A polynomial f(x) has the given zeros of 7-1, and-3

Part A: Using the Factor Theorem, determine the polynomial f (x) in expanded form Show all necessary calculations (3 points)

Part B: Divide the polynomial f (x) by (x²-x-2) to create a rational function g(x) in simplest factored form. Determine g(x) and find its slant asymptote (4 points)

Part C: List all locations and types of discontinuities of the function g(x) (3 points)

The matrix elements are nothing more than the matrix entries. The correct option is B.

The matrix elements are nothing more than the matrix entries. They can be integers, variables, mathematical formulas, or any other type of character included within the matrix.

The value of a₁₄ is the value of the element of the given matrix, where 1 represents the row and 4 represents the column. Therefore, the value of a₁₄ is the element of the first row and the fourth column, which means the value of a₁₄ is 5.

Hence, the correct option is B.

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The equation D = 1.5x/y represents the total distance traveled in km in terms of x.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

We have:

On the first journey, a cyclist traveled 1 1/2 km in x minutes.

As we know,

Speed = distance/time

Distance = 1 1/2 = 3/2 km = 1.5 km

time = x

Speed = 1.5/x

On the second journey, the same cyclist traveled for y hours at the same average speed as on his first journey.

Distance = speed×time

Distannce(D) = (1.5/x)(y)

D = 1.5x/y

Thus, the equation D = 1.5x/y represents the total distance traveled in km in terms of x.

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Answer:

Just think of which number, when you multiply it with 20 will give you -8

and then you multiply that number with -4 to get y. Hope it helps!

Answer:

or D

The results that could be displayed are 3.9 ×10⁻⁶, 3.9 E-6 OR 0.0000039

From the question, we are to determine the results that could be displayed on the calculator screen

The given expression is

(2.6 × 10⁻²)(1.5 × 10⁻⁴)

= 2.6 × 1.5 × 10⁻²× 10⁻⁴

= 3.9 ×10⁻²⁺⁻⁴

= 3.9 ×10⁻²⁻⁴

= 3.9 ×10⁻⁶

= 3.9 E-6 OR 0.0000039

Hence, the results that could be displayed are 3.9 ×10⁻⁶, 3.9 E-6 OR 0.0000039

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Answer:

x = 5.00 cm

Step-by-step explanation:

• area of the rectangle = [tex]x[/tex]   x   [tex](x + 1)[/tex]

                                     = [tex]x^2 + x[/tex]

• area of the circle = π r²

                               = [tex]\frac{22}{7}[/tex]   x   [tex](x + 2)^2[/tex]

                               = [tex]\frac{22}{7}[/tex]   x   [tex](x^2 + 4x + 4)[/tex]

∴   [tex]x^2 + x[/tex]   +    [tex]\frac{22}{7}[/tex]   x   [tex](x^2 + 4x + 4) = 184[/tex]  

⇒  [tex]x^2 + x[/tex]      +   [tex]\frac{22}{7} x^2 \space\ + \space\ \frac{88}{7} x \space\ + \space\ \frac{88}{7} = 184[/tex]

⇒  [tex]\frac{29}{7}x^2 \space\ + \space\ \frac{95}{7}x \space\ - \frac{1200}{7} = 0[/tex]

• Using quadratic formula, where

a = [tex]\frac{29}{7}[/tex]

b = [tex]\frac{95}{7}[/tex]

c = [tex]\frac{-1200}{7}[/tex] ,

[tex]x=\frac{-b \pm \sqrt{b^2-4c}}{2}[/tex]

[tex]x = \frac{-\frac{95}{7}\pm \sqrt{(\frac{95}{7})^2 - 4(\frac{29}{7})(\frac{-1200}{7} ) } }{2(\frac{29}{7})}[/tex]

[tex]x = 5.00 \space\ \space\ \space\ or \space\ \space\ \space\ x = -8.28[/tex]

As length (x) cannot be a negative number,

x = 5.00 cm

Answer:

y=⅓x+b

Step-by-step explanation:

So basically the formula of slope-intercept is:

y=mx+b

and m=⅓

so

y=⅓x+b and it includes the point (0, 6) so:

6=⅓(0)+b===> b=6===> y=⅓x+6

If 30 is half price, then what is full price?

You can set up this problem like this:

30 = x/2

OR

30 = (1/2)x

where x is the full price.

To solve, simply multiply each half by 2:

2(30) = 2((1/2)x)

x = $60

The value of the variable x and y will be 1  2/3 and 4  2/3. Then the correct option is C.

The solution of the equation means the value of the unknown or variable.

The equations are given below.

y = 4x − 2  ...1

y = x + 3    ...2

Subtract equation 1 from 2, then we have

 0 = 3x – 5

3x = 5

 x = 5/3

 x = 1  2/3

Then the value of y will be

y = 5/3 + 3

y = 14 / 3

y = 4  2/3

Then the correct option is C.

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An expression is defined as a set of numbers, variables, and mathematical operations.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p are given below,

If the given expression 2.3p – 10.1 = 6.5p – 4 – 0.01 is simplified, then the expression can be written as,

2.3p – 10.1 = 6.5p – 4 – 0.01

2.3p – 10.1 = 6.49p – 4

Thus, Option A is one of the option.

Using the multiplication property of Equality, if we multiply both the sides of the equation by 100, then we will get,

230p – 1010 = 650p – 400 – p

Thus, c is one of the option.

Hence, the correct options are A and C.

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Answer:

Step-by-step explanation:

Answer:

a) Angle X = 108°

as AD is parallel to EH both the angles are equal

Answer:

108 degrees, vertical angles

Step-by-step explanation:

Angle x is 108 degrees because angle x and angle EFB are vertical angles, meaning that they are equal since opposite angles have the same measures.

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By using trigonometric identities we can solve the trigonometric equation Sin (5x-28) = cos (3x - 50) for x.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The question is incomplete.

The complete question is:

Solve for X given that sin(5X - 28)° = cos(3X - 50)°.​

We have given:

sin(5X - 28)° = cos(3X - 50)°.

[tex]\rm \sin \left(5x-28\right)=\sin \left(\dfrac{\pi }{2}-\left(3x-50\right)\right)[/tex]

[tex]\rm \left5x-28\right= \left\dfrac{\pi }{2}-\left(3x-50\right)\right[/tex]

[tex]\rm x=\dfrac{4\pi n+156+\pi }{16}[/tex]     (n = 0, 1, 2, ...)

[tex]\rm x=\dfrac{\pi +4\pi n-44}{4}[/tex]

Thus, by using trigonometric identities we can solve the trigonometric equation Sin (5x-28) = cos (3x - 50) for x.

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Using the relation between velocity, distance and time, it is found that t = 3 hours.

Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

For this problem, the parameters are given as follows:

d = 15 miles, v = 5 mph

Hence the time in hours is found as follows:

[tex]v = \frac{d}{t}[/tex]

[tex]5 = \frac{15}{t}[/tex]

5t = 15

t = 15/5

t = 3 hours.

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The width of the card to the nearest tenth of an inch is 6.15 inches

Area of a rectangle = Length × Width

88 = (2x + 2) × x

88 = 2x² + 2x

2x² + 2x - 88 = 0

x = -b ± √b² - 4ac / 2a

= -2 ± √2² - 4(2)(-88) / 2(2)

= -2 ± √4 - (-704) / 4

= -2 ± √708 / 4

= -1/2 ± √177/2

x = 6.15 or -7.15 inches

The width of the rectangle can not be negative, so, 6.15 inches is the width.

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1) [tex]\overline{NQ}[/tex] is the bisector of [tex]\angle MNP[/tex] and [tex]\angle NMQ \cong \angle NPQ[/tex] (given)

2) [tex]\angle MNQ \cong \angle QNP[/tex] (a bisector splits an angle into two congruent angles)

3) [tex]\overline{NQ} \cong \overline{NQ}[/tex] (reflexive property)

4) [tex]\triangle MNQ \cong \triangle PNQ[/tex] (AAS)

Assuming [tex]a[/tex] is a non-negative real number...

Raise both sides to the power 2 :

[tex]a^{3/4} = 8 \implies \left(a^{3/4}\right)^2 = 8^2 \implies a^{3/2} = 64[/tex]

which follows from the exponent product property, [tex](x^y)^z=x^{yz}[/tex]. In particular, 3/4 × 2 = 6/4 = 3/2.

Raise both sides to the power 1/3 :

[tex]\left(a^{3/2}\right)^{1/3} = 64^{1/3} \implies a^{1/2} = 4[/tex]

where we use the same property as before, and 4³ = 64. This time, 3/2 × 1/3 = 3/6 = 1/2.

Take the reciprocal of both sides. This negates the exponent, so we end up with

[tex]\dfrac1{a^{1/2}} = \dfrac14 \implies \boxed{a^{-1/2} = \dfrac14}[/tex]

Of course, you could also solve for [tex]a[/tex] immediately by raising both sides of the original equation to the power 4/3. We have 4/3 × 3/4 = 12/12 = 1, so

[tex]a^{3/4} = 8 \implies \left(a^{3/4}\right)^{4/3} = 8^{4/3} \implies a = 8^{4/3}[/tex]

Now 2³ = 8, so [tex]8^{4/3} = \left(8^{1/3}\right)^4 = 2^4 = 16[/tex], and since 4² = 16, it follows that

[tex]a = 16 \implies a^{1/2} = \sqrt{16} = 4 \implies a^{-1/2} = \dfrac14[/tex]

The attached graph represents the graph of the equation 3x + y = 10

The given parameters are:

Represent the number of smoothies with x and the number of candy bears with y.

So, the equation is:

3x + 1y = 10

This gives

3x + y = 10

Next, we plot the graph of the above equation

See attachment for the graph of 3x + y = 10

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The line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

Sarah is going to the movies, and she has $10 to spend on snacks. Smoothies are $3 and candy bars are $1 each. She will be spending all of the $10.

Let's suppose the number of smoothies is x and the number of candy bars is y:

Then, we can frame a linear equation in one variable:

3x + y = 10

Drawing the above the line on the coordinate plane:

Thus, the line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.

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Answer:

69 degrees

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

<1 = 39+ 30

<1 = 69

Answer:

The points present in the first quadrant are of the form (a, b) where a, b>0.

Step-by-step explanation:

The points present in the first quadrant are of the form (a, b) where a, b>0.

In the first quadrant both the abscissa and ordinate are positive.

In the second quadrant the abscissa is negative and ordinate is positive.

In the third quadrant both the abscissa and ordinate are negative.

In the forth quadrant both the abscissa is positive and ordinate are negative.

The examples of points in the first quadrant are (1,0), (2,3), (11,4) and many other.

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Answer: The y-coordinates in the first quadrant are positive. because y represents the profit made, positive y values signify profit. The points in quadrant I represent the baseball team making a profit.

Step-by-step explanation: Source - I took the test.

For the graphed function we can see:

For a function y = f(x), the domain is the set of the possible inputs "x" and the range is the set of the possible outputs "y".

In this case, we can see that in the right side we have a parabola, and on the left side a linear equation which increases up to the left (so it has a negative slope).

Then the domain will be the set of all real numbers.

Similar for the range, as we can see that on the left side, the line goes upwards, while on the right side, the parabola goes downwards. So this function has a range of all real numbers.

Then:

domain = set of all real numbers

range = set of all real numbers.

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Answer:

[tex]\frac{42}{8}[/tex]

Step-by-step explanation:

7/8 <> 0.875

0.875 * 6 = 5.25

5.25 <> 42/8

(<> is used to show decimal to fraction and vice versa [the other way around])

Answer:

80%

Step-by-step explanation:

I'm assuming you meant express 4/5 as a percent and not 4/5%. So simply evaluate 4/5 to get 0.80. Now multiply this value by 100 to get the percentage which gives you 80%

Answer:

4

Step-by-step explanation:

In triangle JKL, the side opposite the 30 degree angle, JL, is half the length of the hypotenuse, KL. Thus, JL has a length of

[tex]4 \sqrt{2} [/tex]

In triangle JML, the hypotenuse is

[tex] \sqrt{2} [/tex]

times the length of the leg, meaning that x = 4

Answer:

y - 10 = 2(x - 3)

Explanation:

Equation:

y - y₁ = m(x - x₁)

Here given:

coordinates: (x, y) = (3, 10)

Inserting value's:

y - 10 = 2(x - 3)  in point slope form

y = 2x - 6 + 10

y = 2x + 4  in slope-intercept form

Answer:

d) y - 10 = 2(x - 3)

Step-by-step explanation:

Given: a line with a slope of 2, and the point (3, 10)

⇒ Point-Slope Form: y - y₁ = m(x - x₁)

where: m is the slope, and (x₁, y₁) is a given point

Substitute the values into the form:

⇒ y - y₁ = m(x - x₁)

⇒ y - 10 = 2(x - 3)

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Answer:

John is 19 and his sister is 23.

Step-by-step explanation:

See attached image.

Answer:

The surface area of the triangular prism is [tex]624cm^{2}[/tex]

Step-by-step explanation:

First find the area of the triangle.

The formula of the area of triangle is: [tex]\frac{1}{2} * h*b[/tex]

h=height

b=base or width.

[tex]\frac{1}{2}*16*12[/tex]

But, since we have two triangles we can skip the [tex]\frac{1}{2}[/tex] because [tex]2*\frac{1}{2} =1[/tex].

[tex]16*12=192[/tex], that is the area of the two triangles combined.

Now let's find the area of the rectangles. I'll start with the diagonal one.

The formula of the area of the rectangle is: [tex]h*b[/tex].

[tex]20*9=180[/tex].

The next rectangle.

[tex]9*16=144[/tex]

The final rectangle.

[tex]12*9=108[/tex]

Now combine all the areas to find the surface area of the triangular prism.

[tex]192+180+144+108=624[/tex]

The surface area of the triangular prism is [tex]624cm^{2}[/tex]

Hope this helps!

If not, I am sorry.

Answer:

angle CAD

Step-by-step explanation:

look at the 3 points that make up the angle