Item 2
A container holds 54.6 gallons of liquid. The container leaks 8.4 gallons per hour.

How many hours will it take for the container to empty?

Enter your answer as a decimal in the box.

If the factors of quadratic function f are (x – 7) and (x + 3). The solution of the quadratic function f will be the negative 3 and 7.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

If the factors of quadratic function f are (x – 7) and (x + 3).

Then the zeroes of function f will be

(x – 7)(x + 3) = 0

                x = 7, -3

Then the solution of the quadratic function f will be the negative 3 and 7.

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The factors of the function after factorization f(x)=[tex]x^{2} -7x-18[/tex] is (x+2) and (x-9)

Given Function  f(x)=[tex]x^{2} -7x-18[/tex] and we have to find the factors of the given function.

The function whose factors are to be found is   f(x)=[tex]x^{2} -7x-18[/tex]

Factorization means finding various expressions which when together multiplied will give the  function itself. Correct combination can only be found by finding the factors of the function. Without finding factors no one can find the solution of an equation or expression also.

f(x)=[tex]x^{2} -9x+2x-18[/tex]

=x(x-9)+2(x-9)

=(x+2)(x-9)

Hence the  factors which when combine together gives function f(x)=[tex]x^{2} -7x-18[/tex] are (x+2)(x-9).

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Option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.

The measurements of the sides and angles of two or more geometrical figures determine their congruence. For example triangle's size is determined by its three sides, and its shape is determined by its three angles.

We have:

The diagram represents an unfolded paper kabuto, a samurai warrior's helmet.

Unfolded paper can be seen in the provided figure. The sheet is square.

The diagonals, in this case, are FN and AK, and the midline is CM and OI. At point R, all of these lines converge.

FR ≅ NR

AO ≅ ON

RC ≅ RO

NO ≅ NM

DV ≅ HV

Thus, option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.

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Answer:

Step-by-step explanation:

Comment

I find the wording a bit confusing. Does the question mean that the laws of algebra determine what single vale of x will make the right side = the left side in both equations?

I think that's the way I will interpret it.

The easiest way to solve both of them is to divide by 4 on both sides of the top equation and divide by 2 on the bottom equation.

Solution

Top equation

4(x - 2) = 1000                                 Divide by 4

4(x-2 )/ 4 = 1000/4          

(x - 2)  = 250                                    Remove the brackets

x - 2 = 250                                       Add 2 to both sides

x - 2 + 2 = 250 + 2                           Combine

x = 252

Bottom equation

2(x - 2) = 50                                      Divide by 2

2(x - 2)/2 = 50/2

(x - 2) = 25                                        Remove the brackets

x - 2 = 25                                          Add 2 to both sides

x - 2 + 2 = 25 + 2                              Combine

x = 27

Conclusion

If the equations are structured the same way but have different numbers then the answers will be unique.

(a) Given [tex]f(x) = x^3[/tex], the derivative is

[tex]f'(x)=3x^2[/tex]

which is exists for all [tex]x[/tex] in the domain of [tex]f[/tex], so [tex]]f[/tex] is differentiable everywhere and satisfies the mean value theorem. There is some number [tex]c[/tex] in the open interval (0, 2) such that

[tex]f'(c) = \dfrac{f(2) - f(0)}{2-0} \iff 3c^2 = \dfrac{8-0}2 = 4[/tex]

Solve for [tex]c[/tex] :

[tex]3c^2 = 4 \implies c^2 = \dfrac43 \implies \boxed{c = \dfrac2{\sqrt3}}[/tex]

We omit the negative square root since it doesn't belong to (0, 2). Graphically, the MVT tells us the tangent line to the curve [tex]f(x)=x^3[/tex] at [tex]x=\frac2{\sqrt3}[/tex] is parallel to the secant line through the endpoints of the given interval.

(b) [tex]f(x)=1+x+x^2[/tex] has derivative

[tex]f'(x)=1+2x[/tex]

By the MVT,

[tex]f'(c) = \dfrac{f(2)-f(0)}{2-0} \iff 1+2c = \dfrac{7-1}2 \implies \boxed{c = 1}[/tex]

(c) [tex]f(x) = \cos(2\pi x)[/tex] has derivative

[tex]f'(x) = -2\pi \sin(2\pi x)[/tex]

By the MVT,

[tex]f'(c) = \dfrac{f(2)-f(0)}{2-0} \iff -2\pi \sin(2\pi c) = \dfrac{0-0}2 \implies \sin(2\pi c) = 0 \\\\ \implies 2\pi c = n\pi \implies c = \dfrac n2[/tex]

where [tex]n[/tex] is any integer. There are 3 solutions in the interval (0, 2),

[tex]\boxed{c = \dfrac12, c = 1, c = \dfrac32}[/tex]

(Pictured is the situation with [tex]c=\frac12[/tex])

Answer:

yes.

but it will be in decimals if you divide by two. And if you divide it by another rank, it will surely give a whole number. please this all I can do for you and add me to your followers

The approximate length of the side EF will be 1 unit.

The complete figure is attached below.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The figure is given below.

The length of EF will be

EF = CF – CE

Then the value of CF will be

CF = BC × cos 30

CF = 2 × 0.866

CF = 1.732

Then the value of CE will be

CE = BC × cos 42

CE = 1 × 0.743

CE = 0.743

Then we have

EF = 1.732 – 0.743

EF = 0.989 ≈ 1

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Both are not earning different salaries.

If a study determines the difference in average salary for subpopulations of mechanical engineers and civil engineers is NOT significant, then the subpopulations of mechanical and civil engineers are not earning different salaries.
Study determines that there is not any significant study so thats why both are not earning.


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Answer:

[tex] {a}^{2} + 2ab + {b}^{2} [/tex]

Step-by-step explanation:

[tex](a + b) {}^{2} = (a + b)(a + b) = {a}^{2} + ab + ab + {b}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]

Hi!

___________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

a^2+2ab+b^2

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

Remember the rule for expanding a binomial squared.

[tex]\twoheadrightarrow\sf (a+b)^2=a^2+2ab+b^2[/tex]

So we square the first term, then multiply the product of the two terms times 2.

[tex]\twoheadrightarrow\sf a^2+2ab+b^2[/tex]

This is our answer.

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

Answer:

[tex] - 3 \frac{5}{7} x - 2\ \frac{1}{2} [/tex]

[tex] \frac{ - 26}{7} - \frac{5}{2} [/tex]

LCM of 7 and 2 is 14

Multiplying (-26/7) with 1/2 (to make the denominator 14) and -5/2 with 1/7

[tex] \frac{ - 26}{7} \times \frac{1}{2} - \frac{5}{2} \times \frac{1}{7} [/tex]

[tex] \frac{ - 26}{14} - \frac{5}{14} [/tex]

[tex] \frac{ - 26 - 5}{14} [/tex]

[tex] - \frac{31}{14} [/tex]

Answer:

2 + 2: 4

or 2 + 2: 5 from the dystopian novel 1984.

The equivalent interest rate is 4.07%.

The money will be compounded 12 times.

The equivalent interest rate is the actual interest rate that an account earns after accounting for number of compounding.

Effective interest rate = (1 + APR / m ) ^m - 1

M = number of compounding

(1 + 0.04/12)^12 - 1 = 4.07%

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An equation is formed of two equal expressions. The medals won by country A, country B, and country C is 79, 26, and 11, respectively.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of medals won by country A, country B, and country C be represented by A, B, and C, respectively. Now, the given conditions can be written as,

1.) The top three countries country A, country B, and country C won a total of 120 medals.

A + B + C = 120

2.) Country B won 11 more medals than country C

B = C + 11

3.) Country A won 38 more medals than the total amount won by the other two.

A = B + C + 38

A - 38 = B + C

Substitute the value of B+C form the last equation to the first equation,

A + A - 38 = 120

A = 79

Now, Substitue the value of A and B(from second equation)  in the first equation,

79 + C + 11 + C = 120

C = 15

Now, substitute the value of C in the second equation,

B = C + 11

B = 15 + 11

B = 26

Hence, the medals won by country A, country B, and country C is 79, 26, and 11, respectively.

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The linear equation that contains the coordinate parts in the given table is: y = 1/3x + 2.

To find the linear equation that contains the coordinate parts in the table given, find the slope (m) and y-intercept (b), then substitute the values into y = mx + b.

Slope (m) using two coordinate parts, (0, 2) and (3, 3):

Slope (m) = change in y / change in x = (3 - 2)/(3 - 0)

Slope (m) = 1/3

y-intercept (b) = 2 [this is the value of y when x = 0)

Substitute the values into y = mx + b

y = 1/3x + 2.

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Answer: 5

Step-by-step explanation:

As all radii of a circle are congruent, [tex]\overline{OX} \cong \overline{OY}[/tex], it follows that [tex]\angle OXY \cong \angle OYX[/tex].

Because arc XY measures 60 degrees, we also know that [tex]m\angle XOY=60^{\circ}[/tex], and thus triangle OXY is equilateral.

Hence, XY=5 because all sides of an equilateral triangle are congruent.

Answer:

5. 540°

Step-by-step explanation:

m<a + m<c = 180°

m<h + m<f = 180°

m<k + m<m = 180°

Then m<a + m<c + m<h + m<f + m<k + m<m = 180° x 3 = 540°

7 = Tenth

7 is the first decimal of the number making it a tenth.

Answer: letter B (answer is 2)

Step-by-step explanation:

Answer:

20ish

Step-by-step explanation:

I would need more info abt the question to answer it more exactly

Answer:

Im pretty sure is is 20 or something like that

Step-by-step explanation:

Answer:

The numerical sum of the degree measures of ∠DEA and ∠AEB is

= 180°

Step-by-step explanation:

supplementary angles :

The meaning of supplementary is related to angles that make a straight angle together. It means, two angles are said to be supplementary angles when they add up to 180 degrees. Two angles that are supplementary to each other, do not have to be next to each other. Two angles are supplementary, if

This means that ∠p + ∠q = 180°.

From the given figure, we can see that:

∠DEA + ∠AEB = 180°

x+25+9x+10 = 180°

10x + 35 = 180°

10x = 180° - 35°

10x = 145°

x = 145/10

x = 14.5°

Get  ∠DEA

∠DEA = x + 25

∠DEA = 14.5 +25

∠DEA = 39.5°

Get ∠AEB:

∠AEB = 9x+10

∠AEB = 9(14.5) + 10

∠AEB = 130.5 + 10

∠AEB = 140.5 °

Hence the value of x,  ∠DEA, and ∠AEB are 14.5°, 39.5°, and 140.5°

so, The numerical sum of the degree measures of ∠DEA and ∠AEB is

= 39.5 + 140.5

= 180° (answer)

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Answer:

60 miles

Step-by-step explanation:

miles that Sophia drove = 3/5 x 100 = 60 miles

A fraction is a way to describe a part of a whole. The distance covered by Sophia and Toby is 300 miles and 200 miles, respectively.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

A fraction can also be described in the form of a percentages, to represent the part of the whole.

Given that the length of the entire trip is 500 miles. Also, the first 3/5 of the trip are covered by Sophia and the last 2/5 of the trip are covered by Toby.

Now, the distance covered by Sophia and Toby will be,

Distance covered by Sophia = (3/5) × 500 miles = 300 miles

Distance covered by Toby = (2/5) × 500 miles = 200 miles

Hence, the distance covered by Sophia and Toby is 300 miles and 200 miles, respectively.

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Answer:

For a principle amount of $1600 and rate 5.4%, the effective annual yield is 5.55% if interest is compounded annually.

Step-by-step explanation:

Concept: The annual percentage yield (APY) or the effective annual yield is the real rate of return earned on an investment, taking into account the effect of compounding interest.

The principle amount is $1600, rate is 5.4% and period is 365 days. The formula to find yield is [tex]Y = (1+\frac{r}{n} )^{n} -1[/tex]. All the values are to be inserted in the formula. Here n = 365 and r = 5.4%.

[tex]Y=(1+\frac{0.054}{365} )^{365} -1\\Y=(1.000148)^{365} -1\\Y=5.55%[/tex]

The annual yield is 5.55%.

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Step-by-step explanation:

[tex] \sin(\pi - x) + \tan(x) \cos(x) (x - \frac{\pi}{2} [/tex]

[tex] \sin( - x + \pi ) + \tan(x) ( \cos(x - \frac{\pi}{2} ) )[/tex]

Sin is odd function, so if you add pi to it, it would become switch it sign.

[tex] - \sin( - x) + \tan(x) \cos(x - \frac{\pi}{2} ) [/tex]

Also since sin is again, a odd function, we can just multiply the inside and outside by -1, and it would stay the same.

[tex] \sin(x) + \tan(x) \cos(x - \frac{\pi}{2} ) [/tex]

Cosine is basically a sine function translated pi/2 units to the right or left so

[tex] \sin(x) + \tan(x) \sin(x) [/tex]

[tex] \sin(x) ( 1 + \tan(x) )[/tex]

The equation that relates x and y is y = (1/3)x if the variables x and y vary directly and x = 18, y = 6.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

The question is incomplete.

The complete question is:

The variables x and y vary directly. Use the given values to write an equation that relates x and y. x = 18 y = 6

From the question:

y ∝ x

y = kx ..(1)

k is the constant of proportionality after removing the proportional sign.

Plug x = 18 and y = 6

6 = 18k

k = 1/3

Plug the value of k in the equation (1)

y = (1/3)x

Thus, the equation that relates x and y is y = (1/3)x if the variables x and y vary directly and x = 18, y = 6.

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The probability notation for the probability of choosing a green marble is P(G)

This is simply defined as the extent to which something is likely to occur.

The probability that an event will occur is given as the ratio of the number of favorable outcomes to the total number of outcomes.

Probability notation is a symbol used in indicating the probability of an occurring event. Since our focus is on the probability of obtaining a green marble, then the probability notation will be P(G). This is illustrated below:

P(G) = nG / nT

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The number of hours spent playing video games is the independent variable and cumulative grade point average is the dependent variable.

An independent variable simply means the variable that's changed to test the effect on the dependent variable.

Here, the number of hours spent playing video games is the independent variable and cumulative grade point average is the dependent variable.

This is because the number of hours is being used to predict cumulative grade point average.

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Answer:

B) 1/8

Step-by-step explanation:

each child born has 50/50 to be a boy or a girl, so, we determine a Bernoulli process where p=0.5, and we need 3 out of 3 successes.

the probability will then be:

(0.5)³=0.125=1/8

Answer: 1.3062

Step-by-step explanation:

0.311 * 4.2 = 1.3062