Which set of ordered pairs represents a function?

Answer:

4

Step-by-step explanation:

use slope formula y2-y1/x2-x1

6-2/2-1

4/1

4 is the slope

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There is exactly one more real solution or there is exactly one more complex solution

Given,

One solution to a quadratic equation is x = -5/3

We have to find the correct statements from the given ones;

A polynomial of degree two is a quadratic equation.

This implies that a polynomial has two solutions.

We already have an answer to the query, which is a true root.

Then, the additional response that we lack can appear in the form of two responses.

It may be a real root or a complicated root, depending on the situation.

The following is the response to this query:

There is exactly one more real solution or there is exactly one more complex solution

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Answer:

x= -7

Step-by-step explanation:

The sum of the angles in a triangle is 180°. This can be abbreviated to ∠ sum of ∆.

Adding the angles in the triangle,

84° +(x +59)° +(x +51)°= 180° (∠ sum of ∆)

2x= 180 -84 -59 -51

2x= -14

Divide both sides by 2:

x= -14 ÷2

x= -7

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Answer: The formula for simple interest is P*R*T/100

Step-by-step explanation: Where P stands for Principal and R for Rate T for Time

Answer:

37

Step-by-step explanation:

4b+10-b = 3b + 10 = 3(9) + 10 = 27 + 10 = 37

The spring is compressed to 95.5 cm to the right if 129 N of force are used.

In this question, we have been given the spring constant k = 283 N/m

if 129 N of force are used then we need to find distance  that the spring compressed to the right.

Let the spring stretch from the equilibrium position x.

An equation for the spring's potential energy is,

PE = 1/2 ​kx^2

129 = 1/2 * 283 * x^2

2 * 129 = 283 * x^2

258/283 = x^2

x^2 = 0.9117

x = 0.9548 m

x = 95.5 cm

Therefore, the spring is compressed to 95.5 cm to the right if 129 N of force are used.

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The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.

Given that,

From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.

Whether the claim is true or false must be determined.

The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.

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Step-by-step explanation:

the x-intercept is the point, where the curve intercepts the x-axis (that means y = 0).

the y-intercept is the point, where the curve intercepts the y-axis (that means x = 0).

y = 10 - 2x

when x = 0, that means y = 10 - 2×0 = 10.

when y = 0, that means 0 = 10 - 2x, 2x = 10, x = 5

x-intercept = (5, 0)

y-intercept = (0, 10)

4y + 9x = 18

x = 0, 4y = 18, y = 18/4 = 9/2 = 4.5

y = 0, 9x = 18, x = 18/9 = 2

x-intercept = (2, 0)

y-intercept = (0, 4.5)

6x - 2y = 44

3x - y = 22

x = 0, -y = 22, y = -22

y = 0, 3x = 22, x = 22/3 = 7 1/3

x-intercept = ( 7 1/3, 0)

y-intercept = (0, -22)

2x = 4 + 12y

x = 2 + 6y

x = 0, 6y = -2, y = -2/6 = -1/3

y = 0, x = 2 + 6×0 = 2

x-intercept = (2, 0)

y-intercept = (0, -1/3)

The number of flags that could possibly be created, given the palette of colors to work with, and the number of stripes, is 360, 360 flags.

The designer has the choice to pick from 15 colors to work with. They will then pick another color, and then another, until they pick five colors to make stripes.

When they pick a single color, the number of choices drops to 14 colors. When they pick 5 colors, they will be left with 11 colors.

The number of possible flags is therefore:

= 15 x 14 x 13 x 12 x 11

= 360, 360 possible flags

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The value of z = 0 + 0i

What is complex numbers ?

A complex number can be represented in the form a + bi, where a and b are real numbers. A complex number is a part of a number system that extends the real numbers by adding an element designated by the symbol I sometimes known as the imaginary unit, and meeting the equation displaystyle i2=-1.

( x + iy ) - 4i ( x - iy ) = 0

x + iy - 4ix + 4i²y = 0

x + i (-4x + y ) + 4y = 0

x + 4y + ( - 4x + y )i = 0

Now two complex numbers are equal if both the real and imaginary parts are equal, which gives you the system of equation

x + 4y = 0 ⇒(1)

-4x + y = 0 ⇒ (2)

Multiplying equation (1) with 4

4x + 16y = 0

Solving the equations

4x + 16 y = 0

-4x + y = 0

      17 y = 0

          y = 0

Putting the value of y in (1)

x + 4(0) = 0

x = 0

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Answer:

AB = 8cm ; BC = 6.5 cm

Step-by-step explanation:

BC = x- 1.5

x * (x-1.5) = 52

x^2 - 1.5x - 52 = 0

Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25

We are searching only positive value

(1.5 + 14.5)/2 = 16 / 2 = 8 cm

AB = 8 cm

BC = 8 - 1.5 = 6.5 cm

The expression m < - 2 7/12 solved for m is m < - 2 7/ 12. Option B

Inequalities are described as a relation which making an unequal comparison between two numbers or expressions.

It is mostly used to compare two numbers on the number line on the basis of their size.

Given the expression;

m+1/3<−2 1/4

Covert to improper fraction

m + 1/ 3 < -9/4

Now, collect like terms

m < - 9/ 4 - 1/3

Find the lowest common multiple

m < -27 - 4 /12

m < -31/ 12

convert to mixed fraction

m < - 2 7/ 12

Hence, the value is m < - 2 7/ 12

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Answer:

89

Step-by-step explanation:

if u divide and multiply theory is equivalent to its nominal answer thus your answer will be 89

The additional information that could be used to prove that ΔXYZ ≅ ΔFEG by ASA or AAS are:

∠Z ≅ ∠G and XZ ≅ FG

∠Z ≅ ∠G and XY ≅ FE .

The AAS is a theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent angles and a pair of non-included sides.

The SAS is also another theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent sides and a pair of included congruent angles.

From the image attached below, we are only given one pair of congruent angles, which is ∠X ≅ ∠F.

Therefore, for both triangles to be congruent by AAS or SAS, the additional information needed are:

∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE .

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a. [tex]123.1(1.069)^3 \approx 150.4[/tex]

b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]

Answer: log2-log6=-log3

Step-by-step explanation:

[tex]\displaystyle\\log2-log6=\\\\log\frac{2}{6} =\\\\log\frac{2(1)}{2(3)}=\\\\log\frac{1}{3} =\\\\log3^{-1}=\\\\-log3[/tex]

Using the proportion , the 5% of 60 would be 3.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that the number of 5% of 60.

5% of 60

= 0.05 x 60

= 3

Therefore, the 5% of 60 would be 3.

Using the proportion , the 5% of 60 would be 3.

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Tracy need 5 weeks to save enough money to buy a new guitar.

Given that,

Tracy is saving to buy a new guitar. Which having costs $253.77(including tax).

Tracy has already saved $136. 27.

Now she needs = 253. 77- 136. 27

                          = $117.50

she can save each week = $23. 50

Tracy will take weeks to save enough money

     = [tex]\frac{117.50}{23.50}[/tex]

     = 5 weeks.

Therefore, Tracy need 5 weeks to save enough money to buy a new guitar.

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Answer:

A

Step-by-step explanation:

Eliminate B and C because they don't pass through (0,1).

Eliminate D because it doesn't decrease quickly enough.

Answer:

A, B, D, E

Step-by-step explanation:

Given expression:

When multiplying decimals, multiply as if there are no decimal points:

[tex]\implies 6 \times 154 = 924[/tex]

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 5 digits.

Put the same number of total digits after the decimal point in the product:

[tex]\implies (0.06) \cdot (0.154)=0.00924[/tex]

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

Answer option A

[tex]\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}[/tex]

When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.

Therefore:

[tex]\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)[/tex]

Therefore, this is a valid answer option.

Answer option B

[tex]\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}[/tex]

Multiply the numbers 6 and 154:

[tex]\implies 6 \times 154 = 924[/tex]

Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).

[tex]\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924[/tex]

Therefore, this is a valid answer option.

Answer option C

[tex]\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}[/tex]

Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:

[tex]\implies 6 \cdot 154 = 924[/tex]

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 3 digits.

Put the same number of digits after the decimal point in the product:

[tex]\implies 0.924[/tex]

Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.

Answer option D

[tex]\boxed{6 \cdot 154 \cdot (0.00001)}[/tex]

Again, employing the technique of multiplying decimals.

As there are a total of 5 digits after the decimals:

[tex]\implies 6 \cdot 154 \cdot (0.00001)=0.00924[/tex]

Therefore, this is a valid answer option.

Answer option E

[tex]\boxed{0.00924}[/tex]

As we have already calculated, (0.06) · (0.154) = 0.00924.

Therefore, this is a valid answer option.

Actual area of bedroom is bigger than the kitchen as per the given measurements and scale.

As per the given question,

Given drawing scale is:

1 : 30

Shape of the kitchen is rectangle with measurements = 12cm by 27cm

Using scale :

Length = 12cm

Actual length = 12 × 30

                      = 360cm

Width = 27cm

Actual width = 27 × 30

                     = 810 cm

Actual area of kitchen = 360 × 810

                                     = 291,600 cm²

Actual area of bedroom = 300,000cm²

300,000 > 291,600

Actual area of bedroom > Actual area of kitchen

Therefore, actual area of bedroom is bigger than the actual area pf kitchen.

The complete question is:

A drawing has a scale of 1:30 On the drawing, a kitchen is a rectangle measuring 12 cm by 27 cm A bedroom has an actual area of 300 000 cm² Which has the bigger actual area, the kitchen or the bedroom? You must show your working.​

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The ordered pair is (3, 1) which is the intersecting point of these two equations.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given, are two equations y = -(2/3)x + 3 and y = 2x - 5.

Now the solution to this system is the common intersecting point of these equations.

With the help of graphing we conclude that the intersecting point is (3, 1) and so is the solution.

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The value of car after 6 years is £498.53

Define Modeling Exponential Decay

Given that,

Dan buys a car =  £700

Depreciates at a rate of = 5.5% per year

The value after 6 years = 700 (1 - 5.5 / 100) ^6

                                       = 498.527 or 498.53

Therefore, the value of car after 6 years is £498.53

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The following are crucial factors in hypothesis testing:

In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test.

Thus, before conducting the hypothesis testing, a null hypothesis as well as an alternative hypothesis are established.

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Answer:

It means that the quantities have the same relative size. In other words they have the same ratio.

Step-by-step explanation:

For example look at the attached files

Answer:

it is a function.

Step-by-step explanation:

The answer is just 3x+6

Answer:

3x+6 can be be the result of 3(x+2) and then you distribute to get 3x+6

If you are asking how to solve you need an equal sign in the equation for example: 3x+6=27 you would have to solve to figure out wht x is. x is any unknown number we use x or any letter in the alphabet to fill in. You have to olve for the variable now.

A General Rule for Solving Equations

Simplify each side of the equation by removing parentheses and combining like terms.

Use addition or subtraction to isolate the variable term on one side of the equation.

Use multiplication or division to solve for the variable.

Step-by-step explanation:

Answer: 50% of her average running speed is her average walking speed

Step-by-step explanation:

60 ÷ 4 = 15
60 ÷ 8 = 7.5
7.5 is half of 15, making it 50% of her running speed.

The completed statement on the exponential model that fits the data in the question is presented as follows;

The exponential model indicates that the plastic production has a 7.88% growth per year. The model predicts that the production 15 years after 1960 was closest to 30 million metric tons, because the correlation coefficient indicates a strong correlation between the model and the data, this prediction is correct.

The correlation coefficient is an indication of the level at which the variables are interdependent.

The table of values in the question can be entered into a spreadsheet application as follows;

The equation for the trendline obtained from MS Excel is presented as follows; f(x) = 9.2179·e^(0.0788·x)

The growth rate from the above exponential function is 7·88% per year

The production 15 years after 1960 is therefore;

f(15) = 9.2179·e^(0.0788 × 15) ≈30.06

The number of plastic produced 15 years after 1960 is about 30 million metric tons

The correlation coefficient obtained from MS Excel is R² = 0,9157, which indicates a strong correlation between the data and the model

The prediction is correct based on the strong correlation between the year and the number of plastic produced.

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