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3 years ago

Solve x2 – 8x + 15 < 0. Select the critical points for the inequality shown.

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

5 0

Answer:

x> 17/8

Step-by-step explanation:

add the numbers

17-8x<0

move the constant to the right-hand side and change its sign

-8x<-17

Divide both side of the inequality by -8 and flip the inequality sign

x>17/8

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Point a pq and r are collinear on pr and pq: pr =2/3. P is located on the origin q is located at (x,y) and r is located at (-12,

dybincka [34]

The values of x and y are 8 and 0 respectively.

Explanation

As 'p' is located at (0,0) and 'r' is located at (-12,0) , that means both 'p' and 'r' are on the x-axis. So point 'q' will be also on the x-axis , and 'q' is located at (x,y)

So, the value of y will be 0. That means the co ordinate of point 'q' is (x, 0)

Now, using the Distance formula, length of 'pq' $= \sqrt{(x-0)^2 +(0-0)^2}= \sqrt{x^2}= x$

and length of 'pr' $= \sqrt{(-12-0)^2+(0-0)^2}= \sqrt{144}=12$

Given that, pq : pr =2/3

So....

$\frac{x}{12} =\frac{2}{3}\\ \\ 3x=24\\ \\ x= \frac{24}{3}=8$

Thus, the values of x and y are 8 and 0 respectively.

8 0

4 years ago

Given the equation 4x2 − 8x 20 = 0, what are the values of h and k when the equation is written in vertex form a(x − h)2 k = 0?

Westkost [7]

The vertex form of the given quadratic equation is

$4(x-1)^{2} + 16 =0$ .

According to the given question.

We have a quadratic equation

$4x^{2} -8x + 20 = 0$

Since, for the standard quadratic form is $ax^{2} +bx + c = y$ , the vertex form of a quadratic equation is $y = a(x -h)^{2} + k$ where (h, k) is the vertex.

And h and k can be calculated as

h = -b/2a and y = k

So, for the given equation $4x^{2} -8x + 20 =0$ the vertex (h, k) is given by

h = -(-8)/2(4) = 8/8 = 1 (X coordinate of vertex)

and,

$y =4x^{2} -8x+ 20$

substitute x = 1 in the above equation for the value of k

Y = 4(1)(1) - 8(1) + 20

⇒ Y = 4 - 8 + 20

⇒ Y = -4 + 20

⇒ Y = 16

so, k = 16 (Y coordinate of vertex)

Now, substitute the value of a, k and h in $y = a(x-h)^{2} + k$ .

⇒ $0 =4(x-1)^{2} + 16$

Therefore, the vertex form of the given quadratic equation is

$4(x-1)^{2} + 16 =0$ .

Find out more information about vertex form of a quadratic equation here:

brainly.com/question/12223454

#SPJ4

6 0

2 years ago

in a store parking lot the ratio of blue cars to silver cars is 2:3 there are 24 blue cars how many silver cars are in the lot

yanalaym [24]

The answer is 36 silver cars

3 0

3 years ago

The table shows the number of candies packed by Machine J. The equation shows the number of candies packed by Machine K. In both

pav-90 [236]

Machine K y= 26x
y = 26 (11)
y = 286 candies in 11 minutes from Machine K

Machine J
90 / 3 = 30 candies a minute * 11 minutes = 330 candies

330 - 286 = 44

Machine J can pack 44 more candies than Machine K in 11 minutes.

3 0

3 years ago

Find the approximate volume. Round to the hundredth when necessary.

Sedaia [141]

Answer:

Volume of Sphere is 33.51 ft^3

Volume of Cylinder is 37.7 m^2

Step-by-step explanation:

Volume of a sphere formula: V = 4 /3πr^3

Volume of a cylinder formula: V = πr^2h

Step 1: Find the volume of the sphere

Since it shows the diameter, you need to divide 4 by 2 to get the radius: 2

V = 4/3*π*(2)^3

V = 33.51 ft^3

Answer: Volume of Sphere is 33.51 ft^3

Step 2: Find the volume of the cylinder

Since it shows the diameter, you need to divide 4 by 2 to get the radius: 2

V = π*(2)^2*(3)

V = 37.7 m^2

Answer: Volume of Cylinder is 37.7 m^2

6 0

3 years ago