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Ad libitum [116K]

3 years ago

5

A pet store sold 49 siamese cats. If the ratio of siamese cats to house cats sold was 7:4, what is the combined amount of cats s

old?
total cars

1 answer:

S_A_V [24]3 years ago

4 0

Answer:

uyygfhuittyuuuujhhtyyuiiyyuuu

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Question 9 of 25

tresset_1 [31]

Answer:

One approach to this problem is to obtain the graph for the given equation.

We need to find every intersection those functions have with the axis 'x' and 'y'

starting with g(x)

g(x=0)=0-3, first point (0,-3) it iis the crossing point with 'x' axis

g(x)=0=x-3, second point (3,0) it iis the crossing point with 'y' axis

Lets do the same for f(x)

g(x=0)=0, this leads to the first point (0,0) it iis the crossing point with 'x' axis and also, with the 'y' axis

We dont need to find any other, since always y=x

By plotting we have the attached picture

Now you can see that g(x) differs from its parent function in that is shifted 3 units to the right, and also 3 units down.

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

How many sets of three consecutive integers are there in which the sum of the three integers equals their product?

skad [1K]

Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

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

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

----------------

0 4x² - x

- 4x² - 4x

-----------------------

0 + 3x - 3

- 3x - 3

---------------------------

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

4 0

2 years ago

Find the midpoint of the segment with the following endpoints.<br> (2,9) and (8,1)

vazorg [7]

Answer:

$\displaystyle (5,5)$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right<u> </u>

<u>Algebra I</u>

Coordinates (x, y)
Midpoint Formula: $\displaystyle (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Step-by-step explanation:

<u>Step 1: Define</u>

Point (2, 9)

Point (8, 1)

<u>Step 2: Identify</u>

(2, 9) → x₁ = 2, y₁ = 9

(8, 1) → x₂ = 8, y₂ = 1

<u>Step 3: Find Midpoint</u>

Simply plug in your coordinates into the midpoint formula to find midpoint

Substitute in points [Midpoint Formula]: $\displaystyle (\frac{2+8}{2},\frac{9+1}{2})$
[Fractions] Add: $\displaystyle (\frac{10}{2},\frac{10}{2})$
[Fractions] Divide: $\displaystyle (5,5)$

7 0

3 years ago

The denominator of a fraction is 9 more than the numerator. if both the numerator and the denominator are decreased by 1 the res

yarga [219]

X/x+9 (original fraction)

x+1/ x+10 = 4/13

x+1=4 so x=3 and x+10=13 so again x=3

now that you have the value of x, substitute it into the original fraction to get:

3/12

5 0

3 years ago

What is the abscissa of the midpoint of the line segment whose endpoints are (5√2,2√3) and (√2,2√3)

xxMikexx [17]

Let
A------> <span>(5√2,2√3)
B------> </span><span>(√2,2√3)

we know that
</span>the abscissa<span> and the ordinate are respectively the first and second coordinate of a point in a coordinate system</span>
the abscissa is the coordinate x<span>

step 1
find the midpoint
ABx------> midpoint AB in the coordinate x
</span>ABy------> midpoint AB in the coordinate y
<span>
ABx=[5</span>√2+√2]/2------> 6√2/2-----> 3√2
ABy=[2√3+2√3]/2------> 4√3/2-----> 2√3

the midpoint AB is (3√2,2√3)

the answer is
the abscissa of the midpoint of the line segment is 3√2

see the attached figure

3 0

3 years ago

Read 2 more answers