I need to simplify this....: 3(2x-10)-3(2x-17)=1
PLS HELLLLLPPPPP

45 and 27.6 degrees are the two complementary angles.

When the right angle is split into two equal parts, each angle is 45°. A 45-degree angle is considered sharp. It is a right angle of half, or a 90-degree angle.

Angles that are complementary are those whose sum is 90 degrees. If the smaller angle has a measure of x, then the complementary angle's measure is 90 - x.

The issue shows that the greater angle (x + 17.4) is 17.4 degrees larger than the corresponding angle's measurement (90 - x). To find x, we can construct the following equation:

x + 17.4 = 90 - x + 17.4

When we simplify and find x, we obtain:

2x = 55.2

x = 27.6

The greater angle's measure is x + 17.4 = 45 degrees, while the smaller angle's measure is x = 27.6 degrees.

The two complementary angles are 27.6 and 45 degrees as a result.

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Answer:

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Step-by-step explanation:

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Hello!

∠AED and ∠BEC are opposite angles

so ∠AED = ∠BEC = 36°.

Answer:

Step-by-step explanation:

A line is represented as follows:

Isolate y in the given equation to get the line in the form above:

Notice that the slope of the line is positive and the y-intercept is 5.

*Remember that the y-intercept of a line is where x=0.

Then, the graph that shows the line is Graph C

Using the normal distribution, it is found that the z-scores are:

a) z = -1.5

b) z = 1.9

c) z = 0

In normal distribution with mean 'μ' and the standard deviation 'σ', the z-score of a measure X is given by:

z = x-μ/σ

It measures how many standard deviations the measure is from the mean, either above the mean(positive z-score), or below(negative z-score).

For first blank: 1.5 standard deviations below the mean, hence z = -1.5.

For second blank: 1.9 standard deviations below the mean, hence z = 1.9.

For third blank: The mean is 0 standard deviations from itself, hence z = 0.

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According to the information given, the equation of the elipse is:

\(\frac{(x - 1)^2}{25} + \frac{(y - 6)^2}{21} = 1\)

The equation of an elipse of center \((x_0, y_0)\) is given by:

\(\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 1\)

In this problem, the center is (1,6), hence \(x_0 = 1, y_0 = 6\).

There is a vertex at (6,6), hence \(a = 6 - 1 = 5\).

The focus at (-1,6) means that \(c = 1 - (-1) = 2\), hence:

\(c^2 = a^2 - b^2\)

\(b^2 = a^2 - c^2\)

\(b^2 = 5^2 - 2^2\)

\(b^2 = 21\)

The equation is:

\(\frac{(x - 1)^2}{25} + \frac{(y - 6)^2}{21} = 1\)

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Answer:

quadratic

Step-by-step explanation:

The type of graph that most represent the height is quadratic, where the children grew faster in the beginning and slowly slow down until adulthood, before slowly getting shorter ( trend, which is most common )

We have the following:

The intersection with the x-axis is when the value of y is 0, that is, the computer already has a value of 0 and has no commercial value.

we found it like this

which means that in 10 years, the computer does not represent a commercial value

to calculate the number of years that have passed when the computer has a value of 2000, y = 2000, therefore we replace

This means that in a total of 5 years the value of the computer will be $ 2000

Answer:

60 and 100

Step-by-step explanation:

Look for 2 multiples of 20 which are also factors of 300.

No need to go all Mathematician.

It's simple, no long explanation needed

Like usual, we can solve this question using an equation. Let’s assume that John’s age is x, and his sister’s age is y.

x = 2y

To figure out John’s age, we need to know his sister’s age. He’s 2 times older than his sister.

x + y = 27

The sum of their ages is 27, and we can substitute the value of x here to figure out y.

2y + y = 27

We can now simplify this, and get y by itself.

3y = 27

Now, we can divide by 3 to get the y by itself.

y = 9

We now know that John’s sister is 9.

Now, using our original equation, we can substitute in the value of y.

x = 2(9)

We can simplify this.

x = 18

John’s age is 18!

Hope this helps.

Answer:

Surface area of the box is 3345cm^2

Step-by-step explanation:

First you need to find the surface area of the sides. In order to find the sides you would do 70cm times 15cm to find one of the area of the sides. This would give you that one of the area is 1050cm^2. Since there are three you need to multiply by 3. This means that all the rectangles on the side would have a surface area of 3150cm^2. Then you need to find the area of the triangles. So the Area= Height times (1/2)base. Area= 13cm* times 7.5cm. Therefore the area of the triangle is equal to 97.5cm^2. Since there are two this means that the surface area of the two triangles would be equal to 195cm^2. Then in order to find the total surface area you would need to add the triangles with the rectangles which is equal to 3150cm^2 plus 195cm^2 which totals to 3345cm^2.

Therefore the total surface area for the triangle box is 3345cm^2

Answer:

The exact value of the other leg is 10.

Step-by-step explanation:

Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.

Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.

Substituting known values, we get:

(10√2)^2 = 10^2 + b^2

200 = 100 + b^2

b^2 = 100

b = 10

Therefore, the exact value of the other leg is 10.

Answer:

49 Dollars

Step-by-step explanation:

If you subtract 70- 30%, you get 49 dollars

Hope this helps =)

Using integration, it is found that the area under the graph of f(x) in the desired interval is of 1 unit squared.

The area under the graph of a curve f(x) between x = a and x = b is given by the following integral:

\(A = \int_{a}^{b} f(x) dx\)

In this problem, the function and the limits of integration are given by:

\(f(x) = \frac{1}{x\ln{x}}\)

\(a = e, b = e^e\)

Hence:

\(A = \int_{e}^{e^e} \frac{1}{x\ln{x}} dx\)

Using substitution:

\(u = \ln{x}\)

\(du = \frac{1}{x} dx\)

\(dx = x du\)

Hence:

\(\int \frac{1}{x\ln{x}} dx = \int \frac{1}{u} du = \ln{u} = \ln{\ln{x}}\)

Applying the Fundamental Theorem of Calculus:

\(A = \ln{\ln{e^e}} - \ln{\ln{e}} = \ln{e\ln{e}} = \ln{\ln{e}} = \ln{e} - \ln{1} = 1\)

Hence, the area under the graph of f(x) in the desired interval is of 1 unit squared.

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Answer:

a. dQ/dt = -kQ

b. \(Q = 9e^{-kt}\)

c. k = 0.178

d. Q = 1.063 mg

Step-by-step explanation:

a) Write a differential equation for the quantity Q of hydrocodone bitartrate in the body at time t, in hours, since the drug was fully absorbed.

Let Q be the quantity of drug left in the body.

Since the rate of decrease of the quantity of drug -dQ/dt is directly proportional to the quantity of drug left, Q then

-dQ/dt ∝ Q

-dQ/dt = kQ

dQ/dt = -kQ

This is the required differential equation.

b) Solve your differential equation, assuming that at the patient has just absorbed the full 9 mg dose of the drug.

with t = 0, Q(0) = 9 mg

dQ/dt = -kQ

separating the variables, we have

dQ/Q = -kdt

Integrating we have

∫dQ/Q = ∫-kdt

㏑Q = -kt + c

\(Q = e^{-kt + c}\\Q = e^{-kt}e^{c}\\Q = Ae^{-kt} (A = e^{c})\)

when t = 0, Q = 9

\(Q = Ae^{-kt} \\9 = Ae^{-k0}\\9 = Ae^{0}\\9 = A\\A = 9\)

So, \(Q = 9e^{-kt}\)

c) Use the half-life to find the constant of proportionality k.

At half-life, Q = 9/2 = 4.5 mg and t = 3.9 hours

So,

\(Q = 9e^{-kt}\\4.5 = 9e^{-kX3.9}\\\frac{4.5}{9} = e^{-kX3.9}\\\frac{1}{2} = e^{-3.9k}\\\)

taking natural logarithm of both sides, we have

\(ln\frac{1}{2} = ln(e^{-3.9k})\\\\-ln2 = -3.9k\\k = -ln2/-3,9 \\k = -0.693/-3.9\\k = 0.178\)

d) How much of the 9 mg dose is still in the body after 12 hours?

Since k = 0.178,

\(Q = 9e^{-0.178t}\)

when t = 12 hours,

\(Q = 9e^{-0.178t}\\Q = 9e^{-0.178X12}\\Q = 9e^{-2.136}\\Q = 9 X 0.1181\\Q = 1.063 mg\)

Answer:

488

Step-by-step explanation:

You divide 28453 by 58.3053278689 and get 488.

For the statement "If a polygon lacks right angles, then it is a parallelogram.", the counter example is -

Option A : a right triangle

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

A counterexample for a conditional statement is an example that satisfies the hypothesis (the first part of the statement) but does not satisfy the conclusion (the second part of the statement).

In this case, the statement is "If a polygon lacks right angles, then it is a parallelogram."

A right triangle is a polygon that lacks right angles, but it is not a parallelogram.

Therefore, a right triangle is a counterexample for this statement.

A square, a regular hexagon, and a rectangle all have right angles, so they are not counterexamples for this statement.

Therefore, the triangle is the counterexample.

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Answer:

6x + 50

5x + 50 + x

Step-by-step explanation:

Answer:

Option 1 : 5x + 50 + x

Option 5: 6x + 50

Step-by-step explanation:

The given expression is 5(x + 10) + x

5(x + 10) = 5x + 50   by expanding the brackets

So

5(x + 10) + x = 5x + 50 + x

The first choice , 5x + 50 + x corresponds to the above so that is a correct choice

Second is incorrect

Third is incorrect

Fourth is incorrect

If we simplify 5x + 50 + x  we get 6x + 50 which is same as the fifth choice

Answer: <

Step-by-step explanation: -26 is less than positive 56

Answer:

5 drops

Step-by-step explanation:

The distance between the points G and H is D = 8 units

Given data ,

Let the distance between 2 points be represented as D

Now , let the first point be G ( 0 , 8 )

Let the second point be H ( 8 , 8 )

Now , let the distance between G and H be D , where

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( 0 - 8 )² + ( 8 - 8 )²

D = √64 units

D = 8 units

Hence , the distance is 8 units

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Answer:

\(11\dfrac{3}{8}\text{cm}\)

Step-by-step explanation:

\(1\dfrac{5}{8}+2\dfrac{9}{16}+2\dfrac{9}{16}+4\dfrac{1}{8}=11\dfrac{3}{8}\)

Hope this helps!

Answer:

\(x=-9\)

Step-by-step explanation:

\(36^{x-3}=1296^{x+3}\\(6^2)^{x-3}=(6^4)^{x+3}\\2(x-3)=4(x+3)\\x-3=2x+6\\x+6=-3\\x=-9\)

To find the surface area of the cone, we use the following formula

S = pi x r x h + pi x r²

Where 'S' represents the surface area, 'r' the radius of the base, and 'h' the slant height.

from your question, we get the following information:

r = 14/2 = 7

h = 20

S = Surface area(the thing we're trying to calculate)

If you just plug those informations into the equation, we get the following

S = 3.14 x 7 x 20 + 3.14 x 7² = 3.14 x 140 + 3.14 x 49 = 593.46 cm²

Then, we get this final answer. The surface area of this cone is 593.46 cm²

Traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Earth to Mars is compared to traveling from Earth to the moon, we need to calculate the difference between the distances.

The distance from Earth to the moon is approximately 3.74 x 10^5 km.

The distance from Earth to Mars is approximately 9.25 x 10^7 km.

To find the difference, we subtract the distance to the moon from the distance to Mars:

9.25 x 10^7 km - 3.74 x 10^5 km

To subtract these numbers, we need to make sure the exponents are the same. We can rewrite the distance to the moon in scientific notation with the same exponent as the distance to Mars:

3.74 x 10^5 km = 0.374 x 10^6 km (since 0.374 = 3.74 x 10^5 / 10^6)

Now we can perform the subtraction:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 km - 0.374 x 10^6 km

To subtract, we subtract the coefficients and keep the same exponent:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 - 0.374 x 10^6 km

Simplifying the subtraction:

9.25 x 10^7 - 0.374 x 10^6 km = 9.249626 x 10^7 km

Therefore, traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Scientific notation is a convenient way to express very large or very small numbers. It consists of a coefficient (a number between 1 and 10) multiplied by a power of 10 (exponent). It allows us to write and manipulate such numbers in a compact and standardized form.

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Answer:

Step-by-step explanation:

The volume of a cube is given by the formula :

a³ (where a is the side length )

So now we have to cube these lengths :

Part A :

(3x²y)³ =

(3x²y)(3x²y)(3x²y) =

(9x^4y²)(3x²y) =

27x^6y³ (This is now fully simplified so our final answer for a)

Part B:  

(5y²)³ =

(5y²)(5y²)(5y²) =

(25y^4)(5y²) =

125y^6 (This is now fully simplified so our final answer for b)

Hope this helped and have a good day