The value of y² is 1/5 ln(3+x¹⁰) + C
What is the separation of variables?
Separation of variables, in mathematics, is any of several strategies for rewriting equations so that each of two variables appears on a different side of the problem. These strategies are used to solve ordinary and partial differential equations.
Here, we have
Given: (3+^10)(/) = ^9/
We have to solve the differential equation by using the separation of variables.
Rewrite as y dy = x⁹/3+x¹⁰ dx
As (3+x¹⁰)' = 10x⁹, we solve
y²/2 = 1/10 ln(3+x¹⁰) + C
y² = 1/5 ln(3+x¹⁰) + 2C
Since C is any constant, y² = 1/5 ln(3+x¹⁰) + C
Hence, the value of y² is 1/5 ln(3+x¹⁰) + C
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Vlad spent 20 minutes on his history homework and then completely solve X math problems that took two minutes to complete what is the equation that could be used to find the value of why the total time that Vlad spent on his homework and what are the constraints on the values of X and y
The total time of homework is represented by T = 2x + 20.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Vlad spent 20 minutes on his history homework and then completely solved X math problems that took two minutes to complete.
The expression can be written as:-
T = 2x + 20 minutes
Here, T is the total time, and x is the number of math problems.
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A town has a population of 78,000 and shrinks at a rate of 3% every year. Which equation represents the town’s population after 5 years?
The equation that represents the town's population is p = 78,000 x 0.97^5.
What is the equation?The equation that represents the town's population is an exponential equation. The general form of exponential equation is f(x) = [tex]e^{x}[/tex]
Where:
x = the variable e = constantThe form o f the equation is:
Future population = present population x (1 - rate of decline/100)^number of years
p = 78,000 x (1 - 3/100)^5
p = 78,000x (1 - 0.03)^5
p = 78,000 x (0.97^5)
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Ask a question about your assignment
Answer: 146
Step-by-step explanation:
HK = GK x 2 because a rectangles diagonals are equal.
73 x 2 = 146
Answer:
146 that should be right
A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100(extremely good quality). The stem-and-leaf display of the data is shown to the right. What percentage of the respondents rated overall television quality with a rating of 50 or below? show answer please A. 56 B. 44 C. 11 D. 40
Approximately 43.3% of the respondents rated overall television quality with a rating of 50 or below. The closest answer choice is D. 40
What is the range of the data?
The range is the spread of your data from the lowest to the highest value in the distribution. It is a commonly used measure of variability. Along with measures of central tendency, measures of variability give you descriptive statistics for summarizing your data set
The stem-and-leaf display shows that the data ranges from 0 to 100.
The leaves on the stem for the number "5" are 0, 0, 1, 2, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9.
This means that 13 of the respondents rated overall television quality with a rating of 50 or below.
To find the percentage of respondents who rated television quality 50 or below, we need to divide the number of respondents who rated television quality 50 or below (13) by the total number of respondents and multiply by 100.
13/30 * 100 = 43.333...
Hence, approximately 43.3% of the respondents rated overall television quality with a rating of 50 or below. The closest answer choice is D. 40%.
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The depth, d, of a lake is 500 m, rounded to the nearest integer.
Write the error interval for d in the form a ≤ d < b.
Answer: The depth, d, of a lake is 500 m, rounded to the nearest integer. The error interval for d is 499.5 ≤ d < 500.5
When a value is rounded to the nearest integer, the possible error is half of the smallest unit of measurement. In this case, the smallest unit of measurement is 1 meter, so the possible error is 0.5 meters. Therefore, the error interval for d is from -0.5 meters to +0.5 meters around the rounded value of 500 meters.
This can be expressed in the form a ≤ d < b as follows:
a = 500 - 0.5 = 499.5
b = 500 + 0.5 = 500.5
So, 499.5 ≤ d < 500.5
Step-by-step explanation:
Calcular el valor numerico de la funcion polinomica.
Gracias al que respondio :)
Los valores de las expresiones polinomicas son:
10*(1/2)^2 - 4*(1/2) = 1/2
(2/3)*(-3/4) - (1/2)*(-3/4)^2 = -25/32
¿Como resolver las expresiones?En este problema queremos encontrar los valores de dos expresiones polinomicas.
La primera es:
10*(1/2)^2 - 4*(1/2)
Primero resolvemos el cuadrado del primer termino, esto da:
10*(1/4) - 4*1/2
10/4 - 4/2
Ahora queremos tener el mismo denominador en ambas fracciones, asi reescribimos la primear como:
5/2 - 4/2
1/2
Ese es el valor numerico.
La segunda expression es:
(2/3)*(-3/4) - (1/2)*(-3/4)^2
Primero resolvemos el cuadrado, recordar que esto cancela el signo negativo:
(2/3)*(-3/4) - (1/2)*(9/16)
Ahora tomamos los productos entre fracciones:
(2/3)*(-3/4) - (1/2)*(9/16)
-6/12 - 9/32
Simplificamos ambas fracciones:
-1/2 - 9/32
Escribimos ambas fracciones con el mismo denominador:
-16/32 - 9/32 = -25/32
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A string measures 30cm. About how many inches long is the string
Answer: 11.811 inches
Step-by-step explanation:
There are about 0.3937 inches in a cm, so the answer is [tex]30(0.3937)=11.811[/tex] inches.
Find the slope of the line that goes through the points (0, 9) and (-2, -4).
refer to exercise 3. calculate the mean of the random variable x and interpret this result in context.
The mean of the random variable x is 4.4. This means that, on average, when x is randomly sampled, the value it will take is 4.4. In other words, the expected value of x is 4.4.
To calculate the mean of the random variable x, we can use the formula [tex]$\mu = \frac{1}{n}\sum x_i$[/tex], where $\mu$ is the mean, $n$ is the number of values, and $x_i$ is the value of the random variable for each observation.
In this case, the mean of x is[tex]$\mu = \frac{1}{5}\sum x_i = \frac{1}{5}(2 + 6 + 4 + 5 + 7) = 4.4$.[/tex]
Interpreting this result in context, the mean of the random variable x is 4.4. This means that, on average, when x is randomly sampled, the value it will take is 4.4. In other words, the expected value of x is 4.4.
The mean of the random variable x is 4.4. This means that, on average, when x is randomly sampled, the value it will take is 4.4. In other words, the expected value of x is 4.4.
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You should have two 2-bit inputs and 4 output bits. The logic required to calculate each bit is on the website. Come and see me if you have problems. You must build your circuit out of logic gates, you cannot use the adder circuits already built. Your assignment must be turned in as a separate .circ file along with your word file or pdf for the other problems. To verify your output, your input/output table should look like this: Using Logisim, design a 2 bit multiplier.
This answer explains how to design a 2-bit multiplier using Logarithm. The circuit requires two 2-bit inputs, A and B, and four output bits, C0, C1, C2, and C3. To build the circuit, two 1-bit full adders are used for each bit of inputs A and B and the outputs are connected accordingly. Finally, the circuit is tested to verify that it is working as expected.
Input A: 0 0
Input B: 0 0
Output C: 0 0 0 0
Input A: 0 0
Input B: 0 1
Output C: 0 0 0 1
Input A: 0 0
Input B: 1 0
Output C: 0 0 1 0
Input A: 0 0
Input B: 1 1
Output C: 0 0 1 1
Input A: 0 1
Input B: 0 0
Output C: 0 0 0 1
Input A: 0 1
Input B: 0 1
Output C: 0 0 1 1
Input A: 0 1
Input B: 1 0
Output C: 0 1 0 0
Input A: 0 1
Input B: 1 1
Output C: 0 1 0 1
Input A: 1 0
Input B: 0 0
Output C: 0 0 1 0
Input A: 1 0
Input B: 0 1
Output C: 0 0 1 1
Input A: 1 0
Input B: 1 0
Output C: 0 1 1 0
Input A: 1 0
Input B: 1 1
1. Start with two 2-bit inputs A and B.
2. Create four output bits, C0, C1, C2, and C3.
3. Create two 1-bit full adders, one for each bit of inputs A and B.
4. Connect the inputs A and B to the inputs of the two respective full adders.
5. Connect the output of the first full adder to the input of the second full adder.
6. Connect the of the second full adder to the output of C0.
7. Create two more 1-bit full adders, and connect the output of the first full adder to one of the inputs of each of the two full adders.
8. Connect the other input of each of the two full adders to the corresponding bit of the inputs A and B.
9. Connect the output of the first 1-bit full adder to the output of C1.
10. Connect the output of the second 1-bit full adder to the output of C2.
11. Create one more 1-bit full adder and connect the output of the second 1-bit full adder and the corresponding bit of the inputs A and B to the two inputs of the logarithm 1-bit full adder.
12. Connect the output of the 1-bit full adder to the output of C3.
13. Test the inputs and outputs to verify that the circuit is working as expected.
This answer explains how to design a 2-bit multiplier using Logisim. The circuit requires two 2-bit inputs, A and B, and four output bits, C0, C1, C2, and C3. To build the circuit, two 1-bit full adders are used for each bit of inputs A and B and the outputs are connected accordingly. Finally, the circuit is tested to verify that it is working as expected.
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On January 3, 2004, after a journey of 300 million miles, the rover Spirit landed on Mars and began sending back information to Earth. It landed only six miles from its target. This accuracy is comparable to shooting an arrow at a target fifty feet away and missing the exact center by what distance?
This accuracy is comparable to shooting an arrow at a target fifty feet away and missing the exact center by the distance; 0.000001 miles
How to solve proportion word problems?Proportion word problems are simply ways of expressing proportion problems in words. For example we share oranges among three people each receiving 2, 3 and 4 respectively and as such the ratio of the proportion is 2:3:4.
Now, we are told that after a journey of 300 million miles, the rover Spirit landed on Mars and began sending back information to Earth. It landed only six miles from its target. This is comparable to shooting an arrow at a target fifty feet away and missing the exact center.
Thus, if the comparable distance missed is x, then we can say that;
x/50 = 6/300000000
x = (6 * 50)/300000000
x = 3/3000000
x = 0.000001
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help what's the answer. What is the value of 12 – 4 + 2h when h = 3?
Answer:
14
Step-by-step explanation:
To find the value of 12 – 4 + 2h when h = 3, we need to substitute the value of h into the expression and simplify.
When h = 3, we can substitute this value into the expression:
12 – 4 + 2h = 12 - 4 + 2*3 = 12 - 4 + 6 = 12 - 4 + 6 = 8 + 6 = 14
So the value of 12 – 4 + 2h when h = 3 is 14.
Answer:
12 - 4 + 2h = 14
Step-by-step explanation:
Given expression,
→ 12 - 4 + 2h
Now we have to use,
→ h = 3
Let's simplify the expression,
→ 12 - 4 + 2h
→ 12 - 4 + 2(3)
→ 12 - 4 + 6
→ 8 + 6
→ 14 => {final value}
Hence, required value is 14.
Rashaad has a loyalty card good for a 10% discount at his local hardware store. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $31.40? Round to the nearest cent.
Rashaad will pay $28.26 after the discount.
What is discount?The discount equals the difference between the price paid for and it’s par value. Discount is a kind of reduction or deduction in the cost price of a product.
Given that, Rashaad has a loyalty card good for a 10% discount, he bought something at $31.40, we need to find the total amount he needs to pay after the discount,
So, the amount he will pay is (100-10) = 90% of the original amount,
90% of 31.40
= 90 % × 31.40
= 90/100 × 31.40
= 2826/100
= 28.26
Hence, he will pay $28.26 after the discount.
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An imported item costs 500$. The retailer's plans to sell with a 70% increase in import price. After selling for a while, the seller decides to discount 20% of the first sale price and continue to discount 10% of the second sale price. Find the final sale price?
Profit is determined using the equation Profit = Selling Price - Cost Price. The final price after discount is $612.
Following this, the formula for calculating profit percentage is: profit percentage = (profit/cost price) x 100.
What is the loss percent formula?
The firm is considered to be losing money if a product's cost price is higher than its selling price; conversely, if the product's cost price is lower than its selling price, a profit might be made. Loss% is equal to Loss/CP multiplied by 100.
Profit is calculated as cost less selling price. Similar to this, the cost price is higher than the targeted selling price when a loss occurs. A profit percentage is computed by dividing the cost price by 100. 100 divided by the cost price is the loss percentage.
Determine the net profit and loss from a company's operations over the course of an accounting period with the help of the profit and loss account, also referred to as the income statement. The trading account's gross profit or loss is transferred to this account.
Given,
the cost price = $500
Selling price = 70% increase in import price
70 / 100 × $500 = $ 350
Selling price = $350 + $500
Selling price = $850
Selling price after 20% discount = 20% of $850
⇒ 0.2 × 850 = 170
⇒ Selling price after 20% discount = $850 - $170 = $680
Selling price after discount 10% = 0.10 × $680 = $68
Selling price after discount 10% = $680 - $68 = $612
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Write in point slope form and slope intercept form.
When given the point-slope form of a line, we first must identify the point and the slope in order to create a graph of the line.
How do you write point-slope form with a point slope?The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept). In order to emphasise the slope and y-intercept of the same line, we can rewrite an equation in point-slope form to be in slope-intercept form, y=mx+b.
Plug the slope and the (x, y) point values into y = mx + b, then solve for b using the substitution method.Point-slope form is represented as y y 1 = m (x x 1), where (x 1, y 1) is the supplied point and m is the given slope.
Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). A graph is usually simple to make.
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The given points can be written in point-slope form as y - 6 = -6(x - 4) and slope intercept form as y = -6x + 30.
How do you write point-slope form with a point slope?The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept). In order to emphasise the slope and y-intercept of the same line, we can rewrite an equation in point-slope form to be in slope-intercept form, y=mx+b.
Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). A graph is usually simple to make.
Given, x intercept = 5
which means when y = 0, x = 5 i.e. (5, 0)
And given a point (4, 6)
using the two points in slope formula
[tex]$\mathrm{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
[tex]$\mathrm{m = \frac{6- 0}{4 - 5}}[/tex]
m = 6/-1
m = -6
Now, as we have slope, put the data in point-slope form
y-y₁ = m(x -x₁)
y - 6 = -6(x - 4) ⇒ point-slope form
y - 6 = -6x + 24
y = -6x + 24 + 6
y = -6x + 30 ⇒ slope intercept form
Thus, the given points can be written in point-slope form as y - 6 = -6(x - 4) and slope intercept form as y = -6x + 30.
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find the third degree polynomial Q such that Q(1)=1 Q'(1)=3 Q"(1)=6 and Q'''(1)=12
Answer:
A third degree polynomial, also known as a cubic polynomial, has the form of
Q(x) = ax^3 + bx^2 + cx + d
Given that Q(1)=1, Q'(1)=3, Q''(1)=6, and Q'''(1)=12, we can use these values to find the coefficients a, b, c, and d.
Q(1) = a(1)^3 + b(1)^2 + c(1) + d = 1
Q'(1) = 3a + 2b + c = 3
Q''(1) = 6a + 2b = 6
Q'''(1) = 6a = 12
Solving for a:
6a = 12
a = 2
Using the value of a, we can substitute it back into the other equations to find b, c and d.
Q''(1) = 6a + 2b = 6
6(2) + 2b = 6
12 + 2b = 6
2b = -6
b = -3
Q'(1) = 3a + 2b + c = 3
3(2) + 2(-3) + c = 3
6 - 6 + c = 3
c = 9
Q(1) = a(1)^3 + b(1)^2 + c(1) + d = 1
2(1)^3 + (-3)(1)^2 + 9(1) + d = 1
2 + (-3) + 9 + d = 1
8 + d = 1
d = -7
Therefore, the third degree polynomial Q that satisfies the given conditions is:
Q(x) = 2x^3 - 3x^2 + 9x - 7
----------------------------------------
the polynomial Q(x) is Q(x) = x^3 + 2x^2 + x + 1
This polynomial satisfies the given conditions Q(1)=1, Q'(1)=3, Q"(1)=6, and Q'''(1)=12.
To check:
Q(1) = 1 + 2(1)^2 + 1(1) + 1 = 1
Q'(1) = 3 + 4 + 1 = 8
Q"(1) = 6
Q'''(1) = 6
It's important to note that the polynomial that I have provided may not be unique, as there may be other third degree polynomials that also satisfy the given conditions.
In the figure below, m VW=69° and m XY = 49°. Find mZXZY.
W
Y
X
Check the picture below.
the sum of two numbers is 22, and their difference is 12. set up two equations to solve using elimination to help you find the numbers. enter the lesser of the two numbers here:
When the sum of two numbers is 22, and their difference is 12, the lesser of the two numbers is 5.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
Let numbers be a and b.
a+b=22
a=22-b
b-a=12
b-(22-b)=12
2b-22=12
2b=34
b=17
a=5
The lesser of the two numbers is 5 when the sum of two numbers is 22, and their difference is 12.
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2. What is the third step in proving by mathematical induction that for every positive integer n, 11" - 6 is divisible by 5, is true?
O Show that 11k - 6 is divisible by 5.
O Assume that 11¹ - 6 is divisible by 5.
O Assume that 11*+1 - 6 is divisible by 5.
Show that 11*+1 - 6 is divisible by 5
To show that 11k+1 - 6 is divisible by 5 using mathematical induction, the first step is to assume that the statement is true for any given positive integer k.
What is the third step in proving by mathematical induction that for every positive integer n, 11" - 6 is divisible by 5, is true?This means that 11k - 6 is divisible by 5.Next, we need to show that this assumption implies that 11k+1 - 6 is also divisible by 5.We can do this by substituting 11k+1 - 6 for 11k + 5 - 11 + 6, which can be simplified to 11k + 5 - 11 + 6.Then, we can subtract 11k from both sides, leaving us with 5 - 11 + 6. Finally, we can add 11 to both sides, resulting in 16, which is divisible by 5.Therefore, 11k+1 - 6 is divisible by 5.To show that 11k+1 - 6 is divisible by 5, we will use mathematical induction.First, we assume that 11¹ - 6 is divisible by 5.Then, we assume that 11*+1 - 6 is divisible by 5.To prove that the statement is true, we must show that 11*+1 - 6 is divisible by 5.We can do this by multiplying both sides of the equation by 11: 11*+1 - 6 = 5(11k - 5).This equation shows that 11k+1 - 6 is equal to 5 times 11k - 5, which is divisible by 5.Therefore, 11k+1 - 6 is divisible by 5.This completes the proof by mathematical induction that for every positive integer n, 11" - 6 is divisible by 5 is true.To learn more about the mathematical induction refer to:
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Write an algebraic expression as indicated.
Roberto has a total of $4000 in two savings accounts. Let x represent the amount in one account. Write an algebraic expression for the amount in the other
account.
Answer:
4000-x
Step-by-step explanation:
both accounts - account x = account y
(x+y) - x = y
Examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution. Does the normal quantile plot depict sample data from a population with a normal distribution? A. Yes. The points are evenly distributed above and below the mean, O. B. Yes. The pattern of the points is reasonably close to a straight line. C. No. The points do not lie close to a straight line. D. No. The points exhibit some systematic pattern that is not a straight-line pattern.
The points are not reasonably close to a straight line, nor is the distribution normal.
Why do normal distributions exist?
In a continuous probability distribution called a "normal distribution," the majority of data points cluster in the middle of the range, while the remaining data points taper off symmetrically toward either extreme.The range's center is also referred to as the distribution's mean. The normal distribution, also known as the Gaussian distribution, is symmetrical about the mean and shows that data that are closer to the mean are more likely to occur than data that are farther from the mean.Like any probability distribution, the normal distribution depicts the distribution of values for a variable.
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The full question is given in the image-
Toby and his little sister are saving up money to buy a joint birthday present for their mother. Toby already has $26 saved and plans to save $14 per week from his allowance. His sister has $28 saved so far and will save $12 per week from hers. The two siblings will soon have saved the same amount towards their mother's gift. How long will that take? How much will each one have saved?
In ------- weeks, Toby and his sister will each have saved $---------
In 1 week, Toby and his sister will each have saved $40.
In how many weeks would the siblings have saved the same amount?The first step is to form a linear equation that represents the equation in the question. A linear equation is an equation that has a single variable that is raised to the power of one.
The form of a linear equation that represents the amount saved by the siblings is:
Total amount saved = amount they have already saved + (number of weeks x amount saved per week)
Amount saved by Toby = $26 + ($14 x w)
$26 + $14w
Amount saved by his sister = $28 + ($12 x w)
$28 + $12w
When the siblings have saved the same amount of money, the two above linear functions would be equal:
$26 + 14w = $28 + $12w
In order to determine the value of w, take the following steps:
Combine and add similar terms:
$14w - $12w = $28 - $26
2w = 2
Divide both sides of the equation by 2
w = 2 / 2
w = 1 week
Total amount that would have been saved = $28 + $12(1)
$28 + 12 = $40.
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Directions: solve for x round to the nearest tenth
Using the trigonometric ratios for the angle A-cosθ= Base/ Hypotenuse =11.8726
What is trigonometric?
Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions in relation to a right triangle are displayed in the figure.
For example, the triangle contains an angle A, and the ratio of the side opposite to A and the side opposite to the right angle (the hypotenuse) is called the sine of A, or sin A; the other trigonometry functions are defined similarly. These functions are properties of the angle A independent of the size of the triangle, and calculated values were tabulated for many angles before computers made trigonometry tables obsolete. Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures.
Here, if we consider the ∠A=θ, then AB is the base, BC is the perpendicular, and AC is the hypotenuse.
And it is given that, ∠A=θ=32°,AB=x, and C=14 units.
Now, using the trigonometric ratios for the angle A-cosθ= Base/Hypotenuse
cosA=AB/AC
cos30°=x/14
x=14×cos32°
=11.8726
≈11.9units
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Find the constant rate of change
Age Height
9 54
10 56
11 58
12 60
The constant change rate will be straight according to the solution.
What does "constant rate of change" mean?When the ratio of something like the output to the input remains constant at every given point along the function, the rate of change is said to be constant. The slope is another name for the constant change rate. For linear functions, the rate of change will be constant.
The rate of change is it always the same?The change rate (slope) is constant for straight lines (always the same). The rate of change for such lines is constant. With the aid of the resources on this page, you may learn how to calculate slope and change rate as well as the rate of change formula.
According to the given data:Age Height
9 54
10 56
11 58
12 60
The constant rate of change will be straight. because the given data will form a straight line on the graph. the rate of change (slope) is constant (always the same). For such lines, the rate of change is constant.
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A builder wants to purchase
countertops that are 15’ long and 24” deep, plus an island countertop that is
48” x 36”, how much total square
footage will be needed for this?
The builder will need a total of 372 square feet of countertop.
SolutionFirst, let's convert all dimensions to feet:
The 15' countertops are 15 * 12 = 180 inches long.
The 24" deep countertops are 24 / 12 = 2 feet deep.
The 48" x 36" island countertop is 48 / 12 = 4 feet wide and 36 / 12 = 3 feet deep.
Next, we can calculate the square footage of each countertop:
The 15' countertops are 180 inches long and 2 feet deep, so the square footage is 180 * 2 = 360 square feet.
The island countertop is 4 feet wide and 3 feet deep, so the square footage is 4 * 3 = 12 square feet.
Finally, we can add the square footage of each countertop to find the total square footage:
360 square feet + 12 square feet = 372 square feet
Therefore, The builder will need a total of 372 square feet of countertop.
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A granola bite contains 27 calories. Most of the calories come from c
grams of carbohydrates. The rest come from other ingredients. One
gram of carbohydrate contains 4 calories.
The equation 4c + 5 = 27 represents the relationship between these
quantities.
Answer the following questions:
1. What could the 5 represent in this situation?
2. Priya said that neither 8 nor 3 could be the solution to the
equation. Explain why she is correct.
3. Find the solution to the equation.
A. 5 represents the number of calories that come from other ingredients.
B. Neither 8 nor 3 satisfies the given equation, so neither 8 nor 3 can be the solution to the equation.
C. The value of c is 5.5.
What are linear equations?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given
equation 4c + 5 = 27
Where c represents the grams of carbohydrates
27 is the total number of calories that are received by the granola bite.
4 is the number of calories from 1 gram of carbohydrates and
5 is the number of calories that are received from other ingredients.
B: Priya said that neither 8 nor 3 could be the solution to the
equation.
substituting 8 and 3 in the equation,
4c + 5
4*8 + 5 = 37≠ 27
4*3 + 5 = 17≠ 27
so 8 and 3 are not solutions of the equation.
C: solution of the equation, 4c + 5 = 27
4c = 27 - 5
4c = 22
c = 22/5
c = 5.5
Hence 5 represents calories from another ingredient,
8 and 3 are not the solution of the equation and the solution of the equation is 5.5.
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S is the sum of 12, 8, 6, 4 and x. What is the value of x if x = 2/5S?
(Linear equations)
Answer:
x = 20
Step-by-step explanation:
Sum of 12, 8, 6, 4 and x is:
S = 12 + 8 + 6 + 4 + x = 30 + x
[tex]\dfrac{2}{5}S = \dfrac{2}{5}\cdot 30 + \dfrac{2}{5}x\\\\=12 + \dfrac{2}{5}x\\\\\\\textrm{But left side is nothing but x}\\\\\textrm{So we get }x = 12 + \dfrac{2}{5}x\\\\\rm{Subtract $\dfrac{2}{5}x$ from both sides}\\\\x - \dfrac{2}{5}x = 12\\\\\dfrac{3}{5}x = 12\\\\x = \dfrac{12 \cdot 5}{3} \\\\x = 20\\\\[/tex]
Verify
12 + 8 + 6 + 4 + 20 = 50
(2/5) x 50 = 20
Joel's town voted on a new law. 48 out of 50
votes were in favor of the law. What is the ratio of the number of votes against the law to the number of votes in favor of the law?
The total number of votes cast is 480
What is the ratio of the number of votes against the law to the number of votes in favor of the law?Ownership of more than 50% of voting shares generally gives the right of control and consolidation. In special cases, control is possible without having to own more than 50% of voting stock.
Let x represent total number of votes.
step1:
We have been given that Joel got 50% of the votes, which was 48 votes more than Sean.
50% of total votes:50/100[tex]x[/tex]=0.50[tex]x[/tex]
Since Joel got 50% of total votes, so Sean got 40% of total votes that is
40/100[tex]x[/tex]=0.40[tex]x[/tex]
Since Joel got 38 votes more than Sean, so we can represent this information in an equation as:
0.50[tex]x[/tex]=0.40[tex]x[/tex]+48
0.50[tex]x[/tex]-0.40[tex]x[/tex]=0.40[tex]x[/tex]-0.40[tex]x[/tex]+48
0.10[tex]x[/tex]=48
step2:
0.10[tex]x[/tex]/.10=48/.10
[tex]x[/tex]=480
Therefore, the total number of votes cast is 480
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Find the limit of the function as x approaches 1 by inspecting the graph.
O 2 O oo O -1 O 5 O 0
The limit of the function is 2 as x approaches 1.
What is limit of a function?in mathematics, the limit of a function is the value that the function approaches as the input (or independent variable) gets closer to a certain value. The limit of a function is a fundamental concept in calculus, and is used to study the behavior of a function as the input gets arbitrarily close to a certain value, but not necessarily equal to it. The limit is usually denoted by the symbol "lim" and it is read as "the limit of f(x) as x approaches a is L" where f(x) is the function, a is the value that x approaches and L is the limit.
so we need to find
[tex]\lim_{x \to \ 1}\frac{x^2-1}{x-1}[/tex] ---(i)
we will observer that the function reduces to [tex]\frac{0}{0}[/tex] form at x=1
factorisation of x² -1 = (x+1)*(x-1)
substituting the value of x² -1 in equation (i) we get
[tex]\lim_{x \to \ 1} x+1[/tex]
=> 2
so the value of [tex]\lim_{x \to \ 1}\frac{x^2-1}{x-1}[/tex] =2
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Complete question:
Find the limit of the function as x approaches 1 .
f(x) = [tex]\frac{x^2-1}{x-1}[/tex]
do the ordered pairs plotted in the graph below represents a function explain
Answer: it's not a function
Step-by-step explanation:
(4,3) (4,-3)
one to many
it isn't a function.
