A box contains 162 marbles which are either red or blue. There are 42 more blue marbles than red marbles. How many blue marbles are in the box? Blue marbles=

The arc length is 0.785 units and the diagonal  is √2 units

The question requires that we determine the lengths of the blue line and the arc

The blue line is the diagonal of the square, whose side length (l) is

l = 1

The diagonal is then calculated as:

[tex]d = l * \sqrt 2[/tex]

This gives

[tex]d = 1 * \sqrt 2[/tex]

[tex]d = \sqrt 2[/tex]

The diagonal divides the vertex of the square into 45 degrees a piece, and the diagonal represents the radius of the arc

This means that:

[tex]r = \sqrt 2[/tex]

[tex]\theta = 45^o[/tex]

The arc length is:

[tex]l = \frac{\theta}{360} * \pi r^2[/tex]

So, we have:

[tex]l = \frac{45^o}{360} * 3.14 * \sqrt 2^2[/tex]

This gives

[tex]l = \frac{282.6}{360}[/tex]

Divide

l = 0.785

Hence, the arc length is 0.785 units and the diagonal  is √2 units

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Answer: [tex]g(x)=9x-7[/tex]

Step-by-step explanation:

See the attached image.

Answer:

10 pounds

Step-by-step explanation:

So you have some given information:

  (Price of cashews per pound) = 3.55

  (Amount of cashes) = 20 pounds

  (Price of peanuts, per pound) = 2.50

Now what you're looking for is the amount of peanuts you need to get a mixture of 3.20 per pound. So to find the price per pound. You would take the entire price and divide it by the amount of pounds. So generally it can be expressed as: [tex]\text{price per pound} = \frac{\text{price}}{\text{pounds}}[/tex] . In this equation we know we already have 20 pounds of cashews and they cost 3.55 per pound. We also know what the price per pound of the mixture is going to be, it's going to be 3.20. In the equation I'll express the amount of peanuts as "P" So we have the equation:

Plug in known values:

[tex]3.20 = \frac{20(3.55) + P(2.50)}{20+P}[/tex]

Multiply:

[tex]3.20 = \frac{71 + 2.5P}{20+P}[/tex]

Multiply both sides by 20 + P

[tex](20+P)(3.20) = 71+2.5P[/tex]

Distribute the 3.20

[tex]64+3.2P = 71+2.5P[/tex]

Subtract 2.5 from both side and subtract 64 from both sides

[tex]0.7P = 7[/tex]

Divide both sides by 0.7

[tex]P = 10[/tex]

So 10 pounds will be needed

Answer:

The shorter piece is 1.5 ft long.

The longer piece is 1.75 ft long.

Step-by-step explanation:

We are given that one piece is 3 inches longer than the other, which we can convert to 0.25 ft. We are also told that the total length of the board is 2.25 ft. This means that the two pieces must have lengths that add up to 2.25 ft.

Therefore, we can set up the equation:

x + (x + 0.25) = 2.25

Solving for x, we find that x = 1.5 ft, which is the length of the shorter piece. The length of the longer piece must then be 1.75 ft.

The value of the expression [tex]\frac{x^2 + 3y^2}{xy}[/tex] is [tex]\frac{6y^2 + 2xy}{xy}[/tex]

The equation is given as:

[tex]x^2 - 2xy - 3y^2 = 0[/tex]

Add 3y^2 to both sides

[tex]x^2 - 2xy = 3y^2[/tex]

Add 3y^2 to both sides

[tex]x^2 + 3y^2 - 2xy = 6y^2[/tex]

Add 2xy to both sides

[tex]x^2 + 3y^2 = 6y^2 + 2xy[/tex]

Divide through by xy

[tex]\frac{x^2 + 3y^2}{xy} = \frac{6y^2 + 2xy}{xy}[/tex]

Hence, the value of [tex]\frac{x^2 + 3y^2}{xy}[/tex] is [tex]\frac{6y^2 + 2xy}{xy}[/tex]

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As the x-values go to negative infinity, the function’s values go to positive infinity.

The end behavior of a function f(x) is given by; lim x → ∞ (f(x))

In the given graph attached, we can see that when as x goes to negative infinity (to the left) the y-values go up (toward positive infinity) since y is pointing upwards.  

Thus, lim x → ∞ (f(x)) = ∞ and as such the correct option is As the x-values go to negative infinity, the function’s values go to positive infinity.

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The x intercept and y intercept of the line x + 3y = 12 are (12, 0) and (0, 4) respectively.

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the line x + 3y = 12

The y intercept is at x = 0, hence:

0 + 3y = 12

y = 4

The x intercept is at y = 0, hence:

x + 3(0) = 12

x = 12

The x intercept and y intercept of the line x + 3y = 12 are (12, 0) and (0, 4) respectively.

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Answer:

13.5

Step-by-step explanation:

8x+y-10x-y=-27

-2x=-27

x=13.5

Answer:

64

Step-by-step explanation:

Answer:

Step-by-step explanation:

The areas of four regions are given. We can simply add them to find the sum. To express them as a product, we need to look at common factors.

The total of the given area expressions is ...

  3x² +2x -6x -4 = 3x² -4x -4 . . . . sum

Extending the table to show common factors of each row and column, we have ...

  [tex]\begin{array}{c|c|c|}&3x&2\\\cline{1-3}x&3x^2&2x\\\cline{1-3}-2&-6x&-4\\\cline{1-3}\end{array}[/tex]

Since each cell of the table is the product of the corresponding common factors, we can write the area as the product ...

  (x -2)(3x +2) . . . . product

The evaluation of the given improper fraction is  0.64071.

We can evaluate improper fractions by simply determining the L.C.M of the denominators and equating it to the numerators.

Given that:

[tex]=\mathbf{\dfrac{2}{6.341} +\dfrac{3}{9.222} }[/tex]

= The L.C.M for 6.341 and 9.222 is 58.476702.

So, we have:

[tex]\mathbf{= \dfrac{18.444}{58.476702} +\dfrac{19.023}{58.476702} }[/tex]

[tex]\mathbf{= \dfrac{18.444+19.023}{58.476702} } }[/tex]

[tex]\mathbf{= \dfrac{37.467}{58.476702} } }[/tex]

= 0.64071

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Answer:

D

Step-by-step explanation:

We will use the 2 coordinates marked on the graph as the reference.

The coordinates are:

A(4,-2)

B(0,3)

We know that the standard form for equation of line is:

y = mx+c

where m is the slope of the equation

and c is the y-intercept.

Very clearly, the y-intercept is where the line intercepts the y line.

and in this case, y-intercept = c = 3.

Now we know that the equation of line is now

y = mx + 3

To find m, the slope, we can use the 2 above coordinates.

slope of line = [tex]\frac{y1-y2}{x1-x2} \\=\frac{-2-3}{4-0} \\=\frac{-5}{4} \\=-\frac{5}{4}[/tex]

(Note: There is a 2nd way to find the slope in this case, let me know if you are interested to find out.)

Equation of line: [tex]y=-\frac{5}{4} x+3[/tex]

Therefore the answer is D.

Answer:

1,2

Step-by-step explanation:

Answer: B. False

Step-by-step explanation:

You assume the inverse of what you intend to prove is true, not the converse.

The probabilities on each branch are shown in the tree diagram, and P(HT) = 2/9.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

The probability of H is 2/3 and the probability of T is 1/3.

P(HT) = P(H in the first trial)P(T in the second trial)

From the tree diagram:

P(HT) = (2/3)(1/3) = 2/9

Thus, the probabilities on each branch are shown in the tree diagram, and P(HT) = 2/9.

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The vertex of the given parabola is the point (3, 25).

If the parabola has roots x₁ and x₂, then the vertex of the parabola is at:

xₙ = (x₁ + x₂)/2

Here the parabola is:

y = (-2 - x)*(x - 8)

We can rewrite that to:

y = -(x + 2)*(x - 8)

Then the two roots are:

x = -2 and x = 8

Then the vertex is at:

xₙ = (8 - 2)/2 = 6/2 = 3

To get the y-value of the vertex, we evaluate the equation in x = 3:

y = -(3+ 2)*(3 - 8) = -5*(-5) = 25

The vertex is (3, 25).

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Answer:

Step-by-step explanation:

its  A y+6=-2

Step-by-step explanation:

whoever created the original question and then probably the people copying it need to focus on writing these things correctly.

I assume this means

log(9) - log(4) ÷ log(3) - log(2)

or is anything combined in brackets ? like it could be e.g. log(4 ÷ log(3)). just as example.

and I guess we mean logarithm to the base of 10, right ?

anyway, if my assumptions are correct, then we only need to follow the regular priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

so, we need to start with the division in the middle, and then do the subtractions.

log(4) ÷ log(3) = 1.261859507...

log(9) - 1.261859507... = -0.307616998...

-0.307616998... - log(2) = -0.608646993...

or was the original question

(log(9) - log(4)) ÷ (log(3) - log(2))

?

that would be way more interesting.

we use the rules of logarithm :

e.g.

log(a×b) = log(a) + log(b)

log(a/b) = log(a) - log(b)

so, we have then

log(9/4) ÷ log(3/2)

and that is equal to

log(3/2 × 3/2) ÷ log(3/2)

(log(3/2) + log(3/2)) ÷ log(3/2) = 1 + 1 = 2

if that is the case, you really, REALLY need to pay more attention to brackets and other symbols in problem definitions.

The true statement is (b) she did not represent the two original factors correctly on the headers

The product expression is given as:

(-2x - 1)(2x - 1)

Expand the expression

(-x - x - 1)(x + x - 1)

This means that the header of the algebra tiles would be:

-x, -x, 1 and x, x and -1

From the figure, we can see that this is incorrectly represented

Hence, the true statement is (b)

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The Surface area of the cylindrical tower is 5181 ft cube.

Surface area of cylinder = 2πr² + 2πrh

where

Therefore,

r = 30 / 2 = 15 ft

h = 40 ft

Surface area of cylinder = 2πr(r + h)

Surface area of cylinder = 30π(40 + 15)

Surface area of cylinder = 30π(55)

Surface area of cylinder = 1650π

Surface area of cylinder = 5181 ft³

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Answer:

Its the last option If you ask me.

Step-by-step explanation:

If the price goes up $1.25 every square yard, then I think its the last one.

Answer:

(-5,0) and (4,0)

x= -5 and x= 4

Step-by-step explanation:

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

                      If two lines are perpendicular to each other, their slopes

                     are negative inverses of each other.

                     Thus,

                    [tex]\boldsymbol{\sf{Slope\:of\:this\:line=4}}}[/tex]

                    [tex]\boldsymbol{\sf{Negative \ Inverse=-\displaystyle\frac{1}{4}}}[/tex]. See how this works?

                    We took 4, then took its opposite, and flopped that over

[tex]\orange\hspace{300pt}\above3[/tex]

Definition-:

Perpendicular lines are lines that intercept each other at a 90 deg. angle, which is usually called the right angle.

Answer:

Spain

Step-by-step explanation:

Pablo Picasso was born in Malaga, Spain.

Answer:

Málaga, Spain

Step-by-step explanation:

Answer:

Making comparisons of numbers or values and considering relationships are also aspects of proportional reasoning.

Example:
A worker being paid by the number of hours he/her worked.

#EDIT #1

Answer:

  17.5 m

Step-by-step explanation:

The height of a parabola above its vertex is proportional to the square of the distance from the vertex.

The towers are 1200 m apart, so each is 600 m from center. The location of interest is 300 m from center, so 1/2 the distance to a tower. Since the height is proportional to the square of the distance, the height half-way to the tower will be (1/2)² = 1/4 the height of the tower.

  (1/2)²×(70 m) = 17.5 m

The height of the cable 300 m from center will be 17.5 meters.

The function that represents the growth of this culture of bacteria as a function of time is; P = 1500e^(1.0986t)

The formula for exponential growth is;

P = P₀e^(rt)

where;

P = current population at time t

P₀ = starting population

r = rate of exponential growth/decay

t = time after start

Thus, from our question we have;

4500 = 1500 * e^(r * 1)

4500/1500 = e^r

e^r = 3

In 3 = r

r = 1.0986

Thus, the function that represents the growth of this culture of bacteria as a function of time is;

P = 1500e^(1.0986t)

For the culture to double, then;

P/P₀ = 2. Thus;

e^(1.0986t) = 2

In 2 = 1.0986t

t = 0.6931/1.0986

t = 0.631 hours

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