5. 6.9Write the decimal as a a fraction or mixed number?

Answer:

y = 1/2 x - 9

Step-by-step explanation:

y = -2x - 4

slope of a perpendicular line =  1/2

y -(-8) = 1/2 (x-2)

y + 8 = 1/2 x - 1

y = 1/2 x - 1 - 8

y = 1/2 x - 9

a) The angles outside the side PQ measure 65° and 25°

The angles outside the side QR measure 85° and 95°

The angles outside the side PR measure 55° and 35°

b) The arc PR, PQ and PR measure 120°

a)

Let us assume that the inscribed square be ABCD and equilateral triangle is PQR.

Let side PR of triangle intersects the quadrilateral at points M and N.

So, we get a triangle DMN outside the equilateral triangle.

Here, ∠DMN = 55°, ∠D = 90°

So, ∠MND = 180 - (90 + 55)

                 = 35°

Similarly,  side PQ of triangle PQR intersects the quadrilateral at points X and Y.

So, we get a triangle AXY outside the equilateral triangle.

From triangle PXM we get the measure of angle PXM which is 65 degrees.

As angle PXM and angle AXY are opposite angles, the measure of angle AXY = 65°

∠A = 90°

So, ∠AYX = 180° - (∠A + ∠AXY )

                 = 180° - (90° + 65°)

                 = 25°

Let the side QR of triangle PQR intersects the quadrilateral at points L and K.

so we get new quadrilateral LKBC

In this quadrilateral ∠B = 90°, ∠C = 90°

From triangle QYL, we get the measure of angle QLY = 95°

So, the measure of ∠KLB = 95° .......(∠QLY and ∠KLB opposite angles)

So, the remaining angle LKC of quadrilateral LKBC would be,

∠LKC = 360° - (∠B + ∠C + ∠KLB)

∠LKC = 360° - (90 °+ 90° + 95°)

∠LKC = 85°

b)

We know that he angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

so, the measure of arc PR = 120°

the measure of arc PQ = 120°

the measure of arc RQ = 120°

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Answer:

It has parallel sides

Step-by-step explanation:

Answer: 800 envelopes

Step-by-step explanation:

Sam and her friends are working at a rate of 100 letters in envelopes per hour per person. So, if there are 4 people helping including sam, you just have to multiply 400 by 2 hours, which will give you 800.

Hence Proved N to N is uncountable set by using a diagonalization argument

What is Diagonalization Argument?

Georg Cantor published the Cantor's diagonal argument in 1891 as a mathematical demonstration that there are infinite sets that cannot be put into one-to-one correspondence with the infinite set of natural numbers. It is also known as the diagonalization argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof.

Proof:

We write f as the sequence of value it generates

that is, say f:N-N is defined as f(x) =x then

we write f as : 1,2,3,4........

similarly if f:N-N were f(x) = 2x then we write it as :2,4,6,8.......

now assume on the contrary that the set of functions from N to N is countable

then,

\(f_{1}\)   :     \(f_{11}\)        \(f_{12}\)       \(f_{13}\) , ...........

\(f_{2}\)   :     \(f_{21}\)        \(f_{22}\)       \(f_{23}\) , ...........

\(f_{3}\)   :     \(f_{31}\)        \(f_{32}\)       \(f_{33}\) , ........... and so on

Here \(f_{ij}\) =\(f_{i}(j)\)

consider the function f as :

f : (\({f11}\) +1 ) , (\({f22}\) +1) , (\({f33}\) +1),.........

Then f wouldn't appear in the list of the function we had above since any \(f_{i}\) would disagree with f at the i th place

Therefore the set of the function from N to N is an uncountable set

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Answer: negative one third

Answer:

-1/3

Explanation:

There's a formula that I'll use to find the slope - it's called the slope formula.

\(\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}\)

Plug in the data:

\(\sf{m=\dfrac{8-4}{-4-8}}\\\\\sf{m=\dfrac{4}{-12}\)

Simplify:

\(\sf{m=-\dfrac{4}{12}}\)

\(\sf{m=-\dfrac{1}{3}}\)

Hence, the slope is negative one-third.

Answer:

a) \( t_{\alpha/2}=\pm 2.447\)

b) \( t_{\alpha/2}=\pm 2.718\)

c) \( t_{\alpha/2}=\pm 2.779\)

d) \( t_{\alpha/2}=\pm 2.650\)

Step-by-step explanation:

Part a

The degrees of freedom are given by:

\( df=n-1= 7-1=6\)

The confidence is 95% or 0.95 the significance would be \(\alpha=0.05\) and the critical values would be:

\( t_{\alpha/2}=\pm 2.447\)

Part b

The degrees of freedom are given by:

\( df=n-1=12-1=11\)

The confidence is 98% or 0.98 the significance would be \(\alpha=0.02\) and the critical values would be:

\( t_{\alpha/2}=\pm 2.718\)

Part c

The degrees of freedom are given by:

\( df=n-1=27-1=26\)

The confidence is 99% or 0.99 the significance would be \(\alpha=0.01\) and the critical values would be:

\( t_{\alpha/2}=\pm 2.779\)

Part d

The degrees of freedom are given by:

\( df=n-1=14-1=13\)

The confidence is 98% or 0.98 the significance would be \(\alpha=0.02\) and the critical values would be:

\( t_{\alpha/2}=\pm 2.650\)

A value of a test statistic defines the upper bounds of a confidence interval, statistical significance in a test statistic is known as the crucial value.

For part a )

n = 7

Calculating the degrees of freedom \(= df = n - 1 = 7 - 1 = 6\)

At \(95\%\) the confidence level, the t:

\(\alpha = 1 - 95\% = 1 - 0.95 = 0.05\\\\\frac{\alpha}{ 2} = \frac{0.05}{ 2} = 0.025\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.025,6} = 2.447\\\\\)

The critical value = 2.447

For part b )

n =12

Calculating the degrees of freedom\(= df = n - 1 = 12 - 1 = 11\)

At \(98\%\) the confidence level , the t:

\(\alpha = 1 - 98\% = 1 - 0.98 = 0.02\\\\\frac{\alpha}{ 2}= \frac{0.02}{ 2} = 0.01\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.01,11} =2.718\\\\\)

The critical value =2.718

For part c )

n = 27

Calculating the degrees of freedom \(= df = n - 1 = 27 - 1 = 26\)

At \(99\%\) the confidence level, the t:

\(\alpha = 1 - 99\% = 1 - 0.99 = 0.01\\\\\frac{\alpha}{ 2} = \frac{0.01}{ 2} = 0.005\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.005,26}=2.779\\\\\)

The critical value =2.779

For part d )

n = 14

Calculating the degrees of freedom \(= df = n - 1 = 14 - 1 = 13\)

At \(98\%\) the confidence level, the t:

\(\alpha = 1 - 98\% = 1 - 0.98 = 0.02\\\\\frac{\alpha}{ 2} = \frac{0.02}{ 2} = 0.01\\\\t_{\frac{\alpha}{ 2}} \\\\df = t_{0.01,13} =2.650\)

The critical value =2.650

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The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.

The graph is given in the question.

As per the given line, we take two points (0, 4) and (5, 8)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 0, y₁ = 4

x₂ = 5, y₂ = 8

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 4 = (8 - 4)/(5-0 )[x -0]

⇒ y - 4 = (4/5)x

⇒ y = (4/5)x + 4

The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.

So, the equation of the line would be y = (4/5)x + 4.

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a)Lucy's acceleration during the last 6 seconds is 1/3 m/s².

b) Lucy's speed at the end of the 80-meter race is 6.67 m/s.

Acceleration is a physical quantity that measures the rate at which the velocity of an object changes with time. It is defined as the rate of change of velocity (v) with respect to time (t), and is usually denoted by the symbol "a".

a) Let's assume that Lucy's speed increases at a constant rate "a" during the last 6 seconds. Then we can use the following kinematic equation to find her speed at 16 seconds:

v = u + at

where "v" is her final speed at 16 seconds,

"u" is her initial speed at 10 seconds,

"a" is her acceleration during the last 6 seconds,

and "t" is the time interval of 6 seconds.

v = u + 2

Substituting these values into the equation above, we get:

u + 2 = u + 6a

Simplifying and solving for "a", we get:

a = 1/3 m/s²

Therefore, Lucy's acceleration during the last 6 seconds is 1/3 m/s².

b) Let's first find Lucy's average speed during the entire 16 seconds:

average speed = total distance / total time

The total distance is 80 meters and the total time is 16 seconds, so:

average speed = 80 / 16 = 5 m/s

Now, we can use the following kinematic equation to find Lucy's final speed "v":

v² = u² + 2as

where "u" is her initial speed at 0 seconds,

"a" is her average acceleration during the entire 16 seconds,

"s" is the total distance of 80 meters,

and "v" is her final speed at 16 seconds.

We can rearrange this equation to solve for "v":

v = √(u²+ 2as)

her speed at 10 seconds is:

u = at = (a)(10) = 10a

Substituting these values into the equation above, we get:

v = √((10a)² + 2a(80))

Simplifying and substituting the value of "a" that we found in part a), we get:

v = 6.67 m/s

Therefore, Lucy's speed at the end of the 80-meter race is 6.67 m/s.

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Answer:

true

Step-by-step explanation:

i believe its true, i may be wrong, if so, im sorry :((

Answer:

here

let ABC is triangle

SO

Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Let the variable n represent the number

\( \sf \longrightarrow \: n\)

\( \sf \longrightarrow \: n - 11\)

➪Thus, The equation is (n-11)

x=4 is the t-coordinate of the f's critical point. For the function f, ascertain whether the point is a relative maximum, relative minimum, or neither.

Given that,

Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x) = (4 - x)/x³ for x > 0

We have to find

(a)Discover the t-coordinate of the f's critical point. For the function f, ascertain whether the point is a relative maximum, relative minimum, or neither.

We know that,

f'(x) = 4-x/x³ = 4/x³ - 1/x²

Critical point f'(x)=0

4-x/x³=0⇒x=4

Therefore, x=4 is the t-coordinate of the f's critical point. For the function f, ascertain whether the point is a relative maximum, relative minimum, or neither.

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Using chain rule, the derivative of the function is 1 / [4x^(3/4) (1 + x^(1/2))].

Let u(x) = √4. Then we can write the given function as d/dx[tan^-1(u(x))].

Recall that the chain rule for differentiation states that d/dx[f(g(x))] = f'(g(x)) * g'(x). Applying this to our function, we have:

d/dx[tan^-1(u(x))] = [d/dx(tan^-1(u))] * [d/dx(u(x))]

To find d/dx(tan^-1(u)), we use the formula for the derivative of the inverse tangent function: d/dx[tan^-1(u)] = u'(x) / [1 + u(x)^2].

To find u'(x), we differentiate u(x) = sqrt4 with respect to x using the chain rule as follows:

d/dx[√4] = (1/2)x^(-3/4) * (d/dx)(x) = (1/2)x^(-3/4)

Therefore, u'(x) = (1/2)x^(-3/4).

Substituting u(x) and u'(x) into the formula for the derivative of the inverse tangent function, we get:

d/dx[tan^-1(u(x))] = [1 / (2x^(3/4) * (1 + x))]

Finally, substituting this expression for d/dx(tan^-1(u)) and d/dx(u(x)) back into our original chain rule expression from step 2, we get:

d/dx[tan^-1(√4)] = [1 / (2x^(3/4) * (1 + x))] * (1/4)x^(-3/4)

Simplifying the expression in step 6 by multiplying the two terms in the denominator and bringing x to the common denominator, we get:

d/dx[tan^-1(√4)] = 1 / [4x^(3/4) (1 + x^(1/2))]

Therefore, the derivative of the function d/dx[tan^-1(√4)] is 1 / [4x^(3/4) (1 + x^(1/2))].

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Answer: rwar

Step-by-step explanation:

The value of x is; x = 3.14

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

cos θ = base / hypotenuse

here, we get,

cos 17 = 3/x

so, we have,

0.956 = 3/x

so, x = 3.14

Hence, The value of x is;x = 3.14

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Answer:

4.9 in

Step-by-step explanation:

6/11 = x/9

6/11 times 9 = x

x = 4.9

The slope of the given line in  the image is -4 , Option A is the answer.

The equation of the straight line is given by

y =mx +c ,

Where m is the slope , C is the intercept

The line is passing through the point

(-1,8)  ,(2,-4)

The slope is given by

m = (y₂-y₁) /(x₂-x₁)

m  = (-4 - 8 )/(2 +1)

m = -12/3

m = -4

Therefore the slope of the given line in  the image is -4 , Option A is the answer.

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The two solutions of the equation:

(6x - 12)/3 + 4 = 18/x

Are x = 3 and x = -3

Here we have the following equation:

(6x - 12)/3 + 4 = 18/x

Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.

Now, let's start by simplifying the left side:

(6x - 12)/3+  4 = 18/x

2x - 4 + 4 = 18/x

2x = 18/x

Now we can multiply both sides by x so we get:

2x^2 = 18

Now divide both sides by 2:

x^2 = 18/2

x^2 = 9

Finally, apply the square root in both sides:

√x^2 = ±√9

x = ±3

The two solutions are x = 3 and x = -3

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Answer:

You got your negatives messed up.  The answer was -5y-4x

Step-by-step explanation:

Expression: -8y + 5x + 3y -9x

Your objective: Simplify the expression

The First step, Combine like terms meaning -8y+3y and -9x+5x

Solve, -8y+3y

That would equal -5y

Next solve -9x + 5x

That would equal -4x

Write your expression in simplest form:

-5y-4x

What you did:

You combined like terms but didn't follow the negative rules

Remember: Positive and Negative =  Negative

                   Negative and Negative = Positive

        For example -8y + 3y

You chose to add -8 and 3 which you got -11

What you were supposed to do was to subtract.

A helpful trick: Since they are like terms you could rearrange the questions like this 3y-8y+5x-9x, You can see that you have to do subtraction left to right

3y-8y= -5y

5x-9x= -4x

Solution: -5x-4x

The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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When a distribution has three or more peaks then it is said to be a multimodal distribution .

In histograms, there are often three types of distributions which are classified according to the number of peaks that they have . A unimodal distribution would be a histogram that has a single peak in its distribution .

Then there are binomial distributions which boast of having two peaks , Then finally, there is the multimodal distribution which is for all distributions with either three peaks, or more than that .

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Answer:

B

Step-by-step explanation:

The value of (f·g)(x) from the given function is -2x³ - x².

The given functions are f(x) = 2x +1 and g(x) = -x².

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here,

(f·g)(x) = f(x) × g(x)

= (2x +1) × (-x²)

= 2x × (-x²) + 1 × (-x²)

= -2x³ - x²

Therefore, the value of (f·g)(x) from the given function is -2x³ - x².

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"Your question is incomplete, probably the complete question/missing part is:"

If f(x) = 2x +1 and g(x) = -x², then find (f·g)(x).

Answer:

x = 100

Step-by-step explanation:

1. To get rid of the denominator of 5, multiply both sides of the equation to get 5

-40 + x = 60

2. Add 40 on both sides to get the variable x by itself

x = 60 + 40

3. Solve

x = 100

Answer:

x=100

Step-by-step explanation:

-8+x/5=12

--8+x/5=12+8

x/5=20

5*20=100

x=100

Answer:

480 square inches

Step-by-step explanation:

width = base = 24 inches

length = height = 40 inches

area of the triangular scarf = 1/2 * base * height

= 1/2 * 24 * 40

= 480 square inches

MARK BRAINLIEST

Answer:

No

Step-by-step explanation:

A triangle is valid if sum of its two sides is greater than the third side. If three sides are a, b and c, then three conditions should be met. 1+2<5

Answer:

b 56

Step-by-step explanation: