Joan wants to reduce the area of her posters to be 2/3 of the original size. Match the original dimensions in the left column with the correct new area in the right column.

Answer:

Step-by-step explanation:

The derivative of a function y = f(x) at the point a is a measure of the rate of change of the function at that point. It is represented by the symbol f'(a) or df/dx.

The derivative can be thought of as the slope of the tangent line to the curve of the function at the point a. It is calculated using the limit definition of the derivative, which states that the derivative of a function at a point is the limit of the difference quotient as the difference between x and a approaches zero.

In other words, the derivative of a function y = f(x) at the point a is the slope of the line that is tangent to the function at that point, and it is calculated using the following formula:

f'(a) = lim(h -> 0) [(f(a+h) - f(a)) / h]

This formula can be used to calculate the derivative of any function at any point. I hope this helps! Let me know if you have any questions.

To find the area of the base of the rectangular prism, we need to find the expression for the area of a rectangle with dimensions equal to the dimensions of the base of the prism.

The volume of a rectangular prism is given by the formula:

Volume = length * width * height

Substituting the given expressions for the volume and the height into this formula, we get:

6x3 + 19x2 + 2x - 3 = (length * width) * (x + 3)

Expanding the right-hand side of the equation, we get:

6x3 + 19x2 + 2x - 3 = length * width * x + length * width * 3

Matching the terms on the left-hand side of the equation with the corresponding terms on the right-hand side, we can see that the expression for the area of the base of the rectangular prism is:

length * width = 6x3 + 19x2 + 2x - 3 - length * width * 3

Simplifying this expression, we get:

length * width = -3x3 - 17x2 - 2x + 3

Therefore, the area of the base of the rectangular prism is given by the expression -3x3 - 17x2 - 2x + 3.

The statement that describes the slope in this equation is that the score of each question is 5

From the question, we have the following parameters that can be used in our computation:

Equation: s = 100 - 5m

Also from the question, we have:

s = The total score

m = the number of questions a student missed

Recall that

s = 100 - 5m

A linear equation is represented as

y = mx + c

Where m = slope

By comparing the equations, we have

m = -5

This means that the slope is -5

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The solution is 80 servings

The number of servings that can be made from 1 gallon is 80 servings

What is an Equation?

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.

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 data ,

Let the number of servings from 1 gallon be = A

Now , the equation will be

The number of cups of milk = 5 cups

The number of servings from 5 cups of milk = 25 servings

So ,

The number of servings from 1 cup of milk = number of servings from 5 cups of milk / 5 cups

Substituting the values in the equation , we get

The number of servings from 1 cup of milk = 25 / 5

The number of servings from 1 cup of milk = 5 servings

Now , 1 gallon = 4 quarts

1 quarts = 2 pints

1 pint = 2 cups

So , 1 gallon = 16 cups

And , number of servings from 1 gallon = number of servings from 16 cups

So ,

The number of servings from 16 cups = number of servings from 1 cup of milk x 16

Substituting the values in the equation , we get

Number of servings from 1 gallon = 5 x 16

Number of servings from 1 gallon = 80 servings

Therefore , the value of A is 80 servings

Hence ,

The number of servings is 80 servings

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Answer:

20%

Step-by-step explanation:

let x = percent savings

$3/lb (cost per lb of a 1 lb pack)

$24/10lb = $2.40/lb (cost per lb for a 10 lb pack)

$3 - $3x = $2.40

-3x = -0.60

x = -0.60/3 = 0.20

0.20 x 100 = 20%

The number of solutions that a system of 2 linear equations in 2 variables can have is explained below.

In the question ,

it is given that ,

the system of 2 linear equations in 2 variables .

we know that the linear equations represent a line .

(i) the two linear equations will have No Solution / Zero Solution if the two lines are parallel .

(ii) the two linear equations will have One Solution/Unique Solution if the two line intersect at a point .

(iii) the two linear equations will have infinitely many solution if the lines overlap on each other .

Therefore , the number of solutions of linear equation is explained above .

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Answer:

Step-by-step explanation:

you cant divide fractions so you multiply the reciprocal so your answer would be

1 11/16

Therefore , the solution of the given problem of squaring comes out to be square of the 13 is 169.

A resultant is referred to as a "Square Number" when a number or integer (not a fraction) is multiplied by itself. For instance, 3 x 3 is 32 when multiplied by itself three times. In essence, the exponential form of multiplying an integer or number by itself is referred to as a square number.

Here,

Try to add up the four stages here.

Multiplication of two-digit numbers using a math shortcut trick

shortcuts: 13 times 13 equals

13X13 = 169 is the answer when a two-digit number is multiplied.

Therefore , the solution of the given problem of squaring comes out to be square of the 13 is 169.

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The smallest number that is divisible by 3 is 3 itself. Every integer that is divisible by 3 is called a multiple of 3.

For example, some of the multiples of 3 are 6, 9, 12, 15, 18, 21, etc. All of these numbers can be obtained by multiplying 3 by an integer.

If a number evenly divides (leaves no residue) into another number, it can be divided. For instance, 34 may be divided by 2 equally, making it a divisible number. However, because doing so would result in a leftover, 34 cannot be divided by 3.

According to the law of three's divisibility, a number is completely divisible by three if the sum of its digits is also divisible by three. Take 308 as an example. To determine whether or not 308 is divisible by 3, add the digits together and find the sum (3+0+8=11).

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2375 is the amount of his investment and 625 is his total profit

The discount on the shares is 5%, so the price of each share is 100 - (5/100)100 = 95.

The total price Yoezer paid for the shares is 2595 = 2375.

To calculate Yoezer's total profit, we need to find the total dividend he received and the price he sold the shares for.

The dividend rate is 15%, so Yoezer received a dividend of (15/100)100 = 15 on each share.

The total dividend he received is 1525 = 375.

The price Yoezer sold the shares for was increased by a premium of 5%, so the selling price was 100 + (5/100)100 = 105.

The total selling price for the shares is 10525 = 2625.

Yoezer's total profit is the selling price minus the price he paid for the shares plus the dividends he received. This is 2625 - 2375 + 375 = 625.

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The height of the tree is 61.92 feet.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

Given that,

Distance of Tamara from tree = 30 feet.

Angle of elevation = 62°.

And the height of Tamara from the ground = 5.5 feet.

To find the height of the tree,

Use trigonometric formula,

tan θ = height / distance

tan 62 = x / 30

1.88 = x / 30

x = 56.42 feet

The total height of tree = x + 5.5 = 56.42 + 5.5 = 61.92 feet

The height of the tree is 61.92 feet.

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5.5 is  is the median of the set of numbers .

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

             Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

Since the number of observations is even, the median is the average of  

                               = (n/2) th and (n/2 +1)th observation.

The average of 5th and 6th observations = (5+6)/2 = 11/2 = 5.5.

Hence, the median of the given set of numbers is 5.5.

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Linear equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.

A linear equation has the following standard form: ax + by + c = 0.

Here, variables x and y and constants a, b, and c are used.

Also, a ≠ 0, and b ≠ 0.

For linear equations, the slope-intercept formula is: y=mx+b

Where m stands for the line's slope and b represents the y-intercept.

The three types of linear equations are point-slope, slope-intercept, and standard form.

When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This is known as linear equations.

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Answer:

A parallelogram

Step-by-step explanation:

A parallelogram is a shape with four sides and two sets of parallel lines. A common example of a parallelogram is a square.

The evaluation of the composite figure comprising of a square and an equilateral triangle is as follows;

9 (a) ∠ABD = 90°

(b) ∠BCD = 60°

(c) ∠ADC = 105°

A composite figure is a figure comprising of two or more regular geometric figures.

9. The shape of the quadrilateral ABDE = A square

The kind of triangle specified for the triangle ΔBCD = Equilateral triangle

The sides of the square ABDE are congruent by the definition of a square

Therefore; AB = BD = DE = AE by the definition of congruency

(a) Angle ∠ABD is a corner of the square ABDE, therefore;

The size of angle ∠ABD = 90° (properties of the interior angle of a square)

(b) The size of angle ∠BCD = 60° (Interior angle of an equilateral triangle)

(c) The size of angle ∠ADC is found as follows;

Triangles ΔAED and triangle ΔABD formed by the diagonal AD are congruent by Side-Side-Side, SSS congruency postulate

∠DAB ≅ ∠ADB (base angles of isosceles triangle ΔABD)

∠DAB = ∠ADB (Definition of isosceles triangles)

∠ABD + ∠DAB + ∠ADB = 180° (Angle sum properties of a triangle)

90° + 2 × ∠ADB = 180° (substitution property)

∠ADB = (180° - 90°) ÷ 2 = 45°

∠BDC = 60° (Interior angle of an equilateral triangle)

∠ADC = ∠ADB + ∠BDC (Angle addition postulate)

Therefore, ∠ADC = 45° + 60° = 105°

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Answer:

32 3/11

Step-by-step explanation:

Happy Holidays!

Answer:

90 miles.

Step-by-step explanation:

65 - 50 = 15

In each hour they have a difference of 15 miles.

In six hours:

6 * 15 = 90 miles

Answer:

There is no real square root of -4 because it is impossible to square any real number and get a negative answer.

You might think -2 could work. However, a negative times a negative is positive → -2(-2) = +4, so the problem would have to be written as [tex]\sqrt4[/tex] instead of [tex]\sqrt{-4}[/tex]. Hence, there is no real square root of -4.

Note the word real, as it is possible to find a non-real answer to [tex]\sqrt{-4}[/tex] using the imaginary number [tex]i[/tex], which represents [tex]\sqrt{-1}[/tex].

Answer: Roots of given quadratic equation are real and distinct.

If a quadratic equation is given by  ,then nature of its roots can be find by it's discriminate (D).

Roots are real and distinct, if D>0

Roots are real and equal, if D=0

Roots are imaginary (no real root exists), if D<0

Step 1:

Write coefficients of x², x and constant term.

Compare the given equation with standard quadratic equation.

Thus,

Roots of given quadratic equation are real and distinct.

Learn more:

1) Find the nature of roots of quadratic equation 2x sq. + 3x - 7=0

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2) Find the nature of the roots of the following quadratic equations. If real roots exist, find them:

(i) 2x² – 3x + 5 = 0 ...

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Step-by-step explanation:

Answer:

Given that a circle has a center (0,4) and the radius 5. 5. So the standard equation of the given circle is x2+(y−4)2=25.

Step-by-step explanation:

The first five terms of the expression are -7,-3,1,5, and 9.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that , F(1) = -3 and F(n) = F(n-1) + 4. Calculate the first term of the sequence,

F(1) = F(1-1) + 4

-3 = F(0) + 4

F(0) = -7

The common difference is calculated as,

d = -3 - 7

d = 4

The third term will be, -3 + 4 = 1

The fourth term will be, 1 + 4 = 5

The fifth term will be, 5 + 4 = 9

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A statistic is a numerical summary of a sample.

A sample statistic is explained as any number computed from a sample of data.

Examples include the sample average, median, sample standard deviation, and percentiles. A statistic is a random variable because it is based on data obtained by sampling technique in which each sample has an equal probability of being chosen.

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Answer:

9r^2+7r-5

Step-by-step explanation:

-15+23r+9r^2-16r+10

=-15 + 9r^2 + 7r +10

= 9r^2 + 7r - 5

Answer:

[tex]9r^2+tr-5[/tex]

The given expression is a polynomial in the variable r. The correct answer among the options provided is D, which has the same terms as the given expression, in the same order, but with an additional term (tr) at the end. The other options do not match the given expression.

3xy has two terms, 3 and xy. The term 3 is a constant and the term xy is a product of two variables.

3xy is a multiplication of three individual components. It consists of three distinct parts, namely 3, x, and y. Each of these components is considered a distinct term, so 3xy has three terms in total. The 3 represents a numerical value, while the x and y are variables that can be assigned any numerical value. When multiplied together, the three terms form a single expression, 3xy, which can then be evaluated for a resulting value.

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a)The chance that no call will be handled in 10 seconds  is 0.0067

b) 0.2642 percent of classes will be processed in two seconds at least.

A figure or ratio that reflects a fraction of 100 is known as a percentage in mathematics. In addition to ratios, fractions, and decimals, it is one of the ways to depict a dimensionless connection between two numbers. Frequently, the symbol "%" is used after the number to indicate percentages.

given,

The number of phone calls handled by the communications switch in a 10-second period is represented by the Poisson random variable n.

a)the chance that no call will be handled in 10 seconds is

for 10 sec= λ= 10*0.5 = 5 calls per sec

P(X=0) [tex]e^{-5}[/tex](5)° / 0!

P(X=0)= 0.0067

b) percent of classes will be processed in two seconds at least is

for 2 sec =λ = 0.5 *2 = 1

P(X≥2) = 1- P(X<2)

= 1-[P(X=2) + P(X=1)]

=0.2642

a)The chance that no call will be handled in 10 seconds  is 0.0067

b) 0.2642 percent of classes will be processed in two seconds at least.

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Your answer is False

The money received by Marcia =  £ 6

According to the given information

The money is shared between Marcia and Becky in the ratio = 1 : 4

Let the money got by Becky  = £ x

Marcia got £ 18 less than Beck = x - 18

So

Taking the ratio

[tex]\frac{1}{4}=\frac{x-18}{x}[/tex]

Cross multiply both the fractions

x = 4(x - 18)

x = 4x - 72

-3x = -72

x = 24

Money got by Beck = £ 24

Money received by Marcia = 24 - 18

                                             = £ 6

Hence

The money received by Marcia =  £ 6

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