The formula for midpoint rule is M =∑ n i = 1 f ( m i ) Δx.
In this equation, I represents the ith rectangle, n the number of rectangles that comprise the area under the curve, f (m I) the function of the curve as defined by the ith rectangle's midpoint, and x the width of each rectangle. In calculus, the midpoint formula may be used to estimate the same area on an x-y plot. It is necessary to give an interval with a lower and upper border where the computed area will begin and stop, as well as the number of units, or subintervals, that the interval will be divided into when computing the area under the curve of a function. More rectangles enhance estimation precision (n).
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Solve |10x + 50| = 0.
Answer:
x = -5
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ |10x + 50| = 0
Then the value of x will be,
→ |10x + 50| = 0
→ 10x + 50 = 0
→ 10x = 0 - 50
→ 10x = -50
→ x = -50/10
→ [ x = -5 ]
Hence, the value of x is -5.
The corresponding data for electricity generated by hydropower are 248 million megawatt hours in 2007 and 277 million megawatt hours in 2012. Write a linear model that represents the number of megawatt hours generated by hydropower as a function of the number of years since 2007.
A linear model can be represented by the equation y = mx + b, where y is the dependent variable (megawatt hours generated by hydropower), x is the independent variable (years since 2007), m is the slope of the line, and b is the y-intercept.
To find the slope (m) and y-intercept (b) for this problem, we can use the two points given: (2007, 248) and (2012, 277).
m = (277 - 248) / (2012 - 2007) = 29 / 5 = 5.8
b = 248 - (5.8)(2007) = 248 - 11456 = -11208
So the linear model representing the number of megawatt hours generated by hydropower as a function of the number of years since 2007 is:
y = 5.8x - 11208
where x is the number of years since 2007.
Sarah ued propertie of operation to write the following three equivalent expreion to
Sarah's error in the expression 3 so the correct answer is option D
Complete Question: Sarah used properties of operations to write the following three equivalent expressions to.
A. There are no errors. All of the expressions are equivalent.
B. Expression 1. Sarah can’t apply the Distributive Property if there are three addends.
C. Expression 2. Sarah can’t combine -4 and -6. She must combine -4 with 8.
D. Expression 3. Sarah applied the Distributive Property but incorrectly multiplied 1/2 (-6).
Expressions 1, and 2 are equivalent because they are using the distributive property to expand the term within the brackets before applying the 1/2 coefficient.
Expression 3 is not equivalent because it does not use the distributive property and does not have the same terms as the other expressions.
Sarah's error in expression 3 is that she did not use the distributive property and the terms inside the brackets are not the same as the other expressions, hence the results are different.
Therefore, Sarah's error in the expression 3 so the correct answer is option D
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I’ll give brainliest :)
Write the rule for the linear function
Answer:
y = f(x) = a + bx
Step-by-step explanation:
Step-by-step explanation: A linear function is a function of the form f(x) = ax + b, where a and b are real numbers. Here, a represents the gradient of the line, and b represents the y-axis intercept (which is sometimes called the vertical intercept).
Challenge You have 2 different savings accounts. For Account A, the simple interest earned after 6 months is $4.88. For Account B, the simple interest earned after 27 months is $24.75. If the interest rate is 3.9% for Account A and 2.2% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
The principal of account A is $250.26
The principal of account B is $500
The account that would earn you more interest in the first month is account B
What are the principals?
Simple interest is the interest earned on an amount of money in a savings account.
Simple interest = principal x time x interest rate
Principal is the amount deposited
Principal = simple interest / ( time x interest rate)
Principal of account A = 4.88 / (6/12 x 0.039) = $250.26
Principal of account B = 24.75 / (27/12 xx 0.022) =$500
Interest earned in the first month:
Account A = (1/12) x 250.26 x 0.039 = .81
Account B = (1/12) x 500 x 0.022 =0.92
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solve for u.
2u + 2.17 = 16.17
Answer:
[tex]\boxed{\bf u=7}[/tex]
Step-by-step explanation:
[tex]\sf 2u+2.17=16.17[/tex]
Subtract 2.17 from both sides:-
[tex]\sf u+2.17-2.17=16.17-2.17[/tex]
[tex]\sf 2u=14[/tex]
Divide both sides by 2:-
[tex]\sf \cfrac{2u}{2}=\cfrac{14}{2}[/tex]
[tex]\sf u=7[/tex]
Therefore, u = 7
______________________
Hope this helps!
Have a great day!
Write the quadratic equation in general form.
40x² = 30
The solution of the equation is x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex].
Now, According to the question:
What is Quadratic Equation?
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:
ax² + bx + c = 0
where x is the unknown variable and a, b and c are the constant terms.
The given equation is :
40x² = 30
40x² - 30 =0
Common factor:
10(4x²- 3) = 0
Divide both sides by the same factor
10(4x²- 3) = 0
4x²- 3 = 0
Use the quadratic formula:
x = -b±[tex]\sqrt{b^2-4ac}[/tex]/ 2a
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula:
4x²- 3 = 0
a = 4
b = 0
c = -3
x = -0±[tex]\sqrt{0^2-4(4)(-3)}[/tex]/ 2(4)
By simplify:
x = ±[tex]\frac{4\sqrt{3} }{8}[/tex]
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x = [tex]\frac{4\sqrt{3} }{8}[/tex]
x = -[tex]\frac{4\sqrt{3} }{8}[/tex]
Rearrange and isolate the variable to find each solution
x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex]
Hence, The solution of the equation is x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex].
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3
At a stream cleanup, the ratio of
adult volunteers to child volunteers
is 7:4. If 20 children volunteer, how
many adults are there?
Answer:
35
Step-by-step explanation:
a=adult c=children
7a:4c
?a:20c
20 is 5 times more than 4 which I found by doing 20/4
So now we multiply 7 by 5 to get 35
35a:20c
There are 35 adults
Expand and combine like terms.
(9c^2+c^6)(9c^2-c^6
Answer: -c^12+9c^4
Step-by-step explanation:
Answer: 81 c^4 - c^12
Step-by-step explanation:
(9c^2+c^6)(9c^2-c^6)
Step-by-step explanation: (9c^2+c^6)(9c^2-c^6)
This is the difference of squares
(a+b) (a-b) = a^2 - b^2
(9c^2) ^2 - ( c^6)^2
81 c^4 - c^12
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The true statements about the function and its graph are:
The graph of the function is a parabola.
The graph of the function opens up.
The graph contains the point (0, 12)
What is the quadratic function?
A quadratic function is a type of polynomial function of degree 2. It is defined as a function of form f(x) = ax² + bx + c, where a, b, and c are constants and a is not equal to 0. The graph of a quadratic function is a parabola, which is a U-shaped curve that opens up or down, depending on the value of the coefficient a.
The value of f(–10) = x² - 5x + 12 = (-10)² - 5(-10) + 12 = 100 - (-50) + 12 = 62, not 82.
The graph of the function is a parabola.
The graph of the function opens up.
The graph of the quadratic function is a parabola that opens up or down, which depends on the coefficient of x². If the coefficient of x² is positive, the parabola opens up, if it is negative, the parabola opens down. In this case, the coefficient of x² is positive, so the parabola opens up.
The graph contains the point (0, 12)
The graph does not contain the point (20, -8) since the x-coordinate is outside the domain of the function.
Hence, The true statements about the function and its graph are:
The graph of the function is a parabola.
The graph of the function opens up.
The graph contains the point (0, 12)
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Mia has $20 less than Brandi. Brandi has d dollars. Write a variable expression for the amount of money Mia has.
Answer: d-20
Step-by-step explanation:
if Mia has $20 less than Brandi, it means Brandi has d dollars, so we subtract Brandi 's money from $20.hope you understood.
Calculate the total water use in Spain if the per capita water use is 810m ^ 3 and the population of Spain is 46.5 million
Total water use in Spain = 810m^3 x 46.5 million = 37,425,000,000 m^3. it is important to be aware of the amount of water used in order to understand and mitigate any potential negative impacts.
1. Given that the per capita water use is 810m^3 and the population of Spain is 46.5 million.
2. Calculate the total water use by multiplying the per capita water use by the population of Spain.
3. Total water use in Spain
= 810m^3 x 46.5 million = 37,425,000,000 m^3
The total water use in Spain is calculated by multiplying the per capita water use (810m^3) by the population of Spain (46.5 million). This yields a total water use of 37,425,000,000 m^3. This number indicates the volume of water used in Spain annually by its citizens. Water use can have a variety of impacts on the environment, such as depletion of water resources, and it is important to be aware of the amount of water used in order to understand and mitigate any potential negative impacts.
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3. Give two examples of four-sided figures that have two acute angles
and two obtuse angles. Draw pictures in your explanation.
Answer:
follow me if this helped
Step-by-step explanation:
A kite is a four-sided figure that has two acute angles and two obtuse angles. The angles are formed by the intersection of the diagonals, which are not parallel.
[asy]
size(5cm);
draw((0,0)--(1,1.5)--(3,1)--(2,-0.5)--cycle);
draw((1,1.5)--(2,-0.5));
label("$A$",(0,0),SW);
label("$B$",(1,1.5),NE);
label("$C$",(3,1),SE);
label("$D$",(2,-0.5),NW);
[/asy]
A bow tie shape is another four-sided figure that has two acute angles and two obtuse angles. The angles are formed by the intersection of the diagonals, which are not parallel.
[asy]
size(5cm);
draw((0,0)--(1,1.5)--(2,0)--(1,-1.5)--cycle);
draw((1,1.5)--(1,-1.5));
label("$A$",(0,0),SW);
label("$B$",(1,1.5),NE);
label("$C$",(2,0),SE);
label("$D$",(1,-1.5),NW);
[/asy]
At the craft tore, Anita bought a bag of yellow and green marble. The bag contained 70 marble, and 30% of them were yellow. How many yellow marble did Anita receive?
There are 21 yellow marbles anita receives
given that
In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.
The term "percent" is derived from the Latin per centum, meaning "hundred" or "by the hundred". The sign for "percent" evolved by gradual contraction of the Italian term per cento, meaning "for a hundred". The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to two circles separated by a horizontal line, from which the modern "%" symbol is derived.
at the craft store , Anita bought a bag of yellow and green marble
The bag contained 70 marble,
30% percentage of them were yellow.
now, we need to find How many yellow marble did Anita receive
= 70 * 30%
= 70 * [tex]\frac{30}{100}[/tex]
= 7 *3
= 21
There are 21 yellow marbles anita receives
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6 times a number plus 15 is equal to 6 times a number minus 41
The given statement as an expression is 6x + 15 = 6x - 41
How to represent the statement as an expressionFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as
6 times a number plus 15 is equal to 6 times a number minus 41
Represent the number with x
So, we have the following representation
6 times x plus 15 is equal to 6 times x minus 41
is equal to implies =
So, we have:
6 times x plus 15 = 6 times x minus 41
Plus implies +, minus implies - and times *
This gives
6x + 15 = 6x - 41
The question does not require that we solve the expression
So, we leave it at 6x + 15 = 6x - 41
Hence, the required expression is 6x + 15 = 6x - 41
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PLEASE HELP
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer in the box.
The constant of proportionality of the graph is 12.
How to find the constant of proportionality?Proportional relationships are relationships between two variables where their ratios are equivalent. In other words, a proportional relationship is one in which two quantities vary directly with each other.
Proportional relationship can be represented mathematically as follows:
y = kx
where
k = constant of proportionalityTherefore, let's use (3, 36) to find the constant of proportionality.
Hence,
y = kx
36 = 3k
divide both sides by 3
3k / 3 = 36 / 3
k = 12
Therefore, the constant of proportionality is 12.
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Given the figure at right.
Find the sum of angles
1, 2, and 3.
53 63 55 56 62 54 59 60 53 61 88 IQR
The interquartile range (IQR) of this dataset is 8.25, it means that half of the observations fall between 53 and 61.25, while half of the observations fall outside of that range.
IQR stands for Interquartile Range, which is a measure of the variability of a dataset. It is defined as the difference between the third quartile (Q3) and the first quartile (Q1). To calculate the IQR, you first need to order the data set and find the median (middle value) of the dataset, and the Q1 and Q3.
Here is the dataset you provided, in order:
53 53 53 54 55 56 59 60 61 62 63 88
The median of the dataset is: (56+59)/2 = 57.5
Q1 is the median of the lower half of the dataset: (53+53+54)/3 = 53
Q3 is the median of the upper half of the dataset: (60+61+62+63)/4 = 61.25
Now you can calculate the IQR:
IQR = Q3 - Q1 = 61.25 - 53 = 8.25
So the interquartile range of this dataset is 8.25, it means that half of the observations fall between 53 and 61.25, while half of the observations fall outside of that range.
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The correct question should be:
"Find the interquartile range (IQR) of the following dataset
53 53 53 54 55 56 59 60 61 62 63 88"
If B is the midpoint of AC and AB = 5 Find BC and AC.
The length of BC is 5
The length of AC is 10
Midpoint of a line: Calculating length of a lineFrom the given information, we are to calculate the length of the given parts of line AC
From the given information,
B is the midpoint of AC
Thus,
We can write that
AB + BC = AC
and
AB = BC
Also, from the given information,
AB = 5
Therefore,
BC = 5
From the equation,
AB + BC = AC
Substitute the values of AB and BC
5 + 5 = AC
10 = AC
AC = 10
Hence, BC = 5 and AC = 10
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two times the defference of a number and three
Solve each system by graphing
As a result, the graph illustrating how one face's side width and diameter are linearly associated is the resolution to the given linear equation problem.
A linear equation is exactly what?One degree is the highest number of levels that can be employed in a linear model. Nonlinearity is the property of any equation having a theoretical extent of at least two. On a map, there is a horizontal line with a straightforward equation. The graph shows the curve that a nonlinear equation produces.
Here,
the side lengths and perimeter of one face are linearly connected.
formula for lines
A regular model is described by the equation y = mx + b.
If b is in fact the y intercept and m is the changing rate, then y and x are variable.
One face's length and perimeter have a linear relationship, as seen by the graph.
As a result, the graph illustrating how one face's edge length or perimeter are linearly associated is the answer to the given linear equation problem.
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What is factor in Grade 8?
So on solving the provided question we can say that factors 8 = 1,2,4,8 factor 20 = 1,2,4,5,10,20
what is prime factor?Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.
here,
factors 8 = 1,2,4,8
factor 20 = 1,2,4,5,10,20
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solve for y 6/y+4=5/y-7
HELP HELP 15 POINTSSSSSS
Answer:
I believe B, E, and F is the answer
Given a pre-image and image, determine if the scale factor is greater than 1, less than 1, or equal to 1.
a. less than 1
b. greater than 1
c. equal to 1
*see attached image for the pre image and image
The scale factor is greater than 1.
Determine if the scale factor is greater than 1, less than 1, or equal to 1?The pre-image and image provided can be used to determine the scale factor between the two shapes.A scale factor is the ratio of the lengths of two corresponding sides of two similar figures.To determine the scale factor, the length of the two corresponding sides must be compared.Looking at the pre-image and image, it can be seen that the pre-image has a longer length than the image.This indicates that the scale factor is less than 1, as the length of the corresponding side in the image is shorter than the pre-image.To confirm this, the lengths of the corresponding sides must be compared.The pre-image has a length of 8 units and the image has a length of 6 units.The ratio of 8/6 is equal to 4/3, which is less than 1.Therefore, the scale factor between the pre-image and image is less than 1.To learn more about the scale factor refer to:
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The temp this week is increasing by 8 deg each day. How much has the temp risen after three weeks?
Answer:
168 deg
Step-by-step explanation:
Assuming the increase in temperature in constant during the 3 weeks, we do the following calculations-
8 deg * 7 = 56 deg / week (Since there are 7 days in a week)
56 * 3 = 168 deg in 3 weeks.
What is the Sin(B)? Need help!
Answer:
Last option: 5/8
Step-by-step explanation:
sin(angle) = opposite / hypotenuse
So, sin(B) = 4/6.4 = 20/32 = 10/16 = 5/8
Hope this helps!
What is the answer please im confused
Answer:
40
Step-by-step explanation:
total: 56+80+40+24 = 200
(80x100)/200
Answer:
What you first want to do is see what all of the numver of students add up to:
80 + 40 = 120
120 + 24 = 144
144 + 56 = 200
So there are a total of 200 votes. 40 of the 200 vote mystery, so you need to find how many times 40 will go into 200. To find this you can just divide.
200/40 = 5
5% prefer mystery books!
Step-by-step explanation:
Hope it helps! =D
I think I did the math wrong, but just by looking Im pretty sure its 5%
Is 16 a factor of 8?
No, number 16 is not representing as a factor of 8. The given statement is false as it is a multiple of 8.
As given in the question,
Given number is equal to 8,
Given factor is equal to 16:
Factors are those numbers which divides the given numbers without leaving any remainder. It exactly divides the given original number.
Here given factor 16 does not divides the given number 8.
Instead 8 divides the the number 16.
here '8' is the factor of the number 16.
And 16 represents as a multiple of 8.
Therefore, the given statement is false and 16 is not considered as a factor of 8 instead it is a multiple of 8.
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Match each system on the left with all words that describe the system on the right. Choices on the right can be used more than
once.
y = 3x - 1
2y - 6x = 4
2y = -x + 6
4y + 2x = 12
y = 2x + 3
x+y=-9
inconsistent
consistent
independent
dependent
So on solving the provided question we cans say that in the following linear equation values are y = -1, -3 , 3
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here ,
as we know that x = 0
so, y = 3x - 1 = -1
2y - 6x = 4 => y = 2
2y = -x + 6 = y = 3
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