The function f(x)= 4x + 3 represents the length of a rectangle. The function g(x)=2x-5 represents the width of the rectangle. Use ( g(4) to determine the area of the rectangle.
57
19
16
3

Answer:

Step-by-step explanation:

tan 45=1

[tex]tan 2\alpha =\frac{2tan\alpha}{1-tan^2\alpha } \\put~\alpha =22.5\\2\alpha =2 \times 22.5=45\\tan~2\alpha =tan~45=1\\1=\frac{2tan \alpha }{1-tan^2\alpha} \\1-tan^2\alpha =2 tan\alpha \\ tan^2\alpha +2tan \alpha -1=0\\tan\alpha =\frac{-2 \pm\sqrt{4+4} }{2} \\=-1\pm\sqrt{2} \\\alpha =22.5\\so ~tan~\alpha ~is~positive.\\so ~tan~\alpha =\sqrt{2} -1[/tex]

Answer:

The amount of money you saved by receiving a discount of 25% is $5.5

Step-by-step explanation:

Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price. Selling price is the actual price at which an article is sold after any reduction or discounts in the cost price.

discount is always calculated on the cost price of the article

formula to calculate the discount and discount %

Discount = List Price - Selling Price

Discount (%) = (Discount/cost price) × 100

here, in the question discount % is given = 25%

cost price of the item = $22

therefore using the above mentioned discount percentage formula:

25 = (Discount/22)×100

25/100 = Discount/ 22

0.25 × 22 = Discount

$5.5     = Discount

thus ,  

the amount of many you saved by receiving a discount of 25% is $5.5

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Answer:

See below

Step-by-step explanation:

The denominator has to be divisible by 6 and 8

  you could choose   24    48    72   96    etc

Answer:

(3(3) × 3(4) ) ÷ 3(2)

(9 × 12) ÷ 6

108 ÷ 6

18

Using percentages, we have that Puja Limbu did 80% of the problems and Raju Lama did 73.3%, hence Puja Limbu had the better performance.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

The percentage for Puja Limbu is:

[tex]P = \frac{8}{10} \times 100\% = 80\%[/tex]

The percentage for Raju Lama is:

[tex]P = \frac{11}{15} \times 100\% = 73.3\%[/tex]

80% > 73.3%, hence Puja Limbu had the better performance.

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Answer:

A = 50x^2+3

B = 75

C = 55

Step-by-step explanation:

[tex]f(x)=2x^2+3\\g(x)=5x[/tex]

A. f(g(x))

[tex]2(5x)^2+3\\2(25x^2)+3\\=50x^2+3[/tex]

B. g(g(3))

[tex]5(5(3))\\5(15)\\=75[/tex]

C. g(f(-2))

[tex]g(2(-2)^2+3)\\g(8+3)\\g(11)\\5(11)\\=55[/tex]

Answer:x>7

Step-by-step explanation:

Its saying a nuber greater than 7 and 3 plus 8 would be 11

Answer:

Given - an equilateral triangle

An equilateral triangle means all sides equal and all angle equal to 60°

In triangle BOA

sin 60° = OB/ AB

√3/2. = 80/AB

AB = 160√3/3

X = 160√3/3

Answer:

It's very simple: divide the 40 m² area by area of 1 one sphere

[tex] \frac{40 \: m {}^{2} }{3.41 \times 15m {}^{2} } = 565[/tex]

Reason:

sorry but here is no options so I am giving you a example so that you can understand by your own!

Answer;

5r+3

2x-6

X4+10

4y-1

Step by step answer;

So the method of identifying the Monomail is if you see a variable in a constant so it is a Monomail !

The error happens in the last line.

The relevant log rule is ln(A) - ln(B) = ln(A/B)

The issue is that the 0 isn't ln(0), so that 0 cannot be thrown into the natural log like that.

What we can do is this set of steps

ln(3x) - 0

ln(3x) - ln(1)

ln(3x/1) ... applying the log rule mentioned

ln(3x)

But these steps are a needlessly overcomplicating things. We can simply go from ln(3x)-0 to ln(3x) in one step. Subtracting off zero doesn't change ln(3x) at all.

--------------------------

Let's continue the steps to solve for x.

ln(x^2) = ln(3x)

x^2 = 3x

x^2-3x = 0

x(x-3) = 0

x = 0 or x-3 = 0

x = 0 or x = 3

Those are the two possible solutions.

However, x = 0 isn't valid because it's not in the domain of ln(x^2). In other words, ln(0) isn't defined. The domain of y = ln(x) is x > 0

This means that x = 3 is the only solution.

An expression can either be an equation or an inequality.

The correct classification of the terms are:

Expression; 4x+20

Inequality: 4x+20>40

Equation: 4x+20=40

We have given that,

{20,18,8,18,10,8,4}

{12,14,16,20,4,8,10}

{12,16,4,20,8,6,8}

To determine the correct classification, we make use of the following highlights

When an expression has the =, then the expression is an equation.

When an expression has any of the following signs>, <, >=, <= or != , then the expression is an inequality.

When the expression is neither an equation nor an inequality, then it is just an expression.

Hence, the correct classifications are:

Expression; 4x+20

Inequality: 4x+20>40

Equation: 4x+20=40

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Based on the given mean absolute deviations, the sample mean absolute deviation will be 2 and the population mean absolute deviation will be 3.8.

= Sum of sample mean absolute deviation / Number

= (0 + 0.5 + 4.5 + 0.5 + 0 + 4 + 4.5 + 4 + 0) / 9

= 2

First find the population mean:

= (10 + 11 + 19) / 3

= 13.3

Population mean absolute deviation:
= 1/3 x ( (10 - 13.67) + (11 - 13.3) + (19 - 13.3))

= 3.8

We can therefore see that the sample mean deviations is a biased estimate of the population mean absolute deviation.

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The figures show that the number of births for Florida and Michigan reduced

From the data sourced, the number of births in Florida in 2010 was 214519 while in 2011, it was 213237. For Michigan, there was decrease from 114717 to 114159.

When a person born during 2011 in the United States is chosen randomly, the person is more likely to have been born in Florida.

The probability that a randomly selected us resident in 2011 was living in Florida will be:

= 18,801,310/308,745,538

= 0.061

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Answer:

4/9, 49%, 4,9

Step-by-step explanation:

4/9=0,444444

49%=0,49

4,9=4,9

Answer:

12

Step-by-step explanation:

Direct Variation. I think it's gonna be like this.

SInce Z is not inversely to y , its varies directly to both.

Then it's,

Z=kxy, where k is constant.

subst. Z=6,x=2 and y=6.

6=k×2×6

6=k×12=12k

6=12k=½

the formula connecting them is

Z=½xy

Z=½×3×8

Z= 1×3×8÷2

Z=24÷2

Z=12.

That's my solution.

Answer:

6

Step-by-step explanation:

21 - 15 = 6

Answer: two congruent segments.

Step-by-step explanation:

idlk im not smart

The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2

The coordinates are given as:

Parallelogram 1: (0, 2), (2, 6), (6, 4), and (4, 0).

Parallelogram 2: (2, 0), (4, -6), (2, -8), and (0, -2)

Next, calculate the base and the height

For parallelogram 1, we have:

Base = (0, 2) and (2, 6)

Height = (6, 4), and (4, 0).

So, we have:

[tex]Base = \sqrt{(0 - 2)^2 + (2 -6)^2} = \sqrt{20}[/tex]

[tex]Height = \sqrt{(6 - 4)^2 + (4 -0)^2} = \sqrt{20}[/tex]

The area is:

Area = Base * Height

Area = √20 * √20

Area = 20

For parallelogram 2, we have:

Base = (0, -2) and (4, -6)

Height = (4, -6) and (2, -8)

So, we have:

[tex]Base = \sqrt{(0 -4)^2 + (-2 +6)^2} = \sqrt{32}[/tex]

[tex]Height = \sqrt{(4 - 2)^2 + (-6 +8)^2} = \sqrt{8}[/tex]

The area is:

Area = Base * Height

Area = √32 * √8

Area = 16

By comparing both areas, we have:

20 is greater than 16 by 4

This means that the area of parallelogram 1 is greater by 4 units

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The number of  days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days

Since from the question, we see that the number of pennies double with each day. It forms a geoemetric progression with

Since the number of pennies after n days equals N = 2ⁿ

Let

So, after n days, the length of the stack of pennies is the geoemetric progression D = 2ⁿ × L

Making n subject of the formula, we have

n = ㏒(D/L)/㏒2

Substituting the values of the variables into the equation, we have

n = ㏒(D/L)/㏒2

n = ㏒(3 × 10¹⁶ m/1.5 × 10⁻³ m)/㏒2

n = ㏒(3/1.5 × 10¹⁹)/㏒2

n = ㏒(2 × 10¹⁹)/㏒2

n = ㏒2 + ㏒10¹⁹/㏒2

n = (19㏒10 + ㏒2)/㏒2

n = (19 + 0.3010)/0.3010

n = 19.3010/0.3010

n = 64.1

n ≅ 64 days

So, the number of  days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days

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Answer:

1/12  mile per minute

Step-by-step explanation:

1/4 mile in 3 minutes

 then miles per minute   is   1/4 mile / 3 min = 1/12  mile/min

Answer:

[tex]\boxed {a, b, c, d}[/tex]

Step-by-step explanation:

Rhombuses, parallelograms, rectangles, and squares cannot be classified as trapezoids as they have 2 pairs of parallel sides each. But quadrilaterals can be classified as trapezoids if they have a pair of parallel sides and a pair of non-parallel sides.

a) rhombuses

b) parallelograms

c) rectangles

d) squares

Answer:

n = 8

Step-by-step explanation:

13n-6 = 98

Solution:

Hence the value of n is 8.

13n - 6 = 98

13n = 98 + 6

13n = 104

n = 104/13

n = 8

The solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)

Equation 1: 1 - cos(x) = 2 - 2sin²(x) from (-π, π)

The equation can be split as follows:

y = 1 - cos(x)

y = 2 - 2sin²(x)

Next, we plot the graph of the above equations (see graph 1)

Under the domain interval (-π, π), the curves of the equations intersect at:

(-π/3, 0.5) and (π/3, 0.5)

Hence, the solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)

Equation 2: 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π)

The equation can be split as follows:

y = 4cos⁴(x) - 5cos²(x) + 1

y = o

Next, we plot the graph of the above equations (see graph 2)

Under the domain interval [0, 2π), the curves of the equations intersect at:

(π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)

Hence, the solutions to 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π) are (π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)

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Answer:

Both the numerator and denominator should be multiplied by the same number to arrive at the equivalent fraction.

Step-by-step explanation:

Equivalent fractions =  two or more than two fractions are said to be equal if both results the same fraction after simplification.

For example, consider the fraction 1/3

Multiplying numerator and denominator with 2, we get 1/3 × 2/2 = 2/6

Multiplying numerator and denominator with 3, we get 1/3 × 3/3 = 3/9

Multiplying numerator and denominator with 4, we get 1/3 × 4/4 = 4/12

Therefore, we can conclude that,

1/3 = 2/6 = 3/9 = 4/12 these are equivalent fractions.

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Answer: 2 and 6/8

Step-by-step explanation:

The vertex-form of the quadratic equation is given by y = (x + 4)² - 13, and the minimum value of y is of -13.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient. If a > 0, k is the minimum value of y, and if a < 0, it is the maximum value.

In this problem, the equation is:

y = x² + 8x + 3.

Completing the squares, the function is:

y = (x + 4)² - 13

13 is subtracted as (x + 4)² = x² + 8x + 16, hence for the equations to be equal 13 has to be subtracted. k = -13 is also the minimum value of y.

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The minimum y-value of the function for the parabolic equation is -13.

The vertex for an up-down facing parabola of the form y = ax² + bx + c is [tex]\mathbf{x_v= -\dfrac{b}{2a}}[/tex]

From the given equation:

y = x² + 8x + 3

The parameters for the parabola are:

a = 1, b = 8, c = 3

[tex]\mathbf{x_v= -\dfrac{8}{2\times 1}}[/tex]

[tex]\mathbf{x_v= -4}[/tex]

If we replace the value of [tex]\mathbf{x_v= -4}[/tex] to find the minimum value of [tex]\mathbf{y_v}[/tex] value, we have:

[tex]\mathbf{y_v = -13}[/tex]

Thus, the parabola vertex is (-4,-13). If a< 0, the vertex is a maximum value and If a>0, the vertex is a minimum value.

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Answer: i think no?

Step-by-step explanation:

AD and BE are both parallel lines (they are parallel to eachother), so they will never intersect

CF and GF intersect at point F (i think)

Bg and Ac intersect at point B (i think)

i dont want to give a definite answer in the event im wrong bc I just learned this like a few weeks ago-

each number under the leaves section would be a dog

answer: 11

Answer:

11

Step-by-step explanation:

Answer:

Refer to the attached image.  I'm not clear on one point.  Yes, it is confusing.

Step-by-step explanation:

See attached image.

Answer:

[tex]\large \boxed{\sf 3x\sqrt[3]{y^5}}[/tex]

Explanation:

[tex]\rightarrow \dfrac{\sqrt[3]{\sf 189x^5y^7}}{\sqrt[3]{\sf 7x^2y^2}}[/tex]

[tex]\rightarrow \sf \sqrt[3]{\dfrac{\sf 189x^5y^7}{\sf 7x^2y^2}}[/tex]

[tex]\rightarrow \sqrt[3]{\sf 27x^3y^5}[/tex]

[tex]\rightarrow \sqrt[3]{\sf 27} \sqrt[3]{\sf {x^3} }\sqrt[3]{\sf y^5}}[/tex]

[tex]\rightarrow \sf 3x\sqrt[3]{y^5}[/tex]