Which shows the equation below written in the form ax^2+bx+c=0?

Suppose a parabola has vertex (6,5) and also passes through the point (7,7). Write the equation of the parabola in vertex form.

jek_recluse [69]

Answer:

Choice B: $y = 2\, (x - 6)^{2} + 5$ .

Step-by-step explanation:

For a parabola with vertex $(h,\, k)$ , the vertex form equation of that parabola in would be:

$\text{$y = a\, (x - h)^{2} + k$ for some constant $a$}$ .

In this question, the vertex is $(6,\, 5)$ , such that $h = 6$ and $k = 5$ . There would exist a constant $a$ such that the equation of this parabola would be:

$y = a\, (x - 6)^{2} + 5$ .

The next step is to find the value of the constant $a$ .

Given that this parabola includes the point $(7,\, 7)$ , $x = 7$ and $y = 7$ would need to satisfy the equation of this parabola, $y = a\, (x - 6)^{2} + 5$ .

Substitute these two values into the equation for this parabola:

$7 = (7 - 6)^{2}\, a + 5$ .

Solve this equation for $a$ :

$7 = a + 5$ .

$a = 2$ .

Hence, the equation of this parabola would be:

$y = 2\, (x - 6)^{2} + 5$ .

4 0

3 years ago

Help me please i so need help

elena55 [62]

Answer:

9

It is 9 because 9 is the only number that multiplied by itself is 81.

5 0

2 years ago

Read 2 more answers

Pollution Rates Assignment

stepan [7]

Answer:

1. a) 4.8 lb

I) 8%

II) 0.384 lb

2. a) 12.5 lb

I) 8%

II) 1 lb

Step-by-step explanation:

Let's begin by listing out the given variables:

mass of pesticide (m) = 12 lb,

40WP (40 weight percent) means the active ingredient comprises 40% of the total mass of the pesticide

a) amount of active ingredient = mass of the pesticide * weight percentage of the active ingredient

x = 12 * 40% = 12 * 0.4

x = 4.8 lb

I. If the soil has an absorption rate of 92%, that means 8% will go into the run-off

The percentage of active ingredient that will end up in the run-off = the percentage of the active ingredient (100%) - the absorption rate

y = (100 - 92)%

y = 8%

II. amount of of active ingredient that will end up in the run-off = amount of active ingredient * the percentage of active ingredient that will end up in the run-off

z = x * y = 4.8 * 8% = 4.8 * 0.08

z = 0.384 lb

2. Let's list out the variables given, we have:

mass of pesticide = 25 lb, weight percent of active ingredient = 50% = 0.5

amount of active ingredient = mass of the pesticide * weight percentage of the active ingredient

x = 25 * 0.5

x = 12.5 lb

I. If the soil has an absorption rate of 92%, that means 8% will go into the run-off

The percentage of active ingredient that will end up in the run-off = the percentage of the active ingredient (100%) - the absorption rate

y = (100 - 92)%

y = 8%

II. amount of of active ingredient that will end up in the run-off = amount of active ingredient * the percentage of active ingredient that will end up in the run-off

z = x * y = 12.5 * 8% = 12.5 * 0.08

z = 1 lb

7 0

3 years ago

Rating Frequency Present Frequency Excellent 18 _______Very Good 25 _______Good 4 _______Fair 1 2Poor 2 4 Total 50 100What do th

nata0808 [166]

Answer:

a) Rating Frequency Percent Frequency

Excellent 18 ___36%____Very Good 25 ___50%____Good 4 ___8%____Fair 1 2% Poor 2 4% Total 50 100 What do these summaries indicate about the overall customer satisfaction with the Delta flight? ____94%______ % customers are satisfied with the Delta Flight Et either a good, very good, or excellent rating. Only ____6%_______% of customers rated the Delta flight Fair or Poor.

b. The online survey questionnaire enabled respondents to explain any aspect of the flight that Failed to meet expectations. Would this be helpful information to a manager looking for ways to improve the overall customer satisfaction on Delta flights? Explain.

Allowing survey respondents to explain their 5-point scale responses would provide helpful information to managers looking for ways to improve customer satisfaction on Delta flights. The ____6______% respondents indicating that the flight failed to meet expectations would have the opportunity to provide detailed information about their expectations.

Step-by-step explanation:

a) Data and Calculations:

Rating Frequency Percent Frequency

Excellent 18 ____36%___

Very Good 25 ____50%___

Good 4 ____ 8%___

Fair 1 ____ 2%___

Poor 2 _____4% __

Total 50 100%

b) Percentage Frequencies are obtained as follows:

Excellent = 18/50 * 100 = 36%

Very Good = 25/50 * 100 = 50%

Good = 4/50 * 100 = 8%

Fair = 1/50 * 100 = 2%

Poor = 2/50 * 100 = 4%

c) Good, very good, and excellent = 47/50 * 100 = 94%

d) Fair or Poor rating = 3/50 * 100 = 6%

e) Moreover, dissatisfied customers can be sources of great information on the performance of a good or service. Though, with only 6% of customers giving a dissatisfaction rating with the Delta flights, it is still important to dive deep to unearth the reasons for their dissatisfaction as this may provide valuable information to improve the services. Usually, this class of customers is the most sincere in most cases, unless their dissatisfaction can be proved to be attitudinal on their own part.

6 0

3 years ago

Find the Inverse for the linear function.<br> J(x)= 5x - 6<br> F1(x)=

kondaur [170]

F-1(x) = x\5 + 6/5
hope this helps

4 0

3 years ago