For the given surface ;
(a) the equation of the tangent is x + y + z = 11 ,
(b) equation of normal is (x - 3) [tex]=[/tex] (y - 3) = (z - 5) .
In the question ,
it is given that ,
the equation of the surface is 2(x-2)² + (y-1)² + (z-3)² = 10 ,
we have to find the equation of the tangent at (3,3,5) .
the partial derivative fₓ = 4(x -2)
[tex]f_{y}[/tex] = 2(y-1) and [tex]f_{z}[/tex] = 2(z-3) .
the partial derivatives at (3,3,5) will be fₓ = 4(3 -2) = 4
[tex]f_{y}[/tex] = 2(3-1) = 4 and [tex]f_{z}[/tex] = 2(5-3) = 4 .
Part(a)
the equation of tangent at the point (3,3,5) is
fₓ(x - x₁) + [tex]f_{y}[/tex](y - y₁) + [tex]f_{z}[/tex](z - z₁) = 0 ,
Substituting the values form above ,
we get ,
4(x-3) + 4(y-3) + 4(z-5) = 0
4x - 12 + 4y - 12 + 4z - 20 = 0
after simplifying , we have 4x + 4y + 4z = 44 .
dividing both sides by 4 ,
we get ,
x [tex]+[/tex] y [tex]+[/tex] z [tex]=[/tex] 11 .
Part(b) ,
the equation of Normal is ;
(x-x₁)/fₓ = (y-y₁)/ [tex]f_{y}[/tex] = (z-z₁)/ [tex]f_{z}[/tex]
(x - 3)/4 = (y - 3)/4 = (z - 5)/4
(x - 3) [tex]=[/tex] (y - 3) [tex]=[/tex] (z - 5)
Therefore , the equation of tangent is x + y + z = 11 , and equation of normal is (x - 3) = (y - 3) = (z - 5) .
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A wire is first bent into the shape of a rectangle with width 5cm and length 16 cm . Then the wire is unbent and reshaped into a triangle. If each side of the triangle has equal length, what is this length?
Hello,
I hope you and your family are doing well!
To find the length of each side of the triangle, we can use the formula for the perimeter of a rectangle: perimeter = 2 * (width + length). In this case, the perimeter of the rectangle is 2 * (5cm + 16cm) = 42 cm. Since each side of the triangle has the same length, and the perimeter of the triangle is equal to the perimeter of the rectangle, the length of each side of the triangle is 42cm / 3 = 14 cm.
Therefore, the length of each side of the triangle is 14 cm.
---
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5 + w - 9 = 8
How do I solve this equation? Please explain step by step
Answer:
w=12
Step-by-step explanation:
w+5-9=8
w-4=8
w=12
Answer:
w = 12
Step-by-step explanation:
Subtract the numbers.
5 + w - 9 = 8
-4 + w = 8
Rearrange terms
-4 + w = 8
w - 4 = 8
Add 4 to both sides
w - 4 = 8
w - 4 + 4 = 8 + 4
Add
w - 4 + 4 = 8 + 4
w = 8 + 4
Add
w = 8 + 4
w = 12
The sum of 7x^2+x+1 and -6x^2-8x-10
Answer:
Step-by-step explanation:
To find the sum of 7x^2+x+1 and -6x^2-8x-10, you can add the two expressions by combining like terms.
7x^2+x+1 + (-6x^2-8x-10)
= (7x^2 + -6x^2) + (x + -8x) + (1 + -10)
= x^2 + -7x + -9
Therefore, the sum of 7x^2+x+1 and -6x^2-8x-10 is x^2 - 7x - 9.
5.6.8 let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e). show that this need not be true if f is continuous but not uniformly continuous.
Proof. (1): To prove {f(xn)} is a Cauchy sequence just need to prove ∀ > 0, ∃N, s.t.,∀n, m > N,
have |f(xn) − f(xm)| < . Since f is uniformly continuous on set E, thus ∀ > 0, ∃δ > 0, s.t.,
∀x, y ∈ E, if |x − y| < δ,then |f(x) − f(y)| < .as {xn} is a Cauchy sequence, then ∃N, s.t.,
∀n, m > N, |xn − xm| < δ, thus |f(xn) − f(xm)| < which proves {f(xn)} is a Cauchy sequence.
(2): for example f(x) = 1
x
, x ∈ (0, 2) which is continuous but not uniformly continuous. {
1
n
} is
a Cauchy sequence, however, {f(xn)} does not converge which proves that it is not a Cauchy
sequence.
Showing that this need not be true if f is continuous but not uniformly continuous.
Given :
let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e).
( 1 )
If f is uniformly continuous on E, then given ε > 0 there is δ > 0 such that if x, y are in E and |x−y| < δ,
then |f(x) − f(y)| < ε. Let (xn) be a Cauchy sequence in E. Then given δ > 0 there is N such that if p, q > N,
then |xp − xq| < δ, and thus |f(xp) − f(xq)| < ε, implying that (f(xn)) is a Cauchy sequence.
( 2 )
Let E = {1, 1/2, 1/3, · · } and f(1/n) = 1 is n is odd, f(1/n) = −1 if
n is even. Then f is continuous but not uniformly continuous. The sequence (xn) = (1/n) in E is Cauchy but the
sequence (f(xn)) = (1, −1, 1, −1, · · ·) is not Cauchy.
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Solve for x Round to the nearest tenth, if necessary.
Answer:
1.7
Step-by-step explanation:
tan30°=1/XX=1/tan30°X=1/0.57741.73191.7(to the nearest tenth)Suppose that the functions g and h are defined for all real numbers x as follows.
g(x)=x-6
h(x)=4 x+3
By using the concept of function, it can be calculated that-
(h.g)(x) = 4x - 21
(h + g)(x) = 5x - 3
(h - g)(-1) = 6
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
a) The given functions are
g(x)= x - 6
h(x) = 4x + 3
(h.g)(x) = h(g(x)) = 4(x - 6) + 3 = 4x - 21
(h + g)(x) = h(x) + g(x) = 4x + 3 + x - 6 = 5x - 3
(h - g)(x) = h(x) - g(x) = 4x + 3 - x + 6 = 3x + 9
(h - g)(-1) = 3 [tex]\times[/tex] (-1) + 9 = 6
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Does it make sense to discuss the similitude between 2 rombii, 2 squares, 2 rectangles, 2 parralelegrams, and 2 conguent polygons
Yes, it makes sense to discuss the similarity between these shapes.
How to determine if it make sense to discuss the similitude between 2 rombii, 2 squares?Two shapes are considered similar if they have the same shape, but possibly different sizes. This means that the angles of the shapes are the same and the sides of the shapes are in the same ratio.
Two rhombi are similar if they have the same angle measures and the lengths of their sides are in the same ratio.
Two squares are similar if they have the same angle measures and the lengths of their sides are in the same ratio.
Two rectangles are similar if they have the same angle measures and the lengths of their sides are in the same ratio.
Two parallelograms are similar if they have the same angle measures and the lengths of their sides are in the same ratio.
Two congruent polygons are similar by definition, since congruent shapes are identical in size and shape.
It is important to note that similarity is different from congruence. Congruent shapes are identical in size and shape, whereas similar shapes have the same shape but possibly different sizes.
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Consider the piecewise function shown on the graph, which is composed of polynomial, constant, and exponential pieces.
10
-10-8-6-4-2 02 4
O
2
D. (-00, 4)
-2.
-6-
-8
-10-
Over which interval of the domain is the function increasing?
A. (1,4)
OB. (-00, 1)
OC. (-00,-4)
10
4
"Increasing" means the y-values are increasing as x-values increase. Or visually, if you were walking along the graph, from left-to-right, where would you be walking uphill?
The uphill portion is from (-infty, -4). Once you get to an x-value of -4, then it levels off (so it's "constant") until you get to x = 1, when it goes downhill (the function is decreasing).
The interval of the domain in which the function is increasing is(-∞, -4). so option C is correct.
What is a piecewise function?A function that is composed of several smaller functions, each with a distinct domain, is said to be piecewise. The term "piecewise" refers to the way in which these sub-functions are defined in terms of various intervals or "pieces" of the function's overall domain.
Given that,
The piecewise function which is discontinuous at x =1
In the interval
(-∞, -4) the value of the function is increasing.
[-4, 1) the value of the function is constant.
(1, ∞) the value of the function is decreasing.
Hence, the function is increasing in the domain (-∞, -4)
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Cindy bought 7/8 yard of ribbion at the craft store. Jacob bought 4/5 the length of ribbon as Cindy. How many yards of ribbon did jacob buy?
Mario makes 6 throw shots out of his first 10 attempts
Ok⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Answer: 4
Step-by-step explanation: If you are trying to see how many Mario missed that would be 4
2. Determine the theoretical probability of rolling a two with one standard die. Write this probability in three equivalent forms: as a fraction, a decimal (rounded to three places), and a percentage (rounded to one decimal place).
The theoretical probability of rolling a two with one standard die in three equivalent form is 1/6, 0.167 and 16.7%
How to determine the theoretical probability?From the question, we have the following parameters that can be used in our computation:
The rolling of a standard die
In this case, we assume that the standard die is a fair die
i.e. the faces have equal chance of appearing
This means that the sample space of the die is
Sample space = {1. 2. 3. 4. 5. 6}
In this sample space, we have
Number of occurrence of 2 = 1
Number of items in the sample space = 6
The theoretical probability of 2 is then calculated as
Probability = Number of occurrence of 2/Number of items in the sample space
Substitute the known values in the above equation, so, we have the following representation
Probability = 1/6 --- in fraction
Evaluate the quotient
Probability = 0.167 -- in decimal
Express as percentage
Probability = 16.7%
Hence, the probability is 16.7%
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everything at a store is on sale. The store offers a 25% discount. The regular price of a t-shirt is 20%. What is the discount price? Please help me.
The discount price of the shirt will be $15.
How to calculate the price?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
From the information, the store offers a 25% discount and the regular price of a t-shirt is $20. Therefore, based on the information illustrated, the main points to note will be:
Discount = 25%
Regular price = $20.
In this case, the discount price will be the difference between the regular price and the discount.
The discount price will be:
= Regular price - Discount
= $20 - ($20 × 25%)
= $20 - $5
= $15
The price is $15.
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Complete question
everything at a store is on sale. The store offers a 25% discount. The regular price of a t-shirt is $20. What is the discount price? Please help me
NEED HELP NOW Convert 110 kilograms to pounds. (1 kilogram = 2.204 pounds)
The required answer in the given problem, given weight of 5 kilograms and convert it to 11.02 pounds. By multiplying the given weight by the conversion factor of 2.204 pounds/kilogram, obtain the weight in pounds.
Conversion from kilograms to pounds:
To convert a weight value from kilograms to pounds, we use the conversion factor of 1 kilogram equals 2.204 pounds. This means that for every 1 kilogram, there are 2.204 pounds. To convert a weight from kilograms to pounds, we multiply the given value in kilograms by the conversion factor.
To convert 110 kilograms to pounds, we can use the conversion factor that states 1 kilogram is equal to 2.204 pounds. Here's the step-by-step process:
Step 1: Write down the given weight in kilograms, which is 110 kilograms.
Step 2: Multiply the given weight by the conversion factor:
110 kilograms x 2.204 pounds/kilogram
Step 3: Perform the multiplication:
110 x 2.204 = 242.44 pounds
Therefore, 110 kilograms is equal to 242.44 pounds.
In the given problem, given weight of 5 kilograms and convert it to 11.02 pounds. By multiplying the given weight by the conversion factor of 2.204 pounds/kilogram, obtain the weight in pounds.
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Multiply by using the Distributive Property. (x2 + 3)(x − 4) =
The expression is obtained by simplifying it by the distributive Property is x³-4x²+3x-12.
What is distributive property?The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example, we can write a(c+b) in the form of (ac+bc).
It is given that, the expression is (x² + 3)(x − 4)
The expression is simplified using the distributive property as,
=(x² + 3)(x − 4)
=x²(x − 4)+3(x − 4)
=x³-4x²+3x-12
Thus, the expression is obtained by simplifying it by the distributive Property is x³-4x²+3x-12.
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The multiplication of the term (x² + 3)(x - 4) using distributive property is x³ - 4x² + 3x - 12.
Distributive property explains to us how to solve expressions in the form of a(b + c).
After apply distributive property, this term converts as ab+ac
The given expression is,
(x² + 3)(x - 4)
Solve by using distributive property formula (a+b)(c+d)= a(c+d) + b(c+d),
x²(x - 4) + 3(x - 4)
Now further simplify by using formula a(b+c) = ab+ac,
x³ - 4x² + 3x - 12.
The required multiplication of the given terms is x³ - 4x² + 3x - 12.
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An observer whose eye level is 5 ft is observing the top of an object with a mirror on the
ground. The mirror is 3 feet from the observer and 12 feet from the object. Calculate the
height of the object.
The height of the object is 20 feet.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
An observer whose eye level is 5 ft is observing the top of an object with a mirror on the ground.
The mirror is 3 feet from the observer and 12 feet from the object.
Using proportion
5/ 3= x/ 12
60= 3x
x = 20 feet
hence, the height of the object is 20 feet.
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Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years.
Answer:
11.6 years
Step-by-step explanation:
1800 = 900 x (1 + 0.06/12)^ 12t
1800 = 900 x (1 + 0.005)^12t
1800 = 900 x (1.005)^12t
1800 = 900 x 1.061678^t
1800/900 = (900 x 1.061678^t)/ 900
2 = 1.061678^t
log(1.061678) 2 = t
t = 11.5813
t = 11.6
Determine whether the expressions are equivalent.
0.4(k+3) is to 0.4 k+1.2
Equivalent. 0.4(k+3)=0.4 k+1.2
Not equivalent. 0.4(k+3)=0.4 k+0.8
Equivalent. 0.4(k+3)=0.4 k+0.4
Not equivalent. 0.4(k+3)=0.4 k+0.4
Both the expressions are equivalent to each other.
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Given expression:
LHS
0.4(k+3)
= 0.4k + 0.4 × 3
= 0.4k + 1.2
RHS
0.4 k+1.2
LHS = RHS
Therefore, both the expressions are equivalent to each other.
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The number of bacteria in a certain population increases Accor to a continuous growth model,with a growth parameter of 9.6% per hour. How many hours does it take for the size of the sample to double
The required number of hours does it take for the size of the sample to double is 11 hours.
What is percentage?Percentages are basically divisions where the denominator is 100. To show that a number is a percent, we utilize the percent image (%) close to the number. For instance, in the event that you got 75 inquiries right out of 100 on a test (75/100), you would have scored 75%.
According to question:Let initial population be x.
As question says number of bacteria increases by 9.6% per hours.
9.6% of x takes 1 hours,
So, in 11 hours size of sample become 105.6%, means almost double of initial size.
Thus, 11 hours will be taken to make size double.
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Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.
A sample of 72 stocks traded on the NYSE that day showed that 29 went up.
You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of a = 0.02.
What is the test statistic for this sample?
Use p rounded to 4 decimal places. (Report answer accurate to 4
decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to 4 decimal places.)
p-value =
The p-value is either less than (or equal to) or
greater than?
This p-value leads to a decision to...
reject the null or accept the null or fail to reject the null?
As such, the final conclusion is that... (select a letter)
A) There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went
up is is more than 0.3.
B) There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that
went up is is more than 0.3.
C) There is sufficient evidence to support the claim that the proportion of stocks that went up is is more
than 0.3.
D) There is not sufficient sample evidence to support the claim that the proportion of stocks that went up
is is more than 0.3.
The test statistic and the p-value of the research are respectively z = 1.9072 and p-value = 0.0283 and the conclusion is that; D) There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is more than 0.3.
How to find the p-value from the research?Let us first of all define the hypotheses;
Null Hypothesis; H₀: p ≤ 0.3
Alternative Hypothesis; Hₐ: p > 0.3
Sample proportion is;
p^ = 29/72 = 0.403
The formula for the test statistic is;
z = (p^ - p)/(√(p(1 - p)/n))
Plugging in the relevant values gives;
z = (0.403 - 0.3)/(√(0.3(1 - 0.3)/72))
z = 1.9072
From p-value from z-score calculator, we have that;
p-value = 0.0283
p-value is greater than the significance value and as such we fail to reject the null hypothesis and conclude that There is not sufficient sample evidence to support the claim that the proportion of stocks that went up
is is more than 0.3.
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Describe how the values of r, x, and y relate to each of sinø, cosø and tanø
the values of r, x, and y are related to the sine, cosine, and tangent of angle ø as:
sin ø = y / r
cos ø = x / r
tan ø = y / x
What is trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In a right triangle, the sides are typically labeled as follows:
The side opposite the angle ø is called the "opposite side" and is labeled "y".
The side adjacent to angle ø is called the "adjacent side" and is labeled "x".
The hypotenuse is the side opposite the right angle and is labeled "r".
The values of r, x, and y can be used to calculate the sine, cosine, and tangent of angle ø. These trigonometric functions are defined as follows:
Sine (sin ø): sin ø = y / r
Cosine (cos ø): cos ø = x / r
Tangent (tan ø): tan ø = y / x
Hence, the values of r, x, and y are related to the sine, cosine, and tangent of angle ø through the above equations.
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Solve the equation for w.
w divided by 1.1 minus 3.9 equals 10.5
6
7.26
13
15.84
W will be 15.84.
What is an equation?The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 has the two expressions 3x + 5 and 14 that are separated by the 'equal' sign.
We know that w divided by 1.1 minus 3.9 equals 10.5
That will be W/1.1 - 3.9 = 10.5
W/1.1 = 10.5 + 3.9
W/1.1 = 14.4
W = 14.4* 1.1
W = 15.84
W will thus equal 15.84.
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A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed. Part A: Find the constant of proportionality. Show every step of your work. (4 points) Part B: Write an equation that represents the relationship. Show every step of your work. (2 points) Part C: Describe how you would graph the relationship. Use complete sentences. (4 points) Part D: How many gallons of water are needed for 10 scoops of drink mix? (2 points)
a) The constant of proportionality of the given problem is; 4
b) An equation that represents the relationship is; y = 4x
c) The graph is as attached.
d) The gallons of water that are needed for 10 scoops of drink mix is; 2.5 gallons
How to find the proportional relationship?The general equation for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope of line which tells us the unit rate of change of y with respect to x
c is the y - intercept
Now, it is pertinent to note that y = mx also represents direct proportionality. Making m the subject gives;
m = y/x
Thus, with proportion, we can say;
y₁/x₁ = y₂/x₂
The proportional relationship will be written as;
y = kx
where k is constant of proportionality
From the question, we can say that;
2 scoops require 0.5 gallon of water
6 scoops require 1.5 gallon of water
a) Thus;
k = 2/0.5
k = 2/(1/2)
k = 2 * 2 = 4
b) Equation that represents the relationship can be written as;
y = 4x + c
Since 2 scoops require 0.5 gallon of water, then;
2 = (4 * 1/2) + c
2 = 2 + c
c = 0
The equation will be; y = 4x.
c) Graph of y = 4x is attached at the end.
d) For 10 scoops of water;
10 = 4x
x = 2.5 gallons of water required.
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Fully simplify. -15xy(15x^5y^3)
Answer:
−225x^6y^4
Step-by-step explanation:
B OA) A Which statements are necessary to prove the two triangles are congruent by SSS? O B) D =CD, AB = C, mzBDA = 90° AD, BD = CD, mzBDA = 90° O a OD) AD AD, BD = CD, AB = AC BD = CD, AB= AC
The statements that are necessary to prove the two triangles are congruent by SSS are AD≅ AD, BD ≅ CD, and AB ≅ AC.
What is congruence?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Here,
To prove that two triangles are congruent using the SSS Congruence criterion, we must establish that all three sides of one triangle are equal to all the corresponding sides of the other.
Thus,
Side AD in ∆ADB is congruent to side AD in ∆ADC.
Side BD in ∆ADB is congruent to side CD in ∆ADC.
Side AB in ∆ADB is congruent to side AC in ∆ADC.
Hence, based on the SSS congruence criterion, it is concluded that both triangles are congruent. i.e AD≅ AD, BD ≅ CD, AB ≅ AC.
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Answer:
D
Step-by-step explanation:
To prove that two triangles are congruent using the SSS Congruence criterion, we must establish that all three sides of one triangle are equal to all the corresponding sides of the other.Thus,Side AD in ∆ADB is congruent to side AD in ∆ADC.Side BD in ∆ADB is congruent to side CD in ∆ADC.Side AB in ∆ADB is congruent to side AC in ∆ADC.Therefore, based on the SSS congruence criterion, it is concluded that both triangles are congruent.The statements necessary to prove that they are congruent by SSS is: D
Need an answer pls will mark Brainliest
Answer:
4 m^3 - 38 m^2 + 57 m - 72 = (4 m^2 - 6 m + 9)(m - 8) + 0
Step-by-step explanation:
Compute (4 m^3 - 38 m^2 + 57 m - 72) ÷ (m - 8) using polynomial long division:
m - 8 | 4 m^3 | - | 38 m^2 | + | 57 m | - | 72
To eliminate the leading term of the numerator, 4 m^3, multiply m - 8 by 4 m^2 to get 4 m^3 - 32 m^2. Write 4 m^2 on top of the division bracket and subtract 4 m^3 - 32 m^2 from 4 m^3 - 38 m^2 + 57 m - 72 to get -6 m^2 + 57 m - 72:
| | | 4 m^2 | | | |
m - 8 | 4 m^3 | - | 38 m^2 | + | 57 m | - | 72
| -(4 m^3 | - | 32 m^2) | | | |
| | | -6 m^2 | + | 57 m | - | 72
To eliminate the leading term of the remainder of the previous step, -6 m^2, multiply m - 8 by -6 m to get -6 m^2 + 48 m. Write -6 m on top of the division bracket and subtract -6 m^2 + 48 m from -6 m^2 + 57 m - 72 to get 9 m - 72:
| | | 4 m^2 | - | 6 m | |
m - 8 | 4 m^3 | - | 38 m^2 | + | 57 m | - | 72
| -(4 m^3 | - | 32 m^2) | | | |
| | | -6 m^2 | + | 57 m | - | 72
| | | -(-6 m^2 | + | 48 m) | |
| | | | | 9 m | - | 72
To eliminate the leading term of the remainder of the previous step, 9 m, multiply m - 8 by 9 to get 9 m - 72. Write 9 on top of the division bracket and subtract 9 m - 72 from 9 m - 72 to get 0:
| | | 4 m^2 | - | 6 m | + | 9
m - 8 | 4 m^3 | - | 38 m^2 | + | 57 m | - | 72
| -(4 m^3 | - | 32 m^2) | | | |
| | | -6 m^2 | + | 57 m | - | 72
| | | -(-6 m^2 | + | 48 m) | |
| | | | | 9 m | - | 72
| | | | | -(9 m | - | 72)
| | | | | | | 0
The quotient of (4 m^3 - 38 m^2 + 57 m - 72)/(m - 8) is the sum of the terms on top of the division bracket. Since the final subtraction step resulted in zero, m - 8 exactly divides 4 m^3 - 38 m^2 + 57 m - 72, and there is no remainder.
| | | 4 m^2 | - | 6 m | + | 9 | (quotient)
m - 8 | 4 m^3 | - | 38 m^2 | + | 57 m | - | 72 |
| -(4 m^3 | - | 32 m^2) | | | | |
| | | -6 m^2 | + | 57 m | - | 72 |
| | | -(-6 m^2 | + | 48 m) | | |
| | | | | 9 m | - | 72 |
| | | | | -(9 m | - | 72) |
| | | | | | | 0 | (remainder) invisible comma
(4 m^3 - 38 m^2 + 57 m - 72)/(m - 8) = (4 m^2 - 6 m + 9) + 0
Write the result in quotient and remainder form:
Answer: 4 m^3 - 38 m^2 + 57 m - 72 = (4 m^2 - 6 m + 9)(m - 8) + 0
What is the solution to 9|x – 8| < 36?
4 < x < 12
x < –4 or x > 12
x > –12 or x < 8
–4 < x < 8
Answer:
4 < x < 12
Step-by-step explanation:
x - 8 ≥ 0
x ≥ 8
If x ≥ 8
9(x-8) < 36
9x - 72 < 36
9x < 36 + 72
9x < 108
9/9 x < 108/9
x < 12
8 ≤ x < 12
if x < 8
9(-x+8) < 36
-9x + 72 < 36
-9x < 36 - 72
-9x < -36
-9/-9 x > -36/-9
x > 4
4 < x < 8
4<x<12
We want to determine if [u, v, w is linearly independent. To do that we write the vectors as columns of a matrix A and row reduce that matrix To check this we add We then add We then add We conclude that times the first row to the second. times the first row to the third. times the new second row to the new third row. OA. The set [u, v, w} is linearly dependent. O B. The set {u, v, w] is linearly independent. C. We cannot tell if the set [u, v, w] is linearly independent or not.
Option C, If your row reduces the matrix A and obtains a row of all zeros except for a single 1 in the rightmost column, then the set {u, v, w} is linearly dependent.
This is because the row of all zeros except for a 1 in the rightmost column indicates that one of the vectors in the set can be expressed as a linear combination of the other vectors.
On the other hand, if your row reduces the matrix A and does not obtain a row of all zeros except for a single 1 in the rightmost column, then the set {u, v, w} is linearly independent. This is because the absence of such a row indicates that none of the vectors in the set can be expressed as a linear combination of the other vectors.
If you are unable to row reduce the matrix A for any reason, then it is not possible to determine if the set {u, v, w} is linearly independent or not.
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Fill in the diagram based on the following information
30% of the total is 12 grams
in this given question 30% of 12 will be 3.6.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
30% of the total is 12 grams
So the given 30% of 12 will be
12*30/100
=3.6
Hence, in this given question 30% of 12 will be 3.6.
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Simplify: 3/8(4a-5)-5/12(3a-4)=1/6
Answer:
Step-by-step explanation:
3/8(4a-5)-5/12(3a-4)=
9/24(4a-5)-10/24(3a-4)=1/6 | x24
9*(4a-5)-10(3a-4)=4
36a-45-30a+40=4
6a=9
a=3/2
Help me with geometry
Answer:
34
Step-by-step explanation:
This is somewhat hard to explain for me. I attached a picture/diagram to help.
They are congruent angles.
Angle N, inside the MNP triangle is 34. Which means the adjacent angle is 56.
The interior angles of a triangle add up to 180.
So to find angle M in triangle LNM, we can do 180 - 90 - 56.
Therefore the m<LMN = 34