Question 7 of 10
Which of the following lists of ordered pairs is a function?
OA. (-1, 2), (2, 3), (3, 1), (2, 5)
B. (2, 5), (3, 6), (2,1)
O C. (2, 5), (3, 6), (6,9)
O D. (1, 2), (4, 0), (3, 5), (4, 3)
SUBMIT

By solving a system of equations we can see that the quadratic equation is:

y = x^2 + 3x + 10

A general quadratic equation is given by:

y = a*x^2 + b*x + c

We want this quadratic equation to pase through the points (-2, 8), (1, 14), and (0, 10).

using the last point, we know that when x = 0, we must have y = 10, then:

10  = a*0^2 + b*0 + c

10 = c

So our quadratic equation is:

y = a*x^2 + b*x + 10

Now we use the other two points to write a system of equations:

8 = a*(-2)^2 + b*(-2) + 10

14 = a*(1)^2 + b*1 + 10

If we simplify these, we get:

-2 = 4*a - 2b

4 = a + b

Isolating a in the second equation we get:

a = 4 - b

Now we replace that in the other equation:

-2 = 4*(4 - b) - 2b

-2 = 16 - 4b -2b

-2 - 16 = -6b

-18/-6 = b = 3

Now that we know the value of b, we replace it in the equation for a:

a = 4 - b = 4 - 3 = 1

Then the quadratic equation is:

y = x^2 + 3x + 10

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Using the Factor Theorem, the quadratic functions are given as follows:

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

For this problem, the roots are given as follows:

[tex]x_1 = -3, x_2 = 8[/tex]

Hence:

f(x) = a(x + 3)(x - 8)

f(x) = a(x² - 5x - 24).

It opens upward with a positive leading coefficient, that is, a > 0, hence one example is a = 1 as follows:

f(x) = x² - 5x - 24.

It opens downward with a negative leading coefficient, that is, a < 0, hence one example is a = -1 as follows:

f(x) = -x² + 5x + 24.

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Answer:

b = 99

Step-by-step explanation:

b and 81° are same- side interior angles and sum to 180° , that is

b + 81 = 180 ( subtract 81 from both sides )

b = 99

The Simplified value of the complex fraction 1 + 2/x / 2 + 3 / 2x is (4x+7)/(4x+3) .

A complex fraction is defined as an expression that has fraction in it's numerator and a fraction in its denominator.

For Example : [tex]\frac{\frac{2}{3} }{\frac{5}{7} }[/tex] is an example of complex fraction.

The given question is

=1 + 2/x / 2 + 3 / 2x

[tex]=1+\frac{\frac{2}{x} }{2+\frac{3}{2x} }[/tex]

Taking LCM in the denominator and solving further,

[tex]=1+\frac{\frac{2}{x} }{\frac{4x+3}{2x} }[/tex]

[tex]=1+\frac{2}{x} *\frac{2x}{4x+3}[/tex]

Cancelling out "x" from both numerator and denominator

we get,

=1+(2*2)/(4x+3)

=1+(4)/(4x+3)

Taking LCM as 4x+3 and solving further we get,

=(4x+3+4)/(4x+3)

=(4x+7)/(4x+3)

Therefore , the simplified value of the expression 1 + 2/x / 2 + 3 / 2x is (4x+7)/(4x+3).

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Answer:

12°

Step-by-step explanation:

The angles of the shape should all add to 360°.

We divide this by 30, because the shape has 30 angles.

360° ÷ 30 = 12°.

This is the measure of each angle, and also the degree of rotation. The shape will look like the original figure each time it is rotated 12°.

The approximate length of each side of the park is 85m .

Pythagoras Theorem states that the sum square of two sides of triangle is equal to the  square of longest side.

According to the question

given that the park is a square

and in square the longest side is it's diagonal and the diagonal is  given to be 120m.

In square all sides of square is same .

let the side be x.

By Applying Pythagoras Theorem in the given ΔABC

[tex]AB^{2} +BC^{2} =AC^{2}[/tex]

Substituting the values  we get

[tex]x^{2} +x^{2} =120^{2}[/tex]

[tex]2x^{2} =120^{2} \\ \\ 2x^{2} =14400\\ \\ x^{2} =7200[/tex]

[tex]x=\sqrt{7200} =60\sqrt{2}[/tex] = 84.85 ≅ 85

Therefore ,  the approximate length of each side of the park is 85m .

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In order to know the appropriate number divisible by 2, 5 and 10. We need to have a look at what type of numbers are divisible by either of these number. So, let's discuss one by one

Divisible by 2

Divisible by 5

Divisible by 10

Let's have a look at the given numbers and see which ones are divisible by 2, 5 and 10

We'll write "yes" for the number which are divisible and "No" for the number which are not divisible by either of them.

105 - only by 5

183 - No

34 - only by 2

238 - only by 2

54 - only by 2

553 - No

260 - yes

85 - only by 5

450 - yes

365 - only by 5

745 - only by 5

360 - yes

270 - yes

390 -  yes

400 - yes

110 - yes

210 - yes

775 - only by 5

438 - only by 2

565 - only by 5

766 - only by 2

906 - only by 2

321 - No

347 - No

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This question is incomplete. You can have a look at the attached picture to know the complete question.

The value of expression  [tex]4\frac{7}{12} +2 \frac{3}{4} + 7\frac{5}{12}[/tex]  is [tex]\frac{157}{12}[/tex].

We solve this type of fraction by firstly simplifying it into proper fraction. For simplifying it into proper fraction, we multiply denominator of the complex fraction with whole number given with fraction and then add the numerator of the complex fraction

e.g. [tex]4\frac{7}{12}[/tex] = [tex]\frac{12*4+7}{12}[/tex]

so, The given question can be written down as [tex]4\frac{7}{12} +2 \frac{3}{4} + 7\frac{5}{12}[/tex]

i.e. [tex]\frac{35}{12} +\frac{11}{4} + \frac{89}{12}[/tex]

Taking LCM and then writing the equation again

[tex]\frac{35+33+89}{12}[/tex]= [tex]\frac{157}{12}[/tex]

Final answer, the simplified value will be [tex]\frac{157}{12}[/tex]

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Each subtraction equation as an addition equation is  mathematically given as

a - 9 = 6 ==> a=6+9

p - 20 = -30==> p+30=20

z - (-12) = 15 ==>  z+12=15

x - (-7) = -10 ==> x+17=0

This is further explained below.

Generally, In mathematics, the summation is the process of adding together a string of any form of numbers, which are referred to as operands or summands; the result is the sum or total of the figures.

In conclusion,

a - 9 = 6 ==> a=6+9

p - 20 = -30==> p+30=20

z - (-12) = 15 ==>  z+12=15

x - (-7) = -10 ==> x+17=0

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2)Main Answer: a)1,8,27,64,125,216,343,512

                        b)I,II,III,IV,V,VI,VII,VIII,IX,X,XI                                    

Concept and definitions should be there:

A conjecture is an educated guess that is based on known information. Example. If we are given information about the quantity and formation of section 1, 2 and 3 of stars our conjecture would be as follows.

Given data

a)Next five terms 1,8,27,64

b)Next five terms I,II,III,IV,V

Solving part

using conjecture

a)Next five terms 1,8,27,64,125,216,343,512

Notice that the difference between consecutive terms is 7.

Conjecture: n3, n=1,2,3...

Final Answer:1,8,27,64,125,216,343,512

b))Next five terms I,II,III,IV,V,VI,VII,VIII,IX,X,XI

Conjecture: n, n=i,ii,iii,...

Final Answe:I,II,III,IV,V,VI,VII,VIII,IX,X,XI

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3)Quastion incompleted

4)Main answer :The number 14 is even and therefore is divisible by 2. This is the correct statement.

Given data

The statement which uses deductive reasoning to draw the conclusion is C. The number 14 is even and therefore is divisible by 2.

Solving part

The number 14 is even and therefore is divisible by 2. This is the correct statement.

Final Answer:The number 14 is even and therefore is divisible by 2. This is the correct statement.

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5)Main Answer:X = -2

Concept and definitions should be there:This solution deals with linear equations with one unknown.

Given data

18x-2(3x+1)=5x-16

Solving part

We simplify the equation first:

18x−2(3x+1)=5x−16

18x+(−2)(3x)+(−2)(1)=5x+−16 (Distribute)

18x+−6x+−2=5x+−16

(18x+−6x)+(−2)=5x−16 (Combine Like Terms)

12x+−2=5x−16

12x−2=5x−16

Then we cancel out:

12x−2−5x=5x−16−5x

7x−2=−16

7x−2+2=−16+2

7x=−14

7x/7 = −14/7

x = -2

Final Answer:x = -2

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The nth term of seuence is 4^n and the formula for finding the nth term of the given sequence is [tex]a_{n} = 4^{n}[/tex] .

According to the given question.

We have a sequence 4, 16, 64, 256, 1024...

As we know that, a sequence or number pattern is an ordered set of numbers or diagrams that follow a rule.

Here,

The first term of the given sequence is 4, or we can say that 4^1 is 4.

The second term of the sequence is 16, or we can say that 4^2 is 16.

The third term of the sequence is 64, or we can say that 4^3 is 64.

The fourth term of teh sequence is 256, or we can say that 4^4 is 256.

So, if we follow the same pattern or the rule we can say that the nth term of the given sequence is 4^n.

Thereofre, the formula for finding the nth term of the given sequence 4,16,64,256,1024, ...... is [tex]a_{n} = 4^{n}[/tex] where n = 1, 2, 3 , 4....

Hence, the nth term of seuence is 4^n and the formula for finding the nth term of the given sequence is [tex]a_{n} = 4^{n}[/tex] .

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The distance between points J(-2 , 6) and K(1 , 4) will be equal to 3.6.

Two points J(-2 , 6) and K(1 , 4) are given .

We have to find out the distance between two points.

What is the distance formula ?

The distance formula is [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] where two points are ([tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) and ([tex]x_{2}[/tex] , [tex]y_{2}[/tex]).

As per the question ;

J ([tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) = J (-2 , 6) and K ([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = K (1 , 4)

and

The distance formula is ;

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex]

So ,

The distance between points J(-2 , 6) and K(1 , 4) will be ;

= [tex]\sqrt{(-2-1)^{2} + (6-4)^{2} }[/tex]

= [tex]\sqrt{(-3)^{2} + (2)^{2} }[/tex]

= [tex]\sqrt{(9)+ (4)}[/tex]

= √13

= 3.6 ( round to nearest tenth)

Thus , the distance between points J(-2 , 6) and K(1 , 4) will be equal to 3.6.

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The equation of the parabola that has vertex at the center and focus at the point (6,0) is x = y²/24

We define what a parabola is

 The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

The canonical equation of a parabola is given by

(y - k)² = 4p(x - h)

The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

v (0, 0)

f (6, 0) the focus is on the right so the parabola is of the form X = Y².

(y - 0)² = 4p(x - 0)

f = (0 + p, 0)

0 + p = 6

p = 0 + 6

p= 6

(y - 0)² = 4*6(x - 0)

(Y)² = 24(X)

x = y²/24

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After solving for equation or inequality 4 x+6 ≥ -6, the value of  x ≥ -3

⇒ 4 x+6 ≥ -6

⇒ 4x ≥ -6-6

⇒ 4x ≥ -12

⇒ x ≥  -12/4

⇒ x ≥ -3

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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With the help of linear equtions it can be concluded that we downloaded 54 songs in which 28 songs were free and 26 songs were paid.

A linear equation is an algebraic equation in which each term has an exponent of one and when graphed produces a straight line. That's why it is considered a 'linear equation.'

Let a represent paid downloaded songs.

Total cost of songs downloaded = a x cost of each additional download.

a x $0.59 = $0.59a

The overall cost of downloaded songs is $15.34.

$15.34 =   $0.59a

Divide both sides of the equation by  $0.59.

a = 26 songs

We downloaded 26 paid songs.

Total songs downloaded = total free songs + total paid songs

Total songs downloaded = 26 + 28 = 54 songs

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Which property does the equation 3(g+h)+2 g=(3 g+3 h)+2 g illustrate?

Distributive property .

What is distributive property?

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The property that justifies the following statement, 5(3 x+1)=15 x+5 is the distributive property.

Distributive property can be described as one of the properties of multiplication which states that if we multiply two or more values that are added together with a number then the result will be the same even if we multiply each value separately with that number and then add them together. This can be given as:

x(y + z) = xy + xz

Therefore, as 5 x 3 = 15 and 5 x 1 =5, we can write the equation 5(3x+1) as 15x + 5 as the result will be the same in both circumstances.

The distributive property not only justifies the equations when two or more values are added but also justifies the equations in which they are subtracted which can be given as:

x(y-z) = xy - xz

So, according to the distributive property, the statement, 5(3 x+1)=15 x+5 is valid.

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Answer:

66

Step-by-step explanation:

An inequality that matches the wingspan of the common sparrow is       9 ≤ x ≤ 15, where x represents the wingspan of the common sparrow.

In this question, we have been given a statement 'The common sparrow has a wingspan of 9 to 15 centimeters. '

We need to write an inequality that matches the wingspan of the common sparrow.

Let x represents the wingspan of the common sparrow.

According to given statement, the common sparrow has a wingspan of 9 to 15 centimeters.

So, the required inequality would be,

9 ≤ x ≤ 15

Therefore, an inequality that matches the wingspan of the common sparrow is 9 ≤ x ≤ 15, where x represents the wingspan of the common sparrow.

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The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth.

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

The distance between two points (x₁, y₁) and (x₂, y₂)  is given by ;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

So,

Distance between A(1,5) and B(-2,-3)

[tex]d = \sqrt {\left( {1 + 2 } \right)^2 + \left( {5 + 3 } \right)^2 }[/tex]

d = 8.544

Roud to nearest tenth ⇒ 8.54  units.

Hence "The distance between A(1,5) and B(-2,-3) is  8.54 rounded to the nearest tenth".

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{3}x\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex][tex]~\dotfill\\\\ \stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}[/tex]

so we're really looking for the equation of a line whose slope is -1/3 and it passes through (2 , -6)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{2}) \implies y +6= -\cfrac{1}{3} (x -2) \\\\\\ y+6=-\cfrac{1}{3}x+\cfrac{2}{3}\implies y=-\cfrac{1}{3}x+\cfrac{2}{3}-6\implies y=-\cfrac{1}{3}x-\cfrac{16}{3}[/tex]

Answer:

I'll go with the last option. c=√Em

Answer:

335

Step-by-step explanation:

you put -18 in for x

you multiply -18 by -18 because it's the exponent of 2

then add 11

The given sequence is not arithmetic as the difference of each consequent term with the previous term is not the same.

Given: 1, 3, 9, 27, ...

Here, 3 - 1 ≠ 9 - 3 ≠ 27 - 9

Since the sequence does not follow the definition of an arithmetic progression, it is not one.

Hence, The given sequence is not arithmetic as the difference of each consequent term with the previous term is not the same.

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Answer:

[tex]\frac{613}{1000}[/tex]

Step-by-step explanation:

Answer: [tex]2x^{2} +17x+36[/tex]

Step-by-step explanation:

FOIL:
[tex]2x^{2} +8x+8x+36[/tex]

Combine like terms:

[tex]2x^{2} +17x+36[/tex]

None of the equations are correct.

What is an equation?

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. In other languages, the word equation and its cognates may have slightly different meanings. In French, an équation is defined as having one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

For perpendicular equations, the product of slope is -1, but none of the options here is have slope whose product with the given equation is -1.

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Answer:

W = -57.6         PS: I'm in 8th grade.

Step-by-step explanation:

W/6 + 7.2 = -2.4   Step 1: Use Inverse operations (subtract 7.2 on both sides)

W/6 = -2.4 - 7.2    Step 2: Combine Like terms (-2.4 - 7.2)

W/6 = -9.6            Step 3: Use Inverse Operations (multiply by 6 on both sides)

W = -9.6 x 6         Step 4: Simplify

W = -57.6