}1&2\\-4&3\\\end{array}\right] *\left[\begin{array}{ccc}4&1\\0&-1\\\end{array}\right] = \left[\begin{array}{ccc}1*4 + 2*0&1*1 + 2*-1\\-4*4 + 3*0&-4*1 + 3*-1\\\end{array}\right]\\\\= \left[\begin{array}{ccc}4&0\\-16&-7\\\end{array}\right][/tex]

That is the solution of the product.

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a) The probability that the player makes exactly 3 of the 5 shots = 0.3087

b) The probability that the player makes exactly 4 of the 5 shots = 0.36015

c) The probability that the player makes all 5 shots = 0.16807

d) The probability that the player makes 3 or 4 of the shots = 0.66885

The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.

The formula for Binomial Distribution is given by

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

where

n = number of trials

x = number of successes

p = probability of getting a success in one trial

q = probability of getting a failure in one trial

q = 1 - p

Given data ,

Let the probability be represented as P

The total number of trials n = 5

The probability of getting a success p = 0.70

The probability of getting a failure q = 0.30

Now , the equation will be

a)

The probability that the player makes exactly 3 of the 5 shots = A

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

n = 5

x = 3

Substituting the values in the equation , we get

A = ⁵C₃ ( 0.70 )³ ( 0.30 )²

A = 10 ( 0.343 ) ( 0.09 )

A = 0.3087

So , probability that the player makes exactly 3 of the 5 shots is 0.3087

b)

The probability that the player makes exactly 4 of the 5 shots = B

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

n = 5

x = 4

Substituting the values in the equation , we get

B = ⁵C₄ ( 0.70 )⁴ ( 0.30 )¹

B = 5 ( 0.2401 ) ( 0.3 )

B = 0.36015

So , probability that the player makes exactly 4 of the 5 shots is 0.36015

c)

The probability that the player makes all 5 shots = C

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

n = 5

x = 5

Substituting the values in the equation , we get

C = ⁵C₅ ( 0.70 )⁵ ( 0.30 )⁰

C = 0.16807

So , probability that the player makes all 5 shots is 0.16807

d)

The probability that the player makes 3 or 4 of the shots = D

D = A + B

D = 0.3087 + 0.36015

D = 0.66885

Hence , the probability is solved

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On solving the provided question we cans ay that the increasing order of the function is  y = 5/2x +10 < y = 3/2x+1/2 < y = 1/2x - 2 < y = 3/4x - 7/3 < y = -1/2x + 1/2 < y = 3/2x - 11/2

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

the increasing order of the function is

y = 5/2x +10 < y = 3/2x+1/2 < y = 1/2x - 2 < y = 3/4x - 7/3 < y = -1/2x + 1/2 < y = 3/2x - 11/2

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To put the streamer on the whole wall we need at least 32 Square feet of the streamer.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given,  to put streamers from concern to corner in both directions and the wall is 4 ft wide and 8ft high.

Since the area of a rectangle:

Area  = Length * width

Thus,

The area of the wall  = 4 * 8

The area of the wall  = 32

So,

The Streamer required = 32 square feet

Therefore, We need at least 32 square feet of streamer to cover the entire wall.

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The exact values of the unit circle is cos θ = 9/25 and sin θ = ( √544/25 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

The terminal side of angle θ intersects the unit circle in the first quadrant at ( 9/25 , y )

So , the equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r²   be equation (1)

Substituting the values of x and y in the equation , we get

( 9/25 )² + y² = 1²

On simplifying the equation , we get

( 81/625 ) + y² = 1

Subtracting ( 81/625 ) on both sides of the equation , we get

y² = 544/625

Taking square roots on both sides of the equation , we get

y = √544/25

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

So , the value of cos θ = 9/25 and sin θ = ( √544/25 )

Hence , the equations are solved

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The correct option is A. 30° for the value of x in the similar triangles right triangles DEF and WXY.

The hypotenuse-leg congruent theorem states that if two right-angled triangles have congruent legs, then their hypotenuses are also congruent.

it also implies that angle D is equal to angle W and angle F is equal angle Y

so;

x + 2x + 90 = 180° {sum of interior angles of a triangle}

3x + 90° = 180°

3x = 180° - 90° {subtract 90° from both sides}

3x = 90°

x = 90°/3 {divide through by 3}

x = 30°

Therefore, the value of x in the similar triangles right triangles DEF and WXY is equal to 30°

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The maximum height the ball reaches is 132 feet.

A ball is tossed upward, and the height H is calculated as follows:

h(t)=  1/2 gt 2 +V 0 t +H 0.

t is the amount of time spent.

The equation in this instance is expressed as h(t)=16t 2 +64t +100.

The solution of the equation h=0 gives the time t at which the item strikes the ground if h(t) is zero, which implies that the ball is at the ground at h=100.

h=−16t 2  +64t+100

h=−16(t 2  + 2+ 2)+ 100−(−16×2 )

h=−16(t−2) 2  + -100 − (−32)

h=−16(t−2 ) 2  +132

The vertex is (2 ,132 ), therefore, the maximum height is 132 feet.

The maximum height the ball reaches is 132 feet.

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