Find the point in which the line meets the plane.
x = 1 - t, y = 3t, z = 1 + t; 2x - y + 3z = 6

Answer:

he is not because triangles can be different sides but they always have to equal 180 if it's a right triangle but if it does not it's a ln acute or obtuse triangle

4 over 6 because when you multiply 2 over 3 by 2 over two the answer is 4 over 6.

The equation of the graph is (a) [tex]\frac{2x^2-8}{x^2+x-6}[/tex]

From the question, we have the following parameters that can be used in our computation:

The graph and the list of options

Next, we test the graph with the options

On the graph, we have:

f(0) = 1.3

f(-1) = -1

From the list of options, the equation that has the above properties is option (a)

Hence, the equation is (a)

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The inverse of the function is given by x=√y-10

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here;  g(x)= (x+10)²

To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

Thus y=(x+10)²

√y=x+10

x=√y-10

Hence, The inverse of the function is given by x=√y-10

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Answer:

Translation and dilation

Step-by-step explanation:

Translation because the points move spaces on the graph, and dilation because it gets bigger/smaller than the other.

Not all square matrices can be diagonalized. If there are just two eigenvectors (up to multiplication by a constant), then the matrix cannot be diagonalized.

A collection of integers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix, are the integers. In addition to several mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital uses as well.

Thus, Not all square matrices can be diagonalized. If there are just two eigenvectors (up to multiplication by a constant), then the matrix cannot be diagonalized.

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The solution of the initial value problem is [tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}[/tex].

Initial value issues are a specific kind of calculus issue. Calculus initial value issues include differential equations with a known beginning condition that identifies the function's value at a certain point. Finding the function that best describes the system is the goal of these puzzles, and this can be accomplished by integrating the differential equation.

There is always an unknown constant present when doing an integration with an indeterminate integral or without initial conditions. The constant of integration is what is commonly indicated by the letter C.

Given that the initial value problem is:

dy/dt= e^(y-t) sec(y)(1+t2)

This can be re written as follows:

dy/ dt = e^(y-t) (1 + t^2) / sec (y)

Separate the derivative in terms of y and t and take integration:

[tex]\int{e^{-y}cos(y)} \, dy = \int {e^{-t}(1 + t^2)} \, dt[/tex]

Integrate the following:

[tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + c\\[/tex]

The initial conditions given are y(0) = 0, substitute the value of the variables as 0:

[tex]\frac{e^{0}}{2} [sin0 - cos0] = -e^{0} [0^2 + 2(0) + 3] + c\\\\\\\frac{1}{2} [-1] = 3 + c[/tex]

c = 5/2

Hence, the solution of the initial value problem is:

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#SPJ4[tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}[/tex]

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Answer:

below

Step-by-step explanation:

x^2 - 19x    ± 39       take 1/2 of the 'x' coefficient square it and add and subtract it

x^2 - 19x +  90.25    - 90.25   ±39

(x-9.5)^2   - 90.25 ±39     so I guess the answer is  90.25

The cost of painting the wall is Rs.48.75 .

The square shape wall whose length is 10m has a door of length 2m and breadth 1m.   It also has a window of length 1m and breadth 0.5m.

Therefore, the cost of painting the wall can be calculated as follows:

cost of painting per meters = Rs0.5 per metre square

Therefore, the area of the wall to be painted will exclude the window and the door.

Hence,

area of wall of the wall to be painted = area of the wall - area of the window - area of the door

Therefore,

area of wall of the wall to be painted = 10² - (1 ×  0.5) - (2 × 1)

area of wall of the wall to be painted = 100 - 0.5 - 2

area of wall of the wall to be painted = 97.5 metres²

Therefore,

1 metres square = Rs0.5

97.5 metres squared = ?

cross multiply

cost to paint the wall = 0.5 × 97.5

cost to paint the wall = Rs.48.75

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Answer:  5 : 18 =  10 : 36

Step-by-step explanation:

The ratio is already in lowest terms so we found an equivalent ratio by multiplying both terms by 2.

Answer:

5 to 18

Step-by-step explanation:

Based on given ratio of 10:11:9, the share for each person is as follows:

Ratio is the relative size of one value or variable compared to another.

Ratios show how much each quantity is contained in another.

Ratios are fractional values obtained as the quotient of one value divided by another, and are depicted in fractions, decimals, or percentages.

The total shareable amount =  £300

The sharing ratio = 10:11:9

The sum of ratios = 30

Simon's share =  £100 (10/30 x  £300)

Sarah's share =  £110 (11/30 x  £300)

Matthew's share =  £90 99/30 x  £300)

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Answer: 7

Step-by-step explanation:

a = 11, b = 7 a = 11, b = 10 a = 28, b = 7 a = 28, b = 10

✓ a = 11, b = 7You just needed to multiply the terms together

The angle of depression is 32°.

The angle of depression is the angle formed when the item being seen is below the observer's level between the horizontal line and the line of sight of the observer.

The angle of depression is the angle formed by the horizontal axis and the downward axis of a line of sight. As an example, if you were perched on top of a hill or other structure and looked down at an object, you might determine the angle of depression. To measure these angles, a theodolite or a clinometer can be used. The maximum depression angle is 90 degrees. It can't be possible because any rational spectator would turn around the instant the object passed beneath him.

Due to the fact that AB is perpendicular to B and AD is the horizontal line of sight, we can conclude that AD AB (given).

∴ ∠DAB = 90°.

We can express this as DAB = DAC + BAC.

alternatively, 90° = ∠DAC + 58°

alternatively, ∠DAC = 90° - 58° = 32°.

The angle of depression is 32°.

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The expanded logarithmic expression is 7log y + log x + 3log z.

The use of a logarithm can be utilised to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. Log interpretation is not that tough. It suffices to know that an exponential equation can also be written as a logarithmic equation in order to comprehend logarithms.

Exponent and logarithm are inverses of one another. This is explained in the section below. John Napier, a mathematician, first developed logarithms as a technique to perform computations simply, and other scientists, engineers, etc. immediately embraced this idea.

The given logarithmic equation is:

log ([tex]y^{7}xz^{3}[/tex])

Now, we can use the properties of logarithms to expand this fully.

Therefore,

log ([tex]y^{7}xz^{3}[/tex]) = log ([tex]y^{7}[/tex]) + log (x) + log ([tex]z^{3}[/tex])

Therefore,

log (y⁷) = 7 log y

log (z³) = 3 log z

Therefore, the expanded logarithmic expression is 7log y + log x + 3log z.

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The given lines are parallel.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: The two equations given are  y = 3/8x +3 &  y = 3/8x + 8/3

We can observe that both the equations are in slope-intercept form we get

the slope of both the lines m=3/8

Two lines are parallel if their slopes are equal and they have different y-intercepts. In other words, perpendicular slopes are negative reciprocals of each other.

Clearly the two given lines have the same slope and different y intercept

Hence, The two lines are parallel

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Casey went too movie for 4 times and Darnell went to movie for 7 times.

Casey and Darnell went to the movies a total of 11 times last month, Darnell went one less than twice as many times as Casey did.

Let us say that Casey went to movie for X times,

So, the amount of times that Darnel went for movie is 2X-1

It is given that they went for a total of 11 times.

We can make a simple algebraic equation by using the above data.

X + 2X - 1 = 11

3X = 12

X = 4

So, Casey went to movie for 4 times and Darnell went to movie for 7 times.

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The solutions of x = 0 or x = y  and y = 0 or y = 1 can then be found. Therefore, the solutions of the equation are (0,0), (0,1), (1,0), and (1,1).

x2 - xy + y2 - x = 0

x(x - y) + y(y - 1) = 0

x(x - y) = 0  and  y(y - 1) = 0

x = 0 or x = y  and y = 0 or y = 1

Therefore, the solutions are (0,0), (0,1), (1,0), and (1,1).

The equation z2 z 1 = 0, when written as (x,y)(x,y) (x,y) (1,0) = (0,0), can be manipulated to x2 - xy + y2 - x = 0. By factoring out the x and y terms, the equation can be rearranged to x(x - y) + y(y - 1) = 0. This then can be further simplified to x(x - y) = 0  and  y(y - 1) = 0. The solutions of x = 0 or x = y  and y = 0 or y = 1 can then be found. Therefore, the solutions of the equation are (0,0), (0,1), (1,0), and (1,1).

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Answer:

B. m2=50 and m3=50

Step-by-step explanation:

Angle m1 and angle m3 combined make a straight line, the angle of a straight line is 180°, so you can do 180-130=50 amd theres you m3. Looking at m1 and m2 its the same thing, we already know m1 is 130° so its the same equation, 180-130=50 and thats m2 angle.

Ps. My hand writing is bad but this is how I solved it.

The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -

f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.

Also, the mean for an exponential distribution is given by u = 1/θ .

In the question it is 22 seconds.

So, the value of θ is 1/22.

Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.

P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -

P(X<x)= F(X) = 1- e^(-θ x) , where x>0.

Putting θ = 1/22 and x= 30 in F(X) , we get -

F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.

So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

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The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -

f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.

Also, the mean for an exponential distribution is given by u = 1/θ.

In the question, it is 22 seconds.

So, the value of θ is 1/22.

Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.

P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -

P(X<x)= F(X) = 1- e^(-θ x) , where x>0.

Putting θ = 1/22 and x= 30 in F(X) , we get -

F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.

So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

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The largest box that can be formed has a volume of 20 cubic feet.

Let's call the side length of the square cutout x. The original piece of cardboard measures 3 feet by 4 feet, so the dimensions of the piece of cardboard after the cutouts are made are (3 - 2x) by (4 - 2x).

When this piece is folded into a box, the length and width of the box will be (3 - 2x) and (4 - 2x) respectively. The height of the box will be x, as that is the height of the cutout squares.

The volume of the box can be found by multiplying the length, width, and height: V = (3 - 2x)(4 - 2x)x

We want to find the maximum volume, so we need to differentiate the expression for the volume and set it equal to zero, and then solve for x.

dV/dx = 2x(4 - 2x) - (3 - 2x)(2x) = 0

2x(4 - 2x) = (3 - 2x)(2x)

2x(4 - 2x) = 2x^2 - 6x^2

-4x^2 + 4x = 0

x(4 - x) = 0

x = 0 or x = 4

Since the side length of the cutout square cannot be negative, we reject x = 0 and keep x = 4. So, the maximum volume will occur when the side length of the cutout squares is 4 feet.

Substituting x = 4 into the expression for the volume, we find:

V = (3 - 2x)(4 - 2x)x = (3 - 2x)(4 - 2x) = (3 - 2x)(4 - 2x) = (3 - 8)(4 - 8) = -5 * -4 = 20 cubic feet

So, the largest box that can be formed has a volume of 20 cubic feet.

Therefore, The largest box that can be formed has a volume of 20 cubic feet.

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The largest box that can be formed has a volume of 20 cubic feet.

Let's call the side length of the square cutout x. The original piece of cardboard measures 3 feet by 4 feet, so the dimensions of the piece of cardboard after the cutouts are made are (3 - 2x) by (4 - 2x).

When this piece is folded into a box, the length and width of the box will be (3 - 2x) and (4 - 2x) respectively. The height of the box will be x, as that is the height of the cutout squares.

The volume of the box can be found by multiplying the length, width, and height: V = (3 - 2x)(4 - 2x)x

We want to find the maximum volume, so we need to differentiate the expression for the volume and set it equal to zero, and then solve for x.

dV/dx = 2x(4 - 2x) - (3 - 2x)(2x) = 0

2x(4 - 2x) = (3 - 2x)(2x)

2x(4 - 2x) = 2x² - 6x²

-4x² + 4x = 0

x(4 - x) = 0

x = 0 or x = 4

Since the side length of the cutout square cannot be negative, we reject x = 0 and keep x = 4. So, the maximum volume will occur when the side length of the cutout squares is 4 feet.

Substituting x = 4 into the expression for the volume, we find:

V = (3 - 2x)(4 - 2x)x = (3 - 2x)(4 - 2x) = (3 - 2x)(4 - 2x) = (3 - 8)(4 - 8) = -5 * -4 = 20 cubic feet

So, the largest box that can be formed has a volume of 20 cubic feet.

Therefore, The largest box that can be formed has a volume of 20 cubic feet.

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The correct answer is option A which is the ordered pair of point P’ will be (8.75, 5.25).

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

here, we have,

If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’

Multiply the coordinates of point P by the scale factor 7/4  to get the coordinates of P'.

Given : P(-5,3)

P' (x,y) = P (-5 x 7/4 , 3 x 7/4)

           = P(-8.75, 5.25)

Therefore the correct answer is option A which is the ordered pair of point P’ will be (-8.75, 5.25).

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Ohm's Law states that the current passing through a conductor is proportional to the voltage across the conductor, and inversely proportional to the resistance of the conductor.

Mathematically, this can be expressed as:

V = IR,

where V is the voltage, I is the current, and R is the resistance of the conductor. The resistance of a conductor is given by:

R = ρℓ/a,

where ρ is the resistivity of the material, ℓ is the length of the conductor, and a is the cross-sectional area.

From Ohm's Law, we can also derive an expression for the electric field inside the conductor:

E = V/ℓ = IR/ℓ = ρI/a

In the case of conductors 1 and 2, the voltage across both conductors is the same (v2 = v1), so the electric field in conductor 2 can be expressed as:

E2 = V2/ℓ2 = v1/(2ℓ1) = ρI2/a2 = (ρ/2a1)I2

Similarly, the electric field in conductor 1 can be expressed as:

E1 = V1/ℓ1 = v1/ℓ1 = ρI1/a1 = (ρ/a1)I1

Finally, the ratio of the electric fields in conductors 1 and 2 can be calculated as:

E2/E1 = (ρ/2a1)I2 / (ρ/a1)I1 = a1/2a1 = 1/2

So, the ratio of the electric fields, E2/E1, is equal to 1/2. This means that the electric field in conductor 2 is half the electric field in conductor 1, despite the fact that the voltage across both conductors is the same. This happens because the cross-sectional area of conductor 2 is twice that of conductor 1, which compensates for the fact that the length of conductor 2 is also twice that of conductor 1.

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The expression to represent the total cost to have 'x' burritos delivered is y = 10x + 5

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

A linear expression can either have two variables or one variable. For example y = 2+3x is an example of linear expression with two variables where x and y are the variable.

Represent the total cost by y

A burritos cost $10 and with $5 delivery fee. This means that the delivery for one burrito will be for x' burrito

therefore y = 10x +5

therefore the equation for x burritos to be delivered is y = 10x+5

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Answer:

The slope of the line that passes through G(-3, 2) and H(7, 2) is 0.

Step-by-step explanation:

The slope of a line can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

In this case, we have two points G(-3, 2) and H(7, 2):

m = (2 - 2) / (7 - (-3))

m = 0

Therefore, the slope of the line that passes through G(-3, 2) and H(7, 2) is 0.

Using the arrangements formula, it is found that there is a 0.0178 = 1.78% probability that all the girls are ahead of all the boys.

The number of possible arrangements of the n elements is the factorial of n, that is:

[tex]A_{n} = n![/tex]

The total number of outcomes is the arrangement of 8 elements, hence:

T = 8! = 40320

The desired number of outcomes is all-girls(5!), then all-boys(3!), hence:

D = 5! × 3! =120× 6=720

Hence, the probability is:

p = D/T =720/40320 = 0.0178

There is a 0.0178 = 1.78% probability that all the girls are ahead of all the boys.

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The different ways of arranging these categories will be 720.

The factor of n is given as the production of the number n, (n - 1), (n - 2)... and 1. Then the factorial of n is given as,

n! = n x (n - 1) x (n - 2) x ... 3 x 2 x 1

We have the group letter (A-F). Then the number of letters is given as,

n = 6 (A, B, C, D, E, F)

Then the different ways of arranging these categories will be given as,

⇒ 6!

⇒ 6 x 5 x 4 x 3 x 2 x 1

⇒ 720

The different ways of arranging these categories will be 720.

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Answer:

[tex]65.1\text{cm}^2[/tex]

Step-by-step explanation:

Area of Rectangle

[tex]A=bh=(8\text{cm})(5\text{cm})=40\text{cm}^2[/tex]

Area of Semicircle

[tex]\displaystyle A=\frac{\pi r^2}{2}=\frac{\pi (4\text{ cm})^2}{2}=8\pi\text{ cm}^2[/tex]

Combined Area

[tex]A_{total}=A_{rectangle}+A_{semicircle}=40\text{cm}^2+8\pi\text{cm}^2\approx65.1\text{ cm}^2[/tex]

Answer:

each member's lunch costs $3.62

Step-by-step explanation:

$209.96 is the total cost of all the members' lunches.  To find the price of 1 lunch, divide 209.96 by 58. You will get 3.62.

11. The measure of ∠EBF = 20°

12. The measure of ∠DBE = 32°.

13. The measure of ∠GBC = 56°.

What is the angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that m∠EBF = 60°, m∠EBG = 2m∠EBF

The m∠EBF is the sum of the angles and the angles are m∠EBG and m∠EBF.

Therefore,

m∠EBF =  m∠EBG + m∠EBF

Putting m∠EBF = 60° and m∠EBG = 2m∠EBF in aboue equation:

60° =  2m∠EBF + m∠EBF

3m∠EBF = 60°

Divide both sides by 3:

∠EBF = 20°.

12.

Given that, m∠ABE = 64°.

From the diagram, m∠ABD = m∠DBE.

The m∠ABE is the sum of the angles and the angles are m∠ABD and m∠DBE.

m∠ABE = m∠ABD + m∠DBE

64° = 2m∠DBE

Divide both sides by 2:

m∠DBE = 32°

13.

Given that, m∠GBH = 28°.

From the diagram, m∠GBH = m∠HBC.

m∠HBC = 28°.

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