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mote1985 [20]
3 years ago
15

Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

dentity the equation for the axis of symmetry, write the solutions and the coordinates of the vertex as ordered pairs. Show as much work as possible for full credit. All work should be done by hand.

Mathematics
1 answer:
inn [45]3 years ago
3 0

Answer:

See explanation

Step-by-step explanation:

1. Factor the function f(x)=-2x^2+16x-30:

f(x)=-2x^2+16x-30=-2x^2+6x+10x-30=-2x(x-3)+10(x-3)=-2(x-3)(x-5).

2. The zeros (or the solutions of the equation f(x)=0) are x=3 and x=5. So? points (3,0) and (5,0) are the points on the graph that are the solutions of the equation.

3. Find the vertex:

x_v=-\dfrac{b}{2a}=-\dfrac{16}{2\cdot (-2)}=4,\\ \\y_v=-2\cdot 4^2+16\cdot 4-30=-32+64-30=2.

Thus, the coordinates of the vertex are (4,2) and the axis of symmetry is the vertical line that passes trough the vertex: x=4.

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[|(x-4)÷(x+5)|]\leq[4]
Katena32 [7]

Answer:

Solutions are;

x = -8

x = -3.2

Step-by-step explanation:

Here, we want to solve the given equation for x

|(x-4)/(x + 5)| = 4

From what we have, this is an absolute value equation and thus, we are going to have two solutions

These are;

x-4/x+ 5 = 4

x-4 = 4(x + 5)

x-4 = 4x + 20

x-4x = 20 + 4

-3x = 24

x = -24/3

x = -8

secondly;

x-4/x+5 = -4

x-4 = -4(x + 5)

x-4 = -4x - 20

x + 4x = -20 + 4

5x = -16

x = -16/5

x = -3.2

3 0
3 years ago
Today, Joel is going to an art museum to see a special exhibit. It takes Joel 25 minutes to
Marina86 [1]

Answer:

6:55 A. M. is the latest time he can leave his house

4 0
2 years ago
a) The mean age of graduate students at a University is at most 31 y ears with a standard deviation of two years. A random sampl
kari74 [83]

Answer:

A.)

H0: μ ≤ 31

H1: μ > 31

B.)

H0: μ ≥ 16

H1: μ < 16

C.)

Right tailed test

D.)

If Pvalue is less than or equal to α ; we reject the Null

Step-by-step explanation:

The significance level , α = 0.01

The Pvalue = 0.0264

The decision region :

Reject the null if :

Pvalue < α

0.0264 > 0.01

Since Pvalue is greater than α ; then, we fail to reject the Null ;

Then there is no significant evidence that the mean graduate age is more Than 31.

B.)

H0: μ ≥ 16

H1: μ < 16

Null Fluid contains 16

Alternative hypothesis, fluid contains less than 16

One sample t - test

C.)

Null hypothesis :

H0 : μ ≤ 12

. The direction of the sign in the alternative hypothesis signifies the type of test or tht opposite direction of the sign in the null hypothesis.

Hence, this is a right tailed test ; Alternative hypothesis, H1 : μ > 12

d.)

If Pvalue is less than or equal to α ; we reject the Null.

3 0
2 years ago
there arre 221 students on a fiel trip five students ride in a van the rest of the students fill the 6 buses enter an equation t
iren2701 [21]

According to the question statement, the total sum of students is 221, which includes the students that ride on bus and the students that ride in a van.

The students that ride in a van are five, the students that ride on bus are 6 times s which is the product of the number of buses and the number of students that are on each bus.

Write all this information into an equation, this way:

6s+5=221

Now, solve the equation for s to find the number of students that are on each bus.

\begin{gathered} 6s+5=221 \\ 6s=216 \\ s=\frac{216}{6} \\ s=36 \end{gathered}

There are 36 students on each bus.

3 0
1 year ago
What are two other names for Xy
NARA [144]

Answer:

In Mathematics, x and y are examples of variables.

You can use any letter as a variable but, make sure to include a let statement when using variables.

A let statement essentially tells what the variable represents.

Ex: let h = houses sold

Hope this helps!

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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