ASAPPP How do I explain what's the difference in the meaning of the "+1" in the following equations: f(x)=2x^2+5x+1. and g(x)=2(x+5)^2+1 ??????

Answers

Answer 1

Answer:

The +1 in f(x) is the y intercept

The +1 in g(x) is the y coordinate of the vertex

Step-by-step explanation:

For f(x), plugging in x = 0 leads to

f(x) = 2x^2+5x+1

f(0) = 2(0)^2+5(0)+1

f(0) = 1

Showing that (0,1) is the y intercept of f(x).

The same is not true for g(x)

g(x) = 2(x+5)^2+1

g(0) = 2(0+5)^2+1

g(0) = 51

-------------------------------

The +1 for g(x) represents the y coordinate of the vertex. Recall that vertex form in general is

y = a(x-h)^2+k

with (h,k) being the vertex. This means we can quickly spot the vertex for g(x) without having to graph. The same cannot be said for f(x) as we need to complete the square to get f(x) into vertex form. Currently, f(x) is in standard form.


Related Questions

Given a geometric sequence with a1 = 3 and a4 = 24, find a2.

Answers

Answer: 6

Step-by-step explanation:

ax/ay=r^(x-y)

in this case it will be

a4/a1=r^(4-1)

24/3=r^3

8=r^3

r=2

----------------------------------

an=a1×r^(n-1) ⇔ geometric sequence formula

a2=3×2^(2-1)

a2=3×2^1

a2=3×2

a2=6

dertermine two numbers that have product of 40 but have sum of 13

Answers

Answer:

8 and 5.

Step-by-step explanation:

8 x 5 = 40

8 + 5 = 13

A right triangle has a perimeter of 24 cm and a hypotenuse of 10 cm. Find the length of the other two sides.

Answers

Answer:

One of the sides is 6 cm and the other is 8 cm

Step-by-step explanation:

Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:

a + b + hypotenuse = 24

a + b + 10 = 24

a + b = 14

b = 14 - a

So now we can right the Pythagorean theorem as follows:

[tex]a^2 + b^2 = hypotenuse^2\\a^2 + (14-a)^2=10^2\\a^2+ 14^2-28\,a+a^2=100\\2\,a^2-28\,a +96=0\\2\,(a^2-14\,a+48)=0\\2\,(a^2-6\,a-8\,a+48)=0\\2(a\,(a-6)-8\,(a-6))=0\\2\,(a-6)\,(a-8)=0[/tex]

and from this expression in factor form to be zero a must be 6 or a must be 8.

Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)

or a = 8 (and therefore b = 14 - 8 = 6)

Perimeter of triangle = Sum of all sides.

One side of triangle = 10 cm

Measure of other two sides will be → 24-10

Other two sides sum will be = 14 cm

Let's assume one side as x and other as 14-x

Now hypotenuse is of 10 cm

According to Pythagorean theoram

Hypotenuse² = Perpendicular ² + base²

→ 10² = (x)² + (14-x)²

→ 100 = x² + (14-x)²

(a-b)² = + -2ab

→ 100 = x² + 196 + x² -28 x

→ 100 = 2x² + 196 - 28x

Taking 2 commen both sides

→ 50 = x² -14x + 98

→ 0 = x² -14x +98-50

→ x² -14 x +48 = 0

Factorising :-

x² - 6x - 8x + 48 = 0

→ x( x -6) -8(x -6) = 0

→ (x-6)(x-8) = 0

→ x = 6 or x = 8

So x is 6 or 8

Other two sides of triangle are 6 cm and 8 cm

Translate to an algebraic expression: 3 times the difference of a number and 4 is 33

Answers

Answer:

3 x (14-3) = 33

Step-by-step explanation:

The algebraic expression will be : 3(x - 4) = 33

Given,

3 times the difference of a number and 4 is 33

Now,

Let the number be x .

So,

Three times the difference of x and 4 will be 33 .

So,

First subtract x-4

Then thrice of this is 33

So,

3(x - 4) = 33

Thus the algebraic expression is 3(x - 4) = 33 .

After solving the expression:

x- 4 = 11

x = 15

Know more about algebra,

https://brainly.com/question/16934260

#SPJ6

The temperature of a city at sunset was -2°F. Overnight, the temperature decreased by 12°F. What was the lowest
temperature overnight in that city?
A. -14°F
OB
14°F
О С.
10°F
D. -10°F

Answers

Answer:

-14 F

Step-by-step explanation:

Sorry it’s the best quality photo I could get

Answers

Answer: Choice C. y = x/2 + 6

Explanation:

The idea is to isolate y getting it by itself. We can do this a number of ways, but possibly the quickest way is to add y to both sides

x/2 - y + 6 = 0

x/2 + 6 = 0+y

x/2 + 6 = y

y = x/2 + 6

This is now in slope intercept form, more or less. We could rewrite the x/2 as (1/2)x to get

y = (1/2)x + 6

Then compare this to y = mx+b and note the slope is m = 1/2 and the y intercept is b = 6.

Side note: the quality of the snapshot is fairly good. I've seen much worse.

A Pythagorean triple is said to be "primitive" if the greatest common divisor of a, b, and c is 1. Use trial and error to find a primitive Pythagorean triple other than (3, 4, 5).

Answers

Answer:

(5, 12, 13)

Step-by-step explanation:

Hello, please consider the following.

[tex](\forall (x,y) \in \mathbb{R}^2) \ \ (x^2-y^2)^2+(2xy)^2=(x^2+y^2)^2\\\\\text{You can develop both expressions to see that this is equal.}\\\\\text{After }(3,4,5)\text{ we can try the triple starting with }5\\\\\text{So, let's search x and y such that } 5=x^2-y^2=9-4=3^2-2^2\\\\\text{And, then, it comes}\\\\(3^2-2^2)^2+(2*3*2)^2=(3^2+2^2)^2\\\\<=> 5^2+12^2=13^2\\ \\\text{So, }(5,12,13)\text{ is a Pythagorean triple}[/tex]

Is it a primitive one?

5 = 1 * 5

12 = 1 * 2 * 2 * 3

13 = 1 * 13

So this is a primitive one.

Thanks

Answer:

5, 12, 13

Step-by-step explanation:

EXERCISE 2.1
(a)
1.
An agent sells some articles for Rs 5,500. What commission does he get at 5%?

Answers

Answer:

250

Step-by-step explanation:

5000×5/100 =250

why because you times it for commission because it what you gain

Does anyone know this

Answers

Answer:

Domain: (-11, 4)

Step-by-step explanation:

Domain is the set of all x-values that can be inputted into a function.

So we look at x-values that can be inserted into the graph.

We notice that we cannot input x = -11 or x = 4 as it is open-pointed but everything inbetween works, so we have (-11, 4) as our domain.

What is the value of x?

Answers

Answer:

itś between 30 and 45 but my best guest is 30

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

because i said so

Use the percent proportion to solve for X. 16 is 32% of x. Find the value of 1.​

Answers

Answer:

I dont get the question, is there suposed to be a chart?

Step-by-step explanation:

Marcella divided 40.8 gallons of paint amount 8 containers. how much paint is in each container?

Answers

Answer:

5.1 gallons

Step-by-step explanation:

Using the information provided, we know that there is of course 40.8 gallons of paint to be divided into 8 containers. This means we must use a division problem to figure out our answer.

We are splitting the 40.8 gallons into the 8 containers so that means our dividend is 40.8 and our divisor is 8. With this information, we can go ahead and put this into an expression of:

40.8/8

If you have a calculator, you can plug that equation in to get 5.1, but if you don't then a bit of easy long division will get you the same answer of 5.1 gallons.

Answer: 51 gallons

Step-by-step explanation:

Let f(x)=2x-6. Solve f^-1(x) when x=2
-5
4
-2
7

Answers

Answer:

4.

Step-by-step explanation:

f^-1(x) is the inverse of f(x). That means that f(x) = 2x - 6 becomes...

x = 2y - 6

2y - 6 = x

2y = x + 6

y = 1/2x + 3.

When x = 2...

y = 1/2(2) + 3

= 1 + 3

= 4.

Hope this helps!

simplify (3x + 2)(4x - 4)

Answers

Answer:

12x² - 4x - 8

Step-by-step explanation:

Use FOIL method

(3x + 2)(4x - 4) = 3x*4x + 3x*(-4) + 2 *4x + 2*(-4)

                        = 12x² - 12x + 8x - 8   {add like terms}

                        = 12x² - 4x - 8

Hint: 3x * 4x  -----> Multiply the coefficients = 3 *4 = 12 and then multiply the variables and for multiplying the two variable, add the powers

x*x =[tex]x^{1+1)=x^{2}[/tex]

3x * 4x = 12x²

write the slope intercept form of the equation of the line through the given point with the given slope through (2,5) , slope 2

Answers

Answer:

y =2x+1

Step-by-step explanation:

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = 2x+b

Substituting the point into the equation

5 = 2(2)+b

5 = 4+b

5-4 =b

b=1

y =2x+1

√36 + √49
Find the perimeter of the rectangle

Answers

Hi

perimeter of rectangle is  : 2 length+2 width .

to progress in math, you must practice.

So , I let you  do the first one which is the esaiest.

48 ) V147+ V147 + V108+V108 =    2V147 +2V108  = 2 ( V147+V108)

Which expression is equivalent to –2(5x – 0.75)?
10x – 0.75
10x + 0.75
–10x – 1.5
–10x + 1.5

Answers

Answer:

-10x+1.5

Step-by-step explanation:

-2(5x-0.75).... distributive property

-10x+1.5

Note:

-&-=+

+&+=+

+&-=-

-&+=-

Hope this helps ;) ❤❤❤

Answer:

d

Step-by-step explanation:

You roll a single die numbered from 1 to 6 twice. The probability of rolling a 6 the first time and an odd number the second is the setup. What is the probability fraction "rolling a 6 the first time"?

Answers

Answer:

1 out of 6

Step-by-step explanation:

(c+5)/(-2)=13

Someone please help

Answers

Answer:

-31

Step-by-step explanation:

-2((c+5)/(-2))=13*-2

c+5=-26

c=-31

Answer:

c = -31

Step-by-step explanation:

(c+5)/(-2)=13

Multiply each side by -2

(c+5)/(-2) *-2=13* -2

c+5 = -26

Subtract 5 from each side

c+5-5 = -26-5

c = -31

What is the circumference of a circle with radius pi?​

Answers

Answer:

2π² or 19.74

Step-by-step explanation:

Circumference of a circle is C = 2πr

Given r = π

Then:

C= 2π*π = 2π²

or

≈19.74

if f(x)=4x+12 is graft on a coordinate plane what is the y intercept of the graph

Answers

Answer: y-intercept = 12

Explanation:
f(x) = 4x + 12
Or y = 4x + 12

Where 4 is the slope and 12 is the y-intercept

1.Which numbers below could be classified as integers? 2.Which number belongs in the shaded portion of the diagram below?

Answers

Answer:

1). Option (3)

2). Option (D)

Step-by-step explanation:

1). Integers are the numbers which are whole numbers with negative or positive notations.

Integers can't be a fraction or a number with decimal.

Out of the numbers given,

-18 and 4 will be the integers

Option (3) is the correct answer.

2). Shaded portion of the diagram represents the rational numbers excluding integers,

By the definition of the rational numbers, any number which can be written as a fraction is a rational number.

Rational numbers → All numbers given are the rational numbers

Integers → [tex]\frac{16}{4}=4, -\frac{30}{5}=6, -\frac{32}{8}=-4[/tex]

Therefore, only one number [tex]\frac{30}{9}[/tex] will lie in the shaded region.

Option (D) will be the answer.

For each problem, find the missing value using the Pythagorean Theorem

Answers

Answer:

Leg₂ ≈ 6.481 or √42

Step-by-step explanation:

a² + b² = c²

(√7)² + b² = (7)²

7 + b² = 49

b² = 42

b = √42

b ≈ 6.481

is the ratio 5:6 equivalent to 3:4​

Answers

Answer:

No!

Step-by-step explanation:

This question is essentially asking if [tex]\frac{5}{6}[/tex] = [tex]\frac{3}{4}[/tex]

Well we can easily tell that it doesn't, but if we want to check, we can do cross multiplication.

So we are trying to find out if 5(4) = 3(6).

5(4) = 20 and 3(6) = 18.

[tex]20 \neq 18[/tex] so [tex]5:6 \neq 3:4[/tex]

They are not equal!

Answer:

No, because the numbers in the given ratio must be multiplied by the same number.

Step-by-step explanation:

Right on E 2020

There are 1,332 people under the age 20 in Pierce City. This represents 14% of the total population. What is the total population

Answers

Answer:

The total population = 9514.2857143 people.

Step-by-step explanation:

Let the total population be represented by X

In the question, we are told that,1332 people are under the age of 20 and this value = 14% of the total population.

Therefore, the total population is calculated as

14% of X = 1332

14/100 × X = 1332

14X/100 = 1332

Cross Multiply

14X = 1332 × 100

X = 1332 × 100/14

X = 9514.2857143

Therefore, the total population = 9514.2857143 people.

How many x or y intercepts can a quadratic function have?
0-2 x-intercepts and 0-1 y-intercept
2 x-intercepts and 1 y-intercept
0-2 x-intercepts and 1 y-intercept
1-2 x-intercepts and 0-1 y-intercept

Answers

Answer:

0-2 x-intercepts and 0-1 y-intercepts

Step-by-step explanation:

A quadratic function can have anywhere from 0 to 2 x-intercepts. This is possible because a function can have 0, 1, or 2 solutions.

A parabola can also have either 0 or 1 y intercepts. It is possible for the function to not intercept the y axis at all, and it is also possible for it to intercept it exactly one time.

please help me on this question

Answers

Answer:

100 ml of concentrate and 350 ml of water

Step-by-step explanation:

2 + 7 = 9 total parts

450/9 = 50

2(50) = 100 ml concentrate

7(50) or 450 - 100 = 350 ml water

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

someone please help, whats the answer for this, write in point-slope form an equation of the line that passes through the point (8, 9) with slope 7. y - _ = _ (x - _)

Answers

Answer :

y=7x-47

Step-by-step explanation:

[tex] (8, 9) = (x_1,y_1) \\ m = 7 \\ y - y_1 = m(x - x _1) \\ y - 9 = 7(x - 8)[/tex]

[tex]y - 9 = 7x - 56 \\ y = 7x - 56 + 9 \\ y = 7x - 47[/tex]

I hope it helps

In a college 65 students are studying Mathematics 50 students are studying science and 35 students are studying both subject. If none of the students study other subjects then how many students are studying in the college how many students are mathematical only how many student are science only​

Answers

Answer:

Step-by-step explanation:

studying Math       65

Studying science   50

studying both          35

student are studying in the college are:(65+50)-35=80 students

student studying math only= 65-35=30

student studying science only = 50-25=15

(ab² + 13b - 4a) + (3ab² + a +7b)

Answers

Answer:

4ab² + 20b - 3a

Step-by-step explanation:

This question most likely asks us to simplify the expression, as factoring is not possible...

(ab² + 13b - 4a) + (3ab² + a + 7b),

ab² + 13b - 4a + 3ab² + a + 7b,

ab² + 3ab² + 13b + 7b - 4a + a,

Solution : 4ab² + 20b - 3a

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