Answer:
Step-by-step explanation:
Lin’s method
- multiply both x and 2 by 7
7x+14 = 91
- add -14 at both members
7x+14-14 = 91-14
7x = 77
- divide the two members by 7
x = 11
Noah’s method
- divide the two members by 7
x+2 = 13
- add -2 at both members
x+2-2 = 13-2
x = 11
Answer:
The solution is x=11
Step-by-step explanation:
The original equation is
7(x+2)=91
Lin uses the distributive property, which states that
a (x+y) = ax + ay
By applying the property to this case,
7(x+2)=91
7x+14=91
Then we subtract 14 on both sides:
7x+14 - 14 = 91-14
7x=77
Finally, we divide by 7 on both sides:
7x÷7 = 77÷7
x=11
Noah starts by dividing each side by 7, so he gets:
7(x+2)÷7 = 91÷7
x+2= 13
Then he can subtract +2 from both sides:
x+2-2 =13 - 2
x=11
So, they get the same result. The similarity between the two methods is that they both divide by 7, while the difference is that Lin has to subtract 14, while Noah has to subtract 2.
What is the mean of 5 7 9 11?
The mean of the following data is 8.
To find: Mean of given numbers.
Given data is 5, 7, 9, 11
Mean: It is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Mean=[tex]\frac{Sum of all observations}{Number of observations}[/tex]Here, sum of observations is 5+7+9+11=32
Sum of observations is 32
Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data
Total number of observation is 4
The number of observations provides information on the total number of values that are contained in the Dataset. This property is intended to provide an indication of the size of a Dataset.
Substituting values in above formula,
=[tex]\frac{32}{4}[/tex]
=8
Therefore, the mean is 8.
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The difference between two numbers is 60. If the large is divided by the smaller number the quetient is 3 and the remender is 12 find two number
The two numbers we have to find are 24 and 84.
So, we have been given that there are 2 numbers, and the difference between them is 60.
Let the two numbers be x and y. Let the larger number be x and the smaller number be y.
x-y = 60
When x is divided by y, the quotient is 3 and the remainder is 12.
By division lemma, we can clearly say x= 3y + 12
Now, we have two equations -
x-y=60 and x=3y+12
=>60+y=3y+12
=> y=24
If y=24 and we know x-y=60. This implies that x is equal to 84.
Hence the two numbers 24 and 84.
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What is the domain for the given function?
3 + 9x
4+5x
Answer:
12x plus 9x
Step-by-step explanation:
true/false if y is a differentiable function of u and u is a differentaible function of u and u is a differentaible function of x, then y is a differentiable function of x
True. If y is a differentiable function of u and u is a differentiable function of x, then the chain rule states that y is a differentiable function of x.
The chain rule states that if y is a function of u and u is a function of x, then the derivative of y with respect to x is equal to the derivative of y with respect to u multiplied by the derivative of u with respect to x. This means that if y is a differentiable function of u and u is a differentiable function of x, then y is also a differentiable function of x.
In mathematics, a function is said to be differentiable at a point if it is possible to define the derivative of the function at that point. The derivative of a function is a measure of how the function changes as its input (or independent variable) changes. It is defined as the limit of the difference quotient, which is a measure of the rate of change of the function over a small interval around the point of interest.
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solve for x in square. Given: (6x-21)
Answer: 3.5
Step-by-step explanation:
To solve for x in a square, you need to find the value of x that makes the square equal to zero. In this case, the square is given by (6x-21), so we can solve for x by setting this expression equal to zero and then solving for x.
To solve the equation (6x-21) = 0, we can use basic algebraic techniques. First, we can add 21 to both sides of the equation to get (6x-21) + 21 = 21. Then, we can use the distributive property to expand the left-hand side of the equation as follows:
(6x-21) + 21 = 21
6x - 21 + 21 = 21
6x = 21
Finally, we can divide both sides of the equation by 6 to find the value of x that makes the square equal to zero:
6x = 21
x = 21 / 6
x = 3.5
Therefore, the value of x that makes the square (6x-21) equal to zero is x = 3.5.
The price of a computer increae from £631 to £776. 13
Determine the percentage change
The price of a computer increase from £631 to £776. 13. The percentage change is 81.3%
As per the given data:
Old value of computer is £631
New value of computer is £776. 13
Percentage Change: Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100.
The phrase percent change says the difference in the percent of the earlier and present quantity.
Percentage change formula is
Percentage Change [tex]=\frac{{New Value - Old Value} }{{Old Value}} \times 100[/tex]
If the result is positive, then it is an increase.
If the result is negative, then it is a decrease.
[tex]=\frac{631}{776.13} \times 100[/tex]
= 0.813 × 100
= 81.3%
Therefore the increase in percentage is 81.3%
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For what values of k the roots of the equation x² 4x?
The equation x² + 4x = 0 has no real roots for any value of k.
The equation x² + 4x = 0 can be solved by using the Quadratic Formula. We can rearrange the equation to be in the form of ax² + bx + c = 0. In this case, a = 1, b = 4 and c = 0. We can then plug these values into the Quadratic Formula to find the roots of the equation.
The Quadratic Formula is x = [-b ± √(b² - 4ac)] / 2a
Plugging in our values of a, b, and c we get: x = [-4 ± √(-4² - 4(1)(0))] / 2(1)
Simplifying this equation we get: x = [-4 ± 0] / 2
The equation simplifies to: x = [-4 / 2] and x = [0 / 2].
Since both of these roots are imaginary, the equation x² + 4x = 0 has no real roots for any value of k.
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Franklin National Life Insurance Company purchased new computers for $300,000. If the rate at which the computers' resale value changes is given by the function V'(t) = 5700(t − 10) where t is the length of time since the purchase date and V'(t) is measured in dollars per year, find an expression V(t) that gives the resale value of the computers after t years. V(t) = dollars How much would the computers sell for after 5 years? (Round your answer to the nearest dollar.) $
To find an expression for V(t), we can integrate V'(t) with respect to t. Doing so, we have:
V(t) = ∫V'(t) dt = ∫5700(t − 10) dt = 5700 ∫(t − 10) dt = 5700 [t^2/2 - 10t] + C
Since V(t) is the resale value of the computers, the constant of integration C should be the initial value of V(t), which is the cost of the computers. Therefore, we have:
V(t) = 5700 [t^2/2 - 10t] + 300000
Now, to find the value of the computers after 5 years, we can substitute t = 5 into the expression for V(t):
V(5) = 5700 [5^2/2 - 10*5] + 300000 = 5700 [25/2 - 50] + 300000 = 5700 [-12.5] + 300000 = -67500 + 300000 = 232500
Thus, the computers would sell for approximately $232,500 after 5 years.
Explanation: The function V'(t) gives the rate at which the resale value of the computers changes with time. In other words, it gives the slope of the function V(t) at any point in time. To find the function V(t) itself, we need to integrate V'(t) with respect to t. The constant of integration C is added to the result of the integration to ensure that the initial value of V(t) is equal to the cost of the computers. Once we have the expression for V(t), we can find the value of the computers at any point in time by substituting the appropriate value for t into the expression. In this case, we found that the value of the computers after 5 years is approximately $232,500.
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Why do we take the square root of both sides?
Therefore , we take the square root of both sides as if two expressions are equal, then their square roots are also equal.
What is square root?The number is derived by multiplying the square root of a positive integer by itself.
For instance, the square root of 25 is 5, since 5 x 5 is 25.
As you can see, 5 is also the square root of 25 because (5) (5) = 25.
The square root of a number is always represented by the symbol, which is √.
Here,
We are using the square to solve a quadratic problem
Remember to take the square root of both aspects of the equation and to utilize both negative and positive roots.
Because of the rule that says if expressions are equivalent, then their square roots are likewise equal, we are able to perform this.
Therefore , we take the square root of both sides as if two expressions are equal, then their square roots are also equal.
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PLEASE HELPP. FINALS DAY. BRAINLIEST ANSWER WILL BE MARKED!!
Rotation would be the first answer...Your second answer would be dilation. If this is wrong, I'm so sorry
20. Let g be a twice-differentiable, increasing function of t. If g(0) 20 and g(10) 220, which of the following must be true on the interval 0 < 10 ? (A) g'(t) 0 for some t in the interval. (B) g) 20 for some t in the interval. (C) g"(t) 0 for some t in the interval. (D) g"(t) > 0 for all t in the interval
For given function the correct solution is g'(t) = 20 for some t in the interval.
A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
For a given function, y = F(x), if the value of y is increasing on increasing the value of x, then the function is known as an increasing function and if the value of y is decreasing on increasing the value of x, then the function is known as a decreasing function.
Given that g(10)= 220
g(0)= 20
So putting values in condition of differentiation for increasing function we get:
[tex]\frac{g(10)-g(0)}{10-0}[/tex]
= [tex]\frac{220-20}{10}[/tex]
=20
Hence as we can see that the correct solution for given function is g'(t) = 20 .
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A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Given that g(10)= 220
g(0)= 20
So putting values in condition of differentiation for increasing function we get:
= 220-20/2
=20
Find the total surface area of the rectangular prism in the figure.
A) 174 cm^2
B) 348 cm^2
C) 522 cm^2
D) 432 cm^2
The total surface area of the rectangular prism in the figure is 348 cm²
How to find the total surface area of the rectangular prismA rectangular prism is a polyhedron in geometry that has two parallel and congruent bases.
It also goes by the name cuboid. Six faces make up a rectangular prism, and each face has a rectangle shape and twelve edges.
The formula for total surface area of a rectangular prism is
TSA = 2 (lh +wh + lw ) Square units
= 2( 8 *9 + 6 * 9 + 8 * 6 )
= 2 (174)
= 348 cm²
The rectangular prism have a Total surface area of 348 cm²
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Kim is a sales representative for a medical software company. She's planning to start saving for her son's college education and her ownretirement. Kim could start contributing to her employer-sponsored_________for retirement and __________for her son's college education.
Kim could start contributing to her employer-sponsored 401 K for retirement and 529 plans for her son's college education.
401(k) is an employer sponsored retirement benefits plan where the employer and employee contribute a percent of the employee's benefits or gross income every payday in order that the funds can be used to to generate further wealth by a way of investment for the benefit of the employees upon retirement.
529 plan on the other hand,is a college savings plan wherein parent,guardian or even the beneficiary(the would college student) saves money at interval with hope of funding the costs of college education
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What is set in math for kids?
In math for kids, a set is a collection of objects or numbers that have been grouped together.
What is set?Set is a collection of distinct elements or objects that are grouped together. Sets can be defined as either finite (having a finite number of elements) or infinite (having an infinite number of elements). Sets are commonly used in mathematics, computer science and other areas of study to represent collections of data or to express logical relationships.
The objects in a set can be anything, such as numbers, shapes, letters, words, and even other sets. Sets are often used in math problems and are a great way to help kids learn basic math skills. They can also be used to teach problem solving and logic. Sets are a fundamental part of mathematics and can be used to help kids understand mathematical concepts.
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on dividing 2272 as well as 875 by 3 digit number n we get the same remainder The sum of the digits Of n is
Answer:
10
Step-by-step explanation:
2272-875=1397
Factors of 1397: 1, 11, 127, 1397
Where's the three-digit number? ==> 127 is the three-digit number
875/127 = 6.889
1397/127=11
2272/127=
(875+1397)/127=
875/127 + 1397/127= ==> substitute 11 for 1397/127 and 6.889 for 875/127
6.889 + 11 = 17.889
Hence, 2272/127=17.889
Hence, 2272 and 875 have the same remainder when divided by 127.
Now add the digits:
1+2+7=10
How much extra do you get for limited capability for work?
You get £354.28 a month extra for limited capability for work.
If you have a "restricted capability for work-related activity," £354.28 per month (the higher rate) is included in your award. An evaluation of one's "work capability" is what determines this. In some cases, the work capability amount cannot be included in your award right away; instead, there is typically a three-month "waiting period." When you submit supporting medical documentation to the Department of Work and Pensions, this will ordinarily start. You should take the work capacity evaluation while you're waiting.
A lesser rate of the work capability amount of £132.89 might have been included in your award prior to April 3, 2017, if you were only determined to have a "limited capability for work" during this assessment (and not a limited capability for job-related activity).
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Which is arranged in order from least to greatest?
When numbers are arranged in ascending order, they are done so from least to largest.
What is the Ascending order?When numbers are arranged in ascending order, they are done so from least to largest.
We must first compare the numbers before we may arrange them in any order.
Compare first, then order.
Numbers arranged in ascending order: Determine how many digits each number has.
Numbers can be arranged in ascending order, from the least value to the highest value.
The arrangement is left to right.
Increasing order is another name for ascending order.
An ascending sort will organize numbers from smallest to largest and text from A to Z because ascending signifies moving upward.
For numbers, descending is going from largest to smallest, and for text, it's from Z to A.
Therefore, when numbers are arranged in ascending order, they are done so from least to largest.
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What is the scale factor from the cliff in the Scale Drawing drawing to the actual cliff? What is the actual height of the lighthouse?
The scale factor from the cliff in the Scale Drawing to the actual cliff is 3, and the actual height of the lighthouse is 30 ft.
What is the scale factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized. It is employed to change the size of an object.
Given:
The actual height from sea to the lighthouse, A = 36ft
The height in the diagram, D = 12
Calculate the scale factor as shown below,
Scale factor = A / D
SF = 36 / 12
SF = 3
Calculate the actual height as shown below,
Actual height = scale factor × height in the diagram
Actual height = 3 × 10 = 30 ft.
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What is the slope of the linear equation 2y 3x − 1?
Let m s the slope of the given equation 2y+3x-1. So m=-3/2.
What is meant by slope?A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is
m =Δy/Δx = change in y/change in x
where "m" represents a line's slope.
Write alternative way to write slope.Slope can also be written as
tanθ = Δy/Δx
The given equation is:
2y+3x-1=0
Separate y
2y= -3x+1
y= -3/2x +1/2
Comparing it with equation of line y=mx+c where m is the slope we conclude that slope of the given equation is m=-3/2.
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What is the slope of 4x Y =- 1?
The slope of 4x - Y = -1 is 4.
We know that the general form of the equation of a straight line is:
y = mx + c,
where y represents the y intercept of the straight line, m represents the slope and c is the constant in it.
Let us re-arrange the given equation 4x - Y = -1 into Y = 4x + 1.
Now we compare this equation Y = 4x + 1 with the general equation of a straight line y = mx + c.
We conclude that here, m = 4 and c = 1.
Hence, we get that the slope of the given equation Y = 4x + 1 is 4.
The question is incomplete, the complete question is:
What is the slope of 4x - Y = -1?
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Solve pls brainliest
Answer:
This data has a positive correlation.
Step-by-step explanation:
As the x-values increase, the y-values increase. Therefore, there is a positive correlation. (positive/positive = positive)
What is the inverse of 3?
The Additive Inverse of the number 3 is -3 that is "Negative 3".
The Inverse (Additive) of the number is defined as the number which when added to original number the result is zero .
the number is given as "3" ,
We let the additive inverse be = "a" ;
According to above definition of additive inverse ,
we get ;
3 + a = 0 ;
On simplifying further ,
we get ;
a = -3 .
the sum of 3 and -3 is written as 3 +(-3) ⇒ 3 - 3 = 0 .
Therefore , the additive inverse is "-3" .
The given question is incomplete , the complete question is
What is the additive inverse of the number 3 ?
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Complete the tasks please helpl
Answer:
Step-by-step explanation:
Last year, Milan opened an investment account with $5200. At the end of the year, the amount in the account had decreased by 7%.
(a) Fill in the blank to write the year-end amount in terms of the original amount. Write your answer as a decimal.
Year-end=amount×Originalamount
(b) Use your answer in part (a) to determine the year-end amount in Milan's account.
Year-endamount:$
If Last year, Milan opened an investment account with $5200. At the end of the year, the amount in the account had decreased by 7%. the year-end amount in terms of the original amount is $364.00 and the year-end amount in Milan's account is $4,836.00.
How to find the year end amount ?a. Year end amount in terms of original amount
Year end amount = Principal × Percentage decrease
Year end amount = $5,200 × 7%
Year end amount = $364.00
b. Year end amount in Milan account
Year end amount = $5,200 -$364
Year end amount = $4,836.00
Therefore the year-end amount in terms of the original amount is $364.00 and the year-end amount in Milan's account is $4,836.00.
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if mary had 23 apples and she give 10 to her fren. how many apples do she have left?
What is the formula of variance and standard deviation of a probability distribution of a random variable?
For a given probability distribution, The random variable also contains discrete values, The variance and standard deviation are computed in terms of Expected values E(X).
What do you mean by random variable?The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a space of potential outcomes, commonly real numbers, to a space of measurement.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
for discrete probability distribution , E(x) = x*P(x)
for continuous probability distribution , E(x) = x *f(x)
Variance = [tex]E(X^2)-(E(X))^2[/tex]
standard deviation = [tex]\sqrt {Variance}[/tex]
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How do you know if an equation is continuous?
Answer:
For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point.
What factors should be taken into consideration when creating a financial plan?
There are four factors that should be taken into consideration when creating a financial plan.
Define financial plan.The process of figuring out how a corporation will be able to afford to meet its strategic goals and objectives is known as financial planning. Typically, a business develops a financial plan right away after establishing its vision and goals.
What is the importance of financial planning?You can reach your financial objectives with the help of financial planning, whether they are to purchase a home for your family, save money for your children's school, have a comfortable retirement, or take a dream vacation. Additionally, it gets you ready for crises and unanticipated circumstances like getting sick, losing your job, or needing home renovations.
4 things to think about when creating your financial plan:
At each stage of your life, think about your requirements and commitments.Set attainable objectives for the short, medium, and long terms.Determine whether your security measures are adequate.Find out about the tax breaks and reliefs that are available to you.To learn more about financial planning visit the link:
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How do you find the value of x and y in an angle?
To find the value of x and y, the length of the side opposite an angle, you need to know the measure of the angle and the lengths of the sides of the angle.
The measure of the angle is usually represented by the letter 'x', and the lengths of the sides are usually represented by the letters 'a' and 'b'. If you know the values of these three quantities, you can use the following formula to find the value of y, which is the length of the side opposite the angle:
y = tan(x) × a
If you know the values of x and y, you can use the following formula to find the value of a, which is the length of the side adjacent to the angle:
a = y / tan(x)
If you know the values of x and a, you can use the following formula to find the value of y:
y = a × tan(x)
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Solve for x.
(x+16)
(4x-5
7
11
13
9
Answer:
soln:
x+16=4x-5
16+5=4x-x
21/3=x
Therefore x=7