∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx is the sum rule in integration.
The sum rule in integration states that if f(x) and g(x) are two functions that are both integrable over a given interval, then the integral of the sum of these functions over that interval is equal to the sum of the integrals of the individual functions over that interval. Mathematically, this can be expressed as:
∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx
The sum rule of integration is: Integral of the sum of two functions is equal to the sum of integration of individual functions.
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What is the solution of 7x 9 16?.
The solution to the equation 7x - 9 = 16 is x = 25/7. This can be achieved by using the addition property of equality and simplifying the equation.
The equation 7x - 9 = 16 can be solved by using The equation's solution can be changed by adding the same amount to either side of the equation, according to the addition property.
To both sides of the equation, add 9.
7x - 9 + 9 = 16 + 9
Simplify the equation.
7x = 25
Divide both sides of the equation by 7.
7x/7 = 25/7
Simplify the equation.
x = 25/7
Therefore, the solution to the equation 7x - 9 = 16 is x = 25/7.
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NEED TO FINISH BY 5!!! WILL MARK BRAINLIEST
Answer:
10 1/8
Step-by-step explanation:
25 3
8
+
-15 1
4
= (25 + -15) + (
3
8
+
-1
4
)
= 10 +
3
8
+
-1 × 2
4 × 2
= 10 +
3
8
+
-2
8
= 10 +
3 + -2
8
= 10 +
1
8
=
10 1
8
A triangular tract of farm land has sides of length 2.1 miles, 1.8
miles, and 2.7 miles. If a bag of fertilizer covers 0.2 square
miles, how many bags of fertilizer are needed to cover the area
of the triangle? Round your answer to the nearest whole
number. NEED THIS ASAP TYSM
Answer: we would need 7 bags of fertilizer to cover the area of the triangle.
Step-by-step explanation:
To find the area of a triangle, we can use Heron's formula. Heron's formula states that the area of a triangle can be found by taking the square root of the semi-perimeter multiplied by the difference of the semi-perimeter and each side length.
The semi-perimeter of the triangle is (2.1+1.8+2.7)/2 = 2.7
The area of the triangle is sqrt(2.7*(2.7-2.1)(2.7-1.8)(2.7-2.7)) = sqrt(2.70.60.9*0) = 1.35
Each bag of fertilizer covers 0.2 square miles, so we need to divide the area of the triangle by the area covered by each bag to find how many bags are needed: 1.35 / 0.2 = 6.75
Rounding up to the nearest whole number, we would need 7 bags of fertilizer to cover the area of the triangle.
75+(4²- 6²) +12=
15³- 16 × 2+28=
Answer:
75+(4²- 6²) +12= 67
15³- 16 × 2+28=3371
Answer this functions question
Answer:
ff(x)=9x-48
Step-by-step explanation:
f(x)=3x-12
ff(x)=f(3x-12)
=3(3x-12)-12
= 9x-36-12
= 9x-48
What is a 2 term polynomial?.
Two term polynomial called as a binomial .
An algebraic equation that has more than two terms, particularly the accumulation of numerous phrases that each include a different power of the same variables known as polynomial.
But when we reduce more than two terms into only two terms we get binomial.
A formula in algebra that expresses the difference or sum of two terms is known as binomial.
For example:
[tex]x^{4} + x y^{2} +x^{2} + x[/tex] is polynomial because it has more than two separate terms which are [tex]x^{4}[/tex] , [tex]x y^{2}[/tex] , [tex]x^{2}[/tex] and [tex]x[/tex]
[tex]x^{2} + y^{2}[/tex] is binomial because it has only two separate terms which are [tex]x^{2}[/tex] and [tex]y^{2}[/tex].
[tex]4x+6y[/tex] is also binomial because it has also only two separate terms which are [tex]4x[/tex] and [tex]6y[/tex]
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JK is a tangent to the circle KLM at K and JML is a straight line. The value of x is
A. 30° B. 45° C. 60° D. 75°
The value of angle x is 45°. Thus, option B is correct.
How to find the value of x?A corner is an angle if it forms a projecting part or a partially enclosed space. An angle is a figure made up of two lines that extend from the same point. a measurement of an angle or the amount of turning required to align or make parallel two lines or planes.
step1:
o is center
JK is a tangent
so <OKJ =90°
<OKM=90°-30°=60°
OM=OK=><OMK=60°
step2:
because LO=LO, LM=LK, ON=OK
So Triangle OLM ≅ Triangle OLK => <LOM=<LOK
so <LOM=150° => <LMO =15°
so 60° +15° =30°+x°=>x= 45
so the answer is B. 45°
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Marshall spins a prize wheel with 4 segments of equal size, one of which is labeled "winner. "
Let X = the number of spins until Marshall wins a prize.
What is the probability that Marshall wins a prize on his 2nd spin?
Recall: P(X = k) = (1 – p)k–1p
Round to 4 decimal places
The probability that Marshall wins a prize on his second spin = 0.1875
Consider an event X = the number of spins until Marshall wins a prize.
Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.
So, the sample space n = 4
For given event x, the possible outcomes = 1
Using the formula of probability,
p = x/n
p = 1/4
p = 0.25
So, the probability of success p = 0.25
q = 1 - p
q = 1 - 0.25
q = 0.75
To find the probability that Marshall wins a prize on his 2nd spin.
Using formula, [tex]P(X = k) = (1 - p)^{k-1}p[/tex]
For k = 2,
[tex]P(X = 2) = (1 - 0.25)^{2-1}\times 0.25[/tex]
P(X = 2) = 0.75 × 0.25
P(X = 2) = 0.1875
Thus, the required probability is 0.1875
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QUICK!! NEED RN!!! HELP ASAP!!!
From 1995 to 2000, the glaciers thinned by 6 ft per year. What was the change in glacier thickness during this period?
SOMEONE PLS HELP
1 1/2 - 3 2/3
Answer:
= -13/6 OR -2.1667
Step-by-step explanation:
1 1/2 - 3 2/3
=3/2 - 11/3
LCM of 2 and 3 is 6
3/2 - 11/3
= 9 - 22
6
= - 13/6 OR -2.5
Answer: is it
-2 1/6
Step-by-step explanation:
Rewriting our equation with parts separated
=1+12−3−23
Solving the whole number parts
1−3=−2
Solving the fraction parts
12−23=?
Find the LCD of 1/2 and 2/3 and rewrite to solve with the equivalent fractions.
LCD = 6
36−46=−16
Combining the whole and fraction parts
−2−16=−216
Simple bro
How do you write greater than 4?.
To show that one value is greater than another, use the "greater than" symbol (>). It can be used to express a comparison between two values in mathematical operations, programming, and other forms of notation.
For instance, the "greater than" symbol can be used to compare integers in mathematical operations. For instance, you would write "x > y" to indicate that x is greater than y. This can alternatively be understood as "x exceeds y."
Other comparison symbols, such as "less than," "greater than," and "less than or equal to," can be used in addition to the "greater than" symbol. These symbols can be used to describe many forms of value comparisons in programming and mathematical processes.
The word "greater than" is represented by the symbol ">," therefore to write "greater than 4" you would write ">4".
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At KFC, the kitchen taff baked 25 chicken leg and 50 wing. The taff had to prepare platter for an office lunch. If each platter will have the ame number of leg and wing, what i the greatet number of platter they can make?
So, each platter will have 25 legs and 25 wings.
To determine the greatest number of platters the kitchen staff can make, you need to find the least common multiple of 25 and 50. This is because each platter must have the same number of legs and wings, so you need to find the smallest number of legs and wings that can be divided evenly into both 25 legs and 50 wings.
The least common multiple (LCM) of 25 and 50 is 50. This means that the greatest number of platters the kitchen staff can make is 50/25 = 2 platters.
Therefore, each platter will have 25 legs and 25 wings.
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Find the least frequent multiple of 25 and 50 to determine the maximum number of platters the kitchen staff can produce. Finding the fewest number of legs and wings that can be equally divided into 25 legs and 50 wings is necessary because each platter must have the same number of legs and wings.
25 and 50 have a least common multiple (LCM) of 50. The maximum amount of platters the kitchen staff is capable of producing is 50/25, or 2 platters.
Therefore, there will be 25 legs and 25 wings on each plate.
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.
Identify the linear equation?Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12
We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.
Take the provided linear equation system into consideration.
3x - 2y = 4 ................(1)
9x - 6y = 12 ..................(2)
Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12
The slopes of the provided equations are also same.
Difference with regard to x for equation (1) yields,
additional to equation (2),
With regard to x, we can differentiate to get,
The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.
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Think about a plan carlo plan to build a grain bin with a radiu of 15ft. The recomended lant of the room i 25
The length x will be 23.994615468 ft or rounded approximately 24 feet.
Roof Length Calculation in FeetThe length x is the distance from the center of the roof to the edge of the roof.
Using trigonometry, we can find the length x by using the equation:x = 15 + (15 * tan(25°)) + 1
The tan(25°) can be found using a calculator or table. With a calculator, we get:tan(25°) = 0.466307658
Substituting this value back into the equation, we get:x = 15 + (15 * 0.466307658) + 1
x = 15 + 6.994615468 + 1
x = 23.994615468 ft
So, the length x = 23.994615468 ft, or approximately 24 feet.
The problem is about finding the length x, which is the distance from the center of the roof to the edge of the roof of a grain bin with a radius of 15 ft and a recommended slant of 25° for the roof. The roof is also required to overhang the edge of the bin by 1 ft. The length x was calculated using trigonometry and found to be approximately 24 feet.
Complete Problems (Question):
Carlos plans to build a grain bin with a radius of 15 ft. The suggested slant of the roof is 25°. He wants the roof to overhang the edge of the bin by 1 ft. What should the length x be? Give your answer in feet and inches.
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how does understanding unit rates help us with unit pricing
The volume of a cube is 8 in³. What is the length of one side?
Answer:
2 in
Step-by-step explanation:
If im not wrong, each side should be 2 inches, as it would have to be 2x2x2 for a volume of 8 inches cubed
Complete the statements describing the process of converting z = 2 + 3i to polar coordinates using technology.
Write the complex number as a point in the complex plane,
(2, 3pi)
(2, 3)
(3i, 2)
(-3, 2)
Substitute _ for a and _ for b.
Options for the first _:
2
2pi
3
3i
Options for the second _:
2
2i
3
3i
Using radians for θ, record the result ___ as your answer in polar coordinate form.
(3.606cos(.983), 3.606sin(.983))
(3.606, 0.983)
3.606
0.983
Answer:
The correct statements describing the process of converting z = 2 + 3i to polar coordinates using technology are:
Write the complex number as a point in the complex plane: (2, 3i)
Substitute a = 2 and b = 3 for the real and imaginary parts respectively.
Using radians for θ, record the result as r = 3.606 and θ = 0.983 as your answer in polar coordinate form: (3.606, 0.983).
To convert a complex number in the form of z = a + bi to polar coordinates using technology, we can use the following steps:
Write the complex number as a point in the complex plane, with the real part as the x-coordinate and the imaginary part as the y-coordinate.
Substitute a for the real part and b for the imaginary part.
Using the Pythagorean theorem, we can find the distance from the origin to the point, which is the magnitude or modulus of the complex number, represented by r.
Using the tangent function, we can find the angle of the point from the positive x-axis, which is the argument or phase of the complex number, represented by θ.
Record the result in polar coordinates as (r, θ), where r is the magnitude and θ is the argument, given in radians.
It's also worth noting that polar coordinates can also be represented in the form of (r, θ ) or (r, arg(z)) or (r, angle(z))
Answer:
z = 2 + 3i
Step-by-step explanation:
What is the relationship between the sine rule and the sine ratio in a right triangle?.
The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle. This is true for any triangle, not just right triangles.
What is the relationship between the sine rule and the sine ratio in a right triangle?.The law of sines relates the ratios of side lengths of triangles to their respective opposite angles. This ratio remains equal for all three sides and opposite angles. We can therefore apply the sine rule to find the missing angle or side of any triangle using the requisite known data.
The ratio of the side and the corresponding angle of a triangle is equal to the diameter of the circumcircle of the triangle. The sine law is can therefore be given as,
[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]
In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.
The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle. This is true for any triangle, not just right triangles.
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Estimation Rita goes to the mall. If b is the number of items she bought, the expression 13.06b+ 29 gives the amount she
spent in dollars at one store. Then she spent 22 dollars at another store. Find the expression which represents the amount
Rita spent at the mall. Then estimate how much Rita spent if she bought 2 items.
What expression represents the amount in dollars that Rita spent at the mall? Help please! This is due tomorrow!
The total amount Rita spend on the mall for 2 items is $77.12.
How to solve the expression to find total amount?When we combine numbers and variables in a valid way, using operations like addition, subtraction, multiplication, division, exponentiation, and other yet unlearned operations and functions, the resulting combination of mathematical symbols is known as a mathematical expression.Given that,
The expression of amount spend on the first store = 13.06b + 29
The amount spend on the second store = 22
Total amount Rita spends= 13.06b + 29 + 22
= 13.06b + 51
Then to estimate the amount Rita spent if she had bought 2 items.
Now, we have the value of b = 2.
So by substituting,
= 13.06 x 2 + 51
= 77.12
Therefore the total amount Rita spend on the mall is $77.12.
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The graphs of f (x) and g (x) are shown below.
Answer:
B) (-∞, 2)
Step-by-step explanation:
Given functions:
[tex]f(x)=x-3[/tex]
[tex]g(x)=-0.5x[/tex]
To find the interval for which (f - g)(x) is negative, set (f - g)(x) less than zero and solve for x:
[tex]\begin{aligned}(f-g)(x)& < 0\\f(x)-g(x)& < 0\\(x-3)-(-0.5x)& < 0\\x-3+0.5x& < 0\\1.5x-3& < 0\\1.5x& < 3\\x& < 2\end{aligned}[/tex]
Therefore, the interval for which the composite function (f - g)(x) is negative is:
(-∞, 2)Can a negative number be an exponential function?.
Yes, it is possible for a negative number to be an exponential function.
The number of times a number is multiplied by itself is indicated by the positive exponent, as we are aware. In contrast, the negative exponent indicates how many times the base number must be divided. The negative exponent, in other words, indicates how many times the reciprocal of the base must be multiplied. 3-2 is a prime example of a negative exponent.Two negative exponents can be multiplied together in the same way as two numbers. Since we are aware that negative exponents can be reduced to fractions, simplifying negative exponents is simple. Converting the negative exponents to their fractional form is the first step in multiplying negative exponents, after which the procedure is the same as multiplying two fractional numbers.
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The probability of events A
and B is
P(A)=1/2
P(B)=1/3
P(A∩B)=1/4.
What is the value of P(A or B)?
Enter your answer as a fraction, like this: 4/25
Answer: 2/3
Step-by-step explanation:
To find the probability of A or B, we can use the formula: P(A or B) = P(A) + P(B) - P(A ∩ B)
Plugging in the given values:
P(A or B) = 1/2 + 1/3 - 1/4
To solve this, we must find a common denominator in order to add the fractions:
P(A or B) = 3/6 + 2/6 - 1/6
Simplifying:
P(A or B) = 4/6 = 2/3
So the value of P(A or B) is 2/3
The points on this graph represent a relationship between x- and y-values. Which statement about the relationship is true?
The statement about the relationship of the data in the table is indicated in the option;
It can not be proportional because the straight line through the points does not go through the originWhat is a proportional relationship?A proportional relationship is one in which one variable (the output variable) is a constant multiple of the input variable, such that a point on the graph of ordered pairs of variable is the point (0, 0), which is the origin.
The points on the graph are; (1, 3.5), (2, 4.5), (3, 5,5)
The slope of the graph is therefore; (4.5 - 3.5)/(2 - 1) = 1
The equation in point-slope form is therefore; y - 3.5 = x - 1
y = x - 1 + 3.5 = x + 2.5
y = x + 2.5
The equation is a linear relationship. The equation is in the form; y = m·x + c, with the slope m = 1 and a y-intercept, c = 2.5
The y-intercept is 2,5, therefore, the graph does not pass through the origin.
The relationship of the line passing through the points, is a linear relationship. The line passing through the points does not pass through the origin, therefore the relationship is not a proportional relationship
The correct option is therefore; It cannot be a proportional because the straight line through the points does not go through the origin.
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1. The population of the country Ghana was 24 658 823 in the year 2010. In the year 2020, Ghana Statistical Service gave an estimated number of people in the country Ghana a 31 072 940.
a. Find the difference in the two data provided.
b. Calculate the sum of the two data to the nearest thousand hundred.
a. the difference in the two data provided =31072940 - 24658823 = 6414117
b. the sum of the two data to the nearest thousand hundred = 31072940 - 24658823 = 55731763
nearest to Thousand hundred = 55730000
PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
9
Step-by-step explanation:
2x + 3y - 2
Putting x=1; y=3
(2x1) + (3x3) - 2
2 + 9 - 2
Now, according to BODMAS, we shall add first.
11 - 2
9
Fat food chain uing platic or tyrofoam in elling their product, make a 5 entence of the problematic ituation
Fast food chains that use plastic or styrofoam containers in selling their products are contributing to the global plastic pollution crisis. Styrofoam and plastic containers, which are not biodegradable, take up to 1000 years to decompose.
Every year, an estimated 8 million metric tons of plastic end up in the ocean, and the majority of it is from single-use plastic products such as those used by fast food chains. This plastic pollution is having a devastating effect on the environment, with marine life ingesting and becoming entangled in the plastic. In addition, the production of styrofoam and plastic containers is highly energy intensive and contributes to the emission of greenhouse gases. This is a problematic situation that needs to be addressed urgently.
The energy intensity of production for styrofoam and plastic containers can be calculated using the formula:
Energy Intensity (EI) = Energy Used (EU) / Output (O)
For example, if it takes 50 kWh of energy to produce a unit of output, the energy intensity of production would be 50 kWh/unit. This highlights the environmental impact of styrofoam and plastic containers, and the urgent need to reduce their use in fast food chains.
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ZA and B are vertical angles. If m/A= (2x +20)° and m/B = (3x + 1)°,
then find the value of x.
Answer:
The value of x is -19.
Step-by-step explanation:
Given that ZA and B are vertical angles and m/A = (2x +20)°, and m/B = (3x + 1)°, we know that ZA and B are congruent, meaning they have the same measure. We can set the two given equations equal to each other: m/A = (2x + 20)° = m/B = (3x + 1)°. Then, by isolating x on one side of the equation, we subtract 20 from both sides of the equation, then subtract 2x from both sides of the equation, which gives us x = -19, thus the value of x is -19.
Answer:
x = 19
Step-by-step explanation:
since vertical angles are equal we can set the value of angles A and B equal and solve for 'x'
2x + 20 = 3x + 1
20 = x + 1
19 = x
Branly. Com math mr klammer ha a garden. One half of her garden i planted in vegetable and the other half i planted in flower he planted cucumber in 1/3 of the vegetable part of the harden how much of the whole garden i planted in cucumber. Brainly
1/6 of the whole garden is planted in cucumber.
What is cucumber ?
Cucumber is a type of vegetable that belongs to the cucurbit family, which also includes melons, squash and gourds. They are typically long, cylindrical in shape, and have a green skin that is typically eaten raw.
The proportion of the garden planted in cucumber is 1/3 of the vegetable part of the garden. To find out what proportion of the entire garden is planted in cucumber, we can use this proportion and multiply it by the proportion of the garden that is planted in vegetables.
Half of the garden is planted in vegetables, so the proportion of the garden planted in vegetables is 1/2.
1/3 of the vegetable part of the garden is planted in cucumber, so the proportion of the garden planted in cucumber is ,
(1/2) x (1/3) = 1/6
So, 1/6 of the whole garden is planted in cucumber.
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Half of the garden is planted in vegetables, so the proportion of the garden planted in vegetables is 1/2.
1/3 of the vegetable part of the garden is planted in cucumber, so the proportion of the garden planted in cucumber is ,
(1/2) x (1/3) = 1/6
1/6 of the whole garden is planted in cucumber
Calculate the average speed of a cyclist that travels 30km in 3 hours
Answer:
V = 10 km/h
Step-by-step explanation:
Formula for speed --> V = X/t being X equal to space and t the time wasted.
X = 30 km
t = 3 hours
then,
V = 30/3
V = 10 km/h
URGENT PLEASE HELP I NEED IT RN! THANKS
7. Critique Reasoning Julio states that he can use the SAS Triangle Congruence
Theorem to prove that two right triangles are congruent. He constructs two right
triangles to have congruent hypotenuses and one set of congruent legs. What does
Julio need to do in order to use the SAS Triangle Congruence Theorem? Explain your
reasoning
Julio needs to prove that two sides of the two triangles are congruent, in addition to the hypotenuse and one set of legs that are already congruent, to use the SAS Triangle Congruence Theorem.
Julio needs to prove that the two triangles have congruent sides in order to use the SAS Triangle Congruence Theorem. This means that he needs to show that one side of one triangle is congruent to a corresponding side of the other triangle and the same applies to the other two sides. This can be done by using methods such as measuring the sides, using algebraic equations, or using geometric constructions.
According to Julio statement, he has already constructed two right triangles to have congruent hypotenuses and one set of congruent legs, which means he has already proved that one side of one triangle is congruent to a corresponding side of the other triangle (hypotenuse) and one set of legs are congruent.
Therefore, Julio need to prove the remaining side of the triangle congruent to the corresponding side of the other triangle. Once he proves this, he can use the SAS Triangle Congruence Theorem to state that the two triangles are congruent.
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