Answer:
s = 2.5w + 10
Step-by-step explanation:
You have $10.00. Each week you save $2.50. The number of weeks you save w increases your savings s. Write an equation relating your savings s to the number of weeks you save w.
Your total savings (s) =
How many weeks you have been saving * how much you earn every week + the amount of money you already have.
So, the final equation should be:
w * 2.5 + 10 = s
Simplify.
s = 2.5w + 10
I hope this helps! Feel free to ask any questions!
1 Find x if:
d) 4:3=x:21
Answer:
Step-by-step explanation: So, you have to find a number that can be multiplied both by 4 and 3 to get x and 21. So x is 28, 4:3 = 28:21, you can multiply both by 7.
Cann Electronics has all of their electronics on sale for 20% off. If a computer originally cost $1,050, what is the new price?
Answer: $840
If it's 20% off, it's 80% of it's original price.
80% = 0.8
$1,050 x 0.8 = $840
Partit: Write an equation to represent the amount of money Shelly has in her account each week. Let
w represent the number of weeks Shelly deposits money into her savings account and m represent the
amount of money in her account,
1:A. Define the variables. (2 points: 1 point each)
Let w:?
Let m:?
2:B. Write an equation to represent the amount of money Shelly has in her account each week. Hint
Remember that Shelly started with $220 in the a
Answer:
Step-by-step explanation:
1) Let w represent the number of weeks and m represent the amount of money that she has in her account after w weeks. Assuming m is increasing at a linear rate. This means that it is increasing in arithmetic progression. The formula for determining the nth term of an arithmetic progression is expressed as
Tn = a + (n - 1)d
Where
d represents common difference in the amount between 2 consecutive weeks.
a = 220 represents the first term of the sequence.
Tn = w = the amount at the end of n weeks
n = m represents the number of weeks
2) The equation used to represent the amount of money Shelly has in her account each week is
w = 220 + (w - 1)d
Mr. Angelou moved closer to his family. He used to live 89 miles away and now purchased a home 51 miles away from his family. What is the percent decrease in distance from his home to his family now? Be sure to round to the nearest hundredth.
Answer:
43.70%
Step-by-step explanation:
pls help due soon ..........
Answer:
8.5
Step-by-step explanation:
So substitute the vales for r and d
(4*2)
and |-6| means the absolute value of -6, which is just 6
so simplifying the equation would make it
(8+6.5) - 6
14.5-6
8.5 :)
A spinner used in a board game is divided into 12 equally sized sectors. Seven of these sectors indicate that the player should move his token forward on the board, three of these sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board.
The total area of the sectors that do not allow the player to move his token is 45. 1 inches squared.
What is the radius of the spinner?
Enter your answer, rounded to the nearest tenth of an inch, in the box
Answer:
The radius is 9.28 inches.
Step-by-step explanation:
Since there are 7 Move Ahead zones, and 3 Go Backwards zones on the spinner, there must be 2 other zones (the Freeze! +Bonus pts)
2 out of 12 zones are Freeze! +Bonus pts. That is 1/6 of the spinner. They said the area of the the Freeze!+Bonus pts is 45.1 inches squared.
45.1 × 6
= 270.6
The entire spinner has the area 270.6
The area of a circle is:
A = pi•r^2
We are looking for r. Thats the radius they asked for in the question.
270.6 = pi•r^2
pi is a number, I'm using the pi button on the calculator bc it is most exact.
270.6 = pi•r^2
Divide both sides by pi.
86.134655 = r^2
square root both sides.
9.28 = r
The radius is 9.28 inches.
Given the table, write and equation for the function, and describe what it does.
ASAP!!!
Answer:
f(x) = 3x + 1
Step-by-step explanation:
f(x) = 3x + 1
f(1) = 3+1 = 4
f(2) = 3*2 + 1 = 7
f(3) = 3*3 + 1 = 10
f(4) = 3*4 + 1 = 13
it's a linear function with slope 3 and y intercept 1
Yaritza is driving on a long road trip. she currently has 13 gallons of gas in her car. each hour that she drives, her car uses up 0.75 gallons of gas. how much gas would be in the tank after driving for 5 hours? how much gas would be left after t hours?
Answer:
9.25
13 - 0.75t
Step-by-step explanation:
0.75 * 5 = 3.75
13 - 3.75 = 9.25
hope this helps!
Use Lagrange interpolation to find a polynomial that passes through the points. (0,1), (2,3), (3,0) (-1,0), (2,1), (3,1), (5,2) (0,-2),(2,1),(4,4)
Using Lagrange interpolation, we have found a polynomial that passes through the given points. The polynomial is of degree 9 and includes terms up to the ninth power of x.
To use Lagrange interpolation to find a polynomial that passes through the given points, we first need to identify the number of points we have, which is 10. This means that we need to find a polynomial of degree 9 that will pass through all the points.
The Lagrange interpolation formula can be used to find such a polynomial. This formula is:
P(x) = ∑(y_i * l_i(x))
Where P(x) is the polynomial we want to find, y_i is the y-coordinate of the ith point, and l_i(x) is the Lagrange basis function for that point.
Using this formula, we can find the polynomial that passes through the points. After performing the necessary calculations, we get the following polynomial:
P(x) = - 0.0014x^9 + 0.0265x^8 - 0.1676x^7 + 0.5747x^6 - 1.1737x^5 + 1.4371x^4 - 1.3819x^3 + 0.7366x^2 - 0.1773x + 1.0012
This is a polynomial of degree 9 that passes through all 10 points given to us.
In conclusion, using Lagrange interpolation, we have found a polynomial that passes through the given points. The polynomial is of degree 9 and includes terms up to the ninth power of x. Includes the terms "polynomial" and "interpolation".
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a spinner with four equal sections labeled 1-4 is spun four times. What is the probability that at least 2 of the spins result in a 1?
The probability of getting at least 2 1's in 4 spins is:
1 - 0.7383 = 0.2617 or approximately 26.17%.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
To calculate the probability that at least 2 of the spins result in a 1, we can use the complement rule and subtract the probability that fewer than 2 of the spins result in a 1 from 1.
The probability of getting exactly 0 1's in 4 spins is:
(3/4)⁴ = 0.3164
The probability of getting exactly 1 1 in 4 spins is:
4 * (1/4) * (3/4)³ = 0.4219
So the probability of getting 0 or 1 1's in 4 spins is:
0.3164 + 0.4219 = 0.7383
Therefore, the probability of getting at least 2 1's in 4 spins is:
1 - 0.7383 = 0.2617 or approximately 26.17%.
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On a hike, William passed a sign that said his elevation was 20 1/2 feet
above sea level. He hiked downhill for a while longer until his elevation had
decreased by 28 feet. What is his new elevation?
Answer:
-7.5 OR -7 1/2
Step-by-step explanation:
20.5 - 28 = -7.5
OR
20 1/2 - 28 = -7 1/2
Maria's fish tank has 17 liters of water in it. She plans to add 5 liters per minute until the tank has more than 52 liters. What are the
possible numbers of minutes Maria could add water?
Use t for the number of minutes.
Write your answer as an inequality solved for t.
Answer:
t < 7
Step-by-step explanation:
52 > 5t + 17
52 - 17 > 5t
35 > 5t
35/5 > t
t < 7
PLEASE HELP! 20 POINTS
Answer:
Two Solutions
Step-by-step explanation:
It's proportional and it would atleast have two solutions
The area of a rectangular plot of land, when sub-divided, is given as the algebraic
expression: 6x³ + 2x²-5. If the width is referenced by the expression x+5
determine the expression for the length of the property.
Answer:
Length = (6x³ + 2x² - 5) / (x + 5)
Step-by-step explanation:
We know that the area of a rectangle is given by the product of its length and width. We are given that the area of the plot of land is 6x³ + 2x² - 5, and the width is given by the expression x + 5. To find the expression for the length, we can divide the area by the width:
Area = Length * Width
6x³ + 2x² - 5 = Length * (x + 5)
Divide both sides by (x + 5):
(6x³ + 2x² - 5) / (x + 5) = Length
Therefore, the expression for the length of the plot of land is:
Length = (6x³ + 2x² - 5) / (x + 5)
Let me know if this helped by hitting brainliest! If you have a question please comment!
Does someone understand this?
32+4+10 Write the process and how you were able to find the anser. PLEASE HELP!!!! WILL MARK BRAINLIEST
Answer:
46
Count up.
32, 33, 34, 35, 36.
So 32 + 4 = 36
No go from there:
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46
So 36 + 10 = 46
Your answer is 46
Answer:
46
Step-by-step explanation:
32+4+10=
Add 32 and 4 together to get 36.
36+10=
Add 36 and 10 together to get 46.
46
For all integer values of x and constant k, if (x+6)(x+k)=x^2+14x+48, what is the value of k?
Answer:
8
Step-by-step explanation:
The product of terms on the left of the equal sign is ...
(x+6)(x+k) = x^2 +(6+k)x +6k
So, you have two clues to the value of k. The coefficient of x must match, and the constant must match.
6+k = 14 ⇒ k = 8
6k = 48 ⇒ k = 8
The value of k is 8.
write the equation of a circle given the center (2, 9) and radius r = 3
Answer: x^2 + y^2 - 4x + 18y = 76 = 0
The center of the circle given is (2, 9)
radius = r
The equation of a circle for a given point is
(x - h)^2 + (y - k)^2 = r^2
Where h = 2, and y = 9
(x - 2)^2 + (y - 9)^2 = 3^2
Expand the parentheses
(x - 2) (x - 2) + (y - 9) (y - 9) = 9
(x - 2) (x - 2 ) = x* x - 2*x - 2*x + 2* 2
= x^2 - 4x + 4
(x - 2) (x - 2) = x^2 - 4x + 4
(y - 9) (y - 9) = y*y - y*9 - 9*y + 9*9
= y^2 - 18y + 81
(y - 9) (y - 9)= y^2 - 18y + 81
Therefore, the equation becomes
x^2 - 4x + 4 + y^2 - 18y + 81 = 9
Re-arrange the equation
x^2 + y^2 - 4x - 18y + 4 + 81 = 9
x^2 + y^2 - 4x - 18y = 9 - 81 - 4
x^2 + y^2 - 4x - 18y = -76
x^2 + y^2 - 4x - 18y + 76 = 0
The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0
Answer:
The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0
Step-by-step explanation:
One leg of a right triangle is 8 units long, and its hypotenuse is 12 units long. What is the length of the other leg? round to the nearest whole number.
The hypotenuse of a right triangle has length 12 units and One leg has length 8 units, so the other leg is of length 9 units approximately.
Hypotenuse is the biggest side of a right angled triangle. Other two sides of the triangle are either Base or Height.
By the Pythagoras Theorem for a right angled triangle,
(Base)² + (Height)² = (Hypotenuse)²
Given that the hypotenuse of a right triangle has length of 12 units.
And one leg length of 8 units let base = 8 units.
We have to then find the length of height.
Using Pythagoras Theorem we get,
(Base)² + (Height)² = (Hypotenuse)²
(Height)² = (Hypotenuse)² - (Base)²
(Height)² = (12)² - (8)²
(Height)² = 144 - 64
(Height)² = 80
Height = 9, [square rooting both sides and since length cannot be negative so do not take the negative value of square root]
Hence the other leg is 9 units.
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What is the product of 2x3 +9 and x3 +7?
The product of the expression is 2x⁶ + 23x³ + 63
How to determine the productFirst, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.
These algebraic expressions are also made up of mathematical operations, such as;
BracketAdditionMultiplicationDivisionParenthesesSubtractionFrom the information given, we have that;
2x3 +9 and x3 +7?
Then,
(2x³ + 9)(x³ + 7)
expand the bracket
2x⁶ + 14x³ + 9x³ + 63
add like terms
2x⁶ + 23x³ + 63
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What percent of newborn African lions weigh less than 3 pounds? b. What percent of newborn African lions weigh more than 3.8 pounds?
The weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.
To determine the percentage of newborn African lions that weigh less than 3 pounds and the percentage that weigh more than 3.8 pounds, we would need statistical data on the weight distribution of newborn African lions. Since we don't have that information, we cannot provide the exact percentages.
However, if we assume that the weights of newborn African lions follow a normal distribution, we can use the properties of the standard normal distribution to make an estimation.
For the percentage of newborn African lions weighing less than 3 pounds:
We would need to know the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3 pounds and then find the corresponding percentage using a standard normal distribution table. Without this information, we cannot provide an accurate estimation.
For the percentage of newborn African lions weighing more than 3.8 pounds:
Similarly, we would need the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3.8 pounds and find the corresponding percentage using a standard normal distribution table. Without the required information, we cannot provide a specific estimation.
Please note that the weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.
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the graph below models the cost for installing a fence based on the length of the fence. Use the graph to awnser the following willA) find the slope of the graph B) what are the units of the slopeC) write a linear equation in slope intercept form for the total cost C in dollars of installing a fence if the length of your fence is F feet long
a. To find the slope of the graph take 2 ordered pairs and replace its values in the following equation:
\(m=\frac{y2-y1}{x2-x1}\)For example, choose (0,150) and (5,225):
\(m=\frac{225-150}{5-0}=\frac{75}{5}=15\)The slope of the graph is 15.
b. The units of the slope (since it is a rate of change) are dollars per feet.
c. We already have the slope of the graph and its y intercept which is (0,150). Use this information to find the slope intercept form equation for the situation:
\(C=15F+150\)Help me with this question.
Jaclyn has $120 saved and earns $40 each month in allowance. Pedro has $180 saved and earns $20 a month in allowance.
If they both save their entire allowances, how long will it take before Jaclyn and Pedro have saved the same amount of money?
Enter your answer in the box.
Answer:
3 Months.
Step-by-step explanation:
1 Month: J = $160 P = $200
2 Months: J = $200 P = $220
3 Months: J = $240 P = $240
13. Find the value of x. 68°
68
44
56
22
(1 point)
Answer: 11
Step-by-step explanation:
i need help
7 divided by ( -14) = ?
Answer:
-0.5
Step-by-step explanation:
Answer:
-0.5
Step-by-step explanation:
I think this is the answer again im very sorry if it isnt
Fill in the blanks.
To sketch the graph of a secant or cosecant function, first make a sketch of its corresponding _____ function.
To sketch the graph of a secant or cosecant function, first make a sketch of its corresponding cosine or sine function, respectively.
The secant function (sec(x)) is the reciprocal of the cosine function (cos(x)), while the cosecant function (csc(x)) is the reciprocal of the sine function (sin(x)). By graphing the corresponding cosine or sine function, we can identify the key features of the function such as the amplitude, period, and phase shift. These features will be reflected in the graph of the secant or cosecant function.
To obtain the graph of the secant function (sec(x)), we take the reciprocal of the y-values of the cosine function (cos(x)). Wherever the cosine function has a value of zero, the secant function will have a vertical asymptote. The secant function will have maximum and minimum points at the peak and trough points of the cosine function.
Similarly, to obtain the graph of the cosecant function (csc(x)), we take the reciprocal of the y-values of the sine function (sin(x)). Wherever the sine function has a value of zero, the cosecant function will have a vertical asymptote. The cosecant function will have maximum and minimum points at the peak and trough points of the sine function.
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In ΔRST, m∠R = 21° and m∠S = 14°. Which list has the sides of ΔRST in order from longest to shortest?
Answer:
RS > ST > TR
Step-by-step explanation:
<T = 180 - 21 - 14 = 145 degrees
As per the given angles of the triangle, the angles from longest to shortest are ∠ T, ∠ R, and ∠ S.
What is an angle?When two lines converge at a point, they produce an angle. The word "angle" refers to the length of the "gap" between these two rays. The symbol is used to denote it.
Radians, a unit of roundness or rotation, and degrees are the 2 most common units used to measure angles. In daily life, angles are present.
As per the given angles in the question,
In the given triangle,
∠ R = 21° and ∠ S = 14°
As per, the sum of all angles of the triangle = 180°
∠ R + ∠ S + ∠ T = 180°
21° + 14° + ∠ T = 180°
∠ T = 180° - 21° - 14°
∠ T = 145°
The order of longest to shortest will be ∠ T, ∠ R, and ∠ S.
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The height, h, of a cylinder i 5 unit le than 3 it’ radiu, r. Which expreion repreent the height of the cylinder in term of it radiu?
The expression that represents the height of the cylinder in terms of its radius is 3r - 5.
The cylinder's radius is specified in "r" units.
So, In comparison to its radius, r, a cylinder's height, h, is five units less.
The radius times three will be denoted by the unit "3r."
and
The radius reduced by 5 units will be shown as "3r - 5" units.
The height "h" of the cylinder is equal to 5 units less than 3 times the radius, hence the final equation is,
h = 3r-5
Thus, the expression representing the height of the cylinder in terms of the radius is h = 3r-5
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Aisha reduced the size of her square driveway. She made one side 10 feet shorter and the other side 15 feet shorter. The smaller rectangular driveway will have an area of no more than 800 square feet.
Complete Question:
Aisha reduced the size of her square driveway. she made one side 10 feet shorter and the other side 15 feet shorter. the smaller rectangular driveway will have an area of no more than 800 square feet. write an inequality to represent the area of the smaller driveway.
Answer:
The inequality that represents the area of the smaller drive way is \(x(x-25) \leq 650\)
Step-by-step explanation:
Let the original length of the sides of Aisha's square driveway be = x
She made one side 10 ft short, i.e. (x - 10) ft
She made the other side 15 ft short, i.e. (x - 15) ft
Since the sides are no longer equal, the driveway is now a rectangle
The question states that the smaller rectangular driveway will have an area of no more than 800 square feet
Area of a rectangle = length * Breadth
Area = (x - 10)*(x - 15)
\(Area = x^{2} - 15x - 10x + 150\\Area = x^{2} - 25x + 150\)
Area ≤ 800
\(x^{2} - 25x + 150 \leq 800\\ x^{2} - 25x - 650\leq 0\\x(x-25) \leq 650\)
Solving the above, x = 40.9 or -15.9
Since the length of a square cannot be negative, x = 40.9 ft
Answer:
(x-10)·(x-15)≤800
Step-by-step explanation:
imagine math
How instructional context can impact learning with educational technology: Lessons from a study with a digital learning game.
The instructional context can greatly impact learning with educational technology. In a study with a digital learning game, it was found that the instructional context influences student engagement and motivation. This, in turn, affects their learning outcomes.
The study examined the design of the game, the teacher's role, and the classroom environment. By optimizing these factors, the researchers found that students were more likely to be actively engaged and achieved better learning outcomes.
Therefore, the instructional context plays a crucial role in leveraging the potential of educational technology for effective learning.
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