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Given the sides of a rectangle are in the proportion 9:14 and the perimeter of the rectangle is 230 cm,

the larger side length is:
What is the area

The slope-intercept form of the equation is y = - mx + b.

The equation of a line can be expressed in a variety of ways. Although they may differ in appearance, all of them describe the same line because multiple equations can describe the same line. However, all linear equations describing the same line are equivalent.

The formula y = mx + b can be used to represent any straight line. Any straight line equation, known as a linear equation, can be expressed as y = mx + b, where m denotes the line's slope and b its y-intercept. The value of y at the line's intersection with the y-axis is its y-intercept.

Given a graph of the equation, choose two points on the line and use them to calculate the slope in order to put the equation in slope-intercept form. This is the answer to the equation's question. Next, determine the y-coordinates, intercept's which should be of the type (0,b). The value in the equation is the y-coordinate.

Thus, the equation derived from the graph is as follows:

Since we are aware that the slope here is negative,

Therefore Our formula is y = -mx + b.

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Answer:

0=0

Step-by-step explanation:

6(4x+3y)=6(-2)

3(8x+6y)=3(-4)

24x+18y=-12

24x+18y=-12

0=0

The proof to show that △STU≅△QUT.

Congruency is a property which implies that two given shapes are equal in respect of their length of corresponding sides, and measure of their corresponding internal angles.

Thus, the proof to show that △STU≅△QUT are explained below;

<QRU ≅ <SRT                           (vertically opposite angle property)

QT = QR + RT          

SU = SR + RU

So that;

QT ≅ SU                                   (Reflexive property of congruent triangles)

TU ≅ UT                                   (common side of congruent triangles)

QU ≅ ST                                    

<SUT ≅ <QTU                         (Reflexive property of congruent triangles)

Therefore, it can be concluded that;

△STU≅△QUT

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The value of the t score for a 90% confidence interval if we take a sample of size 22 is 1.721.

Any member of the family of continuous probability distributions known as the Student's t-distribution (or simply the t-distribution) in probability and statistics is used to estimate the mean of a normally distributed population when the sample size is small and the population's standard deviation is unknown.

The Student's t-test for determining the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and linear regression analysis are just a few commonly used statistical analyses that make use of the t-distribution. Additionally, the Bayesian analysis of data from a typical family produces the Student's t-distribution.

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The percentage of the change is 70% decrease

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

Initial value = 5/4

Final value = 3/8

3/8 is less than 5/4

This means that the percentage is a decrease

We have

Initial value = 5/4

Final value = 3/8

The percentage change is then calculated as

Percentage change = (Final value - Initial value)/Initial value * 100%

Substitute the known values in the above equation, so, we have the following representation

Percentage change = (3/8 - 5/4)/(5/4) * 100%

Evaluate

Percentage change = -70%

Hence, the percentage change is 70% decrease

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Isosceles triangle the vertex angle is twice either base angle is the right statement. Isosceles triangle is a triangle which has two sides of equal length or value.

Isosceles triangle is a triangle that has two side of same value. It is mean that isosceles triangle has to fulfill this condition : two sides of triangle has to be congruent to each other; the third side of isosceles triangle that has not same length to the another side is called the base of the isosceles triangle; the two angles opposite has the same sides are congruent to one another.

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The value of n when y m is the area of a square of length x m, is  2

The value of n when y cm is the  volume of a cube of length x cm, is 3

For area of square, the formula is given by

= length *  length

assuming the length is equal to x

= x * x

= x²

comparing with given formula shows that n = 2

For volume of a cube of length x cm, the formula is given by

= length *  length * length

= x * x * x

= x³

comparing with given formula shows that n = 3

complete question

It is given that y is directly proportional to x".

Write down the value of n when

(i) y m? is the area of a square of length x m,

(ii) y cm is the volume of a cube of length x cm.

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The properties of exponents are (ab)^x = a^xb^x, b² × b^x = b^(2+x), and x⁻² = 1/x². Hence options A, D, E are correct.

What is the property of exponent?

When referring to a mathematical phrase that denotes that a number will be multiplied by itself n times, the terms power and exponent are frequently used interchangeably. That is a valid definition of power, however, in mathematics, the word exponent expressly refers to the amount. n that specifies the number of times it will be multiplied by itself.

There are six properties of the exponent. The properties are

Product of Powers (x^m)(x^n) = x^(m+n)

Power to a Power (x^m)^n = x^(mn)

Quotient of Powers (x^m)/(x^n) = x^(m-n)

Power of a Product (xy)^m = x^m× x^n

Power of a Quotient (x/y)^n = x^n/y^n

Negative exponent  x^(-n)= 1/x^n

According to the Power of a Product:

(ab)^x = a^xb^x

According to the Negative exponent:

7⁻³ = 1/7³

According to the Product of Powers:

b² × b^x = b^(2+x)

According to the Negative exponent:

x⁻² = 1/x².

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The side length of each square piece of fabric is 0.343 feet

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

Square quilt

The readings from the quilt are given as

Using the above as a guide, we have the following:

Number of squares * Area of Individual shapes = Area of quilt

Substitute the known values in the above equation, so, we have the following representation

64 * Area of Individual shapes = seven and fifty-two hundredths feet

Rewrite as

64 * Area of Individual shapes = 7.52

Divide both sides by 64

Area of Individual shapes = 0.1175

Take the square roots

Length of square = 0.343

Hence, the length is 0.343 feet

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The polygons, regarding congruence and similarity, are classified as follows:

a. Similar polygons.

b. Congruent polygons.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

If the transformation is a dilation, the triangles are similar, otherwise the triangles are congruent, as the dilation is the only transformation that changes the side lengths.

For item a, we have that the coordinates of WXYZ are multiples of QRST, meaning that a dilation with a scale factor of k = 3 was part of the transformation, hence the polygons are similar.

For item b, the only change was in the position, hence the side lengths are constant and thus the triangles are congruent.

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Percy will have an amount of $730 in her account.

Interest is the price you pay to borrow money or the cost you charge to lend money.

Given that, Percy puts $600.00 into an account to use for school expenses. The account earns 4% interest, compounded annually, for 5 years,

Formula for CI =

[tex]A = P(1+r)^{t}[/tex]

Where, A = amount

P = principal

r = rate

t = time

Therefore,

A = 600(1+0.04)⁵

A = 600(1.04)⁵

A = 600 × 1.2166529

A = 729.99 ≈ 730

Hence, he will have $730 in her account after 5 years.

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Shaded portion gives the solution set of following in inequality.

What is inequality?

An inequality in mathematics is a relationship that allows us to contrast two (or more) mathematical expressions.

A difference between two values indicates whether one is more than, less than, or not equal to the other.

For example  The strict inequalities like

a > b - “greater than”,

a < b - “less than”.

They are called Strict inequalities, since in each case a and b are not equal.

Here y ≤ [tex]x^2-3[/tex]

for the point (0, 0)

⇒ 0 ≤ 0 - 3

⇒ 0 ≤ -3

which is false thus region is opposite to origin

For y > [tex]x^2+2[/tex]

⇒ 0 > [tex]0^2+2[/tex]

⇒ 0 > 2

which is false thus the region is opposite to origin

Thus shaded portion is solution to given inequality

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Answer:

C

Step-by-step explanation:

The answer is 390

The sine function that models the depth of the tide in this problem is given as follows:

y = 4sin(π/6(x - 0.71)) + 13.

The general format for the sine function in this problem is given as follows:

y = A sin(Bx - C) + D.

In which the parameters of the function are given as follows:

The depth is 5 feet at low tide and 13 feet at high tide, hence the amplitude is calculated as follows:

2A = 13 - 5

2A = 8

A = 8/2

A = 4.

A sine function, with no vertical shift and amplitude of 4, would oscillate between -4 and 4, while this function oscillates between 5 and 13, hence the vertical shift is given as follows:

D = 13.

On a certain day, low tide occurs at 4 a.m. and high tide at 10 a.m, which  means that half the period is of 6 hours, hence the period is of 12 hours and the coefficient B is calculated as follows:

2π/B = 12

B = π/6.

Without phase shift, the low tide would happen at x = 3π/2 a.m. = 4.71 a.m., while it happens at 4 a.m., hence the phase shift is given as follows:

c = 4.71 - 4 = 0.71.

Hence the function is defined as follows:

y = 4sin(π/6(x - 0.71)) + 13.

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A popular way for people to share information and thoughts with others online is through blogging.

A blog is a conversation or informational website published on the World Wide Web that is composed of discrete, frequently informal diary-style text posts, according to the definition of a blog provided by Wikipedia.

This has given rise to a brand-new trend where everyone may now voice their opinions on a given subject.

Other phenomena and artefacts, such as analogue signals, poetry, photographs, music, or other sounds, as well as electrical currents, transmit information in a more continuous manner than do digital signals and other data, which employ discrete signs or algebras to do so.

Information itself is not knowledge, but how it is interpreted is crucial. Raw information can also take the shape of structured data. A collection of data may contain information that may be extracted through analysis by analysts who are experts in their field.

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Answer:

c. [tex]1/216[/tex]

Step-by-step explanation:

The probability of rolling a one is 1/6.

Using the multiplication principle, the desired probability is [tex](1/6)^3=1/216[/tex].

The value of the difference of the value of functions at x = 4 and -5 can be obtained as -39.

A function y = f(x) can be defined as a one to one relation between sets X and Y. The set X is called the domain and Y is called the range of the function.

The given functions are f(x) = 3/2x + 2 and g(x) = 2x² - 3

Then, the value of given functions at x = 4 and -5 can be calculated as,

f(4) = 3/2 × 4 + 2 = 8.

And, g(-5) = 2 × -5² - 3 = 47

Thus, the value of f(4) - g(-5) can be calculated as,

⇒ f(4) - g(-5) = 8 - 47 = -39

Hence, the required value can be obtained as -39.

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After 18 ​years, the investment compounded periodically will be worth (future value) ​$534.55 more than the investment compounded annually.

The future value is the compounded present value of an investment using an interest rate.

The future value can be computed using an online finance calculator.

N (# of periods) = 72 quarters (18 years x 4)

I/Y (Interest per year) = 6%

PV (Present Value) = $8,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $23,369.26

Total Interest = $15,369.26

N (# of periods) = 18 years

I/Y (Interest per year) = 6%

PV (Present Value) = $8,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $22,834.71

Total Interest = $14,834.71

Difference in future value = $5,34.55 ($23,369.26 - $22,834.71)

Thus, compounding an investment quarterly yields a greater future value than annual compounding.

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Answer:

C is the corect answer

Step-by-step explanation:

12x+3=39

12x=39-3

12x=36

x=36:12

x=3

12×3=36

36+3=39

This lesson's goal is to get pupils writing equations to create sequences given tables or visual patterns.

Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with. A sequence is an ordered list of components that follows a predetermined pattern.

As an illustration, the sequence 3, 7, 11, 15,... is one because it follows a pattern where each term is created by adding 4 to the word before it. Simple to complicated, prerequisite learning, whole to portion, and chronology are the sequencing concepts outlined by Print (1993 as quoted in Edith Cowan University, 2001) for content.

The acceptance of these four guidelines as the standards for content sequencing has increased. I consume 1 cookie the first time, then 1/2 the second. I'll eat half of the previous serving every time after that.

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The difference between the amount paid by the company and the premium contribution is given as follows:

FRW 1 298 400.

The difference is obtained applying the proportions in the context of the problem, which is the yearly payment, for the time.

The insurance was purchased on the 25th birthday, and the person died with 65 years old, hence the time period is given as follows:

65 - 25 = 40 years.

He paid a premium of 35 740 FRW yearly, hence the total amount paid is given as follows:

40 x 35 740 = 1,429,600.

A man took a life insurance policy for 2 728 000 FRW on his 25th birthday, hence the difference is calculated as follows:

2,728,000 - 1,429,600 = FRW 1 298 400.

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Solutions to the given inequality are numbers 4 and 5. Thus, the answer is (e) and (f).

To find the solution, first, we solve the inequality for x:

2x - 1 > x + 2

2x - x > 2 + 1

x > 3

Hence, the answer is any number that is greater than 3.

Therefore, the solutions are numbers 4 and 5.

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The complete question is:

Which numbers are solutions to the inequality 2x - 1 > x + 2? Check all of the boxes that apply.

(a) 0

(b) 1

(c) 2

(d) 3

(e) 4

(f) 5

The values of exponent 5, √15, 2 and ∛2.

There are various exponential laws. Numerous mathematical problems involving repeated multiplication operations can be solved using all of the exponent rules. The operations of multiplication and division are made simpler and easier to solve by the laws of exponents.

Given,

The important laws of exponents are given below:

xᵃ ₓ xᵇ = x ᵃ⁺ ᵇ

xᵃ/xᵇ = x ᵃ⁻ ᵇ

(xᵃ)ᵇ = x ᵃᵇ

a⁻ⁿ = 1/aⁿ

a⁽¹/ⁿ⁾ = [tex]\sqrt[n]{a}[/tex]

1: [tex]25^{\frac{1}{2} }[/tex]

25 = 5 x 5 = 5²

[tex]( 5^{2}) ^{\frac{1}{2} }[/tex] = 5 using formula (xᵃ)ᵇ = x ᵃᵇ

2: [tex]15^{\frac{1}{2} }[/tex]

= [tex]\sqrt{15}[/tex] using a⁽¹/ⁿ⁾ = [tex]\sqrt[n]{a}[/tex]

3: [tex]8^{\frac{1}{3} }[/tex]

8 = 2 x 2 x2 = 2³

[tex]( 2^{3}) ^{\frac{1}{3} }[/tex] =  2 using formula (xᵃ)ᵇ = x ᵃᵇ

4: [tex]2^{\frac{1}{3} }[/tex]

= ∛2 using a⁽¹/ⁿ⁾ = [tex]\sqrt[n]{a}[/tex].

Hence values are 5, √15, 2 and ∛2.

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Answer:

a=-1/4

Step-by-step explanation:

a+3 1/4 =5 2/9

change to improper fraction

a+13/4 = 47/9

make sure that both fractions have the same denominator

a+(13/4)9=(47/9)4

a+117/36=108/36

make sure that variable is alone on one side

a=108/36-117/36

a=-9/36= -1/4

a=-1/4

Step-by-step explanation:

a+3 1/4 =5 2/9

change to improper fraction

a+13/4 = 47/9

make sure that both fractions have the same denominator

a+(13/4)9=(47/9)4

a+117/36=108/36

make sure that variable is alone on one side

a=108/36-117/36

a=-9/36= -1/4

Chris has to pay $8.5 for all the fruit.

given:

Oranges are 2 pounds for $1.00. Apples are $2.00 per pound. Chris

bought 5 pounds of oranges and 3 pounds of apples.

       total apple purchase by Chris = 3 pounds

        the total cost of apples (3 * $2 )= $6

         total cost for 5 pounds of orange will be $2.5

   the total cost of fruits is the cost of apples plus the cost of orange

             = ($6+$2.5)= $8.5

therefore, the total amount to be paid by Chris is $8.5

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We can simplify the inequality |x + 3| > 2 to get the compound inequality:

-1 < x

-5 > x

Thus, the correct option is B.

Here we have the following inequality:

|x + 3| > 2

The absolute value part can be "separated" into a compound inequality, we can rewrite this as:

|x + 3| > 2

-2 > x + 3

2 < x  + 3

Now we can solve these two inequalities for x, we will get:

-2 > x + 3

-2 - 3 > x

-5 > x

The second inequality gives:

2 < x + 3

x - 3 < x

-1 < x

Then the compound inequality is:

-1 < x

-5 > x

Then the correct graph is the one in option B.

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Answer:

x=1

Step-by-step explanation:

x+3=4x

x-4x+3=0

-3x=-3

x= -3/-3

x=1

Answer:  

X = 1

Hope this helps!!