Please show working out. 25 points.

Answer:

Being lost on this problem is well-earned.  I don't know what the question is looking for.  There appear to be no options, other than to identify some unique feature of the calculation.

If a polynomial has one root in the form of (a+[tex]\sqrt{b}[/tex]) and a second root in the form of (a-[tex]\sqrt{b}[/tex]) the polynomial must have the form of a^2 + b.

Step-by-step explanation:

I'll take a guess at how this problem wants the sentence to end.  We are told there are two roots a polynomial.  We can write the polynomial as the product of both roots, which would be equal to zero:

(a+[tex]\sqrt{b}[/tex])*(a-[tex]\sqrt{b}[/tex])

Multiply the factors to obtain:

a^2 - a[tex]\sqrt{b}[/tex] + a[tex]\sqrt{b}[/tex] + ([tex]\sqrt{b}[/tex] )^2

a^2 + b

So one might say:

If a polynomial has one root in the form of (a+[tex]\sqrt{b}[/tex]) and a second root in the form of (a-[tex]\sqrt{b}[/tex]) the polynomial must have the form of a^2 + b.

But that's my guess at something that would be a true statement.

Answer:

It would be a diameter

Step-by-step explanation:

The diameter is also a chord.

None of the given equations gives the correct answer, the answer is none of the options.

The equation from the calculation is:

y = 375(0.9834)ˣ

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign "=". Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

The data gives the relation between time and temperature.

We are asked to find the time and temperature relation as an equation.

We are given five equations as options.

a) T(x) = 375(0.5)ˣ

x is time and T is temperature.

Now we will give the value of x = 10 in this equation.

T(10) = 375 * 0.5¹⁰ = 0.366

This is not the value given in the table.

So this is not the equation.

b) T(x) = -50x + 375

  T(10) = -50 * 10 + 375 = -500 + 375 = -125

This is not the equation.

c) T(x) = -25x² + 375

   T(10) = -25 * 10 * 1 0 + 375 = -2500 +375 = -2125

This is not the equation.

d) T(x) = 50x - 375

   T(10) = 50 * 10 - 375 = 500 - 375 = 125

This is not the equation.

e) T(x) = 25x² -75x + 375

  T(10) = 25 * 10 * 1 0 -75 * 10 + 375 = 2500 -750 +375 = 2125

The general form of the exponential equation is:

y = abˣ

375 = ab⁰= a

325 = ab¹⁰

275 = ab²⁰

275/325 = b¹⁰

b = 0.9834

So the equation for this data is:

y = 375(0.9834)ˣ

Since none of the given equations gives the correct answer, the answer is none of the options.

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To convert mcg to mg, divide the mcg value by 1000. Therefore:

1000 mcg = 1000/1000 mg = 1 mg

So, 1000 mcg is equal to 1 mg.



Let A be a symmetric matrix that is invertible. This means that there exists a matrix B such that AB = BA = I, where I is the identity matrix. We want to show that B is also symmetric, that is, [tex]B = B^{T}[/tex]

To prove this, we can use the definition of matrix inversion. We know that AB = I, so we can take the transpose of both sides:

[tex]AB^{T} = I^{T}[/tex]

Using the transpose rules, we can rewrite this as:

[tex]B^{T} * A^{T}[/tex] = I

Now, we can multiply both sides of this equation by A:

[tex]B^{T} * A^{T}[/tex]* A = A

Since A is invertible, we can multiply both sides by A⁻¹ to get:

[tex]B^{T}[/tex] = A⁻¹

Therefore, we have shown that the inverse of a symmetric matrix A, which we denote as A⁻¹, is also symmetric, since A⁻¹ = [tex]B^{T}[/tex], which is the transpose of the matrix B.

Hence, we have proved that if a symmetric matrix is invertible, then its inverse is symmetric as well.

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The two equivalent expressions for the new acreage sold by the landowner are:

Both of these expressions will give the same result, which is the new acreage after the sale.

Another way to find the new acreage is to subtract the sold acreage from the total acreage. This is the same as the first expression, but it may be easier for some people to understand. For example, if the total acreage was 100 acres and the sold acreage was 20 acres, the new acreage would be 100 - 20 = 80 acres.

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Using the formula, we can convert milliliters to teaspoons. 1 milliliter equals 0.202 teaspoons, thus 10ml equals 2.02 teaspoons.

The volume unit is milliliters. A teaspoon is also a volume measure, however it is a smaller unit that is commonly used at dinner settings.

One millilitre is equivalent to 0.202 US teaspoons using normal conversion rates.

As a result, we may define the link using the unit conversion idea.

One milliliter is equal to 0.202 teaspoons in the United States.

For example, 10 milliliters equals 2.02 teaspoons.

As a result, we'll need roughly 2 tablespoons to get 10 ml.

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Answer:

Step-by-step explanation:

x-3 is greater than or less than 7

the equation that represents the value of the car after 5 years is Value of car after 5 years = 21,100 x 0.98^5 = 19,105.08

Given:

The cost price of the car, P = $21100,

The depreciation rate = 2%

Calculate the value of the car after 6 years by the following formula,

A = P (1- r / 100)ⁿ

Here A is the value of the car after 6 years.

Substitute the values,

A = 21100 × (1- 2 / 100)^5,

A = $19,105.08

Therefore, the equation that represents the value of the car after 5 years is Value of car after 5 years = 21,100 x 0.98^5 = 19,105.08

The equation of the normal line to the curve is y = -x + π

To find the equation of the normal line to the curve y = sin(sinx) at x = π, we need to find the slope of the tangent line at x = π and then use that to determine the slope of the normal line. We can find the slope of the tangent line by taking the derivative of y with respect to x and evaluating it at x = π.

y = sin(sinx)

Taking the derivative with respect to x, we get:

dy/dx = cos(sinx) * cosx

At x = π, we have:

dy/dx = cos(sin(π)) * cos(π) = -1 * (-1) = 1

So the slope of the tangent line at x = π is 1. Since the normal line is perpendicular to the tangent line, its slope is the negative reciprocal of 1, which is -1.

Now we need to find the y-intercept of the normal line, which is the point where the line intersects the y-axis. To do this, we can plug in the values of x = π and y = sin(sinx) = sin(sin(π)) = 0 into the equation of the line:

y = mx + b

0 = -1 * π + b

b = π

So the equation of the normal line is:

y = -x + π

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The vertex is (-1, -6) and the axis of symmetry is -1. The function is minimum. The solution has been obtained by using equation of parabola.

What is a parabola?

Any point on a parabola is equally separated from both the focus, or predetermined point, and the fixed straight line (known as the directrix).

We are given f(x) = 2(x + 1)² - 6

We know that a parabola of equation a(x - h)² + k always has its vertex at (h, k) with axis of symmetry at x = h.

So, the vertex here is (-1, -6) and the axis of symmetry is x = -1.

It is a minimum function because there is a positive value before (x - h)².

Hence, the vertex is (-1, -6) and the axis of symmetry is -1 and the function is minimum.

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Answer:

a. AD = 28 mm

b. m/CBD = 90°

c. m/ADC = 90°

d. m/AEB = 45°

e. m/DAC = 135°

Answer: i think the answer would be 75

Answer:

55 chairs.

Step-by-step explanation:

Note the way Liam arranges the chairs.

1) He arranges chairs in 8 rows of the same length, with 7 chairs left over.

8x + 7

2) He arranges chairs in 6 rows of the same length, with 19 chairs left over:

6x + 19

Set the two expressions equal to each other:

8x + 7 = 6x + 19

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 6x and 7 from both sides of the equation:

8x (-6x) + 7 (-7) = 6x (-6x) + 19 (-7)

8x - 6x = 19 - 7

2x = 12

Next, divide 2 from both sides of the equation:

(2x)/2 = (12)/2

x = 12/2

x = 6

Plug in 6 for x in both expressions. It should give the same answer:

8x + 7

8(6) + 7 = (8 * 6) + 7 = (48) + 7 = 55

6x + 19

6(6) + 19 = (6 * 6) + 19 = (36) + 19 = 55

~

Therefore, Liam has 55 chairs in all.

~

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The vertex form of the quadratic equation g is:

g(x) = 25*(x - 4)²

We start with the parent quadratic function:

f(x) = x²

We know that first we apply a translation of 4 units to the right, so we will get:

g(x) = f(x - 4)

And then we compress it horizontally by a factor of 5, then we can write:

g(x) =f( 5(x - 4))

Replacing the actual function we will get:

g(x) = ( 5*(x - 4))²

Distributing the exponent we will get:

g(x) = 5² *(x - 4)²

g(x) = 25*(x - 4)²

That is the quadratic equation in vertex form.

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a. The probability of finding oil is 0.45

b. The probability of finding high-quality oil is 0.25

c. P(medium quality oil) = 0.20

d. P(no oil) = 0.55

The probabilty of finding oil

P(oil) = P(high quality oil) + P(medium quality oil)

= 0.25 + 0.20

= 0.45

b. P(soil high quality oil) = 0.20

P(medium qty) = 0.80

P(no oil) = 0.20

The probability of finding oil is good.

Given the probability of finding good soil, the oil company is more likely to find medium quality oil.

The new probability of finding oil is

P(High quality) + P(medium quality) =

0.15625 + 0.5

= 0.65625

Using the conditional probabilty formula

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[tex]{ \qquad \qquad \huge \rm \underline{ \underline{ \Répondre}}} [/tex]

lets find the equation of line in two point form, considering points (0 , 0) and (-3 , 4)

[tex]\qquad \rm\dashrightarrow \:y - 0= \dfrac{4 - 0}{ - 3 - 0} (x -0)[/tex]

[tex]\qquad \rm\dashrightarrow \:y = - \dfrac{4 }{ 3 } x [/tex]

That's the required equation ~

You can also simply it as :

[tex]\qquad \rm\dashrightarrow \:3y= - 4x[/tex]

[tex]\qquad \rm\dashrightarrow \:4x + 3y = 0[/tex]

The value  1 gallon has 128 fluid ounces(oz)

"How many ounces in a gallon?" This is one of the most frequently asked questions regarding liquid measurements. One gallon equals 8 pints, 4 quarts, or 16 cups. There are 128 fluid ounces in a gallon, and this number depends on whether you use imperial or metric units of measure.

There are 128 US fluid ounces in a US gallon. If you're in the UK, you'll find a gallon at 160 UK fluid ounces. This is because the US fluid gallon is smaller than the British imperial gallon (3,785 liters compared to

,5

6 liters). When converting

Gallons to Fluid Ounces, remember that the US Fluid Ounce is larger than the British Imperial Ounce. A US fluid ounce is 29.5735 ml. For comparison, a UK (Imperial) fluid ounce is 28.

131 ml. So the US has a smaller gallon than the UK, but a slightly larger fluid ounce. It's enough to make your head  explode. For these two conversions you need the following information:

1 gallon (US) = 128 ounces (US, Fluid)

1 gallon (UK) = 160 ounces (UK, Fluid)

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Answer:

Step-by-step explanation:

If a 6-ounce bottle of medicine contains 36 doses, we can use a proportion to find how many doses are in a 15-ounce bottle:

6 ounces / 36 doses = 15 ounces / x doses

Cross-multiplying, we get:

6 x = 36 * 15

6 x = 540

Dividing both sides by 6, we get:

x = 90

Therefore, a 15-ounce bottle of the same medicine contains 90 doses.

the area of the inner cylinder is 2π(e^8/2)ln 8 and the area of the outer cylinder is 2πln 8e^8. The volume is then equal to the integral of the area of the cylindrical

Disk/washer method:

[tex]V = π ∫[ln 8]^8 (e^x)^2 dx\\V = π ∫[ln 8]^8 e^2x dx\\V = π(e^2x/2)|[ln 8]^8\\V = π(e^16 - (e^2(ln 8))^8)/2\\V = (π(e^16 - 64)/2)[/tex]

Cylindrical shells method:

[tex]V = 2π ∫[ln 8]^8 x(e^x) dx\\V = 2π ∫[ln 8]^8 xe^x dx\\V = 2π(x(e^x/2) - (e^x/2)ln x)|[ln 8]^8\\V = 2π((ln 8)(e^8 - 8) - (e^8/2)ln 8)\\V = (2π(e^8 - 64ln 8 - 4e^8))/2\\V = (π(e^16 - 64 - 8e^8))/2[/tex]

The disk/washer method can be used to solve for the volume of the solid generated by revolving the given region about the line x = ln 8. This method involves integrating the area of a ring, which can be formed by subtracting the area of a disk from the area of the washer. In this case, the area of the disk is π(e^2(ln 8))^8 and the area of the washer is π(e^16). The volume is then equal to the integral of the area of the ring, which is π(e^16 - (e^2(ln 8))^8).

The cylindrical shells method can also be used to find the volume of the solid generated by revolving the given region about the line x = ln 8. This method involves integrating the  of a cylindrical shell, which can be formed by subtracting the area of the inner cylinder from the area of the outer cylinder. In this case, the area of the inner cylinder is 2π(e^8/2)ln 8 and the area of the outer cylinder is 2πln 8e^8. The volume is then equal to the integral of the area of the cylindrical

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The car would be worth $9400 in the year 2004.

If the car depreciates by 11% each year, then its value at the end of each year will be 89% of its value at the beginning of the year (100% - 11% = 89%). Therefore, the value of the car after 1 year will be:

$15000 * 0.89 = $13350

The value of the car after 2 years will be:

$13350 * 0.89 = $11881.50

The value of the car after 3 years will be:

$11881.50 * 0.89 = $10576.77

The value of the car after 4 years (in the year 2004) will be:

$10576.77 * 0.89 = $9422.19

Therefore, the car would be worth $9400 in the year 2004.

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Function g lingered for a while.

h = v 0 y 2 2 g . This equation, which only depends on the vertical component of the initial velocity, specifies the maximum height of a projectile above its launch site.

The projectile formula's maximum height from the graph is H = u 2 sin 2 2 g.

An item named g was launched from a higher location when x=0... g(0)> f(0).

A higher point was reached by the object of  g.

When the object was launched, f's slope was greater than g's slope.

The launch velocity of object f was greater.

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Answer: commensalism

Step-by-step explanation:

Melody and her mother aren't hurting each other but also aren't of the same benefit

The relationship that Melody has with her mother is that They have a close bond, but not much mutual understanding.

A story is a fiction or a non fiction narrative which tells us about a series of events or verse, which is narrated in such a way that it takes the interest of the reader.

Most of the fictions convey a certain moral or idea that should be taken in to our life.

Given is a story of a little girl Melody and her mother.

We can clearly seen from the story that, Melody is five year old.

She has a pet named Ollie, which is a fish.

When the fish come out of the bowl by itself, Melody was scared and screamed for help.

But non one heard.

So as a method to rescue Ollie, she put the bowl upside down to save it.

When mother sees it, she misunderstood the situation.

So the relationship between Melody and mother is close bond, but not much mutual understanding.

Hence the correct answer is option D.

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The domain is all real values and the range is y <= 3

From the question, we have the following parameters that can be used in our computation:

The graph

The domian is the set of the input values

In this case, the graph has no restriction on its input

So, we have

Domain = all set of real values

For the range, we have

Maximum y value = 3

So, we have

Range: y <= 3

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Answer:

100

Step-by-step explanation:

The coordinates of the figure are  A''(-3, 1),B''(2,2), C''(-2, -1).

What is the transformation of a point?

The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

Given that the coordinates of the points A, B, C are A(-6,-3), B(-1,-4), C(-5,-1).

The rule of a reflection across the x-axis is (x,y)→(x,-y).

After reflection across the x-axis,

A(-6,-3)→ A'(-6,3)

B(-1,-4)→B'(-1,4)

C(-5,-1)→C'(-5,1)

A rule of translation of 3 units right and 2 units down is (x,y)→(x+3,y-2).

Thus the new coordinates are:

A'(-6,3)→ A''(-6+3,3-2)=A''(-3,1)

B'(-1,4)→ B''(-1+3,4-2)=B''(2,2)

C'(-5,1)→ C''(-5+3,1-2)=C''(-2,-1)

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The basic parts of a circle are the circumference, diameter, radius, and center. The circumference is the outer boundary of the circle, and it is the distance around the circle.

The diameter is a line segment that passes through the center of the circle and connects two points on the circumference. The radius is a line segment that connects the center of the circle to a point on the circumference.

The center is the point in the middle of the circle, and it is equidistant from all points on the circumference. These four basic parts are essential to understanding the properties of circles, such as their area, circumference, and relationships between different parts.

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The amount would $10,000 due in 50 years be worth today if the discount rate were 7.5% is,

P = $7,042

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We know that;

The formula is,

⇒ Amount = P (1 + r)ⁿ

Hence, We get;

10,000 = P (1 + 0.75)⁵⁰

10,000 = P (1.75)⁵⁰

10,000 = P × 1.42

P = 10,000 / 1.42

P = $7,042

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