Bob has a credit limit of $3500 on his credit card . He has a balance of $2200 on the card . How much can he charge before he goes over his limit ?

A 30-60-90 triangle is a special type of right triangle that has angles of 30 degrees, 60 degrees, and 90 degrees. It has the following properties:

The side opposite the 30-degree angle is half the length of the hypotenuse (the side opposite the 90-degree angle).

The side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.

To find the sides of a 30-60-90 triangle, you can use these properties.

If you know the length of the hypotenuse (the side opposite the 90-degree angle), you can find the length of the other two sides using the following formulas:

The side opposite the 30-degree angle: hypotenuse / 2

The side opposite the 60-degree angle: (√3) * (hypotenuse / 2)

If you know the length of one of the other two sides, you can use the above formulas to find the length of the hypotenuse and the other side.

For example, if you know the length of the side opposite the 30-degree angle, you can find the length of the hypotenuse by multiplying it by 2 and the length of the side opposite the 60-degree angle by multiplying it by √3

In summary:

The hypotenuse is always twice the length of the shorter leg.

The longer leg is √3 times the length of the shorter leg.

The hypotenuse is always the longest side in a 30-60-90 triangle.

Answer:

Step-by-step explanation:

plug in a 0 for y and simplify the equation

because 0*(constant of y)=0, so

x*(constant of x)=something, so

something/(constant of x)=x

ans is (x, 0)

$1200 was invested at a mutual fund of 6% profit while $2000 was invested at a mutual fund of 4% profit

An equation is an expression showing the relationship between numbers and variables.

Let x represented the money at 6% profit and y represent the money at 4% interest. A total of $3200 was invested, hence:

x + y = 3200    (1)

If the investor's total profit was $152, therefore:

0.06x + 0.04y = 152         (2)

From both equations:

x = 1200, y = 2000

$1200 was invested at 6% while $2000 was invested at 4%

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The required distance between given pair of points ( 2, 0 ) and ( -2,0 ) is equal to 4 units.

As given in the question,

Given pair of points in the coordinate plane is represented by the coordinates

( x₁ , y₁ ) = ( 2, 0 )

( x₂ , y₂ ) = ( -2,0 )

Apply the standard formula to calculate the distance between two pair of points in the coordinate plane is :

= √(x₂ - x₁ )² + ( y₂ - y₁ )²  

Substitute the values in the formula and calculate the distance between two pair of points :

= √ ( -2 - 2 )² + ( 0 - 0 )²

= √(-4)² + 0²

= √16

= 4

Therefore, the required distance between the given pair of points ( 2, 0 ) and ( -2,0 ) is equal to 4 units.

The above question is incomplete , the complete question is:

What is the distance between the pair of points (2, 0) and (-2, 0) ?

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Answer: The answer is 2

Step-by-step explanation:

The equation y = -5x + 3 is a linear equation.

We know that a linear equation in two variables is nothing but an equation that can be written in the form Ax + By = C,  where A and B are real numbers and A ≠ 0, B ≠ 0.

The above form of equation is called the standard form of a linear equation in two variables.

Here we have been given an equation y = -5x + 3

y = -5x + 3

y + 5x = -5x + 3 + 5x             ........(Add 5x to each side)

y + 5x = (-5x + 5x) + 3           .......(Associative property of addition)

y + 5x = 0 + 3

5x + y = 3                              ........(Commutative property of addition)

Since we can write it in the standard form, Ax + By = C, then we have a linear equation.  

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The area of given figure is 32 ft².

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Given,

the shaded are of shape is 16 ft²

As, twice the area of triangle equals the area of rectangle

⇒ (16 + 16) ft²

⇒ 32 ft²

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Complete Question -

The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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Two polynomials simply mean to sum the coefficients of the same powers, if these situations occur. the result of adding two polynomials will always be another polynomial.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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To calculate equivalent form of an algebraic expression we can use the following :

1) distributing property

2) factoring.

Two mathematical expressions are said to be equivalent if they yield the same result upon solving them. To represent equivalent form an equality (=) sign is used. 3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. To calculate equivalent form by using Distributive Property :

To calculate equivalent form Using Factoring :

This gives you an equivalent form . Again, the equality form, 5xy + 4x = x(5y + 4). Thus, the required equivalent form is determined.

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Answer:

s=17

Step-by-step explanation:

just divide 34 by 2

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{2s = 34}[/tex]

[tex]\textbf{DIVIDE 2 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{2s}{2} = \dfrac{34}{2}}[/tex]

[tex]\textbf{SIMPLIFY it}[/tex]

[tex]\mathsf{s = \dfrac{34}{2}}[/tex]

[tex]\mathsf{s = 17}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 17}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.

Finding the roots of the polynomial will allow you to solve it. P(x) = 0 is obtained by setting each factor to 0 and then calculating x. The polynomial equation can be solved by factoring. For every factor, a value of 0 should be used. 2x4 = 0; (x - 6) = 0; (x + 1) = 0 the answer to x, please.

It's important to note this even if there are only two genuine roots. The final two roots of this equation, which contain the integer I, are not real because I appears in both of them.

There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.

The complete question is,

Calculate the overall number of roots for each polynomial function using the factored form. f (x) = (x + 2)(x - 1) (x - 1) (x - 1) [x - (4 + 3i)] [x - (4 - 3i)].

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Answer:

x = 73⁰

Step-by-step explanation:

all values show are measures of exterior angles

the sum of all exterior angles for any polgon is 360 degrees

to find 'x':

50 + 48 + 59 + x + x + 58 + 39 = 360

combine like terms:

2x + 214 = 360

2x = 146

x = 73

The formula for the sum of all terms is [tex]S_n[/tex]= n(n+1)/2.

Sum most commonly means the whole of two or greater numbers delivered collectively; see addition. A summation additionally known as a sum is the result of arithmetically adding numbers or portions. A summation constantly includes a whole range of terms. There can be as few as two terms, or as many as one hundred, a thousand, or one million. some summations include infinitely many terms.

In arithmetic, the summation is the addition of a chain of any form of numbers, called addends or summands; the result is their sum or general. the combination of two or extra numbers, magnitudes, portions, or details as decided via or as if via the mathematical technique of addition: The sum of 6 and 8 is 14. a selected combination or overall, specifically with regards to money: The fees came to a giant sum.

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Note that the expression when simplified translates to x = -6 (Option 1)

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.

√(x + 14) - √2x + 5) = 1

To solve this, we must square all elements on both sides of the equation. That is:

√(x + 14)² -  √(2x + 5)² = 1²

⇒ x + 14 + 2x + 5 = 1

Collect like terms to arrive at:

3x = -18

x = -18/3

x = -6

Thus the answer to the above expression is x= -6

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Juan's observations are correct, but his incorrect observation is asymptote: x = 0

An exponential function is a mathematical function of the following form: f(x) = aˣ. where x is a variable, and a is a constant called the base of the function.

Given is a graph of an exponential function.

Juan's observations are :-

Initial value: –3

Base: 3

Asymptote: x = 0

Domain: {x | x > 0}

Range: {y | all real numbers}

Studying the graph, we can say his observations are correct but his comment on Asymptote: x = 0 is wrong because, the equation of the horizontal asymptote of the graph of is y = 0, which is the x-axis.

Other than, Asymptote: x = 0, all his comments are true.

Hence, the incorrect observation is asymptote: x = 0

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The expression is simplified to y⁹/12x². Option A

The index form of a number can be described as that number written as an exponential expression.

It is also seen as a single number that is raised to another number.

Other names for index forms are standard forms and scientific notation.

From the information given, we have that;

3x^⁻⁴y⁵/(2x³y⁻⁷)⁻²

expand the exponential bracket of the denominator by mutiplying the values

3x^⁻⁴y⁵/2x⁶y⁻¹⁴

Now, divide the expression into parts, we have;

3/-4 (x^⁻⁴y⁵/2x⁶y⁻¹⁴)

Since we are finding the quotient, subtract the exponents of the denominator from the numerators, we get;

3× -4(x⁻⁴⁺⁶y⁵⁻¹⁴)

Now, add or subtract the exponential values, we get;

-12(x⁻²y⁻⁹)

y⁹/12x²

Hence, the correct option is y⁹/12x²

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Yes, 2x -3y =7 is a Linear equation as the highest power of the variable is linear which is one. Although it has two variables both have one power.

Linear equations are those which have the highest power of variable as one. But it can have n number of different variables. This given equation is called a linear equation with two variables.

Moreover, any expression is called an equation when the expression is equated to some value means the equation is equal to("=") to some other expression, Number, or Zero. And here 2x+3y is being equated to 7 which is a number, So the given expression is an equation.

However if the variables x and y both came together then it will not be linear as x*y will make the power two as one of x and one of y, Which w=makes the highest power of expression two.

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The equation that has one solution will be 4m + 5 = 25. Then the correct option is B.

The equation that has infinitely many solutions will be 2x + 7 - 2x = 7. Then the correct option is C.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

If the variable and constant get eliminated then the equation has infinitely many solutions. If the variable gets eliminated then the equation has no solution.

7. Let's check option B, then we have

4m + 5 = 25

4m = 20

m = 5

8. Let's check option C, then we have

2x + 7 - 2x = 7

2x - 2x = 7 - 7

The equation that has one solution will be 4m + 5 = 25. Then the correct option is B.

The equation that has infinitely many solutions will be 2x + 7 - 2x = 7. Then the correct option is C.

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The linear function that relates y to x is given as y = 2x

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

From the table, using the points (0, 0) and (1, 2):

y - 0 = [(2 - 0)/(1 - 0)](x - 0)

y = 2x

The linear function that relates y to x is given as y = 2x

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a. On the 13th day the company sold the same number of each player.

b. 2,451 players were sold on that day.

a. The day on which the company sold the same number of players can be calculated by equating the values of y that we have ;

y = 191x-32 and y = -x² + 200x + 20

Equating both, we have;

191x-32 = -x² + 200x + 20

⇒x² -200x + 191x-20-32 = 0

⇒x²-9x-52 = 0

⇒x²-13x + 4x -52 = 0

⇒x(x-13)+4(x-13) = 0

⇒(x-13)(x+4) = 0

⇒x = 13 or -4

as days cannot be negative, so we choose only x = 13

This means that the company sold equal numbers of players on the 13th day.

b. To get the number of players sold on that day, we select any of the y equations and substitute x = 13

Thus, y = 191x -32; 191(13) - 32 = 2,451 players

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The complete question is:

The equation below models the numbers of two portable music players (y) and days after both players were introduced (x).

Music player A: y=191x-32 and music player B: y=-x^2+200x+20

1. on what day(s) did the company sell the same number of each player?

2. how many players were sold on THAT day (use your answer from #1

Answer:

Click or copy the link and that is the answer

https://www.leonschools.net/cms/lib/FL01903265/Centricity/Domain/3141/ch%205%20review%20answers.pdf

Step-by-step explanation:

hope it helps :)

mark me as brainliest!

if not try this (copy or paste)

mehttps://www.leonschools.net/cms/lib/FL01903265/Centricity/Domain/3141/ch%205%20review%20answers.pdf

Answer:MP, NP, MN

Step-by-step explanation:

After solving, the solution of the pair of equation is (-1, 0).

In the given question, we have to find the solution of the system of equations y = 4x + 4 and y = -3x - 3.

The given equations are:

y = 4x + 4.....................(1)

y = -3x - 3.....................(2)

Now putting the value of y from equation 1 to the equation 2

4x + 4 = -3x - 3

Subtract 4 on both side, we get

4x = -3x - 7

Add 3x on both side, we get

7x = -7

Divide by 7 on both side, we get

x = -1

Now putting the value of x in equation 1

y = 4(-1) + 4

y = -4 + 4

y = 0

Hence, the solution of the pair of equation is (-1, 0).

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The complete question is:

What is the solution of the system of equations y = 4x + 4 and y = -3x - 3?

Solving the 2 equations will give us the value of x to be -14 and that of y to be 33.

Here we have two equations

2x + y = 5 and 3x - 2y = 4

Now we will use the substitution method to solve the equations

The first equation is

2x + y = 5

or, y = 5 - 2x                                                         [1]

Let 3x - 2y = 4 be equation 2

Substituting the value obtained in equation [1] in [2] we get

3x - 2(5 - 2x) = 4

or, 3x - 10 + 4x = 4

or, x = -14                                                               [3]

Substituting the value of x obtained in equation [3] to equation [1] we get

y = 5 - 2(-14)

or, y = 5 + 28

or, y = 33

Hence, x = -14 and y = 33

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Complete Question

What is the solution of the equations 2x + y = 5 and 3x - 2y = 4?

Answer:

33.56°

Step-by-step explanation:

Base angles of an isosceles triangle are equal.

Base is bisected by a line from top (vertex) of the triangle straight down to form a right angle.  Base, 100 cm, has 2 equal segments, 50 cm each.

Find h, height of the triangle:

h² = 60² - 50²

h = √1100 = 33.17

sin(f) = 33.17/60 = 0.553

m∠f = sin⁻¹(0.553) = 33.56°

Answer: Linda, Laura, Loraine, and Lila run 2 kilometers altogether.

Step-by-step explanation:

0.5 + 0.5 + 0.5 + 0.5 = 2 km

I hope this helps!

Answer:

i can not see the question

Step-by-step explanation:

please upload a New photo

Answer:

Step-by-step explanation:

A study reveals that young people aged 11 to 14 spend an average of 12.5% ​​of a 24-hour day in front of a screen.

70% of that time is spent in front of the television and the rest is spent in front of a computer.

How many hours and minutes do young people aged 11 to 14 spend on average each day in front of:

(a) a screen? (b) television? (c) a computer?

a screen

The expression for the width is x (b) The perimeter of the rectangle in terms of x is x +8

You should understand that the perimeter of a rectangle is the distance round the rectangle

The given parameters that will help us to understand and solve the question are

Area = length * width

This implies that 2x +24 =4x

Collecting like terms =4 = 4x-2x

2x = 24

Therefore x = 24/2 = 12

b)  The perimeter is = L+W+L+W

Perimeter = 2L+w

Where W =x

Perimeter = 2(2x+24) +2(x)

The perimeter = 4x+48 +2x

Therefore the perimeter = 6x+48 or x+8

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