Anyone help please I’m wasting my points for no reason
1 answer:
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Answer:
The graph of the system of equations solves the equation x + 2 = 2x - 7 ⇒ C
Step-by-step explanation:
<em>Let us revise some important notes about the slope and y-intercept of a line</em>
The form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept
- If the line has a positive slope then its direction will be to the right
- If the line has a negative slope then its direction will be to the left
The y-intercept (0, b) is the the point of intersection between the line and the y-axis
- If the line cuts the y-axis at a point above the x-axis, then b is positive
- If the line cuts the y-axis at a point down the x-axis, then b is negative
<em>To solve our question without any calculation, let us find the direction of the slopes and their y-intercepts</em>
∵ The direction of the blue line is to the left
→ That means m in the equation is negative
∴ Its slope is negative
∵ The line intersects the y-axis at point (0, 2)
→ That means b in the equation = 2
∴ The number in the equation is 2
→ Look at the answer we have two answers have negative slope and
y-intercept 2 in the left hand side ⇒ C and D
∴ The equation of the blue line is represented by the left side x + 2
→ that means the equation of the red line is represented by the right side
∵ The direction of the red line is to the right
→ That means m in the equation is positive
∴ Its slope is positive
→ Only C has a positive slope in the right side
∴ The equation of the red line is represented by 2x - 7
The graph of the system of equations solves the equation x + 2 = 2x - 7
<u><em>Another way:</em></u>
<em>You can solve each equation to find the value of x, then substitute it in one side of the equation to find y , the values of x and y must be (4, 1) as the point of intersection of the two lines in the graph</em>
Answer:
SA = 1244.64 square centimeters
Step-by-step explanation:
From the attached figure
The formula of the surface area of the prism is SA = 2B + PH, where
- B is the area of its base
- P is the perimeter of its base
- H is the distance between its bases
The base of the prism is a regular hexagon with side 8 cm
If you join each vertex of the hexagon with its center you will form 6 congruent triangles with base 8 cm and height 6.93 cm
The area of the hexagon = 6 × area of a triangle
∵ The base of the triangle = 8 cm
∵ Its height = 6.93 cm
- The formula of the area of a triangle is A = × base × height
∴ Area of the triangle = × 8 × 6.93 = 27.72 cm²
- Lets find the area of the hexagon
∴ The area of the hexagon = 6 × 27 .72 = 166.32 cm²
∴ B = 166.32 cm²
The formula of the perimeter of the regular hexagon is P = 6 × s, where s is the length of its side
∵ The side of the hexagon is 8 cm
∴ P = 6 × 8
∴ P = 48 cm
∵ The distance between the two bases is 19 cm
∴ H = 19 cm
Substitute the values of B, P and H in the formula of the surface area above
∵ SA = 2(166.32) + (48)(19)
∴ SA = 332.64 + 912
∴ SA = 1244.64 square centimeters