John runs 4 miles in 30 minutes. at the same rate, how many miles would he run in 48 minutes?

The student spends approximately 40% of her total education costs on her books, represented as 0.4 in decimal form.

The student's total education costs are the sum of the tuition fees ($700) and the cost of her books ($400). This comes to a total of $700 + $400 = $1100. The percent of the total education cost that is spent on books is then given by the cost of the books divided by the total cost, or $400 / $1100. When expressed as a decimal, this works out to be approximately 0.36 or 36%, but since we want to the nearest tenth of a percent in decimal form, it becomes 0.4 or 40% to the nearest tenth. Therefore, the student spends 40% of her total education costs on her books.

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Hey there! :)

Perpendicular to y = -3x + 5 ; passes through (2, 6).

Our slope is -3. We know this because it is in the "m" position from slope-intercept form. However, since our equation we're looking for is perpendicular to our given one, we must find the negative reciprocal of -3.

A negative reciprocal is simply a number that is flipped and either given a negative or gets a negative removed.

So the negative reciprocal of -3 is 1/3. This means that our new slope is 1/3.

Now, using point-slope form ( y-y₁=m(x-x₁) ), our new slope (1/3) & (2, 6) , let's find our new equation!

y-y₁=m(x-x₁) y - (6) = 1/3(x - 2)

Simplify.

y - 6 = 1/3x - 2/3

~Hope I helped!~

a) The ratio of new books to used books 5:6.

b) The ratio of used books to all books is 6:11.

The ratio is defined as the representation of one number with respect to the other number or one number is how many times the other number.

The ratio will be calculated as follows:-

a) Since 5 of the books are new, that means that the other books are used. So, there are 11-5=6. The ratio would be 5:6.

b) We know that the number of used books is 6. The ratio is 6:11.

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Answer:

$176·1.06 = $186.56

Therefore, the total amount that Christa paid was $186.56.

Answer:

  use logarithms

Step-by-step explanation:

Taking the logarithm of an expression with a variable in the exponent makes the exponent become a coefficient of the logarithm of the base.

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You will note that this approach works well enough for ...

  a^(x+3) = b^(x-6) . . . . . . . . . . . variables in the exponents

  (x+3)log(a) = (x-6)log(b) . . . . . a linear equation after taking logs

but doesn't do anything to help you solve ...

  x +3 = b^(x -6)

There is no algebraic way to solve equations that are a mix of polynomial and exponential functions.

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Some functions have been defined to help in certain situations. For example, the "product log" function (or its inverse) can be used to solve a certain class of equations with variables in the exponent. However, these functions and their use are not normally studied in algebra courses.

In any event, I find a graphing calculator to be an extremely useful tool for solving exponential equations.

To solve an expression with variables in the exponents, you apply the rules of exponents.

When solving an expression with variables in the exponents, you need to apply the rules of exponents. Here are the key rules:

For example, (27x^3)(4x^2) can be simplified to 108x^5.

You can find the corresponding parts of two congruent triangles by aligning them perfectly on top of each other.

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔDEF

Now , when the triangles are aligned perfectly on top of each other ,

They are corresponding and the and the measures of the angles are same

And , the measure of the legs of the triangles will also be congruent

Hence , the corresponding parts are same

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This question is based on the concept of solving a two linear equation.

Thus, the cost of one bath towel is $9 and one hand towel is $4.

Given:

Number of  ordered of hand towels is 27 and bath towels is 48 and for a bill of $540 for the first hotel.

Number of  ordered of hand towels is 50 and bath towels is 24 and for a bill of $416 for the other hotel.

We need tom determined the cost of one hand towel and one bath towel.

According to the question:

Let the  hand towels be h  and bath towels be b.

Therefore, equation of first hotel is

27h + 48b = 540........(1)

Equation of second hotel is

50h + 24b = 416.........(2)

Now, solving both equation for h and b.

Equation (2) multiplying by -2.

-100 h -48 b = - 832..................(3)

Now, solve equation (1) and (3)

27h + 48b = 540  and -100h - 48b = - 832

⇒ -73 h = - 292

⇒ h = -292 / -73

⇒ h = 4

Therefore, the cost of 1 hand towel is $4.

Now, putting the value of h = 4 in equation (1).

⇒ 27(4) + 48b = 540

⇒ 108 + 48b = 540

⇒ 48b = 540 - 108

⇒ 48b = 432

⇒ b = 432/48

⇒ b = 9

Therefore, the cost of 1 bath towel is $9.

Thus, the cost of one bath towel is $9 and one hand towel is $4.

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The numerical expression 4[(6 - 1) + 3(5 - 2)] evaluates step-by-step following the order of operations. Operations within the parentheses are performed first, followed by multiplication, resulting in a final answer of 56

The student's question involves evaluating a numerical expression, which is a concept in mathematics. We have the expression 4[(6 - 1) + 3(5 - 2)] and want to calculate its value step by step following the order of operations:

Hence, the correct answer to the expression is 56

Answer:

The simplified form of the provided expression is [tex]9.5m^2+1.5n[/tex].

Step-by-step explanation:

Consider the provided expression.

[tex]7m^2+6.5n-4n+2.5m^2-n[/tex]

Arrange the like terms together.

[tex]7m^2+2.5m^2+6.5n-4n-n[/tex]

Add and subtract the like terms as shown below:

[tex]9.5m^2+1.5n[/tex]

Thus, the simplified form of the provided expression is [tex]9.5m^2+1.5n[/tex].

Answer:

The price of 1 gallon of gasoline is $2.90.

Step-by-step explanation:

You buy 8 gallons of gasoline at p dollars per gallon and pay $23.20.

We get the expression:

[tex]8p=23.20[/tex]

We can find one gallon as: p=[tex]\frac{23.20}{8}[/tex]

=> p = $2.90

Hence, the price of 1 gallon of gasoline is $2.90.

Answer:

x=12

Step-by-step explanation:

↓↓↓↓↓↓↓↓↓↓↓↓

Multiplication property of equality is multiply both sides of an equation by the same number does not change the equation.

[tex]\frac{x}{2}=6[/tex]

multiply two both sides

[tex]\frac{2x}{2}=6*2[/tex]

simplify

[tex]6*2=12[/tex]

[tex]12/2=6[/tex]

[tex]12/6=2[/tex]

[tex]2*6=12[/tex]

[tex]x=12[/tex]

Hope this helps!

Answer:

103 degrees

Step-by-step explanation:

Bisectors means you make a line in the middle splitting the angle in half. So you divide A by 2 to get 29 and B to get 48. Then you add them to get 77. And now you only need point m's angle. 180-77 is 103 so the answer they are looking for is 103.

Answer:

75°

Step-by-step explanation:

The angle is our unknown, so we will call it x.  If x is the angle, then its complement is 90 - x (complementary angles add up to 90).  The word "is" means "equals", and "5 times" is multiplying the complementary by 5:

x = 5(90 - x) so

x = 450 - 5x

Combine like terms to get

6x = 450 so

x = 75

The other angle, the complement to that angle, is 90 - 75 = 15

The larger angle is 75°

Answer: [tex]y=\dfrac{-1}{2}(x-2)[/tex]

Step-by-step explanation:

The equation of a line passing through points (a,b) and (c,d) is given by :-

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

Given : The points from which line is passing :  (-6,4) and (2,0)

Then , the equation of the line, in point slope  form, that passes through  (-6,4) and (2,0)will be :-

[tex](y-(0))=\dfrac{4-0}{-6-2}(x-2)\\\\\Rightarrow\y=\dfrac{4}{-8}(x-2)\\\\\Rightarrow\ y=\dfrac{-1}{2}(x-2)[/tex]