1. The product of 6, and a number increased by 2, is -24. What is the number?
Answers
Answer:
Step-by-step explanation: 6* (N + 6) = -24
6*n + 6*6=-24
6n+36=-24
-36 -24
6n=-60
n=-10
Related Questions
the probability that a randomly selected household with a savings account has no checking account is
Answers
The probability that a randomly selected household with a savings account has no checking account is approximately 0.149, or 14.9%.
To compute the probability that a randomly selected household with a savings account has no checking account, we can use Bayes' theorem. Let S denote the event that a household has a savings account, and C denote the event that a household has no checking account.
We want to find P(C | S), the probability that a household with a savings account has no checking account.
Using Bayes' theorem, we have:
P(C | S) = P(S | C) * P(C) / P(S)
We know that 40% of households with no checking accounts have savings accounts, so P(S | C) = 0.4. We also know that 21.5% of households have no checking accounts, 66.9% have regular checking accounts, and 11.6% have NOW accounts, so P(C) = 0.215.
Finally, we can use the law of total probability to find P(S), the overall probability of a household having a savings account:
P(S) = P(S | C) * P(C) + P(S | regular checking) * P(regular checking) + P(S | NOW) * P(NOW)
= 0.4 * 0.215 + 0.716 * 0.669 + 0.793 * 0.116
≈ 0.576
Substituting these values into the equation for Bayes' theorem, we get:
P(C | S) = 0.4 * 0.215 / 0.576
≈ 0.149
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Complete question is:
A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.
Compute the probability that a randomly selected household with a savings account has no checking account.
how to solve number 16
Answers
Answer:
T < -19
Step-by-step explanation:
-6 > t + 13 ( neg & neg = positive)
- 6 - 13 > t
-19 > t
I need help on the one about slope
Answers
If you divide -1/2 and then 4/1 you will get -5/1 or also known as -5
John invests $500 in a savings account with a nominal annual interest rate of 10% compounded quarterly. How many years will it take for the investment to reach $1000? Round to the nearest tenth. If you solve this asap and correctly you are a true star ;)
Answers
It will take 10 years for the investment to reach $1,000.
Sure hope this helps you
Consider the upper half of the ellipsoid f(x, y) = √(1-x^2/9-y^2/16) and the point p(0,2√2) on the given level curve f(x,y)= √2/ 2
Compute the slope of the line tangent to the level curve at P, and verify that the tangent line is orthogonal to the gradient at that point.
Answers
Let's first differentiate f(x, y) with respect to x and y. This can be achieved as follows:
\($$f(x, y) = \sqrt {1 - \frac{x^2}{9} - \frac{y^2}{16}} \\ \frac{\partial f}{\partial x} = \frac{ - x}{3\sqrt {1 - \frac{x^2}{9} - \frac{y^2}{16}}} \\ \frac{\partial f}{\partial y} = \frac{ - y}{4\sqrt {1 - \frac{x^2}{9} - \frac{y^2}{16}}}$$\)
We are given the point\($p(0,2\sqrt{2})$\)on the level curve
\($f(x,y)=\frac{\sqrt{2}}{2}$\)
Now, we have to find the slope of the tangent line to the level curve at \($P$\).The equation of the line tangent to the level curve
\($f(x,y)=c$ at $P(x_1,y_1)$\)
is given by:
\($\frac{\partial f}{\partial x} \biggr\rvert_{(x_1,y_1)}(x-x_1) + \frac{\partial f}{\partial y} \biggr\rvert_{(x_1,y_1)}(y-y_1) = 0$\)
Substituting\($x_1=0$, $y_1=2\sqrt{2}$, and $f(x,y)=\frac{\sqrt{2}}{2}$,\)
we obtain:
\($$\frac{\partial f}{\partial x} \biggr\rvert_\)
\({(0,2\sqrt{2})}(x-0) + \frac{\partial f}{\partial y} \biggr\rvert_{(0,2\sqrt{2})}(y-2\sqrt{2}) = 0$$$$\frac{0-x}{3f(x,y)} + \frac{-y}{4f(x,y)}\)= 0
Simplifying the above equation, we get:
\($$\frac{x}{f(x,y)} = -\frac{4y}{3f(x,y)}$$$$\frac{dy}{dx} = -\frac{3}{4}\frac{f(x,y)}{x}$$\)
The slope of the tangent line to the level curve at \($P$\) is given by \($\frac{dy}{dx}\biggr\rvert_{(0,2\sqrt{2})}$.\)
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I need this fast pls
Answers
Answer:
17%
Step-by-step explanation:
As you may see, the area is 100, so as much there is colored in squares, that will be the percentage, so if you count them, you will see that there are 17, and that will be your answer.
Tell me if I'm wrong :)
Answer:
17%
Step-by-step explanation:
IF YOU SOLVE I WILL BE YOUR BEST FRIEND I SWEAR. ALSO WILL AWARD THE BRAINLIEST THING. PLEASE. I NEED THESE GRADES SO I WONT BE A DISSAPOINTMENT TO MY MY MOM!
Answers
Answer:
see below
Step-by-step explanation:
x⁵ - 8x⁴ + 22x³ - 26x² + 21x - 18 = 0
x = 2, x = ± i, x=3 with multiplicity 2
-----------------------------------------------------
x⁴ - 5x³ + 7x² - 5x + 6 = 0
x = 2, x=3, x = ± i
--------------------------------------------------------
-1 + 4i = 4 + i
i
--------------------------------------------------------
x³ - 26x² + 21x - 18 = 0
x = ± 2i, x = 3/2
--------------------------------------------------------
(1 + i) (-3 - 4i)
= 1 - 7i
--------------------------------------------------------
6.
(-5 + 2i) + (3 - 6i)
= -2 -4i
--------------------------------------------------------
7.
x⁴ + 5x² + 4 = 0
x = ± i , x = ± 2i
--------------------------------------------------------
8.
(7 - i) - (-5 + 6i)
= 12 - 7i
--------------------------------------------------------
9.
(4 - i) (4 + i)
= 17
--------------------------------------------------------
10.
(3 + 8i) (4 - 3i)
= 36 + 23i
? + 59 5/8= 82 2/3 equals what?
Answers
Answer:
23 1/24
Step-by-step explanation:
How i got my answer was that i did the opposite
82 2/3 - 59 5/8 = 23 1/24to find what ? + 59 5/8= 82 2/3 equals to you have to do the opposite of addition which is subtraction and that will help you find the answer/sum of the problem
i really need help..im confused
Answers
The marginal frequencies of chocolate and strawberry are 0.75 and 0.25 and chocolate is greater by 0.5
What are marginal frequencies?Marginal frequency is the ratio between either a column total or a row total and the total sample size.
For example, in a table of students classified by sex and area of study, the number of female students, regardless of area of study, would be one marginal frequency.
The marginal frequency of chocolate is calculated as;
The total frequency of chocolate = 30+45 = 75
The grand frequency = 75+25 = 100
marginal frequency of chocolate = 75/100
= 0.75
The marginal frequency of strawberry = 25/100
= 0.25
The difference in the marginal frequencies of chocolate and strawberry = 0.75 - 0.25 = 0.50
Therefore the marginal frequency of chocolate is greater than strawberry by 0.5
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Veronica wants to buy a new bicycle. The bicycle costs $310. Veronica
opened a savings account with $50. She also got a job and plans to
save $20 a week. How long will it take her to save up enough money
for the bike?
Answers
Step-by-step explanation:
bicycle cost= 310
initial money in savings account= 50
additional money saved per week = 20
number of weeks = w
you have to set up an equation
The equation is...
bicycle cost = additional money saved × w + initial money
Substitute the values
310 = 20w + 50
Solve for w
310 - 50 = 20w +50 - 50
260 = 20w
260÷ 20 = 20w÷ 20
13 = w
It will take 13 weeks for her to have enough money for her bicycle
I hope this helps!!!
Suppose that the economy is experiencing a recession with an estimated recessionary gap of $20 billion. Congress is considering the use of fiscal policy to ease the recession, but due to current political sentiments, it has determined that the maximum spending increase the government is willing to support is $3 billion. It wants to make up the remainder of the recessionary gap using tax cuts.
Answers
To address the recessionary gap of $20 billion, Congress is willing to support a maximum spending increase of $3 billion, leaving a remaining gap of $17 billion that needs to be filled through tax cuts.
In this scenario, fiscal policy is being utilized to counter the recession. The government aims to stimulate the economy by injecting additional funds through increased spending and tax cuts.
However, due to political sentiments, Congress has set a limit on the amount of spending increase they are willing to support, which is $3 billion. As a result, the remaining gap of $17 billion must be addressed through tax cuts.
By implementing tax cuts, individuals and businesses will have more disposable income, encouraging increased spending and investment, which can help alleviate the recessionary pressures and stimulate economic growth.
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A car you bought for $32,000 has a sales tax of 7%. What is the final price
Answers
Answer
34,240
Step-by-step explanation:
32,000 times 0.07 = 2,240 - that's the sales tax so add it to the 32,000 to get 34,240
Show how to use a property of arithmetic to make the addition problem 997+543 easy to calculate mentally. Write equations to show your use of a property of arithmetic. State the property you use and show where you use it. Draw a diagram and use it to explain how to use the "make-a-ten" strategy to add 7 + 5. Write a series of equations that go with the steps in your diagram. Write equations for this diagram. Use base-ten drawings along side the standard algorithm to diagram the regroupings necessary to compute 234 - 47 using the standard algorithm. Clearly indicate your regroupings and results. You may use several diagrams or one - as long as you are clear. Use base-ten drawings along side the standard algorithm to diagram the regroupings necessary to compute 23 + 19 using the standard algorithm. Clearly indicate your regroupings and results. You may use several diagrams or one - as long as you are clear.
Answers
To make the addition problem 997 + 543 easy to calculate mentally, we can use the property of arithmetic called regrouping or carrying.
Determine the arithmetic?By regrouping the numbers based on their place values, we can simplify the addition process.
To add 7 + 5, we can use the "make-a-ten" strategy. Since 7 + 5 equals 12, we can think of it as taking 2 from the units place and carrying it over to the tens place. This results in 1 being added to the tens place, and the units place becomes 2. Therefore, 7 + 5 = 12.
Equations:
7 + 5 = 12
7 = 7 + 0 (regrouping)
12 = 10 + 2 (regrouping)
To compute 234 - 47 using the standard algorithm, we can use base-ten drawings alongside.
2 3 4
- 4 7
__________
1 8 7
We start by subtracting 7 from 4 in the ones place, which requires regrouping. We take 10 from the tens place and add it to the ones place, resulting in 14 - 7 = 7. Then, we subtract 4 from 3 in the tens place, resulting in 3. Finally, we subtract 0 from 2 in the hundreds place, resulting in 2. Therefore, 234 - 47 = 187.
To compute 23 + 19 using the standard algorithm, we can use base-ten drawings alongside.
2 3
+ 1 9
________
4 2
We start by adding 9 to 3 in the ones place, resulting in 12. Then, we add 1 to 2 in the tens place, resulting in 3. Therefore, 23 + 19 = 42.
Therefore, to simplify the mental calculation of 997 + 543, we can utilize the arithmetic property of regrouping or carrying.
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Complete question here:
Show how to use a property of arithmetic to make the addition problem 997+543 easy to calculate mentally. Write equations to show your use of a property of arithmetic. State the property you use and show where you use it. Draw a diagram and use it to explain how to use the "make-a-ten" strategy to add 7 + 5. Write a series of equations that go with the steps in your diagram. Write equations for this diagram. Use base-ten drawings along side the standard algorithm to diagram the regroupings necessary to compute 234 - 47 using the standard algorithm. Clearly indicate your regroupings and results. You may use several diagrams or one - as long as you are clear. Use base-ten drawings along side the standard algorithm to diagram the regroupings necessary to compute 23 + 19 using the standard algorithm. Clearly indicate your regroupings and results. You may use several diagrams or one - as long as you are clear.
If two lines meet and form right angles, then
Answers
Answer:
the lines are perpendicular. the reason it will be perpendicular is because its going to be intersected by those right angles.
Answer:
IF TWO LINES ARE PERPENDICULAR ,THEN THEY MEET TO FORM RIGHT ANGLES .
Step-by-step explanation:
Which of the following numbers is
not equal to the others?
Enter
a. 0.84%
c. 8.4 * 10 ^ - 2
a, b, c, d, or e.
b. (0.21)(0.04)
d.
e. 21/25 * 10 ^ - 2
21/2500
Answers
The number that is not equal to the others is d.
a. 0.84% is equal to 0.0084 in decimal form.
b. (0.21)(0.04) is equal to 0.0084.
c. 8.4 * \(10^-^2\) is equal to 0.084. This is the same as 8.4 divided by 100, which is 0.084.
d. This is the number that is not equal to the others. We don't have the value of d.
e. 21/25 * \(10^-^2\) is equal to 0.0084. When we divide 21 by 25 and multiply the result by \(10^-^2\), we get 0.0084.
To summarize, all of the given numbers (a, b, c, and e) are equal to 0.0084 except for d, which doesn't have a specified value. Therefore, d is the number that is not equal to the others.
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1. prove \(\frac{cos^3(\beta )+sin^3(\beta )}{sin(\theta)+cos(\theta)} = 1-sin(\theta)cos(\theta)\)
2. prove \((csc(\theta)sec(\theta))^2 -\frac{(1-tan^2(\theta))^2}{tan^2(\theta)} =4\)
Answers
1. It is proven that (cos³θ + sin³θ)/(sinθ + cosθ) = 1 - sinθscosθ
2. It is proven that (cosecθsecθ)² - (1 - tan²θ)²/tan²θ = 4
1. How to prove the trigonometric expression?
(cos³θ + sin³θ)/(sinθ + cosθ) = 1 - sinθ + cosθ
We need to show that L.H.S = R.H.S
(cos³θ + sin³θ)/(sinθ + cosθ)
Using the sum of two cubes, we have x³ + y³ = (x + y)(x² - xy + y²)
So, (cos³θ + sin³θ) = (cosθ + sinθ)(cosθ² - cosθsinθ + sinθ²)
= (cosθ + sinθ)(cosθ² + sinθ² - cosθsinθ)
= (cosθ + sinθ)(1 - cosθsinθ)
So, (cos³θ + sin³θ)/(sinθ + cosθ) = (cosθ + sinθ)(1 - cosθsinθ)/(sinθ + cosθ)
= 1 - sinθscosθ
Thus, it is proven that (cos³θ + sin³θ)/(sinθ + cosθ) = 1 - sinθscosθ
2. How to prove the trigonometric expression?(cosecθsecθ)² - (1 - tan²θ)²/tan²θ = 4
WE need to show that L.H.S = R.H.S
(cosecθsecθ)² - (1 - tan²θ)²/tan²θ = (1/sinθcosθ)² - (1 - 2tan²θ + tan⁴θ)/tan²θ
= (1/sinθcosθ)² - 1/tan²θ + 2tan²θ/tan²θ - tan⁴θ/tan²θ
= (1/sinθcosθ)² - 1/tan²θ + 2 - tan²θ
= [(1 - (sinθcosθ)²/tan²θ + 2(sinθcosθ)² - (sinθcosθ)²tan²θ]/(sinθcosθ)²
= [(1 - (sinθcosθ)²cos²θ/sin²θ + 2(sinθcosθ)² - (sinθcosθ)²sin²θ/cos²θ]/(sinθcosθ)²
= [(1 - cos⁴θ + 2(sinθcosθ)² - sin⁴θ]/(sinθcosθ)²
= [(1 - (cos⁴θ + sin⁴θ) + 2(sinθcosθ)² ]/(sinθcosθ)²
Since (cos⁴θ + sin⁴θ = (cos²θ)² + (sin²θ)²
Using the sum of two squares a² + b² = (a + b)² - 2ab
(cos²θ)² + (sin²θ)² = (cos²θ + sin²θ)² - 2cos²θsin²θ = 1 - 2cos²θsin²θ (Since cos²θ + sin²θ = 1)
So, (cosecθsecθ)² - (1 - tan²θ)²/tan²θ = [(1 - (cos⁴θ + sin⁴θ) + 2(sinθcosθ)² ]/(sinθcosθ)²
= [(1 - (1 - 2cos²θsin²θ) + 2(sinθcosθ)² ]/(sinθcosθ)²
= [(1 - 1 + 2cos²θsin²θ + 2(sinθcosθ)² ]/(sinθcosθ)²
= [0 + 4(sinθcosθ)² ]/(sinθcosθ)²
= 4(sinθcosθ)² ]/(sinθcosθ)²
= 4
So, it is proven that (cosecθsecθ)² - (1 - tan²θ)²/tan²θ = 4
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Ethan drew a scale drawing of a house. He used the scale 1 millimeter : 5 meters. The actual
length of the garage is 10 meters. How long is the garage in the drawing?
millimeters
Answers
Answer:
2 millimeters
Step-by-step explanation:
Ethan used the scale 1 millimeter : 5 meters.
This means that 1 millimeter in the drawing represents 5 meters in actual life.
The actual length of the garage is 10 meters. Therefore:
5 meters = 1 millimeter
=> 10 meters = (10 * 1) / 5 = 2 millimeters
The garage is 2 millimeters long in the drawing.
If a ray bisects a right angle, then each newly formed angle measures 45 degrees.
A) Sometimes
B) Always
C) Never
Answers
This is because ‘bisect’ means to spilt exactly in half. If you split 90 degrees in half, you get 45 degrees.
Hope this helps!
Answer:
Always
Step-by-step explanation:
Bisects means to divide in half
90/2 = 45
So the angles are each 45 degrees
How do you find the angles of a 5/12/13 triangle?
Answers
The angles of a triangle with side lengths 5 , 12 and 13 are 90°, 22.63°, 67.38°.
What is Law of cosines formula?In trigonometry, the law of cosines, also known as the law of cosines or cosine formula, basically relates the length of a triangle to one cosine of its angle. It states that if we know the lengths of two sides of a triangle and the angle between them, we can determine the length of the third side. c² = a²+ b² – 2ab cosγ
where a, b, c are the sides of the triangle and γ is the angle between a and b, see image above.
To find the length of a side of a triangle, take △ABC according to the cosine formula, which can be written as follows.
a² = b²+ c²– 2bc cos αb²= a² + c²– 2ac cos βc²= b² + a² – 2ba cos γWe have , a = 5 , b = 12 , c= 13
cos α =( 12² + 13² - 5² )/2×12×13= 288/312
=> α = cos⁻¹(0.923 ) = 22.63°
cos β = (5² + 13² - 12² )/2×13×5 = 50/130
=> β = cos⁻¹(5/13) = 67.38°
cos γ = (12² + 5² - 13² )/2×12×5= 0
=> γ = cos⁻¹(0) = 90°
Hence, the required angles are 90°, 22.63°, 67.38°.
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Connor filled his 75 gallon pool with water in 6.25 hours. How many gallons per hour did he use? *
Answers
Answer:
you’ll get 12 :)
Step-by-step explanation:
to get the anwser you need to divide by 6.25.
75 / 6.25 = 12
Norman is 12 years older than Michael. In 6 years, he will be twice as old as Michael. How old is Michael now?(A) 3(B) 6(C) 12(D) 18(E) 24
Answers
As per the given situation, Michael is option (b) 6 years old now.
The unitary method can be used to solve this problem. To use this method, we must first decide which quantity represents the unit, in this case the unit is one year.
We can then write the given information in terms of the unit. Norman is 12 years older than Michael, and in 6 years, he will be twice as old as Michael. This can be rewritten as 12 units + 6 units = 2(6 units).
This equation can be solved using the unitary method to find that Michael is 6 years old, making answer B the correct answer
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PLEASE HELP ASAP WILL MARK AS BRAINLYEST
The figure shows a carpeted room. How many square feet of the room are carpeted?
5 feet
4 feet
6 feet
10 feet
O 30 square feet
O 32 square feet
O 40 square feet
O 80 square feet
Answers
Answer:
The answer is 40.
Step-by-step explanation:
4x5 for the square part.
2x10 for the rectangle part
add them
A line is perpendicular to y = -1/5x + 1 and intersects the point negative (-5,1) what is the equation of this perpendicular line?
Answers
Answer: y = 5x + 26
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.
We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 1 = 5(x - (-5))
Simplifying further:
y - 1 = 5(x + 5)
Expanding the brackets:
y - 1 = 5x + 25
Rearranging the equation to the slope-intercept form (y = mx + b):
y = 5x + 26
Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.
NEED HELP 50 POINTS.
It takes 29 pounds of seed to completely plant a 3-acre field. How many pounds of seed are needed per acre?
Answers
Per acre = total seed / total acres
Per acre = 29 pounds / 3 acres
Per acre = 9 2/3 pounds of seed.
Answer:
i don't know how precise they want the numbers to be (its almost 10 if rounded), but it takes 9.6 (with repeating .6 forever) per acre.
Step-by-step explanation:
they might want 9.6 or maybe 10 or maybe 9.5
it depends on if they want you to round
A biased spinner can land on 1, 2, 3 or 4.
The table shows the probabilities that the spinner will land on 2 and 4.
1
Number
Probability
2 - 0.33
3 - ??
4 - 0.17
The probability that the spinner will land on 1 is twice the probability
that the spinner will Land on 3.
(a) Complete the table.
Answers
Answer:
Below
Step-by-step explanation:
1 would be 2 * the prob of 3 = 2 * ?? = 2 * ?? <====given
All of the probabilities have to sum to ONE
2 * ?? + .33 + ?? + .17 = 1.0
3 ?? = .5
?? =~ .17
find an example of a commutative ring R with 1 in R, and a prime ideal P (of R) with no zero divisors but R is not an integral domain.
Answers
An example of a commutative ring R with 1, a prime ideal P, and no zero divisors but R is not an integral domain is the ring R = Z/6Z, where Z is the set of integers and 6Z is the ideal generated by 6.
The ring R = Z/6Z consists of the residue classes of integers modulo 6. The elements of R are [0], [1], [2], [3], [4], and [5], where [a] denotes the residue class of a modulo 6.
In this ring, addition and multiplication are performed modulo 6. For example, [2] + [3] = [5] and [2] * [3] = [0].
R has a multiplicative identity, which is the residue class [1]. It is commutative since addition and multiplication are performed modulo 6.
The ideal P = 2R consists of the elements [0] and [2]. P is a prime ideal since R/P is an integral domain, which means there are no zero divisors in R/P. However, R itself is not an integral domain because [2] * [3] = [0] in R, showing that zero divisors exist in R.
Therefore, the ring R = Z/6Z, with the prime ideal P = 2R, satisfies the given conditions.
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please answer, I haven’t no clue how to work it out
Answers
Answer:
C. x-2
Step-by-step explanation:
x² + 7x - 18 = 0
the factor must be p and q from the form.of
(x+p)(x+q) = 0
then find the value of p and q by this rules
p + q = 7
p x q = -18
p = 9
q = -2
(x + 9)(x + (-2)) = 0
(x+9)(x-2) = 0
Answer:
c.) \((x-2)\)
Step-by-step explanation:
The given expression is written in the form \(ac^2+bx+c\). To factor, find two numbers whose sum is b and whose product is c:
_×_=-18
_+_=7
Use -2 and 7:
-2×9=-18
-2+9=7
Substitute the two numbers for b:
\(x^2-2x+9x-18\)
\((x^2-2x)+(9x-18)\)
Factor out common terms. The common term in the first parentheses is x and the common term in the second is 9:
\(x(\frac{x^2-2x}{x} )+9(\frac{9x-18}{9})\\\\x(x-2)+9(x-2)\)
Cancel out one of the parentheses since they have the same terms and plug the factored numbers in:
\((x-2)(x+9)\)
:Done
Check Your Work:
To see if the given factored form is true, simplify it using FOIL:
First, Outside, Inside, Last
\((x-2)(x+9)\)
Multiply the first terms:
\(x*x=x^2\)
Multiply the terms on the outside:
\(x*9=9x\\\\x^2+9x\)
Multiply the inside terms:
\(-2*x=-2x\\\\x^2+9x-2x\)
Multiply the last terms:
\(-2*9=-18\\\\x^2+9x-2x-18\)
Combine like terms:
\(x^2+(9x-2x)-18\\\\x^2+7x-18\)
Therefore, the factored form is true.
HELPPPPPP ASAPPPPPP PLEASEEE
Answers
Answer:
here
Step-by-step explanation:
-3,3
2,3
3,3
4,3
I hope this helped! :D
What do you notice about the decimal forms of the rates?
Answers
Answer: The question is not clear.
Step-by-step explanation:
Investigators measure the temperature of a body found inside a home. The body has cooled to 76.5F°. How long has it been since they died?
Answers
Answer: The cooling of a body can be modeled using Newton's Law of Cooling, which states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. The equation for Newton's Law of Cooling is:
T(t) = T_0 + (T_s - T_0) * e^(-kt)
where T(t) is the temperature of the body at time t, T_0 is the initial temperature of the body, T_s is the temperature of the surroundings, k is the cooling constant, and e is the base of the natural logarithm.
Assuming that the temperature of the surroundings is constant at 68°F, we can use the given information to solve for t:
76.5°F = 68°F + (T_0 - 68°F) * e^(-kt)
Simplifying this equation, we get:
8.5°F = (T_0 - 68°F) * e^(-kt)
Taking the natural logarithm of both sides, we get:
ln(8.5°F / (T_0 - 68°F)) = -kt
Solving for t, we get:
t = -ln(8.5°F / (T_0 - 68°F)) / k
The cooling constant k depends on various factors such as the body's mass, the body's surface area, and the body's initial temperature. For a human body, k is typically estimated to be around 0.00087 per minute.
Assuming that the initial temperature of the body was 98.6°F (the average temperature of a living human body), we can plug in the values and solve for t:
t = -ln(8.5°F / (98.6°F - 68°F)) / 0.00087
t ≈ 16.5 hours
Therefore, it has been approximately 16.5 hours since the person died.
Step-by-step explanation: