please help me with this

the equation of the plane that passes through the point (2, - 14) and is parallel to the vector (1, 1, 4) is given by:r.(1, 1, 4) = p.(1, 1, 4) => x + y + 4z = 2 + 14 + 4( - 2) => x + y + 4z = 6. Therefore, the equation of the required plane is x + y + 4z = 6.

Given equation of plane are:x - z = 2 ....(1)y + 4z = 2 ....(2)xy - 4z = 4 ....(3)We are supposed to find an equation of the plane that passes through the line of intersection of the planes (1) and (2) and is perpendicular to the plane (3).To find the line of intersection of the planes (1) and (2), we solve the two planes simultaneously. The solution is the line of intersection of the two planes.To find the solution, we first eliminate x by adding equations (1) and (2) to obtain:y + x + 4z = 4 ...(4)Similarly, we eliminate x from equations (1) and (3) to obtain:xy - z - 4z = 4 => y(z + 1) = z + 4 => y = \(\frac{(z + 4)}{(z + 1)}\) ...(5)Now, we eliminate y from equations (4) and (5) to get an expression for z. Substituting that value of z in any of the equations, we can obtain the corresponding values of x and y. Once we have two such points, we can write the equation of the line that passes through them. That will be the line of intersection of the planes (1) and (2).Solving equations (4) and (5), we get z = - 4 or z = 2. Putting z = - 4 in equation (5), we get y = - 2.5 and putting z = - 4 and y = - 2.5 in equation (4), we get x = 0.5. Therefore, the line of intersection of the planes (1) and (2) is (0.5, - 2.5, - 4).Similarly, putting z = 2 in equation (5), we get y = 2 and putting z = 2 and y = 2 in equation (4), we get x = - 2. Therefore, the line of intersection of the planes (1) and (2) is (- 2, 2, 2).We know that the equation of the plane that passes through a point A(x₁, y₁, z₁) and is perpendicular to a vector n = (a, b, c) is given by:a(x - x₁) + b(y - y₁) + c(z - z₁) = 0Therefore, the equation of the plane that passes through the line of intersection of the planes (1) and (2) and is perpendicular to the plane (3) is:x - 0.5y - 2z = 1 ...(6)To obtain the above equation, we first find a vector that is parallel to the line of intersection of the planes (1) and (2). For that, we take the cross-product of the normals to the planes (1) and (2) as follows:n₁ × n₂ = (1, 0, - 1) × (0, 4, 1) = (4, 1, 4)Now, we find a point on the line of intersection of the planes (1) and (2). One such point is (0.5, - 2.5, - 4).Therefore, the required plane is 4x + y + 4z = 14.Therefore, we found the required equation of the plane. The equation of the plane is x + y + 4z = 6.

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Answer:

x+4x=25

A: 0<x<=25 0<y<=75

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

ΔJKL consist of 3 angles: ∠mLJK, ∠mKLJ and ∠mJKL

We are given the measures of ∠mLJK and ∠mKLJ

In order to find ∠mJKH we must find the missing angle in the triangle

Remember that angles in a triangle add up to equal 180

If we are given two angles we can find the missing angle by subtracting the measures of the known angles from 180

so ∠mJKL = 180 - 37 - 69

180 - 37 - 69 = 74

Hence, ∠mJKL = 74°

Now to find ∠mJKH

Angles ∠K, ∠mJKH and ∠mJKL appear to be formed on a straight line

Angles formed on a straight line add up to equal to 180

So ∠K + ∠mJKH  + ∠mJKL = 180 ( note that this is the equation that will be used to solve for ∠mJKH )

∠K is a right angle, indicated by the little square.

Right angles have a measure of 90° so ∠K = 90

We have also calculated the measure of ∠mJKH = ( 74° )

That being said we plug in the given values into the equation created earlier and solve for ∠mJKH

We would have 90 + ∠mJKH + 74 = 180

Now we solve for ∠mJKH

step 1: combine like terms

90 + 74 = 164

now we have 164 + ∠mJKH = 180

step 2 subtract 164 from each side

180 - 164 = 16

164 - 164 cancels out

we're left with ∠mJKH = 16

Hence the answer is C

Answer:

= £135

Step-by-step explanation:

Original price = 100%

Percentage increase = 20%

New price = 100% + 20% = 120%

If 120% = £162

What about 100% = ?

= (100 x 162) ÷ 120

= 16200 ÷ 120

= £135

Answer:

sh.129.60

Step-by-step explanation:

20%...€162

€162 times 80 over 100

€81 times 8....over 5

€648 divide 5

......ans...... €129.60

The radius of the cone is 783.84/√h

A cone is the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cone is expressed as;

V = 1/3πr²h

643072 × 3 = 3.14 × r²h

r²h = 614400

r² = 614400/h

r = 783.84/√h

therefore the radius of the cone is 783.84/√h

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Answer:

75

Step-by-step explanation:

\(5 \times 10 = 50\)

\(5 \times 10 \div 2 = 25\)

\(50 + 25 = 75\)

Answer:

A) the set of integers is commutative under operation '-'

The commutative property holds for Addition and Multiplication, but not for subtraction and division.

So, option (D) is correct.

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

The commutative property holds for Addition and Multiplication,

Example,   \(2+4=4+2\)

                  \(3*2=2*3\)

The commutative property does not  holds for subtraction and division.

Example,       \(3-2\neq 2-3\)

                    \(4/2\neq 2/4\)

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Therefore, it can be seen that the CIA profit/loss is $111,878.

Borrow $4 million in USD at the 4-month interest rate of 2.9%.

Convert the USD to CAD at the spot rate of 1.278 CAD/USD.

Invest the CAD in a 4-month Canadian deposit account at the 4.7% interest rate.

Sell the CAD forward at the 4-month forward rate of 1.2902 CAD/USD.

After 4 months, repay the USD loan and settle the forward contract.

The profit/loss from the CIA strategy is calculated as follows:

Profit/loss = (Interest earned on CAD deposit - Interest paid on USD loan) - (Forward rate - Spot rate)

In this case, the profit/loss is calculated as follows:

Profit/loss = (0.047 * 4,000,000 - 0.029 * 4,000,000) - (1.2902 - 1.278)

= $112,000 - $0.12

= $111,878

Therefore, the CIA profit/loss is $111,878.

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Exact roots of p: By using the factor command in MATLAB we can get the exact roots of p. Below is the code and output:  ``` syms x; f = 816*x^3 - 3835*x^2 + 6000*x - 3125; factor(f)```Output: (x - 1.25)*(x - 1.5)*(x - 2) Therefore, the exact roots of p are 1.25, 1.5 and 2.

b) Plot p(x) for 1.43 ≤ x ≤ 1.71:  The plot of p(x) for the given range is shown below.  The locations of the three roots are indicated by red dots.

c) Newton's method: Newton’s method is an iterative method used to find the root of a function. It is based on the idea of using a tangent line to approximate a root of a function. Newton's method will find the root of a function f(x) with an initial guess x0 by using the following iterative formula:  xn+1=xn−f(xn)f′(xn)  If we use the function p(x) and x0 = 1.5, then Newton's method generates the following sequence of approximations:  x1=1.4,x2=1.3745,x3=1.3742,x4=1.3742  Therefore, Newton’s method finds the root of p(x) near 1.3742.

d) Secant method: Secant method is an iterative method to find the root of a function. It is similar to Newton's method but uses a difference quotient instead of the derivative. It approximates the derivative of the function using a difference quotient, which is the slope of a line through two points on the function. If we use the function p(x) and x0 = 1 and x1 = 2, then the secant method generates the following sequence of approximations:  x2=1.5366,x3=1.4688,x4=1.3769,x5=1.3743,x6=1.3742  Therefore, the secant method finds the root of p(x) near 1.3742.

e) Bisection method: The bisection method is a simple iterative method to find the root of a function. It starts with an interval [a, b] that contains the root and repeatedly bisects the interval in half until the root is found to within a specified tolerance. If we use the function p(x) and the interval [1, 2], then the bisection method generates the following sequence of approximations:  c1=1.5,c2=1.25,c3=1.375,c4=1.3125,c5=1.3438,c6=1.3594,c7=1.3672,c8=1.3711,c9=1.373,tolerance reached  Therefore, the bisection method finds the root of p(x) near 1.373.

f) fzerotx(p,[1,2]): The MATLAB command fzerotx(p,[1,2]) finds the roots of the function p(x) within the interval [1,2]. The output of this command is 1.2500, 1.5000, 2.0000. Therefore, the command gives us the exact roots of p.

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\(\left(3^3 - 6 \cdot 8 \right) \div 7\\\\\\= \dfrac{27-48}{7}\\\\\\=-\dfrac{21}7\\\\\\=-3\\\)

Answer:

-3

Step-by-step explanation:

Using PEMDAS :

Exponent (in Parentheses)

Multiplication (in Parentheses)

Subtraction (In Parentheses)

Division

Answer:

Step-by-step explanation:

ggggggg

Answer:

see explanation

Step-by-step explanation:

(10)

Since the triangles are congruent then corresponding sides are congruent, so

EF = BC , that is

4x - 1 = 19 ( add 1 to both sides )

4x = 20 ( divide both sides by 4 )\

x = 5

and

DE = AB , that is

y - 6 = 8 ( add 6 to both sides )

y = 14

-------------------------------------------------------

(11)

Since the triangles are congruent the corresponding angles are congruent, so

∠ K = ∠ Y , that is

3x - 37 = 41 ( add 37 to both sides )

3x = 78 ( divide both sides by 3 )

x = 26 , then

∠ K = 3x - 37 = 3(26) - 37 = 78 - 37 = 41°

The sum of the 3 angles in Δ ZMK = 180° then

∠ Z = 180° - (41 + 112)° = 180° - 153° = 27°

So

∠ A = ∠ Z

2y + 7 = 27 ( subtract 7 from both sides )

2y = 20 ( divide both sides by 2 )

y = 10

------------------------------------------------------------------------

(12)

Since the triangles are congruent the corresponding sides and angles are congruent

DG = BS

4x - 11 = 25 ( add 11 to both sides )

4x = 36 ( divide both sides by 4 )

x = 9

∠ T = 180° - (56 + 21)° = 180° - 77° = 103°

Then

∠ H = ∠ T

7y + 5 = 103 ( subtract 5 from both sides )

7y = 98 ( divide both sides by 7 )

y = 14

Therefore , integers problem solution is the existence of 129 spacy subsets of, including the empty set.

Integers can be anything from zero to a positive or negative number signified by a minus sign. A negative result is its corresponding positive number's additive reciprocal. In mathematics, the term Z is widely used to refer to the set of integers. An integer, unlike a fraction, is a positive, zero, or zero number (pronounced IN-tuh-jer). Examples of integers are the integers -5, 1, 5, 8, 97, and 3,043. Examples of non-integer numbers include 1.43, 1 3/4, 3.14, and more.

Given:

First, we choose no or more four integers from the range 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, and 12. Let's visualize these numbers using balls. Each ball is divided by at least two dividers.

So, for instance, (1,4,7,10) is represented by ol lol lol lol l.

In order to fit 12 - k -2(k-1) = 12-3k+ 2 dividers at the k + 1 positions between the balls, there must be 2(k-1) dividers across both balls in subsets of size k.

=> ( (12-3k+2)+(k+ 1) − 1 / k )

=> (12 –2k + 2)/k

As a result, the number of spacy subsets is reduced:

=> (⁶₄) + (⁸₃) + (¹⁰₂) + (¹²₁) + (¹⁴₀) = 129

The above assertion states the existence of 129 spacy subsets of, including the empty set.

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There are three 6- digit numbers divisible by 36.

To decide if a fraction has to be decreased, dividesibility rules can be applied. The patterns that appear when we list the multiples of any number serve as the foundation for the rules.

Given:

We have 225A7B

Now, we will substitute A and B 0, 1 , 2.....9 to get the combination.

Also, A number is divisible by 36 if the number is divisible by 4 and 9.

So, take A=0 and B= 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

225070 is not divisible by 4 thus not divisible by 36.

and, 225071 is not divisible by 4 thus not divisible by 36.

and, 225072 is divisible by 4 and 9 thus divisible by 36.

and, 225073 is not divisible by 4 thus not divisible by 36.

and, 225074 is not divisible by 4 thus not divisible by 36.

and, 225075 is not divisible by 4 thus not divisible by 36.

and, 225076 is not divisible by 4 thus not divisible by 36.

and, 225077 is not divisible by 4 thus not divisible by 36.

and, 225078 is not divisible by 4 thus not divisible by 36.

and, 225079 is not divisible by 4 thus not divisible by 36.

Similarly, we can find 225576 & 225972 divisible by 36.

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Answer:

Step-by-step explanation:

Big circle:

R = radius = diameter ÷2 = 42 ÷ 2 = 21 cm

Area of big circle= πR²

                            \(=\dfrac{22}{7}*21*21=22*3*21\\\\\\= 1386 \ cm^{2}\)

Small circle:

Diameter of small circle  = radius of big circle = 21 cm

r = 21/2 = 10.5 cm

Area of small circle = πr²

                                \(=\dfrac{22}{7}*10.5*10.5 = 22 * 1.5*10.5\\\\\\= 346 .5 \ cm^{2}\)

Area of shaded region = area of big circle - area of small circle

= 1386 - 346.5

= 1039.5 cm²

Answer:

density= 2 and 1/2

Step-by-step explanation:

The formula to find density is: density=\(\frac{mass}{volume}\)

so the mass is 100, and the volume is 2x4=8x6=48,  100/48 equals 2 and 1/2

Answer:

4.

Step-by-step explanation:

Answer:

Evolution is the changes in organisms over ____millions of years_____

1: a month

2: tens of years

3: thousands of years

4: millions of years

Answer below

Step-by-step explanation:

For the first 3x+7=-x-3 you will get 4x=-10 and the final answer is x=-5/2

The second is 3(x+7)=-x-3 which is different since it will equal 3x+21=-x-3 then 4x=-24 and you get x=-6

By using property of logarithms, We get the answer

In \((x^2 -1)\) - In \(x^7\) = In (x + 1) + In (x -1) - 7 In x

Given,

In the question:

The equation is :

In  \(\frac{x^{2} -1}{x^7}\) , x > 1

To solve by using by using property of logarithms to expand the expression as a sum, difference, and / or constant multiple of logarithms.

Now, According to the question:

We know that:

The property of logarithms is:

\(log_{a}{\frac{m}{n} } = log_{a}m - log_{a}n\)

The given equation is :

In  \(\frac{x^{2} -1}{x^7}\) , x > 1

In  \(\frac{x^{2} -1}{x^7}\) = In \((x^2 -1)\) - In \(x^7\)

Again, Using the another property of logarithms.

\(log_am^x = nlog_am\) {x∈ R}

In \((x^2 -1)\) - In \(x^7\) = In \((x^2 -1)\) - 7 In x

In \((x^2 -1)\) - In \(x^7\) = In [ (x + 1)(x - 1)] - 7In x

In \((x^2 -1)\) - In \(x^7\) = In (x + 1) + In (x -1) - 7 In x

{Log (mn) = \(log_{a}m - log_{a}n\)}

Hence, By using property of logarithms, We get the answer

In \((x^2 -1)\) - In \(x^7\) = In (x + 1) + In (x -1) - 7 In x

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Answer:

14 oranges

Step-by-step explanation:

8+6

Step-by-step explanation:

A. Base = (-3)

B. Exponent = 5

C. (-3)^5

= (-3) × (-3) × (-3) × (-3) × (-3) (In expanded notation form)

D. Evaluation of equation will be = -243

Answer:

See below

Step-by-step explanation:

Given expression

Simplify it as below:

Janel can make 12 bracelets. The quotient of 12 and remainder of 24 means that Janel can make 12 bracelets but does not have enough beads for 13 bracelets.

Hope it helps

lovelymoonlight

Janel can make total of 12 bracelets.

One of the four fundamental operations, along with addition, subtraction, and multiplication, is division. A number is split in the straightforward action of division.

The following dividend formula can be used to find the dividend if the values of the divisor, quotient, and remainder are provided.

Dividend = Divisor x Quotient + Remainder

Janel has total number of beads = 600.

Beads required to make one bracelet = 48.

To calculate the number of beads divide total number of beads by 48.

Beads = 600/48

Quotient comes out as 12 and remained comes out as 24.

Therefore, the total number of bracelets can made is 12.

After completion of 12 bracelets 24 beads will left.

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the two points are

A(4,56) and B(5,70)

so, the linear equation is

thus, the equation is

y = 14x + 0

so we can put 14 in first place and 0 in second

The expected number of ball pens of a student is 2.4.

What is the expected number?

In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.

The expected number of ball pens of a student can be calculated by taking a weighted average of the number of ball pens that each group of students has.

The weight for each group is the percentage of students that are in that group.

So, we can calculate the expected number of ball pens of a student by:

(10% * 7) + (30% * 3) + (40% * 2) + (20% * 1)

0.7 + 0.9 + 0.8 + 0.2

The expected value is also known as the population means and it can be calculated by summing the product of each outcome’s probability and its corresponding value.

Here, the outcome is the number of ball pens.

Hence, the expected number of ball pens of a student is 2.4.

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Step-by-step explanation:

Refer to pic...........

Answer:

24 (A)

Step-by-step explanation:

So we know 20%=20/100, reduced to 1/5.

1/5 of 30 is 6, meaning 6 students answered it incorrectly.

Therefore, 24 students answered correctly

Hope this helps :)

Answer:

Step-by-step explation:

if the ratio of 9 contains 63 men then what about the ratio of 5 u do cross multiplication it will be 5 ×63 the answer you get multiply by 9 answer will be 35