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DiKsa [7]
3 years ago
5

Two parabolas are the graphs of the equations $y=2x^2-10x-10$ and $y=x^2-4x+6$. give all points where they intersect. list the p

oints in order of increasing $x$-coordinate, separated by semicolons.
Mathematics
2 answers:
katovenus [111]3 years ago
8 0
(-2,18):(8,38) Set them equal to each other you get, x^2-6x-16=0, you can factor to get, (x-8)(x+2) to get solutions 8,2 for the x values then plug in for y values.
snow_lady [41]3 years ago
6 0

Answer:

(-2, 18) and (8, 38)

Step-by-step explanation:

First, set the two equations equal to each other to get $2x^2-10x-10=x^2-4x+6$. Combine like terms to get $x^2-6x=16$. To complete the square, we need to add $\left(\dfrac{6}{2}\right)^2=9$ to both sides, giving $(x-3)^2=16+9=25$.

So we have $x-3=\pm5$. Solving for $x$ gives us $x=-2$ or $8$. Using these in our original parabolas, we find the points of intersection to be $\boxed{(-2,18)}$ and $\boxed{(8,38)}$.

Credit: AoPs

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Marco is 8 years younger than his brother Paolo. If their product of their ages is 105, how old is Marco? plz help
Nina [5.8K]

Answer:

Marco's age is 7 years old

Step-by-step explanation:

Let

x ----> Marco's age

y ----> Paolo's age

we know that

x=y-8 ----> y=x+8 ----> equation A

xy=105 ----> equation B

substitute equation A in equation B

x(x+8)=105

x^2+8x-105=0

Solve the quadratic equation

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

x^2+8x-105=0

so

a=1\\b=8\\c=-105

substitute in the formula

x=\frac{-8(+/-)\sqrt{8^{2}-4(1)(-105)}} {2(1)}

x=\frac{-8(+/-)\sqrt{484}} {2}

x=\frac{-8(+/-)22} {2}

x=\frac{-8(+)22} {2}=7

x=\frac{-8(-)22} {2}=-15

Remember that the solution cannot be a negative number

so

The solution is x=7

therefore

Marco's age is 7 years old

4 0
3 years ago
The cost of a taxi ride is equal to $3.50 plus $0.25 for each mile. If a ride costs a total of $6.75 how long was the ride?
jeka57 [31]

Answer:

13 miles

Step-by-step explanation:

Write and solve an equation involving this information, using x as the distance traveled, in miles:

Cost(x) = $6.75 = $3.50 + ($0.25/mile)x

First, subtract $3.50 from both sides, obtaining:  $3.25 = ($.25/mile)x.

Next, divide both sides by $0.25/mile:

        $3.25

x = ------------------ = 13 miles

      $0.25/mile

The length of the taxi ride was 13 miles.

7 0
2 years ago
The same architect wants to draw a room that has an area of 175 ft². What will be the area of the room in his drawing in square
Dominik [7]

Answer:

25,200in²

Step-by-step explanation:

The architect wants to draw a room that has an area of 175 ft². We need to find this measurement in square inches.

<u>Square feet and square inches are different from feet and inches. </u>

We should know that a square foot is 144 square inches.

Multiply 175 * 144.

175 * 144=25200

So the same architect wants to draw a room that should have an area of 25,200in².

<em>Brainilest Appreciated. </em>

3 0
3 years ago
5 people are trying to sit on a long bench of length 30.52\text{ m}30.52 m30, point, 52, start text, space, m, end text. Find th
shusha [124]

Answer:

6.104 m

Step-by-step explanation:

The length of the bench is 30.52 m.

5 people want to sit down on the bench.

We assume they are seated with equal spacing between themselves.

The length occupied by each person will therefore be:

30.52 / 5 = 6.104 m

7 0
3 years ago
Tood knows that the ratio of boys and girls in his class is 3:5. Since 12 of the students are boys, he says there must be 36 stu
Vesna [10]

Answer:

=99

Step-by-step explanation:

7 0
3 years ago
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