Line r is shown in the xy-plane. Line q (not shown) is perpendicular to line r. What is the slope of line q?

Solving by factoring in steps shown below

Answer:

[tex]\textsf{1. \quad $x=1, \quad x=-\dfrac{2}{5}$}[/tex]

[tex]\textsf{2. \quad $x=1, \quad x=3$}[/tex]

Step-by-step explanation:

Solving quadratic equations by factoring

Given equation:

[tex]5x^2=3x+2[/tex]

Subtract (3x + 2) from both sides:

[tex]\implies 5x^2-(3x+2)=3x+2-(3x+2)[/tex]

[tex]\implies 5x^2-3x-2=0[/tex]

Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], and rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies ac=5 \cdot -2=-10[/tex]

[tex]\implies b=-3[/tex]

Therefore, the two numbers are -5 and 2.

Rewrite [tex]b[/tex] as the sum of the two numbers:

[tex]\implies 5x^2-5x+2x-2=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 5x(x-1)+2(x-1)=0[/tex]

Factor out the common term (x - 1):

[tex]\implies (5x+2)(x-1)=0[/tex]

Apply the zero-product property:

[tex]\implies 5x+2=0 \implies x=-\dfrac{2}{5}[/tex]

[tex]\implies x-1=0 \implies x=1[/tex]

Therefore, the solutions are:

[tex]\boxed{x=1, \quad x=-\dfrac{2}{5}}[/tex]

Given equation:

[tex]\implies x^2-4x+3=0[/tex]

Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], and rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies ac=1 \cdot 3=3[/tex]

[tex]\implies b=-4[/tex]

Therefore, the two numbers are -3 and -1.

Rewrite [tex]b[/tex] as the sum of the two numbers:

[tex]\implies x^2-3x-x+3=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x-3)-1(x-3)=0[/tex]

Factor out the common term (x - 3):

[tex]\implies (x-1)(x-3)=0[/tex]

Apply the zero-product property:

[tex]\implies x-1=0 \implies x=1[/tex]

[tex]\implies x-3=0 \implies x=3[/tex]

Therefore, the solutions are:

[tex]\boxed{x=1, \quad x=3}[/tex]

The set of possible dimensions (length and width) of the field are {13.5, 10, 5.5, and 26}.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle  and L is the length of the rectangle

The perimeter = 2W+ L

37 = 2W + L

L = 37 - 2W

Hence,

area = W(37 - 2W)

143 = 37W - 2W²

-2W² + 37W - 143 = 0

W² - 18.5 W + 71.5 = 0

W = 13.5, 5.5

Take the value of W = 13.5

Then,

L = 37  - 2W

L = 37 - 2(13.5)

L = 10 meters

Take the value of W = 5.5

Then,

L = 37  - 2W

L = 37 - 2(5.5)

L = 26 meters

Therefore, the set of possible dimensions (length and width) of the field are {13.5, 10, 5.5, and 26}.

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The algebraic expression for the verbal expression 7 divided by the product of 9 and x is 7/9x.

Given verbal expression is 7 divided by the product of 9 and x.

Hence, the required algebraic expression for given verbal expression is 7/9x.

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The machine can make 25 soda bottles each minute.

The ratio between the change in the values of the y variables and the change in the values of the x variables is known as the slope. It shows how much the y-value changes for every unit change in the x-value.

Given:

The graph shows a relationship between the time and the number of soda bottles a machine can make.

Points are (3,75) and (7,175).

We have to calculate the number of soda bottles the machine can make each minute i.e. rate of the machine.

To determine the rate of the machine which is equal to the slope of the graph,

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] =  [tex]\frac{175-75}{7-3}[/tex] = [tex]\frac{100}{4} =25[/tex]

Therefore, the machine can make 25 soda bottles each minute.

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Answer:

(-2, 2)

Step-by-step explanation:

[tex]B(-5,4) \longrightarrow B'(-5+3, 4-2)=B'(-2, 2)[/tex]

Answer:

$204

Step-by-step explanation:

Salary per hour = $10.20

Therefore salary for 20 hours = 10.20 X 20

                                                  = $204

I hope you understood the answer and it has helped you!!!

Answer:

g(2) = 0

Step-by-step explanation:

g(2) is the value of x.

So, we would place g(2) with x:

g(2) = 2(2) - 4

g(2) = 4 - 4

g(2) = 0

If the given function is g(x)=2x-4, the value of g(2) will be 0.

The function is described as a particular kind of relationship, and each value in the domain is associated with exactly one value in the range according to the function. They have a predefined domain and range.

It is given that the function is, g(x)=2x-4

We have to find g(2).

In order to find the g(2), substitute 2 as the place of x as,

g(x)=2x-4

g(2)=2×2-4

g(2)=4-4

g(2)=0

Thus, for the given function g(x)=2x-4, the value of g(2) will be 0.

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Answer: line mn = 4

Step-by-step explanation:

Note: There's a chance i might be wrong.

Due to de=12, and ef=10, it seems as though a pattern is clear and that ef was -2 the size of de. Since lm is 6,  de got divided by 2, 12/2=6

Therefore, subtract 2 from 6, and you get 4.

Hope this helps

The actual building is tall 56.3 meters

On a scaled drawing a building measures 4.5 cm tall

The scale drawing is 25 meters per 2 cm

The first step is to calculate the equivalent of 1 cm in meters

2 centimetres= 25 meters

1 centimetre= x

cross multiply both sides

2x= 25

x= 25/2

x= 12.5

1 centimetre is 12.5 metres

4.5 centimetres in metres is

= 4.5 × 12.5

= 56.3

Hence the height of the actual building is 56.3 meters

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Answer:

B

Explanation:

Given:

By using HL method of congruence, we can determine that triangle ABC is congruent to triangle EDC. HL method of congruence means that the two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles. Based on the given figure, we see taht the legs AB and DE are congruent. Next, we check for a pair of hypotenuses. So, we need AC congruent to EC.

Therefore, the additional information we needed using HL method of congruence is AC congruent to EC.

Using proportions, it is found that:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures using operations such as multiplication and division to find the unknown variables.

In the context of this problem, we have that:

Hence the minimum width of the flier is found as follows:

2w = 16

w = 16/2

w = 8 inches.

The maximum width of the flier is found as follows:

2w = 24

w = 24/2

w = 12 inches.

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The nth term in the sequence is 30 and the sequence becomes like this: 0, 2, 6, 12, 20, 30

So, the n term that comes next in the sequence is:

We can notice the hidden sequence, that is:

Therefore, the nth term in the sequence is 30 and the sequence becomes like this: 0, 2, 6, 12, 20, 30

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Answer:

drag Traingle B into the box

The similar figure is B. , which have to drag into the table.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

from the given diagram, we get,

the shown figure is a equilateral triangle with all angle =60 degree.

And, as shown, in figure B. we get , a equilateral triangle with all angle 60degree.

Hence, The similar figure is B. , which have to drag into the table.

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The amount for Emiliano tip is $1.8.

From the information, Emiliano buys two coffees for $8.98 and he tips the barista 20% of the bill.

The value of the tip will be:

= Percentage × Value of coffee

= 20% × $8.98

= 0.2 × $8.98

= $1.796

= $1.8 to the nearest cent.

This illustrates the concept of multiplication.

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When the inequality expression 1 > |b - 5| is evaluated, the value of the expression is 4 < b < 6

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The absolute value inequality is given as

1 > |b - 5|

Remove the absolute value inequality symbol

So, we have the following expression

-1 < b - 5 < 1

Add 5 to all sides of the inequality expression

So, we have the following expression

5 -1 < b - 5 + 5 < 1 + 5

Evaluate the sum and the difference in the above inequality expression

So, we have the following expression

4 < b < 6

Hence, the solution to the inequality expression 1 > |b - 5| is 4 < b < 6

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Answer:

your answer would be 160680

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

(18+7)-30

25-30=

-5

1 Chinese yuan could purchase $0.12 and $0.15 in the year 2010 and 2012 respectively.

For the year 2010; we can calculate as follows;

1 US dollar = 8.24 Chinese yuan

x US dollar = 1 Chinese Yuan

using cross multiplication to find x;

8.24x = 1 ×1

8.24x = 1

x = 1 / 8.24

x = $0.12

For the year 2012; we can calculate as follows;

1 US dollar = 6.64 Chinese Yuan

x US dollar = 1 Chinese Yuan

Using cross multiplication to find x;

6.64x = 1

x = 1 / 6.64

x = $0.15

Therefore, one Chinese yuan could purchase $0.12 in 2010 and $0.15 in the year 2012.

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The linear equation that represents the scenario is: y = 235x + 15.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope = (1660 - 955)/7 - 4)

Slope = 705/3

Slope = 235.

Mathematically, the standard form of the equation of a straight line is given by;

y - y₁ = m(x - x₁) or y = mx + c

Where:

By critically observing the graph (see attachment) which models the data in the given table, we can reasonably infer and logically deduce that the linear function is given by: y = 235x + 15.

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When Kimai is making blankets for charity, the proper form of the unit rate is 4 hats per hour.

From the information given, it was stated that Kimai is making blankets for charity. In order to determine how many hats she can make per hour, she created 3/5 of the hats in 1/8 of an hour.

Therefore, the proper form of the unit rate will be:

= Amount of hats / Time

= 3/5 ÷ 1/8

= 3/5 × 8/1

= 4.8

Therefore, the proper rate will be 4 hats per hour.

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Answer: 4 hats per hour

Step-by-step explanation:

Answer:

There are probably multiple answers to this question, but the answer I got was x = 7, and y = 4.

Step-by-step explanation:

First Equation: 9 + 3x. (Below)

3 x 7 = 21

21 + 9 = 30

Second equation: 2x + 4y.

2 x 7 = 14

4x4 = 16

16 + 14 = 30.

———————

Since they both have the same solution it leads me to believe it’s the answer,

[tex]\displaystyle\\Answer:\ y=\frac{4}{3}x-5[/tex]

Step-by-step explanation:

[tex]y=mx+b\\[/tex]

[tex]\displaystyle\\The\ slope\ m=\frac{4}{3} \\\Rightarrow\ y=\frac{4}{3}x+b[/tex]

A line passes through the point (9, 7)

Thus,

[tex]\displaystyle\\x=9\ \ \ \ y=7\\\\7=\frac{4}{3} (9)+b\\\\7=\frac{4(9)}{3} +b\\\\7=\frac{36}{3} +b\\\\7=\frac{3(12)}{3} +b\\\\7=12+b\\7-12=12+b-12\\-5=b\\So,\ y=\frac{4}{3}x-5[/tex]

Answer:

he needs 0.2 more

Step-by-step explanation:

2-7/5=0.6 that means he still has 0.6 left of the boxes.

minus the 4/5= -0.2

so Tom needs 0.2 more to give out that amount.

Answer:

11/10

he needs one more

Step-by-step explanation:

Answer:

37 is the correct answer

Answer:

7500 or 7.5 or 10³ ..... .............

The function that best describes the graph is y = x² + 9x + 18. The correct option is B. y = x² + 9x + 18

From the question, we are to determine the function that best describes the graph

From the graph, we can observe that the roots of the quadratic equation are x = -6 and x = -3

Thus,

(x + 6) and (x + 3) are factors of the quadratic equation.

Then,

Multiplying the factors, we get

(x + 6)(x + 3) = 0

x(x +3) + 6(x + 3) = 0

x² + 3x + 6x + 18 = 0

x² + 9x + 18 = 0

This means the function is y = x² + 9x + 18

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The values of the descriptive statistics of the given data on the scores of the classes in the Algebra class are;

a. Mean; 78.83, Median; 88, Mode; 90, Range; 55

b. Mean; 79.52, Median; 85.5, Mode; 90, Range; 60

c. Mean; 79.52, Median; 78, Mode; 75, Range; 45

d. 19.66

e. 16.87

f. 13.27

g. Class 1

h. Class 3

A descriptive statistic is one that provides an idea of contents of a dataset by outlining the pattern found within the dataset

Mean

The mean of the dataset is given by the formula;

[tex] \displaystyle{Mean = \frac{Sum \: of \: data}{Number \: of \: data}} [/tex]

Median

The median of a dataset is the middle term of a dataset when the data are arranged in increasing order

Mode

The mode of a dataset is the value that occurs most frequently

Range

The range is given by the difference between the maximum and minimum values of the dataset

a. The mean of Class 1 obtained from an application is 78.83

The median = 88

The mode = 90

The range = 55

b. The mean of Class 2 obtained from an application is 79.42

The median = 85.5

The mode = 90

The range = 60

c. The mean of Class 3 obtained from an application is 79.42

The median = 78

The mode = 75

The range = 45

d. The standard deviation is given by the formula;

[tex] \displaystyle{\sigma = \sqrt{\frac{\sum (x_i -\bar x)^2} {N}}}[/tex]

Where;

[tex] \displaystyle{ x_1}[/tex] = The ith data

[tex] \displaystyle{\bar x}[/tex] = The mean

N = The number of data

Solving using a spreadsheet application, we have;

The standard deviation for class 1 = 19.65

e. The standard deviation of class 2 found using a spreadsheet application is 16.87

f. For class 3, the standard deviation is 13.27

g. From the above calculations, the class that has the highest standard deviation is class 1, with a standard deviation of 19.65

The high standard deviation means that there is a lot of variability or variation in the scores of class 1

h. The class that did better is class 3, that has the lowest standard deviation and range as well as one of the highest mean

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Answer:f

Step-by-step explanation: