Which equation correctly applies the distributive property?

A.​ 50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005) ​
B.​−1.2⋅0.57⋅0.5=−1.2⋅0.5⋅0.57​
​C. (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) ​
D.​ −2.5⋅(4⋅1.045)=(−2.5⋅4)⋅1.045 ​

quotient is division

-20/4 = -5

-5 -3=

-8

the number is -8

To solve this, we use Pythagoras' theorem as we have a right-angled triangle formed by the building, its shadow and the line between the top of the building to the end of the shadow. We find that the length of the shadow is approximately 16.7 meters.

To solve this problem, we need to apply Pythagoras' theorem because the building, the shadow and the line between the top of the building to the end of the shadow form a right-angled triangle.  

Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as:

a² + b² = c²

In this scenario, the height of the building is one side of the triangle (a), the shadow is the other side (b), and the line from the top of the building to the tip of the shadow is the hypotenuse (c).

So, to find the length of the shadow, we rearrange the formula to solve for b:

b = sqrt(c² - a²)

Then, we substitute the known values:

b = sqrt( (37m)² - (33m)²) = sqrt(1369 - 1089) = sqrt(280) = 16.7m

So, the length of the shadow is approximately 16.7 meters.

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The model for the object's motion is [tex]h(t) = -16t^2 + 64t + 80[/tex]. It reaches its maximum height of 144 feet at 2 seconds. The object will hit the ground after 5 seconds.

To model the vertical motion of the object, we use the equation:

[tex]h(t) = -16t^2 + 64t + 80[/tex]

where:

Time to Reach Maximum Height

The time to reach the maximum height can be found by using the formula:

[tex]t = \frac{v_0}{|g|} = \frac{64}{32} = 2 seconds[/tex]

Maximum Height

Plug t = 2 seconds into the height equation:

[tex]h(2) = -16(2)^2 + 64(2) + 80 = 144 feet[/tex]

Time to Hit the Ground

To find when the object hits the ground (h(t) = 0), solve:

[tex]-16t^2 + 64t + 80 = 0[/tex]

Using the quadratic formula:

[tex]t = \frac{-64\pm\sqrt{64^2-4(-16)(80)} }{2(-16)}[/tex]

Simplifies to:

t = 5 seconds (since the negative value does not make sense in this context)

The object will hit the ground after 5 seconds.

Answer:4 or less

Step-by-step explanation:

6x+3>27

The positive value of the discriminant implies that there are two real unequal roots and this can be determined by using the formula of the discriminant.

Given :

The quadratic equation is [tex](0=-2x^2+3)[/tex].

The following steps can be used in order to determine the total number of real solutions does the equation have:

Step 1 - Write the given quadratic equation.

[tex]0=-2x^2+0x+3[/tex]

Step 2 - The formula of discriminant is given below:

[tex]D = b^2-4ac[/tex]

where 'b' is the coefficient of 'x', 'a' is the coefficient of [tex]x^2[/tex], and 'c' is the constant.

Step 3 - Now, substitute the values of a, b, and c in the above formula.

[tex]D = (0)^2-4\times (-2)\times 3[/tex]

[tex]D = 24[/tex]

Step 4 - The positive value of the discriminant implies that there are two real unequal roots.

For more information, refer to the link given below:

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Answer:

-27/40

Step-by-step explanation:

Answer:

Outcome Bag of Gold Magic Wand

Relative frequency 0.32 0.68

The relative frequency of getting a bag of gold is .......... reasonably close

.32 is close to 30% so

Alison's claim about the theoretical probability is likely to be 2............true

Further, this means that the theoretical probability of getting a magic wand is most likely 3............1 - 30% = 70%

Step-by-step explanation:

Yes, the opposite of an opposite will always return you to the original value, making it positive if you started with a positive number.

The question refers to the concept of opposites in Mathematics. When considering opposite numbers, the opposite of a positive number is negative, and vice versa. To answer the query, let’s break it down into steps.

So, yes, the opposite of an opposite will always be positive if you start with a positive number. Similarly, the opposite of an opposite will be negative if you start with a negative number, returning to the original number. This concept is crucial in understanding signed numbers and their roles in arithmetic and algebra.

Answer-

[tex]\frac{\log (x+2)}{\log 4}[/tex] is the correct answer.

Solution-

The formula for change of base in logarithm is given by,

[tex]\log_{b}a=\frac{\log_{c}a}{\log_{c}b}[/tex]

If we take the common base as 'e' , the formula becomes,

[tex]\log_{b}a=\frac{\log a}{\log b}[/tex]

Applying this formula,

[tex]\log_{4}(x+2)=\frac{\log (x+2)}{\log 4}[/tex]

∴ As the first option matches with our answer, hence it is the correct answer.

( In the fourth option a bracket is missing, so it is not the correct option)