Answer: a) i) The width of the floor can be expressed in terms of c as: w = c - 2 cm.
ii) The area of the floor can be expressed in terms of c as: A = c * (c - 2) cm^2.
b) If the area of the room is 15 cm^2, then we can write the equation as:
c * (c - 2) = 15.
c) Solving for c, we get:
c^2 - 2c - 15 = 0.
Using the quadratic formula, we find that:
c = 5 or c = -3.
Since the length of the room cannot be negative, we choose c = 5.
Therefore, the length of the room is 5 cm and the width of the room is 3 cm.
Step-by-step explanation:
Which soup has more sodium per cup
Answer:
Soup B
Step-by-step explanation:
Soup A = 5 grams sodium = 12 cups
Soup B = 8 grams of sodium = 13 cups
Find the unit rate, so, soup B has more sodium.
I hope this helps.
Also, next time can you write the question entirely?
10. Jada is standing 10 feet from the base of a tree and spots • nest sitting on a branch. The
angle of elevation from the ground where she is standing to the nest is 55°. Find the height of
the nest.
This is trigonometry in geometry
Answer:
Step-by-step explanation:
so the height will be h.
if given the base length, find h using tangent.
tan55 = h/10ft
h = 10tan55
h = 14.28ft
when looking to invest money in a company by purchasing stock why is it important to look at many companies to invest
It is important to look at many companies to invest and compare their advantages to one another before investing money in a company by purchasing stock.
It's crucial to research a variety of businesses before investing your money in them because you can compare their advantages to one another and determine which one will provide you with a higher return on your investment in addition to a guaranteed return.
It's crucial to take into account a company's financial fundamentals when choosing stocks, such as earnings, operating margins, and cash flow. When considered collectively, these elements can provide a fair picture of the company's current financial situation as well as its prospects for short- and long-term profitability.
Diversification is a portfolio's greatest asset. With diversity, you can more easily manage risk, weather market downturns, and generate better long-term returns. Due to these factors, you'll need a variety of stocks in various industries that can counteract one another.
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Mark needed to buy some items for a science project. The items were priced $3.25, $0.55, $2.95, and $4.25 before tax. If everything in the store was on sale for 20% off, what was the total cost of the items he bought, before tax?
Total cost of items Mark bought = $8.80
What is percentage?The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given,
Price of the items, $3.25, $0.55, $2.95, and $4.25 before tax.
Total price = $11
Discount on items = 20%
Discount = (20/100)11 = $2.20
Cost of the items = $11 - $2.20 = $8.80
Hence, $8.80 is total cost of items Mark bought.
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help pleas read the image this is worth 30 points
Let's consider what the question asks for:
--> change in total cost for each book printed
--> cost to get started
The change in total cost:
--> essentially, the slope value that is given in the equation:
[tex]y=25x+1150[/tex]
--> thus, the change in total cost per book is $25
The cost to get started before printing any books:
--> we can essentially set 'x' equal to 0 to signify no books being printed
yet
[tex]y=25x+1150=25(0)+1150=1150[/tex]
--> the total cost before printing any books is $1150
Answer:
change in total cost for each book printed: $25total cost before printing any book: $1150Answer:
1. The change in total cost for each book printed is $25
2. The cost to get started is $1,150
Step-by-step explanation:
25x + 1150 = Y
-Y/-1 = -25x/-1 - 1150/-1
Y = 25x + 1150
To get the total cost to get started let X = 0
Y = 25x + 1150
Y = 25(0) + 1150
Y = $ 1,150
) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 5 , 7, and 58. Let b represent the number of books.
The equation that represents the number of books purchased will; be 6b - 8 = 58 and the number of books is 11.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Ashley bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6.
Let 'b' be the number of books. Then the equation is given as,
6b - 8 = 58
Simplify the equation, then we have
6b - 8 = 58
6b = 66
b = 11
The equation that represents the number of books purchased will; be 6b - 8 = 58 and the number of books is 11.
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The complete question is given below.
Ashley bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6. How many books did she buy?
Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 58, 8, and 6. Let b represent the number of books. and then solve the equation.
we will flip a balanced coin 3 times and for each toss, record whether we get a head or a tail. write all possible outcomes of this experiment to find the probability that we get exactly 0 tails.
The probability of getting exactly 0 tails is 1/8 or 0.125.
The coin flip experiment involves three independent events, each representing the outcome of one coin flip. Since each coin flip is balanced, the outcome of each event can either be heads (H) or tails (T). Therefore, for each event, there are two possible outcomes.
Since each event is independent, the number of possible outcomes of three events is equal to the product of the number of possible outcomes of each individual event. This means that the number of possible outcomes of three coin flips is equal to 2 * 2 * 2 = 8. The possible outcomes of three coin flips can be listed as follows:
HHH
HHT
HTH
THH
THT
TTH
HTT
TTT
Out of these eight possible outcomes, only one outcome (HHH) results in getting exactly 0 tails. So the probability of getting exactly 0 tails is 1/8 or 0.125.
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a rectangular well is 6 feet long, 4 feet wide, and 10 feet deep. if water is running into the well at the rate of 3 ft3 /min , how fast is the water rising?
The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.
The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.
To calculate this, we can use the following formula:
Rate of Water Rising = Volume of Water Added Per Minute / Total Volume of Well
Rate of Water Rising = 3 ft3/min / 240 ft3
Rate of Water Rising = 1/80 ft per minute
Therefore, The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.
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1/9 multiplied by 1.5
Answer:
1/6
Step-by-step explanation:
You can change 1.5 into a fraction.
1.5 = 3/2
Now you can multiply the two fractions easily: the two numerator values multiply and the two denominator values multiply.
1/9 * 3/2 = 3/18.
You can further simply this fraction by noting that 3 divides into 18.
So the answer is 1/6.
Simplify the expression 12p-8p,4p(3-2)
Answer:
Are these two different equations? Tell me so I can help you.
what is the difference between precession and nutation?
Precession and nutation are two distinct motions of a spinning top or gyroscope. Precession is a slow, uniform motion that results from the gravitational force acting on a spinning top or gyroscope.
It is a slow, uniform motion in which the spinning object's axis of rotation moves in a cone-like motion.
Nutation is a fast, non-uniform motion that is caused by the torque of a nearby force. It is a rapid, irregular motion that causes the spinning object's axis of rotation to wobble back and forth.
Precession is a regular, predictable motion, whereas nutation is an unpredictable, irregular motion. Precession is typically used to describe the motion of a satellite or planet in its orbit, while nutation is used to describe the motion of a spinning top or gyroscope.
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Precession and nutation are two different types of rotational movements in astronomy.
Precession refers to the slow, conical movement of an object's rotational axis, which changes the orientation of the object over time. In the case of Earth, precession causes the direction of the North Pole to change over time.
Nutation, on the other hand, is a rapid, irregular movement of an object's rotational axis. It is caused by the combined gravitational forces of the Sun, Moon, and other celestial bodies on the Earth. Unlike precession, nutation occurs in small, cyclical changes in the orientation of the rotational axis, causing the axis to move slightly back and forth.
In summary, precession is a slow, systematic change in the orientation of an object's rotational axis, while nutation is a rapid, irregular movement of the axis caused by external forces.
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The point T( – 1,2) is rotated 180° clockwise around the origin. What are the coordinates of the resulting point, T'?
The coordinates of the resulting point, T' after the point T( – 1,2) is rotated 180° clockwise around the origin is (1, -2).
To rotate a point 180° clockwise around the origin, you can apply the following transformations:
Reflect the point across the x-axis by negating its y-coordinate.
Reflect the point across the y-axis by negating its x-coordinate.
Starting with T( – 1,2), we first reflect the point across the x-axis, which gives us T'( – 1, -2). Then, we reflect T' across the y-axis, which results in T''(1, -2).
The transformation can be represented as follows:
T' = (x, -y)
T'' = (-x, -y)
Therefore, the final coordinates of T'' are (1, -2).
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what the solution to practice arithmetic sequences as linear functions?
The solution of Representing an arithmetic sequence as a linear function involves finding the equation of a line in the form of y = mx + b.
Here m represents the common difference and b represents the initial term of the sequence. To do this, choose any two terms from the arithmetic sequence and use them to solve for the slope (m) and y-intercept (b). For example, if the two terms are a_n and a_n+k, where k is a constant, you can use the formula: m = (a_n+k - a_n) / k.
Once you have the slope, use one of the two terms and the slope to solve for the y-intercept using the equation y = mx + b. This will give you the equation for the line representing the arithmetic sequence. By using this method, you can practice representing arithmetic sequences as linear functions and find the equation of a line that represents any given arithmetic sequence.
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Solve for h.
Z =
M
g (h-f)
h = 0
X
믐
Ś
PLEASEEEEE WILL MARK!
On solving the provided question, we can say that value of the equation , h = [tex]\frac{M}{Zg} + f[/tex]
Which equation is this?Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol. In this case, 2x4=2.
here,
the equation
[tex]Z=\frac{M}{g(h-f)}[/tex]
[tex]for, h , \\h - f = \frac{M}{(Zg)}\\h = \frac{M}{Zg} + f[/tex]
value of the h will be [tex]\frac{M}{Zg} + f[/tex]
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solve for x and find the value of x
We can write an equation for the interior angles, and we will see that x = 13
How to find the value of x?We want to find the value of x, we can see two adjacent angles on a rectangle, then the sum of these two is equal to 180°, we can write:
3x + 78 + x + 50 = 180
4x + 128 = 180
4x = 180 - 128
4x = 52
x = 52/4 = 13
The value of x is 13.
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If def ~ triangle jkl
what is m
52
58
70
16
The measures angles are 70° and 52°
Similar triangles:The triangle in which the ratio of corresponding is equal and has an equal measure of angles is known as Similar triangle.
If ABC and XYZ are two similar triangles, the corresponding angles must be equal
=> ∠A = ∠X, ∠ B = ∠Y, ∠C = ∠Z
Here we have
ΔDEF and ΔJKL are similar triangles
As we know angles of similar triangles are equal
=> ∠D = ∠J = (9x - 20)°
=> ∠E = ∠K = 52°
=> ∠F = ∠L = (7x - 12)°
As we know the sum of angles in triangles = 180°
=> ∠D + ∠E + ∠F = 180°
=> 9x - 20° + 52° + 7x - 12° = 180°
=> 16x + 20° = 180°
=> 16x = 160°
=> x = 160°/16
=> x = 10°
At x = 10° measures of angles are
=> (9x - 20)° = 9(10) - 20° = 70°
=> (7x - 12)° = 7(10) - 12° = 58°
Therefore,
The measures angles are 70° and 52°
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Help, Find the expression of the nth term of the sequence.
WILL MARK BRANLIEST!
The expression of the nth term of the sequence is 1/n
How to determine the expression of the nth term of the sequence.From the question, we have the following parameters that can be used in our computation:
The sequence definition
From the sequence, we can see that only the denominator increaes by 1
The numerator is constant at 1
Using the above as a guide, we have the following:
Tn = 1/n
Hence, the expression is 1/n
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Given the equation y = 3(2)x
Regarding the exponential function y = 3(2)^x, we have that:
We know that the graph has a y-intercept at (0,3), because the a-value is of 3.We know that the graph models exponential growth, because the b-value is of 2.The numeric value of the function at x = 3 is given as follows: 24.What is the exponential function?An exponential function is defined as follows:
y = ab^(x/n).
In which the parameters are defined as follows:
a is the initial value.b is the rate of change.n is the time needed for the rate of change.The function for this problem is given as follows:
y = 3(2)^x.
Hence the parameters are given as follows:
a = 3 -> y-intercept at (0,3).b = 2 > 1, hence exponential growth.At x = 3, the numeric value of the function is obtained as follows:
y = 3 x 2^3
y = 3 x 8
y = 24.
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Divide the following <3 answer needed asap please!!!
Answer:
Below
Step-by-step explanation:
Divide 3 into all of the coefficients
16 + 12 - 9 now divide 'w' into the variables
16 w^2 + 12 w - 9 Done.
I need help with this
Answer:
Step-by-step explanation:
y=2x-7
y=-1/2x+6
-1/2x+6 = 2x-7
x= 4
y= 2(4)-7
= 1
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Carina hiked at Yosemite National Park for 1.75 hours. Her average
speed was 3.5 mi/h. How many miles did she hike?
O 20 mi
O 6.125 mi
O 2 mi
O 61.25 mi
how to find 20.5% of 1850
Answer:
379.25
Step-by-step explanation:
20.5% of 1850 means 20.5/100 × 1850
0.205×1850
= 379.25
therefore 20.5% of 1850 is 379.25
Suppose you deposited $40 per month into a savings plan for 9 years and at the end of that period your balance was $19,600.What was the amount you earned in interest?
------------------------------------------------------
A. It is impossible to compute without knowing the APR. To find the correct answer, multiply each $40 deposit by the APR, and then multiply the product by the number of months in 9 years.
B. It was $15,280. Calculate the amount deposited over 9 years and then subtract it from the balance of $19,600.
C. It is impossible to compute without knowing the APR. To find the correct answer, divide the number of payments by the APR.
D. It was $15,280. Divide the balance of $19,600 by the number of years,9.
E. It was $30,560. Multiply the balance of $19,600 by the number of years,9.
F. it was $30,560.Calculate the amount deposited over 9 years and then add it to the balance of $19,600.
Answer:
b. It was $15,280. Calculate the amount deposited over 9 years and then subtract it from the balance of $19,600.
Step-by-step explanation:
19,600-4,320 gives you the interest
Answer:
B. It was $15,280.
Step-by-step explanation:
Calculate the total amount deposited:
$40 per month * 12 months per year * 9 years = $4,320
Subtract the total amount deposited from the final balance: $19,600 - $4,320 = $15,280
The result is the interest earned: $15,280.
So, the answer is B. It was $15,280.
1. Suppose a graph passes the horizontal line test: No horizontal line can be drawn that touches the graph in more than one location. Does this mean that the graph represents a function? If not, is there anything special about a graph that passes the horizontal line test? Share your ideas with a classmate.
2. Dotty and Lionel are making a graph comparing a car's age with its gas mileage. Dotty says the graph should show discrete points because the car's age is stated in whole numbers of years. Lionel says they should make a continuous line because age increases gradually, like time. Which student do you agree with and why?
3. Write two linear functions, f(x) and g(x). For example, f(x) = 3x - 7 and g(x) = -2x + 5. Then see whether f(x) - (-g(x)) is equivalent to f(x)+ g(x). Hint: To find -g(x), just change the signs of all the terms in g(x). Discuss whether you think your results would apply to every function..
A graph that passes the horizontal line test represents a function. This is because if a horizontal line can only intersect the graph at one point, it means that each input value (x) has a unique output value (y), which is the definition of a function. This is true.
How to explain the informationI agree with Lionel, the graph should show a continuous line because age increases gradually like time. Also, age is usually not a discrete variable, it's a continuous variable that can have fractional values, so a line graph is more appropriate to represent the relationship between age and gas mileage.
Let's take f(x) = 3x - 7 and g(x) = -2x + 5 as two linear functions.
f(x) - (-g(x)) = 3x - 7 - (-2x + 5) = 3x - 7 + 2x - 5 = 5x - 12
f(x) + g(x) = 3x - 7 + (-2x + 5) = x - 2
So f(x) - (-g(x)) is not equivalent to f(x) + g(x). This result would not apply to every function, as the properties of addition and subtraction of functions depend on the specific functions being used.
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help, will mark as brainliest I PROMISE YOU
Answer:
Below
Step-by-step explanation:
BAC = DAC angle bisector theorem
AC = AC
BCA=BCA given
ABC congruent to ADC ASA theorem
BA = AD triangle congruence theorem
AC = AC "
BC = DC "
a floor plan is given for the first floor of a new house. one inch represents 10 feet. if the walk-in closet is 2/5. in. by 2/3 in. on the floor plan, what are the actual dimensions? (round to the nearest hundredth).
The actual dimensions of the walk-in closet are 4 feet × 6.67 feet.
Finding actual dimensions:To find actual dimensions multiply the given measurement with the measurement given in scale.
In the given problem, given that 1 in = 10 feet which is the scale given, we need to multiply the given measurements that are in the plan with the scale measurement 10 feet.
Here we have
A floor plan is given for the first floor of a new house.
One inch represents 10 feet.
The walk-in closet is 2/5 in. × 2/3 in. on the floor plan
As we know 1 inch = 10 feet
=> 2/5 in = (2/5) × 10 feet = 4 feet
=> 2/3 in = (2/3) × 10 feet = 6.67 feet
Therefore,
The actual dimensions of the walk-in closet are 4 feet × 6.67 feet.
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a force of pounds is required to hold a spring stretched 0.4 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length? $1.8$incorrect2.025
The work done in stretching the spring from its natural length to 0.9 feet beyond its natural length is 3 foot-pounds.
This can be calculated using the equation W = F * d, where W is the work done, F is the force applied, and d is the distance the spring is stretched. In this case, F is 6 pounds and d is 0.5 feet (0.9 feet - 0.4 feet). Thus, W = 6 * 0.5 = 3 foot-pounds.
Force is a concept in physics that describes the influence that can change the motion of an object. Work done is the amount of energy transferred to or from an object when a force acts on it and causes it to move through a distance.
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Correct question:
A force of 6 pounds is required to hold a spring stretched 0.4 feet beyond its natural length.
How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length?
Find the general solution of the differential equation. (Enter your solution as an equation.)
y^3y’=6cos(pix)
Answer:
Find the general solution of the differential equation. (Enter your solution as an equation.)
y^3y’=6cos(pix
Answer:
The differential equation is a separable differential equation, so we can separate the variables and integrate both sides to find the general solution.
Separating the variables, we get:
(y^3)dy = 6cos(pix)dx
Integrating both sides with respect to their respective variables, we get:
(1/4)y^4 = -3sinx + C
Where C is an arbitrary constant of integration.
So the general solution to the differential equation is:
(1/4)y^4 = -3sinx + C
Step-by-step explanation:
let the continuous random variable x denote the current measured in a thin copper wire in milliamperes. assume that the range of x is [0, 20 ma], and assume that the probability density function of x is f (x) 0.05 for 0 x 20. what is the probability that a current measurement is less than 10 milliamperes?
The probability that a current measurement is less than 10 milliamperes can be found by computing the cumulative distribution function (CDF) of the random variable x at 10 milliamperes.
The CDF of a continuous random variable x is defined as the probability that x is less than or equal to a given value.
In this case, we want to find the CDF of x at 10 milliamperes, which we can write as F(10), where:
F(10) = P(X <= 10) = ∫_0¹⁰ f(x) dx
Using the probability density function f(x) given in the problem, we can evaluate the integral to find the CDF:
F(10) = ∫_0¹⁰ 0.05 dx = 0.5
So the probability that a current measurement is less than 10 milliamperes is 0.5. This means that half of the possible current measurements will be less than 10 milliamperes, and half will be greater than 10 milliamperes.
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Find the largest domain of f (x)=x²+1