Ask question

Ask question

All categories

3 years ago

5

The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the grap

h?

2 answers:

svetlana [45]3 years ago

7 0

The vertex is (-2, -9)

Lisa [10]3 years ago

7 0

Answer:

The coordinates of the vertex of parabola are (-2,-9).

Step-by-step explanation:

The given function is

$f(x)=x^2+4x-5$

The vertex of a parabola lies on its axis of symmetry. Since the axis of symmetry is x=-2, tt means the x-coordinate of vertex is -2.

Let the vertex of parabola is (-2,y).

Substitute x=-2 in the given function to find the y-coordinate of vertex.

$f(-2)=(-2)^2+4(-2)-5$

$y=4-8-5$

$y=-9$

Therefore the coordinates of the vertex of parabola are (-2,-9).

You might be interested in

PLZ HELP ASAP!!!!! I NEED IT BADLY!!!!!

Ludmilka [50]

131/5 divided by 11/1
to divide by fractions, you multiply by the reciprocal and the reciprocal of 11/1 is 1/11...
131/5•1/11 and you just multiply across so the answer is every 131/55 miles. if you want it as a mixed number, it's 2 21/55

4 0

3 years ago

The value of the 7 in 27,459 is how many times the value of the 7 in 40,735?

alukav5142 [94]

Answer:

10

Step-by-step explanation:

The 7 in 27,459 is in the <em>thousands</em> place.

The 7 in 40,735 is in the <em>hundreds</em> place.

Any digit in the thousands place has 10 times the value of the same digit in the hundreds place. (The multiplier is 1000, instead of 100.)

_____

In the base-10 number system, each digit location has 10 times the value of the location to its right. The value is determined by the place the digit occupies in the number. That is why it is called a place-value number system.

4 0

3 years ago

Read 2 more answers

Learning Task 3

ASHA 777 [7]

Answer:

1. The sides are: 38.5, 39.5, 40.5 and 41.5

2. Presently, Inzo is 15 years old and Miz is 10 years old

3. $Distance = 3682km$

4. Possible pairs are: (12, 14), (16, 18) and (20, 24)

5. $L < 38m$

Step-by-step explanation:

The question has lots of missing details. See the comment section for complete question

Solving (a):

Given

Shape: Quadrilateral

Sides: Consecutive

$Perimeter = 160$

Let one of the sides be x. The other sides will be x + 1, x + 2 and x + 3.

So, the perimeter is:

$Perimeter = x + x + 1 + x + 2 + x + 3$

This gives:

$160 = x + x + 1 + x + 2 + x + 3$

Collect Like Terms

$160 -1-2-3= x+x+x+x$

$154= 4x$

Divide both sides by 4

$38.5 = x$

$x =38.5$

<em>So, the sides are: 38.5, 39.5, 40.5 and 41.5</em>

<em></em>

Solving (b):

Given

Presently: $Inzo = 10 + Miz$

Five years ago: $Miz - 5= \frac{1}{3} * (Inzo-5)$ --- (Missing from the question)

Required: Determine their present ages

Substitute $10 + Miz$ for Inzo in the second equation

$Miz - 5 = \frac{1}{3} * (10 + Miz - 5)$

$Miz - 5 = \frac{1}{3} * (Miz + 5)$

Multiply both sides by 3

$3Miz - 15 = Miz + 5$

Collect Like Terms

$3Miz -Miz = 15 + 5$

$2Miz= 20$

Divide both sides by 2

$Miz = 10$

Substitute 10 for Miz in $Inzo = 10 + Miz$

$Inzo = 10 + 5$

$Inzo = 15$

<em>So presently, Inzo is 15 years old and Miz is 10 years old</em>

Solving (3):

Given

Express Train:

$Speed = 100kph$

$Time = t$

Local Train:

$Speed = 45kph$

$Time = t + 45$

Required: Determine the distance between A and B

Distance is calculated as:

$Distance = Speed * Time$

For the express train:

$Distance = 100 * t$

For the local train

$Distance = 45 * (45 + t)$

Distance between both stations are equal; So,

$100 * t = 45 * (45 + t)$

$100 t = 2025 + 45t$

Collect Like Terms

$100 t -45t= 2025$

$55t= 2025$

Divide by 55

$t = 36.82$

Substitute 36.82 for t in $Distance = 100 * t$

$Distance = 100 * 36.82$

$Distance = 3682km$

Solving (4):

Let the even numbers be: n and n + 2.

Sum greater than 24: $n + n + 2 > 24$

Sum less than 60: $n + n + 2 < 60$

So, we have:

$n + n + 2 > 24$

$2n + 2 > 24$

Collect Like Terms

$2n > 24-2$

$2n > 22$

$n > 11$

$n + n + 2 < 60$

$2n + 2< 60$

Collect Like Terms

$2n < 60-2$

$2n < 58$

Divide by 2

$n$

So, we have:

$n > 11$ and $n < 29$

So, possible pairs are: (12, 14), (16, 18) and (20, 24)

Solving (5):

Given

$Perimeter < 152m$

Required: Find the possible lengths

Let the length be L.

Perimeter is calculated as:

$Perimeter =4 * L$

$Perimeter =4 L$

So, we have:

$4L < 152m$

Divide through by 4

$L < 38m$

Hence, length is less than 38m (e.g. 37m)

5 0

2 years ago

Mrs. Jackson gives the table below to her students.

krek1111 [17]

M= 20 because the rate of change is -3.

5 0

3 years ago

Read 2 more answers

What is the value of e^infinity and e^-infinity

valentinak56 [21]

E^(∞): This is defined as 'e' being raised to a huge value. Hence the result will definitely be a large number which is also infinity (∞), i.e. e^(∞) = ∞. e^(- ∞) = 1/e^(∞) = 1/∞ = 0.

8 0

3 years ago