Henry purchased a prepaid phone card $40.50 for . Calls cost 10 cents a minute using this card. The credit, C (in dollars), left on the card after it is used for 15 minutes of calls is given by the following. How much credit is left on the card after Henry uses it for minutes of calls?

The equations that can be set up correctly to find the length of the unknown side using the Pythagorean theorem are:

6² + x² = 17²

x² + 6² = 17²

The Pythagorean Theorem is a statement in mathematics that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The theorem can be written as an equation:

c² = a² + b², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Using the Pythagorean theorem, the equations that can be set up correctly to find the value of x are:

6² + x² = 17²

x² + 6² = 17²

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Yes, Urie correctly completed the square to solve the equation 0 = 3x + 9 to the square root of 2 - 9x + 27.

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The formula of commutative property is α + β = β + α or α × β = β × α.

The commutative property is the property that deals with the arithmetic operations of addition and multiplication. So mathematically, if we change the order of the operand and it does not change the result of the arithmetic operation then that particular arithmetic operation is commutative.

If two numbers α and β are given, then the formula of the commutative property of numbers is given as,

α + β = β + α

α × β = β × α

α - β ≠ β - α

α ÷ β ≠ β ÷ α

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The value of 27 5/3 in simplest radical form will be 86 / 3.

The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Here the value of 27 5/3 in simplest radical form will be the calculated thus:

(27 × 3) + 5 / 3

= (81 + 5) / 3

= 86 / 3

The value in radical form will be 86 / 3.

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Answer:The slope of the given line is -4

Step-by-step explanation:

The missing numbers are 14 and 17. there are 50 steps taken to reach the last pebble on this part of the path.

What is the missing number?

Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them.

let's take a look at pebbles along each part of the path, there is 1 number of addition to each pebble number to go on next pebble.

i.e. 12, 13, 14, 15, 16, 17

so, the missing numbers are 14 and 17.

now, as given Hansel and Gretel used a pebble to mark every 10 steps as they walked along the path. How many steps have they taken when they get to the last pebble on this part of the path?

so, to go on next pebble there are 10 steps to walk.

therefore, from starting pebble  number 12 to last pebble number 17, there are 50 steps ( difference between two pebbles is 10 steps).

hence, the missing numbers are 14 and 17. there are 50 steps taken to reach the last pebble on this part of the path.

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Answer:

Step-by-step explanation:

if it is 35 because if you put together two negative numbers they become positive

I hope it helps you :)

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 6x - 7 = 35[/tex]

[tex]\qquad \sf  \dashrightarrow \: 6x - 7 + 7 = 35 + 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: 6x = 35 + 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: 6x = 42[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 7[/tex]

Answer:

To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area......

Step-by-step explanation:

The expression  [tex]$1\frac{2}{7}x -1=26[/tex]  gives {x} value as equivalent to 21.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the expression as -

[tex]$1\frac{2}{7}x -1=26[/tex]

We can write the expression as -

(9/7)x - 1 = 26

(9/7)x = 27

x = (27 x 7)/9

x = 3 x 7

x = 21

Therefore, the expression  [tex]$1\frac{2}{7}x -1=26[/tex]  gives {x} value as equivalent to 21.

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The jazz band has 15 seventh graders playing according to the ratio.

A ratio, which is a number, is a way to represent one quantity as a portion of another. A ratio can only be compared when the two numbers in it have the same unit. To compare two objects, ratios are utilized.

Given One fifth of the 75 seventh graders at Charles School participate in the jazz band.

Presented as a ratio

75 pupils, or 1/5 of them, participate in the jazz band.

75 pupils out of the total play in the jazz band.

15 kids in total participate in the jazz band.

15 seventh graders are therefore playing in the jazz band in accordance with the ratio.

Hence, The jazz band has 15 seventh graders playing according to the ratio.

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c = 14a/28

This equation represents the proportional relationship between the number of apples (a) and the cost in euros (c). The constant of proportionality is 14/28, which means that for every 14 apples, the cost is 28 euros. By dividing both sides by 14, we can also write the equation as a = c/2. This means that for every 2 euros, you can buy one apple.

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Answer: 30,000

Step-by-step explanation:

150,000 x 0.2 = 30,000

The zeros of quadratic function 2x² - 7x + 3 = 0 are 3 and 1/2.

There are several methods for solving a quadratic equation of the form ax² + bx + c = 0. In our case, use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a to find the zeros or the solutions for x.

Plug in the values to the formula and solve for x.

x = (-b ± √(b² - 4ac)) / 2a

x = (--7 ± √(-7² - 4(2)(3))) / 2(2)

x = (7 ± √49 - 24) / 4

x = (7 ± √25) / 4

x = (7 ± 5) / 4

x = 3   ;   x = 1/2

Hence, the zeros of quadratic function 2x² - 7x + 3 = 0 are 3 and 1/2.

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The value of G(2) of the given sequence formula is; -42

The general formula for the nth term of an arithmetic sequence is;

aₙ = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

We have the following parameters;

G(1) = 50

G(n) = 8 - g (n-1)

Thus;

G(2) = 8 - g(2-1)

G(2) = 8 - g(1)

Since (g(1) = 50 ), then we have;

G(2)= 8 - 50

G(2) = -42

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The length and width of the rectangle is 28 feet and 58 feet respectively.

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

Therefore, the perimeter of a rectangle is the sum of the whole 4 sides of the rectangle.

Hence, the perimeter of a rectangle is 172 feet.

perimeter of a rectangle = 2(l + w)

where

l = x

w = 2(x + 1) = 2x + 2

Therefore,

172 = 2(x + 2x + 2)

172 = 2(3x + 2)

divide both sides by 2

172 / 2 = 3x + 2

86 = 3x + 2

86 - 2 = 3x

3x = 84

divide both sides by 3

x = 84 / 3

x = 28

Therefore,

length = 28 feet

width = 2(28) + 2 = 58 feet

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The expression equivalent to - 8.2 - 5 is - 8.2 + (-5)

What is an expression?

A mathematical expression is a phrase that includes at least two numbers or variables, and at least one arithmetic operation. The mathematical operations used can be addition, subtraction, multiplication or division.

Note ,

         - × - = +

         - × + = -

         + × + = +

For the expression - 8.2 - 5

In the above expression, we are subtracting positive integer 5 from -8.2

  So we get the answer as

                 -8.2-5 = = -13.2

Now this is the solution we should get while solving the given options.

  a) 5 - ( -8.2)  = 5 + 8.2 = 13.2

  b) -8.2 + 5 = - 3.2

  c) -8.2 -5 [tex]\neq[/tex] 8.25 (as seen above)

   d) - 8.2 + ( -5) = -8.2 - 5 = -13.2

Comparing the solutions, we get that option(d) matches with the required answer.

Therefore option(d) is the correct expression that gives the same answer.

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Any set of ordered pair cannot be called as a function , the ordered pairs that in which no two different ordered pairs have the same x coordinate is called as a Function .

What is a Function ?

The set of ordered pair (x,y) is called a function, in which no two different ordered pairs have the same x coordinate. and the equation that produces such a set of ordered pairs can be called as function.

For Example : Let us Consider ordered pairs , F = [tex][(1,5) , (3,6)][/tex] ;

we see that ,  the element 1 has the image as 5 , and the element 3 has the image as 6 .

So , we can conclude  that , the each value of x has exactly only one corresponding value of y .

Therefore , the ordered pair can be called as a function .

The given question  is incomplete , the complete question  is

Is any set of ordered pair is called a Function ?

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The three steps of factoring include taking the common component out of the polynomial then simplifying the polynomial such that the most simple values are left and finally rearrangement.

If we are provided with the polynomial that is very complex in nature then first thing we have to do in order to solve the problem related to that polynomial is to factorise the polynomial.

The factory of that particular polynomial can be done by taking out the most common component out of the polynomial in a multiplication.

After this we have to simplify the polynomial such that only the simplest values are left in the polynomial and finally we have to rearrange the polynomial because after such operations on that polynomial the polynomial will not be easy to understand in the first look of it.

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Therefore , the solution of the given problem of expression comes out to be the coefficient of given expression  XYZ  is 1.

By substituting each variable with a number and conducting mathematical functions, an algebraic formula must be checked. The solution variable in the previous example is identical to 6 since 79 + 8 = 87. To evaluate the expression, we can replace the variables values with ones we are familiar with.

Here,

Given :

XYZ

To find the coefficient of given expression ,

Thus,

From observing we can see XYZ

can be written as

=>1*XYZ

Where 1 is coefficient.

Therefore , the solution of the given problem of expression comes out to be the coefficient of given expression  XYZ  is 1.

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Answer:

Step-by-step explanation:

When dividing like bases (x is our base) we simplify by subtracting the exponents, top minus bottom. Since the exponents are fractions, we need a common denominator.

[tex]\frac{1}{5} -\frac{2}{15}=\frac{3}{15} -\frac{2}{15}=\frac{1}{15}[/tex]

thus, the simplification is [tex]x^\frac{1}{15}[/tex]

Answer:

(x 1/5)/(x 2/15)=.

(x1/5)× 15/2x

=15x/10x

=1.5

Answer: -3

Step-by-step explanation: Y=MX+B

Answer:

−3

Step-by-step explanation:

y-5=-3(x-17)

y=-3x+51+5

y=-3x+56

if we have this function:

y=mx+b

The slope is "m".

In this case, m=-3

Answer: sope -3

Answer:

[tex]\huge\boxed{\sf H=18.4\ cm}[/tex]

Step-by-step explanation:

Base = 7 cm

Perpendicular = 17 cm

Hypotenuse = H

[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2\\\\(H)^2=(7)^2+(17)^2\\\\(H)^2=49+289\\\\(H)^2=338\\\\Take \ square\ root \ on \ both\ sides\\\\\sqrt{(H)^2} =\sqrt{338} \\\\H=18.4\ cm\\\\\rule[225]{225}{2}[/tex]

When you are doing calculations, you can usually tell when you need to change base by looking at the problem. If the problem includes fractions, a base other than 10 may be more efficient. If the problem includes exponents, a base other than 10 may be necessary.

When working with numbers, it is important to know what base the numbers are in in order to correctly perform calculations. The base of a number is the number of digits used to express it, meaning that the base of a number can range from base 2 (binary) to base 36 (base 36 uses the numbers 0-9 and the letters A-Z).

Changing the base of a number can be helpful when dealing with fractions, exponents, and other complex calculations. To change the base of a number, divide the number by the base and then divide the remainder by the base, continuing to divide until the remainder equals 0.

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An expansion where image size increased is formed when scale factor k is greater than 1

The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.

The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image.

The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted. Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size.

when the scale factor K is greater than 1 , The image will enlarged

Hence, An expansion will be occur.

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The equation which gives infinite solutions, x-10+x = 8+2x-18.

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. LHS = RHS is a common mathematical formula.

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:

For the infinite solution the both side of equation must contain equal quantity.

For example,

x-10+x = 8+2x-18

now, solving for x

x-10+x = 8+2x-18

2x-10 = 2x-10

-2x = -2x

-10 = -10

As, both sides are equal  which shows the system of equation.

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Answer:

7) B.

8) D.

Step-by-step explanation:

The value of {a} is equivalent to 3.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation of a straight line → y = ax

The points (3, 9) and (–3, –9) are plotted on the coordinate plane using the equation y = ax, this means that -

9 = a x 3

a = 3

and

- 9 = a x - 3

a = 3

Therefore, the value of {a} is equivalent to 3.

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Knowing if your cervix is dilating typically involves a physical examination by a healthcare provider.

During labor, a healthcare provider will check the dilation of your cervix by performing a pelvic exam. They will use their fingers to feel the cervix, which is located at the top of the vagina, and determine the degree of dilation.

Cervical dilation is measured in centimeters, and full dilation is considered to be 10 centimeters. Before labor begins, the cervix is typically closed and has a firm consistency. As labor progresses, the cervix will start to soften and thin out, and will eventually open, or dilate.

Some women might experience Braxton Hicks contractions, which are sometimes referred as "false contractions" as they can be mistaken for the start of labor, but Braxton Hicks contractions do not cause cervical dilation.

It's important to note that dilation is just one of the factors that indicate that labor is imminent. It is not the only factor and some women can have a fully dilated cervix for days before going into active labor.

In conclusion, knowing if your cervix is dilating typically involves a physical examination by a healthcare provider, who will perform a pelvic exam to feel the cervix and determine the degree of dilation.

Cervical dilation is measured in centimeters, with full dilation being 10 centimeters. Be aware that dilation is just one of the factors that indicate labor is imminent.

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The  quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero.

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