Use A Diagram To Show That (3x+1)(x+2) Is Equivalent To 3x2+7x+2. Show Your Work.
Is (x+4) Equivalent To 2x2+8x+8? Explain Or Show Your Reasoning.
Answers
Answer:
1) Please find attached the diagram showing the answer to the question
The area of the diagram is (3x + 1)(x + 2) = 3 dark green squares + 7 light green squares + 2 Plain squares
∴ (3x + 1)(x + 2) = 3·x² + 7·x + 2
2) When x = 1, (1 + 4)² = 25 ≠ 2 × 1² + 8 × 1 + 8 = 18
Therefore, (x + 4)² is not equivalent to 2·x² + 8·x + 8
Step-by-step explanation:
1) In the attached diagram, we have;
For x = 1
(3x + 1)(x + 2) = (3 + 1)(1 + 2)
Therefore, the length of the sides of the rectangle are;
Height = 4, and Width = 3
For x = 1, x² = 1² = 1
∴ 3·x² = 3, 7·x = 7 × 1 = 7, and 2 = 2
Therefore, from the diagram, we have;
The area = (3x + 1)(x + 2) = 3 dark green squares + 7 light green squares + 2 Plain squares
∴ (3x + 1)(x + 2) = 3·x² + 7·x + 2
The diagram for when x = 3 is also included
2) For (x + 4)², we have;
When x = 1, (x + 4)² = (1 + 4)² = 25
However;
When x = 1, 2·x² + 8·x + 8 = 2 × 1² + 8 × 1 + 8 = 18
Therefore;
(x + 4)² is not equivalent to 2·x² + 8·x + 8
1) Please find attached the diagram showing the answer to the question
The area of the diagram is (3x + 1)(x + 2) = 3 dark green squares + 7 light green squares + 2 Plain squares
∴ (3x + 1)(x + 2) = 3·x² + 7·x + 2
2) When x = 1, (1 + 4)² = 25 ≠ 2 × 1² + 8 × 1 + 8 = 18
Therefore, (x + 4)² is not equivalent to 2·x² + 8·x + 8
Step-by-step explanation:
1) In the attached diagram, we have;
For x = 1
(3x + 1)(x + 2) = (3 + 1)(1 + 2)
Therefore, the length of the sides of the rectangle are;
Height = 4, and Width = 3
For x = 1, x² = 1² = 1
∴ 3·x² = 3, 7·x = 7 × 1 = 7, and 2 = 2
Therefore, from the diagram, we have;
The area = (3x + 1)(x + 2) = 3 dark green squares + 7 light green squares + 2 Plain squares
∴ (3x + 1)(x + 2) = 3·x² + 7·x + 2
The diagram for when x = 3 is also included
2) For (x + 4)², we have;
When x = 1, (x + 4)² = (1 + 4)² = 25
However;
When x = 1, 2·x² + 8·x + 8 = 2 × 1² + 8 × 1 + 8 = 18
Therefore;
(x + 4)² is not equivalent to 2·x² + 8·x + 8
Answer: 1) Please find attached the diagram showing the answer - 1
Answer: 1) Please find attached the diagram showing the answer - 1
Answer: 1) Please find attached the diagram showing the answer - 2
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1
3x + -y = 24
Answers
Answer:
The following are the LINEAR functions.
[tex]2x\:+\:4\:=\:3x\:-\:8[/tex][tex]y = 3x - 2[/tex][tex]1[/tex][tex]3x\:+\:-y\:=\:24[/tex]Step-by-step explanation:
We know that linear functions are the equations with a straight line graph in an XY plane.
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So, from the given expressions we can determine that:
1) [tex]y^2=\:5x\:+2[/tex]
[tex]y^2=\:5x\:+2[/tex] is NOT a linear function because the power of y is 2, hence the graph won't be a straight line. Therefore, it is not a linear function
2) [tex]2x\:+\:4\:=\:3x\:-\:8[/tex]
[tex]2x\:+\:4\:=\:3x\:-\:8[/tex]
[tex]x=12[/tex]
This is a linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1
3) [tex]y = 3x - 2[/tex]
[tex]y = 3x - 2[/tex] is a linear function because it is of the form [tex]f(x)=mx+b[/tex] and the power of its x and y variables is 1. Hence, the function has a straight line graph.
4) [tex]y\:+\:x^2\:=\:12[/tex]
[tex]y\:+\:x^2\:=\:12[/tex] is NOT a linear function because the power of x is 2, hence the graph won't be a straight line. Therefore, it is not a linear function.
5) [tex]y\:=\:x^2\:+\:2x[/tex]
[tex]y\:=\:x^2\:+\:2x[/tex] is NOT a linear function because the power of x is 2, hence the graph won't be a straight line. Therefore, it is not a linear function.
6) [tex]1[/tex]
[tex]1[/tex] is a constant function and a constant function is also considered linear in this context, as it is a polynomial of degree [tex]0[/tex] or is the [tex]0[/tex] polynomial.
7) [tex]3x\:+\:-y\:=\:24[/tex]
[tex]3x\:+\:-y\:=\:24[/tex] is a linear function as the power of its x and y variables is 1. Hence, the function has a straight line graph. Therefore, it is a linear function.
In a summary, the following are the LINEAR functions.
[tex]2x\:+\:4\:=\:3x\:-\:8[/tex][tex]y = 3x - 2[/tex][tex]1[/tex][tex]3x\:+\:-y\:=\:24[/tex]Explain the Error
Find the error in the solution, and then solve it correctly.
7x + 21 + 6x = 4
7x + 21 = -2
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7
(select) was subtracted from the left side, but (select) was subtracted from the right side. The
Subtraction Property of Equality states that you can subtract the same number from each side and the
equation will remain true. But 6x and 6 are not the same number (unless x is (select)).
X =
Answers
Answer:
Step-by-step explanation:
7x+21+6x=4 combine terms
13x+21=4 subtract 21 from both sides
13x= -17 divide by 13
x= -17/13
What’s the answer to this? Thanks!
Answers
Answer:
D
Step-by-step explanation:
I used a triangle calculator I'm not really sure how to calculate it by hand. if the angle of sides 4 and 15 is set to 1 then the min is 11.33 and if the andle of sides 4 and 15 are set to 179 then the max is 18.99952
Sorry if this isnt enough, but i am sure.
Answer:
D. 11 < x < 19.
Step-by-step explanation:
The third side x is between 11 and 19 cm.
Consider sides AB (length 4) and BC (length 15) of the triangle.
Consider the angle between AB and BC is slightly less than 180 degrees. To get from point A to point C, we have to travel almost the entire length of A to C, which is from A to B and then B to C, so a bit less than 19 cm.
Consider the angle between AB and BC is slightly more than 0 degrees. To get from point A to point C, we subtract the length of AB (because we're already further along BC), so 15 - 4, a bit greater than 11.
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Answers
Combine like terms
6x - 15 = 111
Add 15 to each side.
Evaluate
6x = 126
x = 21
Plug x back into the equation for angle EFG.
EFG = 3x -20
3(21) - 20
EFG = 43 degrees
Answer:
[tex] m\angle EFG =43\degree[/tex]
Step-by-step explanation:
[tex] m\angle EFG +m\angle GFH = m\angle EFH\\\\
(3x-20)\degree + (3x+5)\degree =111\degree \\\\
(3x-20+3x +5)\degree =111\degree \\\\
(6x-15)\degree =111\degree \\\\
(6x-15) =111 \\\\
6x = 111 + 15\\\\
6x = 126\\\\
x = \frac{126}{6}\\\\
x = 21\\\\
m\angle EFG = (3x-20)\degree\\\\
m\angle EFG = (3\times 21-20)\degree\\\\
m\angle EFG = (63-20)\degree\\\\
m\angle EFG =43\degree\\[/tex]