associated press online provided information from a fiscal analyst stating that during the past 20 years, the average after tax income of the wealthiest 1% of americans had grown from $263,700 to $677,900. what was the percent increase? Round to the nearest percent. ​

Answer:

Sum of the solutions of [tex]x^2+9x+20=0[/tex] is -9.

Product of the solutions of [tex]6x^2+7x=3[/tex] is [tex]-0.50[/tex]

Step-by-step explanation:

1. [tex]x^2+9x+20=0[/tex]

Given:

The expression whose sum of the solution is required is given as:

[tex]x^{2} +9x+20=0[/tex]

For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the sum of the solutions is given as:

Sum = [tex]\frac{-b}{a}[/tex]

Here, [tex]a=1,b=9,c=20[/tex]

Therefore, the sum of the solutions = [tex]-\frac{9}{1}=-9[/tex]

2. [tex]6x^2+7x=3[/tex]

Rewriting the above equation in a standard quadratic equation, we get:

[tex]6x^2+7x-3=0[/tex]

For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the product of the solutions is given as:

Product = [tex]\frac{c}{a}[/tex]

Here, [tex]a=6,b=7,c=-3[/tex]

Therefore, the product of the solutions = [tex]\frac{-3}{6}=-0.50[/tex]

Answer:

Megan is 14

Step-by-step explanation:

Megan is M

Molly is Mo

Mo = 8

M = x

6 + mo = x

6 + 8 = 14

If Molly is 8 years old and there is a 6-year age gap between her and Megan, then Megan must be 6 years older than Molly.

Therefore, Megan is 8 + 6 = 14 years old.

This age gap of 6 years means that Megan was born 6 years before Molly.

Age gaps are calculated by subtracting the younger person's age from the older person's age.

It's important to note that Megan is the older of the two, and the age difference remains constant as they both get older.

Understanding age differences is essential in various contexts, from family dynamics to social relationships and legal matters.

In this case, it's a straightforward calculation, but age gaps can have significant implications in more complex situations, such as legal age requirements, generational differences, and even compatibility in personal relationships.

In this instance, Megan is 6 years older than Molly, and that age gap will remain consistent as they both grow older.

For similar question on age gap.

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Answer:

$21

Step-by-step explanation:

70%=0.7

30*0.7=21

Answer:

$9.00

Step-by-step explanation:

Subtract 70 percent from 30 dollars

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:

Part a) m∠WZY=72°

Part b) m∠XWZ=108°

Part c) m∠WYZ=28°

Step-by-step explanation:

we know that

In a parallelogram opposite angles are congruent and consecutive angles are supplementary

see the attached figure to better understand the problem

Part a) Find the measure of angle WZY

we know that

m∠WZY≅m∠WXY ----> by opposite angles

we have

m∠WXY=72°

therefore

m∠WZY=72°

Part b) Find the measure of angle XWZ

we know that

m∠XWZ+m∠WXY=180° ----> by consecutive angles

we have

m∠WXY=72°

substitute

m∠XWZ+72°=180°

m∠XWZ=180°-72°

m∠XWZ=108°

Part c) Find the measure of angle WYZ

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

In the triangle WZY

m∠ZWY+m∠WZY+m∠WYZ=180°

we have

m∠ZWY=80°

m∠WZY=72°

substitute

80°+72°+m∠WYZ=180°

152°+m∠WYZ=180°

m∠WYZ=180°-152°

m∠WYZ=28°

In a parallelogram, finding angles involves rules like opposite angles being equal and adjacent angles being supplementary. wzy = 72 degrees, xwzc = 80 degrees, and wyz = 108 degrees.

Given:

wxy = 72 degrees

zwy = 80 degrees

To find:

wzy: Opposite angles in a parallelogram are equal, so wzy = wxy = 72 degrees

xwzc: Opposite angles in a parallelogram are equal, so xwzc = zwy = 80 degrees

wyz: Adjacent angles in a parallelogram are supplementary. Therefore, wyz = 180 - wxy = 180 - 72 = 108 degrees

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]

The total cost of all the pizzas that the softball team order can be calculated as 6c + 10f, where c represents the number of cheese pizzas ordered, and f represents the number of four-topping pizzas ordered.

To determine how much the softball team is spending on pizzas, we need to multiply the cost of each type of pizza by the number of each type they are ordering. For the cheese pizzas, that cost $6 each, the cost will be:
6c (where 'c' is the number of cheese pizzas).
For the four-topping pizzas, that cost $10 each:
The cost will be 10f (where 'f' is the number of four-topping pizzas).

Now, to calculate the total cost, we add up the cost of the cheese pizzas and the four-topping pizzas:
Total cost = 6c + 10f

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Answer:

any number less than 15 will work n<15

Step-by-step explanation:

I divided the 6n so I could do 90/6 then equals 15=n so if I do 6 times 15 it would be 90 so that would no be true 90<90 so that means n has to be less than 15

n<15

Answer:

Y=10

Step-by-step explanation:

Answer: y

=

−

6

Hopefully this helps!

The solution of the system of equations is (6 , -7)

Step-by-step explanation:

There are two method to solve the system of equations

Let us use the elimination method with your problem

∵ 3x + 2y = 4 ⇒ (1)

∵ 3x + 6y = -24 ⇒ (2)

- Multiply equation (1) by -1 to eliminate x ⇒ to make the coefficients of x in the two equations have same values and different signs

∵ -3x - 2y = -4 ⇒ (3)

- Add equations (2) and (3)

∴ 4y = -28

- Divide both sides by 4

∴ y = -7

Substitute value of y in equations (1) OR (2) to find x

∵ 3x + 2(-7) = 4

∴ 3x - 14 = 4

- Add 14 for both sides

∴ 3x = 18

- Divide both sides by 3

∴ x = 6

The solution of the system of equations is (6 , -7)

I hope this explanation help you

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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:

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: $12.50

Step-by-step explanation: The median is the middle number in the data set when the data set is written from least to greatest.

To find the median of these numbers, let's start by writing our data set from least to greatest.

$9.84, $11.75, $12.50, $12.98, $13.88

So the median will be the middle number or $12.50.

The median is the middle number of a data set.

$9.84, $11.75, $12.50, $12.98, $13.88

If their isn't a perfect middle number then you take 2 middle numbers and find the number that is between them.

________

Best Regards,

Wolfyy :)

-3w-5(4x-4w)-4x

multiply the bracket by -5

(-5)(4x)=-20x

(-5)(-4w)=20w

-3w-20x+20w-4x

-3w+20w-20x-4x ( combine like terms)

answer:

17w-24x or -24x+17w

Least possible sum of missing digits is 3 that is 3 + 0 and missing numbers are 30

Solution:

Given that number 42,__2 rounded to the hundred place is 42300 .

Need to determine least possible sum of the two missing digits.

first lets see what all numbers can be rounded to 300  

number from 251 to 349 can be rounded to 300 as 251 is more close to 300 than 200 and 349 is closer to 300 than 400.  

But in our case at ones place we are having 2 , so possible numbers having 2 at ones place and in between  251 to 349 are 252 , 262 , 272 , 282 , 292 , 302 , 312 , 322 , 332  and 342.

but we are only concern numbers at hundred and tens place

so now we have 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 and 34.  

Out of this set we want numbers whose sum is least . So if you carefull observer that number is  30 having least sum as 3 + 0 = 3 .

So missing numbers in 42,__2 is 30 and number is 42,302.

Hence we can conclude that least possible sum of missing digits is 3 that is 3 + 0 and missing numbers are 30.

Answer:

232.6 metres after 3.8 seconds.

Step-by-step explanation:

h(t) = -16t² + 122t

a = -16  b = 122  c = 0

Substitute into the quadratic formula

(Ignore the Â)

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

[tex]x =  \frac{-122±\sqrt{122^{2}-4(-16)(0)}}{2(-16)} [/tex]

[tex]x =  \frac{-122±122}{-32} [/tex]

Split the equation at the ±

[tex]x =  \frac{-122+122}{-32}[/tex]        [tex]x =  \frac{-122-122}{-32} [/tex]

[tex]x =  \frac{0}{-32}[/tex]                    [tex]x =  \frac{-244}{-32} [/tex]

[tex]x = 0[/tex]                                       [tex]x = \frac{61}{8}[/tex]

The two x-intercepts at 0 and 61/8. The midpoint of the x-intercepts is the axis of symmetry, which is the x-coordinate of the vertex.

Midpoint = [0 + (61/8)] / 2

Midpoint = 61/16   <= This is the time for maximum height

t = 61/16

t = 3.8125  => Round to t = 3.8

To find the maximum height, substitute t=61/16 into the equation

h(t) = -16t² + 122t

h(61/16) = -16(61/16)² + 122(61/16)

h(61/16) = 232.5625  => Round to h = 232.6

Therefore, the ball will reach the maximum height of 232.6 metres after 3.8 seconds.

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.

Answer:

p=-8

Step-by-step explanation:

Its on the picture

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:

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.

Equation in slope-intercept form of the line that passes through (6,-2) and (12,1) is:

[tex]y =\frac{1}{2}x-5[/tex]

Step-by-step explanation:

Given points are:

(x1,y1) = (6,-2)

(x2,y2) = (12,1)

The slope intercept form is:

[tex]y=mx+b[/tex]

We have to find the slope first

[tex]m =\frac{y_2-y_1}{x_2-x_1}\\=\frac{1-(-2)}{12-6}\\= \frac{1+2}{6}\\=\frac{3}{6}\\=\frac{1}{2}[/tex]

Putting the value of slope

[tex]y = \frac{1}{2}x+b[/tex]

To find the value of b, putting (12,1) in the equation

[tex]1 = \frac{1}{2}(12)+b\\1 = 6+b\\b = 1-6\\b=-5[/tex]

Putting the values of m and b

[tex]y =\frac{1}{2}x-5[/tex]

Hence,

Equation in slope-intercept form of the line that passes through (6,-2) and (12,1) is:

[tex]y =\frac{1}{2}x-5[/tex]

Keywords: Equation of line, slope-intercept form

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To write the equation in slope-intercept form, find the slope and y-intercept using the given points. The slope is 1/2, and the y-intercept is -5. The equation is y = (1/2)x - 5.

To write an equation in slope-intercept form, we need to find the slope (m) and the y-intercept (b). The slope can be calculated using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the slope is (1 - (-2)) / (12 - 6) = 3/6 = 1/2.

Now, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values, we get y = (1/2)x + b.

To find the value of b, we can substitute the coordinates of one of the given points (6, -2) into the equation. -2 = (1/2)(6) + b. Solving for b, we get b = -2 - 3 = -5.

Therefore, the equation in slope-intercept form of the line that passes through (6, -2) and (12, 1) is y = (1/2)x - 5.

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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.

Answer:

9 times a number

Step-by-step explanation:

If a number and a variable are next to each other, you multiply.

Answer:

resistance is 1.5 ohms (1.5 Ω)

Step-by-step explanation:

R varies directly with l

R varies inversely with [tex]d^2[/tex]

We can set-up a proportionality statement as shown below:

[tex]R=k\frac{l}{d^2}[/tex]

Now, Given,

R = 1.50

l = 2

d = 1.5

We substitute and find k (the proportionality constant):

[tex]R=k\frac{l}{d^2}\\1.5=k\frac{2}{1.5^2}\\1.5=\frac{2k}{2.25}\\2k=1.5*2.25\\2k=3.375\\k=1.6875[/tex]

Now, we will use this value of k to solve the problem.

Given,

l = 8

d = 3

and

k = 1.6875

We find R:

[tex]R=k\frac{l}{d^2}\\R=1.6875\frac{8}{3^2}\\R=\frac{1.6875*8}{9}\\R=1.5[/tex]

The resistance is 1.5 ohms (1.5 Ω)

Answer:

20(22-x)

Step-by-step explanation:

Answer:

Area:  42

Perimeter = 26

Step-by-step explanation:

Distance from (4,-7) to (-3,-7) = 7

Distance from (-3,-7) to (-3,3) = 6

These are the length and width of the rectangle.

Area: 7 * 6 = 42

Perimeter = 2*(7+6) = 26