The inverse of the function f(x) =
f(x) = x + 10 is shown.
h(x) = 2x-0
What is the missing value?
0 1
05
O 10
O 20

Answer: 189/760

Step-by-step explanation:

The series can be represented in sigma notation as:

[tex]\sum^{18}_{n=1} \frac{1}{n(n+1)(n+2)}[/tex]

We can perform partial fraction decomposition as follows:

[tex]\frac{1}{n(n+1)(n+2)}=\frac{A}{n}+\frac{B}{n+1}+\frac{C}{n+2}\\\\ \implies 1=A(n+1)(n+2)+B(n)(n+2)+C(n)(n+1)[/tex]

If n = 0, then [tex]1=A(0+1)(0+2) \implies A=\frac{1}{2}[/tex]

If n = -1, then [tex]1=B(-1)(-1+2) \longrightarrow B=-1[/tex]

If n = -2, then [tex]1=C(-2)(-2+1) \longrightarrow C=\frac{1}{2}[/tex]

This means the series can be expressed as:

[tex]\sum^{k}_{n=1} \left(\frac{1}{2n}-\frac{1}{n+1}+\frac{1}{2(n+2)} \right)=\frac{k(k+3)}{4(k+1)(k+2)}[/tex]

Substituting in k=18,

[tex]\frac{18(21)}{4(19)(20}=\boxed{\frac{189}{760}}[/tex]

x y

2,0

1,-2

0,-4

-1,-6

-2,-8

Answer:

The given tessellated plane has translational and rotational symmetry. From the given options, we find that option A is correct.

Step-by-step explanation:

Concept: The symmetry has to be decided in such a way that when it applies to a figure, we get exactly the next figure. In the given figure, we have translational and rotational symmetries. We can translate the triangles to the next position and get the same triangle. Or we can rotate the triangle about the point of contact and get the same triangle.

For example, take the top left triangle. If it is translated towards approximately 30° direction, then we will get the triangle present at the top.

Or when we turn that triangle about the point of contact of that and the topmost triangle, then we can get the topmost triangle.

But there is no reflectional symmetry due to the absence of symmetry line.

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Answer: 96 degrees

Step-by-step explanation: Assuming that angle ℒ is the third measure, then angle ℒ is 96 degrees as all exterior angle measures of a triangle are 360 degrees.

360-264 = 96 degrees = 

ℒ

Please give brainliest if helpful.

Answer:

Speed of light 186000 miles/second.

it takes 500 seconds (approx 8 minutes) for light from the sun to reach Earth.

Step-by-step explanation:

Earth travels around the sun in a slightly oval-shaped orbit, known as an ellipse. Therefore, the planet's distance from the sun changes throughout the year.

However, the average distance from Earth to the sun is about 93 million miles (150 million kilometres). Scientists also call this distance one astronomical unit (AU).

A universe is a big place, and sometimes researchers use astronomical units to communicate how far celestial objects are separated from one another. For example, Jupiter orbits about 5 AU from the sun.

The distance between the earth and the sun d= velocity of light × time taken to reach light from the sun to earth

Distance from Earth to Sun=93000000 miles.

Speed of light = 186000 miles/second.

=>  [tex]\frac{93000,000}{186000}[/tex]

=> 500 seconds.

=> 8.333 minutes

it takes 500 seconds (approx 8 minutes) for light from the sun to reach Earth.

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Using subtraction of perfect squares, it is found that the factored expression is:

9t² - 4 = (3t - 2)(3t + 2).

It is given as follows:

a^2 - b^2 = (a - b)(a + b)

In this problem, the binomial is given as follows:

9t² - 4.

Hence:

Hence the factored expression is:

9t² - 4 = (3t - 2)(3t + 2).

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There will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have a circle and a parabola:

As we know the standard form of a circle:

[tex]\rm (x-h)^2 +(y-k)^2=r^2[/tex]

The standard form of the parabola:

[tex]\rm y = a(x-h)^2+k[/tex]  

If we plug the value of y from the parabola equation in the circle equation, we get a quartic equation(4th order equation)

The solution of the quartic equation will be 4.

Thus, there will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.

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The expression represents the probability of getting exactly 3 heads is,

[tex]C(n,r)(0.5)^3(0.5)^6[/tex]

We have given

Aron flips a penny 9 times.

We have to determine

Which expression represents the probability of getting exactly 3 heads

The binomial distribution is determined as the probability of mass or discrete random variable which yields exactly some values.

The binomial probability formula shown has variables that represent:

[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]

Where n is the total number of trials (here, we flip penny 9 times, hence n = 9).

r is the number we want to find (here, we want the probability of 3 heads, so r = 3).

p is the probability of success (here, success means getting heads.

So, in a coin flip the probability of heads is always 1/2, so p = 1/2).

Therefore, The expression represents the probability of getting exactly 3 heads is;

[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]

[tex]=C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex]

Hence, the expression represents the probability of getting exactly 3 heads is [tex]C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex].

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The probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Given the probability of a child being girl is 0.5, therefore, the probability of a child being boy is 0.5. Now, the probability of at least 3 girls out of 5 is,

Probability (x≥3)

= ⁵C₃ (0.5)³(0.5)² + ⁵C₄ (0.5)⁴(0.5)¹ + ⁵C₅(0.5)⁵(0.5)⁰

= 0.5

Probability (x≤3)

= ⁵C₃ (0.5)³(0.5)² + ⁵C₂(0.5)²(0.5)³ + ⁵C₁(0.5)¹(0.5)⁴ + ⁵C₀(0.5)⁰(0.5)⁵

= 0.8125

Hence, the probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.

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Answer:

2x+3+9

because plyer scored 9 points and throw 2point shotand same number 3

The cosine ratios which are correct for the ΔPQR are CosineP = r/q and CosineR = p/q.

We have,

Δ PQR,

Length of hypotenuse PR = q

The length of PQ = r,

And the length of QR = p

NOw,

We know that Trigonometric ratios of CosineΘ;

CosineΘ = Base/Hypotenuse

So,

CosineP = r/q

And,

CosineR = p/q

So, from the above find out values we can say that these values are given in option (a) and option (d).

Therefore, the cosine ratios which are correct for the ΔPQR are CosP = r/q and CosR = p/q.

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Answer:

6.3 *30= 189; so 4 cotton swabs

Answer:

3

Step-by-step explanation:

374274 =3.74274 x 100000=3.74272x 10^5

Answer:

B

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= x + 8 - 4x - 3 ← collect like terms

= - 3x + 5

Answer:

[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]

Step-by-step explanation:

Add both functions

(f + g)(x) = x + 8 + (-4x - 3)

(f + g)(x) = x + 8 - 4x - 3

(f + g)(x) = x - 4x + 8 - 3

(f + g)(x) = -3x + 5

[tex]\rule[225]{225}{2}[/tex]

Answer:

let the no. of students who failed the examination be X

therefore, no. of students passed = 5x

total no. of students = 582

5x + X = 582

6x = 582

x = 97

no. of students failed the examination = 97

no. of students passed = 97*5 = 485

The median of the distribution is 4.

A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.

The median is the number at the center of the data set.

Arranging the numbers in the histogram in ascending order is: 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 10

1/2 x 22 = 11th number  4

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Answer:

(3, 2)

Step-by-step explanation:

To be considered part of a solution set for the inequality provided, a given point must lie within the shaded region that is graphed. Since we want to find the point that is not included in the solution set for the inequality, we need to find the point that does not lie in the shaded region.

Let's test each point to see which doesn't lie in the region. Refer to the image below if you're having trouble graphing the points:

Hope this helps!

For [tex]x < -5[/tex]:

[tex]x-5 < 0 \Rightarrow |x-5|=-(x-5)=-x+5\\x+5 < 0\Rightarrow |x+5|=-(x+5)=-x-5[/tex]

So

[tex]|x-5|+|x+5|=-x+5-x-5=-2x[/tex]

The transformation of a function may involve any change in the initial function. The correct option is C.

The complete question is:

Each statement describes a transformation of the graph of y = log2x.

Which statement correctly describes the graph of y = log2(x + 3) - 9?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift

Stretching:

Given the initial function y = log2x, now if the function is needed to be transformed to y = log2(x + 3) - 9, then the function is needed to be shifted left by 3 units and down by 9 units.

Hence, the correct option is C.

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Answer:

x=5 y=0

Step-by-step explanation:

cancel out the 4y's and then add the x's together. also add the 5s together. 2x = 10, x = 5, and plug it in, and 5 cancels out, leaving y by itself.

By definitions of the area of a circle and area ratios, we conclude that the area of the circle drawn by Maria is equal to a value of 18π units squared.

In this question we have a circle whose radius (r) is kwown. Besides, we know that Maria draws a circle with double the area of the prior circle. The area of the circle (A) is described by the following formula:

A = π · r²     (1)

Then, we have that the area drawn by Maria is:

A = 2 · [π · 3²]

A = 18π

By definitions of the area of a circle and area ratios, we conclude that the area of the circle drawn by Maria is equal to a value of 18π units squared.

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Answer:

18π units squared

Step-by-step explanation:

On edge

Answer:

Step-by-step explanation:

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

Explanation:

The range of x values is [tex]-1 \le x \le 1[/tex] which means x = -1 is the smallest and x = 1 is the largest possible.

Similarly the smallest y value is y = -1 and the largest is y = 1.

----------

Plug in the smallest x and y value to get

f(x,y) = x+5y

f(-1,-1) = -1+5(-1)

f(-1,-1) = -6

Therefore, the absolute min is -6

----------

Now plug in the largest x and y values

f(x,y) = x+5y

f(1,1) = 1+5(1)

f(1,1) = 6

The absolute max is 6

Answer:

Using the ratio and proportion method, we find that on an average 1.875 rooms can be painted per gallon.

Step-by-step explanation:

Concept: Use the method of ratio and proportion.

In this method, if a relationship is given between two values, then using that relationship we can find another relationship with respect to another variable.

Given that for 2/5 gallons of paint, we can paint 3/4 of rooms. So, for one gallon of paint, divide 2/5 by 3/4.

2/5 gallons of paint = 3/4 rooms

1 gallon of paint = [tex]\frac{\frac{3}{4} }{\frac{2}{5} } = \frac{15}{8} =1.875[/tex] rooms

So, on an average they can paint 1.875 rooms per gallon.

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The bagel shop will earn $9625 in 12 months.

Scatter plot are graphs that identifies relation between x and y variables.

The scatter points are given in the graph and we have to determine the equation that best fits the data .

the points in the scatter plot is

(3,4) and (8,6)

The slope of the equation

y = mx +c is given by

m =(y2 - y1)/(x2-x1)

m = (9-4)/(11-3)

m = 5/8 = 0.625

The equation is

y= 0.625x +2.125

for 12 months

y = 9.625 thousand = 9625 thousand in 12 months

Therefore the bagel shop will earn $9625 in 12 months.

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Answer:

$9,625 is the answer, and $9,300 is the rounded answer

Step-by-step explanation:

general formula: y=ax-b

required form: p=am-b

choose two dots: (11,9), (3,4)

find the slope: 9-4/11-3=5/8 -> p=5/8

put it into an equation: f(11)=6&7/8-b=9, f(3)=1&7/8-b=4

finding the y-intercept: -9+6&7/8=2&1/8, -4+1&7/8=2&1/8 -> b=2&1/8

forming a whole equation: p=5/8m+2&1/8

predict the profit in December: p=7&4/8+2&1/8=9&5/8

the bagel shop will earn $9,625 in December

round them to the nearest tenth:  p=0.6m+2.1

predict the profit in December: p=7.2+2.1=9.3 -> $9,300

Answer:

y = -2x

Step-by-step explanation:

It passes through -5, 10 and 5, -10

gradient = Δy/Δx

gradient = -10 - 10 / 5 -- 5

gradient = -20 / 10

gradient = -2

let's use -5, 10 for y = mx + b

10 = -2(-5) + b

10 = 10 + b

b = 10 - 10

b = 0.

the equation of the line is just y = -2x

C. e

Step-by-step explanation:

[tex] ln( {e}^{e} ) = e ln(e ) = e(1) = e[/tex]

Answer:

h(-1) is -1, h(-0.5) is 0 and h(1) is 1.

Step-by-step explanation:

functions :- an expression, rule or law that defines relationship between one variable and another variable. When a certain condition is fulfilled, then the result is corresponding to that condition.

In the function it is given that when x∈(-2,-1] then we get -1. Now here x=-1 satisfies the given condition. So, the answer will be -1.

In the function it is given that when x∈(-1,0] then we get 0. Now here x=-0.5 lies in the range (-1,0]. So, the answer is 0.

In the function it is given that when x∈(0,1] then we get 1. Clearly, x=1 satisfies this range of values. So, we get 1.

Hence, the Answer is h(-1) = -1, h(-0.5) = 0 and h(1) = 1.

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Answer:

6 and 4

Step-by-step explanation:

Let one number be x.

Then another will be : 4x - 20

In accordance with the question;

x + 4x - 20 = 10

5x = 10 + 20

x = 30/5

= 6

x = 6

4x - 20 = 4×6 - 20 = 4

So, the numbers are 6 and 4.

The values of f(3.52)=26.61 and f(-8.77)=257.05

An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function at an element x of X, denoted by the symbol f(x), is referred to as the image of x under f or the value of f applied to the argument x.

The given function is f(x) = 3x²-3x =3x(x-1)

f(3.52)=3*(3.52)(3.52-1)

=26.61

f(-8.77)=3*(-8.77)(-8.77-1)

=257.05

Therefore, the values of f(3.52)=26.61 and f(-8.77)=257.05

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