Question

7 multiple choice 1 point find the height of a triangle with an area (a) of 35 square inches and base (b) of 7 inches. note: formula for the area of a triangle is a=½bh. 490 inches 2.5 inches 10 inches 122.5 inches 8 multiple choice 1 point find the height of a triangle with an area of 60 square centimeters and a base of 12 centimeters. note: formula for the area of a triangle is a=½bh. 5 cm 6 cm 8 cm 10 cm 9 multiple choice 1 point simplify 2(3x+9)+15 -7x 33 -x or -x +33 24 -x or -x +24 48 -8x or -8x +48 13x +33 or 33 +13x

Explanation:

Question 7

Step1: Substitute values into formula

Given \(A = 35\), \(b=7\), and \(A=\frac{1}{2}bh\). Substitute: \(35=\frac{1}{2}\times7\times h\).

Step2: Solve for \(h\)

First, simplify \(\frac{1}{2}\times7=\frac{7}{2}\). So \(35 = \frac{7}{2}h\). Then \(h=\frac{35\times2}{7}\). Calculate \(35\times2 = 70\), and \(\frac{70}{7}=10\).

Step1: Substitute values into formula

Given \(A = 60\), \(b = 12\), and \(A=\frac{1}{2}bh\). Substitute: \(60=\frac{1}{2}\times12\times h\).

Step2: Solve for \(h\)

Simplify \(\frac{1}{2}\times12 = 6\). So \(60=6h\). Then \(h=\frac{60}{6}=10\).

Step1: Expand the expression

Use the distributive property \(a(b + c)=ab+ac\). For \(2(3x + 9)\), we get \(2\times3x+2\times9=6x + 18\). The original expression \(2(3x + 9)+15-7x\) becomes \(6x+18 + 15-7x\).

Step2: Combine like - terms

Combine the \(x\) terms: \(6x-7x=-x\). Combine the constant terms: \(18 + 15=33\). So the simplified expression is \(33 - x\) (or \(-x + 33\)).

Answer:

C. 10 inches

Question 8