2.Which Equations Represent Linear Functions?a. Y = -2xb. -4y = 3xc.y= 3x^2 -5d. 2x-3y =12 (2024)

The rational numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49

What is a rational number?

A rational number can simply be described as a number that is expressed as the ratio of two even or odd integers.

The denominator of the fraction or ratio must be greater than zero.

Rational numbers are represented mathematically as a quotient, say x/y of two integers such that y ≠ 0, that is, the denominator is not equal r equivalent to zero.

It is formed from dividing on integer(whether odd or even) by another integer.

The numbers; √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49 are all rational numbers

Hence, the numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49

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1) [tex]\angle CDE \cong \angle CED, \angle A \cong \angle B[/tex] (given)

2) [tex]m\angle CDE=m\angle CED, m\angle A=m\angle B[/tex] (definition of congruent angles)

3) [tex]m\angle C+m\angle CDE+m\angle CED=180^{\circ}, m\angle C+m\angle A+m\angle B=180^{\circ}[/tex] (sum of angles in a triangle)

4) [tex]m\angle C+2m\angle CDE=180^{\circ}, m\angle C+2m\angle A=180^{\circ}[/tex] (substitution)

5) [tex]m\angle C=180^{\circ}-2m \angle CDE, m\angle C=180^{\circ}-2m\angle A[/tex] (subtraction)

6) [tex]180^{\circ}-2m \angle CDE=180^{\circ}-2m \angle A[/tex] (transitive)

7) [tex]-2m\angle CDE=-2m\angle A[/tex] (subtraction)

8) [tex]m\angle CDE=m\angle A[/tex] (division)

9) [tex]\angle CDE \cong \angle A[/tex] (definition of congruent angles)

10) [tex]\overline{DE} \parallel \overline{AB}[/tex] (converse of corresponding angles theorem)

She travels 61.2 miles for work each week.

What is addition?

Addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

We have been given that the healthcare worker has 3 shifts each week. The route from her house to the hospital is 9.9 miles and the route back to her house is 10.5 miles.

The distance from her house to the hospital = 9.9 miles

The distance back to her house = 10.5 miles.

The total distance travel in one shift = 9.9 + 10.5 = 20.4 miles

The total distance travel in 3 shift = 3 x 20.4 = 61.2 miles

Hence, She travels 61.2 miles for work each week.

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Angle 2 and angle of 34° are vertical angles, then they are congruent, that is,

[tex]m\angle2=34\degree[/tex]

Angle 6 and angle of 34° are corresponding angles, then they are congruent, that is,

[tex]m\angle6=34\degree[/tex]

Angle 4 and angle of 34° are alternate interior angles, then they are congruent, that is,

[tex]m\angle4=34\degree[/tex]

Angle 7 and angle of 34° are same-side interior angles, then they are supplementary, that is,

[tex]\begin{gathered} m\angle7+34\degree=180\degree \\ m\angle7=180\degree-34\degree \\ m\angle7=146\degree \end{gathered}[/tex]

Angles 4 and 3 are same-side interior angles, then they are supplementary, that is,

[tex]\begin{gathered} m\angle4+m\angle3=180\degree \\ 34\degree+m\angle3=180\degree \\ m\angle3=180\degree-34\degree \\ m\angle3=146\degree \end{gathered}[/tex]

Angles 7 and 5 are vertical angles, then they are congruent, that is,

[tex]\begin{gathered} m\angle5=m\angle7 \\ m\angle5=146\degree \end{gathered}[/tex]

Angles 1 and 3 are vertical angles, then they are congruent, that is,

[tex]\begin{gathered} m\angle1=m\angle3 \\ m\angle1=146\degree \end{gathered}[/tex]

Let's begin by identifying key information given to us:

A is a 3 x 2 matrix

B is a 2 x 3 matrix

AB is the product of 3 x 2 matrix & 2 x 3 matrix. We obtain a 3 x 3 matrix

Therefore, the size of the product of A & B (that is AB) is a 3 x 3 matrix whenever these products exist

Answer:

(d) x²y²(x² − 3xy)

Step-by-step explanation:

You want to identify a rewrite of x⁴y² − 3x³y³ using a common factor among ...

3xy(x³y − x²y) 3xy²(x² − x²y) x²y(xy − 3xy²) x²y²(x² − 3xy)

Simplified

Here, we write the expanded form of the answer choices to see if any is a fit for the given expression.

3xy(x³y − x²y) = 3x⁴y² -3x³y²3xy²(x² − x²y) = 3x³y² -3x³y³x²y(xy − 3xy²) = x³y² -3x³y³x²y²(x² − 3xy) = x⁴y² -3x³y³ . . . . . . . matches the given expression

__

Additional comment

The relevant rule of exponents is ...

(a^b)(a^c) = a^(b+c)

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The approximate correlation of the data shown on the diagram above is: C. -0.5.

The question says we should approximate the correlation using the given scatter plot. Below shows a detailed explanation on how to do a rough estimation of the possible value of the correlation.

What is the Approximate Correlation of a Data?

Correlation Coefficient, r, is a numerical value of -1 to 1, which tells how strongly related two variables are. If the points on a scatter plot form a trendline that slopes upwards, it is a positive correlation. If it slopes downwards, it is a negative correlation.

The magnitude of the correlation coefficient is dependent on how father apart the points are from each other along a trend line. If they are much farther apart from each other, the correlation coefficient would far from 1 and -1, and close to zero. If they are closer, it would be close to 1 or -1, and far from 0.

The scatter plot shows the data points are moderately spaced from each other and the trendline slopes downwards. Therefore, the best estimate for the correlation is: C. -0.5.

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The money which is expected to spend on new word processors during this year is

The probability distribution is

x: 0 1 2 3

f(x) [tex]\frac{1}{10}[/tex] [tex]\frac{3}{10}[/tex] [tex]\frac{2}{5}[/tex] [tex]\frac{1}{5}[/tex]

If the cost of the desired model is $1200 per unit and at the end of the year a refund of 50x2 dollars

So total money spent in this year is [tex]1200x-50x^2[/tex]

Then the equation of expenses will be

[tex]\text{Expenses}=E(1200x-50x^2)[/tex]

We can rewrite it as

[tex]\text{Expenses}=E(1200x)-E(50x^2)[/tex]

[tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex] -----------------(1)

Now the mean of the probability distribution is ,

[tex]E(x)=\sum_{ }^{ }((x_i)(f(x_i))\\=(0\times\frac{1}{10})+(1\times\frac{3}{10})+(2\times\frac{2}{5})+(3\times\frac{1}{5})\\=\frac{3}{10}+\frac{4}{5}+\frac{3}{5}\\\\=\frac{3+8+6}{10}\\\\=\frac{17}{10}\\\\=1.7[/tex]

The variance of the function is

[tex]E(x)=\sum_{ }^{ }(x_i^2)(f(x_i)[/tex]

[tex]=(0^2\times\frac{1}{10})+(1^2\times\frac{3}{10})+(2^2\times\frac{2}{5})+(3^2\times\frac{1}{5})[/tex]

[tex]=\frac{3}{10}+\frac{8}{5}+\frac{9}{5}[/tex]

[tex]=\frac{37}{10}[/tex]

[tex]=3.7[/tex]

On substituting the values in equation (1)

[tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex]

[tex]=1200(1.7)-50(3.7)^2[/tex]

[tex]=2040-684[/tex]

[tex]=1855[/tex]

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The length of the incline of the ramp will be [h] = 12.0415 ft

What is Pythagoras theorem?

According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -

h² = p² + b²

Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.

From the data given, we can consider the ramp construction as right angled triangle. We can write -

base [b] = 12 ft

height [p] = 1 ft

Using the Pythagoras theorem -

h² = (12 x 12) + (1 x 1)

h² = 144 + 1

h = √145

h = 12.0415

Therefore, the length of the incline of the ramp will be [h] = 12.0415 ft

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[This question also has part B. Visit the following link for part B -

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Answer:

Given:

Model : Ship = 3 : 400

The surface area of the model = 7200 cm²

To Find:

The surface area of the actual ship in m²

Let's start with the map scale given:

Model : Ship = 3 : 400

We start by adding in a unit. Usually, we choose the units associated with the model:

Model : Ship = 3 cm : 400 cm

Now, according to tot the question, we know that the actual ship is in m:

Model : Ship = 3 cm : 400 ÷ 100 m

Model : Ship = 3 cm : 4 m

The question asked for surface area, so the units have to be in squares:

Model : Ship = (3 cm)² : (4 m)

Model : Ship = 9 cm² : 16 m²

Now, that we have the units set correctly according to the question requirement, we will find 1 branch of the model:

Model : Ship = 9 cm² : 16 m²

Model : Ship = 9÷9 cm² : 16÷9 m²

Model : Ship = 1 cm² : 16/9 m²

Finally, we can find the required units by multiplying both sides with the required units:

Model : Ship = 1 cm² : 16/9 m²

Model : Ship = 1 x 7200 cm² : 16/9 x 7200 m²

Model : Ship = 7200 cm² : 12800 m²

Answer: The surface area of the ship is 12800 m²

(by the way, this was copied from the same website)

hope this helps :)

The value of y when x is 9 for the proportional relationship between is 31.5.

What is constant of proportionality?

The constant of proportionality is used to show the proportional relationship between the numbers given.

In this case, when x is 2, y is 7. This will be illustrated thus:

y = kx

7 = 2k

Divide

k = 7/2

k = 3.5

Therefore, when x is 9, the value of y will be:

y = kx

y = 3.5 × 9

y = 31.5

Therefore, y is 31.5.

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The first one is TRUE since there are not outliers

The second one is FALSE

The interquartile range is 10, so the third one is FALSE

The data is skewed since the median is not in the middle,so the fourth is TRUE and the fifth is FALSE

The sixth one is TRUE

The last one is FALSE.

Summirizing, we have

True

False

False

True

False

True

False

The True statements are: the graph is a straight line and the line does not pass through the origin. The y-intercept of the line is 2.

What is a linear equation?

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

The equation is given as y = -1/2 x + 2

Then Formula of the linear equation ( in slope-intercept form ):

y = m x + b

m = -1/2, b = 2

0 = - 1/2 ( 0 )+ 2

0 ≠ 2 ( it does not pass through the origin )

- 2 ≠ 2

Therefore, the True statements are:

The graph is a straight line.

The line does not pass through the origin.

The y-intercept of the line is 2.

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The Sarah's path and Marcus path will intersect at the point (5,4) .

In the question ,

it is given that

the park is modeled by the equation y = x − 1 .

On comparing with the slope intercept form ,

we get

the slope as 1 .

Since both the paths are perpendicular ,

the slope for Marcus path is -1 .

hence the equation of line with slope -1 and passing through the point (0,9) is y = (-1)x + c

9 = (-1)0 + c

9 = c

so equation is y = (-1)x + 9

So to find the point of intersection , we solve both the equations .

Substituting y = x − 1 in y = (-1)x + 9 ,

we get

x − 1 = (-1)x + 9

x - 1 = -x + 9

x + x = 9 + 1

2x = 10

x = 5

So, y = 5 - 1 = 4

the point of intersection is (5,4) .

Therefore , The Sarah's path and Marcus path will intersect at the point (5,4) .

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[tex]\begin{gathered} 1pt=0.125gal \\ \\ \\ \text{If }\frac{1}{9}pt\text{ of water is add to 1 gal of paint.} \\ \\ \\ 36\text{gal paint}\cdot\frac{1/9\text{ pt water}}{1gal\text{ paint}}=36\cdot\frac{1}{9}\text{pt water}=4pt\text{ water} \\ \\ \\ 4\text{ pints of water are added to 36 gallons of paint.} \\ \\ \text{Total gallons of paint:} \\ \text{Turn the pints to gallons:} \\ 4pt\cdot\frac{0.125\text{gal}}{1pt}=0.5gal \\ \\ \text{Total gallons of final paint:} \\ 36\text{gal}+0.5\text{gal}=36.5gal \end{gathered}[/tex]

The Null hypothesis will be expressed as u = 0.79 whereas the Alternative hypothesis will be expressed as. u > 0.79

The null hypothesis (H0) may be used to show that there exists no significant variation between variables or that a single variable is not different than its mean. While an alternative Hypothesis (Ha) is a theory that attempts to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean. According to the question we can say that the

Null hypothesis (H0): u = 0.79

Alternative hypothesis (Ha): u > 0.79

Where u may be called as the proportion of their reader that owns a personal computer.

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We know that each bow cost $5.25.

We also know that the woman spent a total of $84.

Lets call x the number of bows she bought.

Then, we can write:

[tex]\begin{gathered} 5.25\cdot x=84 \\ x=\frac{84}{5.25}=16 \end{gathered}[/tex]

The woman bought 16 bows.

Brand A bags typically weigh more because the median of brand A is higher than that of brand B and is denoted as option A.

What is Median?

This is referred to as the middle value which separates the higher half from the lower half of a data or distribution. This is calculated by first ordering the numbers which could be from the lowest to highest or vice versa.

A data sample which has a higher figure as the median means that it has higher values present in the data distribution. This term provides an insight on certain properties of the values of the data which are given.

In this scenario, the median of brand A is higher than that of brand B which means that it has more weight and is therefore the reason why option A was chosen as the correct choice.

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The dimension are 75 * 50 i.e, Width = 50 cm , Length = 75 cm

Define Dimension

A measurable extent of a particular kind, such as length, breadth, depth, or height.

Let,

T = how taller the poster is

W = how wide the poster is

According to question given,

T = W + 25 ---eq(i)

The total height is calculated by multiplying the top border by 5 and the bottom border by 5. The entire height is then multiplied by the border's width, 5, times 2, so there are two tall sides. then multiplying by 5 times 2 widths.The equation looks like that,

5 * (2 (T + 10)) + 5 * (2 * W) = 1350

Now substitute the eq(i) value,

5 * (2 ((W + 25) + 10)) + 5 * (2 * W) = 1350

Now, solve for W,

5 * (2W +50 + 20) + 10W = 1350

10W + 5(70)+ 10W = 1350

20W + 350 = 1350

20W = 1350 - 350

20W = 1000

W = 1000/20

W = 50

Now, put the W value in eq(i)

T = 50 + 25

T = 75

Therefore, The dimension are 75 * 50 i.e, Width = 50 cm , Length = 75 cm

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In order to a set o points define a function, a value of x can't have two different values of y.

Looking at every option, we have in the option C that the value of x = 0 has two different values of y (1 and -1), therefore this set of points do not define a function.

So the answer is C.

Answer:

∠L = 113°∠O = 67°

Step-by-step explanation:

Given a transversal crossing parallel lines and supplementary angles (x+8°) and (2x-5°), you want to find the measures of angles L and O, supplementary to each of these.

Consecutive interior angles

Where a transversal crosses parallel lines, consecutive interior angles are supplementary. Using the given expressions, this means ...

(x +8°) +(2x -5°) = 180°

3x +3° = 180° . . . . . . . . . simplify

x +1° = 60° . . . . . . . divide by 3

x = 59° . . . . . . subtract 1°

Then the acute angle is ...

x+8° = 59° +8° = 67°

and the obtuse angle is ...

2x -5° = 2(59°) -5° = 113°

Relation to other angles

Angle L corresponds to angle (2x-5°), so is congruent:

∠L = 113°

Angle O is an alternate interior angle with respect to angle (x+8°), so is congruent:

∠O = 67°

The cost of endless chicken wings at Restaurant X is $5. So cost equation for n chicken wings at Restaurant X is,

[tex]c=5[/tex]

The cost of chicken wings at Restaurant Z is 20 cents and $1.40 for sauce. So cost equation for Restaurant Z is,

[tex]\begin{gathered} c=\frac{20}{100}\cdot n+1.40 \\ =0.20n+1.40 \end{gathered}[/tex]

So answer is,

Restaurant X: c = 5

Restaurant Z: 0.20n + 1.40

(b)

Plot the system of equation on the graph.

(c)

The lines of two restaurant X and restaurant Z intersect each other at point (18,5). This means that restaurant X and restaurant Z has same cost 5 at n = 18. So both restanurant has same cost for 18 chicken wings.

Answer: 18

The area of a rectangular backyard = 2(4x - 5y)

The algebraic expression has a equivalent expression as = 2 x 4x + 2 x 5y

= 8x + 10y

Using the concept of the equation, it can be concluded that Levi answered the first question wrong and the last two correctly. Thus,

No

Yes

Yes

How to check whether the value of x satisfies the equation?

To check the value of x satisfies the equation, put the value of x and if it matches the resultant, it is correct.

Now solving the first part, x/4=20;x=5

So, putting x=5 in the equation 5/4=1.25 is not matching with the resultant ie. 20.

Therefore, this is the incorrect value of x.

Now solving the second part, 1.5x-8=7;x=10

So, putting x=10 in equation 1.5*10-8= 15-8=7

It matches with the resultant.

Therefore, this is the correct value of x.

Now solving the third part, 4x+6=58; x=13

So, putting x=13 in equation 4(13)+6= 52+6=58

It matches with the resultant.

Therefore, this is the correct value of x.

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Answer:

The cost of cupcakes and cookies are;

[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]

Explanation:

Let x and y represent the cost of a cupcake and cookie respectively.

Given that;

Five cupcakes and two cookies cost $19.75.

[tex]5x+2y=19.75-------1[/tex]

Two cupcakes and four cookies cost $17.50.

[tex]2x+4y=17.50-------2[/tex]

Let's solve the simultaneous equation by elimination;

multiply equation 1 by 2;

[tex]10x+4y=39.50-------3[/tex]

subtract equation 2 from equation 3;

[tex]\begin{gathered} 10x-2x+4y-4y=39.50-17.50 \\ 8x=22 \\ \text{divide both sides by 8;} \\ \frac{8x}{8}=\frac{22}{8} \\ x=2.75 \end{gathered}[/tex]

since we have the value of x, let substitute into equation 1 to get y;

[tex]\begin{gathered} 5x+2y=19.75 \\ 5(2.75)+2y=19.75 \\ 13.75+2y=19.75 \\ 2y=19.75-13.75 \\ 2y=6 \\ y=\frac{6}{2} \\ y=3.00 \end{gathered}[/tex]

Therefore, the cost of cupcakes and cookies are;

[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]

Compound interest exists as the interest you gain on interest. The balance in the account after 2 years is $42266.

What is meant by compound interest?

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

'Compound interest' simply indicates earning interest on your savings, and also, eventually, on the interest that those savings earn.

The appropriate formula is

A = P(1 +r/n[tex])^{(nt)[/tex]

where P = 19,000, r = 0.4, n = 365, t = 2.

substitute the values in the above equation, we get

A = 19,000(1 +0.4/365[tex])^{(365 \times2)[/tex]

simplifying the above equation, we get

A = 42266.7592

The balance in the account after 2 years is $42266.

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The midpoint between the given figures are -2.5 and 5.5 respectively.

What is a midpoint ?

A midpoint is defined as that particular point that divides two separate figures into two equal halves or the centre of two endpoints on a number line.

That is;

point a + point b/2

The figures given are :

Point a = -3

Point b = -2

= -3 + -2/ 2

= -5/2

= -2.5

For points 4 and 7 ;

= 4 + 7 / 2

= 11/2

= 5.5

Therefore, the middle or midpoint of -3 and -2 is -2.5 and the midpoint for 4 and 7 is 5.5.

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Answer:

180°

Step-by-step explanation:Size of the angle between:North and South: 180°East and West: 180°North East and South West: 180°North West and South East: 180°North West and North East: 90°South West and South East: 90°