calculate the shaded area

Answer:  x = {-1, 1, -i√2, i√2, -3, 4}

Step-by-step explanation:

(x² - 1)(x² + 2)(x + 3)(x - 4)(x+1)=0

Set each factor equal to zero and solve.

x² - 1 = 0  →  x² = 1  →  x = ±1

x² + 2 = 0  →  x² = -2  →  x = ± i√2

x + 3 = 0  →  x = -3

x - 4 = 0  →  x = 4

x + 1 = 0  →  x = -1   (note that -1 is a duplicate - solved from the first factor)

Answer:

Answer:  x = {-1, 1, -i√2, i√2, -3, 4}

Step-by-step explanation:

Answer:

1.58

Step-by-step explanation:

Okay. We're solving for t because we need to know how many seconds. From the problem, we know the height (10), but we don't know when that height happens.

[tex]10 = -16tx^{2} -7t+61[/tex]

We can factor by multiplying -16 by 61 first to get -976 and see what multiplies to get -976 AND adds to get -7 at the same time. But we can also use the quadratic formula because, let's be honest, factoring can be a lot of extra work.

[tex]10 = -16t^{2} -7t+61\\\\0 = -16t^{2} -7t+51\\\\t=\frac{-b\pm \sqrt{b^{2}-4ac } }{2a} \\=\frac{-(-7)\pm \sqrt{(-7)^{2}-4(-16)(51) } }{2(-16)} \\=\frac{7\pm \sqrt{49+64(51) } }{-32} \\=\frac{7\pm \sqrt{3313} }{-32}[/tex]

Plug both the plus and the minus versions into your calculator and...

[tex]t\approx -2.02, 1.58[/tex]

There's no such thing as negative time, so -2.02 is automatically disqualified, leaving 1.58 as the answer.

Hope this helps, let me know if I missed anything!

The time takes for the egg to reach the height 10 feet from the ground on the basis of the given quadratic equation will be 1.58 seconds.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

For example, 3x² + 6x + 8 = 0 here x has the highest term as 2 and the coefficient of x² is not zero.

As per the given quadratic equation,

d = - 16t² - 7t + 61

The time t in seconds at d = 10

-16t² - 7t + 61 = 10

16t² + 7t - 51 = 0

The roots of the above quadratic equation will be,

t = [-7 ± √(7² - 4 × 16 × -51 )] /(2 × 16)

t = (-7 ± 57.586)32

t = 1.58 or -2.02

Since, time is always positive thus, t = 1.58 seconds.

Hence "The time takes for the egg to reach the height 10 feet from the ground on the basis of the given quadratic equation will be 1.58 seconds".

For more about the quadratic equation,

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➷ 12x - 8 = 24

Add 8 to both sides:

12x = 32

Divide both sides by 12 to isolate x:

x = 8/3

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Answer: x= 8/3

Step-by-step explanation:

first thing u do is add 8 to the 24 because the operation in front is - , that equals 32

since 12 is multiplied by x you divide 12 by 32 to get x by itself and that equals 8/3

Hope this helps mark me brainliest

7x - 3/8 = 6x -5/8

Subtract 6x from each side:

x - 3/8 = -5/8

Add 3/8 to each side:

x = -5/8 + 3/8

x = -2/8

x = -1/4

Answer:

1/2

Step-by-step explanation:

if the one line's slope is m = –2, then the perpendicular line's slope will be m= 1/2 (the slope of a perpendicular line is the reciprocal of the slope of the first line)

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

I will call [tex]m_{a}[/tex] the slope of line [tex]a[/tex], and [tex]m_{b}[/tex] the slope of line [tex]b[/tex].

For two lines to be perpendicular, the following must be satisfied:

[tex]m_{a}*m_{b}=-1[/tex]

in this case we know:

[tex]m_{a}=-2[/tex]

so:

[tex](-2)*m_{b}=-1[/tex]

And clearing for the slope of line [tex]b[/tex]:

[tex]m_{b}=\frac{-1}{-2} \\m_{b}=\frac{1}{2}[/tex]

The slope of the line [tex]b[/tex] which is perpendicular to line [tex]a[/tex] is [tex]\frac{1}{2}[/tex]

70% × 413 =

(70 ÷ 100) × 413 =

(70 × 413) ÷ 100 =

28,910 ÷ 100 =

289.1

Proof

289.1 ÷ 413 =

0.7 =

0.7 × 100/100 =

0.7 × 100% =

(0.7 × 100)% =

70%

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Answer:

Step-by-step explanation:

s = sequence

[tex]s_{1}[/tex] = first term of sequence

[tex]s_{1}[/tex] = 7

[tex]s_{4}[/tex] = 16

Find the difference between the term number and the values.

Terms:

4 - 1 = 3

Values:

16 - 7 = 9

For every 3 terms, you add 9.

Divide, to find the amount you add for 1 terms.

3 / 3 = 1

9 / 3 = 3

For every 1 terms, you add 3.

[tex]s_{1}[/tex]= 7

[tex]s_{2}[/tex]= 10

[tex]s_{3}[/tex]= 13

[tex]s_{4}[/tex]= 16

[tex]s_{5}[/tex]= 19

[tex]s_{6}[/tex]= 22

Answer:

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

y= 2/3x - 4/3

Step-by-step explanation:

If we want a line parallel to  y=2/3x+7, it will have the same slope

m = 2/3

We have a point (-1,-2), so we can use point slope form

y-y1 = m(x-x1)

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

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

If we want the line in slope intercept form, distribute the slope

y+2 = 2/3 x +2/3

Subtract 2 from each side

y+2-2=2/3x +2/3-2

y = 2/3x +2/3 - 6/3

y= 2/3x - 4/3

This is valid.

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Answer:

V = 60

Step-by-step explanation:

Yes, it is

Best regards

Answer:

yes that is that is that is the right answer hope u get all your homework right

Step-by-step explanation:

Answer:67

Step-by-step explanation:

Answer:

Part a) The exterior surface area is equal to [tex]160\ ft^{2}[/tex]

Part b) The volume is equal to [tex]240\ ft^{3}[/tex]

Part c) The volume water left in the trough will be [tex]84\ ft^{3}[/tex]

Step-by-step explanation:

Part a) we know that

The exterior surface area is equal to the area of both trapezoids plus the area of both rectangles

so

Find the area of two rectangles

[tex]A=2[12*5]=120\ ft^{2}[/tex]

Find the area of two trapezoids

[tex]A=2[\frac{1}{2}(8+2)h][/tex]

Applying Pythagoras theorem calculate the height h

[tex]h^{2}=5^{2}-3^{2}\\h^{2}=16\\h=4\ ft[/tex]

substitute the value of h to find the area

[tex]A=2[\frac{1}{2}(8+2)(4)]=40\ ft^{2}[/tex]

The exterior surface area is equal to

[tex]120\ ft^{2}+40\ ft^{2}=160\ ft^{2}[/tex]

Part b) Find the volume

we know that

The volume is equal to

[tex]V=BL[/tex]

where

B is the area of the trapezoidal face

L is the length of the trough

we have

[tex]B=20\ ft^{2}\\ L=12\ ft[/tex]

substitute

[tex]V=20(12)=240\ ft^{3}[/tex]

Part c)

step 1

Calculate the area of the trapezoid for h=2 ft (the half)

the length of the midsegment of the trapezoid is (8+2)/2=5 ft

[tex]A=\frac{1}{2}(5+2)(2)=7\ ft^{2}[/tex]

step 2

Find the volume

The volume is equal to

[tex]V=BL[/tex]

where

B is the area of the trapezoidal face

L is the length of the trough

we have

[tex]B=7\ ft^{2}\\ L=12\ ft[/tex]

substitute

[tex]V=7(12)=84\ ft^{3}[/tex]

when all goes wrong...choose c my friend.

Answer:

2m/s

2 meters per second

Step-by-step explanation:

Formula for speed is distance (meters) over time (seconds) after you divide you get 2. Please give me the brainliest answer?

:) Hoped this helped!!! Have a good day!!! <3

Answer:

2 Meters per second

Step-by-step explanation:

Answer: OPTION D

Step-by-step explanation:

To solve this problem you must apply the formula for calculate  the surface area of the rectangular prism:

[tex]SA=2(wh+lw+lh)[/tex]

Where w is the width, h is the heigh and l is the lenght.

Based on the rectangular prism shown, you have that:

[tex]w=9.08cm\\h=3.23cm\\l=11.73cm[/tex]

Finally when you substitute values into the formula you obtain the following result:

[tex]SA=2[(9.08cm*3.23cm)+(11.73cm*9.08cm)+(11.73cm*3.23cm)]=347.45cm^2[/tex]

Answer:

D

Step-by-step explanation:

The surface area is the area of all the surfaces, together.

A rectangular prism has 6 rectangular surfaces. We need to add those 6 faces and sum it.

Area = 2 ( 3.23 * 9.08 ) = 58.6568

Area = 2 ( 3.23 * 11.73 ) = 75.7758

Area = 2 ( 11.73 * 9.08 ) = 213.0168

Summing all of them up,

Surface area of Rectangular Prism = 58.6568 + 75.7758 + 213.0168

=347.4494

* Rounding to nearest hundredth, 347.45 cm ^2

Answer:

y = 6

Step-by-step explanation:

Given

y = [tex]\frac{3}{4}[/tex] x + 3 and (4, ? )

Substitute the x- coordinate x = 4 into the equation for corresponding value of the y- coordinate.

x = 4 : y = [tex]\frac{3}{4}[/tex] × 4 + 3 = 3 + 3 = 6

Hence the coordinate point is (4, 6)

Answer:

e=23

Step-by-step explanation:

The equation representing this scenario is e-5=18.

Add 5 to both sides and you get e=23 (eggs)

Answer:

e=23

Step-by-step explanation:

Answer: 10%

Step-by-step explanation: The formula to calculate simple interest is Interest = Principal x Rate x Time

With the number in the formula, 112.50 = 1,250 x r x 1

Simplify:

112.50 = 1,250r

Divide both sides by 1,250:

.1 = r

Therefore, the rate is 10%

Answer:

V=8xxxyyy=8x³y³

Step-by-step explanation:

In the question, V=lwh, the value for l is given to us as 2xy. Because it is a cube, all of the length of the edges are the same, so l=w=h, which means w=2xy and h=2xy.

Plug in w=2xy h=2xy l=2xy into the equation V=lwh.

V=2xy·2xy·2xy

V=(2·2·2)(x·x·x)(y·y·y)

V=8xxxyyy=8x³y³

Answer:

π/64

Step-by-step explanation:

assuming that c= circumference, and the circumference being 2πr(radius), then r=1/8 because 2π/8=π/4. to find the area, we use the formula πr^2, or π*1/8^2, or π/64

Answer: 2/6.

Step-by-step explanation:

This might be wrong but because there are only 6 sides on a number cube, and only two numbers between this probablity this is the most likely correct answer. I apologize if this is wrong.

Answer:

D

Step-by-step explanation:

An exponential function which crosses through (1,3) and (2,9) will have a base of 3 since the y values are multiples of 3.

3^1 = 3

3^2 = 9

This means that the function is y = 3^x.

Answer:   b) (x - 2)(x + 1)(x + 3) = 0

Step-by-step explanation:

Look at the graph to find the x-intercepts (where the graph crosses the x-axis).

x = 2,       x = -1,      and   x = -3

Rewrite them as factors:

x - 2 = 0,  x + 1 = 0, and  x + 3 = 0

Combine the factors through multiplication:

(x - 2) (x + 1) (x + 3) = 0

Answer:

The information given represents lengths of sides of a right triangle with c the hypotenuse. Find the correct missing length to the nearest hundredth. A calculator may be helpful.

a = 18, b = 26, c = ?

A. C=31.78

B. C=31.16

C. C=31.62

D. C=31.46

Step-by-step explanation:

[tex]\sqrt{18^{2}+26^{2}  }[/tex]

the answer is 28

have a good day!

[tex]\huge\text{$x=\boxed{\frac{1}{5}}$}[/tex]

Hey there! To solve this problem, we need to isolate [tex]x[/tex] on one side of the equation.

[tex]\begin{aligned}5(3x+4)&=23\\5\cdot3x+5\cdot4&=23&&\smash{\Big|}&&\text{Distribute the $5$.}\\15x+20&=23&&\smash{\Big|}&&\text{Multiply.}\\15x&=3&&\smash{\Big|}&&\text{Subtract $20$ from both sides.}\\x&=\frac{3}{15}&&\smash{\Big|}&&\text{Divide both sides by $15$.}\\x&=\boxed{\frac{1}{5}}&&\smash{\Big|}&&\text{Divide the numerator and denominator by $3$.}\end{aligned}[/tex]

Answer:

[tex] x = \frac { 1 } { 5 } [/tex]

Step-by-step explanation:

We are given the following equation and we are to find the value of x by making it the subject of the equation:

[tex] 5 ( 3 x + 4 ) = 23 [/tex]

We will start by opening the brackets and expanding the term by multiplying 5 with the terms inside the brackets to get:

[tex] 15 x + 20 = 23 [/tex]

[tex] 15 x = 23 - 20 [/tex]

[tex] 15 x = 3 [/tex]

[tex] x = \frac { 3 }  { 15 } [/tex]

[tex] x = \frac { 1 } { 5 } [/tex]

Answer:

About $31,200

Step-by-step explanation:

Answer:

Completing the square.

Step-by-step explanation:

since there is no "a" term and the bx term is even, completing the square is your best bet.

For this case we have as a simpler method the factorization. We must find two numbers that multiplied as a result +3 and added as a result +4.

These numbers are:

3 and 1.[tex]3 + 1 = 4\\\\3 * 1 = 3[/tex]

So, we have to:

[tex]x ^2 + 4x + 3 =\\(x + 3) (x+1)[/tex]

Answer:

[tex](x + 3) (x + 1)[/tex]

Answer: C

Step-by-step explanation: An open line of credit is a line of credit against which additional debt may be drawn. An open credit line allows you to borrow money against the credit line at different times. You can borrow against it up to the credit limit.

Answer:

[tex]4(3\frac{2}{5})[/tex] is greater

Step-by-step explanation:

step 1

we have

[tex]4(3\frac{2}{5})[/tex]

convert to an improper fraction

[tex]3\frac{2}{5}=\frac{3*5+2}{5}=\frac{17}{5}[/tex]

so

[tex]4(3\frac{2}{5})=4(\frac{17}{5})=\frac{68}{5}[/tex]

step 2

we have

[tex]3(4\frac{2}{5})[/tex]

convert to an improper fraction

[tex]4\frac{2}{5}=\frac{4*5+2}{5}=\frac{22}{5}[/tex]

so

[tex]3(4\frac{2}{5})=3(\frac{22}{5})=\frac{66}{5}[/tex]

therefore

[tex]4(3\frac{2}{5})[/tex] is greater

Final answer:

After converting mixed numbers to improper fractions and multiplying, it is clear that 4 x [tex]3\frac{2}{5}[/tex] is greater than 3 x [tex]4\frac{2}{5}[/tex].

Explanation:

The question asks which is greater: 4 x [tex]3\frac{2}{5}[/tex] or 3 x [tex]4\frac{2}{5}[/tex]. Let's compare these two expressions

First, convert the mixed numbers to improper fractions:

[tex]3\frac{2}{5}[/tex] = (3x5 + 2)/5 = 17/5

[tex]4\frac{2}{5}[/tex] = (4x5 + 2)/5 = 22/5

Next, multiply each by the whole number:

4 x 17/5 = 68/5 = 13.6

3 x 22/5 = 66/5 = 13.2

Therefore, 4 x [tex]3\frac{2}{5}[/tex] is greater than 3 x [tex]4\frac{2}{5}[/tex].