Solve the following by completing the square or squaring both sides using steps illustrated in the lesson content.. Leave answers in radical (EXACT) form. Do not use decimals. -2x+6=-x^2​

The expressions are written as;

h(t)+k(t) = 10t - 1

h(t)−k(t) = -2t + 1

Note that algebraic expressions are described as expressions that are made up of coefficients, variables, terms, constants and factors.

These expressions are made up of arithmetic operations, which includes;

From the information given, we have that;

h(t)=4t

k(t)=t+5t−1

To determine the value of h(t) + k(t), we have;

4t + t + 5t - 1

add the like terms, we get;

10t - 1

To determine h(t) = k(t)

4t- t - 5t + 1

add like terms

-2t + 1

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The equaltion for the line of best fit would be,

y = 0.67x + 4.05

The points on the scatter plot are: (1, 3.8), (2, 5.8), (3, 6.2) , (4, 7.5) , (5, 7.2), (6, 8.3), (7, 9.3), and (8, 8.5 )

First we find the mean of the x-values and mean of the y-values.

The mean of the x-values would be,

[tex]\bar{X}[/tex] = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) / 8

[tex]\bar{X}[/tex] = 4.5

and the mean of the y-values would be,

[tex]\bar{Y}[/tex] = (3.8 + 5.8 + 6.2 + 7.5 + 7.2 + 8.3 + 9.3 + 8.5) / 8

[tex]\bar{Y}[/tex] = 7.075

The sum of squares (SSX) = 42

And the sum of products (SP) = 28.2

Regression Equation would be,

y = mx + c

m = SP/SSX

   = 28.2/42

   = 0.67143

And the y-intercept would be,

c =  4.05357

So, the equation for the line of best fit would be,

y = 0.67143x + 4.05357

Number of Households = 0.67143 (time) + 4.05357

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Find the complete question below.

The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years.

Scatter plot with x axis labeled Time in Years and y axis labeled Number of Households with points at 1 comma 3 and 8 tenths, 2 comma 5 and 8 tenths, 3 comma 6 and 2 tenths, 4 comma 7 and 5 tenths, 5 comma 7 and 2 tenths, 6 comma 8 and 3 tenths, 7 comma 9 and 3 tenths, and 8 comma 8 and 5 tenths.

Anna has $165 left in the jar. The solution has been obtained by using the arithmetic operations.

All real numbers are supposed to be explained by the four fundamental operations, often known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.

We are given that Anna saved $20 in a jar each month for 2 complete years and for 9 months of next year.

So, total months = 9 + 12 + 12 = 33

Now, using the multiplication operation, we get

⇒ Total money saved = 33 * 20

⇒ Total money saved = $660

It is given that she spent 75% of her savings on computer.

So, using the subtraction operation, we get

⇒ Amount left = 660 - 75%

⇒ Amount left = $165

Hence, Anna has $165 left in the jar.

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Answer:

C is the correct answer.

For the given function h(x) the points can be plotted on,

The given function h(x) is having four conditions and each condition can be clearly discussed below:

From, the above analysis we plotted the graph and attaching below.

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Step-by-step explanation:

step A is incorrect.

-40/5 does not equal to -40/-5.

-40/-5 is equal to 40/5 as we can simplify the negative 1 out.

Answer:

The correct answer is step A

An expression to show how many books would be on each table is a/10

To find out how many books would be on each table, we need to divide the total number of books by the number of tables.

First, let's express the total number of books in terms of a and d. Since we are not given any specific numbers for a and d, we can simply use variables to represent them. Therefore, the total number of books is given by a.

Next, we need to divide a by 10, the number of tables. This gives us the expression:

a/10

So, the above expression shows how many books would be on each table if Mrs. Marcus combines her books and magazines and then divides them among 10 different tables.

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Complete question is:

Mrs. Marcus combines her atlases and dictionaries and then divides them among 10 different tables. If a represents the number of atlases and d represents the number of dictionaries Mrs. Marcus has, write an expression to show how many books would be on each table.

The perimeter of the rug is 36ft

Perimeter is the total length around the outside of a shape. The perimeter can be found by adding all the sides of the shape.

Perimeter of a rectangle is expressed as ;

P = 2(l+w)

The area of the rug is 81ft²

area = l× w

length = 9ft

width of the rug = 81/9 = 9ft

Therefore the perimeter of the rug will be

P = 2(l+w)

P= 2( 9+ 9)

P = 2 × 18

P = 36 ft

therefore the perimeter of the rectangular rug is 36ft

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The equation which can be used to find the amount the admission tickets cost would be 4x + 25 = 175. The cost of the admission tickets would therefore be $ 37.50.

The total spent by Ms. Boi was $ 175.00 so this is what the entire equation would be equal to. The cost of admission tickets will be denoted as x because they are the unknown figure.

There are 4 tickets purchased so the equation would be:

4 x Cost of tickets - Parking cost = Total spent

4 x - 25 = 175

The cost of each admission ticket is:

4 x - 25 = 175

x = 150 / 4

x = $ 37.50

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A passenger can travel 6.875 miles for $20 using the given taxi fare function.

To determine how many miles a passenger can travel for $20 using the taxi fare function f(x) = 2.56x + 2.40, we need to set up an equation and solve for x.

The equation we need to solve is:

2.56x + 2.40 = 20

To solve for x, we can start by subtracting 2.40 from both sides of the equation:

2.56x = 17.60

Next, we can divide both sides by 2.56:

x = 6.875

This calculation assumes that the fare is based solely on distance and that there are no additional fees or charges.

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Answer:

87 I think.

Step-by-step explanation:

29 x 3 = 87

Answer:

[tex]30d^2[/tex]

Step-by-step explanation:

Answer: To work out 2.1/0.7 without a calculator, you can use long division as follows:

0.7 | 2.1

    1.4   (3 times 0.7 is 2.1)

   -----

    0.7

    0.0   (there is no remainder)

Therefore, 2.1/0.7 = 3, which means that 2.1 is equal to 3 times 0.7.

Answer:

see below

Step-by-step explanation:

2.1

-----

.7

Multiply the top and bottom by 10 to get rid of the decimals.

2.1 *10 = 21

.7 * 10 = 7

21/7 = 3

Answer:

Subtract the powers, 8-4.

When you simplify that equation itself, the answer is 10,000.

So when you do 10⁴, it's 10,000.

The probability of choosing a red marble is 6/17.

The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes.

To calculate this probability, we can use the formula:

P(red marble) = number of red marbles / total number of marbles

In this case, we substitute the numbers we know:

P(red marble) = 6 / 17

So the probability of choosing a red marble is 6/17 or approximately 0.35.

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Step-by-step explanation:

x = -2 or x = 2

x + 2 = 0 or x - 2 = 0

(x + 2) (x - 2) = 0

x² - 4 = 0

The smallest fraction is 8/12, which is equivalent to 2/3.

To compare fractions, it's best to convert them all to a common denominator.

3/4 is equivalent to 9/12

2/3 is equivalent to 8/12

10/12 is equivalent to 5/6

2/1 is equivalent to 24/12

So, the smallest fraction is 8/12, which is equivalent to 2/3.

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The value of t is given as 2.3 years.

we get the table for function as

t          f(t)

8    350

12   138

16   36

20    4

25   3.2

27    1.3

So it is better to model the data by using an exponential model

using a graphing calculator we get our model as

f(t)=a(b)^t

[tex]f(t)=\boldsymbol{3648.6915(0.7380)^t}[/tex]

we have an exponential decay, so we get a rate of decrease as

b=1-r

r=1-b=1-0.738=0.262=26.2\\%

So the number of polio cases is decreasing by 26.2% per year

The number of polio cases in 2014 is

t=2014-1980=34

f(34)=3648.6915(0.7380)^{34}=0.1991389

this is in thousands so we get the number of cases in 2014 approximately as

[tex]0.1191389*1000 \approx \boldsymbol{119} \textup{ cases}[/tex]

for 1 case of polio :

f(t)=0.001

3648.6915(0.738)^t=0.001

we get

[tex]t=\frac{\ln (\frac{0.001}{3648.6915})}{\ln(0.738)}\approx 50[/tex]

so we get year as

1980+50={2030},

to find half life

[tex]\frac{a}{2}=a(b)^t[/tex]

[tex]b^t=\frac{1}{2}[/tex]

[tex]0.738^t=\frac{1}{2}[/tex]

[tex]t=\frac{\ln (1/2)}{\ln (0.738)}\approx\boldsymbol{2.3} \textup{ years}[/tex]

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Answer:

34

Step-by-step explanation:

This is sequnce has an easy pattern with adding 1 to the difference every time and goes +4, +5, +6 , so the next should be +7

Answer: think it’s a5=34

Step-by-step explanation:

Answer:

The answer is going to 5

Step-by-step explanation:

I hope this helps you

Answer: Yes, y = 9(-5)^x represents an exponential function.

An exponential function is a function in the form y = ab^x, where a and b are constants and b is a positive real number not equal to 1. The base, b, is raised to the power of x, and the resulting value is multiplied by the constant a.

In the given function, we have a = 9 and b = -5. Although b is negative, it is still a real number not equal to 1, so the function is still considered exponential. Furthermore, the exponent x is a variable, which is raised to a constant base -5, meeting the definition of an exponential function.

Therefore, y = 9(-5)^x is an exponential function.

Step-by-step explanation:

Answer:

B. 1

Step-by-step explanation:

Let's use the formula for finding the mean of a set of data:

mean = (sum of all data values) / (number of data values)

We know that the mean is 2.2, and we have all the other data values except for one. Let's call the missing value "x". The total number of data values is 10 (since there are 10 scores listed in the frequency table). So we can set up an equation:

2.2 = (sum of all 10 data values, including x) / 10

Multiplying both sides by 10, we get:

22 = sum of all 10 data values, including x

We can then subtract the sum of the known data values from both sides to find the missing value:

22 - (01 + 12 + 23 + 31 + 42 + 51) = x

22 - (0 + 2 + 6 + 3 + 8 + 5) = x

x = 22 - 24 = -2

However, a quiz score cannot be negative, so we made a mistake somewhere. Checking the frequency table, we see that there are no scores of 0 or 1, so the missing score must be 0 or 1. Let's try both possibilities:

If the missing score is 0:

2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 0*1) / 10

2.2 = 18 / 10

2.2 = 1.8

This is not true, so the missing score cannot be 0.

If the missing score is 1:

2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 1*?) / 10

2.2 = (18 + ?) / 10

22 = 18 + ?

? = 4

So the missing score is 1, and the answer is B.

Answer:

Answer is B

Total scores/total frequency =mean

54/24=2,25

If you added a score of 1

55/25=2,2

Step-by-step explanation:

hope that helps you

The dilation of the object is given by the coordinates:

(-6,-8)
(-2, 0)
(-2, -8)

A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer.

For the first dilation

Original points are

(2,1)

(4,5)

(4,1)

Multiply by scale factor

(2,1) x 2 = (4,2)

(4,5) x 2 = (8, 10)

(4,1) x 2 = (8, 2)

This given us the coordinates of triangle B).

For the second dilation

(2,1)  

(4,5)

(4,1)
Adjust for the center of dilation which is (5,5)

(2,1)  less (5,5) = (-3, -4)

(4,5) less (5,5) = (-1, 0)

(4,1) less (5,5) =(-1, -4)

Multiply the New original point by scale factor

(-3, -4) x 2 = (-6,-8)
(-1, 0) x 2 = (-2, 0)

(-1, -4) x 2 = (-2, -8)

Thus, the new coordinates of the dilated triangle C are:

(-6,-8)
(-2, 0)
(-2, -8).

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Answer:

Step-by-step explanation:

(-2-3)-(4-5)+ (−1+6)−(−9+8)

-5-4+5-1+6+9-8

-9+4+15-8

-5+7

2

Answer:

23.375 in^2

Step-by-step explanation:

To find the area of a rectangle or square, you need to multiple the length by the width.

The length: 8.5

Width: 11

8.5*11 = 93.5

Now we divide by 4

93.5/4

23.375

The likelihood that he or she has a pet given that a student does not have a sibling is 60%. Therefore, the correct option is option D.

Let A denote the event that a student does not have a sibling.

Let B denote the event that a student has a pet.

Then A∩B will denote the event that the student does not have a sibling but he has a pet.

Let P denote the probability of an event in this question.

Then, we have to find the conditional probability of event B which means the likelihood of event B occurring based on the occurrence of event A.

P(B|A)

We know that:

[tex]P(B|A) = \frac{P(A\cap B)}{P(A)}[/tex]

Also from the table, we have:

P(A)=0.25

and P(A∩B)=0.15

Hence,

[tex]P(B|A) = \frac{0.15}{0.25}[/tex]

[tex]P(B|A) = \frac{3}{5}[/tex]

[tex]P(B|A) = 0.6[/tex]

which in percentage is:

0.6 * 100 = 60 %

Therefore, the likelihood that he or she has a pet too is 60% and the correct option is option D.

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Answer:

$2,440 + $1,220 = $3,660

Step-by-step explanation:

If Amanda makes $61,000 a year, and she contributes 4% of her salary to her 401(k), that would be:

$61,000 x 0.04 = $2,440

Since her employer has a 50% match on the first 4% of her salary, they would contribute:

$2,440 x 0.5 = $1,220