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3 years ago

Please help. Solve 2x - 8 < 7.

Mathematics

2 answers:

kotegsom [21]3 years ago

4 0

ANSWER

The correct answer is C

EXPLANATION

The given inequality is:

$2x - 8 \: < \: 7$

Group the constant terms on the right hand side to get;

$2x \: < \: 7 + 8$

Simplify the right hand side

$2x \: < \: 15$

Divide both sides by 2

$x \: < \: \frac{15}{2}$

{x|x<15/2}

The correct answer is C

hram777 [196]3 years ago

4 0

Answer:

$\large\boxed{\left\{x\ |\ x$

Step-by-step explanation:

$2x-8$

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OMG HELP PLEASE LOOK AT THE IMAGE!!!!! IT'S ABOUT Dilations: Scale Factors

Soloha48 [4]

Answer:

The distance is already 3 so with the scale factor you multiply it by 2.

Thus, the answer is 6 ;-;

Step-by-step explanation:

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3 years ago

The slope of the line below is to use the corners of the labeled point to find a point slope equation of the line.

dexar [7]

Answer: Choice A) y - 10 = 2(x - 3)

============================================================

Explanation:

We can rule out choices C and D because this diagonal line has a positive slope (as it moves uphill when moving to the right).

So m = 2 must be the slope.

---------

Recall that

y - y1 = m(x - x1)

represents the point slope form of a linear equation.

The point shown on this graph is (3,10) meaning that x1 = 3 and y1 = 10 pair up together.

So,

y - y1 = m(x - x1)

y - 10 = 2(x - 3)

which points to choice A as the final answer

4 0

3 years ago

Calculus 2. Please help

Anarel [89]

Answer:

$\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}}} \, dx = \infty$

General Formulas and Concepts:

Algebra I

Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

Limits

Right-Side Limit: $\displaystyle \lim_{x \to c^+} f(x)$

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integrals

Definite Integrals

Integration Constant C

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

U-Solve

Improper Integrals

Exponential Integral Function: $\displaystyle \int {\frac{e^x}{x}} \, dx = Ei(x) + C$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx$

Step 2: Integrate Pt. 1

[Integral] Rewrite [Exponential Rule - Rewrite]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \int\limits^1_0 {\frac{e^{-x^2}}{x} \, dx$
[Integral] Rewrite [Improper Integral]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \int\limits^1_a {\frac{e^{-x^2}}{x} \, dx$

Step 3: Integrate Pt. 2

Identify variables for u-substitution.

Set: $\displaystyle u = -x^2$
Differentiate [Basic Power Rule]: $\displaystyle \frac{du}{dx} = -2x$
[Derivative] Rewrite: $\displaystyle du = -2x \ dx$

Rewrite u-substitution to format u-solve.

Rewrite du: $\displaystyle dx = \frac{-1}{2x} \ dx$

Step 4: Integrate Pt. 3

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} -\int\limits^1_a {-\frac{e^{-x^2}}{x} \, dx$
[Integral] Substitute in variables: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} -\int\limits^1_a {\frac{e^{u}}{-2u} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}\int\limits^1_a {\frac{e^{u}}{u} \, du$
[Integral] Substitute [Exponential Integral Function]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(u)] \bigg| \limits^1_a$
Back-Substitute: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(-x^2)] \bigg| \limits^1_a$
Evaluate [Integration Rule - FTC 1]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(-1) - Ei(a)]$
Simplify: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{Ei(-1) - Ei(a)}{2}$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \infty$

∴ $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx$ diverges.

Topic: Multivariable Calculus

7 0

3 years ago

A biology teacher wants to know which dissection his students liked best this semester, so he randomly selects eights students f

natali 33 [55]

Answers:

a) The 40 students selected to participate in the survey (8*5 = 40).
b) The population is the set of all students in his five classes combined.

===========================================================

Explanation:

The teacher wants to know something about his students, so he's only focused on them and no one else. The teacher has 5 classes. Let's say each class has 40 students. That would mean 40*5 = 200 students total are taught by this bio teacher, and these 200 students make up the population. We're not considering any other student in this school since they are not in this teacher's class.

Once the population is well formed and well defined, the sample is drawn from the population. Specifically, the teacher is randomly selecting 8 people from each class. The teacher is using the stratified sample technique. Each class is a stratum, ie, a separate group. The plural of stratum is strata. Because there are 5 classes, and 8 people selected per class, this leads to an overall sample of 8*5 = 40 students. Those 40 students chosen randomly fairly represent the 200 students in the population. Therefore, this process is fairly unbiased.

Be sure not to mix stratified sampling with cluster sampling. Cluster sampling is not performed here because that would mean the teacher randomly selects say 2 classrooms (ie clusters) and samples everyone in each cluster selected. Instead, the teacher is only picking representatives from each class, as if those people were elected to office. As you can probably guess, cluster sampling can be expensive in terms of time and money, so if you need to apply a cluster sample, then it's best to make the clusters as small as possible but also make sure each cluster is reflective of the population.

5 0

3 years ago

The number line show the distance in meters

nadezda [96]

<h3>RESPUESTA</h3><h3>la recta numérica también puede medirse en centímetros</h3>

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4 years ago