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zlopas [31]
3 years ago
11

a rectangular picture measuring 5 in. by 7 in. is surrounding by a frame with uniform width x. Write a quadratic function in sta

ndard form to show the combined area of the picture and frame.​
Mathematics
2 answers:
9966 [12]3 years ago
8 0

Answer:

(4x² + 24x + 35) in²

Step-by-step explanation:

(5+2x)(7+2x)

35 + 14x + 10x + 4x²

4x² + 24x + 35

ale4655 [162]3 years ago
7 0

Answer: A(x) = 4x² + 24x + 35

Step-by-step explanation:

Let x represent the width of the rectangular frame.

The formula for determining the area of a rectangle is expressed as

Area = length × width

The measurement of the rectangular picture is 5 in. by 7 in.

If the width is 5 inches, then the combined width of the picture and frame is 5 + x + x = (5 + 2x) inches

The combined length would be

7 + x + x = (7 + 2x) inches

Therefore, a quadratic function in standard form to show the combined area of the picture and frame would be

(5 + 2x)(7 + 2x)

35 + 10x + 14x + 4x²

A(x) = 4x² + 24x + 35

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Answer:

(2, 12)

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

If we assume that we have 3 groups and on each group from j=1,\dots,n_j we have n_j individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2  

SS_{between=Treatment}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2  

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2  

And we have this property  

SST=SS_{between}+SS_{within}  

The degrees of freedom for the numerator on this case is given by df_{num}=k-1=3-1=2 where k =3 represent the number of groups.  

The degrees of freedom for the denominator on this case is given by df_{den}=df_{between}=N-K=15-3=12.  

And the total degrees of freedom would be df=N-1=15 -1 =14  

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Camilo practica tiro al blanco. En cada disparo acertado puede obtener 5, 8, o 10 puntos. En su última práctica, su puntuación t
Radda [10]

Answer:

20 disparos

Step-by-step explanation:

Primera etapa es de determinar cuantos tiros de Camilo acertaron al blanco.

Sabemos que en su última práctica, obtuvo 99 puntos con una mezcla de 5, 8 y 10 puntos.  Eso puedo se exprimir así:

5x + 8y + 10x = 99

Sabemos también que el obtuvo tantos tiros de 8 puntos que de 10 puntos, entonces

y = z

Podemos mezclar las 2 ecuaciones y substituir y por z:

5x + 8y + 10y = 99

5x +18y = 99

Una ecuación, dos variables... no es fácil... pero son números pequeños y se puede intentar soluciones.  Entonces, cuantas veces podemos multiplicar 5 y 18 para obtener 99?

El más simple es de hacer la tabla de multiplicación de 18 y ver cual número nos deja con un multiple de 5.

18 x 1 = 18 (99 - 18 = 81, no un multiple e 5)

18 x 2 = 36 (99 - 36 = 63, no un multiple de 5)

18 x 3 = 54 (99 - 54 = 45, SI, un multiple de 5)

18 x 4 = 72 (99 - 72 = 27, no un multiple de 5)

18 x 5 = 90 (99 - 90 = 9, no un multiple de 5)

Entonces, sabemos que y = 3 y z = 3

5x + 18 (3) = 99

5x + 54 = 99

5x = 45

x = 9

El tiró 9 veces por 5 puntos, 3 veces por 8 puntos y 3 veces pour 10 puntos.

En total tiró 15 veces.

Si acertó 75% (3/4) de las veces, cuantos tiros total?

\frac{15}{3/4} = \frac{15 * 4}{3} = 20

Camilo tiró 20 veces en total.

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