Factor -9x^2-36x-36 please.
A new law requires that 12% of an individual's income be invested in the stock market. Your accounts show that you need to put $420 in the stock market this year. How much did you earn this year.
A $5,040 B $350 C $504** D $3,500
The problem can be solved by setting up the equation 0.12x = $420, where 'x' stands for your total income. Dividing both sides of the equation by 0.12 gives x = $3500 which is the total annual income. Thus, you earned $3,500 this year.
Explanation:To solve this mathematical problem, you can set up an equation that represents the problem context. You know that 12% of your whole year's income equals $420. So if 'x' represents your total income, the equation becomes 0.12x = $420. To solve for 'x' (your total income), you would divide both sides of the equation by 0.12.
So, x = $420 ÷ 0.12. When you perform this calculation, you'll find that 'x' equals $3,500. Therefore, you earned $3,500 this year.
The answer to the problem is D. $3,500.
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mr. and mrs. boyce bought a house for 96000 in 1995. real estate values in their area increase approximately 4% each year. what was the value of the house in 2007?
The Boyce's house bought for $96,000 in 1995, increased approximately 4% yearly. By applying the compound interest formula, the house's value in 2007 would be approximately $139,254.09.
Explanation:We need to use the compound interest formula to calculate the value of Boyce's house in 2007 because the house price increase is compounded annually. The formula is P(1 + r/n)^(nt). Here, P is the initial amount (i.e., the original house price), r is the annual interest rate (the rate of increase in house value), and n is the number of times interest is compounded yearly. T is the number of years the money is invested.
However, as we deal with annual compounding, the formula simplifies to P(1 + r)^t. In this case, P = $96,000, r = 4% or 0.04, and t = 2007 -1995 = 12 years.
Inserting these values, we get 96000(1 + 0.04)^12 = $139,254.09 (rounded to the nearest cent).
So, according to the 4% annual increase rate, Boyce's house would be worth approximately $139,254.09 in 2007.
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A square sheet of art paper has an area of 625 square inches. what is the minimum side length of an easel that supports the whole sheet of paper?
a.-25
b.25
c.15
d.35(-25 or 25?)
At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 4 km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists’ rates.
The speed of Bicyclist A (heading north) is 16 km/h.
The speed of Bicyclist B (heading south) is 11 km/h.
Given:
- Let x be the speed of bicyclist A (heading north).
- Let y be the speed of bicyclist B (heading south).
- Bicyclist A is 5 km/h faster than Bicyclist B, so [tex]\(x = y + 5\)[/tex] (Equation 1).
- Time from 9:00 to 10:45 is 1.75 hours.
- The total distance covered by both bicyclists during this time is 47.25 km.
From the equation for time and distance, we have:
[tex]\[ x \times 1.75 + y \times 1.75 = 47.25 \][/tex]
Substituting Equation 1 into this equation:
[tex]\[ (y + 5) \times 1.75 + y \times 1.75 = 47.25 \]\[ 1.75y + 8.75 + 1.75y = 47.25 \]\[ 3.5y + 8.75 = 47.25 \]\[ 3.5y = 38.5 \]\[ y = \frac{38.5}{3.5} \]\[ y = 11 \text{ km/h} \][/tex]
Substituting the value of y back into Equation 1:
[tex]\[ x = 11 + 5 \]\[ x = 16 \text{ km/h} \][/tex]
Thus, the correct answer is:
- The speed of Bicyclist A (heading north) is 16 km/h.
- The speed of Bicyclist B (heading south) is 11 km/h.
Question :
At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 4 km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists’ rates.
If x = a + bi and y = –a – bi, x + y = 0
Answer:
inverse property
Which of the following statements is true of chords?
A chord is a line segments.A chord connects two points on a circle.A chord can be a radius of a circle.A chord can be a diameter of a circle.A chord divides a circle into two regions
Which of the binomial is a factor of this trinomial x2-7x-44?
{-4y-11x=36
{20=-10x-10y
Tyrone’s hourly wage is $18 and his net pay is 72% of his earnings. Tyrone spends about $1,800 on his monthly expenses. If Tyrone works 40 hours per week and has no other sources of income, what is his total monthly cash inflow? (Hint: Assume that there are 4 pay periods per month.)
$2073.60 per month
===================
To calculate Tyrone's total monthly cash inflow, we need to determine his weekly and then monthly earnings.
Calculate weekly gross income:
$18/hour * 40 hours/week = $720/weekCalculate net pay per week:
$720/week * 72% = $518.40/weekCalculate monthly cash inflow:
$518.40/week * 4 weeks/month = $2073.60/monthTyrone's total monthly cash inflow is $2073.60.
Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area. Show that under these circumstances the drop's radius increases at a constant rate. ...?
From the given condition, the rate of change of radius is constant.
What is rate of change?How quickly something evolves over time is referred to as its rate of change (ROC).
Given:
Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area.
Let V be the volume of the sphere & S be the surface area.
According to the question,
dV/dt = kS
Since,
V = 4/3πr³
dV/dt = 4πr²dr/dt
S = 4πr²
Putting these values to the above expression,
4πr²dr/dt = k4πr²
dr/dt = k
Therefore, the rate of change of radius is constant.
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If the sum of a number and 6 is multiplied by 5, the result is same as 9 times the number decreased by 2. find the number.
You invest $2000 in a bank account that has 5% annual interest rate, compound ed continously. how much will you have in 5 years?
Which fraction shows a correct way to set up the slope formula for the line that passes through the points (3,7) and (5,7)?
The slope of a line through the points (3,7) and (5,7) is 0, indicating a horizontal line.
To calculate the slope of a line passing through two points, you can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the points are (3,7) and (5,7). Using the slope formula, we get:
m = (7 - 7) / (5 - 3) = 0 / 2 = 0
So, the slope of the line that passes through these points is 0, which means the line is horizontal.
Paul plans to put concrete on a rectangular portion of his driveway. The portion is 12 feet long and 6 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Paul needs is $108.89. Which of the following is closest to the width of the portion of the driveway on which Paul plans to put concrete?
[1 foot = 12inches; 1 yard = 3 feet]
3 feet
5 feet
8 feet
10 feet
Answer:
The answer is b. 5 feet
Step-by-step explanation:
What is the solution to the following bernoulli de?
\[t^2 dy/dx+y^2=ty\]
Eric reflected parallelogram ABCD across the x-axis. If angle A is 125° and angle B is 55°, what is the degree measurement of angle A'?
Answer:
Angle A= Angle A' = 125°
Step-by-step explanation:
We have given that : Eric reflected parallelogram ABCD across the x-axis.
If angle A is 125° and angle B is 55°
To find : Degree measurement of angle A'
Solution :
As it is reflected parallelogram , and by property of reflection it form congruent parallelogram
since it is congruent then measures of angle remain same
by this statement the measure of angle of parallelogram ABCD
remain same or equal to parallelogram A'B'C'D'
⇒Angle A= angle A' = 125°
A triangle has side lengths of 12 cm, 35 cm, and 37 cm. Classify it as acute, obtuse, or right.
acute
obtuse
right
sin10+sin20+sin40+sin50=sin70+sin80.prove it
Determine if the equations are intersecting, parallel, or coincident. bx - ay = 2 ax + by = 3
Answer:
Intersecting
Step-by-step explanation:
After having singled out y on one side of both equations you should have.
Y=b/a• x - 2/-a
And
Y= -a/b • x + 3/b
As you can see they have opposite reciprocals which is an intersection
Simplify each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither. Explain your answers.
(a)6x + 2(2x – 3) = 24 + 9x
(b)25 – 4x = 3(5 – x) + 10 – x
(c)4(x + 2) = 2x + 7 + 2(x – 10)
Use substitution to solve the system
5x+4y=12
Y=2x-10
how is a tangent different from a chord
Answer:
A tangent is a line, ray, or line segment that intersects a circle at exactly one point (called the point of tangency) and contains no points inside the circle. A chord is a segment with both endpoints on a circle. Tangents intersect the circle at one point, while a chord intersects at two.
I've checked this answer, E counted it as correct. Hope this helped!!!
A tangent touches a circle at one point, while a chord connects any two points on the circle's circumference.
A tangent and a chord are both important concepts in geometry, but they have distinct characteristics.
A tangent is a line that intersects a circle at exactly one point, touching the circle's circumference at that point.
It never crosses the circle. Tangents are perpendicular to the radius that intersects the point of tangency.
On the other hand, a chord is a line segment connecting any two points on a circle's circumference. Unlike tangents, chords can intersect the circle at multiple points.
The diameter is a special case of a chord that passes through the center of the circle.
Hence,
Tangents touch a circle at one point, while chords connect two points on a circle's circumference.
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HELP!!
Lily just paid off a $400 loan. She had to pay $60 in interest at a simple annual interest rate of 5%. How many years did Lily have this loan?
A. 2
B. 3
C. 4.5
D. 5
Answer: The correct option is (B) 3.
Step-by-step explanation: Given that Lily just paid off a $400 loan. She had to pay $60 in interest at a simple annual interest rate of 5%.
We are to find the number of years for which Lily had this loan.
Let n be the required number of years.
Also, P = $400, S.I. = $60 and r% = 5%.
Therefore, by the formula of simple interest, we have
[tex]S.I.=\dfrac{Prn}{100}\\\\\\\Rightarrow 60=\dfrac{400\times5\times n}{100}\\\\\\\Rightarrow n=\dfrac{60}{20}\\\\\\\Rightarrow n=3.[/tex]
Thus, the required number of years is 3.
Option (B) is CORRECT.
What are odd numbers 1-35?
Josephine started a business selling cosmetics. She spent $4500 to obtain her merchandise, and it costs her $200 per week for general expenses. She earned $550 per week in sales. What is the minimum number of weeks it will take for Josephine to make a profit? Write an inequality to model the problem.
A.)550w > 4500 + 200w
b.)200w > 4500 + 550w
c.) 550w < 4500 + 200w
d.)200w 4500 + 550w
...?
Answer:
a
Step-by-step explanation:
Final answer:
Josephine will need at least 13 full weeks to start making a profit. The correct inequality that models this economic scenario is 550w > 4500 + 200w.
Explanation:
The minimum number of weeks it will take for Josephine to make a profit in her cosmetics business can be determined by setting up an inequality where the total earnings must be greater than the sum of the initial investment and the running costs. We define w as the number of weeks. Josephine earns $550 per week, so her earnings after w weeks are 550w. The initial investment is $4500 and the weekly expense is $200, so the total expenses after w weeks are 4500 + 200w. To make a profit, the earnings must be greater than the expenses:
550w > 4500 + 200w
To solve for w, we need to collect like terms:
550w - 200w > 4500
350w > 4500
Dividing both sides by 350:
w > 4500 / 350
w > 12.86
This means Josephine will need to work for at least 13 full weeks to make a profit.
logx + log(3x-13) = 1
The solutions for [tex]\log x + \log (3\cdot x - 13) = 1[/tex] are [tex]x_{1} = 5[/tex] and [tex]x_{2} = -\frac{2}{3}[/tex], respectively.
In this question, we are going to solve for [tex]x[/tex] with the help of Logarithm Properties, which are described in the image attached below.
[tex]\log x + \log (3\cdot x - 13) = 1[/tex]
[tex]\log [x\cdot (3\cdot x - 13)] = 1[/tex]
[tex]\log (3\cdot x^{2}-13\cdot x) = 1[/tex]
[tex]10^{\log(3\cdot x^{2}-13\cdot x)} = 10^{1}[/tex]
[tex]3\cdot x^{2}-13\cdot x = 10[/tex]
[tex]3\cdot x^{2}-13\cdot x -10 = 0[/tex]
This is a Second Order Polynomial, which can be solved by Quadratic Formula:
[tex]x_{1} = 5[/tex] and [tex]x_{2} = -\frac{2}{3}[/tex]
The solutions for [tex]\log x + \log (3\cdot x - 13) = 1[/tex] are [tex]x_{1} = 5[/tex] and [tex]x_{2} = -\frac{2}{3}[/tex], respectively.
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Is 89 prime or composite
Answer:
Prime
Step-by-step explanation:
A prime number is a number that has only one factor. A composite number is a number that has more than one factor.
-kiniwih426
Suppose f(π/3) = 3 and f '(π/3) = −7,
and let
g(x) = f(x) sin x
and
h(x) = (cos x)/f(x).
Find the h'(x)
To find h'(x), differentiate the function h(x) = (cos x)/f(x) using the product rule.
Explanation:To find h'(x), we need to differentiate the function h(x) = (cos x)/f(x).
First, let's find the derivative of cos x, which is -sin x.
Next, we need to find the derivative of f(x). Since f(π/3) = 3 and f '(π/3) = −7, we know the slope of the tangent line at x = π/3 is -7.
Using the product rule, we can now differentiate h(x) = (cos x)/f(x) as follows:
h'(x) = [f(x)(-sin x) - cos x(f '(x))]/[f(x)]^2
Vanessa deposited money into a bank account that earned 1.25% simple interest each year. After 1/2 year, she had earned $5.00 in interest on the account. If no other money was deposited into or withdrawn from the account, how much was her initial deposit? Uhh... I was just testing...oops
so the answer is 800. I guarantee you this will be the answer I promise
Final answer:
Vanessa's initial deposit in the bank, earning 1.25% simple interest per year, was $800. This is calculated using the simple interest formula, rearranged to solve for the principal based on the $5 interest earned in half a year.
Explanation:
To find Vanessa's initial deposit, we use the simple interest formula, which is Interest = Principal × Rate × Time. Given Vanessa earned $5.00 in interest in half a year (0.5 years) at a rate of 1.25% per annum, we can rearrange the formula to solve for the principal (initial deposit).
Using the given information: $5 = Principal × 0.0125 × 0.5, we can solve for the Principal as follows:
$5 = Principal × 0.00625
Principal = $5 ÷ 0.00625
Principal = $800
Therefore, Vanessa's initial deposit was $800.