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3 years ago

From 86 books to 150 books

1 answer:

8 0

150 books-86 books= 64 books.

We originally have 86 books, so the percent of increase is:
64 books/ 86 books* 100%= 74.42%

The percent of increase is 74.42%~

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For which value of c is the line y=3x+c a tangent to the parabola with equation y=x2-5x+7

Mrac [35]

Hello :
the slope of tangent in A(x':y') is : f'(x') =3
f'(x) = 2x-5
2x'-3 =3
2x' = 6
x' = 3
f(3)= 3²-5(3)+7=1
1 =3(3)+c
c =-8

7 0

3 years ago

If the coordinates for C' are (4.5, 4.5), which rule best represents the dilation that was applied to rectangle ABCD to create r

Dmitry_Shevchenko [17]

The dilation of rectangle ABCD to create rectangle A'B'C'D' would change the size of the rectangle

The dilation rule is: (x,y) -> k(x,y)

<h3>How to determine the rule of dilation?</h3>

The coordinates of C' is given as:

C' = (4.5, 4.5)

The coordinate of point C is not given.

So, I will apply a general rule

The general rule of dilation is:

(x,y) -> k(x,y)

Where k represents the scale factor.

Assume that k = 3, the the rule would be
(x,y) -> 3(x,y)

Read more about dilation at:

brainly.com/question/3457976

7 0

2 years ago

Find the cosine of the angle between the planes x+y+z=0 and 4x+3y+z=1. Answer: cosθ=

marta [7]

The angle between the planes is the same as the angle between their normal vectors, which are

n₁ = ⟨1, 1, 1⟩

n₂ = ⟨4, 3, 1⟩

The angle θ between the vectors is such that

⟨1, 1, 1⟩ • ⟨4, 3, 1⟩ = ||⟨1, 1, 1⟩|| ||⟨4, 3, 1⟩|| cos(θ)

Solve for cos(θ) :

4 + 3 + 1 = √(1² + 1² + 1²) √(4² + 3² + 1²) cos(θ)

8 = √3 √26 cos(θ)

cos(θ) = 8/√78

4 0

3 years ago

If $1000 is invested at 8% interest, compounded annually, then after n years the investment is worthan = 1000(1.08)ndollars.(a)

Luba_88 [7]

Answer:

Diverge

Step-by-step explanation:

(a)

1st year: $1000 * 1.08^1 = \$1080$

2nd year: $1000 * 1.08^2 = \$1166.4$

3rd year: $1000 * 1.08^3 = \$1259.71$

4th year: $1000 * 1.08^4 = \$1360.49$

5th year: $1000 * 1.08^5 = \$1469.33$

(b) The sequence is divergent, because if we take the derivative of the function with respect to n year:

$(1000*1.08^n)^{'} = 1000ln(n)*1.08^n$

This is a positive, meaning the slope of the function is positive. If we take the second derivative using product rule

$(1000ln(n)*1.08^n)^{'} = 1000\frac{ln(n)}{n}1.08^n$

This is also positive when n > 0. Therefore, the slope is positive and increasing. This means the sequence diverges.

5 0

3 years ago

In 25 words or fewer, compare the mathematical and algebraic expressions.

DedPeter [7]

Answer:

use own words

Step-by-step explanation:

An expression is just a mathematical phrase. In this tutorial, you'll learn about two popular types of expressions: numerical and algebraic expressions. A numerical expression contains numbers and operations. An algebraic expression is almost exactly the same except it also contains variables.

in mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

5 0

3 years ago