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4 years ago

I need help for solving

Mathematics

1 answer:

lys-0071 [83]4 years ago

3 0

5) w/8 =11+5 → w/8=16
w=16÷8=2

6)a/-2 -6=1
a/-2=7
a=7×-2=-14

7)k/2=22
k=44

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Given f(x)=2x^2+3x-5 for what values of x is f(x) positive

kow [346]

Answer:

The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)

Step-by-step explanation:

we have

$f(x)=2x^{2}+3x-5$

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex is a minimum

The coordinates of the vertex is the point (h,k)

step 1

Find the vertex of the quadratic function

Factor the leading coefficient 2

$f(x)=2(x^{2}+\frac{3}{2}x)-5$

Complete the square

$f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-5-\frac{9}{8}$

$f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-\frac{49}{8}$

Rewrite as perfect squares

$f(x)=2(x+\frac{3}{4})^{2}-\frac{49}{8}$

The vertex is the point (-\frac{3}{4},-\frac{49}{8})

step 2

Find the x-intercepts (values of x when the value of f(x) is equal to zero)

For f(x)=0

$2(x+\frac{3}{4})^{2}-\frac{49}{8}=0$

$2(x+\frac{3}{4})^{2}=\frac{49}{8}$

$(x+\frac{3}{4})^{2}=\frac{49}{16}$

take the square root both sides

$x+\frac{3}{4}=\pm\frac{7}{4}$

$x=-\frac{3}{4}\pm\frac{7}{4}$

$x_1=-\frac{3}{4}+\frac{7}{4}=1$

$x_2=-\frac{3}{4}-\frac{7}{4}=-2.5$

therefore

The function f(x) is negative in the interval (-2.5,1)

The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)

see the attached figure to better understand the problem

6 0

4 years ago

A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it.

Nina [5.8K]

Answer:

10 days to complete

Step-by-step explanation:

for mixed rate problems, the sum of each individual reciprocal rates equals the sum of the combined rate

i.e

$\frac{1}{A's rate} + \frac{1}{B's Rate} = \frac{1}{combined rate}$

we are given,

A's rate = 15 days to complete

Combined rate = 6 days to complete

B's rate = need to find

substituting' the given info into the equation above,

1/15 + 1/ (B's Rate) = 1/6

1 / (B's Rate) = 1/6 - 1/15 (convert right side to same denominator)

1 / (B's Rate) = 5/30 - 2/30

1 / (B's Rate) = 3/30

1 / (B's Rate) = 1/10 (taking reciprocal of both sides)

B's rate = 10 days to complete

4 0

4 years ago

Read 2 more answers

I already tried C=pi times diameter but it didn't work so can someone help me please.

slamgirl [31]

C=2pi(diameter)
C=2pi(14)
C=28pi

8 0

3 years ago

Read 2 more answers

Mrs. Friedmon baked a walnut cake for her class.

Setler [38]

That's great.. I'm allergic to walnuts but good for the class. What if some students have allergies though?

5 0

3 years ago

PLEASE I NEED HELP WITH MATH!!!<br><br> 5 points

Nutka1998 [239]

Answer:

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Step-by-step explanation:sjdygmvdmgjkutughvjghyidgufhcjdtsy4awy5rtyhojk

3 0

3 years ago