what value of x makes the equation true -21=+ x = 18

Step-by-step explanation:

point-slope form is

y - y1 = a(x - x1)

with a being the slope, and (x1,y1) being a point on the line.

the general form is

y = ax + b

a is again the slope. and b is the y-intercept (the y value when x = 0).

the slope is the ratio "y coordinate change / x coordinate change".

so, we need to find the slope of the original line :

x - 7y - 9 = 0

x - 9 = 7y

y = 1/7 x - 9/7

so, the original slope is 1/7.

the perpendicular slope turns the original slope upside-down and flips the sign.

so, it is

-7/1 = -7

the point slope form is

y - -4 = -7(x - 6)

y + 4 = -7(x - 6)

for the standard form we only need to do the multiplications and transform the equation into the above form :

y + 4 = -7(x - 6)

y + 4 = -7x + 42

y = -7x + 38

Let θ be equal to 855∘. Sketch θ in standard position. θ = 855∘ is in the fourth quadrant of the coordinate plane θ = 855∘

Hence, we sketch θ in the standard position with its initial side along the positive x-axis.

Find an angle between 0∘ and 360∘ that is coterminal with θ.

The angle between 0∘ and 360∘ that is coterminal with θ is given by:

θ1 = θ - n × 360∘θ1 = 855∘ - 2 × 360∘θ1 = 855∘ - 720∘θ1 = 135∘

Find an angle between −360∘ and 0∘ that is coterminal with θ.

The angle between −360∘ and 0∘ that is coterminal with θ is given by:

θ2 = θ + n × 360∘θ2 = 855∘ + 2 × 360∘θ2 = 855∘ + 720∘θ2 = 1575∘

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Answer:

76.2

Step-by-step explanation:

\(y=\frac{1}{3}x+4\)

Slope-intercept form:

What the variables mean:

Y=the y axis

m=the slope

x=the x-axis

b=the y intercept (the point on the line that crosses the y-axis)

To Calculate the Slope:

1. Find any 2 points on the line

2. The number of units the second point is above the first is the numerator

3. The number of units the second point is to the right of the first is a denominator

(Please see the picture attached)

\(y=\frac{1}{3}x+b\)

To Find the Y-Intercept:

1. Find the point on the line that crosses the y-axis

(Please see the picture attached)

\(y=\frac{1}{3}x+4\)

Answer:

n spherical geometry angles are defined between great circles. ... The sum of the interior angles of a triangle ALWAYS exceeds 180 degrees. In Euclidean Geometry, two lines that intersect form exactly one point. However, in Spherical Geometry, when there are two great circles, they form exactly two intersecting points.

Step-by-step explanation:

Answer:

in riemannian geometry there is only one parallel to the given line.euclud second postulate is a straight line of fininit length that can be continued continuously without bounds

Answer:

28

Step-by-step explanation:

Given formula:

4s

It is given that the variable, s, is equal to 7. Therefore, plug in 7 for s in the expression:

4s

4(7)

Next, multiply straight across:

4 * 7 = 28

28 is your answer.

~

Answer:

answer is 28

Step-by-step explanation:

it is simple put the value of S in formula and then solve

a) The Name of the angle of elevation is ∠c = 83.3°

b) The Name of the Hypotenuse side is AC

c) The Name of the Opposite side is AB

The angle formed between the line of sight and the horizontal is known as the angle of elevation. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

We can use the tangent ratio to determine the angle of elevation:

tan(angle of elevation) = opposite/adjacent

tan(angle of elevation) = 29.25/4.75

tan(angle of elevation) = 6.157

The inverse tangent (tan⁻¹) both sides, we obtain:

angle of elevation = tan⁻¹(6.157)

Using a calculator, we get:

angle of elevation ≈ 81.3 degrees (rounded to the nearest tenth)

The elevation angle is roughly 81.3 degrees.

d) The Name of the Adjacent side is BC

e) The Trig Ratio I will be using is Tan θ = Sin θ/Cos θ because we are  

   given the side Opposite Side & Adjacent Side

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The polynomial 25x² + 36y²  is the sum of the squares.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, 25x² + 36y² which can be written as,

= 5²x² + 6²y².

= (5x)² + (6y)² it is the sum of the squares, The difference of squares would be (5x)² - (6y)².

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Answer:

The polar form is

r = √11a

Explanation:

The given equation is

x^2 + y^2 = 11a

Recall,

x = rcosθ

y = rsinθ

By substituting these values into the equation, we have

(rcosθ )^2 + ( rsinθ)^2 = 11a

r^2cos^2θ + r^2sin^2θ = 11a

r^2cos^2θ + r^2sin^2θ - 11a = 0

By factorizing r^2, we have

r^2(cos^2θ + sin^2θ) = 11a

Recall, cos^2θ + sin^2θ = 1

Thus, we have

r^2 = 11a

Taking the square root of both sides,

r = √11a

The polar form is

r = √11a

Answer:

total bill = $15.23

Step-by-step explanation:

4.5 + 2.5 + 7.5 = 14.5

14.5 x 0.05 = 0.725

14.5 + 0.725 = 15.225 ≈ 15.23

Given:

The function

Required:

What’s all the transformations that happened

Explanation:

The required concepts:

Now,

Answer:

Completed the answer.

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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The average temperature of the coffee between t = 0 and t = 10 minutes is approximately 146 degrees.

Option C is the correct answer.

We have,

To find the average temperature of the coffee between t = 0 and t = 10 minutes, we need to calculate the average value of the temperature function F(t) over that interval.

The formula for the average value of a function f(x) over an interval [a, b] is given by:

Average value = (1 / (b - a)) x ∫[a to b] f(x) dx

In this case,

We want to find the average temperature over the interval [0, 10] minutes, so our formula becomes:

Average temperature = (1 / (10 - 0)) x ∫[0 to 10] F(t) dt

To find the integral of F(t), we need to calculate the antiderivative of F(t):

∫ F(t) dt = ∫ \((72 + 118e^{-0.093t}) dt\)

Using the power rule of integration and the fact that the integral of \(e^x\) is \(e^x\), we can evaluate the integral:

∫ F(t) dt =\(72t - (118 / 0.093) \times e^{-0.093t}\)

Now,

Average temperature = (1 / 10) x ∫[0 to 10] F(t) dt

Average temperature = (1 / 10) x (72(10) - (118 / 0.093) x \(e^{-0.093(10)}\) - (72(0) - (118 / 0.093) x \(e^{-0.093(0)}))\)

Simplifying further:

Average temperature = (1 / 10) x (720 - (118 / 0.093) x \(e^{-0.93}\) - 0)

Using a calculator, we find:

Average temperature ≈ 146 degrees

Therefore,

The average temperature of the coffee between t = 0 and t = 10 minutes is approximately 146 degrees.

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Answer:

\(f(5)=9\)

Step-by-step explanation:

\(f(5)=2(5+3)-7=2(8)-7=16-7=9\)

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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Answer:

x=6

Step-by-step explanation:

Answer:

Step-by-step explanation:

4-8    -2- -6

4^2  8^2

16+64

80

8.9

Answer:

a^n = -6n + 32

Step-by-step explanation:

32 - 6 = 26

26 - 6 = 32 - 6.2 = 20

20 - 6 = 32 - 6.3 = 14

-> a^n = -6n + 32

Answer:

Graph 1, 2, 5, 6 are not functions.

Graph 3, 4 are functions

Step-by-step explanation:

For every input there can only be one output to be a function.

Of the given graphs, only graph[3] and graph[4] represent functions.

A function is a relation between a independent variable and a dependent variable such that the value of dependent variable depends upon the independent one. It is denoted by f(x).

Given are the graphs plotted for different expressions.

Now, for a given expression to be a function, it should have a single unique value of variable [y] in coordination with that of [x]. Of all the graphs given, only the continuous graph[3] and discrete graph[4] have unique or only one unique value of [y] for a value of [x]. So, only graph[3] and graph[4] represent functions.

Therefore, of the given graphs, only graph[3] and graph[4] represent functions.

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Answer:

20/27

Step-by-step explanation:

Answer:

yes, they are equivalent

Step-by-step explanation:

solving each expression fully, you will find that both are equal to 77

Answer:

They are equivalent.

Step-by-step explanation:

7⋅11⋅13+13and7⋅6⋅5⋅4⋅3⋅2⋅1+5 are composite numbers.

The expression (9.6 × 10³) × (6.7 × 10²) can be simplified in scientific notation as  6.432 × 10⁶ , 64.32 × 10⁵ and (9.6 × 6.7) × (10³ × 10²) .

Scientific notation is a means to express values that are either too big or too little to be conveniently stated in decimal form (typically would result in a long string of digits). It is also known as standard form in the UK and scientific form, standard index form, and standard form. Scientists, mathematicians, and engineers frequently utilize this base ten notation because it can make some mathematical operations simpler.

The given expression is : (9.6 × 10³) × (6.7 × 10²)

First we multiply the decimal terms separately.

So  (9.6 × 6.7) = 64.32 and now we multiply the power terms

10³ × 10² = 10²⁺³ = 10⁵ ( By using the properties of exponents)

So in proper scientific notation 64.32 × 10⁵ = 6.432 × 10⁶

Which can also be written as 6.432 × 10⁶ or (9.6 × 6.7) × (10³ × 10²) .

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Answer:

above sea level

Step-by-step explanation:

The two solutions to the equation -6 sec (θ) - 3 = -15 on the Interval [0°, 360°) are θ = 60° and θ = 300°.

The equation -6 sec (θ) - 3 = -15 on the interval [0°, 360°), we will isolate the variable θ.

Let's begin by rearranging the equation:

-6 sec(θ) - 3 = -15

Next, we'll add 3 to both sides of the equation:

-6 sec(θ) = -12

Now, we'll divide both sides of the equation by -6:

sec(θ) = 2

To solve for θ, we need to find the angle whose secant is 2. The secant function represents the reciprocal of the cosine function. In the interval [0°, 360°), the cosine function is positive in the first and fourth quadrants.

In the first quadrant (0° to 90°), we have cos(θ) = 1/sec(θ) = 1/2, which does not hold true.

In the fourth quadrant (270° to 360°), we also have cos(θ) = 1/sec(θ) = 1/2, which is true.

Therefore, one solution to the equation is in the fourth quadrant. We can find this angle by taking the inverse cosine (arccos) of 1/2:

θ = arccos(1/2)

Using a calculator, we find:

θ ≈ 60°

So, one solution to the equation is θ = 60°.

To find the second solution, we can use the symmetry property of the cosine function. Since cos(θ) = cos(360° - θ), we can find the second solution by subtracting the first solution from 360°:

θ = 360° - 60°

θ = 300°

Therefore, the two solutions to the equation -6 sec (θ) - 3 = -15 on the interval [0°, 360°) are θ = 60° and θ = 300°.

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Answer:

\(x=\dfrac{|-246.875-121.175|}{5}\)

Step-by-step explanation:

Given that:

Same distance is drilled by the oil drilling company for 5 days.

Initial elevation = 121.175 feet

Final elevation = -246.875 feet

To find:

The equation to find the value of \(x\) i.e. the distance drilled each day?

Solution:

To find the distance drilled each day, we need to divide the total distance drilled with the number of days taken to drill the total distance.

Total distance drilled can be found by subtracting the initial elevation from the final elevation and taking modulus because distance can not be negative.

Total distance drilled = | Final elevation - Initial elevation |

Total distance drilled = | -246.875 - 121.175 |

Therefore, we can write the expression as:

\(x=\dfrac{|-246.875-121.175|}{5}\)

\(\Rightarrow x=\dfrac{|-368.05 |}{5} =73.61\ ft/day\)

Answer:

838 inches²

Step-by-step explanation:

Finding the area of the countertop including the hole

⇒ Area of countertop including hole: LB

⇒ Area of countertop including hole: (24)(48)

⇒ Area of countertop including hole: 1152 inches²

Finding the area of the hole (sink)

⇒ Area of hole: πr²

⇒ Area of hole: (π)(D/2)²

⇒ Area of hole: (π)(20/2)²

⇒ Area of hole: (π)(10)²

⇒ Area of hole: (π) x 100

⇒ Area of hole: 3.14 x 100 = 314 inches²

Finding the area excluding the hole

1152 - 314 = Area of countertop (excluding the hole)

838 inches² = Area of countertop (excluding the hole)

9.53 fertilizer bags are required to cover a lawn that is rectangular and is 260 feet by 120 feet.

The nitrogen fertilizer type known as urea is inexpensive. This is as a result of its high nitrogen content and the ensuing low costs of storage and transportation.

When all that is required for a soil fertility program is nitrogen, urea can be the best fertilizer to use.

Finding the location of the lawn is the first stage.

Area: 110 feet by 260 feet.

28600 square feet.

Calculating how many bags of fertilizer to purchase is the next step.

Bags = Area x 3,000 feet

Bags: 28600 feet / 3000 feet

9.53 bags total are in the bag.

Inconclusion 9.53 sacks of fertilizer should be bought to cover a lawn that is rectangular and measures 260 feet by 120 feet.

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Answer:A

Step-by-step explanation:

-3 to the left and up 4