Question

1. what is the value of x? round to the nearest tenth, if necessary.

a. ( x approx 1.5 )
b. ( x approx 4.4 )
c. ( x approx 13.5 )
d. ( x approx 19.8 )

1. a rectangular prism garbage can is 15 inches long, 12 inches wide and 30 inches tall. to the nearest tenth, what is the approximate length of its longest diagonal?

a. ( approx 57.0 ) inches
b. ( approx 35.6 ) inches
c. ( approx 30.0 ) inches
d. ( approx 7.5 ) inches

1. what is the length of c on the graph below? round to the nearest tenth, if necessary.

a. ( approx 7.6 )
b. 10
c. 16
d. 58
for numbers ( 10a - 10e ), circle yes or no to indicate if the expression could be used to find the approximate distance between the points on the graph.
10a. ( 5^{2}+6^{2} )
10b. ( sqrt{5^{2}+6^{2}} )
10c. ( |-3 - 3|^{2}-|2+( - 3)|^{2}=c^{2} )
10d. ( |-3 - 3|^{2}+|2-( - 3)|^{2}=c^{2} )
10e. ( |3-( - 3)|^{2}+|-3 - 2|^{2}=c^{2} )

1. what is the approximate distance between the given two points? round to the nearest tenth, if necessary.

( (3,5) ) and ( (-1,2) )
a. ( approx 3.6 )
b. 5
c. ( approx 7.3 )
d. 8

Explanation:

7.

Step1: Aplicar el Teorema de Pitágoras

En un triángulo rectángulo, \(a^{2}+b^{2}=c^{2}\). Aquí, \(c = 10\), \(a=9\) y \(b = x\). Entonces \(x^{2}+9^{2}=10^{2}\).

Step2: Despejar \(x\)

\(x^{2}=10^{2}-9^{2}\)
\(x^{2}=100 - 81\)
\(x^{2}=19\)
\(x=\sqrt{19}\approx4.4\)

Step1: Aplicar la fórmula para la diagonal de un prisma rectangular

La fórmula para la diagonal \(d\) de un prisma rectangular con longitud \(l\), ancho \(w\) y altura \(h\) es \(d=\sqrt{l^{2}+w^{2}+h^{2}}\). Aquí, \(l = 15\), \(w = 12\) y \(h=30\).

Step2: Calcular \(d\)

\(d=\sqrt{15^{2}+12^{2}+30^{2}}=\sqrt{225 + 144+900}=\sqrt{1269}\approx35.6\)

Step1: Encontrar los catetos del triángulo rectángulo

Los catetos del triángulo rectángulo son \(a = 3\) y \(b = 7\) (contando cuadrados en la gráfica).

Step2: Aplicar el Teorema de Pitágoras

\(c=\sqrt{a^{2}+b^{2}}=\sqrt{3^{2}+7^{2}}=\sqrt{9 + 49}=\sqrt{58}\approx7.6\)

Answer:

B. \(x\approx4.4\)

8.