Line r passes through points (5, 3) and (9, 8). Line s is perpendicular to r. What is the slope of line s?

The graph of $y = ax^2 + bx + c$ is shown below. Find $a \cdot b \cdot c$. (The distance between the grid lines is one unit.)

Savatey [412]

Answer:

$a\cdot b\cdot c=\frac{15}{4}$

Step-by-step explanation:

Vertex is the minimum or maximum point of parabola

Vertex of parabola is (h,k)

Therefore, from given graph (-3,-2) is the lowest point.

Vertex of parabola is at (-3,-2).

Standard equation of parabola

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

Substitute the values

$y-(-2)=a(x-(-3))^2=a(x+3)^2$

$y+2=a(x+3)^2$

(-1,0) lies on the parabola.

Therefore, it satisfied the equation of parabola.

$0+2=a(-1+3)^2=4a$

$a=2/4=1/2$

Now, using the value of a

$y+2=1/2(x+3)^2=1/2(x^2+6x+9)$

$y+2=\frac{1}{2}x^2+3x+\frac{9}{2}$

$y=\frac{1}{2}x^2+3x+\frac{9}{2}-2$

$y=\frac{1}{2}x^2+3x+\frac{9-4}{2}$

$y=\frac{1}{2}x^2+3x+\frac{5}{2}$

By comparing with

$y=ax^2+bx+c$

We get

$a=\frac{1}{2}, b=3, c=5/2$

$a\cdot b\cdot c=\frac{1}{2}\times 3\times \frac{5}{2}$

$a\cdot b\cdot c=\frac{15}{4}$

7 0

2 years ago

A fair spinner has eight equal sections.

blagie [28]

Answer:

umm im not sure if its correct but do 2 ( the colors ) times how many times it is spun. so there are 6 .

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

HELPP MEEE 20 POINTS !!! NO BOTS OR I WILL REPORT !!!Which of the following equations describes the line shown below? Check all

Ipatiy [6.2K]

The answer is A I believe.

5 0

3 years ago

Can atriangle be formed with side lengths of 5cm. 10cm and 15cm

andreyandreev [35.5K]

Theorem of cosine:
a²=b²+c²-2bc(cos α) ⇒cos α=-(a²-b²-c²) / 2bc

In this case:
a=15 cm
b=10 cm
c=5 cm

cos α=-(15²-10²-5²) / 2*10*5
cos α=-100 / 100
cos α=-1

A=arc cos -1=180º This is impossible, because:

A+B+C=180º; then B=C=0º This is impossible for make a triangle (B>0 and C>0 if we want to make a triangle).

Therefore: it is not possible can make a triangle with side lengths of 5 cm, 10 cm and 15 cm.

3 0

3 years ago

Read 2 more answers

Let D = {-48, -14, -8, 0, 1, 3, 16, 23, 26, 32, 36} Determine which of the following statements are true and which are false. a)

morpeh [17]

Answer:

$\forall x\in D$ if x is odd then x> 0 is true statement.

$\forall x\in D$ if x is even then x≤0 is false statement.

$\forall x\in D$ If the ones digit of x is 2, then the tens digit is 3 or 4 is true statement.

$\forall x\in D$ if the ones digit of x is 6, then the tens digit is 1 or 2 is false statement.

Step-by-step explanation:

Consider the provided information.

D = {-48, -14, -8, 0, 1, 3, 16, 23, 26, 32, 36}

Part (A) $\forall x\in D$ if x is odd then x> 0

Here only even numbers are less than 0 that means the statement is true.

$\forall x\in D$ if x is odd then x> 0 is true statement.

Part (B) $\forall x\in D$ if x is less than 0 then x is even.

Here only even numbers are less than 0 that means the statement is true.

$\forall x\in D$ if x is odd then x> 0 is true statement.

Part (C) $\forall x\in D$ if x is even then x≤0

Here we can see that 16, 26, 32, 36 are even number and also greater than 0. Thus the statement is false.

$\forall x\in D$ if x is even then x≤0 is false statement.

Part (D) $\forall x\in D$ If the ones digit of x is 2, then the tens digit is 3 or 4.

There is only one number whose ones digit is 2. i.e. 32 also the tens digit of the number 32 is 3. Which makes the above statement true.

$\forall x\in D$ If the ones digit of x is 2, then the tens digit is 3 or 4 is true statement.

Part (E) $\forall x\in D$ if the ones digit of x is 6, then the tens digit is 1 or 2.

Numbers having ones digit 6 are: 16, 26 and 36

Here, the tens digits are 1, 2 and 3 which is contradict to our statement. Hence the provided statement is false.

$\forall x\in D$ if the ones digit of x is 6, then the tens digit is 1 or 2 is false statement.

8 0

3 years ago