Solve the following system to find the point(s) of intersection.
y = x² - 2x - 3
y = 2x - 3

Answer:

298.97 minutes

Step-by-step explanation:

2^x = 1 000 000      where 'x' is the number of 15 minute periods

x = 19.931      15 minute periods = 298.97 minutes

The simplest form of the given expression is 5x^3-5x^2.

We have given that

[tex]2x^3 - x^2 + 3 (x^3 - 4x^2)[/tex]

We have to determine the simplest form of the given expression.

The distributive property of binary operations generalizes the distributive law, which asserts that equality is always true in algebra. elementary.

Use the distributive property we get,

[tex]2x^3 - x^2 + 3 (x^3 - 4x^2)\\=2x^3 - x^2 +3x^3-12x^2\\[/tex]

Add like terms we get,

Therefore we get,

[tex]=5x^3-5x^2[/tex]

Therefore the simplest form of the given expression is 5x^3-5x^2.

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Answer:

-21

Step-by-step explanation:

The measure of x will be 18.81 units.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

The given information are;

Perpendicular = 4

Base = x

Then, Tan ∅ = Perpendicular /Base

Tan 12 = 4/x

x = 4 /0.212

x = 18.818

Hence, the measure of x will be 18.81 units.

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Answer:

4800

Step-by-step explanation:

If a question is asking for the "sum" of numbers, this just means we have to add them altogether.

975+983+923+913+985 = 4779

To find the hundredth place, we use our place value. 4 is in the thousands column, and 7 is in the hundreds. Once we find the hundreds, we need the number to the right of it (7).

7 > 5 so we round up. 7 becomes 8.

4800.

The nature of a graph, which has an even degree and a positive leading coefficient will be up left, up right position

The nature of the graphical representation of a quadratic equation with an even degree and a positive leading coefficient will give a parabola curve.

Given that we have a function f(x) = an even degree and a positive leading coefficient. i.e.

The domain of this function varies from -∞ < x < ∞ and the parabolic curve will be positioned on the upward left and upward right x-axis.

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Answer:

Step-by-step explanation:

Exponent law:

    [tex]\sf \bf a^m * a^n = a^{m+n}\\\\ (a^m)^n = a^{m*n}[/tex]

    [tex]\sf a^{-m}=\dfrac{1}{a^m}[/tex]

       First convert radical form to exponent form and then apply exponent law.

 [tex]\sf \sqrt{3}=3^{\frac{1}{2}}\\\\\sqrt{5}=5^{\frac{1}{2}}[/tex]

[tex]\sf \left(\dfrac{(\sqrt{3}*3^{-2}}{(\sqrt{5})^2}\right)^{\frac{1}{2}}= \left(\dfrac{3^{\frac{1}{2}}*3^{-2}}{(5^{\frac{1}{2}})^2} \right )^{\frac{1}{2}}[/tex]

                      [tex]= \left(\dfrac{3^{\frac{1}{2}-2}}{5^{\frac{1}{2}*2}}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{1-4}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{-3}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\dfrac{3^{\frac{-3}{2}*{\frac{1}{2}}}}{5^{\frac{1}{2}}}\\\\ =\dfrac{3^{{\frac{-3}{4}}}}{5^{\frac{1}{2}}}[/tex]

Answer:

-282

Step-by-step explanation:

Any altitude below sea level would have a negative sign in front of it.

Answer:

65/8

Step-by-step explanation:

1) Turn all numbers into improper fractions: 17/2 - 3/8 = ?

2) Make all denominators the same number by finding the least common factor, which is 8. Multiply the denominator in 17/2, which is 2, by 4 to match the other denominator. And then multiply the numerator (17) by 4 as well so that the fraction still has the same value: 68/8 - 3/8 = 65/8

3) Can not simplify since there are no common factors between 65 and 8.

Answer:

300-6x

Step-by-step explanation:

Trust me

Answer:

DF

Step-by-step explanation:

Paint a picture in your head reflecting the triangle. Just hold A and flip it so A = E , D = B

Answer:

Point Form:

(9,12)

Equation Form:

x = 9

y = 12

Step-by-step explanation:

Answer:

[tex]\fbox{x = 9, y = 12}[/tex]

Step-by-step explanation:

[tex]\textsf {Let's solve by substitution.}[/tex]

[tex]\rightarrow \mathsf {-5x + 4y = 3}\\\rightarrow \mathsf {x = 2y - 15}[/tex]

[tex]\textsf {Substitute for x in the first equation of the system.}[/tex]

[tex]\implies \mathsf {-5(2y-15)+4y=3}[/tex]

[tex]\implies \mathsf {-10y+75+4y=3}[/tex]

[tex]\implies \mathsf {-6y=-72}[/tex]

[tex]\implies \textbf {y = 12}[/tex]

[tex]\implies \mathsf {x = 2(12) - 15}[/tex]

[tex]\implies \mathbf {x = 9}[/tex]

[tex]\textsf {The solution is : x = 9, y = 12}[/tex]

Answer:

Please see attachment.

The first one is a quadrilateral that is not a parallelogram.

The second one is a triangle with a right angle.

Step-by-step explanation:

Hope this helps!

If not, I am sorry.

Answer:

[tex]y=[1]cos([\frac{2\pi }{3}]x)[/tex]

Step-by-step explanation:

Looking at the graph, we can see the domain to be from (0 , 2π).

Now we have to find one period that corresponds to cos(x).

The half-period of cos(x) for this graph appears to be pi/3 and adding another pi/3 gets us 2pi/3 to be our cosine period.

b = 2pi/3

a is the same range as cos(x). Range: (0,0)

y = [a] * cos ([b]*x)

y = [1] * cos([2pi/3]x)

Less workers = more hours

OR the answer might be worded as

More workers = less hours

The equation will be a linear equation from (2, 5) to (4, 10) will be y = 2.5x.

Mathematics is replete with functions, which are necessary for the construction of intricate connections.

A 2-column table with 3 rows. Column 1 is labeled x with entries 2, 4, 5. Column 2 is labeled y with entries 5, 10, 12.5.

Use the information in the table to find the constant of proportionality and write the equation.

The equation will be a linear equation from (2, 5) to (4, 10) will be

(y – 5) = [(10 – 5) / (4 – 2)] (x – 2)

 y – 5 = 2.5x – 5

       y = 2.5x

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Answer:

2.5 and y=2.5x

Step-by-step explanation: i got that question on an edguenity assignment

The solutions to the trigonometric equation in the desired interval are given as follows:

[tex]\theta = \frac{\pi}{3}, \theta = \frac{5\pi}{3}[/tex]

The trigonometric equation is given by:

[tex]\sqrt{3}\cot{\theta} - 1 = 0[/tex]

Solving it similarly to an equation, we have that:

[tex]\sqrt{3}\cot{\theta} = 1[/tex]

[tex]\cot{\theta} = \frac{1}{\sqrt{3}}[/tex]

Since [tex]\cot{\theta} = \frac{1}{\tan{\theta}}[/tex], we have that the equation is equivalent to:

[tex]\tan{\theta} = \sqrt{3}[/tex]

The tangent is positive in the first and in the fourth quadrant. In the first quadrant, the angle [tex]\theta[/tex] with [tex]\tan{\theta} = \sqrt{3}[/tex] is:

[tex]\theta = \frac{\pi}{3}[/tex]

In the fourth quadrant, the equivalent angle is:

[tex]\theta = 2\pi - \frac{\pi}{3} = \frac{5\pi}{3}[/tex]

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The slope of the line parallel to the line on the graph (0,-3) (5,-4) is - 1 / 5

Parallel lines have the same slope.

Therefore,

slope = m = y₂ - y₁ / x₂ - x₁

Therefore,

x₁ = 0

x₂ = 5

y₁ = -3

y₂ = -4

Therefore,

slope = -4 - (-3)  / 5 - 0

slope = -4 + 3 / 5

slope = - 1 / 5

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The solution to the given quadratic expression is x = -1 and x = 5

Given the quadratic equation below

f(x) = x^2 - 4x - 5

Factorize

f(x) = x^2 - 5x + x - 5 = 0
f(x) = x(x - 5) + 1(x - 5) = 0
(x+1)(x-5) = 0
x = -1 and x = 5

Hence the solution to the given quadratic expression is x = -1 and x = 5

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Answer:

x = -1; x = 5

Step-by-step explanation:

Standard Form of a Quadratic Function: f(x) = ax² + bx + c, where a ≠ 0

Given function: f(x) = x² - 4x - 5

⇒ a = 1, b = -4, c = -5

We are asked to solve the following function by factoring. In order to do so, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = -5) and give us the sum of the middle term (b = -4).

Factors that give a product of a • c: 1 • -5 = -5

Factors that give a sum of b: 1 + (-5) = -4

Step 1: Substitute f(x) = 0.

⇒ 0 = x² - 4x - 5

Step 2: Rewrite the equation with the factors.

⇒ 0 = x² + x - 5x - 5

Step 3: Factor out x and -5.

⇒ 0 = (x² + x) + (-5x - 5)

⇒ 0 x(x + 1) - 5(x + 1) [ Factor out the common factor. ]

⇒ 0 = (x - 5)(x + 1)

Step 4: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0)

a) 0 = x - 5 ⇒ 0 + 5 = x - 5 + 5 ⇒ 5 = x

b) 0 = x + 1 ⇒ 0 - 1 = x + 1 - 1 ⇒ -1 = x

Therefore, the missing solution for this quadratic function is x = 5.

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The given expression is equivalent to [tex]\frac{p^{7}q}{160}[/tex]

What are indices?

An index is a small number that tells us how many times a term has been multiplied by itself.

The plural of index is indices.

Below is an example of a term written in index form :[tex]4^{3}[/tex]

4 is the base and 3 is the index.

We can read this as ‘4 to the power 3’

Another way of expressing [tex]4^{3}[/tex] is

4 x 4 x 4 = 64

Indices can be positive or negative numbers.

Given expression can be written as [tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]

Now to simplify the given fractional expression :[tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]

=   [tex]\frac{4^{-2}p^{8}q^{-2}}{10pq^{-3}}[/tex]                    By using the property of exponents is given by:

                                    [tex](a^{m})^{n}=a^{m n}[/tex]

=[tex]\frac{p^{7}q}{10 .16}[/tex]                              By using the property of exponents given by

                                       [tex]a^{m}a^{n}=a^{m + n}[/tex]  and  [tex]a^{-m}= \frac{1}{a^{m}}[/tex]

= [tex]\frac{p^{7}q}{160}[/tex]

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Answer:

The second option

Step-by-step explanation:

If you look at the graph, it appears that from negative infinity to 0, the line is just constant, so the range of that would simply be the constant value or in this case 4. from 0 to infinity it appears the line is decreasing at a constant rate and should go towards negative infinity as x goes towards infinity. So the range would be -infinity < f(x) <= 4

Answer:

B

Step-by-step explanation:

Used elimination method.

first plugged in (0,0)which remove A,D

than saw the line is not solid so chose B

Considering the direction of the wind, it is found that the jet travels faster than the sound during it's journey.

The jet's speed, considering that there is a tailwind, is given by:

J = Plane speed + Wind speed.

In this problem, we have that the speeds are given as follows:

Hence the jet's speed is given by:

J = 550 + 120 = 670 knots.

670 knots > 661 knots, hence the jet travels faster than the sound during it's journey.

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Construct OD and BD. Then, in quadrilateral ABOD, angles ODA and OBA are right angles and thus angle DOB is 130 degrees (since angles in a quadrilateral add to 360 degrees).

So, this means arc DB also measures 130 degrees. Hence, by the inscribed angle theorem, angle BCD is 65 degrees.

Answer:

508.02

HOPE THIS HELPS

Todo <3

Step-by-step explanation:

From calculations, we can say that the given tiles will not fit together perfectly.

If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.

Expression for the measure of the interior angle of a polygon,

Interior angle of a polygon = [(n - 2) * 180]/n

Interior angle of a pentagon = [(5 - 2) * 180]/5 = 108°

Interior angle of a hexagon = [(6 - 2) * 180]/6 = 120°

Interior angle of an octagon = [(8 - 2) * 180]/8 = 135°

To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°

Sum of all interior angles = 108° + 120° + 135° = 363°

Therefore, given tiles will not fit together perfectly.

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You are correct, P(red) = P(green) = 0.25.

Answer:

-1/2

Step-by-step explanation:

IK

Its the first one

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

Answer:

  $24 = $0.40(60)

Step-by-step explanation:

Match the input value and its location in the equation.

__

  $24 = $0.40(60)

_____

Additional comment

When input is liters and output is dollars, the constant of proportionality must have units of "dollars per liter." The dollar sign of these units is not shown in the left panel, but is shown on the answer choices. If you understand units conversion, this should not be a mystery. (The mystery is why the curriculum materials are inconsistent.)

Answer:

(2,3) ; (-2.11)

Step-by-step explanation:

Answer:

(2, 3); (-2, 11)

Step-by-step explanation:

f(x) = x² - 2x + 3

f(x) = -2x + 7

f(x) = f(x)

x² - 2x + 3 = -2x + 7

x² = 4

x = ±2

x = 2

f(2) = -2(2) + 7 = -4 + 7 = 3

x = -2

f(-2) = -2(-2) + 7 = 4 + 7 = 11

Answer: (2, 3); (-2, 11)