Knowing that the result of expanding (x+a)(x-6) is x²+mx-48, find the values ​​of a and m.​

Answer:2^1 × 3^2 × 13^1

Step-by-step explanation:

The probability in decimal form that she will flip head on the next flip of the coin is 0.45

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

Number of flips = 200

Number of times she flips head = 90

Using the above as a guide, we have the following:

The probability that she will flip heads on the next flip of the coin is represented as

P(Head) = Number of times she flips head/Total number of flips

Substitute the known values in the above equation, so, we have the following representation

P(Head) = 90/200

Evaluate the quotient

P(Head) = 0.45

Hence, the probability is 0.45

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Answer:

300

Step-by-step explanation:

The area of the triangle when calculated has an expression of √3/4[(x² - 1)]

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

The triangle

The area of the triangle is

Area = 1/2 absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area =1/2 * (x + 1) * (x - 1) * sin(120)

Evaluate

Area =1/2 * (x + 1) * (x - 1) * √3/2

So, we have

Area = √3/4[(x² - 1)]

Hence, the area is √3/4[(x² - 1)]

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The 5th term of the arithmetic series is  1179/ 19.

The 10th term of the arithmetic series , S is 66.

Using arithmetic formula,

aₙ = a + (n - 1)d

where

Therefore,

66 = a + 9d

The sum of the first 20 terms of S is 1290.

Therefore,

Sₙ = n / 2 (2a + (n - 1)d)

1290 = 10(2a + 19d)

1290 = 20a + 190d

combine the equation

66 = a + 9d

1290 = 20a + 190d

Hence,

a = 66 - 9d

1290 = 20(66 - 9d) + 190d

1290 = 1320 - 180 + 190d

1290 - 1320 + 180 = 190d

190d = 150

d = 150 / 190

d = 15 / 19

Hence,

a = 66 - 9(15  /19)

a = 66 - 135 / 19

a = 1254 - 135/ 19

a = 1119 / 19

Hence, let's find the fifth term.

a₅ = a + 4d

a₅ = 1119 / 19 + 4(15 / 19)

a₅ = 1119 / 19 + 60 / 19

Therefore,

a₅ =  1179/ 19

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The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

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Answer:

To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.

Substituting the values of a, b, and c:

a = 3

b = a² = 3² = 9

c = a³ = 3³ = 27

Now let's simplify the expression:

(a÷b)³×(b÷c)×(c÷a)³

(3÷9)³×(9÷27)×(27÷3)³

Simplifying each term:

(3÷9) = 1/3

(9÷27) = 1/3

(27÷3) = 9

Now we can substitute the simplified values back into the expression:

(1/3)³×(1/3)×9

Simplifying further:

(1/27)×(1/3)×9

1/9

Therefore, the simplified expression is 1/9.

Answer:

12 1 half% (or 12.5%) failed the test

Step-by-step explanation:

Subtract the 87 1 half% (or 87.5%) by 100 to get 12.5%

Answer:

404.25 dollars

Step-by-step explanation:

First, we do 8.35 times 37, and we get 305.25.

Next, we subtract 37 from 45 and get 8.

Then, we do divide 8.25 in half, and get 4.125.

After that we add 4.125 to 8.25 and get 12.375.

Then we do 12.375 times 8 and get 99

Finally, we add 99 and 305.25 together and get 404.25 dollars.

Answer:

The answer is 2/5.

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

Divide both the numerator and denominator by 2, the greatest common factor of both values.

Use law of cosines

a^2 + b^2 - 2ab cos (theta)   = c^2          c is the distance she will have to hike       a = 7.4 m  b = 5 m   theta =38 degrees    

3 miles is the distance lisa have to hike  from the lake to meet Aaron at the campsite

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

Lisa plans to hike 5 miles due north to Lake

Aaron plans to turn 38. east and hike 7.4 miles directly to the campsite.

We need to find the distance Lisa have to hike from the lake to meet Aaron at the campsite

By using law of cosine we find the distance

Use law of cosines

a² + b² - 2ab cosθ   = c²

c is the distance she will have to hike      

a = 7.4 m  

b = 5 m  

θ =38 degrees  

Plug in these values to find the distance

7.4² +5² -2(7.4)(5)cos38=c²

54.76+25-74cos38=c²

79.76-74(0.955)=c²

79.76-70.677=c²

9.083=9=c²

Take square root on both sides

3=c

Hence, 3 miles is the distance lisa have to hike  from the lake to meet Aaron at the campsite

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125 Rs. is the cost price of the given object.

The money that remains after paying your business expenses is your profit. Gross profit, operating profit, and net profit are the three primary types of profit. The largest profit is gross. The amount left over after paying for the sold goods and services is displayed.

Given that the selling price of an object is 150 Rs.

The profit made on that object is 25 Rs.

let "x" be the cost price of the given object.

From the general formula of profit:

Profit = Selling price - cost price

In our case

profit = 150 - x

25 = 150 - x

x = 150 -25

x = 125Rs

therefore, the cost price of the given object is 125 Rs.

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We can write the log expression in terms of the log of x, y, and z as expression 1/2(logx+2logy-8logz).

It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

\(\rm a^b = c\\\\log_ac = b\)

We have an expression in logarithm:

\(=\rm log\sqrt{\frac{xy^2}{Z^8} }\\\\=log(\frac{xy^2}{Z^8})^{\frac{1}{2} }\\\\=\frac{1}{2}log(\frac{xy^2}{Z^8})\)                         \((\rm loga^b = (b)log(a))\)

\(\rm\frac{1}{2} (log(xy^2)-logz^8)\)              \((\rm log(\frac{a}{b} )= loga - logb)\)

\(\rm\frac{1}{2} (log(x)+log(y^2)-logz^8)\)   \((\rm logab = loga+logb)\)

\(\rm\frac{1}{2} (log(x)+2log(y)-8logz)\)

Thus, we can write the log expression in terms of the log of x, y, and z as 1/2(logx+2logy-8logz).

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The length QT is 36 units

The attached image represents the missing information in the question

From the image, we have:

RQ =QT

Substitute known values

5x + 1 = 3x + 15

Evaluate the like terms

2x = 14

Divide by 2

x = 7

Substitute x = 7 in QT = 3x + 15

QT = 3 * 7 + 15

Evaluate

QT = 36

Hence, the length QT is 36 units

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The inequalities in the system of inequalities are y > x² – 2x – 3 and y > 3x + 4

The graph that completes the question is added as an attachment

The parabola

It has a vertex of (1,  -4)

So, we have:

y = a(x - 1)^2 - 4

It passes through (3, 0).

So, we have:

0 = a(3 - 1)^2 - 4

This gives

4a - 4 = 0

Solve for a

a = 1

Substitute a = 1 in y = a(x - 1)^2 - 4

y = (x - 1)^2 - 4

Expand

y = x^2 - 2x + 1 - 4

y = x^2 - 2x - 3

The inner part is shaded.

So, we have:

y > x^2 - 2x - 3

The linear equation

It passes through (0, 4).

So, we have:

y = mx + 4

It passes through (1, 7).

So, we have:

7 = m + 4

Solve for m

m = 3

Substitute m = 3 in y = mx + 4

y = 3x + 4

The upper part is shaded.

So, we have:

y > 3x + 4

Hence, the inequalities in the system of inequalities are y > x² – 2x – 3 and y > 3x + 4

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Answer:

5

Step-by-step explanation:

Answer:

5 Gallons of gasoline

Step-by-step explanation:

This is true because 190÷38 is five. If you want to check the work 38×5 is 190.

I also got it right on edg. 2020

Answer:

15.2

Step-by-step explanation:

I multiplied 40% by 38, which equals 15.2.

Hope this helped, have a good day!

a) There are 2 x 2 = 4 sample points in the sample space

b) Tree Diagram

O D.\nH\nHe\nT\nH\nT\n

Sample space: D. HH, HT, TH, TT

c) P(no tails) = P(HH)

= 1/4

d) P(exactly one tail) = P(HT, TH)

= 2/4

= 1/2

e) P(2 tails) = P(TT)

= 1/4

f) P(at least one tail) = P(HT, TH, TT)

= 3/4

In mathematics, tree diagrams are often used in probability and statistics to show all the possible outcomes of an event. In computer science, they are used to represent the hierarchical structure of files and directories in a file system

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Answer:

the slope intercept form is   y = (1/2)x - 1

Step-by-step explanation:

The slope-intercept form is, y = mx + b

We see from looking at the graph that,

at x = 0, y = -1

So, from this we find that b = -1

at x = 2, y = 0,

now, we find the slope m,

using,

\(m = \frac{y_{2} -y_1}{x_2-x_1}\)

Using x_2 = 2, y_2 = 0,

x_1 = 0, y_1 = -1, we get,

m = (0-(-1))/(2-0)

m = 1/2

So, the slope intercept form is,

y = (1/2)x - 1

Step-by-step explanation:

(1 + ax)⁴(2 - x)³ = (1 + 2ax + a²x²)²(8 - 12x + 6x² - x³) =

(1 + 4a²x² + a⁴x⁴ + 4ax + 2a²x² + 4a³x³)(8 - 12x + 6x² - x³) = ... 6x² + 32a²x² - 48ax² + 16ax² ...

= ... x²(6 + 32a² - 32a) ...

32a² - 32a + 6 = 6

32a(a - 1) = 0 → 32a = 0 → a = 0 OR a - 1 = 0 → a = 1

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

The value of m (slope) is -3

The value of b (y-intercept) is -6

Step-by-step explanation:

First you need to isolate y:

3x + y = −6

y = -3x - 6

The value of m (slope) is -3

The value of b (y-intercept) is -6

Step-by-step explanation:

1. Not a function There is no correlation plus there is two y values for the same x.

2.Not a function, There is two y values for the same x

3.Yes, you can draw a linear line through the points to represent the equation, also there is one x for one y.

4.Yes, this is a step function. It seems there are two y values for same x. but the shaded circle means to include it and the open circle means dont include it so it is a function.

5.No, this is a parabola but this function has two y values for the same x

6. Yes, this is a absolute value function and there is multiple x values for the same y so it IS a function

Graph 3,6,4 represents a function because the x’s do not repeat and it passes the vertical line test. Which means 1,2,5 is not a function because the x's do repeat and it does not pass the vertical line test

Hope this helps

Have a great day/night

Feel free to ask any questions

If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

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Answer:

3/5

Step-by-step explanation:

because there are more red than blue and the fraction is 3/5 and the probability to pick a red worm is a lot higher than the blue. well there are 4 red worms and 1 blue so it would be 3 red worms out of 5 in total. this is more than 1 blue over 5. 3/5 is more than 1/5

hope this helped

Answer: 3/5

Step-by-step explanation:

Since 4 red gummies you have four out of 5 chance of getting red gummies. Without replacement there are now 4 gummies left and 3 red gummies. There for 3 out of 4 chance of getting another red gummy. Since at same time multiply. 4/5*3/4 = 12/20

Which can be simplified to 3/5

The angular motion of the second hand is 720 h , we also have to know the meaning of angular motion.

The body moving along the curved path at a constant angular velocity can be used to describe the angular motion.

As there are 12 hours on a clock, every hour means 360/12 = 30° rotation for the hour hand.

so, for each hour the second hand moves 21600°.

that means 21600/360 = 60 full rotations.

that means one rotation of the second hand is 1 minute.

so, the second hand is truly a second hand (counting the seconds).

60 seconds in a minute (a full rotation by the second hand), that means each second corresponds to 360/60 = 6° rotation of the second hand.

\(the \ ratio \ is\ \frac{30}{21600} = \frac{3}{2160} = \frac{1}{720}\)

that means for every degree the hour hand moves, the second hand does 2 full rotations (2×360°).

h = s×30/21600 = s/720

s = 720 h.

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Answer:

3:4

6 to 8

9/12

15:20

Step-by-step explanation:

Have a great day!!!

Answer:

Step-by-step explanation:

3:4

6 to 8

9/12

15:20