The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds.

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]-8x^2 -40x-50[/tex]

Step-by-step explanation:

[tex]h(g(f(x))\\\\=h(g(2x+5))\\\\=h((2x+5)^2)\\\\=h(4x^2 +20x+25)\\\\=-2(4x^2 +20x+25)\\\\=-8x^2 -40x-50[/tex]

The value of the composite function h(g(f(x))) = -8x² - 40x - 50.

We have,

To find the composition h(g(f(x))), we need to substitute the function g(f(x)) into h(x) and simplify.

Given:

f(x) = 2x + 5

g(x) = x²

h(x) = -2x

First, we find g(f(x)) by substituting f(x) into g(x):

g(f(x)) = g(2x + 5) = (2x + 5)² = (2x + 5)(2x + 5) = 4x² + 20x + 25

Now, we substitute g(f(x)) into h(x):

h(g(f(x))) = h(4x² + 20x + 25) = -2(4x² + 20x + 25) = -8x² - 40x - 50

Therefore,

The value of the composite function h(g(f(x))) = -8x² - 40x - 50.

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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 answer is Figure A.

Given: "If it is an triangle, then it has three vertices.

To find which diagram represents the given statement.

From the first diagram

Triangles have three vertices because they are formed by the intersection of three triangles.

using the second diagram

Three vertices make up the triangle's intersection zone.

Therefore, we cannot infer from the second diagram that a triangle has three vertices.

As a result, figure A represents the stated assertion.

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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:

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°

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!

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.

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

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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Earth science is made of many branches of knowledge concerning all aspects of the Earth system. The main branches are geology, meteorology, climatology, oceanography, and environmental science. Astronomy uses principles understood from Earth to learn about the solar system, galaxy, and universe.

Only recently have humans begun to understand the complexity of our planet Earth. We have only known for a few hundred years that Earth is just a tiny part of an enormous galaxy, which in turn is a tiny part of an even greater universe.

An important component of experiments is the different variables involved. A variable is any parameter in the experiment that can change. This could be a parameter like temperature, weight or height, or it could be more complex, such as life expectancy or growth rate. Depending on how you set up your experiment, you will use different kinds of variables. There are three basic types to be familiar with.

The first type is the independent variable. This is the variable that is manipulated during an experiment. For example, when experimenting with how fertilisers affects plant growth, the fertiliser is the independent variable because this is the variable that you change. It might help to think of the independent variable as the cause of change in the experiment.

In contrast to this, the dependent variable is the variable that is affected during an experiment. In our experiment, our dependent variable would be plant growth since this is affected by the amount of fertiliser applied. If you think of the independent variable as the cause, then the dependent variable is the effect.

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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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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:

about 1800 im sorry if im wrong

Step-by-step explanation:

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:

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.

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.

In the linear equation, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.

A linear equation is modelled in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept of the equation, which is the initial value of y when x is zero.

Using two pair of points from the table, say, (1, 3) and (2, 5), find the slope (m) of the linear equation:

Slope (m) = change in y / change in x = (5 - 3)/(2 - 1)

Slope (m) = 2/1

Slope (m) = 2

To find the y-intercept (b), substitute (x, y) = (1, 3) and m = 2 into y = mx + b

3 = 1(2) + b

3 = 2 + b

Subtract 2 from both sides

3 - 2 = 2 + b - 2

1 = b

b = 1

Thus, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.

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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

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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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]

Answer:

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

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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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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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

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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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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