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Answer: 16, 17, and 18.

Step-by-step explanation: What I'll do I'll just let explain how to solve it and that will instantly solve your question!

The first case of business to make things easier would be to try and put this on a linear equation so...

Let the first integer be x.

Then the next consecutive two integers will be x + 1 and x + 2

x + (x + 1) + (x + 2) = 51 [Sum of the 3 consecutive integers is 51]

-> 3x + 3 = 51

-> 3x = 51 - 3

-> 3x = 48

-> x = 48/3

-> x = 16,

Thus, x + 1 = 17, x + 2 = 18

Therefore, the three consecutive integers are 16, 17, and 18.

Hope it helps ^^

The amplitude and the period of the function are 3 and 2, respectively.

Sinusoidal functions are periodic bounded functions whose form is described below:

y = A · sin (2π · t / T + Ф) + y'

Where:

The period is the horizontal distance between two consecutive peaks or two consecutive bottoms and the amplitude is equal to the half of the distance between a peak and a consecutive bottom. Hence, the amplitude and the period are, respectively:

Amplitude

A = 0.5 · [2 - (- 4)]

A = 3

Period

T = 2 · [0.75 - (- 0.25)]

T = 2

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The factored form of the equation x² + 6x + 8 is (x + 4) (x + 2), that is, option B.

Here, we are given a quadratic equation x² + 6x + 8

We can factorize this equation using the splitting the middle term method.

Here the coefficient of x is 6, hence, we need to spilt 6 in such a manner that the product of the split terms is 8.

6 can be written as 4 + 2 and we can see that 4 × 2 = 8

Hence, we can write the given equation as-

x² + 4x + 2x + 8

= x (x + 4) + 2 (x + 4)

= (x + 4) (x + 2)

Hence, the factored form of the equation x² + 6x + 8 comes out to be (x + 4) (x + 2), that is, option B.

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Myron would need 7.2 hours to cook 3 kilograms of meat.

time = 12 hours

cook = 5 kilograms of meat.

i.e. For 5 kilograms of meat, it takes 12 hours to cook.

Thus, for 3 kilograms of meat,

Multiple 12  by 3 and divided by 5

= 12/5 * 3

= 12 * 3/5

= 36 / 5

= 7.2 hrs.

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Answer:  12 hours

Step-by-step explanation: 5 kilo grams of meet

The probability that the next type of stir fry ordered is shrimp is 0.28.

Given that, the frequency table provided summarizes yesterday's orders at Sizzlin' Skillets.

A frequency distribution table displays the frequency of each data set in an organized way. It helps us to find patterns in the data and also enables us to analyze the data using measures of central tendency and variance. The first step that a mathematician does with the collected data is to organize it in the form of a frequency distribution table. All the calculations and statistical tests and analyses come later.

The given frequency table is

Type of stir fry         Number of orders

Vegetable                       333

Chicken                           666

Pork                                 222

Beef                                 222

Shrimp                             555

As we know, probability of an event = Number of favourable outcomes / Total number of outcomes

Here, the number of favourable outcomes = 555

The total number of outcomes = 333+666+222+222+555 = 1998

So, the probability of getting shrimp = 555/1998

=0.277≈0.28

Therefore, the probability that the next type of stir fry ordered is shrimp is 0.28.

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Answer:

4

Step-by-step explanation:

B= 1

D= -3

Distance between the two? 4 points

1 - (-3) = 4

The the vertices if the triangle is reflected over the y-axis and then dilated by a scale factor of 2 wii be A'(4, 6), B'(0, 0) and, C'(-2, 4).

According to the given question.

The vertices of a triangle ABC are A(-2, 3), B(0, 0), and C(1, 2).

As we know that,

The rule for reflecting a triangle over the y axis is to negate the value of x-coordinate of each point, but leave the y-value the same.

Therefore, the vertices of triangle ABC when it is reflected over y-axis are

A'(2,3)

B'(0, 0)

C'(-1, 2)

Also, when the triangle is dialated by a scale factor 2 then the vertices will be

A'(4, 6)

B'(0, 0)

And, C'(-2, 4)

Hence, the the vertices if the triangle is reflected over the y-axis and then dilated by a scale factor of 2 wii be A'(4, 6), B'(0, 0) and, C'(-2, 4).

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The probability mass function of the binomial distribution is given by:

B. [tex]\frac{n!}{x!(n-x)!} \times p^{x} \times (1-p)^{n-x}[/tex]

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Hence, considering the combination formula, the probability mass function of the binomial distribution is given by:

B. [tex]\frac{n!}{x!(n-x)!} \times p^{x} \times (1-p)^{n-x}[/tex]

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After solving, the factors of equation 4x²+16=34x are:

So,

Given equation: 4x²+16=34x

Then,

Factors are: (x-8) and (4x-2)

Therefore, after solving, the factors of equation 4x²+16=34x are:

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The correct question is given below:
Solve each equation.

4x²+16=34x

If b^{h} < 1 then it will be a vertical stretch.

What authority possesses a power rule?

When a base is raised to a power and then the entire expression is raised to another power, the power of a power rule in exponents is used to simplify the algebraic statement.

A translation of function f is f₁ (x) = bˣ⁻h . It is equivalent to a vertical stretch or vertical compression of function f.

[tex]f_{1} (x) = b^{x - h}[/tex]

If we used the rules of powers, we know that when we have a subtraction in the power of an exponential, it can be split into a division. So the function can be rewritten as

 [tex]f_{1} (x) = \frac{b^{x} }{b^{h} }[/tex]

Remember the original function was

f(x) = bˣ

therefore

[tex]f_{1}(X) = \frac{f(x)}{b^{h} }[/tex]

this means that if [tex]b^{h} < 1[/tex] then it will be a vertical stretch.

If b^{h} < 1  then it will be a vertical stretch.

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A composite function exists as a function that depends on another function. A composite function exists formed when one function exists substituted into another function.

The value of f(f(f(x))) is 1/x

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

A function that depends on another function is referred to as a composite function. When one function is inserted into another, a composite function is produced. For instance, f(g(x)) is the composite function created when x in f is replaced with f(x). f(g(x)). You can interpret f(g(x)) as "f of g of x."

Let the given function be f(x) = 1/x

f(f(x)) = f(1/x) = 1/(1/x)

simplifying the above equation, we get

f(f(x)) = f(1/x) = x  

f(f(f(x))) = f(x) = 1/x

Therefore, the value of f(f(f(x))) = f(x) = 1/x

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The number 102 in the sequence will be closest to 100.

A sequence in which each next term gets increased or decreased from the preceding by a constant value is called an arithmetic progression.

The difference of any two consecutive terms in an arithmetic progression is called the common difference of the AP (arithmetic progression).

Here each terms increases by 8. So, the common difference d is 8.

The first term is given to be 38.

So our sequence will be,

38, 46, 54, 62,...

nth term in an AP can be calculated by using the formula,

aₙ = a₁ + (n-1)d

To find the term nearest to 100,

100 = 32 + (n-1)8

68/8 = (n-1)

9.5 = n

But the value of n can not be a non-integer,

So the term nearest to 100 will be 9th or 10th term.

a₉ = a₁ + (9-1)d

a₉ = 8 + (8 x 8)

a₉ = 94

and,

a₁₀ = a₁ + (10-1)d

a₁₀ = 8 + (9 x 8)

a₁₀ = 102.

We can see,

a₁₀ = 102 is closest to 100.

Hence, 10th term is closest to 100.

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Answer:

14x⁸ - 12x⁶ + 16x⁴

Step-by-step explanation:

To find the required polynomial, multiply 2x² and the quotient.

Multiply each term of (7x⁶ - 6x⁴ + 8x²) by 2x².

2x² * 7x⁶ = (2*7) *x²⁺⁶ = 14x⁸

Required polynomial =2x² *(7x⁶ - 6x⁴ + 8x²)

                                   = (2x²*7x⁶) - (2x²*6x⁴) + (2x²*8x²)

                                    = 14x⁸ - 12x⁶ + 16x⁴

The equation when both cards would have the same amount of money left is 30 = 5p.

An equation is an algebraic expression that has an equal to sign. A linear equation is an equation that has a single variable that is raised to the power of one. When drawn on a graph, a linear equation is a straight line

Amount left on the gift card = value of the gift card - (amount spent on pizza x number of pizzas bought)

Amount left on Jim's gift card = 100 - ($15 x p)

100 - 15p

Amount left on Yoko's gift card = 70 - (10 x p)

70 - 10p

When both cards have the same amount of money left, the two above expressions would be equal

100 - 15p = 70 - 10p

Combine similar terms:

100 - 70 = 15p - 10p

Add similar terms:

30 = 5p

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Answer:

The lines are neither

Step-by-step explanation:

Answer:

A) –2 or 3∕5

Step-by-step explanation:

Two possible cases since we are dealing with absolute values:

7h + 1 = 3h - 7 ; h = -2 here

7h + 1 = -(3h - 7) ; h = 3/5 here

The four ways are :

A cylinder is a 3-dimentional solid shape . It has two parallel bases which are joined by the curved surface. The cylinder has 2 circular bases one on the top and other at bottom and a curved region between them.

Important formulas of cylinder:

Base area of cylinder =  π r²

Surface area of cylinder = 2 π r( r+ h)

Volume of cylinder = π r² h

where,  h defines height and r defines the radius

According to ques ,  [tex]h= k\frac{V}{r^{2} }[/tex]

The four ways are :

1. when the value of volume V is quadrupled

  i.e. V = 4V

  then, h = [tex]k\frac{4V}{r^{2} }[/tex] = 4 ([tex]k\frac{V}{r^{2} }[/tex]) = 4h

2. when the value of radius (r) is halved

 i.e. r = r/2

  then , h =  [tex]k \frac{V}{(\frac{r}{2} )^{2} }[/tex] = [tex]k\frac{4V}{r^{2} }[/tex] = 4 ([tex]k\frac{V}{r^{2} }[/tex]) = 4h

3. when the value of V is enlarged 16 times and the value of r is doubled

  i.e. V= 16 V and r =2r

  then, h =  [tex]k \frac{16 V}{(2r)^{2}}[/tex] = [tex]k\frac{4V}{r^{2} }[/tex] = 4 ([tex]k\frac{V}{r^{2} }[/tex]) = 4h

4. If the values of V and r are quartered

    i.e. V= V /4 and r =r/4

      then, h = [tex]k \frac{(\frac{V}{4} ) }{(\frac{r}{4} )^{2} }[/tex] =  [tex]k \frac{16 V}{(4r^{2})}[/tex] = [tex]k\frac{4V}{r^{2} }[/tex] = 4 ([tex]k\frac{V}{r^{2} }[/tex]) = 4h

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Greetings from Brasil...

Simplified answer to the given expression are :

a) 3/5

b) 2

c) 2.236

What is an mathematical expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

a) given expression is : [tex]\sqrt{\frac{9}{25}}[/tex]

Now, to simplify it we write the factors of 9 and 25 as 3 x 3 and 5 x5 and then take the root of them to get 3/5 as answer.

 [tex]\sqrt{\frac{9}{25}}[/tex] = √(3 x 3)/ √(5 x 5 ) = 3/5

b) given expression is :  [tex]\sqrt{\frac{12}{3}}[/tex]

Now, to simplify it we first divide 12 with 3 that is 4 and then take the root of 4 to get 2 as answer :

 [tex]\sqrt{\frac{12}{3}}[/tex] = √4 = 2

c) given expression is :  [tex]\frac{\sqrt{15}}{\sqrt{3}}[/tex]

Now, to simplify it we first divide 15 with 3 that is 5 and then take the root of 5 to get 2.236 as answer :

[tex]\frac{\sqrt{15}}{\sqrt{3}}[/tex] = √15/3 = √5 = 2.236  

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Answer:

6x2 + 11x

Step-by-step explanation:

First collect like terms:

8x2 - 2x2 + 3x + 8x - 10 + 10 (Ps: x2 and x are not the same!)

Combine them:

6x2 + 11x (the -10 and 10 cancel out)

and this is your polished answer!

Given the perimeter, the length and width of the rectangular family portrait are 20 inches and 31 inches respectively.

The perimeter of a rectangle is expressed mathematically as;

P = 2( l + w )

Given the data in the question;

Let "x" represent the width of the rectangle.

To determine the width and length of the rectangle, plug the given values into the formula above and solve for x.

P = 2( l + w )

102 = 2( ( 2x - 9 ) + x )

102 = 2(  2x - 9 + x )

102 = 2(  3x - 9 )

Apply distributive property

102 = 2(3x) + 2(-9)

102 = 6x - 18

102 + 18 = 6x

120 = 6x

6x = 120

x = 120/6

x = 20

Now, the numerical length and with of the rectangular frame will be;

Width w = x = 20 inches

Length l = 2x - 9 = 2(20) - 9 = 40 - 9 = 31 inches.

Given the perimeter, the length and width of the rectangular family portrait are 20 inches and 31 inches respectively.

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After solving the equation, x = 19/4 Is the value of x in 4x = 19

⇒ 4x = 19

⇒ x = 19/4

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

7. 123

8. 38

10. 65

11. 113

Applying the slope formula, the slope of the line is determined as: 2.

The slope of a line  represented by a table of values can be calculated using any two set of ordered pairs form the given table, and applying the slope formula below:

Slope (m) = y2 - y1/x2 -x1

Using any two points of the line, (0, -0.25) and (1, -0.2), as represented in the table, let:

(0, -0.25) = (x1, y1)

(1, -0.2) = (x2, y2)

Plug in the values

Slope (m) = (-0.2 -(-0.25))/(1 - 0)

Slope (m) = 0.05/1

Slope (m) = 0.05

Thus, the slope of the line as represented by the table of values is calculated as: 0.05.

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Answer:

-3/2

Step-by-step explanation:

Slope:

Rise: The difference between the y -coordinates of the two points is called the rise.

Run: The difference between the x-coordinates of the same two points is called the run.

First plot two points on the line.

(0, 6 )  and (4 , 0)

Rise = 6 - 0 = 6

Run = 0 - 4 = -4

[tex]\sf \boxed{Slope = \dfrac{Rise}{Run}}[/tex]

          [tex]\sf =\dfrac{6}{-4}\\\\=\dfrac{-3}{2}[/tex]

Answer: It is a rational number.

Hence, [tex]2.738[/tex] a rational number.

What is the rationa number?

A rational number is a type of real number, which is in the form of [tex]\frac{p}{q}[/tex] where [tex]q[/tex] is not equal to zero. Any fraction with non-zero denominators is a rational number.

Here [tex]2.73[/tex] acn be written as

[tex]2.73=\frac{2.73}{1}[/tex]

Now, we multiply numerator and denominator by [tex]100[/tex].

So, it would be

[tex]\frac{2.73(100)}{1(100)}\\\\=\frac{273}{100}[/tex]

So, the fraction is written as [tex]2.73[/tex].

Hence, [tex]2.738[/tex] a rational number.

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Answer: x=7

Step-by-step explanation: (3x−2)=19

Add 2 to both sides.

3x=19+2

Add 19 and 2 to get 21.

3x=21

Divide both sides by 3.

x= [tex]\frac{21}{3}[/tex]

​

Divide 21 by 3 to get 7.

x=7

(2)  3x-2

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of [tex]ax^{2}[/tex]

 is [tex]nax^{n-1}[/tex]

.

[tex]3x^{1-1}[/tex]

Subtract 1 from 1.

[tex]3x^{0}[/tex]

For any term t except 0, [tex]t^{0}[/tex] =1.

3×1

For any term t, t×1=t and 1t=t.

answer=3

Step-by-step explanation:

what form should the equation have ?

I assume slope-intercept

y = ax + b

"a" being the slope, "b" being the y-intercept (the y value when x = 0).

but since we have the slope and a point, we can start with the point-slope form and transform it :

y - y1 = a(x - x1)

"a" is again the slope, (x1, y1) is the point.

so,

y - 7 = -5/3 × (x - -3) = -5/3 × (x + 3) = -5x/3 - 5

and therefore

y = -5x/3 + 2