teacher: how can we change the base of a logarithm? student:

Answer:

  (-1, -8)

Step-by-step explanation:

You want the image of P(-8, 1) after rotation 90° counterclockwise about the origin.

The transformation for 90° CCW is ...

  (x, y) ⇒ (-y, x)

Then

  P(-8, 1) ⇒ P'(-1, -8)

__

Additional comment

We observe that this answer is not among the choices listed in this problem statement. We suspect a typo somewhere. The transformations represented by the given choices are ...

  A: reflection across the x-axis and rotation 90° CCW

  B: reflection across the x-axis

  C: reflection across the x-axis and rotation 90° CW

  D: reflection across the origin

These are shown in the second attachment.

Answer:

Step-by-step explanation:

Emma's age= x

Kate's age= x-12

sum of their ages=24

so Emma's age= 24-12

x=24-12

x=12

Emma's age=12

The can's minimum surface area should have a height of 8 cm and a radius of 4 cm.

Given:

The volume of closed right circular cylindrical cans = 128π cm³

As we know the volume of a cylinder = πr²h

By equating;

πr²h = 128π

h = 128/r²

To get the dimensions of a can with minimum surface area;

S = 2πrh + 2πr

Put h = 128/r²;

Therefore, S(r) = 256π/r + 2πr²

                 S'(r) =  -256π/r² + 4πr

                S''(r) = -(2*256π)/r³ + 4π

Now, for S(r) = 0;

               r = 4cm

         for S''(4) > 0 at r = 4 is minimum point.

Hence,

h = 128π/(π*4*4)

h = 8cm

Therefore, the minimum surface area of the can should have a radius of 4 cm and a height of 8 cm.

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The region which have strongest negative correlation is Midwest.

Given that,

From your data folder, import the states.csv dataset into rstudio. create a scatter plot with high (x-axis) and pctdemocrat (y-axis) data points that are colored according to region. Stat smooth is used

To find : Which region has the strongest negative correlation

What Is Negative Correlation?

A link between two variables known as "negative correlation" occurs when one variable rises as the other falls, and vice versa. In statistics, -1.0 denotes a perfect negative correlation, 0 denotes no connection, and +1.0 denotes a perfect positive correlation. The relationship between two variables is always absolutely opposite when there is a perfect negative correlation.

Therefore, the region which have strongest negative correlation is Midwest.

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Joseph removes 5/8 gallon of white paint from a can.The amount of paint in the can  = - 2.8 gallons

Step-by-step explanation:

Let X be the starting amount of paint in the can, in gallons.

"Removes 5/8 gallon" can be written -(5/8)gal

"Adds 3/8 gallon" becomes +(3/8)gal

The result is :  X - (5/8)gal + (3/8)gal = Remaining Paint (gallons)

Consolidating:  Remaining (gallons) = X - (2/8)gal

If we want the overall increase/decrease, subtract the initial volume:

Initial - Remaining = Change in amount of paint in can

Change =  (X-(2/8)gal) - X = - (2/8) gallons

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Answer:

C

Step-by-step explanation:

(h - g)(2)

= h(2) - g(2)

= 2² + 1 - 2(2) = 4 + 1 - 4 = 1

Answer:

ñ/3 and 3√25

Step-by-step explanation:

pi is irrational and the cube root of 25 is irrational :)

The sides of DEF in order from least to greatest will be x + 6, (5x - 8) and (9x + 2).

The total angles that can be found in a triangle is 180°.

Therefore, the angles will be illustrated thus:

x + 6 + (5x - 8) + (9x + 2) = 180°

x + 6 + 5x - 8 + 9x + 2 = 180°

15x = 180°

Divide

x = 180° / 15.

x = 12°

Therefore,

x + 6 = 12 + 6 = 18°

(5x - 8) = 5(12) + 8

= 60 + 8

= 68°

(9x + 2) = 9(12) + 2

= 108 + 2

= 110°

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Answer:

-5.2,-4.75,-9/2

Step-by-step explanation:

Answer:-5.2 -4.75 -9/2

Step-by-step explanation:

92% = 69 questions

100% = 75 questions

The total number of questions on the test is 75 questions.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Total number of answers answered correctly = 69

The percentage of the test questions answered correctly = 92%

This means,

92% = 69

The total number of questions in percentage = 100%

Now,

92% = 69

Multiplying 100/92 on both sides.

100% = 100/92 x 69

100% = 75

Thus,

The total number of questions on the test is 75 questions.

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The values of m<1, m<2, m<3, m<4, m<5, m<7, m<8 are given by 49, 131, 49, 131, 49, 49, 131 respectively.

Given the measure of angle 6 is 131.

We can see that from the figure, angle 6 and angle 2 are corresponding angles and angle 6 and angle 4 are alternative angles.

So, angle 2 = angle 6 = 131

angle 4 = angle 6 = 131

Since angle 1 and angle 4; angle 2 and angle 3 are Linear pairs. So.

angle 3 = 180 - angle 2  = 180-131 = 49

angle 1 = 180 - angle 4 = 180-131 = 49

Since, angle 1 and angle 5; angle 4 and angle 8; angle 3 and angle 7 are corresponding angles to each other.

angle 5 = angle 1 = 49

angle 7 = angle 3 = 49

angle 8 = angle 4 = 131

Hence the values of m<1, m<2, m<3, m<4, m<5, m<7, m<8 are given by 49, 131, 49, 131, 49, 49, 131 respectively.

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The amounts, using proportions, are given as follows:

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem from which the fraction was built.

The tip is of 20% of the total bill of $54.65, hence it's value is given as follows:

Tip = 0.2 x 54.65 = $10.93.

(because 0.2 is the decimal equivalent to the percentage of 20%, then it is multiplied by the total amount to find the desired amount).

The total cost of the meal is given by the sum of the bill of the meal plus the tip, hence:

Total Cost = 54.65 + 10.93 = $65.58.

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Answer: 7. 0 cause there is  not a number next to the 3

-2 is the slope you distribute the -2 by the parenthese

Step-by-step explanation:

Value of angle T is 60°, angle U is 60°, TS is 13 cm and SU is 22.49 cm.

Given in question,

Triangle STU,

TU = 13 cm

∠S = 60°

ST = TU

    = 13 cm

∠U = ∠S    (Their sides are equal)

     = 60°

∠S + ∠T + ∠U = 180°

60 + ∠T + 60 = 180

      ∠T + 120 = 180

                ∠T = 180 - 120

                      = 60

Hence, ∠T is 60°.

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The line of best fit for the data presented in the scatterplot is y = 0.5x. (Option B)

A line of best fit represents a straight line that is the best approximation of the given set of data used to examine the nature of the relation between two variables. It is an educated guess about where a linear equation might fall in a set of data plotted on a scatter plot. The slope-intercept form of a linear equation is given by y = mx + b where m is the slope of the line and b is the y intercept of the graph. For any two points (x1, y1) and (x2, y2), the slope is given by:

m = (y2-y1)/(x2-x1)

Choosing two points from the line say (180, 90) and (220,110),

m = (110 – 90)/(220 – 180) = 20/40 = 0.5

Hence, y = 0.5x + b

Substituting a point from the graph into the equation say (240, 120)

120 = 0.5(240) + b

120 = 120 + b

b = 0

Hence, the equation is y = 0.5x

Note: The question is missing the scatterplot (which is attached) and options which are A. y = -0.5x, B. y = 0.5x, C. y = -2x, D. y = 2x.

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The statement 'If an integer is negative, its absolute value is also its additive inverse.' is True.

In this question, we have been given a statement 'If an integer is negative, its absolute value is also its additive inverse.'

We know that for any non zero real number 'm', the additive inverse is '-m'

as m + (-m) = 0

We know that the absolute value of any non-zero real number is always positive.

Consider a negative integer -p.

The absolute value of -p is |-p| = p

We can observe that -p + p = 0

-p + |-p| = 0

Therefore, the statement 'If an integer is negative, its absolute value is also its additive inverse.' is True.

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Answer: -64 and 64

Step-by-step explanation:

Option (A) is the correct answer: Panel a illustrate Increasing Return to Scale and panel b illustrate Constant Return to Scale.

Return to Scale:

It is the Variation or change in productivity that is the outcome from a proportionate increase of all the input.

Increasing Return to Scale:

An increasing return to scale occurs when the output increase by a larger proportion than the increase in inputs during the production process. For Example: if input is increased by 3 times but output increases by 3.75 times, then the firm or economy has experienced an increasing return to scale. This increase is due to many reasons like division external economies of scale.

Constant Return of Scale:

Constant Return of Scale refers to the production situation in which output increases exactly in the same proportion in which factors of production are increased. In simple words, if factors of production are doubled output will also be doubled. In this case, internal and external economies are exactly equal to internal and external diseconomies. This situation arises when after reaching a certain level of production, economies of scale are balanced by diseconomies of scale. For Example:  A car wash in which one car wash takes 30 minutes. If there is one wash space and two workers running two 8 hours shifts total product would be 32.

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506.433 minutes elapse before the minute hand next points in the same direction as the hour hand.

Conversion of hours to minute:

As we all know, an hour is made up of sixty minutes, therefore

1 hour=60minutes

Thus, all you need to do to convert time from hours to minutes is to multiply the time in hours by 60 to get the time in minutes.

If you want to convert minute to hours divide the given time in minutes by 60.

The hands line up 11 times every 12 hours, or roughly every 1:05.5 hours; the precise number is 1:05.4545 repeating.

The repetition time is 8:43.6363. When expressed in seconds, the result is 8:43:38.1818 repeating, or 8:43:38 and 2/11.

This is 261 and [tex]\frac{9}{11}[/tex] degrees, or 261.818 repeated.

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Answer:

a) 0.566 b)8.62

Step-by-step explanation:

0.56565656...

4th number after decimal is 6, which is greater than 5. the value of 3rd number after dp goes up by 1

therefore 0.566

7×12%=0.84

7+0.84=7.84

7.84×10%=0.784

7.84+0.784=8.62

Answer:

(2.3*10^2)(3*10^5)

in scientific notation 

Step-by-step explanation:

6.9 × 10^7

The required value of the variable x is - 4

A variable in mathematics is an alphabet or phrase that stands in for an unknowable amount, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are utilised. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.

The given equation is :

10-6x + 9x = x+2

On solving this equation we get :

10 + 3x = x + 2

Subtract - 3x on both sides and we will get

10 = - 2 x + 2

Subtract 2 on both sides

we get

8 = -2x

On dividing both sides of the equation by 2 we get

x = - 4

Thus the required value of the variable x is - 4

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Answer:

Step-by-step explanation:

Answer:

x = - 2 ± [tex]\sqrt{\frac{19}{3} }[/tex]

Step-by-step explanation:

3x² + 12x = 7 ← factor out 3 from each term on the left side

3(x² + 4x) = 7

to complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 4x

3(x² + 2(2)x + 4 - 4) = 7

3(x + 2)² - 12 = 7 ( add 12 to both sides )

3(x + 2)² = 19 ( divide both sides by 3 )

(x + 2)² = [tex]\frac{19}{3}[/tex] ( take square root of both sides )

x + 2 = ± [tex]\sqrt{\frac{19}{3} }[/tex] ( subtract 2 from  both sides )

x = - 2 ± [tex]\sqrt{\frac{19}{3} }[/tex]

The inequality is x ≤ 39.2. The actual number of items that can be bought is 39.

There is a set budget of $145 to buy some items. The price of each item is $3.70. We need to form an inequality for the given information and solve it.

Let the number of items be denoted by the variable "x". Then we can say that :

3.70*x ≤ 145

x ≤ 145/3.70

x ≤ 39.2

The actual number of items that can be bought must be a whole number. We will take the greatest integer less than or equal to the solution.

The actual number of items that can be bought is 39.

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She bought 13 books in $58.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Let b represent the number of books.

So, the equation will be

5b - 7 = 58

Now, add 7 to both sides of the equation

5b = 65.

b = 13.

Thus, she bought 13 books at 5 dollars a piece.

After she gets a 7 dollar discount off of 65 dollars, so she paid a total of 58 dollars after the discount.

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By using some exponent properties we will get:

2*(1/b)^15

Remember that the product of exponents can be written as:

(a^x)*(a^y) = a^(x*y)

In this case, we have the expression:

2*b^(-1.5)*b^10

Using the above property we can rewrite:

2*b^(-1.5)*b^10 = 2*b^(-1.5*10) = 2*b^(-15)

And a negative exponent means that we need to take the inverse of the base, then:

2*b^(-15) = 2*(1/b)^15

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The time that it will take Joe to catch up with Mary is; 8 hours

We are told that;

Time Mary leaves the house = 12 pm

Time that Joe leaves the house = 2 pm

Speed of Mary = 45 mi/hr

Speed of Joe = 60 mi/hr

This means that Mary had a 2 hour time lead over Joe.

Thus;

Distance is calculated from the formula;

Distance = Speed * time

Thus;

Distance covered by Mary in the 2 hours lead is;

Distance = 45 * 2 = 90 miles

Thus, time that it will take Joe to catch up with mary is;

t = 2 + (90/(60 - 45))

t = 2 + 6

t = 8 hours

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