1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alex41 [277]
3 years ago
5

Solve the inequality. Check your solutions.

Mathematics
1 answer:
Komok [63]3 years ago
8 0
The inequality is 

7- \frac{2}{b}\ \textless \ \frac{5}{b}

write 7 as 7b/b to have all the expressions in common denominator:

\frac{7b}{b} - \frac{2}{b}\ \textless \ \frac{5}{b}

\frac{7b-2}{b} \ \textless \ \frac{5}{b}

\frac{7b-2}{b}- \frac{5}{b}\ \textless \ 0

\frac{7b-2-5}{b}\ \textless \ 0

\frac{7b-7}{b}\ \textless \ 0

\frac{7(b-1)}{b}\ \textless \ 0

here b=1 is a root and b=0 is not in the domain of the expression, but it still has an effect in the sign of the expression.

the sign table of \frac{7(b-1)}{b} is :

+++++++[0] --------[1] +++++

this means that for values of b to the left of 0 and to the right of 1, the expression is positive, and for values of b in (0, 1), the expression is negative.

that is \frac{7(b-1)}{b}\ \textless \ 0 for b∈(0, 1)

Answer: (0, 1)
You might be interested in
Find all x-intercepts and y-intercepts of the graph of the function.<br> F(x)=x³-4x² - 4x + 16
Lady bird [3.3K]

Answer: (0;16)  (4;0)  (2;0)  (-2;0).

Step-by-step explanation:

Y-intercepts of the graph of the function F(x)=x³-4x² - 4x + 16:

x=0\\F(x)=0^3-4*0^2-4*0+16\\F(x)=16.\\Hence,\  (0;16).

X-intercepts of the graph of the function F(x)=x³-4x² - 4x + 16:

F(x)=0\\0=x^3-4x^2-4x+16\\0=(x^3-4x^2)-(4x+16)\\0=x^2*(x-4)-4*(x-4)\\0=(x-4)*(x^2-4)\\0=(x-4)*(x^2-2^2)\\0=(x-4)*(x-2)*(x+2)\\x-4=0\\x_1=4.\\Hence,\ (4;0)\\x-2=0\\x_2=2.\\Hence,\ (2;0)\\x+2=0\\x_3=-2.\\Hence,\ (-2;0).

8 0
1 year ago
Help on this please, i dont get this problem.
Ahat [919]

Answer:

<h2>A = 37 cm²</h2>

Step-by-step explanation:

Look at the picture.

We have two rectangles:

15cm × 2cm and 7cm × 1cm.

Calculate the areas:

A₁ = 15 · 2 = 30 cm²

A₂ = 7 · 1 = 7 cm²

The area of the figure:

A = A₁ + A₂ → A = 30 cm² + 7 cm² = 37 cm²

5 0
3 years ago
Evaluation: Decisions About Equivalence
lora16 [44]

Answer:

x+x+x+x=4x

x+5=5x

There equivalent

Step-by-step explanation:

x+x+x+x=4x:

count the number of x's they equal 4 so it would be 4x

x+5=5x

you have 5 x's it would equal 5x

3 0
3 years ago
For what values of x is x2-36=5x true?<br> 0 -9 and 4<br> 04 and 9<br> 4 and -9<br> 09 and 4
ipn [44]

Answer:

x = - 4 and x = 9

Step-by-step explanation:

Given

x² - 36 = 5x ( subtract 5x from both sides )

x² - 5x - 36 = 0

Consider the factors of the constant term (- 36) which sum to give the coefficient of the x- term (- 5)

The factors are - 9 and + 4, since

- 9 × 4 = - 36 and - 9 + 4 = - 5, thus

(x - 9)(x + 4) = 0

Equate each factor to zero and solve for x

x - 9 = 0 ⇒ x = 9

x + 4 = 0 ⇒ x = - 4

6 0
3 years ago
Find the GCF of the terms of the polynomial. 30x3 + 16x5<br> a. x3<br> b. 2x3<br> c. 2x5<br> d. 16x
Vladimir79 [104]
You can take out 2x^3 from both terms making it
2x^3 (15+8x^2)
Answer is B
3 0
3 years ago
Other questions:
  • PLEASE HELP!! The amount a string stretches varies linearly with the mass applied to the spring, as can be seen in the video. In
    6·2 answers
  • How can i write 0.632 in 2 other forms
    9·1 answer
  • Which of the following statements is not always true?
    6·2 answers
  • Cindy went to Maggie Moo's for an ice cream cone after school. The ice cream cone had a radius of 3 inch, a
    6·1 answer
  • Using the standard normal table, about what percent of American adults have borderline-high cholesterol levels?
    6·2 answers
  • Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y' = x2y − 1 2 y
    15·1 answer
  • a plot of land is rectangular and has an area of x^2-5x-24m^2 . the length is x+3m. Find the width of the plot.
    14·1 answer
  • FREE
    7·1 answer
  • Given that triangle LMN is<br> similar to triangle GJH, what is<br> the value of x?
    15·1 answer
  • An article bought for Rs 1000 is sold in 4\div5 of the cost price. What is the profit percent ? ​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!