Calcula dos números tales que la suma del primero mas el triple del segundo sea 85 y que la diferencia entre el cuádruple del primero y el doble del segundo sea 102
Sea el primer número = T
Sea el segundo número = U
Las ecuaciones según el enunciado son:
1) T + 3U = 85
2) 4T - 2U = 102
Resolvemos por el MÉTODO DE IGUALACIÓN.
-Despejamos T en las dos ecuaciones.
T + 3U = 85 4T - 2U = 102
T = 85 - 3U 4T = 102 + 2U
T = (85 - 3U)/1 T = (102 + 2U)/4
Igualamos las dos ecuaciones entre sí.
(85 - 3U)/1 = (102 + 2U)/4
Multiplicamos las ecuaciones en cruz.
4 (85 - 3u) = 1 (102 + 2U)
340 - 12U = 102 + 2U
- 12U - 2U = 102 - 340
- 14U = - 238
U = - 238/-14
U = 17
El valor de U lo reemplazamos en uno de los despeje de T para hallar el valor de la misma.
T = (85 - 3U)/1
T = (85 - 3 (17)/1
T = (85 - 51)/1
T = 34/1
T = 34
Rpt. Los números son: 34 y 17
COMPROBAMOS LA SOLUCIÓN.
T + 3U = 85
34 + 3 (17) = 85
34 + 51 = 85
85 = 85
4T - 2U = 102
4 (34) - 2 (17) = 102
136 - 34 = 102
102 = 102
LISTO!
Answer:
The rea of walk way is 32 ft^2.
Step-by-step explanation:
width, w = 8 feet
length, L = 10 feet
width of walkway, d = 2 feet
length of outer, L' = 10 + 2 + 2 = 14 feet
Area of outer, A' = L' x w = 14 x 8 = 112 ft^2
Area of inner, A = L x w = 10 x 8 = 80 ft^2
The area of walkway = A' - A = 112 - 80 = 32 ft^2
The rea of walk way is 32 ft^2.
(2x–5)° + 45° = 180° (sum of consecutive interior angles
=> 2x + 40 = 180
=> 2x = 180– 40
=> x = 140 /2
=> x = 70
The correct answer “the exponent is 4 and the coefficient is -3”
Answer:
1.5*w^2 + 15*w + 36
Step-by-step explanation:
We have to make the width of the portrait be 'w'
in addition to that the height of the frameless portrait (h) = 1.5 times its width, i.e. 1.5 * w
Frame width is 3 inches on all sides.
Therefore the area of the framed portrait is the total area of the portrait plus the area of the frame. The figure representing the above scenario is shown below.
I enclose a figure that allows us to see the problem better, the area of the rectangle ABCD is the area of the framed portrait.
From the figure, we have to:
AB = 3 + w + 3 = w + 6
BC = 3 + h + 3 = h + 6 = 1.5 * 2 +6
We know that the area of the rectangle ABCD is given as the product of the length AB and the width BC. Thus,
Area = (w + 6) * (1.5 * w + 6)
Area = 1.5 * w ^ 2 + 6 * w + 9 * w + 36
Area = 1.5*w^2 + 15*w + 36
That is, the expression for the framed portrait area in terms of the width 'w' is:
1.5*w^2 + 15*w + 36
