Evaluate the following expressions.

Answer: 5.184 ft

Step-by-step explanation:

[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]

The rate at which the water level dropped each hour is 5 / 34 inches per hour.

In order to determine the rate  at which the water level dropped each hour , divide the total decrease in the water level by the total time it took for the water to decrease.

Division is the process of  grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

Change in water level per hour = total decrease / change in time

Change in time = 11 - 8 : 10 = 2 : 50 am = 2 hours 5/6 minutes

Change in water level per hour = 5/12 ÷ 2 5/6

5/12  ÷ 17/6

5 / 12 x 6 / 17 = 5 / 34 inches per hour

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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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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:

multiply ecerything that is in the brackets by 3

[tex]3(x) + 3(2) + 7 \\ = 3x + 6 + 7 \\ = 3x + 13[/tex]

ATTACHED IS THE SOLUTION

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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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:

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.

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:

your answer would be 160680

Step-by-step explanation:

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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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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Answer:

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

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 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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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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Answer:

-5

Step-by-step explanation:

(18+7)-30

25-30=

-5

The carton can hold 8402.7cm3 or 8.4 litres of milk now

Initially, the width and length of the carton are 8.88cm each.

Now, the width and length of the carton are doubled. That is:

The width and length are 2 x 8.88cm = 17.76 cm each

But the height remains the same:  26.64cm

Volume of the carton = width x length x height

                                    = 17.76 x 17.76 x 26.64

                                    = 8402.7 cm3 = 8.4 litres

Therefore, the quantity of milk the carton can hold now is 8402.7 cm3 or 8.4 litres.

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Answer: The area of a circle is 286.37cm².

Step-by-step explanation: The answer to this question can be solved by finding the value of the radius from the circumference and substituting it into the area.

Following are the steps to solve this problem:-

Step 1.  The circumference of the circle is 60cm.

The formula for the circumference of a circle is 2[tex]\pi \\[/tex]r.

Step 2. Calculating the value of radius (r) is 2[tex]\pi[/tex]r=60 cm.

                                                                2x 3.14xr =60cm.

                                                                r= 9.55cm

Step 3. Calculate the area of a circle by using the formula [tex]\pi[/tex]r²

Substituting the valur r( from step 2 ) in the formula

                                                  3.14x9.55x9.55= 286.37cm²

Thus, the answer is 286.37cm²

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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:

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 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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After solving the system of equations using Gaussian elimination we get the values as x = 5 , y = -11 and z=3

Given we have the system of equations as follows:

2x - y + 4z = 33

x + 2y - 3z = -26

-5 x - 3y +5z = 23

Rewrite the system in matrix form and solve it by Gaussian elimination.

[ 2  -1  4     [ 33

 1  2  -3   =  -26

-5  -3  5 ]      23 ]

Now divide row 1 by row 2.

[ 1  -0.5  2        [ 16.5

 1     2   -3    =  -26

-5    -3  5 ]         23 ]

Now R₂ - 1R₁ → R₂

and R₃ + 5R₁ → R₃

[ 1  -0.5  2        [ 16.5

 0   2.5  -5    =  -42.5

 0  -5.5 15 ]       105.5 ]

Divide row 2 by 2.5.

[ 1  -0.5  2        [ 16.5

 0     1   -2    =  -17

 0  -5.5 15 ]       105.5]

R₁+0.5R₂ → R₁

R₃ + 5.5R₂ → R₃

[ 1   0  1          [ 8

 0   1   -2    =  -17

 0    0   4 ]        12 ]

Divide R₃ by 4

[ 1   0  1          [ 8

 0   1   -2    =  -17

 0    0   1 ]         3 ]

Therefore, R₁-1R₃→R₁

R₂ + 2R₃ → R₂

[ 1   0  1          [ 5

 0   1   0    =    -11

 0    0   1 ]        3 ]

therefore x = 5, y=-11 and z = 3.

Hence we solved the system of equations using Gaussian elimination.

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1) The relationship between ∠1 and ∠3 is that they are corresponding angles.

2) The relationship between ∠8 and ∠4 is that they are alternate exterior angles

3) The relationship between ∠2 and ∠3 is that they are supplementary angles.

When it comes to congruent angles, we know that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

Now, in the first figure, we see that there are a total of eight angles and we also see that 2 parallel lines have been intersected by a third one. Thus, some of the angles will be congruent to others. In this case, we see that the relationship between ∠1 and ∠3 is that they are corresponding angles.

Now, in the second figure, we see that there are a total of eight angles and we also see that 2 parallel lines have been intersected by a third one. Thus, some of the angles will be congruent to others. In this case, we see that the relationship between ∠8 and ∠4 is that they are alternate exterior angles because they are formed on the outside of the parallel lines.

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