The expression (x − 4)2 is equivalent to x2 − 16 x2 + 16 x2 − 8x + 16 x2 + 8x + 16

approximately 91.15 grams of HCl are needed to make a 5 M HCl solution using 500 milliliters of water.

To determine the number of grams needed to make a 5 M HCl solution using 500 milliliters of water, we need to consider the molar mass of HCl and the desired concentration.

The molar mass of HCl is approximately 36.46 grams/mol.

First, we need to calculate the number of moles of HCl required to achieve a 5 M concentration:

Molarity (M) = moles of solute / volume of solution (in liters)

Rearranging the equation:

moles of solute = Molarity (M) * volume of solution (in liters)

Given that the desired molarity is 5 M and the volume of solution is 500 milliliters (0.5 liters), we can calculate the moles of HCl required:

moles of HCl = 5 M * 0.5 L = 2.5 moles

To convert moles to grams, we can use the molar mass of HCl:

grams of HCl = moles of HCl * molar mass of HCl

grams of HCl = 2.5 moles * 36.46 g/mol ≈ 91.15 grams

Therefore, approximately 91.15 grams of HCl are needed to make a 5 M HCl solution using 500 milliliters of water.

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The optimal solution point that returns the maximum Z is (x₁, x₂) = (9, 3).

To find the optimal solution for the given linear programming problem, we need to evaluate the objective function Z = 10x₁ + 20x₂ at each feasible point and choose the combination (x₁, x₂) that maximizes Z.

The feasible region is defined by the following constraints:

x₁ ≤ 9

x₂ ≤ 3

x₁, x₂ ≥ 0

Let's calculate the value of Z at each feasible point:

1. (x₁, x₂) = (0, 0)

Z = 10(0) + 20(0) = 0

2. (x₁, x₂) = (0, 3)

Z = 10(0) + 20(3) = 60

3. (x₁, x₂) = (9, 3)

Z = 10(9) + 20(3) = 90 + 60 = 150

4. (x₁, x₂) = (9, 0)

Z = 10(9) + 20(0) = 90

Comparing the values of Z at each feasible point, we see that the combination (x₁, x₂) = (9, 3) yields the maximum value of Z, which is 150.

Therefore, the optimal solution point that returns the maximum Z is (x₁, x₂) = (9, 3).

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The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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393/1000. i think, sorry. :c

The probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Renting Cars Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

Total number of outcomes = C(25, 2) = 300

Total number of favorable outcomes = C(20, 2) = 190

Probability = 190/300 = 19/30 or

= 0.63

Thus, the probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

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Answer:

B

Step-by-step explanation:

Using the rule of exponents

\(a^{-m}\) = \(\frac{1}{a^{m} }\)

Then

f(- 2) = \(3^{-2}\) = \(\frac{1}{3^2}\) = \(\frac{1}{9}\) → B

Answer:

The ruler at store A cost more

Step-by-step explanation:

Ruler A=$0.95 per ruler

Ruler B=$0.92 per ruler

\({\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}\)

\( \star \: \tt \cot \theta = \dfrac{7}{8} \)

\( {\large{\textsf{\textbf{\underline{\underline{To \: Evaluate :}}}}}}\)

\( \star \: \tt \dfrac{(1 + \sin \theta)(1 - \sin \theta) }{(1 + \cos \theta) (1 - \cos \theta) }\)

\({\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}\)

Consider a \(\triangle\) ABC right angled at C and \(\sf \angle \: B = \theta \)

Then,

‣ Base [B] = BC

‣ Perpendicular [P] = AC

‣ Hypotenuse [H] = AB

\( \therefore \tt \cot \theta = \dfrac{Base}{ Perpendicular} = \dfrac{BC}{AC} = \dfrac{7}{8}\)

Let,

Base = 7k and Perpendicular = 8k, where k is any positive integer

In \(\triangle\) ABC, H² = B² + P² by Pythagoras theorem

\( \longrightarrow \tt {AB}^{2} = {BC}^{2} + {AC}^{2} \)

\( \longrightarrow \tt {AB}^{2} = {(7k)}^{2} + {(8k)}^{2} \)

\(\longrightarrow \tt {AB}^{2} = 49{k}^{2} + 64{k}^{2} \)

\(\longrightarrow \tt {AB}^{2} = 113{k}^{2} \)

\(\longrightarrow \tt AB = \sqrt{113 {k}^{2} } \)

\(\longrightarrow \tt AB = \red{ \sqrt{113} \: k}\)

Calculating Sin \(\sf \theta \)

\( \longrightarrow \tt \sin \theta = \dfrac{Perpendicular}{Hypotenuse}\)

\( \longrightarrow \tt \sin \theta = \dfrac{AC}{AB}\)

\(\longrightarrow \tt \sin \theta = \dfrac{8 \cancel{k}}{ \sqrt{113} \: \cancel{ k } }\)

\(\longrightarrow \tt \sin \theta = \purple{ \dfrac{8}{ \sqrt{113} } }\)

Calculating Cos \(\sf \theta \)

\( \longrightarrow \tt \cos \theta = \dfrac{Base}{Hypotenuse}\)

\( \longrightarrow \tt \cos \theta = \dfrac{BC}{ AB} \)

\( \longrightarrow \tt \cos \theta = \dfrac{7 \cancel{k}}{ \sqrt{113} \: \cancel{k } }\)

\(\longrightarrow \tt \cos \theta = \purple{ \dfrac{7}{ \sqrt{113} } }\)

Solving the given expression :-

\( \longrightarrow \: \tt \dfrac{(1 + \sin \theta)(1 - \sin \theta) }{(1 + \cos \theta) (1 - \cos \theta) } \)

Putting,

• Sin \(\sf \theta \) = \(\dfrac{8}{ \sqrt{113} }\)

• Cos \(\sf \theta \) = \(\dfrac{7}{ \sqrt{113} }\)

\( \longrightarrow \: \tt \dfrac{ \bigg(1 + \dfrac{8}{ \sqrt{133}} \bigg) \bigg(1 - \dfrac{8}{ \sqrt{133}} \bigg) }{\bigg(1 + \dfrac{7}{ \sqrt{133}} \bigg) \bigg(1 - \dfrac{7}{ \sqrt{133}} \bigg)} \)

Using (a + b ) (a - b ) = a² - b²

\(\longrightarrow \: \tt \dfrac{ { \bigg(1 \bigg)}^{2} - { \bigg( \dfrac{8}{ \sqrt{133} } \bigg)}^{2} }{ { \bigg(1 \bigg)}^{2} - { \bigg( \dfrac{7}{ \sqrt{133} } \bigg)}^{2} } \)

\(\longrightarrow \: \tt \dfrac{1 - \dfrac{64}{113} }{ 1 - \dfrac{49}{113} } \)

\(\longrightarrow \: \tt \dfrac{ \dfrac{113 - 64}{113} }{ \dfrac{113 - 49}{113} } \)

\(\longrightarrow \: \tt { \dfrac { \dfrac{49}{113} }{ \dfrac{64}{113} } }\)

\(\longrightarrow \: \tt { \dfrac{49}{113} }÷{ \dfrac{64}{113} }\)

\(\longrightarrow \: \tt \dfrac{49}{ \cancel{113}} \times \dfrac{ \cancel{113}}{64} \)

\(\longrightarrow \: \tt \dfrac{49}{64} \)

\(\qquad \: \therefore \: \tt \dfrac{(1 + \sin \theta)(1 - \sin \theta) }{(1 + \cos \theta) (1 - \cos \theta) } = \pink{\dfrac{49}{64} }\)

\(\begin{gathered} {\underline{\rule{300pt}{4pt}}} \end{gathered} \)

\( {\large{\textsf{\textbf{\underline{\underline{We \: know :}}}}}}\)

✧ Basic Formulas of Trigonometry is given by :-

\(\begin{gathered}\begin{gathered}\boxed { \begin{array}{c c} \\ \bigstar \: \sf{ In \:a \:Right \:Angled \: Triangle :} \\ \\ \sf {\star Sin \theta = \dfrac{Perpendicular}{Hypotenuse}} \\\\ \sf{ \star \cos \theta = \dfrac{ Base }{Hypotenuse}}\\\\ \sf{\star \tan \theta = \dfrac{Perpendicular}{Base}}\\\\ \sf{\star \cosec \theta = \dfrac{Hypotenuse}{Perpendicular}} \\\\ \sf{\star \sec \theta = \dfrac{Hypotenuse}{Base}}\\\\ \sf{\star \cot \theta = \dfrac{Base}{Perpendicular}} \end{array}}\\\end{gathered} \end{gathered}\)

\({\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}\)

✧ Figure in attachment

\(\begin{gathered} {\underline{\rule{200pt}{1pt}}} \end{gathered} \)

The rule of inference being used here is Modus Tollens. Modus Tollens is a valid deductive argument form that states if a conditional statement "If P, then Q" is true and the consequent Q is false, then the antecedent P must also be false.

In the given scenario, the conditional statement is "If the guard dog doesn't know a person, then it barks."

The observation that the dog didn't bark (Q is false) leads to the conclusion that the dog must have known the person (the antecedent P is false).

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Step-by-step explanation:

In triangle ADE:

sum of all angles is 180.

3x-10+58+42=180

3x+90=180

3x=180-90

3x=90

x=90/3

x=30

As line DA and CB are parallel:

angle D=angle C

angle y=58

In angle BCE, sum of angles is 180.

z+58+42=180

z+100=180

z=180-100

z=80

Answer:

(9, -5)

Step-by-step explanation:

The vector AC has coordinates (27, -18), because:

21 - (-6) = 27

-13 - 5 = -18

If the ratio of AB to BC is 5 to 4, it means that

AB = [5/(5+4)]AC = (5/9)AC

Therefore, we have

AB = (5/9)AC = (5/9) (27, -18) = (15, -10)

Which means that:

xB - xA = 15 <=> xB - (-6) = 15 <=> xB + 6 = 15 <=> xB = 9

yB - yA = -10 <=> yB - 5 = -10 <=> yB = -10 + 5 <=> yB = -5

So B has coordinates (9, -5).

Answer:

To calculate the interest earned on the R9000 invested at 8%p.a simple interest for 3 years, you'll need to use the formula I = Prt.

I = Interest earned

P = Principal amount (R9000)

r = Rate of interest (8% = 0.08)

t = Time (3 years)

Plugging in the values, we get: I = 9000 x 0.08 x 3 = R2160.

Therefore, the interest earned on the R9000 invested at 8%p.a simple interest for 3 years is R2160.

Answer:

10

Step-by-step explanation:

2*3=6

6+c

6+4=10

Answer:

2 x 3=6

6 + 4=10

Let's denote the lengths of the three sides of the triangle as follows:

Shortest side: x

Middle side: x + 79

Longest side: x + 79 + 379 = x + 458

We know that the perimeter of a triangle is the sum of the lengths of its sides. In this case, we have:

x + (x + 79) + (x + 458) = 3084

Simplifying the equation, we get:

3x + 537 = 3084

Subtracting 537 from both sides:

3x = 2547

Dividing both sides by 3:

x = 849

Therefore, the lengths of the sides are:

Shortest side: x = 849 ml

Middle side: x + 79 = 849 + 79 = 928 ml

Longest side: x + 458 = 849 + 458 = 1307 ml

So, the lengths of the three sides are 849 ml, 928 ml, and 1307 ml, respectively.

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The ratio of the volume of sphere B to the volume of sphere A is (C) 125 if the radius of sphere B is five times that of sphere A.

The correct option is (C)

A sphere is a three-dimensional object that is round in shape. The sphere is defined in three axes, i.e., x-axis, y-axis and z-axis. This is the main difference between circle and sphere. A sphere does not have any edges or vertices, like other 3D shapes.

The points on the surface of the sphere are equidistant from the center. Hence, the distance between the center and the surface of the sphere are equal at any point. This distance is called the radius of the sphere. Examples of spheres are a ball, a globe, the planets, etc.

Let's take the 2 radii:

x where x is 5.

5x where 5x is 25.

Now, calculate the volume of the sphere in both cases.

We know,

Formula of volume of sphere :

V = 4/3πr²

Where r = 5.

V = 4/3πr²

V = 523.59878

Round off: 524 units²

Where r = 25.

V = 4/3πr²

V = 65449.84695

Rounding off: 65450 units²

Now, divide to find the ratio:

65450/524 = 124.90

Rounding off: 125

Therefore, the ratio of the volume of sphere B to the volume of sphere A is (C) 125 if the radius of sphere B is five times that of sphere A.

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Answer:

B, C, E

Step-by-step explanation:

right on edge

Answer:

Step-by-step explanation:

This question bothers on combination. combination has to do with selection.

If 4 faculty members are chosen from total of  8 faculty members, this can be done in 8C4 number of ways.

8C4 = 8!/(8-4)!4!

8C4 = 8!/4!4!

8C4 = 8*7*6*5*4!/4!*4*3*2

8c4 = 8*7*6*5/24

8C4 = 7*5*2

8C4  =70 ways

Similarly,  5 students are to be selected from a pool of 13 students, this can be done in 13C5 number of ways.

13C5 = 13!/(13-5)!5!

13C5 = 13!/8!5!

13C5 = 13*12*11*10*9*8!/8!*5*4*3*2

13C5 = 13*12*11*10*9/120

13C5 = 1,287 ways

The total number of ways the committee can be formed is 8C4 * 13C5 = 70*1287

The total number of ways the committee can be formed is 90,090 ways

Answer:

He begun with 48.

Step-by-step explanation:

48/2 = 24

24+17 = 41

Answer:

46

Step-by-step explanation:

I subtracted 17 from 41 and got 23 so if you add 23 by 23 half you get 46, so in turn Cody started out at 46.

Answer:

-128/147 cm/min

Step-by-step explanation:

\(A=\frac{1}{2}bh \\ \\ 90=\frac{1}{2}(10.5)b \\ \\ b=\frac{120}{7} \\ \\ \\ A=\frac{1}{2} bh \\ \\ \implies \frac{dA}{dt}=\frac{b}{2} \frac{dh}{dt}+\frac{h}{2} \frac{db}{dt} \\ \\ 4=\frac{21}{4}+\frac{db}{dt}+\frac{60}{7} \\ \\ \frac{db}{dt}=-\frac{128}{147}\)

\({ \color{teal}{ \huge{ \textsf{ \textbf{Answer}}}}}\)

We can calculate supplementary angles by subtracting the given one angle from 180 degrees. To find the other angle, use the following formula: ∠x = 180° – ∠y or ∠y = 180° – ∠x where ∠x or ∠y is the given angle.

The supplementary of 97° is (180°-97°)=83°

Answer:

Area of sector of circle = 7.6302 inches (Approx.)

Step-by-step explanation:

Given:

Angle of section = 35°

Radius of circle = 5 inch

Find:

Area of shaded section

Computation:

Area of shaded section  = Area of sector of circle

Area of sector of circle = [θ/360][πr²]

Area of sector of circle = [35/360][(22/7)(5)²]

Area of sector of circle = [0.0972][(3.14)(25)]

Area of sector of circle = [0.0972][78.5]

Area of sector of circle = 7.6302 inches (Approx.)

Given equation of line is,

The two lines are parallel if and only if their slopes are equal.

The line in the form y=mx+c has slope m.

So, compare the given equation of line with y=mx+c it gives ,

slope =m= 1/3.

It is observed that option B) y=1/3x+4 has slope m=1/3 which is equal to the slope of given line.

Answer: option B) y=1/3x+4

The number which has a finite number of digits after the decimal point is a terminating decimal.

The decimal is said to be terminating decimal if that has a finite number of digits after the decimal point. Decimal numbers are used to represent the partial amount of whole just like fractions. The number which has a finite number of digits after the decimal point is referred to as a terminating decimal. A number has a terminating decimal expansion if the digits after the decimal point terminate or are finite. The fraction 5/10 has the decimal expansion of 0.5 which is a terminating decimal expansion because digits after the decimal point end after one digit. Terminating decimal has finite digits and non-terminating decimals do not have finite digits. A number with a terminating decimal is always a rational number.

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The interval of increase for the given function is (-1 , 0) (0 , infinity).

The real-valued functions that tend to rise and decrease with changes in the value of the function's dependant variable are increasing and decreasing intervals of real numbers. You must ascertain the function's first derivative in order to identify intervals of rise and decline.

This is done to determine whether the function's sign is positive or negative. If the value of the function f (x) rises as the value of x rises, the function interval is said to be positive. Instead, if the value of the function f (x) drops as the value of x increases, the function interval is said to be negative.

The given function is:

C(x) = x1/5(x + 6)

Find the derivative of the given function to get calculate the interval of increase and decrease.

The interval of increase is (-1 , 0) (0 , infinity).

Th graph is concave up when derivative of, f is greater than 0. The intervals in which the function depicts this behavior will be the interval that will have a concave up curve.

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Two questions about systems aaa and bbb, the given system is:

System aaa: x = -1/3 and y = -7/3
System bbb: x = -1/3 and y = -7/3

To answer two questions about systems aaa and bbb, let's first clarify the given system:

System aaa:
x - 4y = 9

System bbb:
2x + y = -3

Question 1: Solve system aaa.
To solve system aaa, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the first equation in system aaa, we can isolate x:
x = 4y + 9

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for x in the second equation of system aaa:
2(4y + 9) + y = -3

Step 3: Simplify and solve for y.
8y + 18 + y = -3
9y + 18 = -3
9y = -3 - 18
9y = -21
y = -21/9
y = -7/3

Step 4: Substitute the value of y into the expression for x.
Using the first equation in system aaa:
x - 4(-7/3) = 9
x + 28/3 = 9
x = 9 - 28/3
x = (27 - 28)/3
x = -1/3

Therefore, the solution to system aaa is x = -1/3 and y = -7/3.

Question 2: Solve system bbb.
To solve system bbb, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the second equation in system bbb, we can isolate y:
y = -2x - 3

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for y in the first equation of system bbb:
x - 4(-2x - 3) = 9

Step 3: Simplify and solve for x.
x + 8x + 12 = 9
9x + 12 = 9
9x = 9 - 12
9x = -3
x = -3/9
x = -1/3

Step 4: Substitute the value of x into the expression for y.
Using the second equation in system bbb:
y = -2(-1/3) - 3
y = 2/3 - 3
y = 2/3 - 9/3
y = -7/3

Therefore, the solution to system bbb is x = -1/3 and y = -7/3.

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Answer:

115% increase.

Step-by-step explanation:

129 - 60 = 69 / 60 = 1.15

1.15 x 100 = 115

The recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

From the question, we have the following parameters that can be used in our computation:

This means that

Initial, a = 250 bacterial cultures.

Rate = 3

So, the recursive formulas is

f(n) = 3f(n - 1), where f(1) = 250

For the explicit formula, we have

f(n) = 250(3)ⁿ‐¹

Hence, the recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

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