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3 years ago

What is the midpoint of (-2,3) and (10,3) *simple answer please

Mathematics

1 answer:

Allushta [10]3 years ago

5 0

The "midpoint formula" is the same as the "average formula:"

x-coordinate of the midpoint = average of -2 and 10:

= (-2 + 10) / 2 = 4

y-coordinate of the midpoint = average of 3 and 3:

= (3+3) / 2 = 3

Thus, the midpoint of the given line segment is (4,3).

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A chemistry teacher needs to mix a 20% salt solution with a 80% salt solution to make 25 qt of a 44% salt solution. How many qua

NNADVOKAT [17]

Let there be x quarts of the 20% salt solution, and (25 - x) quarts of the 80% salt solution.
Then the total amount of salt in the 20% portion would be 0.2x, while that from the 80% portion would be (0.8)(25 - x). This would have to total up to (0.44)(25) in the final solution, so the equation is:
0.2x + 0.8(25 - x) = (0.44)(25)
-0.6x + 20 = 11
x = 15 quarts of the 20% salt solution
25 - x = 10 quarts of the 80% salt solution

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3 years ago

Jamal is going to borrow $25,000 from his credit union to buy a used car. The APR is 7% and the length of the loan is 5 years. W

DochEvi [55]

his final charge is going to be 7

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3 years ago

Why does a logarithmic equation sometimes have an extraneous solution?

jonny [76]

The main reason behind this is using properties of logarithm .

when solving

log_2(x+2)+log_2(x-3)=3

There you use multiplication property and make addition to multiplication then you get extraneous solution because in plenty of cases they occur

(-2)²=(2)²

But

-2≠2

Same happens in case of logarithm

6 0

2 years ago

Read 2 more answers

Find the area of the region enclosed by the graphs of the functions

Vaselesa [24]

Answer:

$\displaystyle A = \frac{8}{21}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients
Functions
Function Notation
Graphing
Solving systems of equations

Calculus

Area - Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

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

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

*Note:

Remember that for the Area of a Region, it is top function minus bottom function.

Step 1: Define

f(x) = x²

g(x) = x⁶

Bounded (Partitioned) by x-axis

Step 2: Identify Bounds of Integration

Find where the functions intersect (x-values) to determine the bounds of integration.

Simply graph the functions to see where the functions intersect (See Graph Attachment).

Interval: [-1, 1]

Lower bound: -1

Upper Bound: 1

Step 3: Find Area of Region

Integration

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^1_{-1} {[x^2 - x^6]} \, dx$
[Area] Rewrite [Integration Property - Subtraction]: $\displaystyle A = \int\limits^1_{-1} {x^2} \, dx - \int\limits^1_{-1} {x^6} \, dx$
[Area] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = \frac{x^3}{3} \bigg| \limit^1_{-1} - \frac{x^7}{7} \bigg| \limit^1_{-1}$
[Area] Evaluate [Integration Rule - FTC 1]: $\displaystyle A = \frac{2}{3} - \frac{2}{7}$
[Area] Subtract: $\displaystyle A = \frac{8}{21}$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Area Under the Curve - Area of a Region (Integration)

Book: College Calculus 10e

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3 years ago

What is -138>-6(6b-7)

sertanlavr [38]

First you distribute the six -138>-36b+42 Then you subtract 42 -180>-36b Next, you divide by -36 and since you are dividing by a negative, you turn the sign around 5

6 0

3 years ago