Rewrite the expression (17x3 – 12x2 + 6x - 4)/(x – 1) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor, using the synthetic division method.

Answer:

The original slope is 1, so the slope of the parallel line will also be 1.

The farmer put a total of 47 potatoes in one sack.

Here, we are given that a farmer harvested 192 pounds of Yukon Gold potatoes and 138 pounds of russet potatoes.

He divided the Yukon Gold potatoes evenly among 8 baskets.

Thus, the number of pounds of potatoes in each basket = 192/8

= 24

Similarly, he divided the russet potatoes evenly among 6 baskets.

Thus, the number of pounds of  russet potatoes in each basket = 138/6

= 23

Now, he fills a sack with one basket of Yukon Gold potatoes and one basket of russet potatoes.

n = the number of pounds of potatoes the farmer put in the sack

Thus, n = 24 + 23

n = 47

Thus, the farmer put a total of 47 pounds of potatoes in one sack.

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We can subtract 5x from 7x - 6 like this:

7x - 6 - 5x

Now, we just have to combine like terms, in this case, the terms that have the x variable, like this:

7x - 5x - 6

2x - 6

Then, after subtracting 5x from 7x - 6 we get 2x - 6

Answer:

2 2/4 + 1 3/4 + 2/4 = 4 3/4

4 3/4

Answer:

4 and 3/4

Step-by-step explanation:

2 1/2

+1 3/4

+   1/2

_____

4 and 3/4

ANSWER

EXPLANATION

The area of a triangle using two given sides and the included angle is given as:

where a and b are the sides and C is the included angle.

Therefore, we have to find C given that:

Therefore, we have that:

That is the measure of the included angle.

PLUG IN 2 IN THE PLACE OF X IN THE FUNCTION THEN SIMPLIFY

f(2)= |5×2|

f(2)=|10|

[tex]f(2) = 10[/tex]

ATTACHED IS THE SOLUTION

Answer:

[tex]\rm f(2)=|5\;^*\;2|=|10|=10[/tex]

Step-by-step explanation:

The bars either side of an expression or a value are the absolute value symbol.  "Absolute value" means how far a value is from zero.   Therefore, the absolute value of a number is its positive numerical value.

Given absolute value function:

[tex]f(x)=|5x|[/tex]

To find f(2), substitute x = 2 into the given function:

[tex]\begin{aligned}\implies f(2)&=|5 \cdot 2|\\&=|10|\\&=10\end{aligned}[/tex]

The factoring of the expression 2x² + 7x + 6 is (2x + 3)(x + 2).

It should be noted that a factor of a number is a number that can be multiplied with another number to get the original number.

In this case, 2x² + 7x - 6 will be factored thus:

= 2x² + 7x + 6

= 2x² + 4x + 3x + 6

= 2x(x + 2) + 3(x + 2)

= (2x + 3)(x + 2)

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Answer and Explanation:

If f(x) = x^2 is transformed to h(x)=2x^2 + 15, the below will be the effect on the its graph;

* The graph will be shifted up 15 units

*The graph will be vertically stretched since the value o

x = 10 is the solution to the equation -8 - x = -3( 2x - 4 ) + 3x using DCMAM method.

Given the equation in the question;

First, apply the distributive property to eliminate the parenthesis.

-8 - x = -3( 2x - 4 ) + 3x

-8 - x = -3×2x -3×-4 + 3x

Multiply -3 × 2x

-8 - x = -6x -3×-4 + 3x

Multiply -3 × -4

-8 - x = -6x + 12 + 3x

Next, combine like terms.

Add -6x and 3x

-8 - x = -3x + 12

Next, move variable to one side and constant terms to the other.

-x + 3x =  12 + 8

Add -x and 3x

2x =  12 + 8

Add 12 and 8

2x = 20

Divide both sides by 2

2x/2 = 20/2

x = 20/2

x = 10

Therefore, the value of x is 10.

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Answer:

Perimeter = 65.12 inches, Area = 292.48 square inches

Step-by-step explanation:

Perimeter:

Total perimeter = perimeter of semicircle + perimeter of rectangle (note: excluding the shared line, since that is not on the outside of the shape).

= [tex]\frac{1}{2} 2\pi r[/tex]

= [tex]\frac{1}{2} *2*3.14*8[/tex]

= 25.12

Perimeter = 25.12 + 12 + 12 + 16 = 65.12 inches

Area:
Total area = area of semicircle + area of rectangle

Area of semicircle = [tex]\frac{1}{2} \pi r^{2}[/tex]

= [tex]\frac{1}{2} *3.14* 8^{2}[/tex]

= 100.48

Area of rectangle = l * w

= 16 * 12

= 192

Total area = 100.48 + 192 = 292.48

Answer:

4.

5.

Step-by-step explanation:

Relationships in a right triangle:

The sine of an angle is the length of the opposite side to the angle divided by the hypotenuse.

The cosine of an angle is the length of the adjacent side to the angle divided by the hypotenuse

The tangent of an angle is the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

Question 4:

hypotenuse is 5.

AB is adjacent to an angle of 45º. So

Applying cross multiplication:

Question 5:

Hypotenuse is 10.

BC is opposite to an angle of 60. So

We have a regression model to predict y from the value of x.

The equation of this regression line is:

We then can calculate y for x = 7 as:

Answer: the predicted value of y when x = 7 is y(7) = 20

The first step to this problem is finding the amount of butterfat there are in the 385 gallons milk with 5% of butterfat in it. To do that we need to multiply the percentage by the total amount of milk. This is done below:

There are 19.25 gallons of butterfat on the final mixture, the amount of butterfat from each of the milks we are going to mix need to be equal to that. The first milk contains 8% of butterfat, while the second milk contains 1%. So we have:

Where "x" is the number of gallons from the first milk and "y" is the number of gallons from the second milk. The number of gallons of each milk, when added, should be equal to the number of gallons on the final milk, so we have:

The same is valid for the amount of butterfat.

We have now created a system of equations as shown below:

To solve this system we will multiply the first equation by "-0.01":

Now we need to add both equations.

To find the value of "y" we will use the first equation:

We need 220 gallons from the 8% butterfat milk and 165 gallons from the 1% butterfat milk.

Answer:

3x + y = -3

Step-by-step explanation:

(-4, 9), (2, -9)

(x₁, y₁)  (x₂, y₂)

       y₂ - y₁      -9 - 9          -18          -18

m = ----------- = ----------- = ---------- = ------- = -3

       x₂ - x₁        2 - (-4)      2 + 4        6

y - y₁ = m(x - x₁)

y - 9 = -3(x - (-4)

y - 9 = -3(x + 4)

y - 9 = -3x - 12

   +9           +9

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

y = -3x - 3

Standard Form:

-3x + y = -3

I hope this helps!

Answer:

75.40 cubic meters

Explanation:

Given:

• The diameter of a cylinder is 4 m.

• The height is triple the radius

We want to find the volume of the cylinder.

First, determine the radius of the cylinder.

Next, we find the height.

Substitute these values into the formula for the volume of a cylinder:

The value closest to the volume of the cylinder is 75.40 cubic meters.

To the nearest tenth, the distance across the lake is DE = 207.68 m.

The corresponding side lengths of two triangles that are similar are always proportional to each other.

ΔCDE  and ΔCFG are similar to each other

FG = 142.1 m

FC = 130 m

DF = 60 m

DC = 130 + 60 = 190 m

Therefore,

DE/FG = DC/FC

Substitute

DE/142.1 = 190/130

Cross multiply nearest hundredth

Therefore, applying the similarity theorem, the distance across the lake to the nearest hundredth is DE = 207.68 m

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Answer:

y = -16 (x - 1)^2 + 112

The object lands on the ground in approximately 3.6s

Explanation:

The equation given is that of a parabola.

Now the maximum (local) point of a parabola is the vertex. Therefore, if we want to rewrite our function in the form that would be used to find the maximum height, then that form must be the vertex form of a parabola.

The vertex form of a parabola is

where (h, k) is the vertex.

The only question is, what is the vertex for our function h(t)?

Remember that if we have an equation of the form

then the x-coordinate of the vertex is

Now in our case b = 32 and a = -16; therefore,

We've found the value of the x-coordinate of the vertex. What about the y-coordinate? To get the y-coordinate, we put x = 1 into h(t) and get

Hence, the y-coordindate is k = 112.

Therefore, the vertex of the parabola is (1, 112).

With the coordinates of the vertex in hand, we now write the equation of the parabola in vertex form.

The only problem is that we don't know what the value of a is. How do we find a?

Note that the point (0, 96) lies on the parabola. In other words,

Therefore, the vertex form of the parabola must also contain the point (0, 96).

Putting in t = 0, h = 96 into the vertex form gives

subtracting 112 from both sides gives

With the value of a in hand, we can finally write the equation of the parabola on vertex form.

Now when does the object hit the ground? In other words, for what value of t is h(t) = 0? To find out we just have to solve the following for t.

We could either use h(t) = -16t^2 + 32t + 96 or the h(t) = -16(t - 1)^2 + 112 for the above equation. But it turns out, the vertex form is more convenient.

Thus we solve,

Now subtracting 112 from both sides gives

Dividing both sides by -16 gives

taking the square root of both sides gives

adding 1 to both sides gives

Hence, the two solutions we get are

Now since time cannot take a negative value, we discard the second solution and say that t = 3.6 is our valid solution.

Therefore, it takes about 3.6 seconds for the object to hit the ground.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. The value of P(A) = 1/9.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Total number of 2-digit terms =(99 - 10) + 1 = 90

n(s) = 90

Number of 2 digits that have 4 in tens place = 40, 41, 42 ......49

n(a) = 10

P(A) = n(a)/n(s)

Substituting the values in the above equation, we get

P(A) = 10/90

P(A) = 1/9

The value of P(A) = 1/9.

Therefore, the correct answer is option (d) 1/9.

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Final Exam accounts for 65% of total.

The rest is 100 - 65 = 35%

On the 35%, he has 74% or 74 out of 100.

Let's say the final exam is out of 100 and we want to find how much he can afford to get to take him to "B".

Let's say his score needs to be "x" in order to get B.

The overall weighted average of the course would be counted as:

Breaking it down:

74 out of 100 means WHAT out of 35? (let's call the unknown "y")

y would be:

So, he currently has 25.9 out of 35.

He would need 83 to get overall average to 83%.

He would need:

83 - 25.9 = 57.1 out of 65

That is:

Basically he would need a percentage of 87.85% (MINIMUM) on the final exam to make his overall average to 83% (which is the bare minimum for a B grade).

This is a combination of the form:

So:

Answer:

21

The equation of the line will be  [tex]y = -\frac{3}{5}x -3[/tex]

In the question given, It is stated that the slope of the line is m = -3/5, and the y-intercept of the line is (0, -3). We have to find out the slope-intercept form of the line. To find out the equation of line first the standard equation for slope intercept form is y = mx + b, where m is the slope, and b is the y-intercept.

Now, we have slope m = -3/5 and y-intercept is -3. Putting these values in the slope intercept form we get:

=> y = mx + b

=> [tex]y = -\frac{3}{5}x -3[/tex]

Hence, we get equation of line [tex]y = -\frac{3}{5}x -3[/tex]

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In an ordered pair (x,y), x denotes the domain of the relation, and y denotes the range of the relation.

Knowing this, the three ordered pairs that will form a relation with a range of {-3, 4, 7} are

(-1, -3), (0, 4), and (2,7).

Perimeter = 18 ft

Area = 20 ft ^2

Perimeter = 2l + 2w

Area = lw

Substitution

18 = 2l + 2w

20 = lw

Solve for l

20/w = l

18 = 2(20/w) + 2w

18 = 40/w + 2w

18w = 40 + 2w^2

2w^2 - 18w + 40 = 0

w^2 - 9w + 20 = 0

(w - 5)(w - 4) = 0

w1 = 5 w2 = 4

Conclusion

width = 4 ft

length = 5 ft

Answer:

x ≥ 2

Step-by-step explanation:

Given inequality:

[tex]-\dfrac{4(x+3)}{5} \leq 4x-12[/tex]

Values of x less than 2

Substitute two values where x < 2 into the inequality:

[tex]\begin{aligned}x=1 \implies -\dfrac{4(1+3)}{5} & \leq 4(1)-12\\\\ -\dfrac{4(4)}{5} & \leq 4-12\\\\ -\dfrac{16}{5} & \leq -8 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies -\dfrac{4(0+3)}{5} & \leq 4(0)-12\\\\ -\dfrac{4(3)}{5} & \leq 0-12\\\\ -\dfrac{12}{5} & \leq -12 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]

The values of x < 2 are not solutions to the inequality.

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

Substitute the value of x = 2 into the inequality:

[tex]\begin{aligned}x=0 \implies -\dfrac{4(2+3)}{5} & \leq 4(2)-12\\\\ -\dfrac{4(5)}{5} & \leq 8-12\\\\ -\dfrac{20}{5} & \leq -4\\\\ -4 & \leq -4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

The value of x = 2 is a solution to the inequality.

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

Values of x more than 2

Substitute two values where x > 2 into the inequality:

[tex]\begin{aligned}x=3 \implies -\dfrac{4(3+3)}{5} & \leq 4(3)-12\\\\ -\dfrac{4(6)}{5} & \leq 12-12\\\\ -\dfrac{24}{5} & \leq 0 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

[tex]\begin{aligned}x=4 \implies -\dfrac{4(4+3)}{5} & \leq 4(4)-12\\\\ -\dfrac{4(7)}{5} & \leq 16-12\\\\ -\dfrac{28}{5} & \leq 4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

The values of x > 2 are solutions to the inequality.

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

Therefore, the solution to the inequality appears to be x ≥ 2.  

To check, solve the inequality:

[tex]\begin{aligned} \implies -\dfrac{4(x+3)}{5} &\leq 4x-12\\-4(x+3) &\leq 5(4x-12)\\-4x-12 &\leq 20x-60\\ -24x & \leq-48\\x & \geq 2\end{aligned}[/tex]

When graphing inequalities on a number line:

To graph the solution to the inequality on number line, place a closed circle at x = 2 and shade to the right.  (See attachment).

Answer:

T1 = P2 * V2 / T2 * P1 * V1

Answer:

69

Step-by-step explanation:

400-262=138

138÷2=69

The solution for this function will be x = -1 and x = 3

Quadratic polynomials are those with at least one variable and a variable with a maximum exponent of two. Since the second-degree term is the highest degree term in a quadratic function, it is sometimes referred to as the polynomial of degree 2. In a quadratic function, at least one term must be of the second degree. It has qualities in algebra.

The given function is -2x² + 4x + 6

So, we'll employ the middle term splitting strategy.

-2x² + 4x + 6 = 0

- 2x² + 6x - 2x + 6 = 0

-2x ( x-3) -2 (x-3) = 0

(-2x-2) (x-3) = 0

So, the solution will be

-2x - 2 = 0

-2x = 2

x = 2/-2

x = -1

And, x-3 =0

x = 3

So, the solution of the quadratic function will be

x =-1 and x = 3

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Given the turning points of the graph:

(-1.73, -10.39) and (1.73, 10.39).

Let's determine the range of the graphed function.

The range of a function is the set of all possible values of y.

The y-values are represented on the vertical axis.

From the graph, we can see the function goes up continuously and goes down continuously.

Therefore, we can say the range of the function is real numbers.

Therefore, the range of the function in interval notation is:

(-∞, ∞)

ANSWER:

rRange: (-∞, ∞)

Consider the given unbalanced equation which says " 16 divided by 8 " in the Left Hand Side, while it says " 16 divided by 8 then minus one ". This can be represented as,

Consider two things. First, acording to BODMAS rule, division is dprferred over subtraction. Second,