AREA UNDER A CURVE - GEOMETRY

Answer:

[tex]n=0.001[/tex]

Step-by-step explanation:

[tex](2\times10)+(5\times1)+(3\times n)=25.003\\\\\implies 20 + 5 + 3n = 25.003\\\\\implies 3n+25=25.003\\\\\implies 3n+25-25=25.003-25\\\\\implies 3n = 0.003\\\\\implies n=0.001[/tex]

The scientific notation for the given information is 1 × [tex]10^{-10}[/tex]. Thus, one angstrom is written as 1 × [tex]10^{-10}[/tex] and denoted by A°.

Scientific notation is used to write very large numbers or very small numbers in a simple way that is easy to understand and easy for calculate.

A number is written in scientific notation as follows:

Scientific notation: m × [tex]10^n[/tex]

where m is the absolute value of the number or a decimal number and n is the power and 10  is the base.

The given information is,

One Angstrom = ten billionths part of a meter

Since ten billion = [tex]10^{10}[/tex]

So, ten billionth part of a meter = 1 ×1/[tex]10^{10}[/tex] = 1 × [tex]10^{-10}[/tex].

therefore, the scientific notation for one Angstrom is 1 × [tex]10^{-10}[/tex].

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Hello !

Answer:

4x² + 3x + 4

Step-by-step explanation:

 (3x² + 2x + 3) + (x² + x + 1)

= 3x² + 2x + 3 + x² + x + 1

= 3x² + x² + 2x + x + 3 + 1

= 4x² + 3x + 4

The value of the missing triangle sides and angles are XY = 20.9, YZ = 12.4 and ∠Y = 119°

An equation is an expression that shows the relationship between two or more numbers and variables.

Sine rule is used to show the relationship between the sides and angles of a triangle.

In the triangle XYZ:

∠X + ∠Y + ∠Z = 180° (sine rule)

22 + 39 + ∠Y = 180

∠Y = 119°

Using sine rule:

XY / sinZ = XZ / sinY

XY / sin(39) = 29 / sin(119)

XY = 20.9

Also:

YZ / sinX = XZ / sinY

YZ / sin(22) = 29 / sin(119)

YZ = 12.4

The value of the missing triangle sides and angles are XY = 20.9, YZ = 12.4 and ∠Y = 119°

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The linear function that gives the rule for the table is: y = -8x + 2.

A linear function is modeled by:

y = mx + b

In which:

In this problem, when x = 0, y = 2, hence the y-intercept is of b = 2. When x increases by 1, y decreases by -8, hence the slope is of m = -8, and the rule is given by:

y = -8x + 2.

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Answer:

1: Slope intercept form is y=mx+b, where m is slope and b is the y-intercept. We can use this form of a linear equation to draw the graph of that equation on the x-y coordinate plane.

2: We have 4 ways of solving one-step equations: Adding, Substracting, multiplication and division. If we add the same number to both sides of an equation, both sides will remain equal. If we subtract the same number from both sides of an equation, both sides will remain equal.

A: For example: If you pay 30 dollars a month for your cell phone and 10 cents per minute of usage the monthly cost of using your cell phone would be a linear equation of a function, C, the monthly cost based on the number of minutes you use monthly.

Answer:

Option 3 is the correct answer :)

Step-by-step explanation:

Answer:

Let R be the radius of the tank, H(t) the height of the water at time t, and V(t) the volume of the water. The quantities V(t), R and H(t) are related by the equation

V(t) = πR²H(t) ___(1)

The rate of increase of the volume is the derivative with respect to time,

dV/dt

and the rate of increase of the height is

dH/dt

We can therefore restate the given and the unknown as follows

Given:

dV/dt = 4m³/min

Unknown:

dH/dt

Now we take derivative of each side of (1) with respect to t:

dV/dt = πR²dH/dt

So

dH/dt = 1/πR²dV/dt

Substituting R = 3 m and dV/dt = 4m³/min we have

dH/dt = 1/π(3)² ⋅ 4 = 4/9π

Answer: the height of the water increasing at a rate of

dH/dt = 4/9π²

The proportional graph that corresponds to the situation is: Graph C.

A proportional graph is a straight line graph with a constant of proportionality, k = y/x. The equation of the graph is defined as, y = kx.

The equation, M = 3n, has a constant of proportionality as, k = 3.

In graph C, using a point on the line, (400, 1,200), the constant of proportionality, k = 1,200/400

k = 3.

Therefore, the answer is: C.

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Answer: 1/3

Step-by-step explanation:

7/21=1/3

Answer:

Step-by-step explanation:

hello :

√4=2 and √8=2√2

√4(√8+3). =2(2√2+3)=4√2+6

Answer:

4√2 +6

Step by step explanation:

To find the product of the the above question, we open bracket.

√4(√8+3)

removing brackets.

√4×√8 + √4×3

2√8 + 2×3

2× √4×√2 + 6

2× 2 √2 + 6

4√2 + 6

Answer: D, (272,127)

Step-by-step explanation:

sorry it’s late but just took it on edge

Women can be seated in 89 ways.

Let Sn be the number of possible seating arrangements with n women. Consider n≥3 and focus on the rightmost woman. If she goes back to her seat, then there are Sn−1 ways to seat the remaining n−1 women. If he is sitting in the penultimate seat, then the woman who was sitting there before must now sit in the rightmost seat.

This gives us Sn−2 ways to seat another n−2 woman, so we get the recursion Sn=Sn−1+Sn−2. Starting with S1=1 and S2=2 we can calculate S10=89.

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The temperature in degrees Fahrenheit outside at various times throughout the day is given by the inequality x < 69°F

An equation is an expression that shows the relationship between two or more numbers and variables.

A number line is a straight line with numbers placed at equal intervals.

Let x represent the temperature in degrees Fahrenheit, from the number line:

x < 69°F

The temperature in degrees Fahrenheit outside at various times throughout the day is given by the inequality x < 69°F

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Answer:

last choice

angle 1 and 7 are alternet xterior angles

Step-by-step explanation:

A cubic function is known as a function whose graph is in the shape of a horizontal S.

The graph that meets these requirements is the graph D.

Answer: 30506.49303

Step-by-step explanation:

Answer:

he attempted 30 shots

Step-by-step explanation:

60 percent of 30 is 18 and 40 percent of 30 is 12 so you at 12 plus 18 and get 30

7.6 expressed in p/q form is 7 3/5.

7.6 is in decimal. The decimal is a number that consists of integers and non integer. The integers are to the left of the decimal point and the non-integers are to the right of the decimal point.

In order to convert 7.6 to a fraction, note that 7 is the whole number while 0.6 is the non integer.

7.6 = 7 + 6/10

7 3/5

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[tex]\rm y\ \le2x+1[/tex] , [tex]\rm y\le-x+3[/tex]  , Option B represents the the graph given .

An Inequality is a statement that connects two algebraic expression by an inequality operator.

To determine the solution of the inequalities , the common area that comes under the inequality will be found

The graph plotted using

y ≥ 2x +1 and y ≥ - x+3

it doesn't represent the solution as given in the question graph , graph no.1

The graph given in the question is the solution of the  set of inequalities

This can be understood by Graph 2

[tex]\rm y\ \le2x+1[/tex]

[tex]\rm y\le-x+3[/tex]

As all the inequalities of all the options were plotted  and the solution to the system of inequality is represented by the graph

Therefore Option B is the correct answer.

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Answer:

P' (- 3, 4 ) , Q' (2, 7 )

Step-by-step explanation:

the line passing through the origin and (4, 4 ) has equation

y = x

a point reflected in the line y = x

(x, y ) → (y, x ) , then

P (4, - 3 ) → P' (- 3, 4 )

Q (7, 2 ) → Q' (2, 7 )

Answer:

The 2nd one.

Step-by-step explanation:

The 2nd one is a quadratic function as it is a parabola.

Answer:

[tex]1.\ x^2+y^2=5^2.\\2.\ y^2=9-x.\\3.\ y=2x-2.[/tex]

The thing that I notice about the two triangles in terms of their size and shape is that they  that is the triangles tend to appear to be of the same size and shape.

Congruent triangles are known to be triangles that are said to have both the same shape and also of the same size for the two triangles.

Note that in the case above, we need to understand that the factors of a triangle are composed of 3 angles and the 3 facets and when you put the three together following the description given, a Congruent triangle will be formed.

Therefore, The thing that I notice about the two triangles in terms of their size and shape is that they  that is the triangles tend to appear to be of the same size and shape.

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Answer:

C(t) = 9t + 14

Step-by-step explanation:

write two equations with the given information

x + 6y = 68

x + 3y = 41

(x and y are just random variables, with x being the number of credits from high school and y being the number of credits earned each semester)

subtract (x+3y=41) from (x+6y=68) to get 3y=27

y = 9

then plug back in to one of the equations to find x

x + 3(9) = 41

x + 27 = 41

x = 14

then write the equation for C(t)

C(t) = 9t + 14

because you start with 14 credits from high school then add 9 credits for each semester taken

Carter's salary is $1.1138⁶ more than Salma's salary.

To perform the difference, we need to be able to take a common factor.

We know that Salma's salary is $6.2×10⁴

While Carter's salary is $1.2×10⁶

To get the same common factor, 10⁴, we can divide and multiply Carter's salary by 100, so we get:

[tex]1.2*10^6*\frac{100}{100} = (1.2*100)*(10^6/100) = 120*10^4[/tex]

Then Carter's salary is $120*10⁴

The difference between Carter's and Salma's salaries is:

$120*10⁴ -  $6.2×10⁴ = $113.8*10⁴

If we return to the scientific notation, we get:

$113.8*10⁴  = $1.1138⁶

This means that Carter's salary is $1.1138⁶ more than Salma's salary.

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Answer:

-8m

Step-by-step explanation:

This question only requires to to substitute t = 0 and t = 1 into the equation to find the displacement.

Lets find the displacement at t = 0.

[tex]x(0)=4sin(\pi (0)+\frac{\pi }{2} )\\=4sin(\frac{\pi }{2} )\\= 4m[/tex]

Lets find the displacement at t = 1.

[tex]x(1) = 4sin(\pi (1)+\frac{\pi }{2} )\\=4sin(\pi +\frac{\pi }{2} )\\=-4m[/tex]

Total displacement = Final Position - Initial Position

= x(1)-x(0)

= -4m - 4m

= -8m

The equivalent expressions of 22c + 33d are (a), (c) and (e)

The expression is given as:

22c + 33d

Factor out 11 from the expression

11(2c + 3d)

Multiply by 1

1 * 11(2c + 3d)

Express 1 as -1 * -1

-1 * -1 * 11(2c + 3d)

Evaluate the product

(-11) * (-2c - 3d)

Also, we have:

22c + 33d

Multiply by 1

(22c + 33d) * 1

Express 1 as 3/3

(22c + 33d) * 3/3

Evaluate the product

(66c + 99d) * 1/3

Hence, the equivalent expressions are (a), (c) and (e)

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Answer:

are we supposed to solve the graph

Step-by-step explanation:

The total expenditure is Rs 72,000.

The total expenditure can be determined using this equation:

(total amount spent on a good x total value of circle) / degree of the sector of good

(8000 x 360) / 40 = Rs 72,000

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70 grams of protein are needed per day by a male non-athlete, weighing 87 kilograms.

87 kg x 0.8 g protein/kg/day

= 69.6 g protein/day,

Rounded up to 70 g/day.

Maximum American adults eat approximately a hundred grams of protein consistent with a day or roughly two times the advocated amount. Even on a vegan weight-reduction plan people can effortlessly get 60 to eighty grams of protein for the duration of the day from foods like beans, legumes, nuts, broccoli, and entire grains.

The encouraged Dietary Allowance (RDA), which is the minimal amount you want to be healthy, is 0.8 grams in line with a kilogram (zero.36 grams consistent with pound) of body weight in keeping with day 46 grams for a median woman.

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The statement which is true is  ΔGHI ~ ΔGJK.

This is commonly used in geometry to describe a function which moves object at distances.

This therefore means that translation of ∠I onto ∠K means shifting of point I to point K.

The triangles given are HGI and JGK.

Translation in this scenario therefore means that the triangles are similar only if other angles are mapped to their corresponding angles.

It confirms that ΔGHI ~ ΔGJK thereby making it the most appropriate choice.

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Answer:

ΔGHI ~ ΔGJK

Step-by-step explanation: