the smaller of two numbers is 7/8 of the larger. Their sum is 30. Find the two numbers

Final answer:

The point T lies in the second quadrant of the unit circle when it is at an angular distance of 3π/5 from P(1, 0), because this angle falls between π/2 and π radians.

Explanation:

If T is the point at a distance 3π/5 from point P(1, 0) on the unit circle with its center at (0, 0), to determine in what quadrant T lies, we must consider where this angle places T on the unit circle.

Recall that a point on the unit circle has coordinates (x, y) = (cos θ, sin θ), where θ is the angle measured counterclockwise from the x-axis. An angle of 3π/5 radians is more than π/2 radians but fewer than π radians. Therefore, it falls in the second quadrant of the unit circle, where x-coordinates are negative and y-coordinates are positive.

505/5 = 101

so 101 is the middle number, now add the 2 below it and the 2 above it

99 + 100 + 101 + 102 +103 = 505

Answer:

Option C) The first equation is y= 2/3x-4 when written in slope-intercept form

Step-by-step explanation:

we have

[tex]2x-3y=12[/tex] ----> First equation

The first equation is in standard form

Convert to slope intercept form

Isolate the variable y

[tex]3y=2x-12[/tex]

Divide by 3 both sides

[tex]y=\frac{2}{3}x-4[/tex]

[tex]y=-\frac{3}{5}x+2[/tex] ----> Second equation

The second equation is in slope intercept form

Convert to standard form

Multiply by 5 both sides to remove the fraction

[tex]5y=-3x+10[/tex]

[tex]3x+5y=10[/tex]

Verify each statement

case A) Both equations are in slope-intercept form.

False

Because only the second equation is in slope -intercept form

case B) Neither equation is in slope-intercept form

False

Because, the second equation is in slope -intercept form

case C) The first equation is y= 2/3x-4 when written in slope-intercept form

True (see the procedure)

case D)The second equation is 3x+5y=10 when written in slope-intercept form.

False

Because, the second equation is  3x+5y=10 when written in standard form

Answer:

x = 50 .

Step-by-step explanation:

Given  : Mean of 5,10,15 and x is 20.

To find : What is the x.

Solution : We have given  Mean of 5, 10 , 15 and x is 20.

Mean = 20 .

Mean = [tex]\frac{sum\ of \ data}{Number\ of \ data}[/tex].

Mean = [tex]\frac{5+10+15 +x}{4}[/tex].

20 = [tex]\frac{30 +x}{4}[/tex].

On multiplying both sides by 4

20 * 4 = 30 + x .

80 = 30 + x .

On subtracting both sides by 30.

50 = x

Therefore, x = 50 .

Final answer:

To find the distance between a point and a line, you need to find the equation of the line, find the coordinates of the point, substitute the coordinates into the equation, and calculate the perpendicular distance.

Explanation:

To find the distance between a point and a line, you need to use the formula for the distance from a point to a line. Here are the steps:

First, find the equation of the line.

Next, find the coordinates of the given point.

Substitute the coordinates of the point into the equation of the line to find the perpendicular distance from the point to the line.

The distance between the point and the line is the perpendicular distance found in step 3.

For example, let's say the equation of the line is y = 2x + 3, and the coordinates of the point are (4,5). To find the distance between the point and the line:

The equation of the line is y = 2x + 3.

The coordinates of the point are (4,5).

Substituting the coordinates (4,5) into the equation y = 2x + 3 gives 5 = 2(4) + 3, which simplifies to 5 = 11.

The perpendicular distance from the point to the line is |5 - 11|, which is equal to 6.

Therefore, the distance between the point (4,5) and the line y = 2x + 3 is 6 units.

j= jeans

c= corduroy

jeans = 0.75C

0.75 +c = 42

1.75c = 42

c = 42/1.75 = 24

 jeans cost 24*0.75 = 18

 corduroys cost $24

Jeans cost $18

Answer with Step-by-step explanation:

Let j denote the cost of jeans

and c denotes the cost of corduroy

A pair of jeans cost 75% as much as a pair of corduroy pants.

i.e. j = 0.75c

The total cost for the jeans and corduroy is $42

i.e. j+c=42

⇒ 0.75c+c=42

⇒ 1.75c=42

Dividing both sides by 1.75,we get

c=24

Putting value of c in j= 0.75c gives

j=18

Hence, Cost of jeans=$18

and cost of corduroy=$24

The area of the rectangular board is 2,700,000 mm².

The subject of this question is Mathematics and it's likely suitable for a Middle School student. The question asks for the area of a rectangular board given specific length and width in meters, and requires the answer in square millimeters.

First, let's calculate the area of the rectangular board in square meters (m²) by multiplying the length and the width. So, 1.8 m * 1.5 m equals 2.7 m². Now, to convert the area from square meters to square millimeters (mm²), remember that 1 m² is equal to 1,000,000 mm². Therefore, the area of the board in square millimeters is 2.7 m² * 1,000,000 equals 2,700,000 mm².

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To solve the equation -2x^2 + 3x - 9 = 0, we can use the quadratic formula. This equation does not have any real solutions, but it has complex solutions involving imaginary numbers.

To solve the equation -2x^2 + 3x - 9 = 0, we can use the quadratic formula. Substituting the values a = -2, b = 3, and c = -9 into the formula, we can then simplify to find the solutions for x.

The quadratic formula is given by:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Substituting the values, we have:

x = (-3 ± sqrt(3^2 - 4(-2)(-9))) / (2(-2))

Simplifying further, we get:

x = (-3 ± sqrt(9 - 72)) / -4

x = (-3 ± sqrt(-63)) / -4

Since the square root of a negative number is not a real number, this equation does not have any real solutions. The equation has complex solutions, which involve the use of imaginary numbers.

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Answer:Elevator is +17 above ground level while -22 is below

Step-by-step explanation:

Since it is + and - i know +is positive that mean up and - is negative which mean down so -22 is below while +16 is above

The acrobat's descent on a time versus velocity graph would show an initial linear increase in velocity due to gravity minus frictional force, followed by a sharp negative slope as she comes to a stop at the bottom.

The acrobat's descent can be analyzed by plotting a time (t) versus velocity (v) graph. Initially, the acrobat experiences a frictional force equal to five-ninths of her weight, which creates constant deceleration. For the first three quarters of the descent, her velocity will increase linearly (assuming constant deceleration) until she tightens her grip, which will cause a sharp decrease in velocity until she comes to a complete stop at the bottom. The graph would show a slope that decreases in magnitude over time and then drops to zero when the acrobat comes to rest.

Answer:

The sine value of pi over 6 is:

[tex]\dfrac{1}{2}[/tex]  or 0.5

Step-by-step explanation:

we have to find the value of  [tex]sin\dfrac{\pi}{6}[/tex]

we know that value of  [tex]sin\dfrac{\pi}{6}[/tex]  is [tex]\dfrac{1}{2}[/tex]

Hence, the sine value of pi over 6 is:

[tex]\dfrac{1}{2}[/tex]  or 0.5

I would say D. 7+4 because it is the only one that makes since to me

multiply the 2 together:

3/4 x 4/5 = 12/20 = 3/5 has dead grass

To find the area of the yard that has dead grass, multiply three-fourths (the grassy area) by 4/5 (the dead portion). Simplifying (3/4) × (4/5) gives us 3/5, which means 3/5 of the yard has dead grass.

To determine how much of the yard has dead grass, we need to calculate the portion of the yard covered in grass and then the fraction of it that has died. Given that three-fourths of the yard is covered in grass, we represent this as 3/4. It is known that 4/5 of this grass has died, hence we multiply the two fractions: (3/4) × (4/5).

Performing the multiplication of these two fractions:

Now, simplify the fraction 12/20 by dividing both the numerator and denominator by their greatest common divisor, which is 4:

Therefore, the correct answer is that 3/5 of the yard has dead grass.

Expected income is crucial in choosing a retirement plan because it influences permanent income for savings, the adequacy of funds against inflation, and financial security post-retirement.

Choosing a retirement plan is a vital financial decision; expected income plays a large role because it directly affects a person's ability to save and sustains their lifestyle after they retire. The idea of permanent income, which is the average annual income an individual expects to receive for the rest of their lives, influences how much they allocate to retirement savings. It's crucial for asset accumulation and ensuring financial security.

Retirement funds sourced from plans like private company pensions or defined benefits can be fixed and may not keep up with inflation, leading to a potential loss of purchasing power over time. Therefore, understanding one's expected income helps in selecting retirement plans that can adjust and possibly increase over time to hedge against inflation. Additionally, individuals must consider the impact of future income changes on their current saving and consumption patterns.

Behavioral economics factors in human psychology and behavior, suggesting that individuals may not always make rational financial decisions due to a lack of self-control or understanding of long-term benefits, influencing retirement plan choices. Thus, expected income is a significant consideration for individuals when choosing a retirement plan, as it determines their ability to save enough to maintain their desired lifestyle in retirement.