Find the value of x.​

The value of i where remainder of n/ 4 is 2 is :

i² = -1 .

i² = -1

i⁰ = 1

i¹ = i

i² = -1

i³ = i² x i

  = -1 x i

  = -i

i⁴ = i² x i²

   = -1 x -1

   = 1

The pattern repeats.

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Yes, you are right!

First of all, we will subtract [tex]5[/tex] from each side.

Then we multiply both sides by [tex]4[/tex].

Then add [tex]3[/tex] to each side.

Finally, we divide each side by [tex]2[/tex].

[tex]\boldsymbol{\sf{\cfrac{2x-3}{4}+5=10 }}[/tex]

Multiply the two sides of the equation by 4.

2x - 3+20 = 40

Add −3 and 20 to get 17.

2x+17 = 40

It remains 17 on both sides.

2x = 40−17

Subtract 17 of 40 to get 23.

2x = 23

Divide both sides by 2.

[tex]\boldsymbol{\sf{x=\dfrac{23}{2} \ \ \longmapsto \ Answer }}[/tex]

Answer:

[tex](f \circ g)(2)=2[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=-2x+8\\g(x)=\sqrt{x+7}\end{cases}[/tex]

The composite function (f o g)(x) means to substitute the function g(x) in place of the x in function f(x).  

Therefore (f o g)(2) means to substitute the result of g(2) in place of the x in the function f(x).

[tex]\begin{aligned}\implies (f \circ g)(2) &=f[g(2)]\\&=f(\sqrt{2+7})\\&=f(\sqrt{9}) \\& = f(3)\\& = -2(3)+8\\&=-6+8\\&=2\end{aligned}[/tex]

Answer:

C (0,3)

Step-by-step explanation:

Plot the two equations and the points.  See the attached graph.  The blue area reflects the inequality of y+3x<=8:  many points satisfy this equation and they are all blue.

The red line is equation y-3=x.  There is only one point on this line that is also in the blue area:  (0.3).  The other three points (A, B, and D) do not satisfy either equation.  The metric term for them is losers.

Volume of a cone is given by;

From the queston,

h = 414

diameter = 416, this implies r = d/2 = 416/2 = 208

π = 3.14

substitute the values into the formula

A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

With this in mind we conclude that:

There are 8 values in the data set which are greater than or equal to 20 and less than or equal to 29. This comes from the fact that we have to count how many leafs are in the stem 2.

There are 6 values in the data set which are greater than or equal to 10 and less than or equal to 19. This comes from the fact that we have to count how many leafs are in the stem 1.

There are 14 values in the data set which are greater than or equal to 40 and less than or equal to 49. This comes from the fact that we have to count how many leafs are in the stem 4.

Answer:

  20 cm

Step-by-step explanation:

Given a prism with a right triangle base and a volume of 480 cm³, you want the height of the prism. The base has one side 8 cm, and hypotenuse 10 cm.

The missing edge of the right triangle base can be found using the Pythagorean theorem. It tells us the square of the hypotenuse is the sum of the squares of the other two sides:

  b² = c² +a²

  10² = 8² +a² . . . . . . . use given lengths

  a² = 100 -64 = 36 . . . . subtract 8², simplify

  a = 6 . . . . . . . . . . . . . length of side BC

The area of the right triangle base is ...

  A = 1/2bh . . . . . . . . b is the triangle base; h is its height

  A = 1/2(6 cm)(8 cm) = 24 cm²

The volume of the prism is ...

  V = Bh . . . . . . . . . . . . . . . where B is the base area, and h is the height

  480 cm³ = (24 cm²)h . . . use known values

  h = 20 cm . . . . . . . divide by the coefficient of h

The height of the prism is 20 cm.

The proper test statistic has a value of 13.21.

As a result, repeated measurements of cholesterol levels from the same blood sample are taken to assess a lab technician's consistency.

The desired accuracy is a measurement variance of 2.78 or less. In the event that the lab technician conducts 16 measurements, and the sample's measurement variance is 2.45.

1) n=16 samples were used.

The desired accuracy is a measurement variance of 2.78 or less.

The sample's measurements' variance is 2.45 or less.

We list both the null and alternative hypotheses in response to the query.

Null hypothesis [tex]H_{0}[/tex] = [tex]var^{2} \geq[/tex]  2.78

Alternative hypothesis [tex]H_{a}[/tex] = [tex]var^{2} <[/tex]  2.78

We claim the alternative hypothesis.

2)Calculate the appropriate test statistic's value.

Using Chi-square,

X= ((n-1)(2.45)/(2.78)

X= 15(2.45)/(2.78)

X=36.75/2.78

X= 13.21

Therefore, The value of the appropriate test statistic is 13.21

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Answer:

(1,3)

Step-by-step explanation:

You can use the distance formula to help you solve the answer

Answer:

(1; 3)

Step-by-step explanation:

x = (-1 + 3)/2 = 1

y = (6 + 0)/2 = 3

So we want to find the vertical asymptotes of the function:

Remember that there's a vertical asymptote at points of x where the denominator of the rational function is 0.

So, equal the denominator to zero:

And solve this equation for x as follows:

We could factor

Now, notice that any of both factors could be zero, so:

Therefore, the function has vertical asymptotes at x=6 and x=3.

Answer:

10 : 0.02 (20m)

We paint with:

• red the regions where the function is decreasing,

• green the regions where the function is increasing.

From the graph, we see that the function is:

• decreasing in the intervals (-∞, -1.5) and (2, ∞),

• increasing in the interval (-1.5, 2).

Answer

• Increasing on the interval(s): ,(-∞, -1.5), (2, ∞)

• Decreasing on the interval(s): ,(-1.5, 2)

If two angles be 10x + 5 and 15x - 30 then the value of x = 7.

Let the two angles be 10x + 5 and 15x - 30.

simplifying the above two equations, we get

10x + 5 = 15x - 30

Subtract 5 from both sides

10x + 5 - 5 = 15x - 30 - 5

Simplifying the above equations,

10x = 15x - 35

Subtract 15x from both sides of the equation

10x - 15x = 15x - 35 - 15x

Simplifying the above equation, we get

-5x = -35

Divide both sides by -5

[tex]$\frac{-5 x}{-5}=\frac{-35}{-5}[/tex]

x = 7

Therefore, the value of x = 7.

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The given situation can be solved using the differential equation and the top of the ladder slides downward at 0.417 ft/s.

Let:

x be  the distance from the bottom of the ladder to the base of the wall

y  be the distance from the top of the ladder to the bottom of the wall

When the ladder is still, apply the Pythagorean Theorem,

x² + y² = 13²

5² + y² = 13²

y² = 169 - 25 = 144

y = 12 ft

When the ladder slides, apply the differential equation:

x² + y² = 13²

2x . dx/dt + 2y . dy/dt = 0

Substitute x = 5, dx/dt = 1, y = 12

2 . 5 . 1 + 2 . 12 . dy/dt = 0

24 dy/dt = -10

dy/dt = -5/12 = - 0.417 ft/s

The minus sign indicates that the ladder is sliding downward.

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Solution

The question would like us to evaluate the following expression

- We should deal with the modulus and bracket separately.

- After that, we can then perform the subtraction operation on the results of the modulus and bracket.

- This is done below:

Also,

Thus, combining both results, we have:

Final Answer

The answer is -6

Answer:

-6 hope it helps

thank you

Point D is the centroid of ΔABC, since we know that A.F, BC, and CE are all medians.

A median of a triangle is the line segment that connects the vertex of a triangle to the midpoint of the opposite side. There are usually three medians of a triangle.

The point where the three medians of a triangle intersect each other or meet at is referred to as the centroid of the triangle.

The diagram shows a triangle with three medians that meets at point D in the triangle. Therefore, point D is the centroid of the tringle because lines A.F, BC, and CE are all medians of the given triangle.

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Step 1

Given;

Required; To find the measure of angle F

Step 2

Answer;

Answer:

6

Step-by-step explanation:

Trust

Answer: 48 ft

Step-by-step explanation:

The height gap between the balloons is 60 -40 = 20 feet. That gap is being closed at the rate of 2 + 3 = 5 ft/s, so will be gone in ...

 (20 ft)/(5 ft/s) = 4 s

At that time, the red balloon will have risen (2 ft/s)(4 s) = 8 ft to a height of ...

 40 ft +8 ft = 48 ft

The blue balloon will have descended (3 ft/s)(4 s) = 12 ft to a height of ...

 60 ft -12 ft = 48 ft

The balloons at at 48 ft when they are both the same height.

_____

Time and speed and distance are related by the formula you see on every speed limit sign:

 speed = distance/time . . . . . . . (on the sign, it's "miles per hour")

or

 time = distance/speed

or

 distance = speed × time

_____

If you want equations, you can write them as ...

 h = 40 +2t

 h = 60 -3t

where h is the altitude the balloons have when they are at the same height, and t is the number of seconds it takes to get there.

We're only interested in h, so we can cancel t by multiplying the first equation by 3 and adding that to the second equation multiplied by 2:

 3(h) + 2(h) = 3(40 +2t) +2(60 -3t)

 5h = 120 +6t +120 -6t

 h = 240/5 = 48 . . . . the height in feet at which the balloons are the same height

Answer:

p(-1) = 7

p(2) = -2

Step-by-step explanation:

We have p(x) = 4 - 3x

p(-1) = 4 - 3(-1) = 4 + 3 = 7

p(2) = 4 - 3(2) = 4 - 6 = -2

The factors of the given monomial are given below

What is a monomial?

A monomial is, broadly speaking, a polynomial with just one term in mathematics. There are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variable x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer. If many variables, say x,y,z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a,b,c non-negative integers.

The factors of the monomial 16x²y are 2.2.2.2.x.x.y

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The factors of the monomial are given below

What is a monomial?

A monomial is, broadly speaking, a polynomial with just one term in mathematics. there are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variables x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer, if many variables, say x, y, z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a, b, c non-negative integers.

The factors of the monomial 16x²y are 2.2.2.2.x.x.y

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Albert borrowed $17 from his friend.

Given,

Albert brought some items:

Cost of blanket = $32.75

Cost of pillow = $12.75

Cost of glove = $16.25

Amount paid by Albert = 50

Amount borrowed by Albert from his friend = x

Cashier gave back the change = $5.25

We have to find the amount borrowed by Albert from his friend:

This is simply arithmetic operations:

Total cost in shop = 32.75 + 12.75 + 16.25 = $61.75

Total amount given to the cashier = 61.75 + 5.25 = 67

Amount borrowed by Albert from his friend = Total amount given to the cashier - Amount paid by Albert

x = 67 - 50

x = 17

That is,

Albert borrowed $17 from his friend.

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Answer:

32x – 72

OR

–72 + 32x

Step-by-step explanation:

To use the Distributive Property, just simply follow my steps:

Write the equation:

–8(9 – 4x)

To distribute, multiply the numbers inside the parenthesis by the number outside of the parenthesis SEPARATELY. It should look like this:

(–8 • 9)(–8 • –4x)

(–72)(32x)

Since the 32 is positive, the equation could be written either way:

–72 + 32x

OR

32x – 72

If you want the equation to be fully solved...

Set the equation equal to zero:

32x – 72 = 0

Isolate the variable. Subtract 72 from both sides:

32x – 72 + 72 = 0 + 72

32x = 0 + 72

32x = 72

Divide:

32x/32 = 72/32

x = 9/4 (Improper Fraction Form)

OR

x = 2 (and) 1/4 (Mixed Number Form)

Convert 9/4 to a decimal:

x = 9/4

x = 2.25

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Answer:

C. No because two points with the same x-value have different y-values.

Step-by-step explanation:

(view my screenshot attachment too please)

A function can't have same x-values that appear for multiple different y-values.

In the diagram, (10, 6) and (10, 9) indicate that it isn't a function.

This is because the same 10 appears twice (x-value) but with multiple different y-values (6 and 9).

Answer:

y=2x+6

y=2x+6

Explanation:

Given the equation:

The equation written as a system of equations is:

Opening the bracket in the first equation gives:

Answer:

p = 3

Step-by-step explanation:

y = mx + b They gave us the slope of -1.  We need to find the y intercept.  We will use the x of 9 and the y of 2 to find b.  We will plug these numbers in to find b.

y = mx + b

2 = -1(9) + b

2 = -9 + b  Add 9 to both sides

11 = b

y = -x +11

Now, plug in 8 for x

y = -1(8) + 11

y = -8 + 11

y = 3

In this case p is 3.

The equation that represents the total amount of money Papi's made selling pizzas on Saturday is (39 x $9.99) + (62 x $11.99) + (83 x $13.99)

Equation:

An equation is the mathematical statement which is made up of two expressions connected by an equal sign.

For example, 3x – 2 = 16 is an equation.

Given,

There are three types of pizza varieties are small, medium and large. And the price of them are $9.99, $11.99 and $13.99 respectively.

On Saturday, Papi's sold 39 small pizzas, 62 medium pizzas, and 83 large pizzas.

So, we have to write the equation for the total amount of money Papi's made selling pizzas on Saturday.

To calculate the price of the pizza we have to multiply it by the number of items sold by the cost.

So, the equation to calculate the cost of pizza,

=> number of items sold x cost.

Here we have to write the equation for three types and we have to find the total cost for it,

So, the equation is looks like,

=> (39 x $9.99) + (62 x $11.99) + (83 x $13.99)

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We want to know what's the probability of spinning a number greater than two

There are 2 spinnings greater than two, of a total of 8. therefore, the probability I will be

The probability is 1/4