write the equation of the line that is perpendicular to the line y=-2 and passes through (4,-2)

The missing terms in the two column proof are;

Reason 1; Perpendicular bisector

Reason 2; Definition of perpendicular bisector

Statement 3; CO ≅ BO

Reason 3; Segment division

Reason 4; Reflexive Property of Congruence

Reason 5; Definition of Isosceles Triangle

Reason 6; AAS Congruency Postulate

From the given image, we want to use the two column proof to prove that ΔAOB ≅ ΔAOC

Now, we have the two column proof as follows;

Statement 1; AO ⊥ BC

Reason 1; Perpendicular bisector

Statement 2; ∠AOB and ∠AOC are right angles

Reason 2; Definition of perpendicular bisector

Statement 3; CO ≅ BO

Reason 3; Segment division

Statement 4; AO ≅ AO

Reason 4; Reflexive Property of Congruence

Statement 5; AB ≅ AC

Reason 5; Definition of Isosceles Triangle

Statement 6; ΔAOB ≅ ΔAOC

Reason 6; AAS Congruency Postulate

The final proof is AAS Congruency postulate because it has 2 congruent angles and the non-included congruent side.

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A fraction can be converted into decimal form by dividing it. The answer to these parts are in main body.

What is a decimal?

When we divide a whole into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number.

Main Body:

a) 15/32 = 0.4688

b) 13/64 = 0.2031

c) 9/16 = 0.5625

d) 5/8 = 0.625

e) 7/80 = 0.0875

f) 29/1280 = 0.0227

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The percentage increase in Hayley's fuel bills from 2021 to 2022 is equal to 17.105%.

What is a Percentage Increase?

The phrase "percentage increase" (or "percentage change" in general) refers to the difference between the final and starting values of a quantity, expressed as a percentage of that number's original value.

Steps to Calculate Percentage Increase?

Here, in the question, it is given that,

The original amount (X) or the fuel bill in 2021 is £76.

The new amount (Y) or the fuel bill in 2022 is £89.

So, the Increase (I) in the fuel bills from 2021 and 2022 is calculated as,

[tex]I=Y-X\\\implies I=89-76\\\implies I=13[/tex]

Now, we can calculate the percentage increase in fuel bills from 2021 to 2022 as,

[tex]\%I=\frac{I}{X} \times 100\\\implies \%I=\frac{13}{76} \times 100\\\implies \%I=17.105\%[/tex]

Therefore, the percentage increase in Hayley's fuel bills from 2021 to 2022 is 17.105%.

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Answer:

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If a standardized exam's scores are normally distributed. The z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.

mu = population mean = 1487

sigma = population standard deviation = 314

x =1870

z = (x - mu)/σ

z = (1870-1487)/314

z = 1.22 (approximately)

x =1250

z = (x - mu)/σ

z = (1250-1487)/314

z = -0.75

x =2170

z = (x - mu)/σ

z = (2170-1487)/314

z = 2.18 (approximately)

x =1390

z = (x - mu)/σ

z = (1390-1487)/314

z = -0.31 (approximately)

Therefore the z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.

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The amount in the account is $3499. 2

The formula for determining compound interest is given as;

A = P ( 1 + r/ n) ^nt

Given that;

Substitute the values into the formula, we have;

A = $3000 ( 1 + 0. 04 / 0. 5) ^(0.5× 4)

Find the exponential value

A = $3000 ( 1 + 0. 04 / 0. 5) ^2

A =  $3000( 1+ 0. 08)^2

Expand the bracket, we get;

A = $3000 (1. 08)^2

A = $3000(1. 17)

multiply through

A = $3499. 2

Hence, the value is $3499. 2

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The given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given that the graph of the function has increased and decreasing orders on the coordinate plane.

The interval in which the given graph of the function is increasing is,

(-∞,-6)

(-4,-1)

(3,6)

(8,∞)

Therefore, the given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).

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Answer:

a = 41°

b = 57°

c = 82°

Step-by-step explanation:

all angles in a triangle must add up to equal 180°

Answer:

10 inches

Step-by-step explanation:

What this question is asking you to do is set up a ratio. So all you do is 14/70 = x/50 and solve for x.

Answer:

14inches = 70cents

X inches = 50cents

70x = 50×14

70x = 700

X = 10inches

Regarding the data-set of the temperatures, it is found that:

a) The mean and the standard deviation are given as follows:

b) The histogram is bell shaped.

c) 95% of the days will be between 63.75 ºF and 97.07 ºF.

The first step towards obtaining the mean and the standard deviation is obtaining the relative frequencies, which are the absolute frequencies divided by the number of observations.

The number of observations is:

5 + 309 + 1496 + 1521 + 533 + 6 = 3870.

Considering the midpoint of each interval, the following distribution is built:

The mean is given by the sum of each value multiplied by it's relative frequency, hence:

E(X) = 54.5 x 0.0013 + 64.5 x 0.0798 + 74.5 x 0.3866 + 84.5 x 0.3930 + 94.5 x 0.1377 + 104.5 x 0.0016 = 80.41.

The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, multiplied by their relative frequencies, as follows:

S(X) = sqrt((54.5-80.41)² x 0.0013 + (64.5-80.41)² x 0.0798 + (74.5-80.41)² x 0.3866 + (84.5-80.41)² x 0.3930 + (94.5-80.41)² x 0.1377 + (104.5-80.41)² x 0.0016) = 8.33.

From the histogram, most values are around the mean, with a small percentage of around 0.3% around the bounds, accordingly with the Empirical Rule, hence the distribution is normal.

By the Empirical Rule, a percentage of 95% of the observations is within two standard deviations of the mean, hence:

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Answer: (1/3)x - 8

Step-by-step explanation:

one - third means 1/3

one - third of a number means (1/3)x

       ( x being the number )

Eight less means -8

Eight less than 1/3 of an number is (1/3)x - 8

Representing length and width relationship of a rectangle, and the perimeter given by length of wire using inequality gives

The perimeter of a rectangle, P is given by the formula

P = 2(L + W) ≤ 57 units of wire

width, W = 2 units

length, L = 1 + W

= 1 + 2

= 3

The perimeter of the rectangle is given by

P = 2(L + W)

plugging the values of L and W

P = 2 (3 + 1)

P = 2 (4 )

P = 8 units

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Answer:

0=0

Step-by-step explanation:

Answer: Infinite Solutions

Step-by-step explanation:

Hello! Let's solve this equation.

[tex]\sf{6x-5=6x-5}[/tex]

↓

[tex]\sf{6x=6x-5+5}[/tex]

↓

[tex]\sf{6x=6x}[/tex]

[tex]\sf{6x-6x}[/tex]

↓

[tex]\sf{0}[/tex]

[tex]\textbf{So as you see, all the terms \textit{cancel out.}}\\\textbf{The \textsf{given equation} has \textit{\underline{infinite solutions.}}}\\\textbf{The equation is true for any x-value.}[/tex]

[tex]_ < \!\!\!\rule{300}{1}\!\!\!_ >[/tex]

Answer:

13

Step-by-step explanation:

56/7 = 8

13 - 5 = 8

15/7 = 13 - 5

The missing number in the expression is 13.

We have,

To find the missing number in the equation 56 / 7 =? - 5, solve for the unknown value.

Unknown value = x

Starting with the equation 56 / 7 = x - 5, simplify the left side:

56 / 7 = x - 5

8 = x - 5

x = 8 + 5

x = 13

Thus,

The missing number in the expression is 13.

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a. The expense function in terms of p is  - 280p + 34, 000

b.  At a price of $10.00, 7, 600 widgets are demanded

c.  It costs  $31, 200 to produce the number of widgets from part b

We have that;

To express the expense function in terms of p, we have to take the following steps;

Substitute the value of q in the demand function into the function for the expense, we get;

Expense function = 2( -140p + 9,000) + 16, 000

Now, expand the bracket, we get;

Expense function = - 280p + 18, 000 + 16, 000

collect and add like terms

Expense function = - 280p + 34, 000

If p = $10. 00

Then,

Demand function is q = -140(10) + 9,000

expand the bracket

q = - 1400 + 9, 000

q = 7, 600

Substitute q in expense function

E = 2.00q + 16,000

E = 2. 00(7600) + 16, 000

E = $31, 200

Hence, the expense function is - 280p + 34, 000

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Answer: 10 rows of rose plants

Step-by-step explanation:

The number of rose plants in first, second third,..., and last row are respectively.

23,21,19,....,5.

number of rose plants: n

The sequence 23,21,19,....,5 is an A.P. with first term a(=23), common difference d(=−2) and n

=a+(n−1)d

⟹5=23+(n−1)×−2

⟹5=23−2n+2⟹20=2n⟹n=10

The number line with the numbers -3, 1 and 3 is shown by the image at the end of the answer.

The correct statements regarding the number line are given as follows:

Integer numbers are numbers that do not have decimal parts, they are either positive or negative, but exact.

These numbers are plotted marking a symbol such as a X or a circle on the number line.

The number line is increasing, so the negative numbers appear before the positive numbers.

This means that if a number a is to the left another number b, the number a is less than b, hence:

As the order in which the numbers appear is given as follows:

-3, 1 and 3.

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The  equation of line in slope intercept form

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

Slope = [tex]\frac{1}{5}[/tex]

Point = (-2, 2)

Required equation of line =

[tex]y - 2 = \frac{1}{5}(x - (-2))\\5y - 10 = x + 2\\5y = x + 2 + 10\\5y = x + 12\\y = \frac{1}{5}x + \frac{12}{5}\\[/tex]

The graph has been attached here.

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Means if a number is bigger than other number.

The number of pathology tests that were completed during the year by Levine Labs are 34,800 tests.

Note that Material quantity variation - Material quantity variation describes the cost difference caused by variations in the actual material used and the standard material to be utilized.

Material quantity Variance =

(Actual material used- Standard material used) x Standard cost

(50000-no of test x 1.5) x 0.4 = -880

-2200 = 50000-(No of test*1.5)

No of test x 1.5 = 52,200

No of test =  52,200/1.5

No of test = 34,800

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The linear equation in the slope-intercept is:

y = (-1/5)*x  - 26/5

And it can be written as:

y = (-1/5)*(x + 1) - 5

We can write the equation for line L as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is equal to -1.

So if we want our line to be perpendicular to y= 5x, then we must have:

a*5 = -1

a = -1/5

So our line is something like:

y = (-1/5)*x + b

And the line passes through (-1, -5), replacing these values:

-5 = (-1/5)*-1 + b

-5 = 1/5 + b

-5 - 1/5 = b

-26/5 = b

The linear equation is:

y = (-1/5)*x  - 26/5

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Answer:

Step-by-step explanation:

A=60

B=75

C=45

D=60

E=75

F=45

G=90

Using the circle graph, the costs to attend the public university are as follows:

A circle graph, or a pie chart, is used to visualize information and data.

Therefore, the circle graph is shows the percentage cost for tuition/fees, room, board, and computer costs.

The cost to attend a public university in a recent year is $16,241.

Using the pie chart, let's find the cost of the various fees.

Therefore,

cost of tuition and fees = 36.9% of 16,241

cost of tuition and fees = 36.9 / 100 × 16241

cost of tuition and fees = 599292.9 / 100

Therefore,

cost of tuition and fees = $ 5992.929

cost of room = 31.5% × 16241

cost of room = 31.5 / 100 × 16241

cost of room = $5115.915

Hence,

cost of board = 24.9% of 16241

cost of board = 24.9 / 100 × 16241

cost of board = $ 4044.009

Hence,

computer cost = 6.7% of 16241

computer cost = 6.7 / 100 × 16241

computer cost =  $1088.147

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The transformations of g(x) that would result in odd functions are (a)-g(x)   , (b)g(2x)  and (d)g(–x) ,

In the question ,

it is given that,

the function is g(x) = 3x³ + x

We know that the function f(x) is called an odd function if f(-x) = -f(x) .

Option(a)

the transformation is given as -g(x)

-g(x)  = -(3x³ + x) = -3x³ - x

g(-x) = 3(-x)³ + (-x) = -3x³ - x

so , this is odd function .

Option (b)

the transformation is given as g(2x)

g(-2x) = 3(-2x)³ + (-2x) = -24x³ - 2x

-g(2x) = -{3(2x)³ + (2x)} = -( 24x³ + 2x ) = -24x³ - 2x

so , this is  odd function .

Option (c)

the transformation is given as g(x)-3

(g(-x) - 3) =  3(-x)³ + (-x) - 3 = -3x³-x-3

-(g(x) - 3) = -{(3x³ + x) -3} = -3x³ - x +3

So, so , this is not an odd function

Option (d)

the transformation is given as g(-x)

g(-(-x)) = g(x) = 3x³+x

-g(-x) = -(3(-x)³ + (-x)) = -(-3x³ - x) = 3x³+x

so , this is odd function .

Therefore, the odd transformations are -g(x)   , g(2x)  and g(–x) ,

The given question is incomplete , the complete question is

The function g(x)=3x³+x is an odd function. Which transformation of g(x) would result in odd functions? Check all that apply

(a) -g(x)

(b) g(2x)

(c) g(x) − 3

(d) g(–x)

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Answer:0.8

Step-by-step explanation:

0.8 can be used for 1 student and 40. :)

The values are;

i, For 1 student, it would take = 1 1/5 days

ii. For 40 students, 48 days

First, we need to know that proportion is an equation made equal to another.

From the information given, we have that;

50 students in a hostel had provisions for 60 days.

This is represented as;

50 students = 60 days

Then, we get that;

i, If 50 students = 60 days

1 students = x days

cross multiply the values

x = 60/50

x = 1 1/5 days

ii.  If 50 students = 60 days

40 students = x days

x = 60(40)/50

divide the values

x = 48 days

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Answer:

Step-by-step explanation:

$2.40             12.45 mi
___        *        ___          =   ?  ;
1  mi.               1              

The units of miles— "mi" —cancel out to "1" ;

   since:  " mi/ mi = 1 "

  and we have:
    $2.40  * 12.45  =  ?  ;

                             =  $29. 88 ; {using a calculator};

       ⇒ which corresponds to:  Answer choice:  [D]:  $29.88 .
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