Build Your Math Skills 2A, Round decimals to the nearest hundredth (0.01): 42.988

Answer:

NMK= 22

Step-by-step explanation:

From N to K equals 177.

N to M equals x

K to M equals to 107

L equals 35

35    177

x        107

it equals to 21.158

Round up to the nearest ones or whole number

Part (a)

We'll use the distance formula.

[tex](x_1,y_1) = (-4,-7) \text{ and } (x_2, y_2) = (5,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-5)^2 + (-7-(-2))^2}\\\\d = \sqrt{(-4-5)^2 + (-7+2)^2}\\\\d = \sqrt{(-9)^2 + (-5)^2}\\\\d = \sqrt{81 + 25}\\\\d = \sqrt{106}\\\\d \approx 10.2956\\\\[/tex]

The diameter is exactly [tex]\sqrt{106}[/tex] units long which approximates to roughly 10.2956 units. Round that decimal value however your teacher instructs.

========================================================

Part (b)

We divide the diameter in half to get the radius.

Therefore, the radius is exactly [tex]\frac{\sqrt{106}}{2}[/tex] units long which is approximately 5.1478 units.

Answer:

1 + x  meters.

Step-by-step explanation:

A square has 4 equal sides so each side will have a length equal to the square root of the area.

Side length = √(1 + 2x + x^2)

                   = √(1 + x)(1 + x)

                   = 1 + x.

Answer:

Step-by-step explanation:

Because there is sound and a tune that plays again anytime people are shown having fun at the carnival, the Kit Kat commercial is effective. When the sound is silenced, the commercial's lyrics will come to the viewer's thoughts without any further thought.

Answer:

3

Step-by-step explanation:

-2 * 3= -6

-1 * 3= -3

0 *3= 0

1 *3 = 3

2* 3 = 6

3 * 3 =9

Answer:

? = 3

Step-by-step explanation:

To find the value of ?, substitute one of the ordered pairs from the table [except (0, 0)] into the given formula and solve for ?.

Given formula:

[tex]\sf y=\boxed{?} \:x[/tex]

Substitute x = 1 and y = 3 into the formula:

[tex]\sf 3=\boxed{?} \:1[/tex]

To isolate ? divide both sides by 1:

[tex]\implies \sf \dfrac{3}{1}=\dfrac{\boxed{?} \:1}{1}[/tex]

[tex]\implies \sf 3=\boxed{?}[/tex]

Therefore, ? = 3:

[tex]\implies \sf y=3x[/tex]

Check by inputting another value of x from the table into the found formula and comparing the calculated y-value:

[tex]\sf x=-2 \implies y=3(-2)=-6 \quad \boxed{\sf correct}[/tex]

[tex]\sf x=3 \implies y=3(3)=9 \quad \boxed{\sf correct}[/tex]

Given that, Aakash has a fever, if  his body temperature during the day was 99.2°F and by evening his body temperature has increased by 3.4°F, Aakash's body temperature in the evening is 102.6° Fahrenheit.

The body temperature is simply a measure of how well a human body can produce and get rid of heat. the normal body temperature is or 37 degrees Celsius or 98.6 degrees Fahrenheit.

Given the data in the question;

To get Aakash body temperature in the evening, we simply add the initial body temperature and the the temperature increase.

Temperature in the evening = 99.2° Fahrenheit + 3.4° Fahrenheit

Temperature in the evening = 102.6° Fahrenheit

Given that, Aakash has a fever, if  his body temperature during the day was 99.2°F and by evening his body temperature has increased by 3.4°F, Aakash's body temperature in the evening is 102.6° Fahrenheit.

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The polynomial A is represented as x - 2, making option A the right choice.

In the question, we are asked to find the correct representation of A, when the algebraic expression (x² + x)/(x + 3) can be rewritten as the algebraic expression A + 6/(x + 3), where A is a polynomial.

Thus, we can write an equation,

A + 6/(x + 3) = (x² + x)/(x + 3),

or, A + 6/(x + 3) - 6/(x + 3) = (x² + x)/(x + 3) - 6/(x + 3) {Subtracting 6/(x + 3) from the both sides of the equation}

or, A = (x² + x)/(x + 3) - 6/(x + 3) {Simplifying},

or, A = (x² + x - 6)/(x + 3) {Subtracting the two fractions with the same denominator (x + 3)},

or, A = (x² + 3x - 2x - 6)/(x + 3) {Mid-term factorization},

or, A = {x(x + 3) - 2(x + 3)}/(x + 3) {Taking common},

or, A = {(x - 2)(x + 3)}/(x + 3) {Taking (x + 3) common},

or, A = x - 2 {Cancelling (x + 3) from the numerator and the denominator}.

Thus, the polynomial A is represented as x - 2, making option A the right choice.

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Answer:

Step-by-step explanation:

x = time

y = elevation

At x = 0  ,  y  = 0

It takes the submarine 2 hours to make descent of 2100 ft

=> x = 2 , y  = - 2100

Slope = ( -2100 - 0)/(2 - 0)  =  -1050

y - 0 = -1050 ( x -0)

=> y = -1050x

1050x  + y = 0

represent the relationship between the submarine's elevation and time.

Considering that a fraction is not defined when the denominator is zero, the equation is not defined for an angle of 90º.

A fraction is not defined when the denominator is zero.

In this problem, the expression is given by:

cos(θ)/(1 - sin(θ)) + cos(θ)/(1 + sin(θ)) = 4.

The denominators are zero in two cases:

Hence the equation is not defined for an angle of 90º.

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The completed table will have values filled into it accordingly from left to right and the downwards.

The concept of relative frequencies involves expressing the frequency of occurrence of events as a fraction of a whole frequency.

Hence, it follows that the blank space on the top-leftmost corner of the table can be filled with the value; 4/5 = 0.8.

For the top-rightmost blank space in the table, the required value is; 2/754 = 0.0027.

For the bottom-leftmost blank space, the required value to fill the table is; 1/5 = 0.2.

For the bottom-rightmost blank space, the required value is; 752/754 = 0.9973.

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The degenerate conic that is formed when a double cone is sliced at the ap-ex by a plane parallel to the base of the cone is a Point.

When a plane that is parallel to the base of a double cone is used to slice the ap-ex, the conic section formed is a circle.

Circles lead to a Point degenerate conic being formed because a single point will be formed on the double cone that separates the shape.

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According to the total interest gained, the sum deposited by Madan Bahadur was Rs 4,000.

For the principal [tex]P[/tex] and the rate of interest [tex]r\%[/tex] per annum, the total interest after [tex]t[/tex] years is given by the formula: [tex]I=\dfrac{Prt}{100}[/tex].

Given that after 5 years Madan Bahadur got a net interest of Rs 1900 after charging 5% of the total interest as income tax where the rate of interest was 10% p.a.

Suppose the sum deposited was [tex]P[/tex] and the total interest was [tex]I[/tex].

So, the net interest would be [tex]I_n=I-I\times \frac{5}{100}=\frac{19I}{20}[/tex].

Now, given that the net interest [tex]I_n=1900[/tex]. So, we must have [tex]\frac{19I}{20}=1900\\\Longrightarrow I=\frac{1900\times 20}{19}\\\therefore I=2000[/tex]    (1)

Thus, the total interest after 5 years is Rs 2,000.

Also, using the above formula for the total interest, the total interest of the sum [tex]P[/tex] at the rate [tex]r=10\%[/tex] p.a. after [tex]t=5[/tex] years would be [tex]I=\frac{Prt}{100}=\frac{P\times 10\times 5}{100}=\frac{P}{2}[/tex].

So, we must have from (1),

[tex]\frac{P}{2}=2000\\\Longrightarrow P=2000\times 2\\\therefore P=4000[/tex]

Therefore, according to the total interest gained, the sum deposited by Madan Bahadur was Rs 4,000.

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The graph of the function f(x) = -(x+1)^2 shows that the domain of the function f(x) = -(x+1)² is: -∞ < x < ∞. The range of the function is f(x) ≤ 0.

The graph of a function is the arrangement of all ordered pairs of the function. Typically, they are expressed as points in a cartesian coordinate system. The graph of f is the collection of all ordered pairings (x, f(x)) such that x lies inside the domain of f.

The graph of a function might similarly be defined as the graph of the equation y = f(x). As a result, the graph of a function is a subset of the graph of an equation.

From the given information: the graph of the function f(x) = -(x+1)² can be determined if the domain, the range, and the vertex of the function are known.

Since the parabola curve from the graph shows that the graph is facing down, then the function is negative and decreasing.

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1.) maximum value

2.) for no values of x

3,) when x > -1

4.) all real numbers

5.) all numbers less than or equal to 0

Answer:

Math allows the animator to find the unknowns from a set of equations and to work out the aspects of the geometric figures when dealing with the objects that move and change.

Step-by-step explanation:

To learn more:

weusemath.org/?career=animator

Hope this helps!

From the equation we see that the center of the circle is at (-2,3) and the radius is 9.

So using the distance formula we can see if the distance from the center to the point (8,4) is 9 units from the center of the circle...

d^2=(8--2)^2+(4-3)^2  and d^2=r^2=81 so

81=10^2+1^2

81=101  which is not true...

So the point (8,4) is √101≈10.05 units away from the center, which is greater than the radius of the circle.  

Thus the point lies outside or on the exterior of the circle...

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The time it will take Lucas to paint the house using rate is 3 hours

They both paint the same house.

Lucas and Jacob can paint a house in 1 hour working together.

Jacob works alone, he can paint the house in 1.5 hours.

Therefore, the time it will take Lucas to paint the house using rate is as follows:

let

x = time it will take Lucas to paint the house

1 / 1 = 1 / x + 1 / 1.5

1  = 1.5 + x / 1.5x

cross multiply

1.5x = 1.5 + x

1.5x  - x = 1.5

0.5x = 1.5

divide both sides by 0.5

x = 1.5 / 0.5

x = 3

Therefore, the time it will take Lucas to pain the house is 3 hours.

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Answer:

c = 15

Step-by-step explanation:

expand the left side and compare with like terms on the right side

2x(4x + 5) + 3(4x + 5) ← distribute parenthesis

= 8x² + 10x + 12x + 15 ← collect like terms

= 8x² + 22x + 15

compare to ax² + bx + c

then c = 15

Answer:

about 1800 im sorry if im wrong

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x + 1 = 4x - 19

Solve for x

2x + 1 = 4x - 19

2x - 4x = -19 - 1

-2x = -20

x = 20 : 2

x = 10

----------------

check

2 * 10 + 1 = 4 * 10 - 19

21 = 21

the answer is good

Answer: [tex]\Large\boxed{x=10}[/tex]

Step-by-step explanation:

2x + 1 = 4x - 19

Add 19 on both sides

2x + 1 +19 = 4x - 19 + 19

2x + 20 = 4x

Subtract 2x on both sides

2x + 20 - 2x = 4x - 2x

20 = 2x

Divide 2 on both sides

20 / 2 = 2x / 2

[tex]\Large\boxed{x=10}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex]\frac{133}{66}[/tex]

Step-by-step explanation:

we require 2 equations with the repeating digits placed after the decimal point.

let x = 2.01515... ( multiply both sides by 10 and 1000 )

10x = 20.1515.... (1)

1000x = 2015.1515... (2)

subtract (1) from (2) thus eliminating the repeating digits

990x = 1995 ( divide both sides by 990 )

x = [tex]\frac{1995}{990}[/tex] = [tex]\frac{133}{66}[/tex] ← in simplest form

gradient = rise/run

= 2/1

= 2

So,it's the first option, y=2x

Hope this helps!

The point with the greatest distance to the origin is given by:

B. (-3, 3).

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The origin is given by point (0,0), hence the distance of a point (x,y) to the origin is given by:

D = sqrt(x² + y²).

Hence the distances for each point given in the problem are:

Hence option B has the greatest distance.

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Answer:

70°

Step-by-step explanation:

This is a question on angle properties.

Angle K + 35 + 75 = 180 (Sum of angles in a triangle)

Angle K + 110 = 180

Angle K = 180 - 110 = 70°

Answer:

angle k = [tex]\boxed {70}^\circ[/tex]

Step-by-step explanation:

The angles in a triangle add up to 180°.

∴ ∠k + 75° + 35° = 180°

⇒ ∠k + 110° = 180°

⇒ ∠k = 180° - 110°

⇒ ∠k = 70°

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {a}^{2} - 64 }{ {a}^{2} - 10a + 24} \sdot \cfrac{ {a}^{2} - 12a + 36 }{ {a}^{2} + 4a - 32} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{( {a}^{} + 8)(a - 8) }{ {a}^{2} - 6a - 4a+ 24} \sdot \cfrac{ {a}^{2} - 6a - 6a + 36 }{ {a}^{2} + 8a - 4a- 32} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{( {a}^{} + 8)(a - 8) }{ {a}^{} (a - 6) - 4(a - 6)} \sdot \cfrac{ {a}^{} (a - 6) - 6(a - 6) }{ {a}^{}(a + 8) - 4(a + 8)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{( {a}^{} + 8)(a - 8) }{(a - 6) (a -4)} \sdot \cfrac{ (a - 6) (a - 6) }{ {}^{}(a - 4)(a + 8)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{(a - 8) }{(a -4)} \sdot \cfrac{ (a - 6) }{ {}^{}(a - 4)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{(a - 8)(a - 6) }{(a -4) {}^{2} } [/tex]

Or [ in expanded form ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {a}^{2} - 8a - 6a + 48 }{ {a}^{2} - 8a + 16 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {a}^{2} -14a + 48 }{ {a}^{2} - 8a + 16 } [/tex]

Answer:

[tex]\dfrac{(a-8)(a-6)}{(a-4)^2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{a^2-64}{a^2-10a+24} \cdot \dfrac{a^2-12a+36}{a^2+4a-32}[/tex]

Factor the numerator and denominator of both fractions:

[tex]\textsf{Apply the Difference of Two Squares formula} \:\:\:x^2-y^2=(x-y)(x+y):[/tex]

[tex]\begin{aligned} a^2-64 & =a^2+8^2 \\ & =(a-8)(a+8)\end{aligned}[/tex]

[tex]\begin{aligned}a^2-10a+24 & =a^2-4a-6a+24\\& = a(a-4)-6(a-4)\\ & = (a-6)(a-4) \end{aligned}[/tex]

[tex]\begin{aligned}a^2-12a+36 & =a^2-6a-6a+36\\& = a(a-6)-6(a-6)\\ & = (a-6)(a-6) \end{aligned}[/tex]

[tex]\begin{aligned}a^2+4a-32 & =a^2+8a-4a-32\\& = a(a+8)-4(a+8)\\ & = (a-4)(a+8) \end{aligned}[/tex]

Therefore:

[tex]\dfrac{(a-8)(a+8)}{(a-6)(a-4)} \cdot \dfrac{(a-6)(a-6)}{(a-4)(a+8)}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{ac}{bd}[/tex]

[tex]\dfrac{(a-8)(a+8)(a-6)(a-6)}{(a-6)(a-4)(a-4)(a+8)}[/tex]

Cancel the common factors (a + 8) and (a - 6):

[tex]\dfrac{(a-8)(a-6)}{(a-4)(a-4)}[/tex]

Simplify the numerator:

[tex]\dfrac{(a-8)(a-6)}{(a-4)^2}[/tex]

The graph of the given equation is shown below

From the question, we are to determine the graph that represents the given equation

The given equation is

4x - 3y = -1

The graph of the equation is shown below

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The calculations show that this pyramid's volume is equivalent to:

5.2h/3 cm3.

A polyhedron constructed by joining a polygonal base and a point, is called a pyramid. A lateral face is a triangle formed by the base edge and  vertex of each base. Conic solid with a polygonal basis describes it. The number of vertices, faces, and edges on a pyramid with an n-sided base is n + 1.

Base area = 5.2 [tex]cm^2[/tex].

Height in centimeters is equal to h.

The following formula is used to determine a pyramid's volume mathematically:

Base area divided by height equals one-third of the volume.

When we enter the parameters into the formula, we get;

Volume = 1/3 *5.2* h

Volume = 5.2h/3 [tex]cm^3.[/tex]

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I understand that the question you are looking for is :

A solid right pyramid has a regular hexagonal base with an area of 5. 2 cm2 and a height of h cm. a solid right pyramid has a regular hexagonal base with an area of 5. 2 centimeters squared and a height of h centimeters. which expression represents the volume of the pyramid? one-fifth(5. 2)h cm3 start fraction 1 over 5 h infraction(5. 2)h cm3 one-third(5. 2)h cm3 start fraction 1 over 3 h infraction(5. 2)h cm3

Answer:

Since the graph looks like this, I would say solid line

By the use of the completing the square method, the maximum height of the path of the water 3 ±√29/4 + 9 m.

What is called distance?

h = -4x² +24x -29

Now we have;

0 = -4x² +24x -29

-4x² +24x -29= 0

x² - 6x = -29/4

(x - 3)² = -29/4 + 3²

(x - 3)² =  -29/4 + 9

x = 3 ±√29/4 + 9 m

Therefore, the maximum height of the path of the water  x = 3 ±√29/4 + 9 m

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