Question 9 of 10
Solve (x-3)² = 5.
A. x=-3+√√5
B. x=3+√5
C. x = 8 and x = -2
OD. x=5± √√3

Using the equation y = -3x - 1, the missing values are in the ordered pairs, (−3,y) and (x,2), are: x = -1 and y = 8.

An algebraic equation is an expression that has variables. The values of those variables, when plugged into the equation would make the equation true.

Given the equation, y = -3x - 1, substitute x = -3 into the equation to find y:

y = -3(-3) - 1

y = 9 - 1

y = 8

The missing value in the ordered pair is: (-3, 8).

To find the missing value of x in (x, 2), substitute y = 2 into the equation, y = -3x - 1:

2 = -3x - 1

2 + 1 = -3x

3 = -3x

3/-3 = x

x = -1

The missing value is (-1, 2).

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The volume of the fish tank required = 0.154 m^3.

A fish tank has a capacity = 154L.

Capacity of fish tank in Litre = Volume of the fish tank in meter cube

So the volume of the fish tank required in cubic meter.

For the volume we required a conversion of litre into meter cube.

Cubic meters and liters are two common metric units of volume.

1 cubic meter is 1000 liters.

To convert liters to cubic meters, you simply need to move the decimal point three places to the left. In other words, divide a value in liters by 1000 to get an answer in cubic meters.

1L = 0.001 m^3

So 154L = 0.154 m^3

So the volume of the fish tank required = 0.154 m^3.

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The fraction that represents the percentage of 57% is presented as follows:

57/100.

A fraction is represented by the division of a term x by a term y, according to the equation presented as follows:

Fraction = x/y.

The terms are know as numerator and denominator, respectively, as follows:

For a percentage of a%, the equivalent fraction is obtained as follows:

Hence, for a percentage of 57%, as is the case in this problem:

Hence the fraction is:

57/100.

The problem asks to represent the percentage as a fraction.

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As per the proportional relationship, the constant of the proportionality is 1/3

Proportional relationship

A relationship is said to be proportional if each pair of data values are related in the same way, by multiplying by a factor.

The standard form of proportional relationship is written as.

y = k x

where k refers the constant of proportionality.

Given,

The table shows the proportional relationship between h and j.

Now, we need to find the constant of proportionality from h to j and we have to express the answer as a fraction in reduced terms.

We know that the standard form of the proportionality is written as,

y = k x

So, here y takes the value of j and x takes the values of h.

Then we have to take the points as (18, 6) and apply t on the standard form to get the value of k,

=> 6 = k (18)

Here we need the value of k, so move the number to the other side then we get,

=> k = 6/18

When we reduce this, then we get,

=> k = 1/3

Therefore, the constant of proportionality is 1/3.

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According to the solving the Angle m = 124

An angle with something like a vertex point at 180 degrees is considered to be a straight angle in geometry. Basically, it produces a straight line with sides that are turned away from the vertex. "Flat angles" is another term for it.

A straight line appears to have a straight angle. Here's an illustration of a straight angle. a straight line that has a half circle in the middle and at the top to symbolize a straight angle.

The sum of all angles in triangle  = 180.

Angle A = 56

Angle B = 68

Angle C =

A + B + C = 180

56 + 68 + C = 180

124 + C = 180

C = 180 - 124

C = 56

if Angle C = 56

so we know the property of straight angle:

= Angle m + 56 = 180

Angle m = 180 - 56

Angle m = 124

According to the solving the Angle m = 124

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The correct statement of the expression (x + 6) / ( x² - 9x + 18 ) is f(x) is increasing for all x > 6

Information given in the question

f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity

This is written as (x + 6) / ( x² - 9x + 18 )

factorizing the denominator gives

(x + 6) / {( x - 6)( x - 3)}

In the denominator

At x = 6 and at x = 3 the equation will result to infinity which is a very high value. hence:

f(x) is decreasing for all x < 6: contains  x = 3 and result to a higher value

f(x) is decreasing for all x < 3: will result to negative numbers which will end up increasing

f(x) is increasing for all x < 3: contains values which will be decreasing like x = 4

Therefore the correct option is f(x) is increasing for all x > 6

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Step-by-step explanation:

speed = distance / time

to get distance, we have to multiply by time.

the speed the 2 busses are moving seat from each other is

x + (x + 17) = 2x + 17

x = the speed of one bus

x + 17 = the speed of the other bus.

so, after 4 hours the distance between them is

(2x + 17) × 4 = 836

2x + 17 = 209

2x = 192

x = 96 km/h

bus 1 travels at 96 km/h.

bus 2 travels at 96+17 = 113 km/h.

The value of the test statistic of the hypotheses is; -17.969

The test statistic is defined as a number, calculated from a statistical test, which is used to find if your data could have occurred under the null hypothesis.

We are given;

Sample size; n = 1160

Sample proportion; p^ = 88% = 0.88

Population proportion; p = 97% = 0.97

The claim is about the population proportion (p) in the hypotheses. Since we are told that fewer than 97% of adults have a cell phone, then the claim is; p < 0.97

The null hypothesis is expressed as;

H₀: p = 0.97

The alternative hypothesis is expressed as;

Hₐ: p < 0.97

The value of the test-statistic is gotten from the formula;

z = (p^ - p)/(√(p(1 - p)/n))

z = (0.88 - 0.97)/(√(0.97(1 - 0.97)/1160))

z = -17.969

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64x³+125y³

= (4x+5y)( 16x²-20xy+25y²)

a³ + b³ = ( a + b )( a² - ab + b² )

64x³ + 125y³

= ( 4x )³ + ( 5y )³

= ( 4x+5y )[ (4x)²- (4x)(5y)+(5y)²]

= (4x+5y)( 16x²-20xy+25y² )

simplification of expression will be g - 2

Our expression is  g - 16/4 + 2

16/4 = 4

so we c will write it as

g - 4 + 2

which can be further simplified to

g - 2

Therefore, our simplified expression comes out to be g - 2.

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The expression that shows the result of applying the distributive property is 21y - 7/11 (option D).  

The distributive property states that an expression that has this form a(b + c) can be solved as a x (b + c) which becomes ab + ac.  

Thus, to solve an expression using the distributive property, multiply the term in the brackets by the term outside the brackets. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is x.

7(3y - 1/11)

= 7 x (3y - 1/11)

= 21y - 7/11

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Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Total socks= 10

White socks= 8

Total T- shirts= 9

White T- shirts = 2

Now, The probability of choosing a white pair of socks is

= 8/10

= 4/5

and, The probability of choosing a white tee shirt is

= 2/9

and, The probability of both being white is

= 4/5 x 2/9

= 8/45

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After solving the Algebraic expression we gets Tim needs 3.05 lbs. and 2.95 lbs. Metal.

Algebraic expressions are constructed using integer constants, variables, and the addition, subtraction, multiplication, and division operations of basic arithmetic.

To form the Algebraic expression

Let x be the quantity of silver at 29% and y the quantity at 80%

Then x*28% + y*61% = 6*54%

and x + y = 6

 Let y = 6-x then

29*x + (6-x)*80= 324

29*x + 480- 80*x = 324

51*x = 156 and x = 156/51 = 3.05 lbs.

so y = 6 - x = 2.95 lbs.

Hence,

Tim needs 3.05 lbs. and 2.95 lbs. Metal.

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Answer: 15 books

Step-by-step explanation:

Given that the weight of 6 books is 1.260 kg

⟹ weight of each book is [tex]\frac{1.260}{6}[/tex] = 0.210kg

Let the number of books that will weigh 3.150 kg be x

as we know that

weight of x books is 0.210x kg

⟹0.210x=3.150

⟹x= [tex]\frac{3.150}{0.210}[/tex] = 15

The number of books is 15

15 books will weigh 3.150 kg.

Given the weight of 6 books is 1.260 kg

⟹ weight of each book is  

1.260/6

=0.210 kg

Let x be the total number of books that weigh 3.150 kg.

as we are aware

weight of x books is 0.210x kg

⟹0.210x=3.150

⟹x= 3.150/0.210

=15

So, the number of books is 15.

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Answer:

1,344

Step-by-step explanation:

First, find how many steps he climbs every day

32*6=192

Now, multiply that by 7 to see how many he climbs in a week

192*7=1,344

Answer:

[tex]d=7[/tex]

[tex]a_9=59[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]3[/tex] and the second term is [tex]10[/tex], then each successive term in the sequence is [tex]7[/tex] more than the previous term. The common difference is [tex]7[/tex] ( [tex]d=7[/tex] ).

The formula representing the arithmetic sequence is:

[tex]a_n=7n-4[/tex]

Therefore, the ninth term in the sequence is:

[tex]a_9=7(9)-4[/tex]

[tex]a_9=63-4[/tex]

[tex]a_9=59[/tex]

Answer:

As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give  call to its mother.

Step-by-step explanation

He said hi Ma.

Length= 80 and width = 16 cm in the rectangle .

What is rectangle?

let side = x cm

              = x( 24 + 4x) = 1408

              = 24x + 4x² = 1408

               ⇒ 4x² + 24x - 1408  = 0

                   4 ( x² + 6x - 352 ) = 0

                      x² + 6x - 352 = 0

                      x² + 22x - 16x - 352 = 0

                      x( x + 22 ) - 16 ( x + 22) = 0

                       ( x - 16 ) ( x + 22 ) = 0

 x= 16 , -22

we take x = 16 because distance never be negative

 length = 16 + 4 * 16 = 80 cm

  width = 16 cm

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A) The bunny population after every 2 months is f(T)=5T+20

B) The bunny population after 16 weeks is x=29.205

C) The number of months that the bunny population to reach 300 bunnies is 112 months.

All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.

Given,

0 months -------- 20 bunnies

2 years ------- 80 bunnies

In two years, bunnies are increased by,

=80-20

=60

2 years ------>60

1 year ------>30

A) f(T)=mT + b

1 year -----> 12 months -----> 30 bunnies

12/6 months ------>30/6 bunnies

2 months -----> 5 bunnies

f(T)= initial population+ increased population in two months

f(T)=20+5

f(T)==25

f(T)= 2.5T+20

f(T)=5T+20

Where T =time in months

B) For 10 years ------> 10 bunnies

52 weeks -------->30 bunnies

16 weeks ------?

x=(16*30)/52

x=29.205

C) 1 month -------> 2.5 bunnies

 ? ---------------->280 bunnies

x=280/2.5

x=112 months

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Answer:

A) The bunny population after every 2 months is f(T)=5T+20

B) The bunny population after 16 weeks is x=29.205

C) The number of months that the bunny population to reach 300 bunnies is 112 months.

What is meant by population?

All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.

Given,

0 months -------- 20 bunnies

2 years ------- 80 bunnies

In two years, bunnies are increased by,

=80-20

=60

2 years ------>60

1 year ------>30

A) f(T)=mT + b

1 year -----> 12 months -----> 30 bunnies

12/6 months ------>30/6 bunnies

2 months -----> 5 bunnies

f(T)= initial population+ increased population in two months

f(T)=20+5

f(T)==25

f(T)= 2.5T+20

f(T)=5T+20

Where T =time in months

B) For 10 years ------> 10 bunnies

52 weeks -------->30 bunnies

16 weeks ------?

x=(16*30)/52

x=29.205

C) 1 month -------> 2.5 bunnies

? ---------------->280 bunnies

x=280/2.5

x=112 months

The hypothesis are given as follows:

H0: p = 0.301; H1: p ≠ 0.301.

a) The level of significance is of 0.05.

b) The sampling distribution is given by: The standard normal, since np > 5 and nq > 5.

The test statistic is of: z = -2.09.

c) The p-value is of: 0.0366.

At the null hypothesis, it is tested if there is not enough evidence to conclude that the proportion has changed, hence:

[tex]H_0: p = 0.301[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the proportion has changed, hence:

[tex]H_1: p \neq 0.301[/tex]

The test statistic is given by the equation presented as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

The parameters of the equation are listed as follows:

The values of these parameters for this test are:

[tex]\overline{p} = \frac{52}{220} = 0.2364, p = 0.301, n = 220[/tex]

Hence the value of the test statistic is of:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.2364 - 0.301}{\sqrt{\frac{0.301(0.699)}{220}}}[/tex]

z = -2.09.

We have a two-tailed test, as we are testing if the proportion is different of a value.

Hence, using a z-distribution calculator, with z = -2.09, the p-value is of 0.0366.

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The trigonometric identity presented in this problem is proved trough the answer, reaching an answer 1 = 1.

The identity is presented as follows:

[tex]\csc{\beta} + 1 = \frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}}[/tex]

Then we take the right side of the denominator, and apply the subtraction of perfect squares to the denominator, as follows:

[tex]\frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}} \times \frac{\sec{\beta} + \tan{\beta}}{\sec{\beta} + \tan{\beta}} = \frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}}[/tex]

The following identity relates the square of the secant and of the tangent:

[tex]\tan^2{\beta} + 1 = \sec^2{\beta}[/tex]

Hence:

[tex]\sec^2{\beta} - \tan^2{\beta} = 1[/tex]

Thus the remaining expression is:

[tex]\frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}} = \cot{\beta}(\sec{\beta} + \tan{\beta})[/tex]

The equations of the cotangent, secant and tangent are given as follows:

Hence:

[tex]\cot{\beta}(\sec{\beta} + \tan{\beta}) = \frac{\cos{\beta}}{\sin{\beta}}\left(\frac{1}{\cos{\beta}} + \frac{\sin{\beta}}{\cos{\beta}}\right) = \frac{1}{\sin{\beta}} + 1[/tex]

One divided by the sine is the cosecant, as follows:

[tex]\frac{1}{\sin{\beta}} = \csc{\beta}[/tex]

Hence the simplified expression is:

[tex]\csc{\beta} + 1[/tex]

Which is equivalent to the right side of the expression, hence an identity of the format 1 = 1 is reached and the identity is proven.

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$12000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (12000)(0.04)(3) \implies I = 1440[/tex]

The slope-intercept form is

    y = - x + 1

Given points are  (2, - 1)

          and  y = x + 4

The product of slopes of perpendicular lines is  - 1

   so ,  m = - 1/1  =  -1

     ∴ y = -1 (x) + b

       y  = - x + 1

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Answer:

x = -11

Step-by-step explanation:

2x - 7 = 3x - 2x - 18

2x - 7 = x - 18

collect like terms

2x - x = 7 - 18

x = -11

Answer:

a^-6 or 1/a^6

Step-by-step explanation:

(a³)-²

=a^-6

=1/a^6

Answer: daniel and sarah will deposit the same amount

The marginal cost is the labor utilized in order to provide an additional cost of a haircut.

The marginal cost is the extra cost of generating one additional unit of output.

The example of a haircut, the marginal cost is the labor utilized in order to provide an additional haircut; employees offer their time, which is valued in pay, resulting in the marginal cost of labor.

Thus, in all circumstances, such as the sandwich and Ferris Wheel, there will be an additional labor cost because labor is necessary to make each of the items.

Change in cost / Change in quantity Equals Marginal cost.

The firm will incur an increased labor expense because of one more haircut, and the laborer will be paid more because of the rise in one more quantity of haircut delivered. This pay rise is the marginal cost.

Thus, the marginal cost is the labor utilized in order to provide an additional cost of a haircut.

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According to the solving the probability will be 0.159.

The area of mathematics known as probability deals with numerical assessments of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed in percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.

The incidence rate is = 0.2%  or 0.002

The false negative rate is = 8%  or 0.008

The false positive rate is = 1%  or 0.001

The probability is

0.01*(1-0.002) + 0.95*0.002

= 0.00998 + 0.0019 = 0.01188

Probability that a person who tests positive actually has the disease would be represented as:

Let the probability be represented by = p

p * 0.01188 = 0.95 * 0.002

p = 0.0019/0.01188

p = 0.159

Hence, probability is 0.159

According to the solving the probability will be 0.159.

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