Identify this prism and describe it using the following vocabulary terms: base, edge, face, and vertex.

90° clockwise rotation<br> Help please

maria [59]

Answer:

E' (-2,5)

F' (-3,1)

G' (-2,-1)

H' (0,3)

Step-by-step explanation:

The rule for 90 degree clockwise rotation is (h,k) -> (k,-h). This means flip the x-value's sign and then switch x and y's position. For example E (-5,-2), first flip x's sign (5,-2) and then switch x and y's places (-2,5).

4 0

3 years ago

Find the area of the region bounded by the line y=3x-6 and line y=-2x+8.

Vikentia [17]

Answer:

A = 12/5 units

Step-by-step explanation:

USING ALGEBRA:

We can find the intersection point between these two lines;

y = 3x - 6

y = -2x + 8

Set these two equations equal to each other.

3x - 6 = -2x + 8

Add 2x to both sides of the equation.

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

Multiply and simplify.

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6

Add 6 both sides of the equation.

6 = 3x

Divide both sides of the equation by 3.

x = 2

Set the second equation equal to 0.

(II) 0 = -2x + 8

Add 2x to both sides of the equation.

2x = 8

Divide both sides of the equation by 2.

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a Triangle:

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = (1/2) · (2) · (12/5)

Multiply and simplify.

A = 12/5

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

3 0

3 years ago

Which system of linear inequalities is graphed?

ANEK [815]

To determine the system of inequality that has been graphed, we need to be very smart.

Observe that all the equations are the same.

Also note that all the lines are solid. This should tell you that the inequities should involve.

$\ge \:or\: \le$

Therefore the answer is between option A and B.

So we choose a point in the solution region to discriminate between A and B.

Let us choose the origin since that is easy to evaluate.

We substitute into option A to get.

$y\le 3x-1\:and\: x+ 3y \ge 6$

$0\le 3(0)-1\:and\: 0+ 3(0) \ge 6$

$0\le -1\:and\: 0\ge 6$

The above statements are false

We now substitute into option B

$y\ge 3x-1\:and\: x+ 3y \le 6$

$0\ge 3(0)-1\:and\: 0+ 3(0) \le 6$

$0\ge-1\:and\: 0 \le 6$

Both statements are true, therefore the correct answer is option B.

8 0

3 years ago

2ln(4x –7) –1=11 Solve for x to the nearest 100th

ArbitrLikvidat [17]

2(4x - 7) -1 = 11
8x - 14 -1 = 11
8x - 15 = 11
+ 15 + 15
8x = 26
/8 /8
x = 3. 25 ------> Rounded: 3.30

3 0

3 years ago

What are the key aspects of the graph of f(x) = x2 – b2, where b is a real number?

netineya [11]

Given equation is $f\left(x\right)=x^2-b^2$ .

Now we need to find about what are the key aspects of the graph of $f\left(x\right)=x^2-b^2$ , where b is a real number.

We know that square of any number is always positive.

then $b^2$ must be a positive number.

So that means for any real number b, as the value of b increases then graph of f(x) shifts downward by $b^2$ units as compared to the graph of parent function $f\left(x\right)=x^2$

3 0

3 years ago

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