Answer:
(x+3)
Step-by-step explanation:
Volume = Base area × height
Base area = x²+5x+6
= x²+2x+3x+6
= x(x+2)+3(x+2)
= (x+2)(x+3)
Since the length is the longer side, length = (x+3)
Dimensions of the box are:
(x+2)×(x+3)×(x+4)
An inelastic collision occurs between a large truck and smaller sedan. Calculate the final velocity of the objects and explain the direction they will be traveling with the following data from before the collision: Small sedan mass = 1300 kg initial velocity = 20 m/s Truck mass = 7100 kg Initial Velocity 15 m/s
The final velocity is 15.8 m/s in the forward direction
Step-by-step explanation:
An inelastic collision occurs when the two object after the collision stick together.
In any case, the total momentum of the system is conserved before and after the collision, in absence of external forces. Therefore, we can write:
[tex]p_i = p_f\\m u + MU = (m+M)v[/tex]
where in this problem:
m = 1300 kg is the mass of the small sedan
u = 20 m/s is the initial velocity of the small sedan
M = 7100 kg is the mass of the truck
U = 15 m/s is the initial velocity of the truck
v is the final combined velocity of the small sedan + truck
Here we have taken both the velocity of the sedan and the truck in the positive (forward) direction
Solving the equation for v, we find the final velocity:
[tex]v=\frac{mu+MU}{m+M}=\frac{(1300)(20)+(7100)(15)}{1300+7100}=15.8 m/s[/tex]
And since the sign is positive, this means that is direction is the same as the initial direction of the sedan and the truck, so forward.
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Suppose you are choosing between two roads. The first route is 40 miles at 25 mph, and the second road is 65 miles at 55 mph. Which route would get you there faster, and in what amount of time?
The second route, in 1.6 hours
B. The first route, in 1.6 hours
C. The first route, in 1.18 hours
D. The second route, in 1.18 hours
Answer:
D. The second route, in 1.18 hours
Step-by-step explanation:
The appropriate relation is ...
time = distance/speed
The time required on the first route is ...
time1 = (40 mi)/(25 mi/h) = 40/25 h = 1.6 h
The time required on the second route is ...
time2 = (65 mi)/(55 mi/h) = 65/55 h = 1 2/11 h ≈ 1.18 h
__
The second route requires a shorter time, so will get you there faster. The second route will get you there in 1.18 hours.
What is the pressure difference Δp=pinside−poutside? Use 1.28 kg/m3 for the density of air. Treat the air as an ideal fluid obeying Bernoulli's equation.
This is an incomplete question, here is a complete question.
A hurricane wind blows across a 7.00 m × 12.0 m flat roof at a speed of 150 km/h.
What is the pressure difference Δp = p(inside)-p(outside)? Use 1.28 kg/m³ for the density of air. Treat the air as an ideal fluid obeying Bernoulli's equation.
Answer : The pressure difference will be, [tex]1.11\times 10^3Pa[/tex]
Step-by-step explanation :
As we are given:
Speed = 150 km/h = 41.66 m/s
Density = [tex]\rho=1.28kg/m^3[/tex]
Area = A = 7.00 m × 12.0 m
Formula used :
[tex]\Delta P=\frac{1}{2}\times \rho \times v^2[/tex]
Now put all the given values in this formula, we get:
[tex]\Delta P=\frac{1}{2}\times (1.28kg/m^3)\times (41.66m/s)^2[/tex]
[tex]\Delta P=1.11\times 10^3Pa[/tex]
Thus, the pressure difference will be, [tex]1.11\times 10^3Pa[/tex]
A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 24 feet. What should the rectangle's dimensions be in order to maximize the area of the window and, therefore, allow in as much light as possible?
To maximize the area of the Norman window, solve for the dimensions of the rectangle. Substitute the expression for 'h' in terms of 'w' into the area formula. Take the derivative of A with respect to 'w', set it equal to zero, and solve for 'w'.
Explanation:To maximize the area of the Norman window, we need to find the dimensions of the rectangle. Let's denote the width of the rectangle as 'w' and the height as 'h'. The perimeter of the rectangle can be expressed as 2w + h + πh = 24 feet. Rearranging the equation, we have (2 + π)h + 2w = 24. Since we want to maximize the area, we can solve for 'h' in terms of 'w' using this equation.
Next, we can substitute the expression for 'h' in terms of 'w' into the area formula for the window, which is A = wh + (π/4)w^2. Simplifying this expression, we get A = (w(2 + πw))/4. To find the dimensions that maximize the area, we can take the derivative of A with respect to 'w', set it equal to zero, and solve for 'w'. This will give us the width of the rectangle. Once we have the width, we can substitute it back into the equation for 'h' to find the height.
By solving these equations, we can find the dimensions of the rectangle that will maximize the area of the Norman window, allowing in as much light as possible.
How many possible combined page count and color choices are possible? How does this number relate to the number of page size choices and to the number of color choices
ANSWER:
1. How many possible combined page count and color choices are possible?
There are 3 choices for page size and 4 choices for color, and also, there are 3*4=12 possibilities to combine page size and color.
Number possibilities to combine and number of choices for size is: 12:3=4:1
Number of possibilities to combine and number of choices for color is 12:4=3:1
2. How does this number relate to the number of page size choices and to the number of color choices
There are 12 possibilities to combine size and color.
Number of possibilities to combine and number of choices for size is 4:1
Number of possibilities to combine and number of choices for color is 3:1
Answer:
We have 12 possibilities to combine page size and color.
Number of possibilities and number of choices is 12:4 that is 3:1
Step-by-step explanation:
have a nice day.
If the probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during the next month, what is the greatest possible value for the probability that neither of these two events will occur.
P(A) =0.54
P(B)= 0.68
P'(A)= 1-0.54 = 0.46
P'(B)= 1- 0.68 = 0.32
The probability of neither of both event will occur:
= P'(A)×P'(B)
=0.46 × 0.32
=0.1472
If you have a bank account that is modeled bybthe following equation, how much money would you have after 10 years. A=5000e 0.10t. Using the problem solving Temple with rational functions.
The money after 10 years is $ 13591.4091
Solution:
Given that,
If you have a bank account that is modeled by the following equation:
[tex]A = 5000e^{0.10t}[/tex]
To find: Money after 10 years
How much money would you have after 10 years
Substitute t = 10 in above given equation
[tex]A = 5000 \times e^{0.10 \times 10}\\\\A = 5000 \times e^{1}\\\\A = 5000 \times 2.71828\\\\A = 13591.4091[/tex]
Thus money after 10 years is $ 13591.4091
a. Is the statement "Every elementary row operation is reversible" true or false? Explain. A. True, because interchanging can be reversed by scaling, and scaling can be reversed by replacement. B. False, because only scaling and interchanging are reversible row operations. C. True, because replacement, interchanging, and scaling are all reversible. D. False, because only interchanging is a reversible row operation.
The statement "Every elementary row operation is reversible" is true because interchanging can be reversed by scaling, and scaling can be reversed by replacement (Option A is correct).
The statement "Every elementary row operation is reversible" is true.
The correct choice is: A. True, because interchanging can be reversed by scaling, and scaling can be reversed by replacement.
- Interchanging rows (row swapping) can be reversed by another interchange.
- Scaling a row by a non-zero scalar can be reversed by scaling it by the reciprocal of that scalar.
- Replacement operations (adding or subtracting multiples of one row from another) can also be reversed by adding or subtracting the same multiples in the opposite direction.
So, all three elementary row operations (replacement, interchanging, and scaling) are reversible, which makes option A the correct choice.
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The statement 'Every elementary row operation is reversible' is true. All the three types of elementary row operations, i.e., scaling, interchanging, and replacement, can be reversed using appropriate methods.
Explanation:The statement 'Every elementary row operation is reversible' is indeed true. The three types of elementary row operations, i.e., scaling, interchanging, and replacement, are all reversible. Scaling can be reversed by multiplying the row by the reciprocal of the scale factor. Interchanging rows can be undone by simply interchanging them again. Replacement can be reversed by applying a replacement operation with the opposite sign.
For example, if you multiply a row by a factor of 3 (scaling), you can reverse this by multiplying the row by 1/3. If you interchange row 1 and row 2, you can reverse this by interchanging these two rows again. Finally, if you replaced row 1 by adding 2*row 2 to it, you could reverse this by replacing row 1 by subtracting the same 2*row 2 from it.
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A test of intelligence is given to a subject. The subject scores 110 on the first administration. Six months later, the same subject is given the same test again and receives a score of 75. After another six months has passed, the subject is given the test one last time and receives a score of 138. What conclusions can be drawn from these scores?The scores are not valid.
Answer:
True, the scores are not valid.
Step-by-step explanation:
The test supposed to be measuring intelligence. We can assume that the intelligence of most people relatively stable (will not change too much over a short amount of time), and can expect it should go upward with brain growth and education. But the test seems to give a huge decrease from the first and second results. Then the third result is a huge increase that even higher than the first test.
We don't know the true value of the subject, but seeing the huge gap for every repetition we can tell that the test result lacks precision.
i need help asap please dont type random anwsers, that will result in it being deleted. GIVING BRAINLIEST ONLY TO CORRECT, INCORRECT IS DELETED.
Answer:
The area of the rectangle TOUR is 80.00 unit².
Step-by-step explanation:
The area of a rectangle is computed using the formula:
[tex]Area\ of\ a\ Rectangle=length\times width[/tex]
Since the dimensions of the rectangle are not provided we can compute the dimensions using the distance formula for two points.
The distance formula using the two point is:
[tex]distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
Considering the rectangle TOUR the area formula will be:
Area of Rectangle TOUR = TO × OU
The co-ordinates of the four vertices of a triangle are:
T = (-8, 0), O = (4, 4), U = (6, -2) and R = (-6, -6)
Compute the distance between the vertices T and O as:
[tex]TO=\sqrt{(4-(-8))^{2}+(4-0)^{2}}\\=\sqrt{12^{2}+4^{2}} \\=\sqrt{160} \\=4\sqrt{10}[/tex]
Compute the distance between the vertices O and U as:
[tex]OU=\sqrt{(6-4)^{2}+(-2-4)^{2}}\\=\sqrt{2^{2}+6^{2}} \\=\sqrt{40} \\=2\sqrt{10}[/tex]
Compute the area of rectangle TOUR as follows:
[tex]Area\ of\ TOUR=TO\times OU\\=4\sqrt{10}\times 2\sqrt{10}\\=80\\\approx80.00 unit^{2}[/tex]
Thus, the area of the rectangle TOUR is 80.00 unit².
Answer:
This answer is just here so you can give the other guy brainliest, as there can only be brainliest if there are two answers.
Step-by-step explanation:
Give that guy brainliest
The hourly operating cost of a certain plane, which seats up to 295 passengers, is estimated to be $3,945. If an airline charges passenger a fare of $95 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x. P(x) = Specify the domain. 0 lessthanorequalto x lessthanorequalto infinity 0 lessthanorequalto x lessthanorequalto 295 0 < x < 295 295 lessthanorequalto x lessthanorequalto infinity What is the least number of passengers it must carry to make a profit? The Metropolitan Company sells its latest product at a unit price of $3. Variable costs are estimated to be 50% of the total revenue, while fixed costs amount to $6,600 per month. How many units should the company sell per month to break even, assuming that it can sell up to 5,000 units per month at the planned price? units
Answer:
42 passengers 4400 unitsStep-by-step explanation:
Please refer to the picture below
A three-phase lesson format provides a structure for students to have inquiry on a topic, engage in the content through action and discussion and time to reflect and make connections. What statement below demonstrates the Before related agendas?
A) Be sure the task is understood.
B) Let go
C) Provide extensions.
D) Identify future problems.
Answer:
A) Be sure the task is understood.
Step-by-step explanation:
The principle "Make sure the mission is understood, performed, and achieved."
Another way we talk about this principle in the Navy is through the idea of "intrusive leadership." In some respects both "micromanagement" and "intrusive leadership" sound terrible.
Think about certain great managers and leaders you have had in your career yet again. Probability are they will be the ones who asked you those difficult questions, too.
They moved everyone to new technical levels, and eye for detail. When you said you knew what you were doing or when you announced the progress of a project, they didn't necessarily take it to face value.
Do people who work for non-profit organizations differ from those who work at for-profit companies when it comes to personal job satisfaction? Separate random samples were collected by a polling agency to investigate the difference. Data collected from 422 employees at non-profit organizations revealed that 377 of them were "highly satisfied." From the for-profit companies, 431 out 518 employees reported the same level of satisfaction. Find the standard error of the difference in sample proportions.
Answer:
0.0223
Step-by-step explanation:
Given the following data x(1) = 377, n(1) = 422, x(2) = 431, n(2) = 518
The sample proportion is the number of success divided by the sample.
P(1) = x(1)/n(1) = 377/422 = 0.8934
P(2) = x(2)/n(2) = 431/518 = 0.8320
Formular for the standard error of the difference in sample proportions
S.E = √p(1)q(1)/n(1)+P(2)q(2)/n(2)
S.E = √p1(1-P1)/n1+P2(1-P2)/n2
By substitution we have that,
S.E = √0.8934(1-0.8934)/422+0.8320(1-0.8320)/518
S.E = 0.0223
X minus 12 is 30 what’s the answer
Answer:
x=42
Step-by-step explanation:
x-12=30
x=30+12
x=42
To solve for x in this equation, we want to get x by itself on the left side of the equation. Since 12 is being subtracted from x, to get x by itself, we need to add 12 to the left side of the equation. If we add 12 to the left side, we must also add 12 to the right side.
On the left side, -12 and +12 cancel each other out so we are simply left with x. On the right side, 30 + 12 is 42 so we have x = 42.
It's important to understand that we can check our answer by substituting 42 back into the original equation.
So we have (42) - 12 = 30.
42 - 12 is 30 so we have 30 = 30 which is a true statement so our answer, x = 42, is correct.
Melody has hired a new accountant. He has gathered her pay stubs and is trying to determine how many CDs were sold during each month of the previous year. Her pay stub for June indicates that she made $4,889 in that month. Write an equation her accountant could use to determine how many CDs were sold in June
Answer:
The required equation is [tex]4889=4850 +3n[/tex].
Step-by-step explanation:
Consider the provided information.
Melody has a new job recording for the All-Time Favorites record label.
She is paid a monthly base salary of $plus $3 for each CD sold.
Her pay stub for June indicates that she made $4,889 in that month.
Let n represents the number of CDs she sold.
Therefore, the required equation is [tex]4889=4850 +3n[/tex].
x-6y +4z=-12
x+y-4z=12
2x + 2y + 5z =-15
Systems of equations with three variables and three equations
Answer:
x = 0 , y = 0 , z = -3
Step-by-step explanation:
Solve the following system:
{x - 6 y + 4 z = -12 | (equation 1)
x + y - 4 z = 12 | (equation 2)
2 x + 2 y + 5 z = -15 | (equation 3)
Swap equation 1 with equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
x + y - 4 z = 12 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Subtract 1/2 × (equation 1) from equation 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - (13 z)/2 = 39/2 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Multiply equation 2 by 2/13:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Subtract 1/2 × (equation 1) from equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
0 x - 7 y + (3 z)/2 = -9/2 | (equation 3)
Multiply equation 3 by 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
0 x - 14 y + 3 z = -9 | (equation 3)
Swap equation 2 with equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y + 3 z = -9 | (equation 2)
0 x+0 y - z = 3 | (equation 3)
Multiply equation 3 by -1:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y + 3 z = -9 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 3 × (equation 3) from equation 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 2 by -14:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 2 × (equation 2) from equation 1:
{2 x + 0 y+5 z = -15 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 5 × (equation 3) from equation 1:
{2 x+0 y+0 z = 0 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 1 by 2:
{x+0 y+0 z = 0 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Collect results:
Answer: {x = 0 , y = 0 , z = -3
To solve the given system of equations, use the method of elimination to eliminate one variable at a time and solve for the remaining variables.
Explanation:To solve the system of equations:
x - 6y + 4z = -12
x + y - 4z = 12
2x + 2y + 5z = -15
We can use the method of substitution or elimination. Let's use the method of elimination:
Multiply the second equation by 2:Multiply the third equation by 3:Add the new second and third equations to the first equation:Solve the resulting equation:Therefore, the solution is x = -5, y = 4, and z = 1.
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Evaluate 13−0.5w+6x13-0.5w+6x 13−0.5w+6x 13, minus, 0, point, 5, w, plus, 6, x when w=10w=10 w=10 w, equals, 10 and x=12x=\dfrac12 x= 2 1 x, equals, start fraction, 1, divided by, 2, end fraction .
Answer: 6x^13-1.5w+156x+13 is the answer to the first equation and is that another equation?
The expression 13 - 0.5w + 6x evaluates to 11 when substituting w=10 and x=1/2.
Explanation:The problem is to evaluate the expression 13 - 0.5w + 6x given the values w=10 and x=1/2. Following the order of operations, we first substitute the given values into the expression.
13 - 0.5(10) + 6(1/2) = 13 - 5 + 3 = 11.
The result of the evaluated expression is 11.
1. Type an equation in the equation editor that uses 2 fractions with parentheses around one of them. Example: [tex]\frac{2}{3}[/tex] + (- [tex]\frac{1}{2}[/tex]) = [tex]\frac{4}{6} - \frac{3}{6} = \frac{1}{6}[/tex]
2. Type an expression that has two terms with exponents, and one with a square root. Example: [tex]2^{3}[/tex] + [tex]9^{2}[/tex] + [tex]\sqrt{16}[/tex]
3. Type a compound inequality similar to the one below, but with different numbers. It should be set up the same, with all the symbols in the same places. [tex](\frac{3}{5} )^{2}[/tex] · [tex]^{3} \sqrt{10} \leq x^{3} - 2x + 5 \leq \sqrt{\frac{1}{3}[/tex]
Answer:
i) [tex]\frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}[/tex] [tex]\Rightarrow[/tex] \frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}
ii)[tex]4^{3} + 8^{2} + \sqrt{9}[/tex] [tex]\Rightarrow[/tex] 4^{3} + 8^{2} + \sqrt{9}
iii) [tex](\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}} \Rightarrow \hspace{0.2cm}[/tex] (\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}}
Step-by-step explanation:
i) [tex]\frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}[/tex] [tex]\Rightarrow[/tex] \frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}
ii)[tex]4^{3} + 8^{2} + \sqrt{9}[/tex] [tex]\Rightarrow[/tex] 4^{3} + 8^{2} + \sqrt{9}
iii) [tex](\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}} \Rightarrow \hspace{0.2cm}[/tex] (\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}}
The US GDP (Gross Domestic Product) for 2014 was a reported 17.555 trillion dollars. The current US population is about 320 million people. Round all answers to the nearest hundredth.
Answer:
1. 1.76x10^13,
2. 3.20x10^8,
3. 5.5x10^4
Step-by-step explanation:
Answer:
Step-by-step explanation:
GDP/POPULATION
1755x10^13/3.2x10^8 = .05484x10^5
=5.484x10^4
= 5.49x10^4
Triangle A''B''C'' is formed by a reflection over x=-3 and dilation by a scale factor of 3 from the origin. Which equation shows the correct relationship between ABC and A''B''C'?
Answer: Segments AB / A"B" = √13 / 2 x √13
Step-by-step explanation:
The Triangle's vertices are at points A(-3,3), B(1,-3) and C(-3,-3).
• The reflection over x = 1 shows vertices A, B and C below:
A(-3,3)→A'(5,3);
B(1,-3)→B'(1,3);
C(-3,-3)→C'(5,-3).
• The Dilation by a scale factor of 2 from the origin is expressed as:
(x,y)→(2x,2y)
Therefore,
A'(5,3)→A''(10,6);
B'(1,3)→B''(2,6);
C'(5,-3)→C''(10,-6)
The attachment below completed the calculations and shows the segment in a simple graph.
!!!!URGENT!!!!
Find the first 3 Iterations of the function here: g(x)=1/3x+1 if you have an initial value of 2.
An example on how to complete it below.
Answer:
1st it: g(2)=1/3(2)+1=0.67+1=1.67
2nd it: g^2(2)=1/3(1.67)+1=0.56+1=1.56
3rd it: g^3(2)=1/3(1.56)+1=0.52+1=1.52
Answer:
The first three iterations are 1.67, 1.56 and 1.52
Step-by-step explanation:
Given the function g(x)=1/3x+1
To get the first threw iteration with initial value of x = 2
First iteration at x= 2:
g(2) = 2/3+1
g(2) = (2+3)/3
g(2) = 5/3 = 1.67
Second iteration will be when x = g(2) = 5/3
g²(2) = g(5/3) = 1/3(5/3) + 1
g²(2) = g(5/3) = 5/9 + 1
g²(2) = g(5/3) = 14/9 = 1.56
Third iteration will be at when
x = g²(2) = 14/9
g³(2) = g(14/9) = 1/3(14/9) + 1
g³(2) = g(14/9) = 14/27 + 1
g³(2) = g(14/9) = 41/27 = 1.52
The first three iterations are 1.67, 1.56 and 1.52
The number of people estimated to vote in an election was 7,000. The actual number of people who voted was 5,600.
What is the question that is being asked?
The perimeter of a rectangular note card is 18 inches. The area is 18 square inches. What are the dimensions of the note card?
Answer:
6 by 3
Step-by-step explanation:
a rectangle as 2 equal sides. so if we know that it is 6 by 3, then 6+6+3+3
=12+6=18
the area of a rectangle is base * height. so 6 * 3 = 18
Answer: the length is 6 inches and the width is 3 inches.
Step-by-step explanation:
Let L represent the length of the rectangular note card.
Let W represent the width of the rectangular note card.
The formula for determining the area of a rectangle is expressed as
Area = L × W
Area of the note card would be
LW = 18 - - - - - - - - - - - - 1
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
Perimeter of the note card would be
2(L + W) = 18
(L + W) = 9 - - - - - - - - - - - - 2
Substituting L = 9 - W into equation 1, it becomes
W(9 - W) = 18
9W - W² = 18
W² - 9W + 18 = 0
W² - 6W - 3W + 18 = 0
W(W - 6) - 3(W - 6) = 0
W - 6 = 0 or W - 3 = 0
W = 6 or W = 3
Substituting W = 3 into equation 1, it becomes
3L = 18
L = 18/3 = 6
A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 6.6 days. Its average brightness is 2.6 and the brightness changes by /-0.6. Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time t, where t is measured in days:
(a) Find the rate of change of the brightness after t days.
(b) Find the rate of increase after one day.
Answer:
a) Rate of brightness after t days = B(t) = 2.6 + 0.6sin(2×3.142 t /6.6)
b) 0.57
Step-by-step explanation:
Given
Number of days=6,6 days
Average brightness =2.6
B(t)= 2.6 + 0.6 sin (2× 3.142t/6.6)
b) B(1day) = 0.6 ×(2×3.142/6.6)cos (2×3.142/6.6)
B(1 day) = 0.6 × (6.248/6.6)cos 0.952
B(1 day) =0.6 × 0.952 ×0.9999
B(1day) = 0.5711
= 0.57
A pizza chain was willing to pay $1 to each person interviewed about his or her likes and dis- likes of types of pizza crust. Of the people interviewed, 200 liked thin crust, 270 liked thick crust, 70 liked both, and 50 did not like either type of crust. What was the total cost of the survey?
Answer:
Total cost of the survey = $450
Step-by-step explanation:
Given:
Cost for each person = $1
Liked thin crust = 200 people
Liked thick crust = 270 people
Both crust like = 70 people
50 people did not like either type of crust.
We need to find the total cost of the survey.
Solution:
Number of people who like thin crust or thick crust.
⇒ 200 + 270 - 70
⇒ 470 - 70
⇒ 400
So, 400 people likes thin crust OR thick crust.
And, also 50 peoples did not likes either thin crust OR thick crust.
So, we add 50 people who did not like any type of pizza.
⇒ 400 + 50
Therefore, total cost of the survey = $450
From January to June, a company spent $60 per month on office supplies. In July the price of office supplies increased by 15% and remained the same for the rest of the year. How much did the company spend an office supplies for the year
Answer:
$774
Step-by-step explanation:
We have been given that from January to June, a company spent $60 per month on office supplies. In July the price of office supplies increased by 15% and remained the same for the rest of the year.
Let us find increased cost of supplies as shown below:
[tex]\text{Increased cost of supplies}=60+\frac{15}{100}\times 60[/tex]
[tex]\text{Increased cost of supplies}=60+0.15\times 60[/tex]
[tex]\text{Increased cost of supplies}=60+9[/tex]
[tex]\text{Increased cost of supplies}=69[/tex]
There are 6 months from January to June, so cost of supplies on these 6 months would be 6 times $60.
There are 6 months from July to December, so cost of these months would be 6 times $69.
Total cost will be equal to sum of these two amounts.
[tex]\text{Amount spent on office supply in the year}=6\times \$60+6\times \$69[/tex]
[tex]\text{Amount spent on office supply in the year}=6( \$60+\$69)[/tex]
[tex]\text{Amount spent on office supply in the year}=6( \$129)[/tex]
[tex]\text{Amount spent on office supply in the year}=\$774[/tex]
Therefore, $774 were spent on office supplies.
The nieces is it a ladder to clean the outside of her second-story windows the lashes is it is 24 feet long and she puts the base of the lead 13 feet away from the house in order to avoid her flower girl that's how high up the side of the house does the Ladder reach
Answer: 20 feet
Step-by-step explanation:
in the attachment
The ladder reaches approximately 19.8 feet up the side of the house, as determined using the Pythagorean theorem.
Explanation:The question is asking us to find the height the ladder reaches up the side of the house. This is a problem dealing with right triangles and can be solved using the Pythagorean theorem, which is a^2 + b^2 = c^2, where 'a' and 'b' are the shorter sides (base and height of the house) and 'c' is the hypotenuse (the ladder).
In this case, the ladder is 24 feet long (this is our c), and the base of the ladder is 13 feet from the house (this is our a). We are trying to find b (the height of the house the ladder reaches).
Substitute these values into the Pythagorean theorem and solve for 'b':
13^2 + b^2 = 24^2
b^2 = 24^2 - 13^2
b = sqrt(24^2 - 13^2)
So, the height that the ladder reaches up the side of the house is approximately 19.8 feet.
Learn more about Pythagorean theorem here:https://brainly.com/question/28361847
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Brenda is building a square fence. She places a fence post at (─3,2). What is the location of the post (in which quadrant) that reflects (─3, 2) across the y-axis?
The location of the reflected post will be in the first quadrant at point (3, 2).
To reflect a point across the y-axis, we simply negate the x-coordinate while keeping the y-coordinate unchanged.
Given the point (-3, 2), when we reflect it across the y-axis, the x-coordinate becomes positive 3, while the y-coordinate remains 2. Therefore, the reflected point is (3, 2).
Since the original point (-3, 2) lies in the second quadrant (negative x, positive y), the reflected point (3, 2) will lie in the first quadrant (positive x, positive y).
having trouble with this and 3 others (part 3)
Answer:
a.) 23
b.) y=14
c.) 23
d.) -23
e.) T=8
f.) f=1/8
Step-by-step explanation:
a.) general equation is Asin((2π/T))
A is the amplitude. It's A value is 23
b.) Midline = vertical_shift = 14
c.) max = positive amplitude value = 23
d.) min = negative amplitude = -23
e.) Factor out 2π from your angular frequency to get the period.
ω = π/4 = (2π)/8 = (2π)/T
Period = 8
f.) Frequency is just the inverse of the period.
f = 1/T = 1/8
use multiplier method to increase £88 by 14%. you must show all your working out
Answer:
£100.32
Step-by-step explanation:
£88 + 14% × £88 = £88×(1 +0.14)
= 1.14×£88
= £100.32 . . . . using a calculator
£100.32 is £88 increased by 14%.
Final answer:
£100.32
Explanation:
To increase an amount by a certain percentage using the multiplier method, you can use the following steps:
Convert the percentage increase to a decimal by dividing by 100. In this case, 14% becomes 0.14.Add 1 to the decimal to get the multiplier. Here, 1 + 0.14 = 1.14.Multiply the original amount by the multiplier. So, £88 multiplied by 1.14 gives us the increased amount.Let's do the calculation:
Step 1: Convert the percentage to a decimal. 14% / 100 = 0.14Step 2: Calculate the multiplier. 1 + 0.14 = 1.14Step 3: Multiply £88 by the multiplier. £88 x 1.14 = £100.32