if p and q are the robots of the equation 3x^2 _ 16x + 2 = 0, find the value of p+q(1+ p).
​

Since the line Lloyd drew also passed through the point (1, n) for some number n, the number n represents: (A) the price, in dollars, per ounce of pumpkin.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, the points on a cartesian coordinate are generally written as an ordered pair (x, y) which represents the horizontal line and vertical line respectively.

Since the line Lloyd drew also passed through the point (1, n) for some number n, we can reasonably infer and logically deduce that the number n represents the price, in dollars, per ounce of pumpkin.

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Complete Question:

Lloyd bought two pumpkins. On a coordinate grid, he plotted each pumpkin’s weight (x), in ounces, and price (y), in dollars. He then drew a straight line that passed through both points and the origin. The line he drew also passed through the point (1, n) for some number n. What does the number n represent?

(A) the price, in dollars, per ounce of pumpkin

(B) the price, in dollars, of one of the pumpkins

(C) the weight, in ounces, of one of the pumpkins

(D) the weight, in ounces, of a pumpkin with a price of $1.00

Answer:

-5/14

Step-by-step explanation:

common denomatior is 14

-9/14 + 4/14 (since 2/7 and 4/14 are the same thing)

numerator: -9+4=-5

denominator stays the same.

-5/14 is your answer

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

These fractions have denominators in common, so let's find them!

7 x 2 = 14, so 2/7 also equals 4/14.

9/14 + 4/14 = 13/14

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

Have a wonderful day/night! :)

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Answer:

20

Step-by-step explanation:

multiples of 4 (4,8,12,16,20....)

multiples of 10 (10,20....)

Answer:

Step-by-step explanation:

Given system:

Multiply the second equation by - 4 (the opposite of the coefficient of x in the first equation) then add up the two equations, this will eliminate x and we'll solve it for y.

Find x:

Solution is: (-6, 2)

4x - 9y = -42 -------------(1)

-4x - 20y = -16 -----------(2)

-9y -20y = -42 -16

-29y = -58

y = 2

x + 5*2 = 4

x + 10 = 4

x = 4 - 10

x = -6

Answer:

(-6,2)

Answer:

The answer to that question is 58

4y +5x = 8

y= -3x+5

The slope-intercept form of the equation of the line through the given points =  1) through: (0, 2) and (4, -3)

              2 ) through: (0, 5) and (2, -1)

The general formula for slope-intercept form is y = mx + b, where m represents the slope of the line, and b represents the y-value of the line's y-intercept. The slope-intercept form of a linear equation makes it easier for us to identify how steep a line is and where it crosses the y-axis.

1) through: (0, 2) and (4, -3)

m = y2-y1 /x2-x1

m= -3-2/4-0

m=-5/4

y = mx

y-y1 = m(x-x1)

y- 2 = -5/4(x-0)

y-2= -5x/4

4(y-2) = -5x

4y -8 = -5x

4y +5x = 8

2 )  through: (0, 5) and (2, -1)

m = y2-y1 /x2-x1

m= -1-5/2-0

m= -6/2

m= -3

y = mx

y-5 = m(x-0)

y-5 = -3(x)

y-5 = -3x

y= -3x+5

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Answer: i cheated last year so i dont remember any of this

Step-by-step explanation:

Answer:

222

Step-by-step explanation:

Answer:

Exactly $13.125 (approx $13.13)

Step-by-step explanation:

52.50 divided by 4 is 13.125. 1 shirt costs exactly $13.125. Round the half cent up to a whole cent.

Answer:f

(

x

+

2

)

=

3

x

+

2

Step-by-step explanation:

Answer:

h=-2

Step-by-step explanation:

17+4h+2=1−5h

19+4h=1-5h

4h=-18-5h

9h=-18

h=-2

[tex]\bf\implies[/tex]29 times they visit their club.

Step 1) : Based on the given conditions, formulate:

[tex] \bf \longrightarrow{39.16 + 7.65x = 55.69 + 7.08x}[/tex]

Step 2) : Solve the equation

[tex] \bf \longrightarrow{39.16 + 7.65x = 55.69 + 7.08x}[/tex]

[tex] \bf \longrightarrow{7.65x - 7.08x= 55.69 - 39.16}[/tex]

[tex] \bf \longrightarrow{0.57x= 55.69 - 39.16}[/tex]

[tex] \bf \longrightarrow{0.57x= 16.53}[/tex]

[tex] \bf \longrightarrow{x= \frac{16.53}{0.57} }[/tex]

[tex] \bf \longrightarrow{x= \frac{1653}{57} }[/tex]

[tex] \bf \longrightarrow{x= 29 }[/tex]

The point on the number line which is closest to  √130 is 11

According to the question we need to find the number closest to the √130

We know that the √130 = 11.4

And 11.4 number lies between 11 and 12 . That is

               11< 11.4 <12

But as we see on the number line 11 is much closest than the number 12 on the number line.

Also the

         distance between 11 and 11.4 is 0.4

  and distance between 11.4 and 12 is 0.6 .

Thus distance between 11 and 11.4 is small.

Hence 11 is closest point to √130 on the number line.

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Answer: 2044.444444444 repeating

Step-by-step explanation:

divide 18400/9 and that's what you get in long division

The exponential decay function for 24 mg sample is given as  

[tex]F(t) = 24 (0.5)^{\frac{t}{5730} }[/tex])   and 0.64mg carbon - 14 will remain after 30 millennia.

Exponential function that represent the decay is given as :

           [tex]F(t) = a (0.5)^{\frac{t}{h} }[/tex]       (1)

where,   F(t) = amount remaining after time t

               a = amount of sample is decayed

               t = time in years

               h = half life years

The values that we have been given are :

       a = 24 mg sample

       h = 5730 years

Putting the required values in equation (1) we get

          [tex]F(t) = 24 (0.5)^{\frac{t}{5730} }[/tex]     (2)

 Now we need to find how much carbon-14 remains after 30 millennia.

That is we have to find F(t) for t = 30 millennia = 30000 years

      [As 1 millennium = 1000 years]

Putting the required values in equation (2) we get

        [tex]F(t) = 24 (0.5)^{\frac{30000}{5730} }[/tex]

       [tex]F(t) = 24 (0.5)^{5.236}[/tex]

        F(t) = 24*0.027

       F(t) = 0.64 mg

Thus 0.64mg carbon - 14 will remain after 30 millennia.

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Answer: The length of the cell in stand form is 5.4x10-6 m = 0.000000054 m

Step-by-step explanation:

It is given by that the size of a bacterial is 0.000000054 m , which can be with in as 5.4x10-6 m in standard form

We need to find the value of m.

Clearly the standard form of

0.000000054 = 5/10000000

                         = 5 x 1/10000000

                         = 5 x 1/[tex]10^{6}[/tex]

0.000000054 = 5 x [tex]10^{-6}[/tex]

Therefore,

                      5 x [tex]10^{-m}[/tex] = 5 x [tex]10^{6m}[/tex]

and the value of m = 6

So,

The length of the cell in stand form is 5.4x10-6 m = 0.000000054 m

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Answer:

82

Step-by-step explanation:

if g(3)= substitute a as 3 = (3)^3 +5(3)^2= 27+45= 72

if f(3)= substitute a as 3= 2(3) +4=10

join them up since it said there to add  g(3) +f(3)

72 +10= 82

The translation of word problems into mathematics equations enables the determination and prediction of precise values in real life situations.

First part:

The work rate of one person if 3 people takes two days to do a job is given by the equation;

[tex] \frac{1}{C} + \frac{1}{C} + \frac{1}{C} = \frac{3}{C} = \frac{1}{2} [/tex]

Which indicates that one person takes 6 days to get the same work done

Second part;

Where the costs of a combination of cakes and orange drinks can be expressed using the equations;

2•c + o = 0.4

3•c + 3•o = 0.9

It indicates that a cake costs $0.1, and an orange drink costs $0.2

Third part;

Precision is required to conduct a scientific experiment remotely

A word problem in science is the expression of sufficient or significant background information of a problem is given using every day language, rather than using mathematical notations.

First part;

An example word problem is as follows;

The translation of the above question is as follows;

Let C represent the work rate or the number of days one person takes to do the same work, we have;

[tex] \frac{1}{C} + \frac{1}{C} + \frac{1}{C} = \frac{3}{C} = \frac{1}{2} [/tex]

Which gives;

[tex]C = \frac{3}{ \frac{1}{2} } = 6[/tex]

The number of days it takes one person to do the work, C = 6 days

Second part;

A word problem that involves multi step linear equations is as follows;

How much does a cake cost

How much does an orange drink cost

Solution;

Let c represent the cost of a cake and let o represent the cost of an orange drink, we have;

2•c + o = 0.4...(1)

3•c + 3•o = 0.9...(2)

Multiplying equation (1) by 3 and subtracting equation (2) from the result, gives;

3×(2•c + o) - (3•c + 3•o) = 3×0.4 - 0.9

Which gives;

3•c = 0.3

c = 0.3/3 = 0.1

c = 0.1

The cost of one cake, c = $0.1

From equation (1), we have;

2•c + o = 0.4

Which gives;

2×0.1 + o = 0.4

o = 0.4 - 2×0.1 = 0.2

The cost of one orange drink, o = $0.2

Third part;

The consequence that might occur if the measurement were not precise is that the vehicle and equipment may not be able to make it back to the surface.

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The equation that can be used to determine the value of x is 7x + 18 = 65

Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines

The figure that completes the question is added as an attachment

The given parameter is the angles in the figure

From the figure, we have the following angles:

Angle 1 = 23

Angle 2 = 7x - 5

Angle 3 = 67

The relationship between the above angles is

Angle 1 + Angle 2 = Angle 3

This is so because the angles 1 and 2 are adjacent angles and they add up to angle 3

Substitute the known values in the above equation

So, we have

23 + 7x - 5 = 65

Collect the like terms in the above equation

So, we have

23 - 5 + 7x  = 65

Evaluate the like terms in the above equation

So, we have

18 + 7x  = 65

Rewrite the above equation as

7x + 18 = 65

Hence, the equation that can be used to determine the value of x is 7x + 18 = 65

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The equation of the line in slope-intercept form is: y = 6.

Given that the points, (-4,6) and (4,6) lie on a line, the steps below shows how to write the equation of the line in slope-intercept form.

Step 1: Find the slope of the line:

Slope (m) = change in y / change in x = (6 - 6)/(-4 - 4)

Slope (m) = 0/-8

Slope (m) = 0

Step 2: Substitute m = 0 and (x, y) = (4, 6) into y = mx + b to find the value of b

6 = 0(4) + b

6 = 0 + b

6 = b

b = 6

Step 3: Substitute m = 0 and b = 6 into y = mx + b

y = 0(x) + 6

y = 0 + 6

y = 6

In conclusion, the equation of the line in slope-intercept form is: y = 6.

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Based on the fact that no less than a third of the juniors went to prom and there were 37 juniors, the minimum amount of juniors at the school was 111 juniors

The school paper reported that out of the total juniors in school, no less than a third juniors went to prom.

We also know that 37 juniors went to prom. Assuming that 37 juniors represents a third of the juniors, the minimum amount of juniors at the school can be found as:

= Number of juniors who went to prom / Proportion of juniors who went to prom

Solving for the minimum amount of juniors at the school gives:

= 37 / 1/3

= 37 x 3/1

= 111 juniors

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The density of an object with a mass of 180 grams and a volume of 45 cm is 0.4 kg/m.

What is density?

So the formula will be d = m / v

The mass of the object is 180 g

The volume of the object is 45 cm

Putting the value in the formula

d = 180 g / 45 cm = 0.4 kg/m

Thus, the density of an object will be 0.4 kg/m.

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The correct statements among given statements are statement C and E.

What is a rational number ?

If p & q are any two numbers where q is not equal to 0, then the fraction in form p/q is called as rational number.

A number is given which is √22.

√22 = 4.69041576

Let's check which of the statements are correct.

A.

√22 is not rational number as the number has non - terminating decimal value which is 4.69041576 and it doesn't lies between 10 and 12. So , this option is not correct.

B.

This option is also not correct as the value of √22 nearly equals 4.69 is and not greater than 4.691.

C.

The value of √22 is 4.69041576.

If we round off to the nearest hundredth , 9 is at the hundredth place , so the value will be 4.69. This is a correct option.

D.

√22 is not a rational number as the number has non - terminating decimal value which is 4.69041576 but it lies between 4 and 5. So , this option is not correct.

E.

The value of √22 is 4.69041576. We can observe that the decimal number doesn't repeat. So , this is a correct option.

F.

As we know √22 is not a rational number we can't represent it as fraction. This option is not correct.

Therefore , the correct statements among given statements are statement C and E.

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Answer:

23

Step-by-step explanation:

x=3  PEMDAS says that exponents go first so 3x3=9  then 2x9=18+5=23

The solution of the equation √5 x + 1 - 2√x = 1 is [tex]\frac{4}{5}[/tex].

An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

Consider the equation,

√5 x + 1 - 2√x = 1

Subtracting 1 from each side of the equation.

√5 x + 1 - 2√x - 1 = 1 - 1

√5 x - 2√x = 0

√5 x = 2√x

Dividing each side of the equation by √x.

( √5 x/√x ) = ( 2√x / √x )

√(5x) = 2

Squaring each side of the equation.

[ √(5x) ]² = (2)²

5x = 4

Dividing by 5 from each side of the equation.

( 5x/5 ) = ( 4/5)

x = 4/5

Now checking the extraneous solution:

[tex]\sqrt{5}x + 1 -2\sqrt{x} =1\\\sqrt{5}(\frac{4}{5} ) + 1 - 2(\sqrt{\frac{4}{5} } ) = 1\\ \frac{4}{\sqrt{5} } + 1 - \frac{4}{\sqrt{5} } = 1\\ 1 = 1[/tex]

The solution for the equation is 4/5.

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Answer:

8

Step-by-step explanation:

WHYYY

the total amount of fruit slices eaten = 15

1st meal = 7

2nd mean = x

now do this

7+x=15

x=15-7

x=8

Answer:

(y - y1) = m(x - x1)

Step-by-step explanation:

(y - y1) = m(x - x1)