Maya throws a rock
straight up from the edge
of a 192-foot cliff and into
the ocean. After two
seconds, the rock
reaches a maximum
height of 256 feet. Four
seconds later, the rock
enters the ocean
Write an equation to
model the scenario.
Answer:
Step-by-step explanation:
2.256 = 4x
So first Maya throws the rock from the 192-foot cliff into the ocean.
After 2 seconds, the rock reaches a maximum height of 256 feet;
so 2 seconds, 256 feet - 2.256After 4 seconds, the rock reaches the ocean.
so 4 seconds, it reaches the ocean but we don't know how many feet. ( x )-- 4 seconds, x feet.equation: 2 . 256 = 4 . xGood luck!
The required equation that represents the scenario is x = 64 * 2 + 256 * 4
Given that,
Maya throws a rock straight up from the edge of a 192-foot cliff and into the ocean. After two seconds, the rock reaches a maximum height of 256 feet. Four seconds later, the rock enters the ocean. To write an equation to model the scenario.
the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
let the total distance covered by the rock vertically be x,
now,
Distance traveled by the rock vertical upward in 2 seconds = 2 * (256 - 192)
= 2 * 64
Distance traveled by the rock vertical downward in 4 seconds = 4 * 256
Total distance,
x = 2 * 64 + 4 * 256
Thus, the required equation that represents the scenario is x = 64 * 2 + 256 * 40.
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What is the value of X?
Answer:
x=2
Step-by-step explanation:
A line that intersects a circle in two points is called a secant line, and this is the case for both line DE and AE.
For two secant lines that intersect outside of the circle, such as the ones here, we can say that
CE * DE = BE * AE
Therefore, we need to then define these lines.
CE is x+4, BE is x+1, AE = (BE + AB) = 11+x+1 = 12+x, and DE = (CE + DC) = 1+x+4 = 5+x
We then have
(x+4) * (5+x) = (x+1) * (12+x)
expand
5x + x² + 20 + 4x = 12x+x²+12+x
x²+9x + 20 = x²+13x+12
Next, we want to congregate all values to one side so we can solve for x. This can be done by subtracting both sides by (x²+13x+12) to get
-4x + 8 = 0
subtract 8 from both sides to isolate the x and its coefficient
-4x = -8
divide both sides by -4 to isolate the x
x = 2
Clare asks Andre to play the following number puzzle:
Pick a number
Add 2
Multiply by 3
Subtract 7
Add your original number
Andre’s final result is 27.
Which number did he start with?
Answer:
The answer is 7.
Step-by-step explanation:
7 + 2 is 9.
9 x 3 =27
27 - 7 =20.
Since the original number is 7 then we add 7 to 20.
7 + 20 = 27.
So, the number he started with is 7.
The senior classes at High School A and High School B planned separate trips to Lake Compounce. The senior class at High School A rented and filled 6 vans and 7 buses with 412 students. High school B rented and filled 6 vans and 9 buses with 504 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
Answer:
Number of students in vans =15 and bus =46
Step-by-step explanation:
use variables for the vans and buses
let x= vans and y=buses
Now solve the 2 equations simultaneously
remember to number your equations
6x+7y=412..........1
6x+9y=504.........2
make x the subject of one equation
and label it equation 3
6x=412—7y
\(x = \frac{206}{3} - \frac{7y}{6} .............3\)
subs 3 into 2
\(6( \frac{206}{3} - \frac{7y}{6} ) + 9y = 504\)
\(412 - 7y + 9y = 504\)
\( - 7y + 9y = 504 - 412\)
\(2y = 92\)
\(y = 46...................4\)
subs 4 into 1
\(6x + 7(46) = 412\)
\(6x + 322 = 412\)
\(6x = 412 - 322\)
\(6x = 90\)
\(x = 15\)
Therefore there are 15 students in each van and 46 students in each bus.
What is Y =- 2 on a graph?.
The equation y = -2 is represented on the graph as shown below :
Use the slope-intercept form to find the slope and y-intercept.
The slope, m, represents the steepness of a line. The slope of the line is also termed as gradient, sometimes. The y-intercept, b, of a line, represents the y-coordinate of the point where the graph of the line intersects the y-axis.
The slope-intercept form is
y = mx + b, where m is the slope and b is the y-intercept.
y = mx + b
Find the values of m and b, using the slope-intercept equation.
y = -2
m = 0, b = -2.
The slope of this line = m = 0
The y-intercept = -2, therefore a point on the line = (0,-2)
Finding two points on the line:
(0,-2), (1,-2)
Thus, the equation y = -2 on graph is shown below.
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A. It is not a number square.
B. Key = 5
C. Key = 4
Answer:
C, the key of the number square is 4
Step-by-step explanation:
Suppose 30= ”a” multiplied by 60 what is 30 divided by “a”
Your answer is 60.
We can write the given statement in equation form:
\(30 = 60a\)
Now, if we divide both sides by "a", we get:
\(\frac{30}{a} = 60\)
Because (60 × a)/a = 60.
You can also answer this question by solving for a, and then dividing 30 by this value:
30 = 60a
÷ 60
1/2 = a
Therefore, 30 ÷ 1/2 = 60.
I hope this helps!
Rebecca carries a balance on her credit card each month. Today is the first day of the new. 28-day billing cycle. The current balance is x and the APR is 24%.
Rebecca is buying a friend an expensive gift that costs $1,400 that she plans to put on her credit card. This will be her only purchase this month. Sed she will be
making this purchase on the last day of the month. Part A if her finance charge will be $51 write and solve an equation to determine her current balance on her credit card show your work. Part B How much in finance charges can she save by making the purchase on the last day of the billing cycle
Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.
Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.
How do equations work?
A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.
Equation symbols (=) are used to represent equations.
A finance charge is what?
The interest and other fees levied on credit cards are included in a finance charge.
Typically, the finance charge is based on a stated APR (annual percentage rate).
The month's billing cycle lasts for 28 days.
Balance at current starting = x.
APR = 24%, or annual percentage rate.
The monthly percentage rate (MPR) equals 2% (24% divided by 12).
The final day's purchase cost $1,400.
$51 is the total finance fee for the month.
($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.
$50 ($51 - $1) serves as the initial balance's finance charge.
The starting balance at this time is x = $2,500 ($50 x 2%).
Current Beginning Balance Equation: x = 51 - 1 0.02
($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.
Finance charge savings from buying on the last day equals $27 ($28 - $1).
By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.
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What do pie charts usually show? A. 600/1600 What are pie charts good for? B. a small part, share or number of the whole the proportion of C. 75% What does each segment of the circle represent? D. 80%,4/5 the percentage of over a quarter of E. summarizing categorical data. a small proportion of F. represents a certain category. a large proportion of G. 400/1600 four-fifths H. More than 25% I. show the components of a whole. J. a part, share, or number considered in comparative relation to a wh- three fifths K. 7/10 or 70% 7 out of 10 L. a larg part, share or number of the whole three quaters M. about 0.442 N. an amount expressed as if it is part of a total which is 100 When are pie charts not useful? P. 60% 25%= 44.2%
Pie charts usually show the components or categories of a whole.
A pie chart is a circular graphical representation used to display categorical data. It divides the circle into sectors, where each sector represents a specific category or component.
The size of each sector or "slice" is proportional to the relative frequency or proportion of the category it represents. The whole circle represents the total or 100% of the data being summarized.
Pie charts are good for summarizing categorical data and visually representing the distribution or composition of different categories within a dataset.
They provide a clear visual depiction of the proportions and relative sizes of the categories. Pie charts are especially useful when you want to emphasize the comparisons between different categories or show the relationship between parts and the whole.
However, there are cases where pie charts are not useful or may not be the most appropriate choice. For instance:
1. When there are too many categories: Pie charts become less effective when there are numerous categories, as the slices can become too small and difficult to interpret.
2. When the data is continuous or numerical: Pie charts are primarily used for categorical data, and other types of charts like bar charts or line graphs are more suitable for representing continuous or numerical data.
3. When precise comparisons or exact values are necessary: Pie charts provide a visual overview of proportions but do not accurately convey precise numerical values. In such cases, using a table or other types of charts may be more appropriate.
4. When the data has overlapping or similar proportions: Pie charts can be misleading if the categories have similar proportions, as it becomes challenging to differentiate between the slices.
It is important to consider the specific context and data characteristics to determine whether a pie chart is the most effective and informative visualization choice.
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Let "x" = square root of 6 + the square root of 7. What two consecutive integers does "x" lie between? Can you please explain in words, how you got the answer?
Answer:
(5, 6)
Step-by-step explanation:
\(x=\sqrt{6}+\sqrt{7}\approx2.45+2.65\approx 5.10\\\\\boxed{5<x<6}\)
I evaluated the expression on my calculator.
__
You can guess that the sum is nearly 2√6.5 = √26. This is between √5² and √6², so the root is likely between 5 and 6.
Dora wants to paint the walls, ceiling and floor of her
playhouse. The dimensions of the playhouse are 3 m long
by 4 m wide by 5 m high. What is the total area that she
must paint?
Answer:
Step-by-step explanation:
gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. it forms a pile in the shape of a right circular cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 25 feet high?
Below is the answer
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Write the equation of the line that passes through (2, -10) and has a slope of -3.
Answer:
y = -3x - 4
Step-by-step explanation:
y = mx + b
-10 = -3 (2) + b
-10 = -6 + b
b = -4
MATH PLS HELP
(7h+9)+(4h+4)
Answer:
11h+13
Step-by-step explanation:
7h+4h=11h
9+4=13
Answer:
11h+13
Step-by-step explanation:
Combine like terms.
in a sample of 100 steel canisters, the mean wall thickness was 8.1 mm with a standard deviation of 0.6 mm. find a 95% confidence interval for the mean wall thickness of this type of canister.
The wall of this type of canister is 7.984.
What is standard deviation?
Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.
Given, mean = 8.1 mm
number of canister n = 100
standard deviation = 0.6
Standard error due to sampling:
= standard deviation/ square root of n
=0.6/10
= 0.06.
The mean wall thickness is
= 7.984
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If u understand this May u please help me please
Answer:
y=-(2/3)x-3
Step-by-step explanation:
The rectangle has a length of -2x + 10 and a width of 10. a) Find the area of the rectangle and simplify.
Answer:
Area = -20x + 100Perimeter = -4x + 40Step-by-step explanation:
Given rectangle with
Length l = - 2x + 10 Width w = 10To find
AreaPerimeterSolution
A = lwA = (-2x + 10)*10 = -20x + 100P = 2(l +w) P = 2( -2x + 10 + 10) = 2( -2x + 20) = -4x + 40
A farmer wants to create a rectangular pen for his hogs. The fence should be at least 60 feet long and the
distance around it should be no more than 310 feet. What are the possible dimensions?
Valid dimensions for the rectangular pen that satisfy the given constraints are: L = 20 feet, W = 10 feet; L = 40 feet, W = 20 feet; L = 80 feet, W = 75 feet.
What are the permissible dimensions for the rectangular pen based on the given constraints of minimum length and maximum perimeter?To find the possible dimensions for the rectangular pen, we need to consider the constraints given: the fence should be at least 60 feet long and the distance around it should be no more than 310 feet.
Let's assume the length of the rectangular pen is L and the width is W.
The perimeter of a rectangle is given by the formula: P = 2L + 2W.
According to the constraints:
The fence should be at least 60 feet long, so we have the inequality: 2L + 2W ≥ 60.
The distance around the fence should be no more than 310 feet, so we have the inequality: 2L + 2W ≤ 310.
We can solve these inequalities to determine the possible dimensions.
2L + 2W ≥ 60:
We can rearrange this inequality as L + W ≥ 30.
2L + 2W ≤ 310:
We can simplify this inequality as L + W ≤ 155.
The possible dimensions for the rectangular pen are any values of L and W that satisfy both inequalities:
L + W ≥ 30
L + W ≤ 155
This means the length and width must be positive numbers that add up to 30 or more, but no more than 155. Since there are infinitely many possible combinations, here are a few examples of valid dimensions that satisfy the constraints:
- L = 20 feet, W = 10 feet (perimeter: 60 feet)
- L = 40 feet, W = 20 feet (perimeter: 120 feet)
- L = 80 feet, W = 75 feet (perimeter: 310 feet)
These are just a few examples, and there are many other combinations that would satisfy the given constraints.
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Complete the double number line to show the other values of fat and protein.
The double number line which shows the other values of fat and protein is: option B.
What is a number line?A number line is a type of graph with a graduated straight line which contain numerical values that are placed at equal intervals along its length.
For the fat component, we have:
Fat = 2n = 0, 2, 4, 6, 8.
For the protein component, we have:
Protein = 11n = 0, 11, 22, 33, 44.
Note: n represent integers such as 0, 1, 2, 3 and 4.
In conclusion, the double number line which represent the other values of fat and protein is shown in the image attached below.
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Complete Question:
One serving of beef je-rky contains 2 grams of fat and 11 grams of protein. Complete the double number line to show the other values of fat and protein.
4. Ash has $1,500 to invest. The bank he has selected offers continuously compounding interest. What would the interest rate need to be for Ash to double his money after 7 years? You may use your calculator and solve graphically, or you may use logarithms. Round your answer to 3 decimal places
The interest rate needed for Ash to double his money after 7 years with continuously compounding interest is approximately 9.897%.
To find the interest rate, we can use the continuous compounding formula:
A = Pe^(rt)
Where A is the final amount, P is the initial amount, e is the mathematical constant e (approximately 2.71828), r is the interest rate, and t is the time.
If Ash wants to double his money, then the final amount is 2P. We can substitute the given values and solve for r:
2P = Pe^(rt)
2 = e^(rt)
ln(2) = rt
r = ln(2)/t
Substituting t = 7, we get:
r = ln(2)/7
Using a calculator to evaluate this expression, we get:
r ≈ 0.099
Rounding to 3 decimal places, the interest rate needed for Ash to double his money after 7 years with continuously compounding interest is approximately 9.897%.
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Please help! People on my last post didn’t help :(! I’ll give brainliest.
Bill keeps a colony of honeybees on his property. He has created an expression to represent
the number of honeybees that are in the colony t years after he decided to create the colony.
The expression Bill created is -1644 + 160t2 – 144.
After deciding to create the colony, it took a fair amount of time to prepare before actually
getting bees in his colony. After some time, the population in the colony started to decrease;
eventually Bill lost his colony.
(The questions are listed in the photo)
Answer:
It is 7823
Step-by-step explanation:
This is the right answere because it shows us how each number is placed and what we do with it
An eagle is perched in a tree 75 feet above sea level. Directly below the eagle, a fish is swimming in a lake 18 feet below sea level. What is the distance between the eagle and fish
Answer:
93 feet
Step-by-step explanation:
Eagle is 75 feet from sea level
The fish is 18 Feet below sea level
Add the 2 values 75+18 = 93
93 Feet
-- Gage Millar, Algebra 1/2 and Pre-Calc Tutor.
Is this right if not what’s the correct answer
hey friend your answer is
I hope it will helpful for you
mark as brainest answer
thank you
Alicia estimates that the surface area of a rectangular prism with a length of 11 meters,a width of 5. 6 meters,and a height of 7. 2 meters is about 334 cubic meters. Is her estimate reasonable?Explain your reasoning
Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.
To determine whether Alicia's estimate of the surface area of the rectangular prism is reasonable, we first need to check if her calculation of the volume of the rectangular prism is correct.
The formula for calculating the volume of a rectangular prism is:
Volume = length x width x height
Substituting the given values in the formula, we get:
Volume = 11 meters x 5.6 meters x 7.2 meters
Volume = 449.28 cubic meters
As we can see, Alicia's estimate of 334 cubic meters is significantly lower than the actual volume of the rectangular prism, which is 449.28 cubic meters. Therefore, her estimate of the surface area is likely to be incorrect as well.
It is also important to note that the problem statement asks about the estimate of the surface area, not the volume. However, since the formula for calculating the surface area of a rectangular prism also involves the dimensions of length, width, and height, it is highly likely that Alicia's estimate of the surface area would also be incorrect given her miscalculation of the volume.
In conclusion, Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.
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what is the domain of h
what is the average rate of change
y - 3 = -12 (x + 4)
Answer:
\( - 12x\)
Step-by-step explanation:
\(y - 3 = - 12(x + 4) \\ y - 3 = - 12x - 48 \\ y = - 12x - 45\)
Thr answer is the slope.
Answer:
\(-\frac{3}{10}\)
Step-by-step explanation:
The average rate of change of a function f ( x ) over the interval [ a , b ] is
\(=\frac{f(b)-f(a)}{b-a}\)
\(f(x)=\frac{3}{x-2}\)
and \([a,b]=[4,7]\)
\(f(b)=f(7)=\frac{3}{7-2}=\frac{3}{5}\)
\(f(b)=f(4)=\frac{3}{4-2}=\frac{3}{2}\)
The rate of change is
\(=\frac{f(b)-f(a)}{b-a}\)
\(=\frac{\frac{3}{3} -\frac{3}{2} }{7-4}\)
\(=-\frac{9}{10} *\frac{1}{3} =-\frac{3}{10}\)
Plxzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz helpe me if you can
Write an expression for the sequence of operations described below.
multiply 9 by the difference of 6 and 4
Answer:
not sure
Step-by-step explanation:
6-4 =2
2*9=18??
I'm not sure, since that was simple math, can you clarify by what you meant the difference of 6 and 4.
The table shows the number of cups of water required when cooking different amounts of rice.
Amount of
Rice
(cups) Amount of
Water
(cups)
2 5
3 7.5
5 12.5
8 20
Which statements apply to the ratio of rice and water? Choose two options.
The amount of rice is the dependent value.
The amount of water is the dependent value.
The amount of rice is the independent value.
The amount of water is the independent value.
The values cannot be labeled as dependent or independent without a given equation.
Answer:
C The amount of rice is the independent value
Step-by-step explanation:
The table in your question was formatted a bit off but im assuminng that it was meant to show that the amount of rice is the x value and the amount of water was the y value.
The x value is always the independant variable and the y value is the dependant variable. This is because the value of y will depend on x. In other words, the amount of water needed is going to depend on the amount of rice used.
Hope this helps
biblical tithing basically means you will give ______ percent of your income to the lord. 20 5 10 25
Biblical tithing basically means you will give 10 percent of your income to the lord.The word tithe refers to "tenth" or "tenth part," so biblical tithing implies offering one-tenth of one's income to the church.
Biblical tithing is the method of giving the first fruits of one's labor to the Lord. Tithing originated from the Old Testament in which people would offer 10% of their harvest to the Lord.Tithing is a way of giving back to God as well as to others, according to the Bible.
As a result, Christians are required to tithe a tenth of their earnings. While this might appear to be a significant amount of money, if Christians can trust God with their finances, they can discover that he blesses them in ways they never imagined. In the New Testament, there is no specific requirement to tithe, but Christians are urged to give generously to the church and those in need.
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Find the missing number:
√25 x √25 = 25 x?
(A) 1
(B) 5
(C) 10
(D) 25
Step-by-step explanation:
since sqrt(25)×sqrt(25) = 25, then x can be any number, because x = x in all cases. and then both sides of the equation are always equal, no matter what value we give x, as long as x is a factor in both sides.
sqrt(25)×x×sqrt(25) = 25x
is always true for every x.
if the question would be
sqrt(25)×x×sqrt(25) = 25
then the answer can only be x = 1. because for every other value of x the equality is destroyed.