Work out the radius of this circle.
circumference = 46 mm
mm
Not drawn accurately

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions. x<3 is the inequality describes all the solutions to 11(3 - x) < -2x + 6

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

The given inequality is 11(3 - x) < -2x + 6

We need to separate the variable x.

11(3 - x) < -2x + 6

33-11x<-2x+6

Let us shift -2x from RHS to LHS and 33 from LHS to RHS

2x-11x<6-33

Divide both sides by -9

-9x<-27

x<3

Therefore the solution to inequality 11(3 - x) < -2x + 6 is x<3.

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Define Ratios and proportions:

A ratio is the comparison between two different quantities while proportion is an equality of two ratios.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given data,

Ratio of hours to lawns mowed

    15 hours ⇒ 5 lawns

    1 hour ⇒ X lawns

     5 : 15 = 1:X

      5/15 = 1/X

Cross multiply,

We can write,

       5X= 15

        X = 15/5

        X = 3 lawns

Therefore,

Rate of lawns mowed per hour = 3 lawns / 1 hour

     = 3 lawns per hour.

Hence,

The number of lawns that could be mowed in 1 hour is 3 lawns.

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Answer:

350

Step-by-step explanation:

Okay, so we have a total of 639 tickets that they were sold. Using both students and adults tickets.

And also we know that the students r 61 fewer than the adults. So X minus 61.

X -61 = 289.

350 -61= 289

It's gonna be a total of 289. And we can check our results, X plus Y. So 350 plus 289. It's gonna be a total of 639.

The image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)

The complete question is added as an attachment

The coordinates of the triangle are given as

R = (-4, 1)

S = (-4, 4)

T = (-2, 1)

The transformation is given as

The rule of the transformations is

(x, y) = 3(x, y)

So, we have

R' = 3 * (-4, 1) = (-12, 3)

S' = 3 * (-4, 4) = (-12, 12)

T' = 3 * (-2, 1)= (-6, 3)

Hence, the image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)

See attachment for the image of the transformation

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Based on the information, it should be noted that there's an increase in percentage of 30%.

Based on the information, it should be noted that the following can be illustrated:

Original amount = 30

New amount = 39

Therefore, it should be noted that the change in percentage will be:

= Change in amount / Old amount × 100

= (39 - 30) / 30 × 100

= 9/30 × 100

= 30%

Therefore, there's a increase in percentage of 30%.

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An equation for the likelihood that Gordon does not win, in the form of such a combined single fraction:

= [tex]$\frac{4}{n+4}$[/tex]

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 as well as 1, where 0 denotes the event's impossibility and 1 represents certainty.

The addition rule, the multiplication rule, and indeed the complement rule are the three main rules related with basic probability.

Formulate based on the provided conditions:

[tex]$1-\frac{n}{n+4}$[/tex]

Look for the common denominator as well as write additional numerators above it denominator:

[tex]$\frac{n+4-n}{n+4}$[/tex]

Rearrange and collect related terms:

[tex]$\frac{(n-n)+4}{n+4}$[/tex]

Gather coefficients for similar terms:

[tex]$: \frac{(1-1) \times n+4}{n+4}$[/tex]

The product of two polar opposites is 0:

[tex]$: \frac{0 n+4}{n+4}$[/tex]

Use the Multiplication Zero Property:

[tex]$\frac{4}{n+4}$[/tex]

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Two or more expressions with equal sign is called as Equation. If mWVY = 70 is an angle then mYVX =165 we get by solving the equation x-13=70.

Two or more expressions with equal sign is called as Equation.

mWVY = 70

From the figure we can observe that mWVY =x-13

By this we form an equation

x-13=70

x-13=70

x=70+13

x=83.

So value of x is 83.

Now mYVX=2x-1

2(83)-1

166-1

=165

Therefore mYVX is 165 degree when  mWVY = 70.

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Answer:

For 2 more panes of glass it will cost $5.70.  

Step-by-step explanation:

To find the price of each pane of glass you take the total price/ total panes of glass.  

25.65/ 9 = $2.85.

If he wanted one more pane of glass it would be $2.85 but since you asked for two you multiply by 2 and get $5.70.  Hope this helps!

Answer:

A

Step-by-step explanation:

if it is meant literally as stated (lead AND nickel), then the check was only for both to be present.

and then A is the correct answer (L n N : intersection of both sets).

if it would have the typical meaning (we say we check for L and A, but mean inclusive "or" : either L or N or both), then B would be correct.

Answer:

I'm assuming you inserting the variable x was a mistake.

Step-by-step explanation:

The least common multiple of 18 and 42 is 126.

[tex]\bold{Step-by-step}[/tex]

[tex]\mathrm{"LCM"}[/tex]

[tex]18 \times 7 = 126\\42 \times 3 = 126[/tex]

Any concerns, let me know, have a great day!

The side of square is (B) 5.7m

We are given the formula relating side and area of square. Using the mentioned formula to find the value of side of square.

Side² = Area

Rewriting the equation according to side of the square -

Side = √Area

Keep the values in formula to find the value of side of square

Side = √32

Finding square root of the number to find the value of side of square

Side = √(8×4)

Side = √(4×2×4)

Side = 4√2

Side = 4×1.414

Performing multiplication  to find the value of side of square

Side = 5.66

Side = 5.7 meters

Hence, the side of square is (B) 5.7m

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Answer:

75.3°

Step-by-step explanation:

Applies the Law of Cosines

15 represents the larger side and its opposite angle will be C

[tex]15^{2} =10^{2} +14^{2} -2(10)(14)cosC[/tex]

[tex]225=296-280cosC[/tex]

[tex]-280cosC=225-296[/tex]

[tex]cosC=\frac{-71}{-280}[/tex]

[tex]C=ArcCos(0.25357)[/tex]

C = 75.3°

Hope this helps

The slope of the line is 1 / 3

The slope of a line is a measure of its steepness.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

Mathematically, the slope of a line can be described as follows;

slope = change in y / change in x

Therefore,

slope = y₂ - y₁ / x₂ - x₁

Let's take two points from the graph

(0, 2)(3, 3)

where

x₁ = 0

x₂ = 3

y₁ = 2

y₂ = 3

Hence,

slope = 3 - 2 / 3 - 0

slope = 1 / 3

Therefore, the slope of the line is 1 / 3

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The answer is ( 2x-1) (3X+2)

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, and is a factorization of the polynomial x² – 4.

STEP 1-: Combine like terms

6z²-3Z-2+4Z

6Z²+1Z-2

STEP 2-: Multiply by 1

6Z²+1Z-2

6Z²+Z-2

STEP 3-: Use the sum-product pattern

6Z²-3Z-2+4Z

6Z²+4Z-3Z-2

STEP4-: Common factor from the two pairs

6Z²+4Z-3Z-2

2Z(3Z+20) -1 (3Z+2)

STEP 5-:Rewrite in factored form

2Z(3Z+20) -1 (3Z+2)

(2Z-1) (3Z+2)

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The function for the given text in the form y = mx + b is y = 10m + 100.

The starting point for the function y = -3x + 9 is 9.

The output when x = 12 is

Linear functions take the form:

y = mx + b

m is the rate of change and b is the constant or flat fee

The linear function for Mr. Bergman's situation is:
y = 10m + 100

The starting point for a function is the constant so the starting point for  y = -3x + 9 is 9.

The output when x = 12 is:

= - 3(12) + 9

= -36 + 9

= -27

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The value of x for the equation log₇343=x will be 3.

Logarithmic function properties. You have encountered several characteristics during your study of algebra, including the commutative, associative, and distributive properties.

These characteristics make it easier to simplify a complex statement or equation. With logarithms, the same holds true.

For log₇343=x

It can be expressed in the form of -

343 = 7ˣ

It can be further expressed as -

7³ = 7ˣ

As base is same,

x = 3

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Answer:

Remember the length times width formula. You aren't supposed to multiply every side if there is more than one equivalent length/width. Just multiply the first two you see.

Step-by-step explanation:

[tex]6 \times 5 = 30[/tex]

Therefore,

Chris will use 30 square yards for his two gardens.

I hope it helps, let me know if you have other concerns about anything related to this question.

The measured angle ABD=24° and ABC=71°

The figure in the question is either a triangle or a quadrilateral, but this has not been stated. It is possible to solve this regardless of shape. The accompanying graphic shows the two potential shapes and angles.

Now, based on the information provided, we may deduce that line BD divides angle ABC into two parts: Angle ABC is equal to angle ABD plus angle DBC.

Additionally, we know that angle DBC is 47 degrees and angle ABC is 1 degree less than 3 times angle ABD.

Angle ABC Equals 3x-1 if angle ABD is x.

Angle ABC also equals Angle ABD plus Angle DBC.

Changing the values in the equations above 3x-1 = x+47 ⇒ 2x = 48⇒ x = 24

Angle ABD thus equals 24 degree, and angle ABC = 3(24)-1 = 71-1 = 71 degree

∴∠ABD=24° and ∠ABC=71°

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The square play space would provide more efficient use of fencing than an equilateral triangle.

What is a square?

A closed geometrical figure that has four equal sides making an angle of 90° with each other is called square. The diagonals of a square bisect each other at a right angle.

Examining which shape would efficiently use fencing

Given a play space, we need to find out, of its square or equilateral triangle shape, which one would use fencing more efficient

Applying mathematics, we get,

Square fencing play space provides more use of fencing than an equilateral triangle because, in the case of a square, all sides are equal and these make 90 degrees angle.

Hence, the square play space would provide more efficient use of fencing than an equilateral triangle.

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The logarithmic equation for 1/4 = 8⁻²/₃ is :

[tex]log_8(\frac{1}{4}) = \frac{-2}{3}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  is an exponential function is  [tex]a^N=x[/tex] then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex]

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

According to statement,

1/4 = 8⁻²/₃

as , exponential function is  [tex]a^N=x[/tex]  can be converted to logarithmic function as  [tex]log_ax=N[/tex]

here, a = 8, N= -²/₃ , x = 1/4

therefore, logarithmic equation is :

[tex]log_8(\frac{1}{4}) = \frac{-2}{3}[/tex]

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Answer:

the answer is 4 hundreds because starting from the decimal point is hundreds

Answer: 90 miles.

Step-by-step explanation:

Since 12 is 1/5 of an hour, you can simply multiply 18 by 5 to get 90.

Answer:  x  ≤ 4.5

Step-by-step explanation:

Since there is a closed circle on 4.5 and the ray is going left we know that x is ≤ 4.5

Answer:

1/243

Step-by-step explanation:

Answer:1314 or 13.14%

Step-by-step explanation:yes

if the point I is between points H and J, then the numerical length of hj is 14 units

The given parameters are

IJ= 3x + 3

HI = 3x - 1

HJ = 3x  + 8

The above implies that the point I is between points H and J

So, we have

HJ = HI + IJ

Substitute the known values

3x + 8 = 3x + 3 + 3x - 1

Evaluate the like terms

3x = 6

Divide by 3

x = 2

Substitute x = 2 in HJ = 3x  + 8

HJ = 3 x 2 + 8

Evaluate

HJ = 14

Hence, the numerical length of hj is 14 units

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The constant term of this polynomial function with real coefficients will be - 240.

We are given the zeroes of the equation as:

16 and 1 - 2i

Now, we know that, the imaginary root are always in a pair, so the third root will be:

1 + 2i

This means that the factors of the cubic polynomial will be:

(x - 16)

(x - [1 - 2i])

(x - [1 + 2i])

The leading coefficient is 3, so the polynomial function will be:

y = 3 (x - 16) (x - [1 - 2i]) (x - [1 + 2i])

Now, the constant term will be:

3 (- 16) (1 + 2i) (1 - 2i)

( - 48) (1 - 4i²)

= ( - 48) (5)

= - 240

Therefore, the constant term of this polynomial function with real coefficients will be - 240.

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Answer:

LCD = 30

Equivalent Fractions with the LCD

1/10 = 3/30

1/6 = 5/30

Step-by-step explanation:

Rewriting input as fractions if necessary:

1/10, 1/6

For the denominators (10, 6) the least common multiple (LCM) is 30.

LCM(10, 6)

Therefore, the least common denominator (LCD) is 30.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/10 = 1/10 × 3/3 = 3/30

1/6 = 1/6 × 5/5 = 5/30