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larisa [96]
3 years ago
14

there were 132 children at the museum on Saturday. on Sunday, there were 61 children. how many children were there on Saturday a

nd Sunday?
Mathematics
2 answers:
NISA [10]3 years ago
8 0

132  children + 61 children = 193 children

Unless some of the children who went on Sunday also went on saturday.

love history [14]3 years ago
3 0

There was 193 children at the museum on Saturday and Sunday.


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You are looking at a 260 foot by 180 foot building lot to subdivide and build two houses. Your town requires 1/2 acre (one acre
Varvara68 [4.7K]

Answer:

You have 1.07 acres in this building lot and you can only build 2 houses.

Step-by-step explanation:

You are looking at a 260 foot by 180 foot building lot to subdivide and build two houses.

We are given that 1 acre = 43,560 square feet.

In this building plot (260 foot by 180 foot), the area is:

260 * 180 = 46,800 square feet

Hence, the number of acres we have in this lot is:

\frac{46800}{43560} = 1.07

Since your town requires 1/2 acre to build a house, the number of houses that you can build on it will be:

\frac{1.07}{\frac{1}{2} } = 1.07 * 2 = 2.14

Since the number of houses can only be whole number, we approximate to nearest whole number ≅ 2 houses.

You have 1.07 acres in this building lot and you can only build 2 houses.

4 0
3 years ago
17. A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find
Pavlova-9 [17]

Answer:

r = 3.74cm

Step-by-step explanation:

Given

Hemisphere

Radius = 7cm

Cone

Height = 49m

Required

Determine the radius of the cone

First, we calculate the volume (V1) of the hemisphere.

V_1 = \frac{2}{3}\pi r^3

Substitute 7 for r

V_1 = \frac{2}{3}\pi * 7^3

V_1 = \frac{2}{3}\pi * 343

V_1 = \frac{686}{3}\pi

Volume (V2) of a cone is:

V_2 = \frac{1}{3}\pi r^2h

Because the lead is cast into a cone, then they have the same volume.

So, we have:

\frac{686}{3}\pi = \frac{1}{3}\pi r^2h

686 =  r^2h

Substitute 49 for h

686 =  r^2 * 49

Divide both sides by 49

r^2 = \frac{686}{49}

r^2 = 14

r = \sqrt{14

r = 3.74cm

<em>Hence, the radius of the cone is 3.74cm</em>

5 0
3 years ago
HELP PLEASE PLEASE :’(
Svet_ta [14]

Practice:

1. A.

2. D. y=5+0.84x-0.03x^2, x>=0

3. B. y=2/x, x>0

Quiz:

1. A C E. (-4,4) (0,0) (6,9)

2. A. y=-1/3x+19/3

3. D. x=2y^2-1, y>=0

4. B. y=3/x^2, x>0

8 0
3 years ago
Find the parity of the following if a and b have different parities.<br> (5a - 3b)(a² + 5b) + 2
sp2606 [1]

9514 1404 393

Answer:

  odd

Step-by-step explanation:

If 'a' and 'b' have different parity, the result has odd parity.

__

<u>Assume a=odd, b=even</u>

  (5·odd -3·even) = odd

  (odd^2 +5·even) = odd

  (odd)(odd) +2 = odd

__

<u>Assume a=even, b=odd</u>

  (5·even -3·odd) = odd

  (even^2 +5(odd)) - odd

  (odd)(odd) +2 = odd

_____

The attached verifies this with numbers.

4 0
2 years ago
A) x+4
KiRa [710]

Answer:

  a) f(x) = x(x +4)(x -5)

  b) g(x) = (x -6)(x -2)(x^2 +2x +4)

  c) h(x) = (x +7)(x -3)(x -4)

Step-by-step explanation:

To factor completely generally means to find binomial factors that have integer constants. It is helpful to be familiar with the idea of "greatest common divisor", and what the product of two binomial factors looks like. In particular, there are a couple of special forms that can be useful. One of them is the difference of squares. Another is the difference of cubes.

  a² -b² = (a -b)(a +b)

  a³ -b³ = (a -b)(a² +ab +b²)

In the general case, the product of binomial factors is ...

  (x -a)(x -b) = x² -(a+b)x +ab

The coefficient of the x-terms is the sum of the binomial constants; the constant term is their product.

__

<h3>a)</h3>

The given cubic has no constant term. That is, every term has a factor of x, so that is one of the factors.

  f(x) = (x)(x^2 -x -20)

The given factor of x+4 tells you the constant in the other factor is -20/4 = -5.

  f(x) = x(x +4)(x -5)

__

<h3>b)</h3>

We observe that the ratios of pairs of coefficients are ...

  1 : -6 and -8 : 48 = 1 : -6 . . . . . pairs of coefficients have the same ratio

That means we can factor each pair of terms:

  g(x) = x^4 -6x^3 -8x +48

  g(x) = x^3(x -6) -8(x -6) = (x^3 -8)(x -6)

Using the difference of cubes formula, the factorization is ...

  g(x) = (x -2)(x^2 +2x +4)(x -6)

Note: the quadratic factor has irrational complex roots.

__

<h3>c)</h3>

The quadratic factor of this cubic can be found by dividing it by the given factor. That is most easily accomplished using synthetic division. Explaining how to do that is beyond the scope of this answer. The first attachment shows that the resulting factorization is ...

  h(x) = (x +7)(x^2 -7x +12)

The quadratic is factored by finding two factors of 12 that have a sum of -7. The positive sign of their product (12) tells you both will be negative.

  12 = (-1)(-12) = (-2)(-6) = (-3)(-4)

The pair of factors with a sum of -7 is -3 and -4. These are the constants in the remaining binomial factors:

  h(x) = (x +7)(x -3)(x -4)

_____

<em>Additional comment</em>

A graphing calculator can be an invaluable tool for factoring higher-degree polynomials. The graph of h(x) in the second attachment, for example, shows you the zeros are -7, 3, 4, so the factors are (x+7)(x-3)(x-4).

For a function like g(x), you can find the real zeros from the graph, then you can find the quadratic by factoring out the associated factors. The vertex of the quadratic curve helps you write the expression for that. (see the third attachment)

  g(x) = (x -2)(x -6)((x +1)^2 +3) . . . . quadratic factor in vertex form

  g(x) = (x -2)(x -6)(x^2 +2x +4)

4 0
2 years ago
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