Why is the expression 5(3x + 2) equivalent to 15x + 10

the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Given data:

The expression for the function is f(x)=6x^2 -11x+3.

The expression for the roots of f(x) is,

Thus, the roots of the given function is 1/3 and 3/2.

well, if it was 300 and now is 350, it went up by 50 bucks, that's the inflation amount.

if we take 300 to be the 100%, what is 50 bucks off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 300 & 100\\ 50& x \end{array} \implies \cfrac{300}{50}=\cfrac{100}{x}\implies 6=\cfrac{100}{x} \\\\\\ 6x=100\implies x=\cfrac{100}{6}\implies x=\cfrac{50}{3}\implies x\approx 16.7\)

Answer:

15%

Step-by-step explanation:

Percent increase in the original price of jacket = 15%

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given,

Original price of jacket = $110

Increased price of jacket = $126.5

Increased amount = $126.5 - $110

                               = $16.5

Increased amount in percentage = ($16.5/$110) × 100

                                                       = 0.15 × 100

                                                       = 15%

Hence, 15% is increase in the original price of jacket.

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height of the house is 28.4 ft

shadow of the house = 57 feet

height of the house = ?

Height of the girl = 4.7 feet

shadow of the girl = 9.4m

The formula:

height of the house/shadow of the house = height of the girl/shadow of the girl

Answer:

Here we can take advantage of exactly the property suggested by Xisca... that is, sqrt(44)=2sqrt(11), which reduces the calculation to more accuracy with a lesser knowledge of the squares of numbers.

As a first approximation, we know that 33*33=1089, or 3.3*3.3=10.89, which is already very close to 11.  

Thus a first approximation to sqrt(44)=2sqrt(11)=2*3.3=6.6 (approximately).

To refine the calculation of sqrt(11), we use Newton's approximation, namely

a better approximation is given by 3.3 + (11 - 3.3^2) / (2*3.3) = 3.3+0.11/6.6 = 3.3+1/60

which gives

sqrt(44) = 2(3.3+1/60) = 6.6+1/30 = 6.6333,

actually accurate almost to the nearest 1/10000.

All of the above can be done mentally

For those who need help with rounding to the nearest hundredth (0.01), we drop digits AFTER the 2nd decimal, namely *.**33.  If the first digit dropped is 5 or more, add one to the last digit retained, otherwise, retain only the two digits after the decimal.  In this case, the first digit dropped is 3, so it will simply be dropped.  The final answer is then 6.63, to the nearest hundredth.

Given:

The taxi charges $3.50 for the first mile and then $2.75 for each mile.

The total charge is $ 18.63.

The equation is given as,

Put the values in the equation,

Answer: Juan's taxi ride to the movie is approximately 6.5 miles.

All the possible values for the number 'x' will be less than or equal to 1,350.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The remainder of a number and 5 in addition to 25 is something like 45.

Let the number be 'x'. Then the inequality is given as,

x / (5 + 25) ≤ 45

x / 30 ≤ 45

x ≤ 1,350

All the possible values for the number 'x' will be less than or equal to 1,350.

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Answer:

I think the answer will be the infinity sign=1 whole, 1/9

Answer:

60 of each

Step-by-step explanation:

water          juice

12                10

24               20

36               30

48               40

60               50

                  60

Answer:

12

Step-by-step explanation:

Given that,

f(x) = 2x² - 3x + 7

To find the value of f ( 2.5 ), replace x with 2.5 and solve the equation.

Let us solve it now.

f(2.5) = 2(2.5)² - 3×2.5 + 7

f(2.5) = 12.5 - 7.5 + 7

f(2.5) = 12

Answer:

\(f(x) = 2 {x}^{2} - 3x + 7 \\ f(2.5) = 2 {(2.5)}^{2} - 3(2.5) + 7 \\ f(2.5) = 12.5 - 7.5 + 7 \\ \boxed{f(2.5) = 12}\)

Answer:

42

Step-by-step explanation:

similar triangles

24/x = (24+8)/x+14

that looks complicated so we do

8/24 = 14/x

or

24/8 = x/14

3 = x/14

x = 3*14

x = 42

we test it with the first equation

24/42 = 32/56

simplify

4/7 = 4/7

true so 42 is correct

Answer:

59

Step-by-step explanation:

Step-by-step explanation:

a dilation does not shift objects.

it makes them bigger or smaller.

and because this is done by adjusting the point coordinates, it can also seemingly move the larger or smaller projection image.

a dilation with factor k converts every point

(x, y) into (x×k, y×k).

that's it.

you only need to mark the new points and then connect them.

15.

k = 2

A = (1, 1), A' = (2, 2)

B = (2, -1), B' = (4, -2)

C = (-2, 0), C' = (-4, 0)

16.

k = ¼

A = (0, 4), A' = (0, 1)

B = (4, -4), B' = (1, -1)

Can = (-4, -4), C' = (-1, -1)

17.

k = ½

A = (4, 4), A' = (2, 2)

B = (4, 8), B' = (2, 4)

C = (6, 4), C' = (3, 2)

D = (6, 6), D' = (3, 3)

18.

k = 1 ½ = 3/2

A = (2, 0), A' = (2×3/2, 0×3/2) = (3, 0)

B = (0, -2), B' = (0, -3)

C = (-2, 1), C' = (-3, 3/2) = (-3, 1.5)

D = (1, 2), D' = (3/2, 3) = (1.5, 3)

19.

k = 2

A = (2, 0), A' = (4, 0)

B = (2, 2), B' = (4, 4)

20.

k = ½

A = (2, 4), A' = (1, 2)

B = (6, 2), B' = (3, 1)

Answer:

20

Step-by-step explanation:

Answer: is 20 much fabric she needs

Step-by-step explanation: anna  needs 20 fabirc

Answer:

B) 26

Step-by-step explanation:

Since the triangle is a right triangle angle 1 and 2 should add to 90 degrees. you would evaluate 6x+2+16x=90. 22x+2=90. 2x=88x. x=4. Plug 4 into the equation for angle 1. 6(4)+2=26

Answer:

3K

Step-by-step explanation:

Answer:

e is 63 degrees

d is 31 degrees

Answer:

6). x + 70° + 70° = 180°

x + 140° = 180°

x = 180° - 140° = 40°

Therefore x is equal to 40°

7). y + 55° +60° = 180°

y + 115° = 180°

y = 180° - 115° = 65°

Therefore x is equal to 65°

8). n + n + 50° = 180°

2n + 50° = 180°

2n = 180° - 50° = 130°

n = 130°/2 = 65°

Therefore both the angles are 65°

Explaination:

All the angles of a triangle always add up to 180°

Answer:

146.66

Step-by-step explanation:

The only automorphism of a well-ordered set is the identity.

To prove this statement, we need to show that any automorphism of a well-ordered set must be the identity function. An automorphism is a bijective function that preserves the order structure of the set.

Assume we have a well-ordered set (W, ≤), where W is the set and ≤ is the order relation.

Let f: W → W be an automorphism of the set.

We aim to prove that f is the identity function, i.e., f(x) = x for all x ∈ W.

Suppose, for contradiction, that there exists an element a ∈ W such that f(a) ≠ a.

Since f is a bijective function, there must exist some b ∈ W such that f(b) = a.

Since (W, ≤) is well-ordered, there is a least element c in the set {x ∈ W : f(x) ≠ x}.

Let d = f(c). Since f is an automorphism, f(c) ≠ c, and thus d ≠ c.

Since (W, ≤) is well-ordered, there is a least element e in the set {x ∈ W : f(x) = d}.

Consider the element f(e). Since f is a bijective function, there must exist some f^{-1}(f(e)) = e' ∈ W such that f(e') = f(e) = d.

By the definition of automorphism, f(f^{-1}(y)) = y for all y ∈ W. Applying this property to e', we have f(f^{-1}(f(e'))) = f(e') = d.

However, f^{-1}(f(e')) = e' ≠ c, and thus f(e') ≠ d. This contradicts the fact that e is the least element in the set {x ∈ W : f(x) = d}.

Therefore, our assumption that there exists an element a such that f(a) ≠ a is false.

Since we assumed f(a) ≠ a for arbitrary a ∈ W, it follows that f(x) = x for all x ∈ W.

Hence, the only automorphism of a well-ordered set is the identity function.

Therefore, we have proven that the only automorphism of a well-ordered set is the identity function.

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Answer:

Step-by-step explanation:

x = 774.37(0.972)

x = 752.68764

x = 752.69  km

descending order???? OK... 97652

Answer:

89.8ft

Step-by-step explanation:

678-672=6, the value for line ZW

Using Pythagoras theorem, then t²+6²=90²

t²=90²-6²

t²=8100-36

√t²=√8064

t=89.8ft

Answer:

sum = 37 + -18 =19

difference = 37 - -18 = 55

Step-by-step explanation:

Answer:

Step-by-step explanation:

The full surface area is:

Correct choice is D

Step-by-step explanation:

SA = 12(3 + 4 + 5) + 2(½ × 3 × 4)

SA = 12(12) + 2(2 × 3)

SA = 144 + 2(6)

SA = 144 + 12

SA = 156 cm²

Therefore

Surface area of prism is 156 cm². Option D

Answer:

Down Here.

Step-by-step explanation:

Ok, let's try it this way.

Step 2:

Statement: CD = CD

Reason: Reflexive property

The sides are shared so they are equal

Step 3:

Statement: ∠ACD ≅ ∠BCD

Reason: Def. of angle bisector

Step 4:

Statement: ΔACD≅ΔBCD

Reason: SAS

-Chetan K

An absolute value inequality for given graph is |x| ≤ 6

In this question, we have been given a graph of a number line.

We need to write an absolute value inequality for given graph.

From the given graph, we can observe that the value of x lies between -6 to 6.

i.e., -6 ≤ x ≤ 6

We know that, for a real number 'm', the absolute value function for m would be,

|±m| = m

So, -6 ≤ x ≤ 6

|x| ≤ 6, which is required inequality.

Therefore,  an absolute value inequality for given graph is |x| ≤ 6

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Answer:

a

Step-by-step explanation:

Answer:

Percent of people satisfied with the​ car  = 70%

Step-by-step explanation:

Given:

Total number of people survey = 1,400

Number of people satisfied with the​ car = 980

Find:

Percent of people satisfied with the​ car

Computation:

Percent of people satisfied with the​ car  = [Number of people satisfied with the​ car / Total number of people survey]100

Percent of people satisfied with the​ car  = [980 / 1400]100

Percent of people satisfied with the​ car  = 70%