Write an equation for the line shown pictured in the graph.

Question 1- explain how Sheldon immediately knew howard was incorrect?

Dmitrij [34]

Answer:

Part 1) In the procedure

Part 2) In the procedure

Step-by-step explanation:

Part 1) Observing the graph

The roots are x=-1/2 and x=4

Remember that, the roots are the x-values when the value of y is equal to zero (the x-intercepts)

That's why Sheldon immediately realizes Howard's solution is incorrect

Part 2) we have

$y=2x^{2}-7x-4$

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

equate the equation to zero

$2x^{2}-7x-4=0$

so

$a=2\\b=-7\\c=-4$

substitute

$x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(2)(-4)}} {2(2)}$

$x=\frac{7(+/-)\sqrt{49+32}} {4}$

Howard's error is in this step, is wrong with the sign of the number 7, is positive instead of negative

$x=\frac{7(+/-)\sqrt{81}}{4}$

$x=\frac{7(+/-)9}{4}$

$x=\frac{7(+)9}{4}=4$

$x=\frac{7(-)9}{4}=-1/2$

4 0

3 years ago

Certain items are purchased jointly. If each person pays 8 coins, the surplus is 3 coins, and if each person gives 7 coins, the

Karo-lina-s [1.5K]

Answer:

7 people purchase the items and they used 53 coins

Step-by-step explanation:

Let x represent the number of people.

Let y be the number of coins needed to purchase the items.

If each person pays 8 coins, the surplus is 3 coins. This is illustrated below:

8x = y + 3 (1)

if each person gives 7 coins, the deficiency is 4 coins. This is illustrated below:

7x = y — 4 (2)

Solving by elimination method: subtract equation(2) from equation (1). This is illustrated below:

8x = y + 3 (1)

— (7x = y — 4) (2)

x = 7.

Next, Substituting the value of x into any of the equation to obtain y. In this case I will be using equation 1 as illustrated below:

8x = y + 3 (1)

8(7) = y + 3

56 = y + 3

Collect like terms

y = 56 — 3

y = 53

Therefore, 7 people purchase the items and they used 53 coins

7 0

3 years ago

The value of 9 in 456,790.

QveST [7]

The value of 9 there is 90 since it is in the tens place.

3 0

3 years ago

72 The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Fin

katrin [286]

Answer:

18√2

Step-by-step explanation:

The smaller triangle sharing a vertex with the larger one is similar and half the area. That means its linear dimensions are √(1/2) = (√2)/2 times those of the larger triangle.

The line segment of interest has length ...

36 × (√2)/2 = 18√2

_____

The ratio of area of similar figures is the square of the ratio of their linear dimensions. Thus the ratio of linear dimensions is the square root of the ratio of area.

6 0

3 years ago

Justin bought a package of pens that contained one black one blue and one red pen he randomly pulled two pens out of the package

Nataly_w [17]

A:
black,blue
black,red
blue,red

B:
red,black
red,blue
red,green
black,blue
black,green
blue,green

5 0

3 years ago