What is the greatest common factor (GCF) of 48 and 32?

Answer: y=2x-2

Step-by-step explanation:

X intercept is 1

Hence,

(1,0)

Thus,

(1,0)     (-1.-4)

                      Equation of a straight line:

                             \(\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }\)                

x₁=1       x₂=-1        y₁=0        y₂=-4

\(\displaystyle\\\frac{x-1}{-1-1} =\frac{y-0}{-4-0} \\\\\frac{x-1}{-2} =\frac{y}{-4} \\\\\)

Multiply both parts of the equation by -4:  

(2)(x-1)=y

2x-2=y

Answer:

\(y=2x-2\)

Step-by-step explanation:

The x-intercept is when the line crosses the x-axis, so when y = 0.

Therefore, the two points on the line are:

To find the equation of the line when given two points from the line, first find the slope:

\(\textsf{slope}\:(m)=\dfrac{\textsf{change in $y$}}{\textsf{change in $x$}}=\dfrac{-4-0}{-1-1}=2\)

Now substitute the found slope and one of the points (1, 0) into the point-slope form of a linear equation:  

\(\implies y-y_1=m(x-x_1)\)

\(\implies y-0=2(x-1)\)

\(\implies y=2x-2\)

Therefore, the equation of the line is:

\(y=2x-2\)

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

9

Step-by-step explanation:

so sorry if im too late...

Answer:

72cm

Step-by-step explanation:

Original length of the cube = 9cm

Perimeter of the original cube = 4L

Perimeter of the original cube = 4(9)

Perimeter of the original cube = 36cm

If the cube is increased by a factor of 3, new length will be 3(9) = 27cm

Perimeter of the new cube = 4*27

Perimeter of the new cube = 108cm

Difference =108 - 36

Difference = 72cm

Hence the new cube is 72cm larger than the original

Answer:

72cm

Step-by-step explanation:

The numbers of small cabinets are 50 and the numbers of large cabinets are 15.

A "system" of equations is a set or collection of equations that you deal with all together at once.

Given that, Lee is packing a truck with small and large filing cabinets. The large cabinets weigh 40 pounds, and the small cabinets weigh 25 pounds.

To optimize the load, the total load weight should be a total of cabinets 1850 pounds.

Let the number of the small cabinets be x and that of large be y,

Establishing the equations,

x+y = 65

x = 65-y.......(i)

25x+40y = 1850........(ii)

Solving the equations,

25(65-y)+40y = 1850

1625-25y+40y = 1850

15y = 225

y = 15

Put y = 15 in eq(i)

x = 65-15

x = 50

Hence, the number of small cabinets is 50, and the number of large cabinets is 15.

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Answer:

The Perimeter is 4.5in and the Area is 1.125in²

Step-by-step explanation:

Perimeter is gotten by adding up the length/height of every side of the polygon (1.5in + 1.5in + 0.75in + 0.75in), while the Area of a rectangle is gotten by multiplying the height and length. (1.5in × 0.75in)

Answer:

Step-by-step explanation:

1. Simplify the expression

2. Find the greatest common factor of the numerator and denominator ( divide)

(1.50)/ (14.50)

3. Factor out and cancel the greatest common factor

Answer is 1/14

Step-by-step explanation:

yes, in a similar way as division is a shortcut for repeated subtraction.

you do know, that you normally have to add the points win in a game, right ?

so, your score grows by 200 points each time you score.

that means

200

200

200

...

200

what do you think you do to get the total ? you add all the points.

you don't multiply them, because e.h 200×200 would be the shortcut of adding 200 for 200 times.

but you did not have 200 hits, you only got 12 hits.

so, you either do the effort of adding 200 12 times, or you simply multiply 200 by 12 (as this is the mentioned shortcut).

and you don't just add 12 to 200. that would give you only 212. and you did not earn 12 points to add. you earned 12 times 200 points to add.

that is how multiplication works and helps with additions.

Answer:

its yes

bc yeah just......do it

Answer:

The equation of a circle centered in the point (a, b) and with a radius R.

(x - a)^2 + (y - b)^2 = R^2

Then, if you move the circle to the left, then you are decreasing the value of b.

Where b = 0 means that the center of the circle lies on the y-axis.

When you move the graph to the right you will be increasing the value of b.

Answer:

The variable h changes as the center of the circle moves horizontally. The sign of h is negative when the center is to the left of the y-axis and positive when it is to the right of the y-axis. The sign of the variable h flips when the center moves across the y-axis.

Step-by-step explanation:

plato answer from Equation of a Circle: Tutorial :)

This link will take you to a quizlet that is on this lesson with the other answers and test question answers!!

https://quizlet.com/519491317/geometry-b-unit-7-flash-cards/#:~:text=Move%20the%20center%20of%20the%20circle%20vertically%20so%20it%20lies,of%20the%20circle%20moves%20vertically.

1)  XY' + Z + X'Z' + YZ'

2) equation 2 is correct.

3) equation 3 is incorrect .

1)

Simplifying algebraically,

XY' +Z+ (X' + Y)Z'

So,

XY' + Z + X'Z' + YZ'

2)

D(A + B)(A + B')C

Simplifying,

(AD + DB) (A + B')C

Further,

ADC + AB'CD + ABCD + BB'CD

ACD + ABCD + AB'CD

= ACD

Thus equation 2 is correct .

Hence proved .

3)

(a + b)(b + c)(c + a) = f1

Simplifying further,

abc + ab + bc + ac = f1

Let f2 = (a'+ b')(b' + c')(c' + a')

Simplify further,

f2 = a'b'c' + a'b' + b'c' + a'c'

Here,

f1 ≠ f2

Thus we disprove equation 3 .

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Answer:

Not factor-able

To find the corresponding x where the function assumes a certain value, we draw a horizontal line on the desired function value. For f(x) = 2, we have:

The intercept between the horizontal line and our graph happens at (0, 2), therefore, we have:

To evaluate graphically a function, we check the corresponding value for the desired x value on the horizontal axis. For x = 2, we have:

Then

The bill's price is $9,968.10. The correct answer is option 5

To calculate the price of the Treasury bill, we can use the formula for bank discount yield:

BDY = (Discount / Face Value) * (360 / Days) * 100

Given:

Bank discount yield (BDY) = 1.32%

Days until maturity (Days) = 87

Face Value = $10,000

Let's rearrange the formula to solve for the discount:

Discount = (BDY / 100) * (Face Value) * (Days / 360)

Discount = (1.32 / 100) * $10,000 * (87 / 360)

Discount ≈ $31.9

The price of the Treasury bill can be calculated by subtracting the discount from the face value:

Price = Face Value - Discount

Price = $10,000 - $31.9

Price ≈ $9,968.10

Therefore, the bill's price is approximately $9,968.18.

Among the given answer choices, the correct option price is 5) $9,968.10.

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the speed is a minimum at t = 4.

To find when the speed is a minimum, we need to determine the derivative of the speed function with respect to time and find where it equals zero.

The speed of a particle is given by the magnitude of its velocity vector, which is the derivative of the position vector with respect to time. In this case, the position vector is r(t) = (t^2, 7t, t^2 - 16t).

The velocity vector is obtained by taking the derivative of the position vector:

v(t) = (2t, 7, 2t - 16)

To find the speed function, we calculate the magnitude of the velocity vector:

|v(t)| = sqrt((2t)^2 + 7^2 + (2t - 16)^2)

= sqrt(4t^2 + 49 + 4t^2 - 64t + 256)

= sqrt(8t^2 - 64t + 305)

To find when the speed is a minimum, we need to find the critical points of the speed function. We take the derivative of |v(t)| with respect to t and set it equal to zero:

d(|v(t)|)/dt = 0

Differentiating the speed function, we get:

d(|v(t)|)/dt = (16t - 64) / (2 * sqrt(8t^2 - 64t + 305)) = 0

Simplifying the equation, we have:

16t - 64 = 0

Solving for t, we find:

16t = 64

t = 4

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Answer:

A

Step-by-step explanation:

Because for A, the question is "How many weeks until the bank is full?" which is looking for X. That part is checked off. It says 100x+50=710. 710 is the total in A too so that is checked off. In the equation, the piggy bank starts with 50 coins so that is checked off. Everything is in order so A is the answer. WEAR A  MASK AND STAY SAFE DURING THIS HARD TIME! ;)

Answer:

The answer is D

Step-by-step explanation:

The original equation ..

100x +50 = 710

100x=710-50

100x=660

Divide on both sides

X =6.6

When you solve equation D in the same way, the same result will appear

The probability helps us to know the chances of an event occurring. The two events can not be independent.

The probability helps us to know the chances of an event occurring.

\(\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

As it is given that the probability of event A is 0.3, while the probability of event B is 0.5. And the probability of events A and B is 0.25.

Since we know that the probability of two independent events occurring together is given by the formula,

\(P\rm{(A\ and\ B)}=P(A) \times P(B)\)

Therefore, the probability of two events together can be written as,

\(P\rm{(A\ and\ B)}=P(A) \times P(B)\)

                   \(=0.3 \times 0.25\\\\=0.075\)

Since the probability of the two events occurring together if the two independent events are 0.075, therefore, the two events can not be independent.

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This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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When 5x²-3x=0, x will either be 0 or 6/10. The value of x will be (1+29i)/5 or (1-29i)/5 if 5x²-2x+6=0.

ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable a,0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem. The answer could be simple or complicated. In mathematics, a quadratic equation is one of degree 2, which means that its maximum exponent is 2. A quadratic has the standard form y = ax^2 + bx + c, where a, b, and c are all integers and a cannot be zero. All of these are examples of quadratic equations: y = x^2 + 3x + 1.

Here

a. 5x²-3x=0

=(-b±√(b²-4ac))/2a

a=5

b=-3

c=0

=3±(√-3²-4*5*0)/2*5

=3±3/10

x=0,6/10

b. 5x²-2x+6=0

=(-b±√(b²-4ac))/2a

a=5

b=-2

c=6

=2±(√(-2)²-4*5*6)/2*5

=2±(√(4-120))/10

=2±(√116)i/10

2±(2√29)i/10

x=(1±√29i)/5

For 5x²-3x=0, value of x will be either 0 or 6/10. For 5x²-2x+6=0, value of x will be (1+√29i)/5 or (1-√29i)/5.

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Answer:

8(x + 3)

Step-by-step explanation:

Answer:

b)0,2..................

Answer:  -185  (choice D)

=========================================================

Explanation:

Note how x+1 follows immediately after x. That's what "consecutive" means by definition. An example of consecutive integers would be 7,8,9,10.

Adding those two said integers will lead to -371

first+second = -371

x+(x+1) = -371

2x+1 = -371

2x = -371-1

2x = -372

x = -372/2

x = -186

x+1 = -186+1 = -185

Note how -186+(-185) = -371 to confirm the answer.

The two consecutive integers that add to -371 are -186, -185. The larger of the two is -185 since it's more to the right on the number line.

The answer is option D.The solution is in the attached file.

Answer:

35 minutes

Step-by-step explanation:

this requires us to find out how long it took and because both times given to figure this out are within the same hour it is easy to figure out in this case, 50 - 15 = 35. This is not as simple with all problems like this but because of the times given in this problem its much easier.

The value of angle RTW in the intersecting chords is proved as 15⁰.

From the diagram, we were given that length SW is the diameter of the circle R.

Also, arc ST IS given as 30⁰.

The proof that angle RTW is 15⁰ is determined as follows;

The value of  angle SRT is calculated as;

m∠SRT = arc ST = 30⁰ (interior angles of intersecting secants)

The value of angle TRW is calculated as;

m∠TRW = 180 - m∠SRT  (sum of angles in a straight line)

m∠TRW = 180 - 30

m∠TRW = 150⁰

Since SW is the diameter;

RT = RW = radius of the circle

If length RT is equal to length RW, then triangle RTW is an isosceles triangle.

∠RTW + ∠RWT + ∠TRW  = 180 (sum of angles in a triangle)

∠RTW = ∠RWT

2∠RTW + ∠TRW = 180

2∠RTW + 150 = 180

2∠RTW = 180 - 150

2∠RTW = 30

∠RTW = 30 / 2

∠RTW = 15⁰ (PROVED)

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Answer:

d

Step-by-step explanation:

Answer:

the answer is d.

Step-by-step explanation:

Answer:

y = 1/2x + 6

Step-by-step explanation:

y = 1/2x + b

2 = 1/2(-8) + b

2 = -4 + b

6 = b

Answer:

5 is correct answer for you kindly inform ation

The probability that the sample average falls outside the 3-sigma control limits of the X-bar chart is 0.27%.

The 3-sigma control limits are calculated using the standard deviation of the process. If the process is in control, then 99.73% of the sample averages will fall within the 3-sigma control limits. The remaining 0.27% of the sample averages will fall outside the control limits.

In this case, the sample size is 4, which is smaller than the sample size of 9 that was used to construct the control chart. This means that the control limits for the sample of size 4 will be narrower than the control limits for the sample of size 9.

As a result, the probability that the sample average falls outside the control limits will be higher for the sample of size 4.

Specifically, the probability that the sample average falls outside the 3-sigma control limits for a sample of size 4 is 0.27%. This means that there is a 0.27% chance that the new employee will observe a sample average that falls outside the control limits, even if the process is in control.

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