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zhuklara [117]
3 years ago
13

tim has a large collection of books. the number of paperback books he owns is three less than four times the number of hardcover

books, in total tim had 447 books how many hardcover books does he own
Mathematics
2 answers:
grandymaker [24]3 years ago
8 0

Answer:

tim has 90 hardcover books

Step-by-step explanation:

yan [13]3 years ago
6 0
We can solve this by setting up a couple of equations.

Let's allow x to represent the number of paperbacks Tim owns, and allow y to represent the number of hardcover books he owns.

Using the information in the question, we can write the equations:

1) x = 4y-3
2) x+y=447

Let's rearrange equation 1 so that it is in standard form:

x-4y=-3

And then let's multiply equation 2 by 4 so that we can cancel out y when we solve the system of equations:

4(x+y=447)
4x+4y=1,788

Then we can add the two equations and solve for x:

   1)  x-4y=-3
+ 2) 4x+4y=1,788
------------------------------------
5x=1,785

x=357

So now we now the number of paperback books Tim has is 357. Let's plug this into one of the original equations to solve for the number of hardcover books (y):

357+y=447
y=90

And now we know that Tim owns 90 hardcover books.
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What is an equation of a line which passes through (6,9) and is perpendicular to the line whose equation is 4x − 6y = 15?
Svetllana [295]

<u>Given:</u>

The equation of the line passes through the point (6,9) and is perpendicular to the line whose equation is 4 x-6 y=15

We need to determine the equation of the line.

<u>Slope</u>:

Let us convert the equation to slope - intercept form.

-6 y=15-4x

   y=\frac{2}{3}x-\frac{5}{2}

From the above equation, the slope is m_1=\frac{2}{3}

Since, the lines  are perpendicular, the slope of the line can be determined using the formula,

m_1 \cdot m_2=-1

  \frac{2}{3} \cdot m_2=-1

      m_2=-\frac{3}{2}

Therefore, the slope of the equation is m=-\frac{3}{2}

<u>Equation of the line:</u>

The equation of the line can be determined using the formula,

y-y_1=m(x-x_1)

Substituting the point (6,9) and the slope m=-\frac{3}{2} in the above formula, we get;

y-9=-\frac{3}{2}(x-6)

Simplifying the terms, we get;

2(y-9)=-3(x-6)

2y-18=-3x+18

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3 0
3 years ago
Please help!!
timofeeve [1]

Answer:

y = 2/3x

Step-by-step explanation:

So we know, when lines are perpendicular that they share the same slope. The slope in the equation of y = 2/3x + 7 is 2/3x. So, we have our slope. Now, we just need to find our b. We plug in the point that you gave us into the equation y = mx + b.

3 = 2/3(2) + b

we multiply the denominator 3 by 2, then divide that by the numerator 2.

3 = 3 + b

subtract 3 from itself and from the opposite side of the equal side 3.

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in the end, there is no b for this equation. Our answer is

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ella [17]

Answer:

m∠Q = 61°

m∠S = 61°

m∠R = 58°

Step-by-step explanation:

Since we have an isosceles triangle, we know that ∠Q and ∠S are congruent.

Step 1: Definition of isosceles triangle

2x + 41 = 3x + 31

41 = x + 31

x = 10

Step 2: Find m∠Q

m∠Q = 2(10) + 41

m∠Q = 20 + 41

m∠Q = 61°

Step 3: Find m∠S

Since m∠Q = m∠S,

m∠S = 61°

Step 4: Find m∠R (Definition of a triangle)

Sum of angles in a triangle adds up to 180°

m∠R = 180 - (61 + 61)

m∠R = 180 - 122

m∠R = 58°

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