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poizon [28]
3 years ago
7

Ben is decorating his home with vases of flowers. He bought glass vases that cost $22 each and ceramic vases that cost $14 each.

The total cost of the vases came to more than $172. Also, Ben bought no more than 10 vases in all.
Which system of inequalities can be used to determine the number of glass vases, x, and the number of ceramic vases, y, that Ben could have bought?
Mathematics
2 answers:
Evgen [1.6K]3 years ago
6 0

Answer:

Step-by-step explanation:

x + y = 10

22x + 14y = 172

-22x - 22y = -220

22x + 14y = 172

-8y = - 48

y = 6 ceramic vases

x + 6 = 10

x = 4 glass vases

Pepsi [2]3 years ago
5 0

Answer:

Step-by-step explanation:

cost of glass vases x=22 $

cost of ceramic vases y=$14

22x+14y >172

or 11x+7y>86

x+y≤10

x   y          11x+7y

1   9            11+63=74

2  8            22+56=78

3  7            33+49=82

4   6           44+42=86

_________________

5   5          55+35=90

6   4          66+28=94

7   3          77+21=98

8  2          88+14=102

9  1          99+7=106

he can buy glass vases in the following combinations .

(x,y)→(5,5),(6,4),(7,3),(8,2),(9,1)

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Let f(x) = 4x-5 and g(x) = 3x, find (f/g)(x). Do not simplify.
masha68 [24]

Answer:

(f/g)(x) = f(x)/g(x) = [4x-5]/[3x]

4 0
3 years ago
A
telo118 [61]

Answer:

1 La longitud de las nuevas cuerdas = 5 metros y 9 metros

2 El costo de las paletas = $ 3

El costo de las gomitas = $ 3

Step-by-step explanation:

1) Sea la primera mitad de la cuerda representada por = a

Deje que la segunda mitad de la parte superior esté representada por = b

a + b = 14 metros

De la pregunta, se nos dice que ok, la mitad es 4 metros más larga que la otra

a = b + 4

Por lo tanto

b + 4 + b = 14 metros

2b + 4 = 14 metros

2b = 14 - 4

b = 10/2

b = 5 metros

a = b + 4

a = 5+ 4

a = 9 metros

Por lo tanto, la longitud de las nuevas cuerdas = 5 metros y 9 metros

2)

Representemos el costo de las paletas = p

Costo de gomitas = g

De la pregunta 2 se nos dice que:

Tu vas a la tienda con un amigo y compras 6 paletas y 2 gomitas. Si tú pagas $ 24

Por tanto: 6p + 2g = 24 ....... Ecuación 1

Tu amigo pide 1 paleta y 10 gomitas. y tu amigo $ 33

p + 10g = 33 ....... Ecuación 2

p = 33 - 10g

Sustituya p por 33 - 10g en la Ecuación 1

6p + 2g = 24 ....... Ecuación

6 (33-10 g) + 2 g = 24

198 - 60 g + 2 g = 24

-58g = 24-198

-58g = - 174

g = -174 / -58

g = $ 3

Para encontrar p

p = 33 - 10g

p = 33 - 10 × 3

p = 33 - 30

p = $ 3

Por lo tant,

El costo de las paletas = $ 3

El costo de las gomitas = $ 3

6 0
2 years ago
A and b are natural numbers. The diameter of cell a is 2.3 , and the diameter of cell b is 2.3 .
Pani-rosa [81]

After clarification we see the respective diameters are

A = 2.3 \times 10^{-a}

B = 2.3 \times 10^{-b}

We're asked about the ratio

A:B =  2.3 \times 10^{-a} :  2.3 \times 10^{-b} = 10^{-a} : 10^{-b} = 10^b : 10^a = 10^{b-a} : 1

Now we can go through the choices.

A. If a = 4 and b = 6, then cell a is 100 times greater than cell b.

A:B=10^{6-4}:1 = 100:1

It would be more proper to say the diameter of cell A is 100 times the diameter of cell B, but yes, this is TRUE.

B. If a = 4 and b = 6, then cell b is 100 times greater than cell a.

FALSE. 10 to the minus 4 is 100 times bigger than 10 to the minus 6, so a is bigger.

C. If a = 4 and b = 6, then cell a is 2 times greater than cell b.

FALSE. We already calculated its 100 times bigger.

D. If a = 4 and b = 6, then cell b is 2 times greater than cell a.

FALSE.


8 0
3 years ago
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Valentin [98]
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&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ 9}}\quad ,&{{ 18}})\quad 
%  (c,d)
&({{ x}}\quad ,&{{ y}})
\end{array}\qquad
%   coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)

\bf \left( \cfrac{x+9}{2}~,~\cfrac{y+18}{2} \right)=\stackrel{\textit{midpoint}}{(14,16)}\implies 
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x+9=28\\
\boxed{x=19}\\
-------\\
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0.76 is the answer
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