The solution to the linear function M(x) = 180 is of x = -5.
What is a Linear Function Equation?The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.
In this problem, the function is defined as follows:
M(x) = 120 - 12x.
M(x) represents the balance remaining on the gift card after x movie tickets priced at $12 are purchased.
The domain of the situation is given as follows:
x ≥ 0. {discrete}
As the number of tickets cannot assume negative neither decimal values.
The equation is:
M(x) = 180.
The solution is calculated as:
120 - 12x = 180
12x = -60
x = -60/12
x = -5.
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Carly spent $13.25 on supplies to make lemonade. At least how many glasses of lemonade must she sell at $0.20 per glass to make a profit?
Answer:
66.25
technically 67 glasses
Step-by-step explanation:
On Friday, there is an 80% chance of snow. On Saturday, there is a 7 out of 9 chance that it will snow. On Sunday, there is a 75
14% chance that it is going to snow. Which day has the least chance that it will snow?
Answer: There is an approximate 10.7% probability that it will snow on Sunday, making it the day with the lowest likelihood of snow.
Step-by-step explanation: Snow is highly likely on Friday with an 80% probability. The likelihood of no snowfall occurring on Friday is 20%, which can be calculated by subtracting 0.8 (or 80%) from 1.
There is a high probability of snowfall on Saturday with a 7 in 9 likelihood. In simpler terms, the probability can be reduced to 7 out of 9 or around 0.78. The likelihood of snowfall on Saturday is 78%, therefore the chance of no snow on that day is 22% which is equivalent to 1 minus 0.78.
There is a high likelihood of snow on Sunday with a probability of 75 out of 100 or 14 out of 19. It is possible to reduce this to a likelihood of 0.7514, or about 0.107. The likelihood of Sunday not having snow is equivalent to subtracting 0.107 from 1, resulting in a 0.893 or 89.3% probability.
A game is played by spinning the two spinners
shown. Players match the results of the
spinners to combinations on their game cards.
How many different combinations are possible?
There are 36 different combinations possible when spinning the two spinners in the game, obtained by multiplying the number of outcomes on each spinner (6 × 6 = 36).
What is combination?A combination is a way of selecting a group of items from a larger set without regard to the order, often represented as unordered arrangements of objects, used in mathematics, statistics, and various fields of science.
According to the given information:
To determine the total number of different combinations possible in the game, we need to multiply the number of outcomes on each spinner. The first spinner has six equally likely outcomes (1, 2, 3, 4, 5, or 6), and the second spinner also has six equally likely outcomes (A, B, C, D, E, or F). Therefore, the total number of different combinations possible is:
6 (number of outcomes on the first spinner) × 6 (number of outcomes on the second spinner) = 36
So, there are 36 different possible combinations that can be obtained from spinning the two spinners. These combinations can be used to match with the combinations on the players' game cards and determine the winner of the game.
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A scientist removed a sample of 37.8 grams of a chemical from a containerThe sample was 4(1)/(4) grams less than (1)/(5) of the total mass of the chemical in the container. What was the measure of the total chemical in the container? Show your work.
Please help quickly!
Answer:
(d) 3 × [A2] + [A1] ⇒ [B1]
(c) -2 × [B1] + [B2] ⇒ [C2]
Step-by-step explanation:
Given three systems of equations, you want to know the operations that transform one system to the next.
A to BEquation B2 is unchanged from equation A2, eliminating choices B and C.
Equation B1 is not a simple multiple of equation A1, eliminating choice A.
Knowing the answer is choice D, we need to find the multiplier k of equation A2 that is being added to A1. We can find that using the x-coefficients:
k(-3) +5 = -4
-3k = -9 . . . . . subtract 5
k = 3 . . . . . . . divide by -3
Then we have ...
3 × [A2] + [A1] ⇒ [B1] . . . . . . . choice D
B to CUsing the same tactics as above, we see that [C1] is unchanged from [B1], eliminating choices A and D.
[C2] is not a simple multiple of [B2], eliminating choice B.
Using the y-coefficient to find k, we have ...
k(1) +2 = 0
k = -2 . . . . . . . . subtract 2
Then we have ...
-2 × [B1] + [B2] ⇒ [C2] . . . . . . . . choice C
__
Additional comment
We found the equation multiplier, which we called "k", by looking at an arbitrary variable coefficient. Which of the numbers we use in this process is immaterial. That is, we could use either coefficient, or the right-side constant, and we would get the same result.
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i need help someone . i need help on my iready
It wants you to multiply (5) x (8) = 40/3
Help me it’s due tmrw
To rewrite the equation of the circle in graphing form, we need to complete the square for both the x and y terms.
x² + 6x + y² - 4y = -9
Step 1: Move the constant term to the right side of the equation.
x² + 6x + y² - 4y + 9 = 0
Step 2: Group the x terms and the y terms separately.
(x² + 6x) + (y² - 4y) + 9 = 0
Step 3: Complete the square for the x terms. To do this, take half of the coefficient of x (which is 6), square it, and add and subtract it inside the parentheses.
(x² + 6x + 9 - 9) + (y² - 4y) + 9 = 0
(x + 3)² - 9 + (y² - 4y) + 9 = 0
(x + 3)² + (y² - 4y) = 0
Step 4: Complete the square for the y terms. To do this, take half of the coefficient of y (which is -4), square it, and add and subtract it inside the parentheses.
(x + 3)² + (y² - 4y + 4 - 4) = 0
(x + 3)² + (y - 2)² - 4 = 0
Step 5: Move the constant term to the right side of the equation.
(x + 3)² + (y - 2)² = 4
The equation is now in graphing form, which is:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
Comparing the equation to the graphing form, we see that the center of the circle is (-3, 2) and the radius is 2. Thus, the graph of the circle is centered at (-3, 2) with a radius of 2.
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In each graphic, the triangle was dilated to create the image triangle. Determine which scale factor was used for each dilation by dragging the correct scale factor to each graph.
pls help me
The scale factor applied for each dilation are-
For ΔABC - scale factor = 2For ΔDEF - scale factor = 1/2For ΔGHJ - scale factor = 1/3For ΔKML - scale factor = 3Explain about the term scale factor :The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
The form will be smaller if the scaling factor is a fraction. Reduction is the term for this. Therefore, a scaling factor of 1/2 suggests that the fresh shape is equal to half of the old shape.
Part a: For ΔABC
Length AB = 2 units
Length A'B' = 4 units
A'B' = 2 *AB
Hence, For ΔABC - scale factor = 2
Part b: For ΔDEF -
Length DF = 2 units
Length D'F' = 1 units
D'F' = 1/2 DF
Hence, For ΔDEF - scale factor = 1/2
Part c: For ΔGHJ
Length GH = 3 units
Length G'H' = 1 units
G'H' = 1/3 GH
Hence, For ΔGHJ - scale factor = 1/3
Part d: For ΔKML -
Length KM = 2 units
Length K'M' = 6 units
K'M' = 3*KM
Hence, For ΔKML - scale factor = 3
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Listen Which statement correctly describes the scatter plot?
O The scatter plot shows clustering near the point (3, 5).
O The scatter plot does not show any pattern at all.
O The scatter plot shows clustering near the z-value of 3.
O The scatter plot shows clustering near the y-value of 3.
The statement that correctly describes the scatter plot is
The scatter plot does not show any pattern at all.What is scatter plotA scatter plot is a type of data visualization that displays the relationship between two numerical variables.
It is a graph that uses dots or points to represent the values of each variable, with one variable plotted on the x-axis and the other on the y-axis.
The position of each dot on the graph represents the values of the two variables for a single observation or data point.
Scatter plots are commonly used to identify patterns or relationships between variables, such as correlation or causation.
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72° (x+4)° Write an equation that can be used to find the value of x.
Answer:
In a triangle, the sum of the interior angles is 180 degrees. So, we can set up the following equation:
72° + (x+4)° + A = 180°
where A is the measure of the third angle in the triangle.
Simplifying the equation, we get:
(x+4)° + 72° + A = 180°
x + 76° + A = 180°
Subtracting 76° from both sides, we get:
x + A = 104°
Therefore, an equation that can be used to find the value of x is x + A = 104°, where A is the measure of the third angle in the triangle. Note that we do not have enough information to solve for x or A individually, but we can use this equation to relate the two angles in the triangle.
Measure the scissors to the nearest 1/8 inch (look at pic)
A. 3 inches
B. 2 /78 inches
C. 2 5/8 inches
D. 2 6/8 inches
The minimum number of cuts John needs to make to cut a 5-inch piece of paper using scissors with blades that are 4 and 3/8 inches long is either one or two
To determine the minimum number of cuts John needs to make to cut a 5-inch piece of paper using scissors with blades that are 4 and 3/8 inches long:
Subtract the length of the blades from the desired length of the paper:
5 - 4 3/8 = 1/8 inch
Therefore, the minimum number of cuts John needs to make are 4 and 3/8 inches long is either one or two, depending on whether he chooses to fold the paper or not.
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--The complete Question is, John needs to cut a piece of paper using a pair of scissors. He measures the scissors to the nearest 1/8 inch and finds that the length of the blades is 4 and 3/8 inches. If John wants to cut a piece of paper that is exactly 5 inches long, what is the minimum number of cuts he needs to make? --
What is limf(x) where f(x) is as shown in the table
As x approaches 2 from both sides, the values of f(x) do not approach a single value, and f(x) does not have a limit. The answer is option (d).
What is limit of a function?The calculus concept known as the limit of a function describes how a function behaves when the input variable approaches a particular value.
The phrase "lim f(x) as x approaches a" (or "limit of a function f(x) as x approaches a") describes what occurs to the output of the function when x approaches a value without actually reaching a.
The limit can be expressed in terms of two-sided, left-sided, or right-sided limits, depending on whether x approaches a from both sides, the left, or the right.
We must look at the values of f(x) as x approaches 2 in order to determine lim f(x) as x approaches 2.
Looking at the table, we can see that the values of f(x) rise from 3.99 to 4 as x approaches 2 from the left (that is, as x approaches 2 while remaining smaller than 2). The values of f(x) decline from -5 to -5.01 as x moves towards 2 from the right (that is, as x approaches 2 but staysgreater than 2).
The limit of f(x) as x approaches 2 does not exist because the values of f(x) do not approach a single integer as x approaches 2 from both sides.
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Ver en español
The Udderly Delicious Cheese Factory produces 200 blocks of cheddar cheese and 200 blocks of Swiss cheese each day. The factory uses 5 quarts of milk to make a block of cheddar cheese and 6 quarts of milk to make a block of Swiss cheese. How many total gallons of milk does the factory use each day?
Therefore , the solution of the given problem of ratio comes out to be the Udderly Delicious Cheese Factory needs 550 gallons of milk in total.
What is a ratio?A group comprising values both variable "a" and "" that seem to be equal is found using the straightforward formula "a / b," whenever "b" might be a greater number than zero. A ratio is created by combining two ratios. The ratio , fraction could have been 1:1 if there were just one guy and three women. There are 1/4 men and 3/4 women in the group.
Here,
For cheddar cheese, multiply the quantity of blocks by 200 and the amount of milk consumed by each block by 5.
200 blocks of cheddar cheese divided by 5 quarts per block equals a total of 1000 quarts.
For Swiss cheese, the formula is as follows: 200 blocks of Swiss cheese, or 6 quarts of milk per block.
200 blocks of Swiss cheese divided by 6 quarts per block equals 1200 quarts of milk in total.
Total milk used equals the sum of the milk required to make cheddar cheese and the milk used to make Swiss cheese, or 1000 quarts plus 1200 quarts, or 2200 quarts.
We can convert quarts to gallons by dividing by 4 because there are 4 quarts in a gallon.
= 1000 quarts + 1200 quarts
= 2200 quarts
We can convert quarts to gallons by dividing by 4 because there are 4 quarts in a gallon.
=> Total gallons of milk used = 2200 quarts / 4 quarts/gallon = 550 gallons
Thus, to make 200 blocks of cheddar cheese and 200 blocks of Swiss cheese each day,
the Udderly Delicious Cheese Factory needs 550 gallons of milk in total.
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WZ and XR are diameters find the measure of XZ in circle C
The length of XZ in circle C is equal to the √34. This can be found using the Pythagorean theorem and the fact that XZ is a radius of the circle.
As WZ and XR are diameters, they intersect at the center of the circle, which we'll call point O.
Since WX is a chord of the circle, we can use the perpendicular bisector of WX, which passes through O, to find the length of XZ.
Let's call the midpoint of WX point M. Then OM is perpendicular to WX and bisects it.
So we have two right triangles, OXM and MXZ. We know that OM = 5 and XM = 3 (half of WX).
Using the Pythagorean theorem, we can find the length of OX:
OX² = OM² + MX²
OX² = 5² + 3²
OX² = 34
OX = √(34)
Since XZ is also a radius of the circle, we have XZ = OX = √(34).
Therefore, the measure of XZ in circle C is √(34).
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on tuesday, a local gas station had 135 135135 customers. the table above summarizes whether or not the customers on tuesday purchased gasoline, a beverage, both, or neither. based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?
The probability that a randomly selected gas station customer on that day did not purchase gasoline is 10/27.
We know that, the probability of any event is the ratio of the number of favorable case to that event to the total number of cases.
The total number of customers in that Gas Station on that day = 135
According to the data table,
Number of customers did not purchase gas but purchased beverage = 35
Number of customers neither purchase gas nor beverage = 15
So total number of customers did not purchase gas = 35 + 15 = 50
Here number of favorable cases = 50
So the probability that a randomly selected gas station customer on that day did not purchase gasoline = 50/135 = 10/27.
Hence the required probability is 10/27.
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The given question is incomplete. The complete question is -
"On Tuesday, a local gas station had 135 customers. The table above summarizes whether or not the customers on Tuesday purchased gasoline, a beverage, both, or neither. Based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?
Customer Purchases at a Gas Station"
A jar contains 30 red marbles, 50 blue marbles and 20 white marbles. you pick one marble from the jar at random. find the probability of selecting a marble that is not blue
Answer:
50/100 or 1/2 or 50%
Step-by-step explanation:
total = 30 + 20 + 50 = 100
the probability of choosing a marble that is not blue is equal to the total minus all marbles that are blue therefore 100-30-20=50 therefore the probability is 50/100 or 1/2 or 50%
Question 9(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Histogram is the ideal type of graphic to depict the data from the school's random sample of 100 students.
Explain about the Histogram:A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of dataset in a series of equal-sized numerical intervals.
The independent variable is represented is along horizontal axis and indeed the dependent variable is plotted along of the vertical axis in the most popular type of histogram.A histogram is a type of bar graph that displays how frequently something occurs over a range of time. Histograms compare a variety of data, as opposed to bar graphs, which compare defined amounts.Given that-
The most efficient sort of graphic to show the data would be a histogram.A histogram is an illustration of a graph that shows the proportion of data points within such a range of values.It is a useful tool for showing data distribution and also can aid in the identification of trends and patterns.The best sort of graph to use is a histogram because it displays the frequency of data points.Thus, Histogram is the ideal type of graphic to depict the data from the school's random sample of 100 students.
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x2=441 -1
what wouod it be
Answer:
The answer for x is 11
Step-by-step explanation:
x²=144-1
Square root of both sides
√x²=√144-1
x=12-1
x=11
The Chang family is on their way home from a cross-country road trip.
During the trip, the function D(t)=2,280-60t can be used to model their distance, in miles, from home after t hours of driving.
Part A:
Find D(15) and interpret the meaning in the context of the problem.
To find D(15), we simply substitute t = 15 into the function:
D(15) = 2,280 - 60(15)
D(15) = 2,280 - 900
D(15) = 1,380
Therefore, when the Chang family has been driving for 15 hours, they are 1,380 miles away from home.
Interpreting this result in the context of the problem, we can say that the family has made good progress on their trip and has covered a distance of 1,380 miles from home.
Equation
Situation
A plant in Zahra's garden grows 0.8 inches
taller each week. After x weeks, the plant has
grown 6 inches.
Meaning of x
Answer:
if no initial high im guessing 4.8 weeks
Step-by-step explanation:
4.8 divied by .8 = 6
Answer:
7 week 3 days and 12 hour
Step-by-step explanation:
x is the required week and to calculat it
1st for 1 week= o.8 inch
x = 6 inch
2nd u solve it after u solve it u get 7.5 but week dosen't said by decimals so u will multiply 0.5 by days of the week which is 7 .
3rd u will get 3.5 as we said before for days we can't use decimals so yo will multiply 0.5 by hour which 24 then u will get 12 . so the answer is 7 week 3 days and 12 hour .
Two friends live 7 miles apart. One Saturday, the two friends set out on their bikes at 8am and started riding towards each other. One rides at 0. 2 miles per minute, and the other rides at 0. 15 miles per minute. At what time will the two friends meet?
The time when the two friends will meet is 8:20 am.
We can start by finding the combined speed at which the two friends are approaching each other. This can be found by adding their individual speeds:
0.2 miles/minute + 0.15 miles/minute = 0.35 miles/minute
This means that the friends are approaching each other at a combined speed of 0.35 miles/minute.
To find out how long it will take for the friends to meet, we can use the formula:
time = distance / speed
In this case, the distance is 7 miles (since they are 7 miles apart) and the combined speed is 0.35 miles/minute. So we can solve for time as follows:
time = 7 miles / 0.35 miles/minute = 20 minutes
Therefore, it will take the two friends 20 minutes to meet each other while biking towards each other.
Since they started biking at 8am and it took them 20 minutes to meet, they will meet at 8:20am.
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Baron Blakk decided to start saving. He deposited seven thousand kroner at the start of each year. He always received a fixed interest rate of 2.3%. How much interest had he received in total after eight years? Give the answer to two decimal places.
The amount of interest that Baron Blakk would receive in total after eight years would be 6, 118. 03 krona
How to find the interest ?To find the interest that Baron Blakk received in eight years of savings, we first need to find the future value of the savings. We can do this with the Future value of annuity due formula as this is an annuity and it is an Annuity due as it is paid at the beginning of the year.
The total value after eight years is:
= Amount saved x ( Future value of annuity, interest, number of years)
= 7, 000 x 8. 87
= 62, 118.03 Krona
The interest earned is:
= Total value - ( Amount saved )
= 62, 118.03 - ( 7, 000 x 8 )
= 6, 118. 03 krona
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Help me please. I beg I really need help I need a better grade
The correct statements for the triangles are given as follows:
<Z is a right angle.The length of the hypotenuse of triangle STU is a² + b².The longest side of triangle XYZ is XY.What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The Pythagorean Theorem holds true for triangle XYZ, hence:
<Z is a right angle -> as the Pythagorean Theorem is true.The longest side of triangle XYZ is XY -> hypotenuse.For triangle STU, the symbol shows that it a right triangle, hence the hypotenuse length is obtained as follows:
a² + b².
Which is equals to the hypotenuse length of XYZ.
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Número que sumado da 4 y multiplicado 5
Answer:
Aquí respondemos a la pregunta: "¿Qué dos números se multiplican por 4 y suman 5?"
La respuesta a tu pregunta es:
1 y 4
A continuación ilustramos y demostramos que 1 y 4 se multiplican por 4 y suman 5:
1 × 4 = 4
1 + 4 = 5
¿Estás preguntando porque estás tratando de averiguar cómo factorizar la siguiente ecuación cuadrática?
x2 + 5x + 4 = 0
Si es así, la solución para factorizar la ecuación cuadrática anterior es:
(x+1) (x+4)
Para resumir, dado que 1 y 4 se multiplican por 4 y suman 5, sabes que lo siguiente es cierto:
x2 + 5x + 4 = (x + 1 ) (x + 4)
Step-by-step explanation:
A toy manufacturer produces its toys according to the production function: (10 PTS) Q = 4K + 5L where Q = output of toys per hour K = capital input per hour L = labor input per hour Answer the following questions. YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT. a) If K = 20, how much L is needed to produce 400 toys per hour? b) If L = 40, how much K is needed to produce 500 toys per hour?
a) To find out how much L is needed to produce 400 toys per hour when K is equal to 20, we can use the production function formula provided, which is Q = 4K + 5L.
To solve for L, we can rearrange the formula as follows: Q - 4K = 5L 400 - 4(20) = 5L 320 = 5L L = 64
Therefore, to produce 400 toys per hour with K = 20, the manufacturer would need 64 units of labor input per hour.
b) Similarly, to find out how much K is needed to produce 500 toys per hour when L is equal to 40, we can use the production function formula: Q = 4K + 5L
Substituting the given values, we get: 500 = 4K + 5(40) 500 = 4K + 200 4K = 300 K = 75
Therefore, to produce 500 toys per hour with L = 40, the manufacturer would need 75 units of capital input per hour.
In conclusion, the production function formula provides a useful tool for toy manufacturers to produce a desired level of output. By manipulating the formula, the manufacturer can also calculate the maximum output possible given a certain combination of inputs.
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How many square kilometers are equivalent to 28.5 cm2?A) 2.85 × 10-9 km2 D) 2.85 × 10-4 km2B) 2.85 × 10-6 km2 E) none of theseC) 285 km2
The number of kilometres that are equivalent to 28.5 cm² is 2.85 × 10⁹ km². Hence, after careful consideration concerning every option, the required answer for the given question is Option A.
Here, we have to depend on the principles of conversation of units and using this principles derive a formula.
To convert 28.5 cm² to km², we have to implement the formula
Total number of square centimeters x 1.0 x [tex]E^{-10}[/tex] = Total number of square kilometers .
The number of kilometres that are equivalent to 28.5 cm² is 2.85 × 10⁹ km². Hence, after careful consideration concerning every option, the required answer for the given question is Option A.
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(1 point) a 17 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 16 feet above the ground?
When the top of the ladder is 16 feet above the ground, the foot of the ladder is moving away from the wall at a speed of approximately 3.86 feet per second.
This is a related rates problem involving a ladder leaning against a wall. Let's denote the distance of the foot of the ladder from the wall as x, and the height that the top of the ladder reaches as y. We are given that dy/dt = -2 ft/s (since the top is slipping down the wall) and we want to find dx/dt (the speed at which the foot of the ladder is moving away from the wall) when y = 16 ft.
Using the Pythagorean theorem, we have:
[tex]x^2 + y^2 = 17^2[/tex]
Differentiating implicitly with respect to time, we get:
[tex]2x(dx/dt) + 2y(dy/dt) = 0[/tex]
Substituting the given values, we get:
[tex]2x(dx/dt) + 2(16)(-2) = 0[/tex]
Simplifying, we get:
[tex]2x(dx/dt) = 64[/tex]
Dividing both sides by 2x, we get:
dx/dt = 64/(2x)
We know that y = 16, so we can use the Pythagorean theorem to solve for x:
[tex]x^2 + 16^2 = 17^2x^2 = 17^2 - 16^2x^2 = 33[/tex]
Taking the square root, we get:
[tex]x = sqrt(33)[/tex]
Substituting this into our expression for dx/dt, we get:
[tex]dx/dt = 64/(2*sqrt(33)) ≈ 3.86 ft/s[/tex]
Therefore, when the top of the ladder is 16 feet above the ground, the foot of the ladder is moving away from the wall at a speed of approximately 3.86 feet per second.
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If the length of a rectangle prism is doubled, it’s width is tripled, and it’s height remains the same, what is the volume of the new rectangle prism?
If in a rectangular-prism, the length is doubled, width is tripled and height is same, then the volume of new rectangular prism will be 6 times the original-prism.
The "Volume" of a 3-D object is defined as the amount of space that object occupies in three-dimensional space. It is a measure of the total capacity or size of the object
Volume of a rectangular prism is ⇒ Volume = Length × Width × Height,
If the length of the rectangular prism is doubled, the new length would be 2 times the original length.
If the width is tripled, the new width would be 3 times the original width, and
If the height remains the same, it would be the same as the original height.
Let the original length be = "L", width be = "W", and height be = "H",
So, New Length = 2L , New Width = 3W, New Height = H (remains unchanged),
So, volume of new rectangular prism is :
⇒ New Volume = (New Length)×(New Width)×(New Height),
⇒ (2L) × (3W) × H
⇒ 6LWH
Therefore, volume of "new-rectangular prism' is 6 times volume of original rectangular prism.
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5. Find the perimeter and area
*Triangle- based prism*
Step-by-step explanation:
for the perimeter you have to say two brackets live plus height plus with plastic
Page 1:
1
A
1=1.5 m
75°
0
B
wiper
1) What is the radius?
2) What is the angle measure?
3) What formula can you use to find the area?
4) What is the area of the space swept by the wiper?
گے
1. The radius (r) of the space swept is 1.5 m; 2. The angle measure is 75°.
3. The formula to use is Area = ∅/360 * πr²; 4. Area of the space is approximately 1.47 m².
What is the Area of a Sector?The formula to use to find the area of a sector is given as:
Area = ∅/360 * πr², where:
r is the radius; and ∅ is the angle measure.
From the image given, we will solve the problem as follows:
1. The radius (r) = 1.5 m
2. The angle measure (∅) = 75°
3. The formula is:
Area = ∅/360 * πr²
4. Plug in the values:
Area = 75/360 * π * 1.5²
Area ≈ 1.47 m²
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