find the area of the shaded shape pls quickly​

The exponential function illustrated as f(x)=50(1.02)^x has a growth rate of 2%.

The exponential function is a mathematical function that is represented by e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

In this case, the function is given as:

f(x)=50(1.02)^x

It should be noted 1 + 2% = 1.02 which us the value in the parentheses.

In conclusion, the growth rate is 2%.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Find inverse of given function :

[tex]\qquad❖ \: \sf \:y = \sqrt{x} + 7[/tex]

[tex]\qquad❖ \: \sf \: \sqrt{x} = y - 7[/tex]

[tex]\qquad❖ \: \sf \:x = (y - 7) {}^{2} [/tex]

Next, replace x with f-¹(x) and y with x ~

[tex]\qquad❖ \: \sf \:f {}^{ - 1} (x) = (x - 7) {}^{2} [/tex]

we got our inverse function.

Condition : x should be greater or equal to 7

because we will get same value of y for different x if we also include values less than 7.

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\longrightarrow\bold{f(x)= \sqrt{7}}[/tex]

To solve for the inverse of a function we begin by re-writing the function as an equation in terms of y.

[tex]\bold{Becomes,}[/tex]

Next step we switch sides for x and y variables and then solve for the y variable as shown below,

[tex]\longrightarrow\sf{y= \sqrt{x}+7}[/tex]

[tex]\bold{Then,}[/tex]

[tex]\longrightarrow\sf{x= \sqrt{y}+7}[/tex]

[tex]\small\bold{Solve \: for \: y \: and \: subtract \: 7 \: from \: the \: both \: }[/tex] [tex]\bold{sides,}[/tex]

[tex]\longrightarrow\sf{x-7= \sqrt{y}}[/tex]

[tex]\small\bold{Square \: both \: sides }[/tex]

[tex]\sf{(x-7)^2=(\sqrt{y})^2}[/tex]

[tex]\sf{(x-7)^2=y}[/tex]

We now re-write in function notation. Take note however that this is the inverse:

[tex]\bold{Where \: y}[/tex] [tex]\sf{=(x-7)^2 }[/tex]

[tex]\longrightarrow\sf{y= (x-7)^2 }[/tex]

[tex]\huge\mathbb{ \underline{ANSWER:}}[/tex]

[tex]\large\boxed{\sf A. \: \: f^{-1}(x)= (x − 7)^2 , \: for \: \underline > 7 }[/tex]

The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

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Answer:

D.= √29

Step-by-step explanation:

The distance between the two complex numbers,

Z₁=a+bi and Z₂=c+di in the complex plane is

[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]

In the Cartesian plane, the distance between, one point and other is (x₁,y₁) and (x₂,y₂) is the distance formula is

[tex]d = \sqrt{(X₂-X₁)² + (Y₂-Y₁)²} [/tex]

To find the distance between the two complex numbers using the formula

[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]

where,

[tex]d = \sqrt{(a - b) {}^{2} + (d - b) {}^{2} } \\ d = \sqrt{(6 - 4) {}^{2} + ( - 2 - 3) {}^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 5) {}^{2} } \\ d = \sqrt{4 + 25} = \sqrt{29 \\ } [/tex]

The linear functions with their slopes ranked from least to greatest are given as follows:

E. I, K, J.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we have that:

Hence the linear functions with their slopes ranked from least to greatest are given as follows:

E. I, K, J.

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Answer:

B

Step-by-step explanation:

It's B

Answer:

Option B

Step-by-step explanation:

The equation is:

[tex]y=10-2x[/tex]

when x=2

[tex]y=10-2(2)010-4=6[/tex]

When x = 3

[tex]y=10-2(3)=10-6=4[/tex]

When x=4

[tex]y=10-2(4)=10-8=2[/tex]

Hope this helps

Answer:

Step-by-step explanation:

base=b=7.2yd

height =h=7yd

area of parallelogram = b x h

.                                    =7.2yd x 7yd

                                     =50.49[tex]yd^{2}[/tex]

The area of the shape is 35 square units

The given shape is a trapezoid, and it has the following side lengths

Parallel bases = 6 and 8

Height = 5

The area of the shape is then calculated as:
A = 0.5 * (sum of parallel bases) * height

Substitute the known values in the above equation

A = 0.5 * (6 + 8) * 5

Evaluate the product

A = 35

Hence, the area of the shape is 35 square units

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The area of the given trapezoid is given as 35 square units

The given shape is quadrilateral known s a trapezoid. The formula for calculating the are of the trapezoid is expressed as;

A = 1/2(a+b)*h

where

a and b are parallel sides

h is the height of the trapezoid.

Given the following parameters

a =6units

b = 8 units

h - 5 units

Substitute to have:

A = 1/2(6 + 8) * 5

A = 1/2(14) *5

A = 7 * 5

A = 35 square units

Hence the area of the given trapezoid is given as 35 square units

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Answer:

Points ABC and points OBC form two separate triangles. Triangle ABC is made up of angles BAC, ABC, ACB, while triangle OBC is made up of angles BOC, OBC, OCB. Since interior angles of triangles add up to 180 degrees, m<BAC + m<ABC + m<ACB = 180 and m<BOC + m<OBC + m<OCB = 180. 180 is equal to 180, so m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB.

Since OB bisects <ABC and OC bisects <ACB, m<ABO = m<OBC and m<ACO = m<OCB. We can also say that m<ABC = 2m<ABO and m<ACB = 2m<ACO. Substitute and simplify the equation.

m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB

m<BAC + 2m<ABO + 2m<ACO = m<BOC + m<ABO + m<ACO

m<ABO + m<ACO = m<BOC - m<BAC

Both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.

To find at what time will both trains leave the station together again if both of them left the station together at 6:30 am:

Therefore, both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.

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The probability that exactly 12 of them are strikes is 0.09.

In this question,

Number of pitches, n = 22

Probability of throwing a strike for each pitch, p = 0.431

Then, q = 1 - p

⇒ q = 1 - 0.431

⇒ q = 0.569

Number of strikes, x = 12

The probability that exactly 12 of them are strikes can be calculated using Binomial expansion,

[tex]P(X=x)=nC_xP^{x}q^{(n-x)}[/tex]

⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{(22-12)}[/tex]

⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{10}[/tex]

⇒ [tex]P(X=12)=(\frac{22!}{12!10!} )(0.431)^{12}(0.569)^{10}[/tex]

⇒ P(X=12) = (646646)(0.000041)(0.00355)

⇒ P(X=12) = 0.09431 ≈ 0.09

Hence we can conclude that the probability that exactly 12 of them are strikes is 0.09.

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answers :

a.

coordinates of A are (2,4)

b.

coordinates of B are (6,0)

i.

(4,2) is the midpoint

ii.

y = -3x + 18 is the parallel line

Step-by-step explanation:

a.

if two things are equal to the same thing then they are equal to each other

y = 4

2x + y = 8 is y = -2x +8 so

-2x +8 = 4

-2x = -4

x = 2

coordinates of A are (2,4)

b.

if two things are equal to the same thing then they are equal to each other

y=0

3x+y=18 is y = -3x+18 so

-3x+18=0

x = 6

coordinates of B are (6,0)

midpoint formula is

(X1+X2)/2 , (Y1+Y2)/2

(2,4) (6,0)

(X1+X2)/2 , (Y1+Y2)/2

(2+6)/2 , (4+0)/2

(4,2) is the midpoint

parallel line has the same x value

so for a line parallel to 3x+y=18 or y = -3x+18

the parallel line would be

y = -3x

point slope formula

point slope formulay - y1 = m (x - x1)

3x+y=18 or y = -3x+18 was 6,0 at y = 0

y - y1 = m (x - x1)

y - 0 = m (x - x1)

since it's a parallel line the m has to be the same

(6,0)

y - 0 = -3 (x - 6)

y = -3x + 18 is the parallel line

¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉

Pascal's triangle is a triangle written in such a way that it forms the coefficients of a binomial expansion. The coefficients of the terms are gotten through combination.

Combination is the number of ways r in which n objects can be selected. It is given by ⁿCₓ = n!/x!(n - x)!

Since we have ¹³C₈ + ¹³C₉ and we want to write it as a single term, we have that

So,  ¹³C₈ + ¹³C₉ =  13!/8!5! +  13!/9!4!

= 13!/(8! × 5 × 4!) +  13!/(9 × 8! × 4!)

= 13!/8!4![1/5 + 1/9]

= 13!/8!4! × [(9 + 5)/45]

= 13!/8!4! × 14/45]

= 13!/8!4! × 14/(9 × 5)]

= 14 × 13!/8! × 9 × 4! × 5)]

= 14!/9!5!

= 14!/9!(14 - 9)!

= ¹⁴C₉

So,  ¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉

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Comparing it to a system of equations, the expression is represented as follows:

18g + 5.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, we consider g as the variable. Then:

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A pendulum that swings fully once in 1.9 seconds has a length of 2.93 feet.

A basic pendulum is a machine in which the point mass is hung from a fixed support by a light, inextensible string.

Length of pendulum is defined as the distance between the point of suspension to the center of the bob and is denoted by " 1 ".

Given the equation:

[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]

where L is the length in feet and T is the time in seconds.

Given that T = 1.9sec,

Hence:

[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]

L = 2.93 feet

A pendulum that swings fully once in 1.9 sec has a length of 2.93 feet.

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Answer:

(4) (x + 6)(x - 1)

Step-by-step explanation:

Given expression

[tex]x { }^{2} + 5x - 6[/tex]

Find numbers when they are multiplied gives 6 and when they are added which gives 5.

Thus, these numbers are -1 & 6.

[tex]x {}^{2} + 6x - x - 6 \\ x(x + 6) - 1(x + 6) \\ (x + 6) \: \: (x -1 )[/tex]

Can also check the multiplied values of these two values.

Hope it helps!

Answer:

(4)

Step-by-step explanation:

Determine two multiples which when multiplied gives - 6(the last term in the equation), when added, gives +5 (the middle term in the equation).

Multiples are: +6 and -1

input the two multiples in place of the middle term (+5x)

=x^2+6x-1x-6

Collect like terms

=x(x+6)-1((x+6)

Answer= (x+6)(x-1)

Confirm answer above:

Open bracket

x(x-1)+6(x-1)

x^2-x+6x-6

x^2+5x-6 (initial equation).

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \:g(f( - 5)) = 5[/tex]

[tex]\textsf{\underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:f(x) = |2x + 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = |2( - 5) + 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = | - 10+ 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = | - 1| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = 1[/tex]

next,

g(f(-5)) represents value of y at x = f(-5) = 1

hence,

[tex] \qquad \large \sf {Conclusion} : [/tex]

y=5(14-x)(x) quadratic equation best models the volume of the box .

What is volume of cuboid?

Perimeter = 2(width + length) =28

Let x=width of base, then length of base = (28/2)-x = 14-x

Volume of box = length*width*height

=x(14-x)*5  ⇒ 5x(14-x)(x)

Therefore, y=5(14-x)(x) quadratic equation best models the volume of the box .

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Answer:

[tex] \frac{3}{2} [/tex]

Step-by-step explanation:

From the attached photo, we can deduce:

(2,2) as (x1,y1)

(-2,-4) as (x2,y2)

Slope Formula =

[tex] \frac{y1 - y2}{x1 - x2} [/tex]

Now we can substitute these values into the formula to find the slope.

Slope of line =

[tex] \frac{2 - ( - 4)}{2 - ( - 2)} \\ = \frac{2 + 4}{2 + 2} \\ = \frac{6}{4} \\ = \frac{3}{2} (reduced \: to \: simplest \: form)[/tex]

Answer:

It gets more complicated with a six-sided die. In this case if you roll the die, there are 6 possible outcomes (1, 2, 3, 4, 5 or 6). Can you figure out what the theoretical probability for each number is? It is 1/6 or 0.17 (or 17 percent).

Answer:

25 / 4

Step-by-step explanation:

To find the left sum, you need to....
1.) Find Δx

2.) Find [tex]x_{k-1}[/tex]

3.) Find ∑[tex]^n_{k=1}f(x_{k-1})[/tex]Δx

4.) Solve for the left sum

Answer:

90ft

Step-by-step explanation:

43,560ft² = L × l

43,560ft² = 484ft × l

43,560ft² ÷ 484ft = l

l = 90ft

P/10 = 7.2/3

P = 7.2x10/3

P=72/3

P= 24

Option (a) Sample

Sample is the research that analyzes a portion of an entire population.

A sample is a condensed, controllable portion of a bigger group. It is a subgroup of people with traits from a wider population. When populations are too big for a statistical test to include every potential participant or observation, samples are utilized.

By permitting researchers to obtain the same results from a sample as they would from the population, sampling helps researchers save money. Non-random sampling is much less expensive than random sampling since it reduces the expense of locating participants and obtaining their data.

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Correct answer is C. the number of times blue ball appears is 56

Given,

probability of picking a green ball is 0.5,

the probability of picking a blue ball is 0.4,

the probability of picking a red ball is 0.1.

a ball is picked and replaced = 140

Probability = (the number of ways of achieving success) / (the total number of possible outcomes)

Probability provides information about the likelihood that something will happen. Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects.

For this item, the number of times that we should expect that a blue ball is picked should be the product of the number of times  and the probability of picking a blue ball (which is equal to 0.4)

                            = (140)(0.4) = 56

Therefore, we should expect that the blue ball will be picked 56 times.

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Answer:

(x-y)(x-y)(x-y)= x²-yx+x²-yx-yx+y²-yx+y²

2x²-4yx+2y²

(y-x)(y-x)= y²-yx-yx+x²

y²-2yx+x²

-(y²-2yx+x²) = -y²+2yx-x²

2x²-4yx+2y²-y²+2yx-x²= x²-2yx+y²

or

(x−y−1)(x−y)² ≡ x³−x²+3xy²+2xy−y³−y²−3yx³

The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Length of Charles garden = 12.5 m * 12 = 150 m

Length of Stephen chain = 150 m /18 = 25/3 m

Breadth of Charles garden - 25/3 * 10 = 250/3 m

Area of Charles garden = 150 m * 250/3 m = 12500 m =

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Answer:

(f^−1)′(6)=1/(f'(f^-1(6)))

(f^−1)′(6)=1/(f'(f^-6)))

I hope this helps.

The point which is indicated in the task content; (1, 2) represents; parking costs $2 per hour for the entire day.

What is the interpretation of the point given in the task content; (1,2)?

It follows from convention that the coordinate systems are structured such that the independent variable, x be placed 1st and the dependent variable, y be placed second.

Consequently, since the cost of parking is dependent on the time for which the car is parked, then, it represents parking costs 2 per hour for the entire day.

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Answer:

0.2857

Step-by-step explanation:

We want to determine,

The probability that the battery life is at least 11 hours is 0.2857.