What is the surface area of the figure? 9 ft 9 ft 15 ft 15 ft 4 ft

Your answer is correct. The two "bases" of the trapezoid are the line segments (0, 0)-to-(y, 0) and (0, x)-to(z, x), with lengths y and z, respectively. Then the average of the bases is [tex]\frac{y+z}2[/tex]. (We know they're the bases because the line segments are parallel.)

We multiply this by the height, which is given by the length of the line segment (0, 0)-to-(0,x), or x.

Hence the area is

[tex]\dfrac{x(y+z)}2[/tex]

(which is identical to what you have).

First lets simplify to slope intercept (y=mx+b)

y=[tex](2x-7)/-3[/tex]

y=-2/3x+7/3

Point 1: (0,7/3) as when x is 0, y=7/3.
Point 2: lets plug x in as 3 to cross cancel.

[tex]\frac{-2}{3} *\frac{3}{1} = \frac{-2}{1}[/tex]

So (3,-2).

Lets do point 3: plug in -3.

[tex]\frac{-2}{3} *\frac{-3}{1} = \frac{2}{1} = 2[/tex]

So (-3,2).

Your three points are (0,2.33 repeat) or (0,7/3), (3,-2) and (-3,2)

Hopefully this helps you out, heart if it was helpful and please do not hesitate to ask any questions. I have also attached an image of the line

#learnwithbrainly

If m VB = 60°  and m BS = 30°, then m ∠3 =15°.

A tangent is a line passing by touching the perimeter of the circle, perpendicular to the line joining the center and touch point.

Given, PB tangents PV, PU secants

If m VB = 60°  and m BS = 30°, then m ∠3 =

The measurement of the external angles is the semi difference of the arcs it consists.

∠3 = 1/2 (60 - 30)

∠3 = 15°

Thus, If m VB = 60°  and m BS = 30°, then m ∠3 =15°.

Learn more about tangent.

https://brainly.com/question/23265136

#SPJ1

i ) 3(2x - 3) = 4(2x + 4)

[tex]6x - 9 = 8x +1 6 \\ \\ 6x - 8x = 16 + 9 \\ \\ - 2x = 25 \\ \\ x = - \frac{25}{2} .[/tex]

ii )2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)

[tex]2x + 4 + 5x + 25 = 4x - 32 + 2x - 4 \\ \\ 7x + 29 = 6x - 36 \\ \\ 7x - 6x = - 36 - 29 \\ \\ x = - 65.[/tex]

2. 3x /4 - 7 /4 = 5x + 12

[tex] \frac{3x}{4} - \frac{7}{4} = 5x + 12 \\ \\ \frac{3x}{4} - 5x = 12 + \frac{7}{4} \\ \\ \frac{3x - 20x}{4} = \frac{48 + 7}{4} \\ \\ \frac{ - 17x}{4} = \frac{55}{4} [/tex]

cancel 4 from both sides

[tex] - 17x = 55 \\ \\ x = \frac{ - 17}{55} .[/tex]

3. x +7 - 8x/3 = 17/6 - 5x/8

[tex]x + 7 - \frac{8x}{3} = \frac{17}{6} - \frac{5x}{8} [/tex]

put x = 4

[tex]4 + 7 - \frac{ 8\times 4}{3} = \frac{17}{6} - \frac{5 \times 4}{8} \\ \\ 11 - \frac{32}{3} = \frac{17}{6} - \frac{20}{8} \\ \\ \frac{33 - 32}{3} = \frac{68 - 60}{24} \\ \\ \frac{1}{3} = \frac{8}{24} \\ \\ \frac{1}{3} = \frac{1}{3} .[/tex]

L.H.S. = R.H.S.

4. Let 3 consecutive integers : x , x+1 , x+2

As per the question : 2x + 3(x+1) + 4(x+2) = 56

9x + 11 = 56

Transpose 11 to RHS

9x = 45

Divide both sides by 9

x = 5 ,

x + 1 = 5 + 1 = 6

x + 2 = 5 + 2 = 7

Numbers are 5 , 6 and 7 .

5. Let the age of Jane’s younger sister is x.

Age of Jane will be x + 6

As per the question, after 10 years the sum of their ages will be 50.

After 10 years,

age of Jane = x + 16

age of her younger sister = x + 10

Therefore,

x + 16 + x +10 = 50

2x + 26 = 50

2x = 24

x = 12

Thus, the present age of Jane’s younger sister is 12 years.

And of Jane’s is 12 + 6 = 18 years.

6. Let the breadth of rectangular swimming pool be x metres.

Then, its length = (2x + 2) metres.

We know that the Perimeter of a rectangle

= 2(Length + Breadth)

= 2(2x + 2 + x) = 6x + 4

According to the given condition, we have

6x + 4 = 154

6x = 154 − 4

6x = 150

[Dividing both sides by 6]

x = 25

Thus, breadth = 25 m and

length = 25 × 2 + 2 = 52 m .

7. Let the digit in ten's .

Place be x and the digit in the one's place be y.

x − y = 5 ⟶ (i)

Two digit number = 10x + y

Two digit after reversing the digits = 10y + x

According to question ,

10x + y + 10y + x = 99

11x + 11y = 99

x + y = 9 ⟶ (ii)

On adding (i) and (ii),

2x = 14

x = 7

Putting the value of x in equation (i)

x − y = 5

y = 2

Number = 10x + y

=72 .

8. Let the speed of the steamer in still water be x km/h.

Then , the speed downstream = (x+2) km/h

and the speed upstream = (x−2) km/h

Given , distance covered in 4 hours downstream = distance covered in 5 hours upstream

4(x + 2) = 5(x − 2)

4x + 8 = 5x − 10

4x − 5x = − 10 − 8

[Transposing 5x to LHS and 8 to RHS]

−x = −18 or x = 18 km/h .

9. Let the number of notes of different denomination be x.

∴ Numbers of Rs 100 notes , 50 notes and Rs 10 notes will be 2x , 3x and 5x respectively.

Amount of 100 Rs notes ⇒Rs 100 × 2x = 200x

Amount of 50 Rs notes ⇒Rs 50 × 3x = 150x

Amount of 10 Rs notes ⇒Rs 10 × 5x = 50x

As per the question

Total amount = 400000

200x + 150x + 50x = 400000

400x = 400000 , x = 1000

No of Rs 100 notes = 2x = 2 × 1000 = 2000

No of Rs 50 notes = 3x = 3 × 1000 = 3000

No of Rs 10 notes = 5x = 5 × 1000 = 5000 .

10. Let the age of the man be x

Then age of his son becomes (x − 24)

2 years later from now,

Age of man will be = x + 2

and age of his son will be = (x − 24 + 2) = x − 22

According to question,

2(x − 22) = x + 2

i.e., 2x − 44 = x + 2

i.e., x = 46

Therefore ,

Present age of man = 46 years

And present age of his son = 46 − 24 = 22 years .

Answer:

m=0 , b=41

Step-by-step explanation:

Answer:

a= 30

b=60

c=105

Step-by-step explanation:

A forms a vertical angle with another angle that measures 30 degrees, therefore,

a= 30 degrees.

Since a is 30 degrees and a and b are in the same triangle with a 90-degree angle and all interior angles in a triangle equal 180 degrees.

Then, 30+90+b=180

120+b=180

b=60

Angle c and an angle that equals 75 degrees are supplementary. meaning that they add up to 180 degrees.

180-75=c

105=c

[tex]\huge\underline\red{Answer -}[/tex]

[tex]\bold{8 \frac{2}{5} }\: \\\\ \implies \: \frac{5 × 8 + 2}{5} \: \\ \\ \implies \: \frac{ 40 + 2}{5} \\\\ \implies \frac{42}{5} \\\\ \rightarrow \:\boxed {reciprocal \: = \frac{5}{42} } \\ \\[/tex]

hope helpful ~

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{8 \dfrac{2}{5}}\\\\\mathsf{= \dfrac{8\times5+2}{5}}\\\\\mathsf{= \dfrac{40 + 2}{5}}\\\\\mathsf{= \dfrac{42}{5}}\\\\\mathsf{=\dfrac{5}{42}}\\\\\huge\text{Therefore, the answer should be: \boxed{\mathsf{\dfrac{5}{42}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

In the expressions that we are given, we can note that there is a negative in all of them. This means that we can factor out the negative.

With the negative factored out, it will look like this: [tex]-(\frac{8}{11} + \frac{3}{4} + \frac{1}{4} )[/tex]
The reasoning for this is because you distribute the negative to each term. For example 8/11 is a term, and so is 3/4, and 1/4. So our first answer is D.

Another way we can do this is by combining like terms. We see that in the denominator for -3/4 and -1/4 they both share 4. We can combine it so it becomes -4/4 or -1. It would be E.

The third way we can do this is by rewriting it. Answer A rewrites it so that it is + -, effectively just -. This allows us to treat the equation as if it were the original one.

Hopefully this helps you out, brainliest would help me out.
#GetVerifiedAnswers #LearnWithBrainly

Using proportions, it is found that the coordinates of the treasure as given as follows: (7.6, 8.8).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Researching the problem on the internet, the coordinates are as follows:

The treasure is buried between a rock and a tree in a 5:9 ratio, hence the expression is:

[tex]Ts - R = \frac{5}{14}(Tr - R)[/tex]

Hence, for the x-coordinate:

[tex]x - 3 = \frac{5}{14}(16 - 3)[/tex]

x - 3 = 5 x 13/14

x = 7.6.

For the y-coordinate:

[tex]y - 2 = \frac{5}{14}(21 - 2)[/tex]

y - 2 = 5 x 19/14

y = 8.8.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer: the answer is b

Step-by-step explanation:

Answer:

C = 2√(πA) units

Step-by-step explanation:

Answer:

80 students are female

Step-by-step explanation:

21 are male meaning 19 are female

9 are female in French

12 are female in Spanish

total = 40

2x + 40 = 120

2x = 80

x = 40

females'  = 80

total = 80

Answer:

There is no line plot

Step-by-step explanation:

Answer:

So, the answer is 20

Step-by-step explanation:

[tex]f(x) = \frac{1}{2} x + 10 = = = > \\ f(x) - 10 = \frac{1}{2} x = = = > \\ 2f(x) - 20 = x = = = > \\ {f}^{ - 1} (y) = 2y - 20 = = = > {f}^{ - 1} (x) = 2x - 20[/tex]

The missing value of the inverse function is 20.

Option D is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To find the inverse of a function, we usually replace f(x) with y, then solve for x in terms of y, and finally replace y with the inverse function notation h(x).

So let's do that with the given function:

f(x) = (1/2)x + 10

y = (1/2)x + 10

2y = x + 20 (multiply both sides by 2 to isolate x)

x = 2y - 20 (subtract 20 from both sides)

Now we can replace x with h(x) and y with x to get the inverse function:

h(x) = 2x - 20

Thus,

The missing value is 20.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ5

Answer:

okay so I can't see the last option on ur sheet but when u graph this equation the point that lies on the curve is (2,-3) so that is the vertex but if I move up this curved line it passes through the Y axis at (0,-1), the Last answer that I can't see it wouldn't happen to be (-1,6) would it

Answer:

y=55x

Step-by-step explanation:

(y1-y2)/(x1-x2)=(165-55)/(3-1)=55

55 is the slope

To find y-intercept:

y=55x+b

substitute 1 for x and 55 for y

55=55(1)+b

b=0

So y= 55x

the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x. To write the equation of the line that passes through the points (3, 165) and (1, 55), you can use the point-slope form of a linear equation, which is: y - y₁ = m(x - x₁)

where (x₁, y₁) is one of the points on the line, m is the slope of the line.

First, calculate the slope (m) using the given points (3, 165) and (1, 55):

m = (y₂ - y₁) / (x₂ - x₁) = (55 - 165) / (1 - 3) = (-110) / (-2) = 55

Now that you have the slope (m = 55) and one of the points (let's use (3, 165)), you can plug them into the point-slope form:

y - 165 = 55(x - 3)

Now, you can simplify and rewrite this equation in slope-intercept form (y = mx + b):

y - 165 = 55x - 165

To isolate y, add 165 to both sides:

y = 55x

So, the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x.

to know more about equation:

https://brainly.com/question/32543980

#SPJ3

Answer:

No solution

Step-by-step explanation:

Answer:

$16,400

Step-by-step Explanation:

Step 1: We multiply $10,000 by 16%, getting $1,600.

Step 2: We then multiply $1,600 by 4 (which is given). That gives us $6,400.

Step 3: Add that to $10,000. We get $16,400 as the answer!

Answer:

Simple interest = P  x  r  x  t

                         = 10,000  x  16/100  x   4

                         =  $6400

Final amount = P (1 +rt)

                       = 10,000 (1 + 16/100  x  4)

                       = $16400

(or you can just add the simple interest to the principle amount to get the final amount)

The foci of the hyperbola represented by (0, –6) and (0, 6). Then the correct option is B.

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

The equation of the parabola is given below.

5y² – 4x² – 80 = 0

Then the equation can be written as

y² / 4 – x² / 5 – 4 = 0

  y² / 16 – x² / 20 = 1

Then the value of eccentricity will be

a² = 16 and b² = 20

Then we have

e = √[1 + (b² / a²)]

e = √[1 + (20 / 16)]

e = 1.5

Then the focus of the parabola will be

⇒ (0, ±ae)

⇒ (0, ± 4 x 1.5)

⇒ (0, ±6)

⇒ (0, –6) and (0, 6)

Then the correct option is B.

More about the hyperbola link is given below.

https://brainly.com/question/12919612

#SPJ1

Answer:

eyyyyyyyyyy wassupppppppp

Answer:

240%

Step-by-step explanation:

Volume of a prism is Bh (area of the base * height)

Let's start with the small prism.

B=125

h=12

Volume = 125*12 = 1500 cubic cm

Bigger prism base are is 160% of 125. 1.6 * 125 = 200

Height is 6 cm more = 12+6 = 18

V = 200 * 18 = 3600

To find the percentage, divide 3600 by 1500. You get 2.4, which is 240%

Answer:

43

Step-by-step explanation:

because if you add it up thats how you get that

Step-by-step explanation:

look at the attachment above

Answer:

[tex]\textsf{1)} \quad -\dfrac{1}{16}e^{-4x}\left(4x+1\right)+\text{C}[/tex]

[tex]\textsf{2)} \quad - \cos x+\dfrac{2}{3} \cos^3 x - \dfrac{1}{5} \cos^5 x +\text{C}[/tex]

Step-by-step explanation:

Question 1

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration of $e^{ax}$} \\\\$\displaystyle \int e^{ax}\:\text{d}x=\dfrac{1}{a}e^{ax}+\text{C}$\\\\for $a\neq 0$\\\end{minipage}}[/tex]

Given integral:

  [tex]\displaystyle \int xe^{-4x}\:\text{d}x[/tex]

Using Integration by parts:

[tex]\textsf{Let }\:u=x \implies \dfrac{\text{d}u}{\text{d}x}=1[/tex]

[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=e^{-4x} \implies v=-\dfrac{1}{4}e^{-4x}[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x & =uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x\\\\\implies \displaystyle \int xe^{-4x}\:\text{d}x & =-\dfrac{1}{4}xe^{-4x}-\int -\dfrac{1}{4}e^{-4x}\: \text{d}x\\\\& =-\dfrac{1}{4}xe^{-4x}+\int \dfrac{1}{4}e^{-4x}\: \text{d}x\\\\& =-\dfrac{1}{4}xe^{-4x}-\dfrac{1}{16}e^{-4x}+\text{C}\\\\& =-\dfrac{1}{16}e^{-4x}\left(4x+1\right)+\text{C}\end{aligned}[/tex]

Question 2

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\\ \end{minipage}}[/tex]    

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]

Rewrite the given integral:

[tex]\begin{aligned}\displaystyle \int \sin^5 x \: \text{d}x & =\int (\sin x)^4 \cdot \sin x \: \text{d}x\\& =\int (\sin^2 x)^2 \cdot \sin x \: \text{d}x\end{aligned}[/tex]

Use the trig identity  [tex]\sin^2x+\cos^2x \equiv 1[/tex]  to rewrite  [tex]\sin^2x[/tex] :

[tex]\implies \displaystyle \int \sin^5 x \: \text{d}x = \int (1-\cos^2 x)^2 \cdot \sin x \: \text{d}x[/tex]

Integration by substitution

[tex]\textsf{Let }\:u=\cos x \implies \dfrac{\text{d}u}{\text{d}x}=-\sin x \implies \text{d}x=-\dfrac{1}{\sin x}\: \text{d}u[/tex]

Therefore:

[tex]\begin{aligned}\implies \displaystyle \int \sin^5 x \: \text{d}x & = \int (1-u^2)^2 \cdot \sin x \cdot -\dfrac{1}{\sin x}\: \text{d}u\\& = \int -(1-u^2)^2 \: \text{d}u\\ & =\int -1+2u^2-u^4 \: \text{d}u\\& =-u+\dfrac{2}{3}u^3-\dfrac{1}{5}u^5+\text{C}\end{aligned}[/tex]

Finally, substitute  [tex]u = \cos x[/tex]  back in:

[tex]\implies \displaystyle \int \sin^5 x \: \text{d}x=- \cos x+\dfrac{2}{3} \cos^3 x - \dfrac{1}{5} \cos^5 x +\text{C}[/tex]

Answer:

5,208,469

Step-by-step explanation:

5,000,000 + 200,000+ 8,000 + 400+60+9

5,000,000

  200,000

    00,000

       8,000

          400

            60

              9

5,208,469

Answer:

f'(x) = 7x^4 (5 ln(x) + 1) + x^2

Explanation:

[tex]\sf Let \ f(x)=7x^5 ln(x) + \dfrac{1}{3} x^3[/tex]

Properties used while differentiating:

[tex]i) \quad \sf \dfrac{d}{dx} (ln(x)) = \dfrac{1}{x}[/tex]

[tex]ii) \quad \sf \dfrac{d}{dx} (x^n) = n(x)^{n-1}[/tex]

[tex]iii) \quad \sf \dfrac{d}{dx}(uv)=u \dfrac{dv}{dx}+v \dfrac{du}{dx}[/tex]

Begin solving:

f'(x) =

[tex]\Longrightarrow \sf \dfrac{d}{dx}\:\left(7x^5\:ln\left(x\right)\:+\:\dfrac{1}{3}\:\:x^3\right)[/tex]

[tex]\Longrightarrow \sf \dfrac{d}{dx}\:\left(7x^5\:ln\left(x\right)\right) + \dfrac{d}{dx}\left(\dfrac{1}{3}x^3\right)[/tex]

[tex]\Longrightarrow \sf \dfrac{d}{dx}(7x^5)\:\ \times ln\left(x\right) + \dfrac{d}{dx}(ln(x)) \times \ 7x^5 + \left(3\:\times \dfrac{1}{3}x^{3-1}\right)[/tex]

[tex]\Longrightarrow \sf 5(7x^{5-1})\:\times\ ln(x) + \dfrac{1}{x} \:\times\ 7x^5 \ + x^2[/tex]

[tex]\Longrightarrow \sf 35x^{4} ln(x) + \ 7x^4 \ + x^2[/tex]

[tex]\Longrightarrow \sf 7x^4(5 ln(x) + 1) \ + x^2[/tex]

Answer:

[tex]4\sqrt{26}[/tex]

Step-by-step explanation:

The distance formula is [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].

Thus we can plug the numbers in:

[tex]\sqrt{(-2-(-6))^2+(10-(-10))^2}[/tex]

[tex]\sqrt{(4)^2+(20)^2}[/tex]

[tex]\sqrt{16+400}[/tex]

[tex]\sqrt{416}[/tex]

[tex]4\sqrt{26}[/tex]

Answer:

Step-by-step explanation:

volume of a cuboid = Length × Width × Height Cubic units

6 × 11 × 6 =

66 * 6 =

396 Km³

to the nearest hundred

400 Km³

Answer:  A B C

Step-by-step explanation:

A whole number is like 1,500 and a nonwhole number is like 33.2 or like 55/100.  

And have a good day.

Answer:

all of the above

Step-by-step explanation:

please mark me as brainliest