the equation of the line with a slope of 6 and y-intercept of -1 is:
• y=-6x+1
• y=x-10
• y=-5x-10
• y=6x-1

Answer:

\(C(x,y) = (8,5)\)

Step-by-step explanation:

Given

\(A(x_1,y_1) = (4,1)\)

\(B(x_2,y_2) = (10,8)\)

Required

Partition into 2:1

Here, we'll make use of the following formula:

\(C(x,y) = (\frac{nx_1 + mx_2}{m + n},\frac{ny_1 + my_2}{m + n})\)

Where

\(m:n = 2:1\)

Substitute values for m,n,x1,x2,y1 and y2

\(C(x,y) = (\frac{1 * 4 + 2 * 10}{1 + 2},\frac{1 * -1 + 2 * 8}{1 + 2})\)

\(C(x,y) = (\frac{24}{3},\frac{15}{3})\)

\(C(x,y) = (8,5)\)

Answer:

(x,y)=(-3,-7)

Step-by-step explanation:

step 1

y=2x-1

y=3x+2

=

2x-1=3x+2

y equals x times 5 is the answer because 2 times 5 is 10 and so on and so forth hope this helps :D

Given a metal rod of length 31 cm placed in a magnetic field of strength 2.3 T, oriented perpendicular to the field, you need to consider the following:

1. The metal rod is 31 cm in length.
2. The magnetic field strength is 2.3 T (tesla).
3. The rod is positioned perpendicular to the magnetic field, which means that the angle between the rod and the magnetic field is 90 degrees.

In this scenario, the rod is placed in such a way that it experiences the full effect of the magnetic field due to its perpendicular orientation.

When a metal rod of length 31 cm is placed in a magnetic field of strength 2.3 T, oriented perpendicular to the field, it will experience a force. The force on the rod will be given by the formula F = BIL, where B is the magnetic field strength, I is the current flowing through the rod, and L is the length of the rod.

Since the rod is not connected to a circuit, there is no current flowing through it. Therefore, the force on the rod will be zero. However, if a current is passed through the rod, it will experience a force perpendicular to both the magnetic field and the direction of the current flow. The magnitude of the force will depend on the strength of the magnetic field, the current flowing through the rod, and the length of the rod.

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Answer:

addition

Step-by-step explanation:

addition and subtraction undo each other same with multiplication and divsion

Answer:

To find -134 + 53, add the ones place (4+3=7) and the tens place (5+3=8), giving you -81.

Answer: -81.

Answer:

-81

Step-by-step explanation:

You subtract the absolute values and take the sign of the larger absolute value.

Absolute value is the distance from zero.  This will be a positive number

134 - 53 = 81

The sign will be negative because the sign of the higher absolute value number is negative.  134 has a larger absolute value than 53 and it is negative, so our answer is negative.

Helping in the name of Jesus.

Step-by-step explanation:

We have 2x + 6y = 22.

When x = 5,

=> 2(5) + 6y = 22

=> 10 + 6y = 22

=> 6y = 12

=> y = 2.

Hence y = 2 when x = 5.

Answer:

A. y=-5/3x+1

Step-by-step explanation:

Answer:

The intersection of a line and a plane can be a/an ;

Step-by-step explanation:

83 boxes are required to carry 800 books.

According to the question:

One Box can hold weight = 30 pounds

We know that ,  1 pound= 0.45 kg

hence, 30 pounds = 30 x 0.45 = 13.5kg  

hence,  one box can carry 13.5 kg of weight.

Now,

Weight of 1 book = 1.4 kg

So, Total Weight of 800 books= 1.4 x 800 kg

And , No. of boxes required to carry 800 books = (1.4 x 800)/13.5 = 82.96

                                                                             or approximately 83 boxes

Hence, 83 boxes are required to carry 800 books.

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The time required for the ball to reach the ground is 10.25 seconds

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The punter kicks the ball into the air

The equation to determine the pathway is h = -16t² + 82t

where t is the time taken in seconds to reach the height h

So ,

Time taken by the football to reach ground is calculated from the equation

At the ground , the height will be 0

So , h = 0

Substituting the value for h in the equation , we get

0 = -16t² + 82t

Adding 16t² on both sides , we get

16t² = 82t

Divide by t on both sides , we get

16t = 82

Divide by 4 on both sides , we get

4t = 41

Divide by 4 on both sides , we get

t = 10.25 seconds

Hence , the time taken by the football to reach the ground is 10.25 seconds

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Answer:

About 11.4

Step-by-step explanation:

There are 3.78541178 liters in a gallon.

Round that up to the nearest 100 and you get 3.8

Multiply 3.8 by 3.

You get 11.4

Answer:

What is the question from Solving inequalities unit portfolio task 2-3?

Step-by-step explanation:

Comment it down below and I will solve it! :D

Answer: Carlos pays $74.00

Step-by-step explanation:

103.6/56 = 1.85

40 x 1.85 = 74

Answer:

-3, -2, -0.8, -1/10, 1/2, 0.8, 7

The order of the set of sign numbers from least to greatest is,

- 3, - 2, - 0.8, - 0.1, 0.5, 0.8, and 7.

A number that is followed by the plus sign (+) to denote a positive value or the minus sign (-) to denote a negative value.

A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.

Given, A set of signed numbers - 1/10, - 0.8, 0.8, - 2, 7, 1/2, and - 3.

let us convert them into decimals, - 0.1, - 0.8, 0.8, - 2, 7, 0.5, and - 3.

The order from least to greatest is,

- 3, - 2, - 0.8, - 0.1, 0.5, 0.8, and 7.

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Answer:  see proof below

Step-by-step explanation:

Use the following Sum to Product Identities:

sin (A) - sin (B) = 2 cos (A+B)/2 · sin (A-B)/2

sin (A) + sin (B) = 2 sin (A+B)/2 · cos (A-B)/2

Given:  sin Ф = k sin β      -->   (sin Ф)/(sin β) = k

Proof RHS → LHS

\(\text{RHS:}\qquad \qquad \qquad \dfrac{k-1}{k+1}\tan\dfrac{\theta+\beta}{2}\)

\(\text{Given:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-1}{\frac{\sin \theta}{\sin \beta}+1}}\cdot \tan\dfrac{\theta +\beta}{2}\)

\(\text{Simplify:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-\frac{\sin \beta}{\sin \beta}}{\frac{\sin \theta}{\sin \beta}+\frac{\sin \beta}{\sin \beta}}}\cdot \tan\dfrac{\theta +\beta}{2}\\\\\\.\qquad \qquad \qquad = \dfrac{\sin \theta -\sin \beta}{\sin \theta +\sin \beta}\cdot \tan\dfrac{\theta +\beta}{2}\)

\(\text{Product to Sum:}\qquad \quad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \tan\dfrac{\theta +\beta}{2}\)

\(\text{Expand:}\qquad \qquad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \dfrac{\sin\frac{\theta +\beta}{2}}{\cos \frac{\theta +\beta}{2}}\)

\(\text{Simplify:}\qquad \qquad \quad \quad \dfrac{\sin \frac{\theta +\beta}{2}}{\cos \frac{\theta+ \beta}{2}}\\\\\\.\qquad \qquad \qquad \quad =\tan\dfrac{\theta +\beta}{2}\)

 \(\text{LHS = RHS:}\quad \tan\dfrac{\theta +\beta}{2}=\tan\dfrac{\theta +\beta}{2}\quad \checkmark\)

The work done in propelling the lunar module from the surface of the moon to a height of 40 miles is 3,571,607,996 Joules.

This can be calculated as follows:

Weight of the lunar module on the surface of the Earth = 12 tons
converting weight to mass = weight/acceleration due to gravity
mass = 12 x 1000 / 9.81
mass = 1,224.6 kg

The force required to lift the module off the surface of the moon is equal to its weight, which is given by the formula:
force = mass x acceleration due to gravity
force = 1,224.6 x 1.62
force = 1,982.8 N

Calculating the total distance traveled:
distance = 1,737.1 + 64.37
distance = 1,801.47 km

Calculating the work done:
work = force x distance
work = 1,982.8 x 1,801,470
work = 3,571,607,996 J

Therefore, the work done in propelling the lunar module from the surface of the moon to a height of 40 miles is 3,571,607,996 Joules.

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Answer:

HI = 34

Step-by-step explanation:

KL  is a mid segment of the triangle and is half the length of HI , that is HI is twice KL , so

HI = 2 × KL

8x - 14 = 2(- 25 + 7x)

 8x - 14  = - 50 + 14x ( subtract 14x from both sides )

- 6x - 14 = - 50 ( add 14 to both sides )

- 6x = - 36 ( divide both sides by - 6 )

x = 6

Then

HI = 8x - 14 = 8(6) - 14 = 48 - 14 = 34

Answer:

length of rectangle = 5

width of rectangle = 5

Area of rectangle = 25

Step-by-step explanation:

Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:

\(y=x\,(10-x)=10x-x^2\)

Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.

Recall that the formula for the x of the vertex of a quadratic of the form :

\(y=ax^2+bx+c\)

is given by the formula:

\(x_{vertex}=-\frac{b}{2\,a}\)

which in our case gives:

\(x_{vertex}=-\frac{b}{2\,a}\\x_{vertex}=-\frac{10}{2\,(-1)}\\x_{vertex}=5\)

Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.

The area of the rectangle is therefore the product of these two values: 5 * 5 = 25

Which should coincide with the value we obtain when we replace x by 5 in the area formula:

\(y=10x-x^2\\y=50-(5)^2\\y=50-25\\y=25\)

Answer:

B.

Step-by-step explanation:

I did 46.20 divided by 12 and I got my answer.

Answer:

$3.85 per gallon

Step-by-step explanation:

46.20/12 = 3.85

Answer:

46 degrees

Step-by-step explanation:

Total angular measurement for a triangle = 180

180 - 92 - 42 = 46 degrees

Answer:

hexagonal prism

Solution

For this case we have the following function:

And we want to find the steps to obtain the above function from this one:

So we can do the following:

Reflection over the x axis

horizontal shift to the left 2 units

Given integral : F(x) = ∫1x √(6+t²) dt. Let u= 6 + t² and du/dt = 2t.=> du = 2t dt. Now F(x) = ∫1x √(6+t²) dt can be written as F(x) = ∫[u(1)=7]u(x) (1/2)√u du= (1/2)∫[u(1)=7]u(x) u^1/2 du.

Now integrating w.r.t. u, we get:

F(x) = (1/2) * (2/3) * [u^(3/2)]7x= (1/3) (x√(6+x²) - 7√13.

)Now to find (F-1)(0), we need to find the value of x for which F(x) = 0.(F-1)(0) => F(x) = 1.

Now (F-1)(0) will be equal to x, when

F(x) = 1.F(x) = (1/3) (x√(6+x²) - 7√13)1 = (1/3) (x√(6+x²) - 7√13)x√(6+x²) - 7√13 = 3......................................(1)Squaring both the sides of equation (1), we get:

x²(6+x²) - 14√13 x + 13 = 9x^4+6x²+1 - 84x + 169 = 36x^4-48x²+100.

Solving this quartic equation, we get two positive roots as x = 2 and x = 5/3.

Now, we can easily verify which one of the roots is correct by putting it back in equation (1) to check which of them satisfies the equation.

Hence, (F-1)(0) = 2.

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Answer:

reflection

Step-by-step explanation:

the trapezoid in the picture is reflected vertically from point D

have a nice day!!

Answer:

C. The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f.

Step-by-step explanation:

It's a given that f(x) = x^2 so that means g(x) = f(x) - 9 means g(x) = x^2 - 9

in slope intercept form y = mx + b, b is the y-intercept

since g(x) is just f(x) with the y-intercept as -9 we know that the vertex of the parabola moves downwards 9 units

---

Hope this helps! :) If so, please mark my answer as brainliest

Function g(x) is the translation of function f(x). The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f(x). The correct statement is C.

\(f(x)=x^{2}\).

\(g(x) = f(x) - 9.\)

From the above functions it is clear that the equation for the graph of g(x) will be,

\(g(x)=x^{2} -9\).

The equation \(y=mx+c\) is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

Since The y intercept of function f(x) is zero.

Hence in the function g(x), it is 9 units below the intercept of the function f(x). Thus the correct option is C.

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The z-scores for the 10th and 90th percentiles are -1.28 and 1.28, respectively. The mean and standard deviation of the performance scores can be determined using the z-scores and the z-score formula.

a. To find the z-scores associated with the 10th and 90th percentiles from the standard normal distribution, we can use a standard normal distribution table or a calculator. The 10th percentile corresponds to a z-score of approximately -1.28, and the 90th percentile corresponds to a z-score of approximately 1.28.

b. To calculate the mean and standard deviation of the performance scores, we can use the z-score formula and the information given. Let's denote the mean as μ and the standard deviation as σ.

For the 10th percentile (z = -1.28):

-1.28 = (380 - μ) / σ

For the 90th percentile (z = 1.28):

1.28 = (160 - μ) / σ

Solving these two equations simultaneously will give us the values of μ and σ.

c. To find the performance score a manager must exceed to receive an A grade, we need to find the z-score associated with the top 3% of the standard normal distribution. The z-score corresponding to the top 3% is approximately 1.88. Using the z-score formula, we can calculate the corresponding performance score:

1.88 = (X - μ) / σ

Solving this equation for X will give us the performance score needed to receive an A grade.

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Lindas plant is ′89′ cm tall at the end of the year.

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

Given

Initial length of Morgans plant = 42 cm

Final length of Morgans plant after an year = 57 cm

Increase in length of Morgans plant in that year = (Final length − Initial length) of the Morgans plant

= 57 cm − 42 cm

= 15 cm

Therefore, the Increase in length in Morgans plant is ′15′ cm.

Now given, Lindas plant grew twice as many centimeters as Morgans plant.

Increase in length of Lindas plant = 2 × Increase in length of Morgans plant

= 2 × 15 cm

= 30 cm

Therefore, the Increase in length of Lindas plant is ′30′ cm.

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