While testing a new pesticide, an agricultural scientist uses two functions to predict the yields of two same-sized potato farms that have different soil conditions. The scientist's predicted yield, in tons, of the first farm can be represented by the following function, where x is the liters of pesticide he uses per acre of the farm. His predicted yield, in tons, of the second farm can be represented by the following function, where x is the liters of pesticide he uses per acre of the farm. If the scientist uses the same amount of pesticide on the two farms, select the function that accurately represents the predicted combined yield from both farms.
f(x)= -2.43x^2+10.37x+9 and g(x)= -3.43^2+13x+25


A. h(x)= -5.86x^2 + 23.37x + 34
B. h(x)= -5.86x^2 + 2.63x + 34
C. h(x)= -x^2 + 2.63x + 16
D. h(x)= x^2 + 2.63x - 16

Answer:

8 years

Step-by-step explanation:

Use formula

[tex]I=P\cdot r\cdot t,[/tex]

where

I = interest

P = principal

r = rate (as decimal)

t = time

In your case,

I = $175.84

P = $314

r = 0.07, then

[tex]175.84=314\cdot 0.07\cdot t\\ \\175.84=21.98t\\ \\t=\dfrac{175.84}{21.98}\\ \\t=8[/tex]

The question asks for the duration of an investment. We use the formula for simple interest to solve this. By plugging the known values into the rearranged formula for time, we can find the duration of the investment.

The question asks for how long the principle was invested if you received $175.84 on $314 invested at a rate of 7%. The calculation is based on the formula for simple interest, which is I = PRT (Interest = Principal x Rate x Time). From the question, we know that the Interest (I) is $175.84, the Principal (P) is $314, and the Rate (R) is 7% or 0.07 when expressed as a decimal.

We need to find the Time (T), which can be rearranged from the formula as T = I / (P x R). By plugging the values into this formula, we get T = 175.84 / (314 x 0.07). Solving for T will give the time period the money was invested for.

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Answer:

D.) 7:3

Step-by-step explanation:

First, find the LCM of the numbers, which is 8.

Then divide each number by 8

56÷8=7 24÷8= 3

Then, put them in a ratio

7:3

Answer:

A

Step-by-step explanation:

Right now, our ratio of male to female is 24:56. We need to reduce this, kind of like how you would reduce a fraction. 24÷8=3 and 56÷8=7, so our new ratio is 3:7.

Answer:

Step-by-step explanation:

4x = 38

x= 38/ 4

x = 9 1/2

The question is incomplete and the figure is missing. Here is the complete question with the figure attached below.

In the figure, sin ∠MQP = ______.

A. Cos N and Sin R

B. Sin R and Sin N

C. Cos N and Sin M

D. Cos R and Sin N

Answer:

D. Cos R and Sin N

Step-by-step explanation:

Given:

∠MQP = 56°

sin (∠MQP) = sin (56°)

Consider the triangle NMR,

m ∠N = 56°, m ∠R = 34°

sin (∠N) = sin (56°)

So, sin (∠MQP) = sin (∠N) = sin (56°) ---------- (1)

Now, we know that, [tex]\sin x=\cos(90-x)[/tex]

Therefore, sin (∠N) = sin (56°) = cos (90°-56°) = cos (34°)

Now, from the same triangle NMR,

[tex]\cos (\angle R)=\cos (34\°)[/tex]

Therefore, sin (∠N) = cos (∠R)  ------------- (2)

Hence, from equations (1) and (2), we have

sin (∠MQP) = sin (∠N) = cos (∠R)

So, option D is correct.

The Academy Awards, also known as Oscars, are prestigious awards recognizing achievements in the film industry. The OscarsSoWhite controversy raised concerns about diversity and representation in Hollywood.

Academy Awards, commonly known as Oscars, are prestigious awards in the film industry recognizing outstanding achievements in various categories. The controversy surrounding the OscarsSoWhite highlighted issues about diversity and representation in Hollywood.

Answer:

Area of parallelogram is equal to the product of base and height, the area is the product of [tex]\pi r[/tex] and r, or [tex]\pi r^{2}[/tex].

Step-by-step explanation:

We are finding the area of a circle by an alternative method.

What we do is split the circle into multiple sectors and then arrange them in the form of a parallelogram and find the area of this parallelogram.

Area of parallelogram = base[tex]\times height[/tex]

Hence area is the product of base and height.

Base = [tex]\pi r[/tex]

Height = r

Area is the product of [tex]\pi r[/tex] and r = [tex]\pi r^{2}[/tex]

                                   Question #15

Step-by-step explanation:

A notation such as [tex]T_{(-1, 1)}oR_{y-axis}[/tex] is read as:

"a translation of (x, y) → (x - 1, y + 1) after a reflection across y-axis.

The rule of reflection of point (x, y) across y-axis brings (x, y) → (-x, y), meaning that y-coordinate remains the same, but x-coordinate changes its sign.

As ΔABC with coordinates A(1, 3), B(4, 5) and C(5, 2). Here is the coordinates of ΔA'B'C' after the glide reflection described by [tex]T_{(-1, 1)}oR_{y-axis}[/tex].

                                            [tex]R_{y-axis}[/tex]                                   [tex]T_{(-1, 1)}[/tex]  

A(1, 3)              →                A'(-1, 3)               →                    A"'(-2, 4)

B(4, 5)             →                B'(-4, 5)               →                    B"'(-5, 6)

C(5, 2)             →                C'(-5, 2)               →                    C"'(-6, 3)

                                        Question #16

Step-by-step explanation:

A glide reflection is said to be a transformation that involves a  translation followed by a reflection in which every  point P is mapped to a point P ″ by the following steps.

As ΔABC with coordinates A(-4, -2), B(-2, 6) and C(4, 4).

Translation : (x, y)  → (x + 2, y + 4)

Reflection : in the x-axis

The rule of reflection of point (x, y) across x-axis brings (x, y) → (x, -y), meaning that x-coordinate remains the same, but y-coordinate changes its sign.

Hence,

ΔABC with coordinates A(-4, -2), B(-2, 6), C(4, 4) after (x, y)  → (x + 2, y + 4) and reflection in the x-axis.

A(-4, -2)         →     A'(-2, 2)     →     A''(-2, -2)    

B(-2, 6)          →    B'(0, 10)       →     B''(0, -10)

C(4, 4)            →    C(6, 8)         →      C''(6, -8)

Keywords: reflection, glide reflection, translation

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Answer:

to find how much taller Chiquita’s completed snowman is than Rhonda's completed Snowman  

We divide the Height of the Chiquita’s snowman by the height of Rhonda’s Snowman

 i.e. 7.456/8.532 = 0.87

Step-by-step explanation:

Let Vr1 be the volume of Rhonda’s first ball, and Vc1 be the volume of Chiquita’s first ball. Since the balls are spheres the formula for obtaining their Volume value is given as   V= (4/3) x ∏ r3  

Since from the question we were told that the first snowball for Rhonda and Chiquita’s Snowman are the same.

Let’s assume that the Vr1 =Vc1=10m²  

So to find the radius we make r the subject of formula so r =∛(3V/4∏)  where V is equal to 10 for the first spheres and ∏  is a constant with value 3.142 so  

r1 = ∛(3×10/4)×3.142   = 1.337m

For the Second Snow ball of Rhonda’s Snowman  

Given from the question that first Snow ball is 20% less than the Second Snow Ball

Let Vr2 Denote the volume of the second Rhonda’s Snowball  

Vr2 = 20% of Vr1 + Vr1

       = 20% of 10 + 10

       = (20/100) x 10 + 10

       = 12m²

So to find the radius of the second ball for Rhonda’s Snowman

Let r2 denote the radius of the second ball  

 r2 = ∛(3×12/4)×3.142   = 1.420m

For the Third Snow ball of Rhonda’s Snowman  

Given from the question that Second Snow ball is 20% less than the Third Snow Ball

Let Vr3 denote the volume of the third Rhonda’s Snowball

Vr3 = 20% of Vr2 +Vr2  

             = (20/100) x 12 +12

             = 14.4m²

  So to find radius of the Third ball for Rhonda’s Snowman

Let r3 denote the radius of the second ball  

  r3 =  ∛(3×14.4/4)×3.142   = 1.509m

For the Second Snow ball of Chiquita’s Snowman  

Given from the question that first Snow ball is 20% greater than the Second Snow Ball

Let Vc2 denote the volume of the second Chiquita’s Snowball

For   Vc2 = Vc1 - 20% of Vc1

               = 10 – (20/100) x 10

So to find the radius of the second ball for Chiquita  

Let c2 denote the radius of the second ball  

c2 =    ∛(3×8/4)×3.142   =1.240m

For the Third Snow ball of Chiquita’s Snowman  

Given from the question that Second Snow ball is 20% greater than the third Snow Ball

Let Vc3 denote the volume of the third Chiquita’s Snowball

For Vc3 = Vc2 - 20% of Vc2

             = 8 – (20/100) x 8

             = 6.4m²

So to find the radius of the second ball for Chiquita  

Let c3 denote the radius of the second ball  

  c3 =∛((3×6.4/4)×3.142)   = 1.151m

Therefore Height of Rhonda’s Snowman = Dr1 + Dr2 + Dr3  

          = 2×r1 +2×r2 +2×r3

          = (2×1.337) + (2×1.420) + (2×1.509)

         = 8.532m

Therefore the Height of Chiquita’s Snowman = Dc1 + Dc2 +Dc3

       = 2×c1 +2×c2 +2×c3

       = (2×1.337) + (2×1.240) + (2×1.151)

      = 7.456m

No to find how much taller Chiquita’s completed snowman is than Rhonda's completed Snowman  

We divide the Height of the Chiquita’s snowman by the height of Rhonda’s Snowman

 i.e. 7.456/8.532 = 0.87

Note: if we assume another value for Vr1 = Vc1 we will still get the same ratio.

Answer:

The width of the Iphone 11 pro max is 3.36 in.

Step-by-step explanation:

since both iPhones are proportional, you will need to find the ratio of what their proportion is to one another. the length of one iphone is 5.2, and the length of the other iphone is 6.24. Therefore, the ratio of proportion to each other would be 5.2/ 6.24. to find the width of the iphone 11 pro max, you will need to use the following equation: 5.2/6.24 x 2.8/? (unknown side)      

this gives you the equation 6.24 x 2.8 = 5.2 x ?  (unknown side)

(the question mark is the unknown side of the iphone 11 pro max)

6.24 x 2.8 / 5.2 = ? (unknown side)

therefore the unknown side of the iphone 11 pro max is 3.36 in.

By using the concept of proportions, the width of the iPhone 11 Pro Max, when it's proportional to iPhone 11 Pro, is approximately 3.36 inches.

The given problem involves finding a proportional measurement. The iPhone 11 pro has dimensions 5.2 inches (length) and 2.8 inches (width). If the iPhone 11 Pro Max is proportional in size and has a length of 6.24 inches, we can find its width using the ratio between the length and the width of the iPhone 11 pro.

We will set up a proportion like this:

[tex]5.2/2.8 = 6.24/x[/tex]

Where x is the width of the iPhone 11 Pro Max. Solving for x will give us the width:

[tex]2.8 * 6.24 = 5.2 * x\\x = (2.8 * 6.24) / 5.2[/tex]

After solving this equation, we find that the width of the iPhone 11 Pro Max is approximately 3.36 inches.

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Answer:

122

Step-by-step explanation:

6x+3y-4=6(20)+3(2)-4=120+6-4=126-4=122

Answer:

y=3/2 x + 5

Step-by-step explanation:

[tex]y = mx + c[/tex]

Firstly, find m (gradient).

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

m= 8-(-1)/ 2-(-4)

m= 9/ 6

m= 3/2

Please leave gradient in improper fraction if its value is not a whole number.

Now substitute m into the equation:

y= 3/2 x + c

Then substitute a coordinate to find c:

When y= 8, x= 2,

8= 3/2 (2) + c

8= 3 + c

c= 8 - 3 = 5

Thus, the equation of the line is y= 3/2 x + 5.

Answer:

6.2 miles per hour

Step-by-step explanation:

Given: Philip ran 200 feet.

           Time taken is 22 seconds.

First lets find out speed of Philip.

Speed= [tex]\frac{distance}{time}[/tex]

∴ Speed= [tex]\frac{200}{22} \ ft/sec[/tex]

Speed= 9.09 ft/sec.

Now, converting speed feet per second to miles per hours.

Remember, 1 miles= 5280 ft and 1 hours= 3600 seconds.

∴ Speed in miles per hour= [tex]9.09\times \frac{\frac{1}{5280} }{\frac{1}{3600} }[/tex]

⇒ Speed in miles per hour= [tex]9.09\times \frac{3600}{5280}[/tex]

⇒Speed in miles per hour= [tex]9.09\times 0.68= 6.19 \frac{mi}{h}[/tex]

∴ Philip ran at a speed of 6.2 miles per hour(nearest tenth decimal).

Answer: Each cup has 4 blueberries and 5 raspberries.

Step-by-step explanation:

Since we have given that

Number of blueberries = 36

Number of raspberries = 45

We need to find the number of each type if she wants to put an equal number of blueberries and an equal number of raspberries into each cup.

So, H.C.F. of 36 and 45 = 9

So, Number of blueberries would be

[tex]\dfrac{36}{9}=4[/tex]

Number of raspberries would be

[tex]\dfrac{45}[9}=5[/tex]

Hence, each cup has 4 blueberries and 5 raspberries.

Answer:

[tex]\large\boxed{if\ x\neq-3\ \wedge\ y\neq0\ \wedge\ x\neq y\ \wedge\ x\neq -y}[/tex]

second

[tex]\large\boxed{y\neq0\ \wedge\ x\neq-y\ (y\neq-x)}[/tex]

Step-by-step explanation:

We know that dividing by 0 is impossible.

Therefore, the denominator of the expression must be different from 0.

[tex]\text{For}\\\\\dfrac{(x-y)^2}{2xy+6y}\times\dfrac{4x+12}{x^2-y^2}\\\\\\2xy+6y\neq0\qquad(1)\\\\x^2-y^2\neq0\qquad(2)[/tex]

[tex](1)\\2xy+6y\neq0\qquad\text{distribute}\\\\2y(x+3)\neq0\iff2y\neq0\ \wedge\ x+3\neq0\\\\2y\neq0\qquad\text{divide both sides by 2}\\\boxed{y\neq0}\\\\x+3\neq0\qquad\text{subtract 3 from both sides}\\\boxed{x\neq-3}\\==========================\\(2)\\x^2-y^2\neq0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\(x-y)(x+y)\neq0\iff x-y\neq0\ \wedge\ x+y\neq0\\\boxed{x\neq y}\ \wedge\ \boxed{x\neq-y}[/tex]

[tex]\text{For}\\\\\dfrac{2(x-y)}{y(x+y)}\\\\y(x+y)\neq0\iff y\neq0 \wedge\ x+y\neq0\\\\ \boxed{y\neq0}\ \wedge\ \boxed{x\neq-y}[/tex]

x=y+3 and 30x+80y=640 is the system of equations for given statement where x represents the number of commercials and y represent the number of movies on which Anna's songs were played.

Step-by-step explanation:

Given,

Earning for song played in commercial one time= $30

Earning for song played in movie one time = $80

Let,

x represent the number of  commercials Anna's song played.

y represent the number of movies Anna's song played.

According to given statement;

Anna's songs were played on 3 more commercials than movies

x=y+3    

her total earnings on the royalties from all commercials and movies was $640.

30x+80y=640

x=y+3 and 30x+80y=640 is the system of equations for given statement where x represents the number of commercials and y represent the number of movies on which Anna's songs were played.

Keywords: linear equation, substitution method

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Final answer:

To solve the question, two variables are defined: c for commercials and m for movies. The system of equations is $30c + $80m = $640 and c = m + 3, representing Anna's royalties from commercials and movies.

Explanation:

The student's question involves creating a system of equations to determine the number of commercials and movies on which Anna, a songwriter who collects royalties, had her songs played. We are given that Anna earns $30 from each commercial and $80 from each movie her songs are played in. It is also known that her songs were played in 3 more commercials than movies, and she earned a total of $640. To formulate the system of equations, we introduce two variables: let c represent the number of commercials and m represent the number of movies.

The first equation represents the total earnings based on the number of plays:
$30c + $80m = $640.

The second equation represents the relationship between the number of commercials and movies:
c = m + 3.

Combining these two equations gives us a system that can be solved to find the values of c and m.

By substituting the second equation into the first equation, we can create a system of equations:

30(M + 3) + 80M = 640

30M + 90 + 80M = 640

110M + 90 = 640

110M = 550

M = 5

Now that we have found the number of movies (M = 5), we can substitute this value back into the equation C = M + 3 to find the number of commercials:

C = 5 + 3

C = 8

The third angle will be: 30°

Step-by-step explanation:

Amy is cutting a triangle so we know that the sum of interior angles of a triangle is 180 degrees

She has already cut two angles of 75 degrees, which means she has cut a total of 150 degrees

So,

Let x be the third angle then the sum of all angles will be: 150+x

So,

[tex]150+x = 180\\x = 180-150\\x = 30[/tex]

Hence,

The third angle will be: 30°

Keywords: Angles, triangle

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Answer:

30*

Step-by-step explanation:

Answer:

x = - 6z

Step-by-step explanation:

The equation of quantities in direct variation is

y = kx ← k is the constant of variation

Here k = - 6, thus

x = - 6z ← equation of variation

Jayden ran [tex]\frac{6}{25}[/tex] of a kilometers in one minute

Solution:

Given that Angel and Jayden were at track practice

The track is two-fifth kilometers around

[tex]\text{ track length } = \frac{2}{5} \text{ kilometers}[/tex]

Angel ran 1 lap in 2 minutes

Jayden ran 3 laps in 5 minutes

To find: distance ran by Jayden in 1 minute

3 laps were run by Jayden in 5 minutes

3 laps = 5 minutes

"x" laps = 1 minute

Therefore laps run by Jayden in one minute is:

On cross multiplication we get,

5x = 3

[tex]x = \frac{3}{5}[/tex]

Therefore Jayden ran [tex]\frac{3}{5}[/tex] laps in 1 minute

Distance covered is:

Total track length = [tex]\frac{2}{5} \text{ km}[/tex]

Distance ran in 1 minute = [tex]\frac{3}{5} \times \frac{2}{5} = \frac{6}{25}[/tex]

Thus Jayden ran [tex]\frac{6}{25}[/tex] of a kilometers in one minute

Answer:

1 / (1 + x²)

Step-by-step explanation:

Derivative of a function by first principle is:

[tex]f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]

Here, f(x) = tan⁻¹ x.

[tex]f'(x)= \lim_{h \to 0} \frac{tan^{-1}(x+h)-tan^{-1}x}{h}[/tex]

Use the difference of arctangents formula:

[tex]tan^{-1}a-tan^{-1}b=tan^{-1}(\frac{a-b}{1+ab})[/tex]

[tex]f'(x)= \lim_{h \to 0} \frac{tan^{-1}(\frac{x+h-x}{1+(x+h)x} )}{h}\\f'(x)= \lim_{h \to 0} \frac{tan^{-1}(\frac{h}{1+(x+h)x} )}{h}[/tex]

Next, we're going to use a trick by multiplying and dividing by 1+(x+h)x.

[tex]f'(x)= \lim_{h \to 0} \frac{tan^{-1}(\frac{h}{1+(x+h)x} )}{h}\frac{1+(x+h)x}{1+(x+h)x} \\f'(x)= \lim_{h \to 0} \frac{1}{1+(x+h)x} \frac{tan^{-1}(\frac{h}{1+(x+h)x} )}{\frac{h}{1+(x+h)x}}[/tex]

We can now evaluate the limit.  We'll need to use the identity:

[tex]\lim_{x \to 0} \frac{tan^{-1}x}{x} =1[/tex]

This can be shown using squeeze theorem.

The result is:

[tex]f'(x)= \lim_{h \to 0} \frac{1}{1+(x+h)x}\\\frac{1}{1+x^2}[/tex]

Answer:

[tex]Hypotenuse=10[/tex]

Step-by-step explanation:

For this exercise you can use the following Trigonometric Identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

Let be "x" the hypotenuse of this right triangle.

You can identify from the figure that, in this case:

[tex]\alpha=60\°\\\\opposite=5\sqrt{3}[/tex]

Then, knowing these values you can substitute them into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:

[tex]sin(60\°)=\frac{5\sqrt{3}}{x}[/tex]

Finally, you need to solve for "x" in order to find the lenght of the hypotenuse.

This is:

[tex]x*sin(60\°)=5\sqrt{3}\\\\x=\frac{5\sqrt{3}}{sin(60\°)}\\\\x=10[/tex]

Answer:

x = -2

y = 3

Step-by-step explanation:

Since y = 3x +9, substitute this value in the first eq.

4x + 5(3x+9) = 7 ===> 4x + 15x + 45 = 7 ===> 19x = 7-45 ==> 19x = -38 ===>

===> x -38/19 ===> x = -2

Replace this value in the second eq.

y = 3(-2) + 9 ===> y = -6 + 9 ===> y = 3

Answer:

Cotton Gin

Explanation:

A cotton gin – meaning "cotton engine" – is a machine that quickly and easily separates cotton fibers from their seeds, enabling much greater productivity than manual cotton separation.[1] The fibers are then processed into various cotton goods such as linens, while any undamaged cotton is used largely for textiles like clothing. The separated seeds may be used to grow more cotton or to produce cottonseed oil.

Handheld roller gins had been used in the Indian subcontinent since at earliest AD 500 and then in other regions.[2] The Indian worm-gear roller gin, invented sometime around the 16th century,[3] has, according to Lakwete, remained virtually unchanged up to the present time. A modern mechanical cotton gin was created by American inventor Eli Whitney in 1793 and patented in 1794. Whitney's gin used a combination of a wire screen and small wire hooks to pull the cotton through, while brushes continuously removed the loose cotton lint to prevent jams. It revolutionized the cotton industry in the United States, but also led to the growth of slavery in the American South as the demand for cotton workers rapidly increased. The invention has thus been identified as an inadvertent contributing factor to the outbreak of the American Civil War.[4] Modern automated cotton gins use multiple powered cleaning cylinders and saws, and offer far higher productivity than their hand-powered precursors.[5]

Eli Whitney invented his cotton gin in 1793. He began to work on this project after moving to Georgia in search of work. Given that farmers were desperately searching for a way to make cotton farming profitable, a woman named Catharine Greene provided Whitney with funding to create the first cotton gin. Whitney created two cotton gins: a small one that could be hand-cranked and a large one that could be driven by a horse or water power.

The invention from the late 1700s is Cotton Gin. It was invented by Eli Whitney in 1793.

A cotton gin means “cotton engine”. It is a machine that quickly and easily sorts cotton fibers from their seeds, enabling much larger productivity than manual cotton separation.

Eli Whitney began to work on this project after moving to Georgia in search of work. At that time, farmers were desperately searching for a way to make cotton farming profitable.

The fibers of cotton are then processed into various cotton goods such as linens, while undamaged cotton is used largely for textiles like clothing. The separated seeds may be used to grow more cotton or to produce cottonseed oil.

Therefore, Cotton Gin is an invention from the late 1700s.

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Answer:

[tex] - {x}^{2} + x + 24[/tex]

Step-by-step explanation:

Subtract the functions:

[tex]f - g = (36 - {x}^{2} ) - (8 - x)[/tex]

Simplify:

[tex](36 - {x}^{2} ) - (8 - x) \\ 36 - {x}^{2} - 8 + x \\ - {x}^{2} + x + 24[/tex]

Answer:

x= [tex]-2\pm \sqrt{11}[/tex]

Step-by-step explanation:

Here is the correct question: Using the quadratic formula to solve

x²+4x - 7. what are the values of x.

Solving by using quadratic formula.

Formula: [tex]\frac{-b\pm \sqrt{b^{2}-4(ac) } }{2a}[/tex]

∴  In the expression [tex]x^{2} +4x-7[/tex], we have a= 1, b= 4 and c= -7.

Now, subtituting the value in the formula.

=[tex]\frac{-4\pm \sqrt{4^{2}-4(1\times -7) } }{2\times 1}[/tex]

= [tex]\frac{-4\pm \sqrt{4^{2}-4(-7) } }{2}[/tex]

Opening parenthesis.

= [tex]\frac{-4\pm \sqrt{16+28 } }{2\times 1}[/tex]

= [tex]\frac{-4\pm \sqrt{44}}{2}[/tex]

We know 2²=4

= [tex]\frac{-4\pm \sqrt{2^{2}\times 11 }}{2}[/tex]              

we know √a²=a

= [tex]\frac{-4\pm 2 \sqrt{11 }}{2}[/tex]

Taking 2 as common in the expression.

= [tex]\frac{2(-2\pm \sqrt{11}) }{2}[/tex]

Cancelling 2

= [tex]-2\pm \sqrt{11}[/tex]

Hence we get, [tex]x=-2\pm\sqrt{11}[/tex]

Answer: 6

Step-by-step explanation: First rewrite 10 as 10/1 and 1 and 2/3 as 5/3.

Mixed numbers can be changed to improper fractions by multiplying the denominator by the whole number and then adding the numerator. We then put out numerator over our old denominator.

So we have 10/1 ÷ 5/3 or 10/1 × 3/5.

It's important to understand that dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division to multiplication and flip the second fraction.

Now multiplying across the numerators and across the denominators, we have 30/5. Notice however that 30/5 is not in lowest terms so we divide the numerator and the denominator by the greatest common factor of 30 and 5 which is 6 and we end up with 6.

Therefore, 10 ÷ 1 and 2/3 = 6.

Final answer:

To find 10 divided by 1 2/3, convert the mixed number to an improper fraction (5/3), multiply by the reciprocal (3/5), and simplify the result to get 6.

Explanation:

To divide 10 by 1 2/3, first, we need to convert the mixed number 1 2/3 into an improper fraction. The mixed number 1 2/3 can be written as 5/3 because 1 (which is 3/3) plus 2/3 equals 5/3.

Next, we apply the rule for dividing fractions: we multiply by the reciprocal of the divisor. So, we take 10 (which is the same as 10/1) and multiply it by the reciprocal of 5/3, which is 3/5.

The multiplication looks like this: 10/1 × 3/5 = 30/5.

The result of 30/5 can be simplified to 6, which is the answer in simplest form. Therefore, 10 divided by 1 2/3 equals 6.

Answer:

Length of the envelope = 14

Width of the envelope = 5.6

Step-by-step explanation:

Let the width of the rectangle be  x

Then the length of the rectangle will be [tex]2\frac{1}{2} \times x[/tex]

Also the length of the plastic band to cover the  front and back of the envolpe =  [tex]39\frac{3}{8}[/tex]

To cover one side th band required is

=>[tex]\frac{39\frac{3}{8}}{2}[/tex]

=>[tex]\frac{\frac{315}{8}}{2}[/tex]

=>[tex]\frac{\frac{315}{8}}{2}[/tex]

=>[tex]{\frac{315}{16}[/tex]

=>39.4

We know that the perimeter of the rectangle is

=> 2( L + B) = [tex]{\frac{39.4}{2}[/tex]

=> 2( [tex]2\frac{1}{2} \times x + x[/tex]) = 19.7

=> 2( [tex]\frac{7}{2}x) = 19.7 [/tex]

=>  [tex]3.5x = 19.7 [/tex]

=> [tex] x = \frac{19.7}{3.5} [/tex]

=>  [tex]x = 5.6[/tex]

Now length of the envelope =

=>  [tex]2\frac{1}{2} \times x [/tex]

=>  [tex] 2.5 \times 5.6 [/tex]

=> 14

The problem involves setting up a relationship equation using the width and length of a rectangle and solving the equation to find the width and length. The length of the plastic band is given, which helps in creating the equation.

In this problem, the rectangular envelope has its length, which is 2 1/2 times the width. There is a plastic band that wraps around the envelope and it is given that the total length of this plastic band is 39 3/8 inches. Thus, the length of the plastic band is equal to twice the length of the envelope plus twice the width of the envelope.

Let us denote the width of the envelope by w. Therefore, the length of the envelope is 2.5w. Setting up an equation using this information, we have: 2*(2.5w) + 2w = 39 3/8. Simplifying this equation, we get: 5w + 2w = 39 3/8, 7w = 39 3/8. To find the width, we can divide both sides of the equation by 7, yielding w = 39 3/8 / 7.

Having calculated the width, the length is simply 2.5 times this value. Therefore, we have found both the width and length of the rectangle envelope.

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Answer:

The greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.

Step-by-step explanation:

Given:

A group can rent pairs of skis and snowboards by the week. They get a reduced rate if they rent 7 pairs of skis for every 3 snowboards rented. The reduced ski rate is $45.50 per pair of skis per week, and the reduced snowboard rate is $110 per snowboard per week.

The sales tax on each rental is 16%.

The group has $2,500 available to spend on ski and snowboard rentals.

If the ratio of pairs of skis to snowboards is 7:3.

Now, to find the greatest number of pairs of skis and snowboards rentals.

So, the rent of 7 pairs of skis = [tex]7\times 45.50=\$318.50.[/tex]

And the rent of 3 pairs of snowboards = [tex]3\times 110=\$330.[/tex]

So, total rental amount of 7 pairs of skis and 3 pairs of snowboards:

[tex]318.50 + 330 = 648.50.[/tex]

Now, to get the rental amount after sales tax:

648.50 + 16% of $648.50.

[tex]=648.50 +\frac{16}{100}\times 648.50.[/tex]

[tex]=648.50+103.76[/tex]

[tex]=\$752.26.[/tex]

The total rental amount after sales tax = $752.26.

As the group has available $2,500.

So, the sets according to the given ratio:

[tex]2500\div 752.26 = 3.32.[/tex]

[tex]=3\ sets.[/tex]

Thus, there are 3 sets of the ratio 7:3.

So, the rental price according to sets are:

The rent of Skis:

[tex]7\times 3 = 21[/tex] 

[tex]21\times 45.50= 955.50[/tex]

The rent of snowboards:

[tex]3\times 3 = 9[/tex]

[tex]9\times 110 = 990[/tex]

So. the total rental amount of skis and snowboards according to sets are:

[tex]955.50 + 990 = 1,945.50[/tex]

Now, the amount of rent after sales tax:

$1945.50 + 16% of $1945.50.

[tex]=1945.50+\frac{16}{100}\times 1945.50[/tex]

[tex]=1945.50+311.28=\$2256.78.[/tex]

Thus, the total cost = $2256.78.

Now, to get the greatest number of pairs of skis to snowboards that can be rent:

[tex]2,500 - 2,256.78 = 243.22[/tex]

The cost of 21 pair of skis and 9 pairs of snowboards is $2256.78 and the group has available only $2500 to spend.

Thus, they can rent only 21 pairs of skis and 9 pairs of snowboards.

Therefore, the greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.

Answer:

Step-by-step explanation:

Answer:

about 11 years

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=?\ years\\ P=\$4,000\\ A=\$8,000\\r=9\%=9/100=0.09[/tex]

substitute in the formula above

[tex]8,000=4,000(1+0.09t)[/tex]

solve for r

[tex]2=(1+0.09t)[/tex]

[tex]0.09t=2-1[/tex]

[tex]0.09t=1[/tex]

[tex]t=11.1\ years[/tex]