Anna's cars can travel to 8 miles on 6 gallons of gas write an equation to represent the distance y and mild and car driven on x gallons of gas

The completed statement is

         i) f(4) is 1/2

         ii) f(x) = 4 when x is 8

A domain of a function refers to "all the values" that go into a function. The domain of a function is the set of all possible inputs for the function.

The range of a function is the set of all its outputs.

According to the question the ordered pairs are given as

      R = { (8,4) , (-2/3,3) , (11,-1) , (4,1/2)}

Here the domain are  : ( 8,-2/3,11,4)

and range are : (4,3,-1,1/2)

Hence the values are :

   i) f(4) = 1/2

   ii) f(x) = 4 when x = 8

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The final answer in scientific notation is 6×10¹⁴.

When the numbers are in scientific notation, the multiplication is accompanied with addition of exponents. So, the numbers will be multiplied and exponents will be added.

Writing the equation to find the product by performing the calculation -

Product = 2×10⁷ × 3×10⁷

To perform addition of exponent of the number 10⁷ and to perform the multiplication of the number rewriting the equation

Product = (10⁷⁺⁷)×(2×3)

Adding the exponent and performing multiplication of the numbers to find the product of the given numbers in scientific notation

Product = 10¹⁴×6

Hence, the final answer on multiplication of given numbers is 6×10¹⁴.

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The geometric mean between pair of numbers 12 and 9 is 10.39

We know that for a sequence of numbers x1, x2,.., xn

The formula of geometric mean is,

[tex]\Pi = \sqrt[n]{x_1.x_2...x_n}[/tex]

In this question, we have been given two numbers 12 and 9

We need to find the geometric mean between pair of numbers, 12 and 9.

Using the formula for the geometric mean,

[tex]\Pi = \sqrt[n]{x_1.x_2...x_n}[/tex]

In this question, we have two numbers.

So, the value of n is 2.

[tex]\Pi = \sqrt{12\times 9}\\\\\Pi=\sqrt{108}\\\\ \Pi=10.39[/tex]

Therefore, the geometric mean between pair of numbers 12 and 9 is 10.39

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The solution to the linear inequation is x>1/2 .

It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The solutions for inequalities can be given by: a graph in a number line or numbers.

For solving this exercise, it is necessary to find a number solution for the given inequality.

15−2(2x−1)<15

15-4x+2 < 15

-4x < -2

4x > 2

x > 2/4

x> 1/2

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The triangle having vertices X(-7,-3), Y(-2,-5), Z(-4,-1)  is obtuse.

According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:

acute if [tex]a^{2} + b^{2} < c^{2}[/tex]

obtuse if  [tex]a^{2} + b^{2} > c^{2}[/tex]

right if  [tex]a^{2} + b^{2} = c^{2}[/tex]

XY = [tex]\sqrt{(-2 + 7)^{2} + (-5 + 3)^{2} }[/tex]

∴ XY = 5.38

YZ = [tex]\sqrt{(-4 + 2)^{2} + (-1 + 5)^{2} }[/tex]

∴YZ = 4.47

ZX = [tex]\sqrt{(-4 + 7)^{2} + (-1 + 3)^{2} }[/tex]

∴ ZX = 3.60

∴The longest side is XY = 5.38.

Hence, a = YZ, b = ZX and c = XY;

Consider [tex]a^{2} + b^{2}[/tex] :

= [tex]4.47^{2} + 3.60^{2}[/tex]

= 32.94.

Now consider [tex]c^{2}[/tex]:

= [tex]5.38^{2}[/tex]

= 28.94.

Thus, [tex]a^{2} + b^{2} > c^{2}[/tex]

Hence, the triangle is obtuse.

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18 triangles area unit required to compose a vicinity that's one square meters.

A square with a locality of one square metre is rotten into nine identical little squares. every little sq. is rotten into 2 identical triangles.

1 square metre is rotten into nine identical little squares.

So there area unit nine little squares in one square metre.Each little sq. is rotten into 2 identical triangles therefore nine little squares is rotten into 9(2) = eighteen identical triangles

Hence, one square metre is rotten into eighteen identical triangles.

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The product of given integers 28, -5 and 17 is -2380.

The given numbers are the product of 28, -5 and 17.

We need to find the product of the given numbers.

The product of two integers with like signs is equal to the product of their absolute values.

(i) The product of two positive integers is positive.

(ii) The product of two negative integers is positive.

(iii) The product of one positive and one negative integer is negative.

The product of 28, -5 and 17 is calculated as follows:

Now, 28 × (-5) × 17

= (28 × (-5)) × 17

= (-140) × 17

= -2,380

Therefore, the product of given integers 28, -5 and 17 is -2380.

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Answer:

-2380 (None of the option)

Step-by-step explanation:

Now we have to,

→ find the product of 28, -5 and 17.

Let's solve the problem,

→ x = 28 × ((-5) × 17)

→ x = 28 × -85

→ [ x = -2380 ]

Hence, the answer is -2380.

The equation of line for the given values of m and y - intercept is y = 6x + 5,

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

The standard equation of the line is y = mx + c

Now, we are given,

m = 6 and y - intercepts = (0,5)

Now, putting it in the equation,

y = 6x + 5, which is our desired equation

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The  simplification of the given expression 0.4(k - 0.1) + 0.5(3.3 - k) is 1.61 - 0.1k.

According to the question.

We have an expression.

0.4(k - 0.1) + 0.5(3.3 - k)

As we know that, simplification of an expression means to write an equivalent expression which contains no similar terms.

Therefore, the simplification of the given expression 0.4(k - 0.1) + 0.5(3.3 - k) is given by

0.4(k - 0.1) + 0.5(3.3 - k)

= 0.4k - 0.04 + 1.65 - 0.5k

= 1.61 - 0.1k

Hence, the  simplification of the given expression 0.4(k - 0.1) + 0.5(3.3 - k) is 1.61 - 0.1k.

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Answer:

Step-by-step explanation: You may have a chance of getting 20 questions correct while another 20 wrong. So if you have 1/2 the probability with your class it would be around 20 correct and 20 wrong.

The additional cost required to pay for a 30 minutes call is 49.4 cents.

What is a word problem?

A word problem is defined as a mathematical problem written in form of words or sentences. These are assigned to students to determine their hold on the concepts.

Calculation of cost of calling 30 minutes

The cost for calling 4 minutes is 7.6 cents

The cost for calling 1 minute is 7.6 / 4

= 1.9

The cost for calling 30 minutes = 1.9 × 30

= 57 cents

The word 'more' in the word problem specifies the additional cost needed to make a 30-minute call i.e. it requires the difference between the cost of a 4-minute call and a 30 minutes call.

More cost = còst for calling 30 minutes- cost for calling 4 minutes

= 57 - 7.6

= 49.4 cents

Hence, the additional cost required to pay for a 30 minutes call is 49.4 cents.

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The matching of the probability will be:

Flip a coin 3 times and get heads every time. = 1/8.

Flip a coin to get tails up and roll a number cube to get an even number. - 1/4

Roll a number cube and get a 4 and 5 - 1/36

Draw an ace and then a 7 from a deck of cards with replacement - 1/169.

Flip a coin 3 times and get heads every time will be:

= (1/2)³

= 1/8.

Flip a coin to get tails up and roll a number cube to get an even number will be:

= 1/2 × 3/6

= 3/12

= 1/4

Roll a number cube and get a 4 and 5 will be:

= 1/6 × 1/6

= 1/36

Draw an ace and then a 7 from a deck of cards with replacement is 1/169.

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The probability that she chooses 3 particular books to check out from the 10 initial books is 0.0574

In this question,

Paige is choosing between 10 books at the library.

We need to find  the probability that she chooses 3 particular books to check out from the 10 initial books.

The probability of choosing 1 book = 1/10

So, the probability of success (p) = 1/10

the probability of failure (q) = 9/10

Using Binomial probability distribution,

P(x = 3) = [tex]^{10}C_3\times (\frac{1}{10} )^3\times (\frac{9}{10} )^7[/tex]

P(x = 3) = 120 × 0.001 × 0.4783

P(x = 3) = 0.0574

Therefore,  the probability that she chooses 3 particular books to check out from the 10 initial books is 0.0574

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The required transformation would be in the variable because the slope of parallel lines is always the same.

A line can be defined by the shortest distance between two points is called as a line.

Here,
Line MR is drawn with the endpoints M and R, and another line M'R' is drawn which is parallel to line MR. There is a property of parallel lines that the slope of the parallel lines is always equal. , So the slope of lines are equal there must be a change in variable x and y which describes the translation of the line M'R'.

Thus, the required transformation would be in the variable because the slope of parallel lines is always the same.

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The value of different f(x) for different value of 'x' in the given graph is f(-3) = -1 , f(-2)=0. f(-5)= 3, f(-4) =0

Given that, The f(x) graph we can observe that it is a shifted parabola.

We can translate the parabola vertically to produce a new parabola that is similar to the basic parabola. The function [tex]y=x^2 + b[/tex] has a graph which simply looks like the standard parabola with the vertex shifted b units along the y-axis. Thus the vertex is located at (0,b). If b is positive, then the parabola moves upwards and, if b is negative, it moves downwards.

Similarly, we can translate the parabola horizontally. The function[tex]y =(x-a)^2[/tex]has a graph which looks like the standard parabola with the vertex shifted a units along the x-axis. The vertex is then located at (a,0). Notice that, if a is positive, we shift to the right and, if a is negative, we shift to the left.

So, for the given question

b = parabola shift unit along y-axis = -1 units

a = parabola shift unit along x-axis = -3 units

So, equation of parabola = [tex]f(x)=y = (x+3)^2-1[/tex]

Now,

for x = -3. f(-3)=[tex](-3+3)^2-1=-1[/tex]

So, f(-3)= -1

x = -2. f(-2)=[tex](-2+3)^2-1=0[/tex]

So, f(-2)= 0

x = -5. f(-5)=[tex](-5+3)^2-1 = 3[/tex]

So, f(-5)= 3

x = -4. f(-4)=[tex](-4+3)^2-1=0[/tex]

So, f(-4)= 0

Therefore, from the graph f(x),  value of f(x) for diiferent value of x is f(-3)=-1. f(-2)=0.f(-5)=3.f(-4)=0.

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Answer:

x

Step-by-step explanation:

When you add them, you get 4/4x which is also known as 1x.

Answer:

the answer would be n/4 + 9/2

Step-by-step explanation:

-

Answer:

source please?

Step-by-step explanation:

Without a source I cannot

The inequality can be simplified to:

x > -1

And the graph can be seen in the image below.

Here we have the inequality:

5x + 8 > 3

To solve this, we need to isolate the variable x in one side of the inequality.

5x + 8 > 3

We subtract 8 in both sides:

5x > 3 - 8

5x > -5

Now we divide both sides of the inequality by 5.

x > -5/5

x > -1

Now, to graph this, we need to do an open circle at x = -1, and shade all the region to the right of this point, like in the example below.

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Answer:

1) m = rise/run = x - x/y - y

2) Slope(m) = -2

    Question 2

m = 1 - (-5)/ -3 - (0)

m = 1 + 5/-3 - (0)

m = 6/-3 - (0)

m = 6/-3 + 0

m = 6/-3

= -2

Simplification form of the given complex fraction [tex]\frac{x}{\frac{1}{x+\frac{1}{y} } }[/tex] is  (xy)/ (xy+1).

As given in the question,

Given complex fraction is [tex]\frac{x}{\frac{1}{x+\frac{1}{y} } }[/tex]

Simplify the given complex fraction by taking the least common multiple,

[tex]\frac{x}{\frac{1}{x+\frac{1}{y} } }\\\\\\=\frac{x}{\frac{1}{\frac{xy+1}{y} } } \\\\\\=\frac{xy}{xy+1}[/tex]

Therefore, the simplification form of the given complex fraction [tex]\frac{x}{\frac{1}{x+\frac{1}{y} } }[/tex] is  (xy)/ (xy+1).

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Mrs. Fields teaches synthetic geometry.

What is synthetic geometry?

The study of geometry without the use of coordinates or equations is known as synthetic geometry, sometimes known as axiomatic geometry or even pure geometry. To make inferences and find solutions, it uses the axiomatic approach and the instruments that are immediately associated to it, namely the compass and straightedge.

Mrs. Fields uses a compass, straightedge, pencil and protractor to teach geometry. And all these are used to either draw or measure and no formulas are needed anywhere, so it is synthetic geometry.

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x is equal to the -10 or less than the -10

Inequality:

In mathematics, 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. Inequalities can be posed either as questions, much like equations, and solved by similar techniques, or as statements of fact in the form of theorems. For example, triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than or equal to the length of the remaining side. The mathematical analysis relies on many such inequalities (e.g., the Cauchy-Schwarz inequality) in the proofs of its most important theorems.

In mathematics, an inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.[1] It is used most often to compare two numbers on the number line by their size. There are several different notations used to represent different kinds of inequalities:

The notation a < b means that a is less than b.

The notation a > b means that a is greater than b.

In either case, a is not equal to b. These relations are known as strict inequalities,[1] meaning that a is strictly less than or strictly greater than b. Equivalence is excluded.

In contrast to strict inequalities, there are two types of inequality relations that are not strict:

The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or, equivalently, at most b, or not greater than b).

The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or, equivalently, at least b, or not less than b).

The relation not greater than can also be represented by a ≯ b, the symbol for "greater than" bisected by a slash, "not". The same is true for not less than and a ≮ b.

The notation a ≠ b means that a is not equal to b; this inequation sometimes is considered a form of strict inequality.[2] It does not say that one is greater than the other; it does not even require a and b to be member of an ordered set.

In engineering sciences, less formal use of the notation is to state that one quantity is "much greater" than another,[3] normally by several orders of magnitude.

The notation a ≪ b means that a is much less than b.[4]

The notation a ≫ b means that a is much greater than b.[5]

This implies that the lesser value can be neglected with little effect on the accuracy of an approximation (such as the case of ultra relativistic limit in physics).

In all of the cases above, any two symbols mirroring each other are symmetrical; a < b and b > a are equivalent, etc.

Solution :

1/2x+8 [tex]\leq[/tex] 3

1/2x [tex]\leq[/tex] 3-8

1/2x[tex]\leq[/tex]-5

x  [tex]\leq[/tex] -5 x 2

x[tex]\leq[/tex] -10

x is equal to the -10 or less than the -10

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The standard deviation of the number of residents in the sample who were born in Colorado is 7.82

PC = Indicates the real population of residents born in Colorado  

PC = 0.427 shows estimated proportion for residents born in Colorado

nC = 250 sample size selected

Let X = random variable of interest

n = 250 , p = 0.427

Now the probability mass function is given by

P(X) =  (nCx)(p)^x(1-p)^n-x

Here (nCx) means combinatory and its formula is:

nCx = n! / (n-x)!x!

Let's calculate the expected value by the given formula.

E(X) = np = 250 x 0.427 = 106.75

The standard deviation for the random variable is given by:

sd(X) = √np(1-p)

sd(X) = √250 x 0.427 x (1-0.427) = 7.82

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Using adjacent angles, The value of a given figure, the value of E = 132°

What is an Adjacent angle?

When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end. When adjacent angles have a same vertex and side, they can be a complimentary angle or supplemental angle.

draw a line EOF parallel to AB

now EF || AB and CD||AB

∵ AB || EF and AO is a transversal

we have

∠AOF+∠OAB=180°

∠AOF+108 = 180 °

∠AOF=72 °

∵ EF|| CD and OC is transversal

so

∠COF+∠OCD=180°

∠COF+112° = 180°

∠COF=60°

∴∠AOC=∠AOF+∠COF

=72 ° + 60°

=132°

Hence the value of E = 132°

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A cyclic polygon is inscribed in a circle, and the circle is its circumscribed circle or circumcircle. The radius of the inscribed circle or sphere, if it exists, is the inradius or filling radius of a given outer figure.

An inscribed angle in geometry is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle formed by two given points on a circle at a given point on the circle.

An inscribed polygon is one with all of its vertices on a circle. The circle is encircled by the polygon, and the polygon is encircled by the circle. (It's a polygon inside a circle) A circumscribed polygon is one with each side tangent to a circle.

A cyclic polygon is inscribed in a circle, and the circle is its circumscribed circle or circumcircle. The radius of the inscribed circle or sphere, if it exists, is the inradius or filling radius of a given outer figure.

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Answer:

AH

Step-by-step explanation:

the two lines that are vertical on both lines show that they are both congruent (the same length)

Answer:

B -3>(-11)

Step-by-step explanation:

because of integers

Answer:

P = 2x + 14

Step-by-step explanation:

The perimeter of a shape is the total measurement of all the edges of a shape.

P = 12 + (x - 12) + 1 + [(x-5) - (x-12)] + [12 - 1] + (x-5)

P = 12 + x - 12 + 1 + [ x - 5 - x + 12] + 11 + x - 5

P =  x + x + 12 - 12 + 1 + 7 + 11 - 5

P = 2x + 14