for what values of k does the line y=kx-2 and the parabola y=1+5x-2x^2

i) touch

ii) intersect

iii) not intersect

The solution set of the given homogeneous system in parametric vector form is (x1,x2,x3)=(s,-2,-5)

Parametric vector form:

If there are m-free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors:

x = s1v1 + s2v2 + ··· + sm vm. This is called a parametric equation or a parametric vector form of the solution.

A common parametric vector form uses the free variables as the parameters s1 through sm

Given is a system of equations

We are to solve them in parametric form.

x1 + 3x2 + x3 = 0 --------(1)

-4x1 + 9x2 + 2x3 = 0 ---------(2)

-3x2 - 6x3 = 0--------(3)

From equation(3)

-3x2=6x3

x2=-2x3

substitute in equation(1) and equation(2)

x1+3(-2x3)+x3=0

x1-6x3+x3=0

x1-5x3=0

x1=5x3

So the solution in parametric form is (x1,x2,x3) = (s,-2,5) for all real values.

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Answer:

You can tell if two fractions are proportional by using cross multiplication. Only equivalent fractions are proportional. To do this, multiply the denominator, the bottom number in the fraction, of the first fraction with the numerator, the top number in the fraction.

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

so -x-6 and x-4 are both = to y so that means they are both = to each

other so -x-6=x-4 add x to both sides -6=2x-4 add 4 to both sides 2x = -2 simplify by divide by 2 so x=-1

Answer:

Take the second equation and add 4 to both sides, this gives you x=y+4. The plug in y+4 on the first equation, so y=-(y+4)-6, distribute the negative to everything inside the parentheses, and you get y=-y-4-6. Combine like terms and you get y=-y-10, then add y to both sides, you get 2y=-10, divide both sides by 2 and you get y=-5.

Then plug -5 into the second equation and you get -5=x-4, add 4 to both sides and you get -1=x.

If you want to check your answer, just plug in x and y to either of the equations and see if it makes a true statement.

Answer:

Step-by-step explanation:

You have to use the distance formula to find that distance.  The formula is:

\(d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)

Let's call the first point x1, y1 (4, -1) and the second point x2, y2 (0, -2). Plugging into our formula then gives us this:

\(d=\sqrt{ (0-4)^2+(-2-(-1))^2}\)

which simplifies to

\(d=\sqrt{(-4)^2+(-1)^2}\) which is

\(d=\sqrt{17}\) ≈ 4.123 units

Answer:

Please check the explanation.

Step-by-step explanation:

We know that if we multiply 3 and 4, we get 12.

In other words, 3 × 4 = 12

Thus, 3 and 4 are factors of 12.

now

Given the expression

\((a+b+c)(d+e+f)\)

The given expression consists of two factors which are:

We also know that an expression can consist of terms, a term may be a constant or a variable. It can be both as well.

For example, in the expression, 4b + 2, 4b and 2 are terms.

so,

Answer:

37,349

Step-by-step explanation:

month 1

27870 x .05 = 1394

27870 + 1394 = 29264

month 2

29264 x .05 = 1463

29264 + 1463 = 30727

month 3

30727 × .05 = 1536

30727 + 1536 = 32263

month 4

32263 x .05 = 1613

32263 + 1613 = 33876

month 5

33876 x .05 = 1694

33876 + 1694 = 35570

month 6

35570 x .05 = 1779

35570 + 1779 = 37349

Answer:

35,570

Step-by-step explanation:

solution 1 - Multiply by 5%, 6 times. Easter to calculate without a calculator, long process.

1. 27870*1.05= 29,263.5

2. 29263.5*1.05=30726.675

3.repeat

4.repeat

5.repeat

6.repeat

if it's hard for you to multiply by 1.05, you can always divide by 20 or divide by 10 then by 2 (like the below)

1. 27870÷10= 2,787

2. 2787÷2= 1393.5

3. 27870+1393.5 = 29263.5

solution 2 -Fast but probably needs a calculator

1. 27870*1.05^(5)= 35570

1.05 = monthly increase

power of 5 = ^(5) = 6 months - 1 = 5

Answer:

c. although set a, is a proper function, with y being the function of x, c is the answer.

Answer:

It would be:

4 5/9 x 1/2

4 5/9 x 10/10

4 5/9 x 6

Step-by-step explanation:

Answer:there is no g .no h

Step-by-step explanation:how can we tell u have a calculator right

Answer:

Based on the information, the pollster's conclusion makes sense.

To know if the pollster is right with his conclusion we must perform the following operation.

In accordance with the above, we can infer that the pollster concludes that 54% of the people surveyed are equivalent to 545 people correctly because 0.86 is a minimum margin of error for this type of statistics. In addition, it can be inferred that the pollster correctly uses the statistics and study parameters of a sample to establish a correct conclusion.

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To find the value of x when (fog)(x) = -8, we first need to find the composition of f and g, which is given by (fog)(x) = f(g(x)). To do this, we substitute g(x) into the expression for f(x) and simplify:

f(g(x)) = f(1) when g(x) = 1

f(g(x)) = f(-2) when g(x) = -2

f(g(x)) = f(3) when g(x) = 3

f(g(x)) = f(-4) when g(x) = -4

f(g(x)) = f(4) when g(x) = 4

There is no value of x for which (fog)(x) = -8.

Using the table given in the question, we can find the values of f(g(x)) for each possible value of g(x):

f(g(x)) = f(1) = -2

f(g(x)) = f(-2) = 0

f(g(x)) = f(3) = 32

f(g(x)) = f(-4) = 8

f(g(x)) = f(4) = 4

Therefore, (fog)(x) = -8 is not possible. The closest value we can get to -8 is by setting g(x) = -4, which gives f(g(x)) = f(-4) = 8. Thus, there is no value of x for which (fog)(x) = -8.

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The Logarithmic function is  \(g(y)=\log_2y\).

\(x=3\) is the length corresponding to the strength 8 Pa

The relation between the length and the strength of the building materials is given by an exponential function, \(f(x) = 2^x\) ,

where x is the length.

We have to convert this function into a logarithmic function where the strength is given as 8 Pa.

Let \(y = f(x)\)

i.e., \(y=2^x\)  where y represents the strength.

We know that logarithmic function is the inverse of the exponential function up to the bases.

Taking Logarithm on both sides, we get,

\(log y = x log 2\)

⇒ \(x=log_2y\)

i.e., the length is given by the function  \(g(y)=\log_2y\)  when y, the strength is known. This is the required logarithmic function.

So when the strength, y = 8 Pa,

the length, \(x = log_2 8\)  ⇒ \(x=log_2 2^3\)

⇒ \(x=3\) is the length corresponding to the strength 8 Pa.

The question provided is incomplete. Here you can find the complete question:

Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x) = \(2^x\), where x is the length. Explain how he can convert this equation to a logarithmic function when strength is 8 Pascals.

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\(\huge \bf༆ Answer ༄\)

The shown pair of Angles are known as Adjacent Angles, because they have one Arm in common.

Answer:

if there is a total of 360 degrees on every circle how much is left?

Answer:

x = 136°

Step-by-step explanation:

It is the same corresponding angle

Hope this helps

Take the square root of each side.

\(\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5\)

Answer:

0.15893 is irrational

0.7 is rational

5 1/25 is rational

-17 is rational

Answer:

2 1/4

Step-by-step explanation:

hope this helps

The graph of the inequality is a straight line that passes through point 3 and represents the solution set.

A mathematical statement known as an inequality in mathematics examines two values or quantities and determines whether they are equal or not. Ranges of values or equation solutions can also be described by inequality. Inequality x 10 defines all x values that are less than or equal to 10, whereas inequality x > 3 represents all x values that are more than 3. For a visual representation of the range of values that fulfil an inequality, inequality's can be graphed on a number line.

The given inequality is 4x - 2 < 10

The inequality can be written as:

4x < 10 + 2

4x < 12

x < 3

Hence, the graph of the inequality is a straight line that passes through point 3 and represents the solution set.

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Answer:

\(37.7\ \text{foot}\)

Step-by-step explanation:

The length of the edging will be equal to the circumference of the circular flower garden.

Here, the diameter of the circular garden is \(d=12\ \text{foot}\)

Circumference of a circle is given by

\(C=\pi d\\\Rightarrow C=3.14\times 12\\\Rightarrow C=37.68\approx 37.7\ \text{foot}\)

The length of the edging is \(37.7\ \text{foot}\).

Answer:

x = 36

Step-by-step explanation:

The opposite of division is multiplication. So we would want to start off by multiplying 3 by both sides to get rid of the fraction.

Hope this helps

The resolution of the human eye is ultimately limited by the pupil diameter.

When the pupil diameter is 2.18mm, the smallest diameter spot the eye can produce on the retina is determined by the diffraction limit, which can be calculated using the formula:

θ = 1.22 * (λ / D)

where θ is the angular resolution, λ is the wavelength of light (typically around 550 nm for the visible spectrum), and D is the pupil diameter (2.18mm in this case). To find the smallest diameter spot on the retina, you would need to multiply the angular resolution by the distance from the lens to the retina (approximately 17mm for an average human eye).

However, the information provided is insufficient to calculate the exact smallest diameter spot. Additionally, factors like the density of photoreceptor cells in the retina also play a role in determining the resolution of the eye.

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Answer:

the worm line would be 4 inches long

The total distance traveled by the particle over the time interval [1, 5] is 12 units.

To find the total distance traveled, we need to consider both the magnitude and direction of the velocity function. Since the velocity function given is in meters per second (m/sec), the total distance traveled will be measured in meters.

To calculate the total distance, we need to consider the intervals where the velocity function changes its sign. In this case, the velocity function is linear and increasing, starting at t = 1 with a velocity of 3 m/sec. From t = 1 to t = 3, the particle moves in the positive direction, covering a distance of (3t - 9) × (t - 1) = 12 units. From t = 3 to t = 5, the particle moves in the negative direction with the same magnitude, covering a distance of (-1) × (3t - 9) × (t - 3) = 12 unit

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Stem-and-leaf plots contain original data values where histograms do not. Therefore, option B is the correct answer.

The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values.

The "stem" is used to group the scores and each "leaf" shows the individual scores within each group.

The advantage of a stem leaf diagram is it gives a concise representation of data. The advantage of a frequency histogram is, that it is visually strong. Histograms are usually preferable to stem and leaf diagrams in large data sets. The disadvantage of a stem leaf diagram is not visual.

Therefore, option B is the correct answer.

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

Explanation:

Sine is given to be negative, and so is tangent. This only happens in quadrant Q4

Recall that y = sin(theta), so if sin(theta) < 0, then we're below the x axis.

If tan(theta) < 0, then this means cos(theta) > 0

So we have y < 0 and x > 0 which places the angle somewhere in Q4.

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

Draw a right triangle as shown below in the attached image. We have AC = 25 and BC = 7. Use the pythagorean theorem to find that AB = 24

So this is what your steps may look like

a^2+b^2 = c^2

7^2+b^2 = 25^2

b^2+49 = 625

b^2 = 625-49

b^2 = 576

b = sqrt(576)

b = 24

So because AB = 24, we know that the cosine of the angle is adjacent/hypotenuse = 24/25

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

As an alternative, you could use the trig identity

sin^2(x) + cos^2(x) = 1

and plug in the given value of sine to solve for cosine. The cosine value result will be positive since we're in Q4.

So,

sin^2(x) + cos^2(x) = 1

(-7/25)^2 + cos^2(x) = 1

(49/625) + cos^2(x) = 1

cos^2(x) = 1 - (49/625)

cos^2(x) = (625/625) - (49/625)

cos^2(x) = (625-49)/625

cos^2(x) = 576/625

cos(x) = sqrt(576/625)

cos(x) = sqrt(576)/sqrt(625)

cos(x) = 24/25

This is effectively a rephrasing of the previous section since the pythagorean trig identity is more or less the pythagorean theorem (just in a trig form)

Answer:

a) It is not possible to find the mean because these are words, not numbers.

b) If we put these words in alphabetical order, we have:

blue, blue, green, purple, purple, purple, red, red

The median word here is purple.

c) It is possible to find the mode, which in this case is the word that appears the most times in this list. That word is purple, which appears three times.

Answer:

its c

Step-by-step explanation:

easy 23 simple mulitply then add

Quantities that are proportional to each other are,

A) radius and diameter of a circle

B) radius and circumference of a circle

C) radius and area of a circle

D) diameter and circumference of a circle

E) diameter and area of a circle​

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

We know the radius of a circle is r and the diameter of a circle is 2r.

We also know that the circumference of a circle is 2πr and the area of a circle is π(r)².

Now the quantities that will be related to each other are the quantities that are together linked in the formula of circumference and area.

∴ Radius and diameter of a circle, Radius, and circumference of a circle, Radius and area of a circle, Diameter and circumference of a circle, and Diameter and area of a circle​ all are related to each other and are directly proportional.

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The molecular, total ionic, and net ionic equations for the given reactions are as follows:

4) Molecular equation: 2 KNO3(aq) + 3 FeBr3(aq) → 6 KBr(aq) + Fe2(NO3)3(aq)

  Total ionic equation: 2 K+(aq) + 2 NO3-(aq) + 3 Fe3+(aq) + 6 Br-(aq) → 6 K+(aq) + 6 Br-(aq) + Fe2+(aq) + 6 NO3-(aq)

  Net ionic equation: 3 Fe3+(aq) + 6 Br-(aq) → Fe2+(aq) + 6 Br-(aq)

5) Molecular equation: 2 HI(aq) + BaCO3(s) → BaI2(aq) + H2O(l) + CO2(g)

  Total ionic equation: 2 H+(aq) + 2 I-(aq) + Ba2+(aq) + CO3^2-(aq) → Ba2+(aq) + 2 I-(aq) + H2O(l) + CO2(g)

  Net ionic equation: 2 H+(aq) + CO3^2-(aq) → H2O(l) + CO2(g)

4) In the molecular equation, potassium nitrate (KNO3) reacts with iron (III) bromide (FeBr3) to form potassium bromide (KBr) and iron (III) nitrate (Fe2(NO3)3). In the total ionic equation, all soluble compounds are represented as dissociated ions. The net ionic equation is obtained by eliminating spectator ions, which are ions that appear on both sides of the equation and do not participate in the actual reaction. In this case, the net ionic equation shows that three iron(III) ions (Fe3+) react with six bromide ions (Br-) to form two iron(II) ions (Fe2+).

5) The molecular equation represents the reaction between hydroiodic acid (HI) and barium carbonate (BaCO3) to produce barium iodide (BaI2), water (H2O), and carbon dioxide (CO2). In the total ionic equation, the soluble compounds are dissociated into their constituent ions. The net ionic equation is derived by eliminating spectator ions. In this case, the net ionic equation shows that two hydrogen ions (H+) react with the carbonate ion (CO3^2-) to form water and carbon dioxide.

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