True or False: The origin would be included in the solution set for the inequality: y < 2x - 5

Answers

Answer 1

Answer: Sorry. That inequality would not include the origin.

It says that 'y' is everything less than x-5 .

When x=0, the origin is at y=0, but the limit of the inequality is way down at -5.

Answer 2

Answer: $0<2\cdot0-5\n 0<0-5\n 0<-5\n$

False.

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Also the last one is a N—Find the measure of each missing angle in each triangle

Which function's graph has a y-intercept of 2? A. f(x) = 3x + 2 B. f(x) = 0.5(2)* + 1.5 C. f(x) = 0.5(2)* + 1 O D. f(x) = 1.5(2)

Answers

d because it goes together

What are the vertical asymptotes of the function above?1) x= -1 and x = -2
2) x= -1 and x = 2
3) x= 1 and x = -2
4) x = 1 and x = 2

Answers

Answer:

third option

Step-by-step explanation:

Given

f(x) = $(5x+5)/(x^2+x-2)$

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

solve x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

The vertical asymptotes are x = 1 and x = - 2

Average national teachers salaries can be modeled using the equation y=9.25(1.06)^n , where y is the salary in thousands of dollars and n is the number of years since 1970A) graph the function
B) using this model, what can a teacher expect to have as a salary in year 2020?
Please help !

Answers

$y=9.25(1.06)^(n)$
Plug in $n$ to find $y$ .
$n$ would be $50$ because $2020-1970=50$ .

Use order of operations to solve.
$y=9.25(1.06)^(50) \n y=9.25(18.42) \n y=170.39$

Since $y$ is the salary in thousands, multiply $170.39$ by $1000$ .
$170.39*1000=17039$

A teacher can expect to have about $17,039 as a salary in the year 2020.

Final answer:

The average national teachers salaries can be graphed by plotting points on a coordinate plane. Using the provided equation, we can calculate the salary for the year 2020 to be approximately $99,460.

Explanation:

To graph the function, we need to plot points on a coordinate plane. We can do this by choosing different values of n and calculating the corresponding values of y. For example, if n = 0, then y = 9.25(1.06)^0 = 9.25. If n = 1, then y = 9.25(1.06)^1 = 9.81. Continuing this process, we can find multiple points and plot them on the graph.

To find the salary for the year 2020, we can plug in n = 2020 - 1970 = 50 into the equation. y = 9.25(1.06)^50 ≈ 99.46 thousand dollars, which is approximately $99,460.

Learn more about Average national teachers salaries here:

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The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.a. 8/9
b. 2

Answers

the answer would be 2

Solve using logs 5^(3x-6)=125

Answers

$5 ^(3x-6) =125 \n \n 5 ^(3x-6) =5^3 \n \n3x-6 =3 \ \ |+6 \n \n3x=3+9 \n \n3x=12 \ \ /:3 \n \nx=(12)/(3) \n \nx= 3$

In two or more complete sentences, explain the theorem used in solving for the range of possible lengths of the third side, AB of triangle ABC

Answers

Answer:

Step-by-step explanation:

In triangle if two sides are known and included angle is known we can use cosine formula as follows:

Say in a triangle, sides a,b are known and also included angle C

Then the third side

$c^(2) =a^(2)+b^(2) -2abCos C$

Since all values on right side are known, we can find the third side c easily.

Case II:

If alternately two sides and one angle not included is known. i.e we know a,b and either angle A or B.

then to find third side we use sine formula.

$(a)/(sinA)=(b)/(sinB) =(c)/(sinC)$

Using the above we can find the unknonwn side c easily.

You can use the Pythagorean Theorem to find the length of the third side AB (Identified as "x" in the figure attached in the problem), which says that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs:
a² = b²+c²
As we can see the figure, the triangle does not have an angle of 90°, but it can be divided into two equal parts, leaving two triangles with a right angle. We already have the values of the hypotenuse and a leg in triangle "A" , so we can find the value of the other leg:
b = √(a²-c²) b = √(10²-4²) b = 9.16
With these values, we can find the hypotenuse in the triangle "B": x = √b²+c² x = √(9.16)²+(4)² x = 10

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