A scientist had 3/ 5 liter of solution. He used 7/ 12 of the solution for an experiment.
How many liters of solution did the scientist use for the experiment

Answer:

The area of the triangle is, [tex]56 cm^2[/tex]

Step-by-step explanation:

Area of the triangle(a) is given by:

[tex]a = \frac{1}{2} \cdot bh[/tex]           ....[1]

where,

b is the base and h is the height of the triangle.

As per the statement:

Given:

h = 8 cm

b = 14 cm

Substitute in [1] we have;

[tex]a = \frac{1}{2} \cdot 8 \cdot 14 = 4 \cdot 14[/tex]

⇒[tex]a = 56 cm^2[/tex]

Therefore, the area of the triangle is, [tex]56 cm^2[/tex]

The solutions of the quadratic equation [tex]8m^2 + 20m = 12[/tex] by factoring method are [tex]m = \dfrac{1}{2}[/tex] and [tex]m = - 3[/tex]

Using the formula of the quadratic equation which states that,

The roots of the standard form of a quadratic equation [tex]ax^2 + bx + c = 0[/tex] are calculated as,

[tex]x = \dfrac{- b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Given that,

A quadratic equation,

[tex]8m^2 + 20m = 12[/tex]

Now, simplify the equation,

[tex]8m^2 + 20m = 12[/tex]

Subtract 12 on both sides,

[tex]8m^2 + 20m - 12 = 0[/tex]

Take 4 as a common term,

[tex]4 (2m^2 + 5m - 3) = 0[/tex]

Since, [tex]4 \neq 0[/tex]

[tex]2m^2 + 5m - 3 = 0[/tex]

Apply the factoring method in the above equation,

[tex]2m^2 + 5m - 3 = 0[/tex]

[tex]2m^2 + (6 - 1)m - 3 = 0[/tex]

[tex]2m^2 + 6m - m - 3 = 0[/tex]

[tex]2m (m + 3) - 1(m + 3) = 0[/tex]

[tex](2m - 1) (m + 3) = 0[/tex]

This gives two solutions,

[tex]2m - 1 = 0\\2m = 1\\m = \dfrac{1}{2}[/tex]

[tex]m + 3 = 0\\m = - 3[/tex]

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Final answer:

To find out how many solar toys are Disney characters, multiply the total number of toys by the fraction of toys that are Disney characters.

Explanation:

To find out how many solar toys are Disney characters, we need to multiply the total number of toys by the fraction of toys that are Disney characters. In this case, 2/7 of the toys are Disney characters. So, we can calculate:

Number of solar Disney toys = Total number of solar toys × Fraction of Disney toys

Number of solar Disney toys = 28 × 2/7 = 8

Therefore, there are 8 solar toys that are Disney characters.

The equation of the tangent line to the curve is derived by first finding the slope of the tangent line at a certain point using implicit differentiation. After finding the slope, we then use the point-slope form of a linear equation to get the equation of the tangent line.

To find an equation of the tangent line to the curve given by the equation xey + yex = 5, it's necessary to find the derivative of the function, which gives us the slope of the tangent line at any point. Implicit differentiation is the key here, since y is not explicitly solved in terms of x.

Differentiating the given equation implicitly with respect to x, we get: exy + yex +ex + yex = 0. From this, we can express dy/dx (the derivative of y with respect to x, i.e., the slope of the tangent line) in terms of x and y.

Next, simply plug in the given coordinates of the point at which we are finding the tangent into this dy/dx equation. This gives the slope of the tangent line at the specific point.

To finally find the equation of the tangent line, use the point-slope form of a linear equation y - y1 = m(x - x1), where m is the slope we found, and (x1, y1) are the coordinates of the point. Substitute these values in, and that gives the equation of the tangent line to the curve at the point.

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Answer:

The Americans would pay millions of dollars to defend their country, but not 1 cent towards the bribe in response to the XYZ affair. Hope this helps! :)

Step-by-step explanation:

I'm smart

Answer:

-The rays extend infinitely and the angle is made by the rays which have a common endpoint.

Step-by-step explanation:

A ray starts from one point and extends in one direction forever.

An angle is the space between two intersecting lines at or close to the point where they meet. In this case two rays intersect each other at one point

Answer: y+9=-4(x-4)

Step-by-step explanation:

A P E X

Answer:

linear increasing

Step-by-step explanation:

Answer:

[tex]g(f(x))=-9x^2[/tex]

Step-by-step explanation:

[tex]f(x) = -3x^2[/tex]

[tex]g(x) = 3x[/tex]

WE need to find composition of function g(f(x))

To find g(f(x)) we replace f(x) in g(x)

[tex]g(f(x))= g(-3x^2)[/tex]

Now we replace -3x^2 inside g(x)

[tex]g(-3x^2)=3(-3x^2)= -9x^2[/tex]

[tex]g(f(x))=-9x^2[/tex]

Final answer:

Bobby has 12 tech decks, Ricky has 20 tech decks, and Terry has 36 tech decks.

Explanation:

Let's represent the number of tech decks each child has using variables.

Let's say Bobby has x tech decks. Since Ricky has 8 more tech decks than Bobby, Ricky has x + 8 tech decks. Terry has triple the number of tech decks that Bobby has, so Terry has 3x tech decks.

Now, we can set up an equation to represent the total number of tech decks:

x + x + 8 + 3x = 68

5x + 8 = 68

5x = 60

x = 12

So, Bobby has 12 tech decks, Ricky has 12 + 8 = 20 tech decks, and Terry has 3 * 12 = 36 tech decks.

The number of permutations possible is 468000.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

The first two places are occupied by letters.

The last 3 places are occupied by numbers.

The permutation for the first 2 places is: [tex]26P_2[/tex]

The permutation for the last 3 places is: [tex]10P_3[/tex]

The total permutation is:

[tex]26P_2 \times 10P_3\\\\=468000[/tex]

Hence the correct option is option C.

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By applying the concept of Least Common Multiple (LCM), which is 12 in this case, we realize that Eddie will perform all three activities on the same day again after 12 days and that the day will be a Friday.

If Eddie goes jogging every other day (2 days), lifts weights every third day (3 days), and swims every fourth day (4 days), then we must find the LCM of 2, 3, and 4 to find out when will he do all three activities on the same day again.

The LCM of 2, 3, and 4 is 12. Therefore, Eddie will perform all three activities on the same day after 12 days. If he begins on Monday, he will surprisingly end up on a Friday, as the 12th day falls on a Friday. This is because, typically, 7 days from Monday is another Monday. Therefore, five additional days (to total 12) will fall on a Friday.

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In Figure 4, in the triangle ΔABC, DE is parallel to BC, i.e., DE||BC.

A triangle is one of the most basic geometric figures, having 3 sides, 3 angles, and 3 vertices.

By the theorem of the triangle, if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. Let's check the theorem holds for which triangle in the given figures.

Figure 1:

[tex]\frac{AD}{BD} = \frac{6}{15} =\frac{2}{5}[/tex]

[tex]\frac{AE}{CE} = \frac{6.6}{17.5} =\frac{66}{175}[/tex]

Since, [tex]\frac{AD}{BD}\neq \frac{AE}{CE}[/tex],

Here, in triangle ABC, DE is not parallel to BC.

Figure 2:

[tex]\frac{AD}{BD} = \frac{5}{12}[/tex]

[tex]\frac{AE}{CE} = \frac{6}{15} =\frac{2}{5}[/tex]

Since, [tex]\frac{AD}{BD}\neq \frac{AE}{CE}[/tex],

Here, in triangle ABC, DE is not parallel to BC.

Figure 3:

[tex]\frac{AD}{BD} = \frac{4}{12} =\frac{1}{3}[/tex]

[tex]\frac{AE}{CE} = \frac{5}{16}[/tex]

Since, [tex]\frac{AD}{BD}\neq \frac{AE}{CE}[/tex],

Here, in triangle ABC, DE is not parallel to BC.

Figure 4 :

[tex]\frac{AD}{BD} = \frac{5.5}{15}[/tex]

     [tex]= \frac{55}{150}\\ = \frac{11}{30}[/tex]

[tex]\frac{AE}{CE} = \frac{6.6}{18}[/tex]

     [tex]=\frac{66}{180}\\ =\frac{11}{30}[/tex]

Since, [tex]\frac{AD}{BD} = \frac{AE}{CE}[/tex],

Therefore, in triangle ABC, DE is parallel to BC, i.e., DE||BC.

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The answer would be negative 9 (-9)