When Mr. Jackson got in his car yesterday, the odometer read 187,198.9 km. When he got home, the reading was 187,399.4 km. How far did Mr. Jackson drive?

The values in Manu’s list of rational roots he should try in the synthetic division, in light of these findings is

"Manu should try first +1/4,+1/2 and +1."

This is further explained below.

Generally, Because the lower and higher bonds are located between -6 and 1, Manu should have only analyzed the potential rational zeros that fall between those two numbers.

A lower bond indicates that the feasible rational zero cannot be lower than -6, and therefore the higher number that may be achieved cannot be more than 1.

In this manner, Manu will get an opportunity to test. This approach of rationalization based on bonds aims to reduce the number of potential solutions.

Therefore, if Manu discovers through the synthetic division that the possible roots are +1/4,+1/2,+1,+5/4,+2,+5/2,+4,+5,+10,+20, then he should only consider those inside the intervals marked by the lower and upper bounds, which are +1/4,+1/2,+1, because the rest is greater than 1. This is because the rest of the possible roots are higher than 1.

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CQ

Manu determines the roots of a polynomial equation p(x)=0 by applying the theorems he knows. He organizes the results of these theorems. From the fundamental theorems of algebra, Manu knows there are 3 roots to the equation. From Descartes' rule of sign, Manu finds no sign changes in p(x) and 3 sign changes in p(-x). The rational root theorem yields +1/4,+1/2,+1,+5/4,+2,+5/2,+4,+5,+10,+20 as a list of possible rational roots. The lower bound of the polynomial is -6. The upper bound of the polynomial is 1. What values in Manu's list of rational roots should he try in synthetic division in light of these findings?

The area between the solid line (y=x+4) and the dotted line (y=-2x-2) represents the system of inequalities solution set.

Two linear inequalities system on a coordinate plane. The first has a solid line graphed with a negative slope of one, a negative y-intercept, and a shaded origin area. The area encompassing the origin is shaded, and the second is a dashed vertical line 3 units to the left of the origin.

x ≥ –3; y ≥ x – 2

x > –3; 5y ≥ –4x – 10

x > –3; y ≥ –x + 1

x > –2; y ≥ –x – 1

The solution set for the system of inequalities is represented by the region between the solid line (y=x+4) and the dotted line (y=-2x-2).

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(a) Amount of data entered

(b) R

(c) Average temperature

Let's begin by identifying key information given to us in the graph:

The reciprocal parent function is given as 1/f(x). This is better written as shown below

When the value for x is greater than zero, the function is positive as shown below:

When the value of x is lesser than zero, the function is negative as shown below:

Therefore, the correct answer is option A (The function is negative when x < 0)

8a. The length of the robot arm, and the angle in radian and degrees are as follows

8b. The length of the robot arm, and the angle in radian and degrees are as follows

8a

i. let the length of the robot arm be r

The length of the lever arm using the points is done by

r^2 = ( -26 )^2 + ( -15 )^2

r^2 = 676 + 225

r^2 = 900

r = √ 900

r = 30

ii. theta in radian

tan θ = opposite / adjacent

tan θ = y direction / x direction

tan θ = -15 / -26

tan θ = 15/26

θ = Arc tan ( 15/26 )

θ = 29.9816 degrees

θ ≈ 30 degrees

θ ≈ 30 degrees + 180 = 210 degrees

In radian

π = 180 degrees

? = 210 degrees

we cross multiply to get

? * 180 degrees =  π * 210 degrees

? =  π * 210 degrees / 180 degrees

= 7π/6 radian

8b

i. let the length of the lever arm be r

The length of the lever arm using the points is done by

r^2 = ( -30 )^2 + ( 52 )^2

r^2 = 900 + 2704

r^2 = 3604

r = √ 3604

r = 60.033

r ≈ 60

ii. theta in radian

tan θ = opposite / adjacent

tan θ = y direction / x direction

tan θ = -30 / 52

tan θ = -30/52

θ = Arc tan ( -30/52 )

θ = -29.9816 degrees

θ ≈ -30 degrees (clockwise direction)

In radian

π = 180 degrees

? = 30 degrees

we cross multiply to get

? * 180 degrees =  π * 30 degrees

? =  π * 30 degrees / 180 degrees

= π/6 radian

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The value of (x) that satisfy the equation → - 3 - 23x = - 14(x - 21) - 15(x + 33) is x = - 33.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Given is the following equation -

- 3 - 23x = - 14(x - 21) - 15(x + 33)

The given equation is -

- 3 - 23x = - 14(x - 21) - 15(x + 33)

Simplifying for (x), we get -

- 3 - 23x = - 14x + 294 - 15x - 495

- 23x + 14x + 15x = 3 + 294 - 495

6x = - 198

x = - 33

Therefore, the value of (x) that satisfy the equation → - 3 - 23x = - 14(x - 21) - 15(x + 33) is x = - 33.

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y= 3x +14 (a)

y=-4x (b)

Replace the value of y (b) on equation (a), and solve for x

-4x = 3x+14

-4x-3x = 14

-7x = 14

x= 14/-7

x = -2

Replace the value of x on any initial equation and solve for y:

y= -4 (-2) = 8

y=8

Answer:

1*v=3,0.1+14y=-1 : v=3,y=-0.07857

[1.v=3}

[0.1+14y=-1]

v=3,y=-0.07857

Step-by-step explanation:

Answer:

Step-by-step explanation:

Starting from tan x, you can find sec x, because of the trigonometric identity 1 + tan2 x = sec2 x.

1 + (-4/3)2 = 1 + 16/9 = 25/9 = sec2 x.

So sec x = ±√(25/9) = ±5/3.  But since x is in Quadrant II, sec x has to be negative.  That's because sec x has the same sign as cos x, because sec x = 1 / cos x.  We know that cos x is negative is Quadrant II, therefore so is sec x.  So sec x = -5/3.

Since sec x and cos x are reciprocals of each other, cos x = 1/sec x = -3/5.

Now use the identity sin2 x + cos2 x = 1, to find sin x:

sin2 x + (-3/5)2 = 1

sin2 x + 9/25 = 1

sin2 x = 16/25

sin x = ±4/5

Again, we know that sin x is positive in Quadrant II, so sin x = 4/5.

Now that we know sin x and cos x, we can use the double angle formulas to find sin 2x and cos 2x.

sin 2x = 2 sin x cos x = 2 (4/5) (-3/5) = -24/25

cos 2x = cos2 x - sin 2 x = (-3/5)2 - (4/5)2 = 9/25 - 16/25 = -7/25

Finally use the identity tan x = sin x / cos x to find tan 2x:

tan 2x = sin 2x / cos 2x = (-24/25) / (-7/25) = -24/-7 = 24/7

they answer is 6a because you mines 10-4 and you get 6 then just put the loke 6a

Answer:

The answer is -23/2 or -11.5

Step-by-step explanation:

Answer:

[tex]\frac{-8}{5}[/tex]

Step-by-step explanation:

Slope is the change in y over the change in x

[tex]\frac{y_{2 - y_{1} } }{x_{2 - y_{1} } }[/tex]

(-2,4) is ([tex]x_{1}[/tex], [tex]y_{1}[/tex])

(3. -4) is ([tex]x_{2}[/tex],[tex]y_{2}[/tex])

[tex]\frac{-4 - 4}{3 - -2}[/tex] = [tex]\frac{-8}{3+ 2}[/tex] = [tex]\frac{-8}{5}[/tex]

Answer:

-8 / 5

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -4 -4)/( 3 - -2)

   = -8/ ( 3+2)

   = -8 / 5

During a basketball game, you made 11 shots of either 2 or 3 points. You scored a

total of 25 points. How many shots of each point value did you make?

Let

x -----> number of shots of 2 points

y -----> number of shots of 3 points

we have that

x+y=11

x=11-y -----> equation A

and

2x+3y=25 -----> equation B

substitute equation A in equation B

2(11-y)+3y=25

solve for y

22-2y+3y=25

y=25-22

y=3

Find the value of x

x=11-3

x=8

therefore

The given function is increasing over these following intervals:

B. -2 ≤ x ≤ -1.

C. 0 < x < 1.

Considering the given definitions on the bullet points above, the behavior of the function can be separated as follows:

Items B and C have subsets of the interval -2.5 ≤ x ≤ 2.5, hence the function is increasing on those intervals, and they are the correct options for this problem.

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Answer:

B

Step-by-step explanation:

if the number is x then 3 times the number is 3x

the difference is the subtraction of 3x and 4 , that is

3x - 4

Jake's weekly rate of eating of cake slices is 11.6

Given,

Number of equal slices of cake = 12

Number of slices Jake eaten after 3 days = 5

We have to find the weekly rate of eating;

Here,

Number of days in a week = 7

Jake eaten 5 slices in 3 days so, 7 - 3 = 4

Again after 3 days 5 slices.

Then,

4 - 3 = 1

That is, Jake eaten 10 slices of cake in 6 days.

Number of cake slices eaten in 1 day = 5/3 = 1.6

Therefore,

Weekly rate of eating is 10 + 1.6 = 11.6

That is,

Jake's weekly rate of eating of cake slices is 11.6

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Since y is a parabolla, there will be two values for y = 19. We already know that x = 1 is one value, to find the other, we can substitute y = 19 on the equation and solve for x to get the following:

the solutions of the equation are x = 1 and x = -7. Since we already have that (1,19) is a point on the graph, then we have that the other point is (-7,19)

The years of education as per the given equation, for a person whose father had 14 years of education is 14.966 years.

What is education?

A planned activity, education has objectives like knowledge transmission or character and skill development. The development of understanding, reason, kindness, and honesty may be some of these goals.

As given in the question,

respondent's years of education is represented by y, and

respondent's father years of education is represented by x,

The equation for the least squares regression line for predicting a respondent's years of education is given as:

y = 9.996 + 0.355x

The year of education of respondent's father is given as 14

So putting the value of x in the given equation as 14:

we get,

y = 9.996 + 0.355(14)

y = 14.966

Hence, the years of education for a person whose father had 14 years of education is 14.966 years.

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The box has 3 white balls and 4 black balls.

Total number of balls = 3 + 4 = 7

First draw:

The probability of getting a white ball is given by

Second draw:

Notice that after the first draw the ball is put back in the box.

The probability of getting a white ball is given by

At least one of the balls is white means that one white ball or two white balls.

We have already found the probability of getting one white ball that is P(x=1) = 3/7

The probability of getting two white balls is

Finally, the probability of at least one white ball is

Therefore, the probability of the event that at least one of the balls is white is 30/49

Answer:

  (d)  Isosceles right

Step-by-step explanation:

You want to know the classification of a triangle with angles 45°-45°-90°.

The largest angle is 90°, a right angle. Any triangle containing a right angle is a right triangle.

Two of the angles have the same measure. This means the triangle is an isosceles triangle.

The triangle is classified as an isosceles right triangle.

__

Additional comment

A triangle whose largest angle is less than 90° is an acute triangle. If the largest angle is greater than 90°, it is an obtuse triangle.

If no sides are the same length, the triangle is scalene. If two sides are the same length, the triangle is isosceles. If all three sides are the same length, it is an equilateral triangle.

Larger angles are opposite longer sides, so if angles are the same, their opposite sides are the same.

It can be worthwhile to remember that the side length ratios in an isosceles right triangle are 1 : 1 : √2.

Answer:

Given that,

To find the sum of the first 5 terms.

First, to find the first 5 terms of the given sequence.

The given sequence is 2,-8,32,-128,...

It follows geometric series with initial term 2, and common ratio as -4

The explicit formula of the given sequence is,

To find the 5th term of the sequence,

Put n=5 in the above equation we get,

Since common ratio is less than 1, we get the sum of the series formula as,

Substituting the values we get,

The sum of the first 5 terms of the given series is 410.

Answer is: option B: 410

Based on the given equivalences, you have:

7 m = 7(100 cm) = 700 cm

700 cm = 700 (2.54 in) = 1,778 in

Hence, there are 1,778 inches in 7 meters

The area of a triangular shape is given by the following formula

where,

base, b = 10 ft

height, h = 7 ft

therefore,

thus, the answer is 35 ft^2

As we can see, there are 8 parts in our circle but 4 parts belong to wedge 2 and 5. Then, the probability of landing on 4 or 6 is given by

because part 4 and part 5 are disjoint sets. Since there are 8 parts in our circle, we have

which gives

which corresponds to option B

log ( √2.86668684 ) is value of logarithm 18 .

What is logarithm used for in math?

[tex]log_{b} \sqrt{18}[/tex]  = [tex]log_{b} = log_{b} \sqrt{15} + log_{b} \sqrt{3}[/tex]

                 = log( √15 + √3 )

                = log ( √1.0986 * 1.6094  + √1.0986 )

                = log ( √1.76808684 + √1.0986 )

                = log ( √2.86668684 )

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In order to find the center of the circunscribed circle, we can use the midpoint theorem because the center point is in the middle of any two vertices

that is, if we take points (9,23) and (8,16) the midpoint C is given as

which gives

So the center of the circle is the point (8.5,19.5)

On the other hand, the radius is equal to the distance from any vertex to the center. If we take the vertex (8,16), we get

which gives

so, the radius measure 3.54 units.

Now, lets prove that the answer are correct. In order to do that, we can choose the other vertices and apply the same procedure as above.

So the vertices are (5,20) and (12,19). Again, the center is the midpoint between these points and is given as

which is the same center as above.

Now, the distance from the center to vertec (5,20) is

which is the same radius obtained above. Then, the answers are correct.

The coordinate pair is between the third and fourth quadrants, on the y-axis.

Remember that the quadrants are:

First quadrant: x > 0, y > 0.

Second quadrant: x < 0, y > 0.

Third quadrant: x < 0, y < 0.

Fourth quadrant: x > 0, y < 0.

In this case our coordinate pair is (0, -1/2).

So it will be between the third and fourth quadrants.

And yes, because one of the variables is zero, it is on the y-axis (just between the two quadrants).

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By Calculating the Constant of Proportionality, we get,

1. 5 cups of yellow paint is required for 1 cup of blue paint.

2. For 4 cups of blue paint, 20 cups of yellow paint is required.

   For 5 cups of blue paint, 25 cups of yellow paint are required.

3. Cups of Yellow Paints = 5* Cups of Blue Paints

4. The constant of Proportionality is 5.

Let the cups of blue paint = x

and cups of yellow paint = y

From the table, we can infer that to make the same shade of green, we need to mix 5 cups of yellow color with 1 cup of blue.

We have, To make the same shade of green,

we need to mix 5 cups of yellow color with 1 cup of blue.

we need to mix 10 cups of yellow color with 2 cups of blue.

we need to mix 15 cups of yellow color with 3 cups of blue.

So, here we can see a relationship between the two colors, blue (x) and green(y)  

Let k be the constant of proportionality, then, we have :

10 = k *2

k =[tex]\frac{10}{2} = 5[/tex]

Hence, For one cup of blue paint, we need 5 cups of yellow paint to make the same shade of green.

And the equation of the same is y =kx, that is y =5x....equation(1)

To make new pair of numbers that would make the same shade of green.

We can use the equation 1,

for x = 4, we need y = 20

foe x =5, we need y = 25

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Let's call C the weight of the Cashews and B the weight of the Brazil nuts.

Since the professor wants to sel a 32 pound mixture, we have the following equation:

Now, since the price of the mixture will be $5.37 per pound, this means the price of the whole mixture will be

This leads us to the followin equation:

Now we have a system of equations:

To solve it, let's isolate one of the variables in the first equation by subtracting B from both sides of it:

Now, let's use this value of C in the second equation:

To solve this equation, let's subtract 198.4 from both sides of it:

Then, let's divide both sides by -1.9:

Using this value of B in the first equation will give us:

These would be the values of B and C round to two decimals. If we want, we can also write them as integer numbers. so the mix would need to have 18 pounds of cashews and 14 pounds of Brazil nuts.