Answer:
x = 1016 in and 18 inStep-by-step explanation:
Area formula
A = wl, where w- width, l- length of rectangleGiven
l = x + 8w = x + 6A = 288 in²As per formula
288 = (x+6)*(x+8)Solving for x
x² + 14x + 48 = 288x² + 14x - 240 = 0x= (-14 ±√14²+4*240)/2x =(- 14 ± 34)/2x = 10,x = -24, discounted as negativeSides of rectangle are
l = 10 + 8 = 18 inw = 10 + 6 = 16 in[tex] \LARGE{ \underline{ \purple{ \rm{Required \: answer:}}}}[/tex]
GiveN:
Length of the rectangle = x + 8Width of the rectangle = x + 6Total area = 288 in²What to find?
Value of xLength and breadth accordingly.Step-wise-Step Explanation:
Area of the rectangle can be calculated by Length × Breadth. We have their values, Simply plug in the formula.
⇒ Length × Breadth = 288 in²
⇒ (x + 8)(x + 6) = 288
⇒ x² + 14x + 48 - 288 = 0
⇒ x² + 14x - 240 = 0
Finding the zeroes by using middle term factorisation,
⇒ x² + 24x - 10x - 240 = 0
⇒ x(x + 24) - 10(x + 24) = 0
⇒ (x - 10)(x + 24) = 0
Then x = 10 or -24. Since the sides cannot be negative, the value of x will be 10 inches (Answer)
Sides of the rectangle:
Length = x + 8 = 18 in.Width = x + 6 = 16 in.Zoe, Latoya, Christina, and Rhoda each used a different method to verify that Negative 2 (3 x minus 12) = negative 6 x + 24. Zoe Latoya Christina Rhoda Step 1 Substitute opposite values of x into both expressions. Substitute the same value of x into both expressions. Substitute opposite values of x into both expressions. Substitute the same value of x into both expressions. Step 2 The expressions are equivalent if the values of the expressions are equal. The expressions are equivalent if the value of one of the expressions is zero. The expressions are equivalent if the values of the expressions are opposites. The expressions are equivalent if the values of the expressions are equal. Whose method can be used to verify that the distributive property was correctly applied to the expression?
Answer:
d) Rhoda's method
Step-by-step explanation:
We are given an Algebraic expressions
Negative 2 (3 x minus 12) = negative 6 x + 24.
= -2(3x - 12) = -6x + 24
Distributive property states that:
a(b - c) = ab - ac
2(3x - 12) = -2 × 3x - (-2 ×12)
= -6x + 24
From the above question, we can deduce the following information:
a) Zoe
Step 1
Substitute opposite values of x into both expressions.
2(3x - 12) = -6x + 24
Lets say x = 1, opposite of 1 = -1
Hence
2(3 × 1 - 12) = -6(-1) + 24
-2(3 - 12) = 6 + 24
-6 + 24 = 6 + 24
18 ≠ 18
Step 2.
The expressions are equivalent if the values of the expressions are equal.
Zoe is wrong
b) Latoya
Step 1
Substitute the same value of x into both expressions.
Step 2
The expressions are equivalent if the value of one of the expressions is zero.
Latoya is wrong
c) Christina
Step 1
Substitute opposite values of x into both expressions.
Step 2
The expressions are equivalent if the values of the expressions are opposites.
Christina is wrong
d) Rhoda
Step 1
Substitute the same value of x into both expressions
-2(3x - 12) = -6x + 24
Let say x = 1
-2(3 × 1 - 12) = -6(1) + 24
-2(3 - 12) = -6 + 24
-6 + 24 = -6 + 24
18 = 18
Step 2
The expressions are equivalent if the values of the expressions are equal.
Therefore, Rhoda method is correct
Answer:
Rhoda
Step-by-step explanation:
sub same values of x into both expressions. The expressions are equivalent if the values of the expressions are equal
Alex is a truck driver for a local retail store. He drove
20,250 miles in 9 months. At this rate, how many months
will it take Alex to drive 6,750 miles?
Its a grid question.
Answer:
3 months
Step-by-step explanation:
in order to find how many months it would take for Alex to drive 6,750 miles we have to find how many miles he drives in a month so you would have to divide 20,250 by 9:
20,250/9 = 2,250 miles per month
you then divide 6,750 by 2,250 to get the number it months it would take him to drive 6,750 miles:
6,750/2,250= 3
It would take him 3 months to drive 6,750 miles
alex will take 3 months to drive 6,750 miles
Here are pairs of equivalent expressions—one in standard form and the other in factored form. Find the missing numbers. Type the answers in the boxes below. 1. x2 + x + and (x+1)(x+17) 2. x2+9x+14 and (x+2 )(x + ) 3. x2−7x+10 and (x−2 )(x − ) 4. x2−9x+20 and (x − )(x − )
1. The missing number is 17.
2. The missing number is 7.
3. The missing number is 5.
4. The missing numbers are 4 and 5.
1. For the expression x^2 + x + ?, we can find the missing numbers by comparing it to the factored form (x+1)(x+17). By expanding the factored form, we get x^2 + 18x + 17. Therefore, the missing number is 17.
2. For the expression x^2 + 9x + 14, we can find the missing numbers by comparing it to the factored form (x+2)(x+?). By expanding the factored form, we get x^2 + 2x + ?x + 2?. We need to find two numbers that multiply to 14 and add up to 9. The numbers that satisfy these conditions are 2 and 7. Therefore, the missing number is 7.
3. For the expression x^2 - 7x + 10, we can find the missing numbers by comparing it to the factored form (x-2)(x-?). By expanding the factored form, we get x^2 - 2x - ?x + 2?. We need to find two numbers that multiply to 10 and add up to -7. The numbers that satisfy these conditions are -2 and -5. Therefore, the missing number is 5.
4. For the expression x^2 - 9x + 20, we can find the missing numbers by comparing it to the factored form (x-?)(x-?). By expanding the factored form, we get x^2 - ?x - ?x + ?. We need to find two numbers that multiply to 20 and add up to -9. The numbers that satisfy these conditions are -4 and -5. Therefore, the missing numbers are 4 and 5.
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This is an example of an Undamped Forced Oscillation where the phenomenon of Beats Occurs.
Find the solution of the initial value problem:
x''+33.64x=4cos(6t),x(0)=x'(0)=0
x(t)=
Undamped forced oscillation and Beats Phenomenon Undamped forced oscillation:In an undamped forced oscillation, the amplitude of oscillation can become very large if the driving force is close to the natural frequency of the oscillator. Such oscillations are observed, for example, in the vibrations of a guitar string when it is plucked.
The energy input from the plucking causes the string to vibrate at its natural frequency.Beats phenomenon:Beats are the oscillations that result when two sound waves of slightly different frequencies interfere with one another. They are the result of the difference between the frequencies of the two waves. Beats are commonly observed in music and are a fundamental concept in sound and acoustics.
Now, let's find the solution of the given initial value problem:The given equation is x''+33.64x=4cos(6t) with x(0)=0 and x'(0)=0.To solve this, first, we need to find the homogeneous solution, xh(t) by solving the auxiliary equation as:r²+33.64=0r = ±√(-33.64) = ±5.8jAs the roots are imaginary, the general solution for the homogeneous equation is:xh(t) = c1cos(5.8t) + c2sin(5.8t)where c1 and c2 are constants.
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A business orders 330 flowers for their employees on Valentine's Day. Roses cost
$4.50 each, carnations cost $3.00 each, and lilies cost $2.50 each. There are 20
more lilies than roses. The total of the order came to $1,080.00. How many of each
type of flower were ordered? Write a system of equations that represents the
scenario.
Answer:
Roses = x = 100
Carnations = y = 110
Lilies = z = 120
Step-by-step explanation:
Roses = $4.50
Carnations = $3.00
lilies = $2.50
Total flowers ordered = 330
Total cost = $1,080
Let
Roses = x
Carnations = y
Lilies = z
x + y + z = 330
4.50x + 3y + 2.50z = 1080
There are 20
more lilies than roses
z = x + 20
Substitute z = x + 20 into the equations
x + y + (x + 20) = 330
4.50x + 3y + 2.50(x + 20) = 1080
x + y + x + 20 = 330
4.50x + 3y + 2.50x + 50 = 1080
2x + y = 330 - 20
7x + 3y = 1080 - 50
2x + y = 310 (1)
7x + 3y = 1030 (2)
Multiply (1) by 3
6x + 3y = 930 (3)
7x + 3y = 1030 (2)
Subtract (3) from (2)
7x - 6x = 1030 - 930
x = 100
Substitute x = 100 into (1)
2x + y = 310
2(100)+ y = 310
200 + y = 310
y = 310 - 200
= 110
y = 110
Substitute the value of x and y into
x + y + z = 330
100 + 110 + z = 330
210 + z = 330
z = 330 - 210
= 120
z = 120
Roses = x = 100
Carnations = y = 110
Lilies = z = 120
Section A (15 Marks) Risk and Return State Pr(ₐ) rₐ Pr(ᵦ) rᵦ
1 0.2 10% 0.25 12%
2 0.6 15% 0.40 20%
3 0.2 20% 0.35 18%
Given the probability distribution above, determine (Calculate) and compare the: 1. Expected return (means) 2. Variance
3. Standard deviation
Security B has a higher expected return of 17.2%, but it also has a higher risk as measured by its higher variance and standard deviation. On the other hand, Security A has a lower expected return of 12%, but it also has a lower risk as measured by its lower variance and standard deviation.
The expected return, variance, and standard deviation for the given probability distribution are as follows: 1. Expected Return.
The expected return is the average of all the possible returns, weighted by the probability of each return occurring. It can be calculated as follows:
Expected Return of Security A = (0.2 x 10%) + (0.6 x 15%) + (0.2 x 20%)= 12%Expected Return of Security B = (0.25 x 12%) + (0.4 x 20%) + (0.35 x 18%)= 17.2%.
Thus, Security B has a higher expected return of 17.2%, compared to Security A's expected return of 12%.2..
VarianceThe variance measures the average deviation of each return from the expected return. It is calculated as follows:Variance of Security A = [(0.2 x (10% - 12%)²) + (0.6 x (15% - 12%)²) + (0.2 x (20% - 12%)²)] = 1.44%.
Variance of Security B = [(0.25 x (12% - 17.2%)²) + (0.4 x (20% - 17.2%)²) + (0.35 x (18% - 17.2%)²)] = 7.57%Thus, Security B has a higher variance of 7.57%, compared to Security A's variance of 1.44%.3.
Standard DeviationThe standard deviation is the square root of the variance and measures the dispersion of the returns around the expected return. It is calculated as follows:
Standard Deviation of Security A = √1.44% = 1.2%Standard Deviation of Security B = √7.57% = 2.75%Thus, Security B has a higher standard deviation of 2.75%, compared to Security A's standard deviation of 1.2%.
In conclusion, Security B has a higher expected return of 17.2%, but it also has a higher risk as measured by its higher variance and standard deviation. On the other hand, Security A has a lower expected return of 12%, but it also has a lower risk as measured by its lower variance and standard deviation.
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The greatest common factor of 60w5y3 and 78 wy2 is
6 wy2
6 w5y3
13 w5y3
2 wy2
Answer:
is that a question
Step-by-step explanation:
Dominique bought 7.5 pounds of peanuts at $4.00 per pound. How much should she have paid?
Answer:
30
Step-by-step explanation:
Dominique should have paid $30
ex: 7.5 x 4.00= 30
The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to each other and to the original triangle.
The length of the altitude is 9 units.
To solve this problem, we can use the geometric relationship in a right triangle between the lengths of the altitude, the hypotenuse, and the segments it divides.
Let the length of the altitude be 'h'. According to the problem, the altitude divides the hypotenuse into segments of lengths 6 and 9. Let's denote the lengths of these segments as 'x' and 'y', respectively.
Using the properties of similar triangles, we can set up the following proportion:
h / x = y / (x + y)
Cross-multiplying the proportion:
h(x + y) = xy
Expanding:
hx + hy = xy
Rearranging the equation:
hx - xy = -hy
Factoring out 'h':
h(x - y) = -hy
Dividing both sides by (x - y):
h = -y
From the given information, we know that the lengths of the segments are 6 and 9. So, we substitute x = 6 and y = 9 into the equation:
h = -(9)
h = -9
The length of the altitude is 9 units.
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Question
The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 6 and 9. What is the length of the altitude?
hello I'm in algebra 1 and I'm not understanding graphing using point slope form
At the bank teller's window, arrivals and service times are randomly distributed (Poisson and exponential distributions, respectively). There is only one teller at the window. If the arrival rate is 8 customers per hour, and the service rate is 15 customers per hour, what is the utilization of the teller, as a percentage? (It is a single channel, single server, single phase, unlimited waiting space model). (calculate answer to two decimal places)
The utilization of the teller is approximately 53.33%.
To calculate the utilization of the teller, we need to compare the arrival rate and the service rate. The utilization represents the fraction of time the server (teller) is busy serving customers.
The arrival rate is given as 8 customers per hour, which means that, on average, 8 customers arrive at the teller's window in one hour. This follows a Poisson distribution.
The service rate is given as 15 customers per hour, indicating that, on average, the teller is able to serve 15 customers in one hour. The service times follow an exponential distribution.
Utilization is calculated as the ratio of the arrival rate to the service rate. In other words:
Utilization = Arrival rate / Service rate
Substituting the given values:
Utilization = 8 / 15 ≈ 0.5333
To express this as a percentage, we multiply the result by 100:
Utilization = 0.5333 * 100 ≈ 53.33%
Therefore, the utilization of the teller in this scenario is approximately 53.33%. This means that, on average, the teller is occupied serving customers about 53.33% of the time, and the remaining time is idle or available for serving new customers.
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when calculating the impedance of a series r-l circuit, the total . a. series reactance is equal to the sum of the reactances in series b. resistance is equal to the sum of the resistances in series c. impedance is equal to the complex sum of the total series resistance and total series reactance d. all of the above
When calculating the impedance of a series R-L circuit, the total impedance is equal to the complex sum of the total series resistance and total series reactance. Therefore, the correct option is (c) impedance is equal to the complex sum of the total series resistance and total series reactance.
A series R-L circuit contains resistance and inductance components connected in series across an AC source. The voltage across both the resistance and the inductor is the same in a series R-L circuit. It is the total current through the circuit that is in phase with the resistor's voltage and 90° out of phase with the inductor's voltage. The inductive reactance is denoted by XL, which is a function of the inductor's value and the frequency of the AC supply.In an R-L circuit, there are two types of impedances: total impedance and phase angle. The total impedance Z is equal to the complex sum of the circuit's resistance and reactance. It is measured in ohms (Ω).Resistance is equal to the sum of resistances in series, and series reactance is equal to the sum of reactances in series.
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Find the measure of angle J in the isosceles triangle.
62 degrees
31 degrees
38 degrees
76 degrees
Answer:
76 degrees
Step-by-step explanation:
JK=KL and their angles are equal hence <KJL and <KLJ are the same.
sum of angle in triangles is 180 degrees.
x°+x° +28°=180°
x= 76 degrees
what us 3 1/3 Divided by 4
Answer:
0.8333333
Step-by-step explanation:
Answer: 7/8
-------------------
Solve this problem, and identify the percent, amount, and base. What percent of 50 is 20 ? Percent =40, Amount =20, Base =50
Percent =40, Amount =50, Base =20
Percent =50, Amount =10, Base =20
Percent =20, Amount =10, Base =50
The percentage of 50 that is 20 is 40 percent. The correct option therefore is the first option;
Percent = 40, Amount = 20, Base = 50What is the formula for finding a percentage?The percentage of an amount within a base can be found using the formula;
Percent = (Amount/Base) × 100
Therefore, the percentage an amount represents in a base can therefore be found using the above formula.
The percentage required is the percentage in 50 represented by 20
Therefore the percentage is; Percent = (20/50) × 100 = 40%
The correct option is therefore;
Percent = 40, Amount = 20, Base = 40
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Y-3=2(x+1)
Complete the missing value in the solution to the equation.
(-1, )
y=3 if x=-1
Step-by-step explanation:
First, plug in -1 for x then add inside parentheses and distribute:
y-3=2(-1+1)
y-3=2(0)
y-3=0
Next, add 3 to both sides of the equation to get the answer for y:
y-3=0
y+3=+3
y=3
Final answer:
(-1, 3)
To find the product of a 3-digit number and a 1-digit number,
you can multiply the ones, multiply the tens, multiply the
hundreds, and find the sum of each
Answer:
each number is the answer
Step-by-step explanation:
02.Cl.Algebrala
What is the value of a in the following equation?
-2(3a - 2) = (7 - 3a)
o 1/5
O 1/3
O3
O 5
Answer:
a = -1
Step-by-step explanation:
-2(3a - 2 ) = 7 - 3a-6a + 4 = 7 - 3a-6a = (7 - 4 ) - 3a-6a = 3 - 3a-6a + 3a = 3-3a = 3 a = -1-2 (3a-2)=(7-3a)
-6a+4=7-3a
-6a+3a=7-4
-3a=3
a=3/-3
a= -1
value of a is -1
The seventh-grade class at Morton Ranch Junior High has a goal of selling 300 tickets to the annual teacher versus students basketball game. By the end of the week, they had sold 30% of the tickets. How many tickets had they sold?
Answer:
I'm pretty sure the answer would be 90
Step-by-step explanation:
300 x 0.3 = 90
10 points
Which equation best represents the relationship between the x and y values?
Х
Y
-2
7
2
-5
4
-11
6.
-17
10
-29
A y = x + 9
B y = x2 + 3
Cy=-3x + 1
Dy = x-7
Answer: C) y = -3x + 1
Step-by-step explanation:
x y
-2 7
2 -5
4 -11
6 -17
10 -29
Choose any two coordinates to find the slope: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
m = -6/2
= -3
Choose any point and plug it into the Point-Slope formula: [tex]y-y_1=m(x-x_1)[/tex]
y - 7 = -3(x + 2)
y - 7 = -3x - 6
y = -3x + 1
please help me I'm being timed
The nth term of the sequence is n-4.
a) Work out the first three terms of the sequence.
b)Work out the tenth term of the sequence.
Answer:
see explanation
Step-by-step explanation:
To find the first 3 terms, substitute n = 1, 2, 3 into the n th term formula, that is
n = 1 : 1 - 4 = - 3
n = 2 : 2 - 4 = - 2
n = 3 : 3 - 4 = - 1
The first 3 terms are - 3, - 2, - 1
Similarly find the tenth term by substituting n = 10 into the formula
10 - 4 = 6
The tenth term is 6
Mr. Weimer budgets 15 % of each pay check for savings. his check is for $164 . how much does he save ?
Answer:
$24.60
Step-by-step explanation:
$164 x .15= $24.60
Answer:
24.6
Step-by-step explanation:
15% = 0.15
164×0.15=24.6
24.6 is what he saves out of 164$
Matina made deposits of $2,000 at the beginning of each year for four years. The rate she earned is 5% annually. What's the value of Martina's account in four years?
The value of Matina's account in four years, considering the $2,000 deposits at the beginning of each year and a 5% annual interest rate, would be approximately $8,620.25.
To calculate the value of Matina's account in four years, we can use the formula for the future value of an ordinary annuity.
The formula is:
[tex]FV = P \times [(1 + r)^n - 1] / r[/tex]
Where:
FV is the future value of the annuity
P is the periodic payment or deposit amount
r is the interest rate per period
n is the number of periods.
P = $2,000 (deposit amount)
r = 5% = 0.05 (annual interest rate)
n = 4 (number of years)
Plugging in the values into the formula:
[tex]FV = $2,000 \times[(1 + 0.05)^4 - 1] / 0.05.[/tex]
Simplifying the expression:
[tex]FV = $2,000 \times [1.05^4 - 1] / 0.05[/tex]
Calculating the exponential term:
[tex]1.05^4\approx 1.21550625[/tex]
Plugging in the calculated value:
[tex]FV = $2,000 \times (1.21550625 - 1) / 0.05[/tex]
[tex]FV ≈ $2,000 \times 0.21550625 / 0.05[/tex]
FV ≈ $8,620.25
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A package of 3 pairs of insulated costs $22. 47 What is the unit price of the pairs of gloves?
Answer:
7.49
Step-by-step explanation:
22.47 divided by 3
1.14 x 10^7/ 3.8 x 10^-7=
Answer:
3x10^23
Step-by-step explanation:
thats what i got on my calculator
Answer:
[tex]3 \times {10}^{14} [/tex]
Step-by-step explanation:
[tex] \frac{1.14 \times {10}^{7} }{3.8 \times {10}^{ - 7} } \\ = 3 \times {10}^{7 - ( - 7)} \\ = 3 \times {10}^{7 + 7} \\ = 3 \times {10}^{14} [/tex]
.............................................................................
Alex has a collection of coins, consisting of nickels and dimes that total to
$3.90. If the number of dimes is 4 more than 3 times the number of
nickels, find the number of each kind of coin.
Answer pleaseeeeee
Answer:
10 nickels and 34 dimes
Step-by-step explanation:
What is the value of x?
6 (-3 -x) - 2x = 14
Answer:
x= -5 hope this helps
Step-by-step explanation:
did the math
. Thomas bought two fans for ₹ 725 each .He sold one of them at a gain of 8% and the other at a loss of 4%. Find his gain or loss on the whole transaction.
Answer:
So i actually had the same question last year and a friendo sent me the answer its not mine originally so please dont give me brainliest but i hope this helps you, just like it helped me
Step-by-step explanation:
