Alice plants carrots in a rectangular garden bed. The garden bed has a width of 1.5
meters and an area of 6 square meters. Which equation and solution correctly represent
2, the length, in meters, of the rectangular garden bed?



Help

Method used:-

Completing the square method.

Steps :-

[tex]( x - 1 ) ( x + 2 ) = - 2\\x^{2}+x-2=-2 \\x^{2}+x=-2+2 \\x^{2}+x=0[/tex]

Now, make the left hand side of the equation by adding the square of ½ to both sides of the equation.

[tex]x^{2}+x+\left(\frac{1}{2}\right)^{2}=\left(\frac{1}{2}\right)^{2} \\x^{2}+x+\frac{1}{4}=\frac{1}{4} \\\left(x+\frac{1}{2}\right)^{2}=\frac{1}{4} \\\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}} \\[/tex]

Simplify the equation. You'll get a +ve & -ve value.

[tex]x+\frac{1}{2}=\frac{1}{2} \\x+\frac{1}{2}=-\frac{1}{2}[/tex]

Simplify it further.

[tex]\boxed{\sf\:x=0}\\ \boxed{\sf\:x=-1 }[/tex]

The solutions are :-

x = 0 & x = -1

______

Hope it helps ⚜

Answer:

Okay, to graph this equation we need to graph the y-intercept first.  This time its 7 for you, meaning 0,7.  So graph (0,7) as your first point.  Then we have your slope, which is -2/3`.  So, from (0,7) we will do rise/run.  So, our next point will be (3,5).  We went down 2 and ran 3.  Since its negative, we went DOWN.

-

if you want a third point, just ask!

-

Hope this helps.

-

<3

Answer:6_1/4

Step-by-step explanation:

They are different by a multiple of 3, for example, 3_1/4 * 3 = 9_3/4, etc.

This means that you just have to divide 18_3/4 bu 3, which is 6_1/4

If 2 angles are formed on a line, then they make a supplementary / linear pair of angles, i.e, both the angles form 180°.

Here,

Angle A = 80°

Angle B = x°

So,

Angle A + Angle B = 180°

80° + x° = 180°

x° = 180° - 80°

x° = 100°

=》 Angle B = 100°

_____

Hope it helps ⚜

Step-by-step explanation:

the first step in my opinion would be find the norm(s) in this scenario.

100 pounds is a good norming weight.

the speed of these 100 pounds with a 10 HP motor is

50ft/30sec = 5/3 ft/s

so, then let's ask next what size of motor is needed to lift the same 100 pounds 40 ft in 40 seconds

40ft/40sec = 1 ft/s

to get the same speed as in the first case the motor need to be weaker (to move slower). and that goes by the same factor as the ratio between the 2 speeds :

5/3×f = 1

f = 3/5

10 HP × f = 10 × 3/5 = 30/5 = 6 HP

so, it takes a 6 HP motor to lift these same 100 pounds 40 ft in 40 seconds.

and now, how strong must the motor be to lift 800 pounds (= 8 times the original 100 pounds) with the same speed ?

well, 8 times

8×6 = 48 HP

so, it would take a 48 horsepower motor to lift 800 pounds 40 ft in 40 seconds.

the equation would then be

HP = p/100 × 6 = 6p/100 = 3p/50

HP = horsepower

p = pounds

the rest I cannot really answer, as I don't know your class and it's contents.

I hope I covered the topics of your class with that solution.

Answer:

x=1.2

Step-by-step explanation:

2(5x-4)=4

distribute 2 to 5x and -4

10x-8=4

add 8 to negative 8 and 4

10x=12

now divide both sides by 10

10x/10= 12/10

x=1.2

The value of x for the logarithmic expression will be x=1.2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is log2(5x-4)=4. The value of x will be calculated as,

2(5x-4)=4

Distribute 2 to 5x and -4,

10x-8=4

Add 8 to negative 8 and 4,

10x=12

Now divide both sides by 10,

10x/10= 12/10

x=1.2

Therefore, the value of x for the logarithmic expression will be x=1.2.

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Answer: I think its C

Step-by-step explanation:

Answer: NO GAIN for the shopkeeper

Step-by-step explanation:

20/100 *5000=1000

Answer:

492.99

Step-by-step explanation: x = amount invested at 12%

y = amount invested at 9%

---

x + y = 20287

0.12x = 0.09y + 492.99

---

put the system of linear equations into standard form

---

x + y = 20287

0.12x - 0.09y = 492.99

The amount invested at 14% is $4144 and the amount invested at 12% is $9894.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

We are given that;

Investment at 14%= $14,038

Investment at 12%= $984.34

Now,

Let x be the amount invested at 14% and y be the amount invested at 12%. Then we have:

x + y = 14038 (total amount invested)

0.14x - 0.12y = 984.34 (difference in interest)

We can solve this system of equations by substitution or elimination. For example, by elimination, we can multiply the first equation by 0.12 and subtract it from the second equation to get:

0.02x = 82.88

x = 4144

Then we can plug x into the first equation and get:

y = 14038 - 4144

y = 9894

Therefore, the simple interest will be $4144 and $9894.

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Answer:

what kind kind of prob

Step-by-step explanation:

dp you have a Story

Answer:

there is no picture to explain your qustion and im confused

Step-by-step explanation:

Answer:

x > -1

Step-by-step explanation:

-10 < x - 9

Add 9 to each side

-10+9 < x - 9+9

-1 < x

x > -1

Answer:

Step-by-step explanation:

- 10 < x - 9

- 10 + 9 < x - 9 + 9

- 1 < x

x > - 1

Answer:

1/2, or 0.5

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

(f/g)(5)=

f(5)=(5)2+1÷g(5)=5-4

10+1/1

11/1

(f/g)=11

The required simplified value of the given function as (f/g)(5)  is 26.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
f(x) = x² +1

f(5) = 5² + 1
f(5) = 26

g(x) = x - 4
g(5) = 5 - 4 = 1

f/g(5) = f(5) / g(5)
       = 26 / 1 = 26

Thus, the required simplified value of the given expression (f/g)(5)  is 26.

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Answer:

$8,698.50

Step-by-step explanation:

289.95x30= $8,695.50

Answer:

D

Step-by-step explanation:

[tex]y = 3\sqrt{2}[/tex]

Just use pythagorean theorem, very simple.

c = [tex]\sqrt{a^{2}+b^{2} }[/tex]

In your case c is y

your answer calculated will come out to 4.24 but put in terms your teacher wants will be

[tex]y = 3\sqrt{2}[/tex]

Answer:

9 quarters and 14 nickles

The number of quarters is 9.

The number of nickels is 14.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

Number of quarters = x

Number of nickels = y

Now,

1 quarter = $0.25

1 nickel = $0.05

Two equations are:

x + y = 23 ____(1)

x = 23 - y _____(2)

0.25x + 0.05y = 2.95 _______(3)

Putting (2) in (3) we get,

0.25(23 - y) + 0.05y = 2.95

5.75 - 0.25y + 0.05y = 2.95

5.75 - 2.95 = 0.20y

2.8 = 0.20y

y = 2.8/0.20

y = 14

Now,

x + y = 23

x = 23 - 14

x = 9

Thus,

There are 9 quarters and 14 nickels.

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Answer:

50-2

Step-by-step explanation:

there is 50 donuts and 2 that are frosted :)

Step-by-step explanation:

2 have frosting, therefore 50-2 = 48 don't.

so, the ratio is for frosting vs. non-frosting

2 : 48 (which would be also 1 : 24).

Answer:

65.4 degrees

Step-by-step explanation:

cos(x) = 5/12

x = arccos(5/12), which is approximately  65.3756816 (on calculator). to the nearest tenth that is 65.4

Complementary angles have a submission of 90 degrees thus :

[tex]angle \: \: A + angle \: \: B = 90°[/tex]

[tex](4x - 28)° + (4x - 8)° = 90°[/tex]

[tex]4x + 4x - 28 - 8 = 90[/tex]

Collect like terms

[tex]8x - 36 = 90[/tex]

Add both sides 36

[tex]8x - 36 + 36 = 90 + 36[/tex]

[tex]8x = 126[/tex]

Divide both sides by 8

[tex] \frac{8x}{8} = \frac{126}{8} \\ [/tex]

[tex]x = 15.75[/tex]

_____________________________________________

Now let's find the measure of A :

[tex]A = 4x - 28[/tex]

[tex]A = 4 \times (15.75) - 28[/tex]

[tex]A = 63 - 28[/tex]

[tex]A = 35°[/tex]

And we're done...

Don't have a good day , Have a great day ♡

Answer:

|279|

Step-by-step explanation:

so when ur doing absolute value you js need distance so lets work with the problem, if ur 279 feet below water u would need to get to zero feet below sea level (ground lvl) to do so how many feet towards ground lvl would u go? (279 clearly) so the distance from how many feet under u are to the ground lvl is ur absolute value.

Tbh in school they over complicate it if u need an absolute number from a negative number like -279 (as it is in the problem) you would js make it a positive (if its positive 279 u js say the absolute value is 279)

(also the absolute value is the distance between the number and zero so yh u can put that)

Your Question is incomplete..

Diana is baking bread, and the original recipe calls for 1 1/2 teaspoons of yeast and 2 1/2 cups of flour. Diana will use the entire contents of a packet that contains 2 1/4 teaspoons of yeast and will use the same ratio of ingredients called for in the original recipe. How many cups of flour will Diana use?

Answer:

3 3/4

Step-by-step explanation:

To figure out how many cups of flour Diana will use, you can set up a proportion.

1 1/2 = 3/2

2 1/2 = 5/2

2 1/4 = 9/4

Floor required for 3/2 teaspoons of yeast = 5/2

Floor required for 9/4 teaspoons of yeast = (5/2 / 3/2) * 9/4

= 5/2 * 2/3 * 9/4

= 15/4 = 3 3/4

Answer:

(The question is not complete so I will complete it)

Diana is baking bread, the original recipe calls for 1 1/2 teaspoons of yeast and 2 1/2 cups of flour. Diana will use the entire contents of a packet that contains 2 1/4 teaspoons of yeast and will use the same ratio of ingredients called for in the original recipe. How many cups of flour will diana use ?

A) 1 7/8

B) 3 1/2

C) 3 1/2

D) 3 3/4

E) 4

Step-by-step explanation:

The correct answer is D

To figure out how many cups of pour diana will use, you can set up a proportion

1 1/2 = 3/2

2 1/2 = 5/2

2 1/4 = 9/4

Flour required for 9/4 teaspoons of yeast = (5/2 / 3/2) * 9/4

= 5/2 * 2/3 * 9/4

= 15/4 = 3 3/4

Answer: D) 3 3/4

The amount that should deposit monthly is $164.98

The formula for calculating the compound amount is expressed as:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Substitute the given values into the formula to have:

[tex]75000=P(1+\frac{0.075}{12} )^{12(18)}\\75000 = P(1.00625)^{216}\\75000 =P(3.84125)\\P = \frac{75000}{3.84125}\\P= \$19,524.89[/tex]

Hence the amount of money they started with is $19,524.89.

Amount to deposit monthly = 19,524.89/120

Amount to deposit monthly = $164.98

Hence the amount that should deposit monthly is $164.98

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Answer:

y = 4 (-3) - 2

y = -12 - 2

y = -14

Step-by-step explanation:

Answer:

The abstract science of number, quantity, and space. Mathematics may be studied in its own right ( pure mathematics ), or as it is applied to other disciplines such as physics and engineering ( applied mathematics )..

Ex :- Plus , minus

Mathematics is a very important field of study in human society that can be described as the study of:

Mathematics is a science and one that is constantly evolving to allow us better understand our surroundings.

There are several ways to study the subjects described above such as by applying them to things such as engineering and other sciences, or simply studying them on their own.

In conclusion, math is a science of numbers.

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Answer:

32 large lemonades

Step-by-step explanation:

4 gallons = 512 ounces

512 ounces / 16 ounces

= 32 large lemonades.

Answer:

1. 27

2. 48

3. 40

Step-by-step explanation:

3 to the power of 2 is 9 (3×3)

9×3=27. (8-5=3)

6 to the power of 2 is 36 (6×6)

36+12=48. (4×3=12)

42-2=40

Answer:

Step-by-step explanation:

It is a parrallelogram, the two lines are Parallel to each other meaning they will never cross each other

The given xy- plane is a parallelogram.

A plane figure is called a parallelogram when it have four sides, in which opposite sides are parallel to each other and each side is equal in length to its opposite side.

If [tex](x_{1},y_{1} })[/tex] and [tex](x_{2},y_{2})[/tex] are the two points then the distance between these points is given by

[tex]d=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1} ) ^{2} }[/tex]

Where, d is the distance between two points.

According to the given question

We have a plane figure PSTO

And the coordinates of points P, S, T, and O are (a, b), (a + c, b), (c, 0) and (0,0) respectively.

Now, the length of the sides by distance formula

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

PS = [tex]\sqrt{c^{2}+0 }[/tex]

PS = c

Similarly,

ST =[tex]\sqrt{(a+c-c)^{2}+(b-0)^{2} }[/tex]

ST = [tex]\sqrt{a^{2} +b^{2} }[/tex]

TO = [tex]\sqrt{(c-0)^{2}+(0-0)^{2} }[/tex]

TO = [tex]\sqrt{c^{2} }[/tex]

TO = c

And, PO = [tex]\sqrt{(a-0)^{2}+(b-0)^{2} }[/tex]

PO = [tex]\sqrt{a^{2} +b^{2} }[/tex]

From the above calculation we found that

PS = TO

PO = ST

⇒ Length of the  opposite sides of the plane figure are equals.

And from the given figure we can see that the opposite sides are also parallel to each other.

Therefore, the given xy- plane is a parallelogram.

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