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4 years ago

quadratic function has x intercepts of (0,0) and (10,0) what is the x value of the minimum of the parabola explain how you know

Mathematics

1 answer:

MakcuM [25]4 years ago

6 0

ANSWER

x=5

EXPLANATION

The given quadratic function has x intercepts of (0,0) and (10,0) .

The x-value of the minimum point lies on the axis of symmetry of this graph.

The axis of symmetry is the midline of the x-intercepts

$x = \frac{0 + 10}{2}$

The x-value of the minimum point is

$x = 5$

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Tell whether the data in the table can be modeled by a linear equation. Explain.

anastassius [24]

Answer:

y = -3x + 7

Step-by-step explanation:

Choosing two points from the given table:

Let (x1, y1) = (-3, 16)

(x2, y2) = (-1, 10)

Plug these given values into the slope formula:

m = (y2 - y1)/(x2 - x1)

= (10 - 16) / (-1 - (-3))

= -6 / (-1 + 3)

= -6/2

= -3

Therefore, the slope is -3.

Next, choose one of the points and plug into the <u>point-slope form</u>:

Let's use (-1, 10) as (x1, y1):

y - y1 = m(x - x1)

y - 10 = -3(x - (-1))

y - 10 = -3(x + 1)

y - 10 = -3x - 3

Add 10 on both sides to isolate y:

y - 10 + 10 = -3x - 3 + 10

y = -3x + 7

8 0

3 years ago

Five years from now, the sum of the ages of a women and her daughter will be 40 years. The difference in their present age is 24

Tomtit [17]

Answer:

Daughter age = 3 years

Step-by-step explanation:

Let x be the age of the women and y be the age of the daughter.

Given:

After five year the sum of the women and daughter age = 40

$(x+5)+(y+5)=40$

At present the sum of the women and daughter age

$x+5+y+5=40$

$x+y+10=40$

$x+y=40-10$

$x+y=30$ --------------(1)

So the sum of the present age is $x+y=30$

The difference in their present age is 24 years.

$x-y=24$

$x=24+y$

Now we substitute x value in equation 1.

$(24+y)+y=30$

$24+2y=30$

$2y=30-24$

$2y=6$

$y=\frac{6}{2}$

$y=3\ years$

Therefore, the daughter age is 3 years.

7 0

4 years ago

The Lynx star middle linebacker, Nat, is paid $500,000. He is guaranteed a 25% raise for each of the next three years. What will

shutvik [7]

Answer:

Nat's salary after 3 years = 976562.5 $

Explanation:

Salary of Nat = $500,000

Raise in salary for next three years = 25 % = 0.25

Salary of Nat after 1 year = 500,000 + 0.25 * 500,000 = 625000 $

Salary of Nat after 2 years = 625000 + 0.25 * 625000 = 781250 $

Salary of Nat after 3 years = 781250 + 0.25 * 781250 = 976562.5 $

So, Nat's salary after 3 years = 976562.5 $

Easy Method;

No of years considering = 3

Initial salary = $500,000

Rate of increase = 0.25

Final salary $= 500,000(1+0.25)^3=976562.5$ $

Nat's salary after 3 years = 976562.5 $

3 0

3 years ago

M is the incenter of triangle ABC. Find the lengths of MD and DC. (Look at pic)

Deffense [45]

Answer:

Part 1) $MD=9\ units$

Part 2) $DC=12\ units$

Step-by-step explanation:

Step 1

Find the length of MD

we know that

The incenter is the intersection of the angle bisectors of the three vertices of the triangle. Is the point forming the origin of a circle inscribed inside the triangle

In this problem

$MD=ME=MF$ ------> is the radius of a circle inscribed inside the triangle

we have that

$MF=9\ units$

therefore

$ME=9\ units$

$MD=9\ units$

Step 2

Find the length of DC

we know that

In the right triangle MDC

Applying the Pythagoras theorem

$MC^{2} =MD^{2}+DC^{2}$

we have

$MD=9\ units$

$MC=15\ units$

substitute

$15^{2} =9^{2}+DC^{2}$

$DC^{2}=225-81$

$DC=\sqrt{144}\ units$

$DC=12\ units$

6 0

4 years ago

If a car travels 825 miles in 15 hours and the car travels at an constant rate how many miles does the car travel in 1 hour?

Doss [256]

Answer:

55 miles

Step-by-step explanation:

Given data

DIstance = 825 miles

Time = 15 hours

Speed= distance/time

Speed= 825/15

Speed= 55 miles per hour

Given that we want to find the distance traveled in 1 hour, we have

Distance= Speed*time

Distance= 55*1

Distance= 55 miles

Hence the car will travel 55 miles in 1 hour

7 0

3 years ago