help fill out the proof

as I read it, what I get is that

x = returned profits or yielded interest from investment in A

y = returned profits or yielded interest from investment in B

T = total amount invested or namely  A + B.

4000 were invested in A, and it yielded 5%, what's 5% of 4000? (5/100)(4000) = 200 = x.

we know the total amount is T, since A get 4000, B must have gotten T - 4000, or the slack.  We also know that B yielded a 2% profit, well, what's 2% of T - 4000?  (2/100)(T-4000) = y.

we also know that, whatever "x" and "y" are, their sum total yielded a 4% returns from T, or the total principal, what's 4% of T?  (4/100)T = 0.04T.

[tex]\bf \begin{cases} T=\textit{total principal}\\[-0.5em] \hrulefill\\ A=4000\\ x = \stackrel{\textit{5\% of A}}{200}\\[-0.5em] \hrulefill\\ B=T-4000\\ y=\stackrel{\textit{2\% of B}}{0.02(T-4000)} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{5\% of A}}{200}+\stackrel{\textit{2\% of B}}{0.02(T-4000)}~~=~~\stackrel{\textit{4\% of T}}{0.04T} \\\\\\ 200+0.02T-80=0.04T\implies 120+0.02T=0.04T\implies 120=0.02T \\\\\\ \cfrac{120}{0.02}=T\implies 6000=T~\hfill \stackrel{~\hfill \textit{invested in B}}{6000-4000\implies 2000}[/tex]

Answer:

1 x 48 = 48

2 x 24 = 48

3 x 16 = 48

4 x 12 = 48

6 x 8 = 48

8 x 6 = 48

12 x 4 = 48

16 x 3 = 48

24 x 2 = 48

48 x 1 = 48

Step-by-step explanation:

Answer:

The factor pair for 48 is 1,2,3,4,6,8,12,16,24 and 48

Your welcome!

Answer:

4.5 hours

Step-by-step explanation:

we know that

A postal carrier can deliver to 130 houses in  2.5 hour

so

using proportion

Find out how many hours will  it take to deliver to 234 houses

[tex]\frac{130}{2.5}\ \frac{houses}{hours} =\frac{234}{x}\ \frac{houses}{hours} \\\\x=234(2.5)/130\\\\x=4.5\ hours[/tex]

Answer:

The answer is 45 minutes.

Step-by-step explanation:

30 divided by 10 is 3. So it's 3 minutes per book. 3 multiplied by 15 is 45.

Answer:

C

Step-by-step explanation:

For example

[tex]y = 77 \\[/tex]

The answer is C: by itself on one side of the equal sign and a value on the other.

Let's go through the detailed steps of isolating the variable with each option in mind.

Option: C - by itself on one side of the equal sign and a value on the other.

Given equation:[tex]\(3x + 7 = 16\)[/tex]

Step 1: Identify the Variable

The variable in the equation is [tex]\(x\).[/tex] We want to isolate [tex]\(x\)[/tex] to find its value.

Step 2: Isolate Terms with the Variable

Move terms containing the variable to one side of the equation. Here, we'll move [tex]\(3x\)[/tex] to the left side by subtracting [tex]\(7\)[/tex] from both sides:

[tex]\[3x + 7 - 7 = 16 - 7\][/tex]

This simplifies to:

[tex]\[3x = 9\][/tex]

Now, the term [tex]\(3x\)[/tex] is isolated on the left side of the equation.

Step 3: Perform Inverse Operations to Isolate the Variable

Since [tex]\(x\)[/tex] is being multiplied by [tex]\(3\),[/tex] to isolate [tex]\(x\),[/tex] we divide both sides by [tex]\(3\):[/tex]

[tex]\[\frac{3x}{3} = \frac{9}{3}\][/tex]

This simplifies to:

[tex]\[x = 3\][/tex]

Now, the variable [tex]\(x\)[/tex] is isolated on the left side of the equation, and its value is [tex]\(3\).[/tex]

By following these detailed steps, we have successfully isolated the variable  [tex]\(x\)[/tex] on one side of the equal sign and a specific value (option C) on the other side, demonstrating equality between the two sides of the equation.

Answer:

3 min 42 seconds

Step-by-step explanation:

1 minute=60 seconds so 7 minutes = 420 seconds. Plus the other 24 is 444 seconds. 444/2=222 so its 222 seconds or 3 minutes and 42 seconds

7 min = 7 x 60 sec = 420 sec

420 sec + 24 sec = 444 sec

444sec : 2 = 222 sec

222 sec = 3x60sec + 42sec = 3 min 42 sec

Answer:

[tex]\large\boxed{-6x^6+4x^4-3x^3+4x^2+12}[/tex]

Step-by-step explanation:

[tex]4x^2-6x^6+2x^3+12-5x^3+4x^4\\\\=-6x^6+4x^4+2x^3-5x^3+4x^2+12\qquad\text{combine like terms}\\\\=-6x^6+4x^4+(2x^3-5x^3)+4x^2+12\\\\=-6x^6+4x^4-3x^3+4x^2+12[/tex]

Answer:

The slope intercept form of both given equations is : y =  - 3 x - 4.

Step-by-step explanation:

Here, the given equations are:

y +7 = -3 ( x - 1 )

and 3 x + y = - 4

Now,the SLOPE INTERCEPT FORM of any given equation is given as:

y = m x + C : here, C = Y - intercept, m = Slope

Consider equation (1):

y +7 = -3 ( x - 1 )    ⇒ y + 8 = - 3 x  + 3

or, y = -3x + 3 - 7 = -3x - 4

 ⇒ y =  -3x  -4

Hence, the slope-intercept form of the given equation is y =  -3x  -4.

Consider equation (2):

3 x + y = - 4    ⇒ y  = -4  - 3 x

 ⇒ y =  -3 x  - 4

Hence, the slope-intercept form of the given equation is y =  -3x  -4.

Final answer:

The solution in slope-intercept form for both given equations is y = -3x - 4, showing that they represent the same line.

Explanation:

To find the solution in slope-intercept form for the given equations y+7=-3(x-1) and 3x+y=-4, we need to solve for y in terms of x for each equation.

For the first equation, solve for y:

y + 7 = -3(x - 1)

y = -3x + 3 - 7

y = -3x - 4 (Slope-intercept form of the first equation)

For the second equation, solve for y:

3x + y = -4

y = -3x - 4 (Slope-intercept form of the second equation)

After solving, we observe that both equations have the same slope-intercept form, which indicates that these are actually the equations of the same line.

Answer: 6 LB 12 OZ

16 OZ in a LB

9 LB - 2 LB = 7 LB

4 OZ - 12 OZ difference of 8 OZ

4 - 4 = 0 then 16 OZ in a LB

4 remaining - 16 = 12 dropping the 7 LB to 6 LB

Step-by-step explanation:

First, turn into just ounces (1lb. = 16oz.)

9 lb 4 oz = 148 oz

2 lb 12 oz = 44 oz

Second, subtract.

148 - 44 = 104 oz

Third, turn into pounds and ounces.

104 oz = 6 lb 8 oz

______

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Answer:

8 minutes

Step-by-step explanation:

It takes 2 minutes every 2 floors, and Floor 9 is 8 floors away from Floor 1, so 2x4=8.

The expression that can be used to find 20% of 950 is 20/100 × 950

20% of 950

= 20/100 × 950

= 0.2 × 950

= 190

Therefore, the 20% of 950 is given by 190

Learn more about percentage:

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To find 20% of 950, you use the formula (Percentage / 100) × Whole. By applying the formula, 20% of 950 is calculated to be 190.

To find 20% of 950, you can use the formula for finding a percentage of a number:

Part = (Percentage / 100) × Whole

In this case, the percentage is 20 and the whole is 950. Now apply the formula:

Part = (20 / 100) × 950

Part = 0.2 × 950

Part = 190

Therefore, 20% of 950 is 190.

Answer:

[tex]f(x)=x^3-7x-6[/tex]

Step-by-step explanation:

If x = 3 is a root of a polynomial f(x), then x - 3 is a factor of this polynomial.

If x = -2 is a zero of a polynomial function f(x), then f(-2) = 0 and x - (-2) = x + 2 is a factor of f(x).

If x = -1 is an x-intercept of the function, then y = 0 and x - (-1) = x + 1 is also a factor of the function f(x).

Therefore, the polynomial expression is

[tex]f(x)=(x-3)(x+2)(x+1)[/tex]

In standard form:

[tex]f(x)=(x-3)(x^2+2x+x+2)=(x-3)(x^2+3x+2)=x^3+3x^2+2x-3x^2-9x-6=x^3-7x-6[/tex]

Answer:

C. log(1/3)

Step-by-step explanation:

Remember the quotient/subtraction rule for logs:

log2 - log6 can be written as log(2/6)

Hence, it's equal to C. log(1/3)

Hope this helps!

Mark brainliest if you think I helped! Would really appreciate!

The expressions that are equivalent to [tex]\( \log 2 - \log 6 \)[/tex] are options A and C.

The correct option is (A&C).

To solve [tex]\( \log 2 - \log 6 \)[/tex], we can use the property of logarithms that states:

[tex]\[ \log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right) \][/tex]

Given [tex]\( \log 2 - \log 6 \)[/tex], applying the above property:

[tex]\[ \log 2 - \log 6 = \log\left(\frac{2}{6}\right) = \log\left(\frac{1}{3}\right) \][/tex]

So, the expression \[tex]( \log 2 - \log 6 \)[/tex] is equivalent to [tex]\( \log\left(\frac{1}{3}\right) \)[/tex], which matches option C.

Now, let's check the other options:

A. [tex]\( \log(2) + \log\left(\frac{1}{6}\right) \)[/tex]

  This expression can be simplified using the properties of logarithms to [tex]\( \log\left(2 \times \frac{1}{6}\right) = \log(1/3) \),[/tex]  which is equivalent to the original expression. So, option A is also correct.

B. [tex]\( \log 2 \)[/tex]

  This option is not equivalent to the original expression. It only represents [tex]\( \log 2 \),[/tex] not the difference of [tex]\( \log 2 \) and \( \log 6 \).[/tex]

D. [tex]\( \log 3 \)[/tex]

  This option is not equivalent to the original expression. It only represents [tex]\( \log 3 \)[/tex], which is unrelated to the expression [tex]\( \log 2 - \log 6 \).[/tex]

So, the expressions that are equivalent to [tex]\( \log 2 - \log 6 \)[/tex] are options A and C.

Answer:

x=1+sqrt(14) & 1-sqrt(14).

Step-by-step explanation:

(1x+1)(1x-3)=0

(x+1)(x-3)=0

m(x)=(x+1)(x-3)=10

(x+1)(x-3)=10

x^2+x-3x-3=10

x^2-2x-3=10

x^2-2x-3-10=0

x^2-2x-13=0

Apply the quadratic formula with a=1, b=-2 and c=-13.

The answer is x=1+sqrt(14) & 1-sqrt(14).

Answer:

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-\text{slope}\\b-\text{y-intercept}\\\\\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\\text{then}\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2[/tex]

[tex]\text{We have the equation of a line in the standard form:}\ Ax+By=C.\\\\\text{Convert to the slope-intercept form:}\\\\4y-2x=12\qquad\text{add}\ 2x\ \text{to the both sides}\\\\4y-2x+2x=2x+12\\\\4y=2x+12\qquad\text{divide both sides by 4}\\\\\dfrac{4y}{4}=\dfrac{2x}{4}+\dfrac{12}{4}\\\\y=\dfrac{1}{2}x+3\to\boxed{m_1=\dfrac{1}{2}}[/tex]

[tex]\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{Put the value of the slope and the coordinates of the given point (-1, 4)}\\\text{to the equation of a line:}\\\\4=-2(-1)+b\\\\4=2+b\qquad\text{subtract 2 from the both sides}\\\\4-2=2-2+b\\\\2=b\to b=2\\\\\bold{FINALLY:}\ y=-2x+2[/tex]

[tex]\text{Convert to the standard form:}\\\\y=-2x+2\qquad\text{add}\ 2x\ \text{to the both sides}\\\\y+2x=-2x+2x+2\\\\2x+y=2[/tex]

Answer:

The length of each side of triangle are 19 ft, 24 ft and 38 ft.

Step-by-step explanation:

Let the length of second side be x.

Now given:

Length of first side is 2 times length of second side.

Length of first side = 2x

Also, Length of third side is 5 ft longer than the second side.

Length of third side = 5+x

Perimeter of triangle = 81 ft.

We need to find the length of each side.

Now perimeter of triangle is sum of all three sides of triangle.

Therefore;

Perimeter of triangle =  Length of first side + length of second side + Length of third side.

[tex]2x+x+5+x=81 ft\\4x+5=81ft\\4x= 81 -5 ft\\4x = 76ft\\x= \frac{76}{4} = 19 ft[/tex]

Length of Second Side = 19 ft.

Length of First side = [tex]2x= 2\times19 = 38 ft[/tex]

Length of Third side = [tex]5+x= 5+19=24ft[/tex]

Hence the Length of triangles are 19 ft,38 ft,24 ft.

Answer:

I don't know how this is math but...

The Gulf of Tonkin Resolution authorized President Lyndon Johnson to “take all necessary measures to repel any armed attack against the forces of the United States and to prevent further aggression” by the communist government of North Vietnam. Hope I helped! ☺

Answer:

It gave the president the ability to send troops without congressional approval.

Step-by-step explanation:

Answer:  The second one is correct I believe

Step-by-step explanation:

The sizes of the angles are 34° , 44° , 102°

Step-by-step explanation:

The given is:

We need to find the size of each angle in the triangle

∵ The size of the smallest angle = x°

∵ The size of the largest angle is 3 times the size of the smallest angle

∴ The size of the largest angle = x × 3 = (3x)°

∵ The third angle is 10° more than the smallest angle

∴ The size of the third angle = (x + 10)°

Add the size of the three angles and equate the sum by 180°

∵ The sum of the sizes of the interior angles of a Δ is 180°

∴ x + (3x) + (x + 10) = 180

∴ x + 3x + x + 10 = 180

- Add like terms

∴ 5x + 10 = 180

- Subtract 10 from both sides

∴ 5x = 170

- Divide both sides by 5

∴ x = 34

∵ x is the size of the smallest angle

∴ The size of the smallest angle is 34°

∵ 3x is the size of the largest angle

∴ The size of the largest angle = 3(34) = 102°

∵ x + 10 is the size of the third angle

∴ The size of the third angle = 34 + 10 = 44°

The sizes of the angles are 34° , 44° , 102°

Learn more:

You can learn more about the triangles in brainly.com/question/1479138

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Answer:

Distributive Property.

Answer:

-35

Step-by-step explanation:

20-(7+4)*5

20-(11)(5)

20-55

-35

Answer:

10^7

Step-by-step explanation:

So we would start with 10 and a trick to help you is when your turning a number with 10 at the start with each number you raise it by is how many 0 it will have behind it for example 10,000,000 would be 10^7 cause you have 0 zeros in it.

10,000,000 in exponent form is 10⁷. Therefore, 20,000,000 can be written as 2 × 10⁷. This provides a concise mathematical way of expressing large numbers.

To write 10,000,000 using exponents, we recognize that this number is a power of 10. Specifically, 10,000,000 can be written as 10 to the power of 7. This is because:

10,000,000 = 10⁷

When you multiply 10 by itself 7 times (10 × 10 × 10 × 10 × 10 × 10 × 10), you get 10 million. Therefore, the population of Australia, which is more than 20,000,000 people, can be written as:

20,000,000 = 2 × 10,000,000 = 2 × 10⁷

In an ordered pair for a Cartesian coordinate system, the input is represented by the x-axis. It is denoted as the first value in an (x, y) pair and represents the horizontal direction in a two-dimensional space.

In an ordered pair, the input is typically represented by the x-axis in a Cartesian coordinate system. An ordered pair is denoted as (x, y), where 'x' represents the input or independent variable, and 'y' represents the output or dependent variable. For instance, in a function such as y = mx + b, 'x' would be the input and 'y' would be the output. This input value corresponds to the position along the horizontal x-axis.

While the y-axis represents the vertical direction or output value, the x-component of a vector is a dot product with the unit vector in the x-direction. For two-dimensional vector problems, it's also easier to pick a coordinate system that has one horizontal axis (x) and one vertical axis (y), projecting the vectors onto these axes.

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Final answer:

In an ordered pair (x, y), the x-axis represents the input which is the horizontal direction on the Cartesian coordinate system.

Explanation:

In an ordered pair, such as (x, y), the x-axis represents the input, which is the horizontal direction, and the y-axis represents the output, which is the vertical direction. In the Cartesian coordinate system, the origin, where the x and y axes intersect, is the point of projection.

By convention, the positive x-axis generally extends to the right, and the positive y-axis extends upwards. The x-coordinate corresponds to the position along the x-axis while the y-coordinate corresponds to the position along the y-axis.

Considering the definition of probability, the probability that the family visits the museum or rides the ferry is 81%.

Definition of Probabitity

Probability  is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

Union of events

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.

Events and probability in this case

Let A be the event that a family visits the City Museum, and B be the event that a family rides the Three Rivers Ferry. The given probabilities are:

P(A)= 0.46

P(B)= 0.47

P(A and B)= P(A∩B)= 0.12

In this case, considering the definition of union of eventes, the probability that a course has a final exam or a research project is calculated as:

P(A∪B)= P(A) + P(B) -P(A∩B)

P(A∪B)= 0.46  + 0.47 -0.32

P(F∪R)= 0.81= 81%

Finally, the probability that the family visits the museum or rides the ferry is 81%.

Answer:

Step-by-step explanation:

Answer:

If you factorise it you should get (3y+5)(2y+1)

Answer:

I think the only one is A

Answer:

3\8 I think is the answer

Step-by-step explanation:

I know because I know!

Answer:

8 3/8

Step-by-step explanation:

I have study island too

To find the diameter of the semicircle, divide the circumference of the whole circle by 2. Given that the perimeter of the semicircle is 35.98 meters, the diameter would be approximately 22.87 meters.

To find the diameter of the semicircle, we first need to find the circumference of the entire circle and then divide it by 2. The formula for the circumference of a circle is C = π * d, where C is the circumference and d is the diameter.

Given that the perimeter of the semicircle is 35.98 meters, the circumference of the whole circle will be twice that value. So, 2 * 35.98 = 71.96 meters.

Now we can use the formula C = π * d to solve for the diameter: 71.96 = π * d. Dividing both sides of the equation by π gives us d = 71.96 / π.

Using a calculator, we can approximate π to 3.14. So, d = 71.96 / 3.14 = 22.87 meters.