Joe wants to add cucumbers to his garden and knows the rectangular area is represented by x^2 - 4x - 21 square units. What expressions would represent the length and width of the cucumber field?

Answers

Answer 1

Given:

The area of rectangular garden is [tex]x^2-4x-21[/tex] square units.

To find:

The length and width of the cucumber field.

Solution:

The area of a rectangle is:

[tex]A=l\times w[/tex]

Where l is length and w is width of the rectangle.

The area of rectangular garden is [tex]x^2-4x-21[/tex] square units.

We need to find the factors of [tex]x^2-4x-21[/tex] to get the length and width.

[tex]A=x^2-4x-21[/tex]

Splitting the middle term, we get

[tex]A=x^2-7x+3x-21[/tex]

[tex]A=x(x-7)+3(x-7)[/tex]

[tex]A=(x-7)(x+3)[/tex]

Area of a rectangle is the product of length and width.

Therefore, the length and width of the rectangle are [tex](x-7)[/tex] units and [tex](x+3)[/tex] units.


Related Questions

two significant figures, 18.96 x 2.03 is

Answers

is there a picture that comes w this problem?

Please help I don’t understand

Answers

Answer:

8/15

Step-by-step explanation:

The ratio of perpendicular to base is tan B .

Here ,

=> tan B = 8 ft/ 15ft

=> tan B = 8/15

Help and explain please and thank you !!!!!!!

Answers

Answer:

[tex]q = 3[/tex]

Step-by-step explanation:

[tex]3q−2=7[/tex]

[tex]3q=7+2[/tex]

[tex]3q=9[/tex]

[tex]q = \frac{9}{3} [/tex]

[tex]q = 3[/tex]

Hope it is helpful....
Option C is correct. The other person is wrong. They forgot the two lines flip the equation. This is an equation that can be solved. Look at the picture below to understand the simplified steps. Give brainiest plz. I have never had it before. Thx.

how do you solve 2x+320=425

Answers

you need to invert each operation so first start by subtracting 320 from each side that leaves 2x=120 then divide each side by 2 to get x by itself leaving the answer as x=60

Answer:

how to solve your problem

Step-by-step explanation:

2x320=425

subtract both 320 both from sides of the equation

2x+320-320=425-320

subtract numbers

2x=105

divide both sides of equation by the same terms

2x/2=105/2

simplify

x=105/2

answer is x=105/2

Determine if the conditional statement is true or false given the following: p is false. q is false. Is -q -p true or false?

Answers

Hello,

if p is false then ~p is true

if q is false then ~q is true

if ~p is true and ~q is true then ~q and ~p is true

How can an expression written in either radical form or rational exponent form be rewritten to fit the other form? Explain thoroughly and thank you for your time.

Answers

Answer:

Step-by-step explanation:

We'll start with going form exponential to radical, since it may be easier to follow. For example,

[tex]x^{\frac{4}{3}[/tex] can be written, in radical form, as

[tex]\sqrt[3]{x^4}[/tex]. What happens is that the denominator of the fraction serves as the index (the number that sits in the bend of the radical) and the numerator serves as the power on the variable (or number, if that's the case). Let's look at another one:

[tex]4^{\frac{2}{3}[/tex] becomes

[tex]\sqrt[3]{4^2}=\sqrt[3]{16}=\sqrt[3]{8*2}=2\sqrt[3]2}[/tex]

And you can go the other way with it. For example,

[tex]\sqrt[5]{x^4}[/tex] becomes

[tex]x^{\frac{4}{5}[/tex], etc. Get it?

Answer:

When you're given a problem in radical form, you may have an easier time if you You can rewrite every radical as an exponent by using the following property — the top ... For example, 643/2 is easier if you write it as (641/2)3 = 83 = 512 rather than (643)1/2,  Rewrite the entire expression using rational exponents.

If the vertex of a parabola is (-4, 6) and another point on the curve is (-3, 14), what is the coefficient of the squared expression in the parabola's equation?

Answers

Answer:

[tex]y=a(x-h)^{2} +k[/tex]

[tex](x,y)=(-3,14)[/tex]

[tex](h,k)=(-4,6)[/tex]

[tex]14=a(-3-(-4))^{2})+6[/tex]

[tex]14=a(-3+4)^{2} +6[/tex]

[tex]14=a(1)^{2} +6,-6[/tex]

[tex]8=a[/tex]

[tex]ANSWER:8[/tex]

--------------------------

HOPE IT HELPS

HAVE A GREAT DAY!!

Which applies the power of a power rule properly to simplify the expression (710)5?

Answers

Answer:

I45

Step-by-step explanation:

In how many ways the word CHAMPION can be arranged without repetition of there are no conditions?​

Answers

149 (give brainliest for all of the words)

What number line model represents the expression 5 1/2 + (-3)

Answers

Answer:

(A)

Step-by-step explanation:

The bottom arrow goes to 5 1/2, and then because adding -3 is the same as subtracting 3, the top arrow correctly goes back 3, resulting in an answer of 2 1/2.

Hope it helps (●'◡'●)

factories ((x+2)+3x+6. 2a(a-1)-a+1​

Answers

Answer:1. = 4x+8  

2. 2a²-a+1

Step-by-step explanation:

1. ((x+2)+3x+6.  2. 2a(a-1)-a+1​

((x+2)+3x+6

= x+2+3x+6

= 4x+8

2a(a-1)-a+1

2a²-2a-a+1

2a²-a+1

The mass of the moon is 7.343 × 10^19 tonnes. The Earth has a mass of 81 times bigger than that of the moon. Work out the mass of the Earth.

Answers

Answer:

= 7. 343 × 10^19 ×81

= 1.377 × 10^21

7^9 = ????? My daughter needs help with this really quick!

Answers

Answer: 40353607

Step-by-step explanation:

[tex]7^9\\[/tex] = 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 = 40353607

You borrow $25,000 to buy a boat. The simple interest rate is 4%. You pay the loan off after 10 years. What is the total amount you paid for the loan?

Answers

Answer:

$35000

Step-by-step explanation:

A = P(1+rt)

A = 25000*(1+4%*10)

A = 35000

BRAINLIEST PLEASEEEEEEEEEEE

Find the length of side xx in simplest radical form with a rational denominator.

Answers

Answer:

Solution given:

Relationship between perpendicular and hypotenuse is given by sin angle

Sin 30°=opposite/hypotenuse

½=[tex]\frac{x}{9}[/tex]

x=[tex]\frac{9}{2}[/tex]

The value of x is [tex]\frac{9}{2}[/tex]

a^2-2(a+b)-b^2 plz can anyone solve this factorization​

Answers

Step-by-step explanation:

Hope it helps If u have any confusion regarding this kindly inform me , i will try my best to answer

[tex]\tt\displaystyle\ \star a^2-b^2=(a-b)(a+b)\star\\\\ a^2-2(a+b)-b^2=a^2-b^2-2(a+b)=\\\\\underline{(a+b)}(a-b)-2\underline{(a+b)}=\boxed{(a+b)(a-b-2)}[/tex]

Factor the expression (-x^2 + 5x + 24.), and use the factors to find the x-intercepts of the quadratic relationship it represents.

Type the correct answer in each box, starting with the intercept with the lower value.

The x-intercepts occur where x =
and x =
.

Answers

Answer:

[tex]{ \bf{let \: \: { \tt{ - {x}^{2} + 5x + 24} \: \: be \: \: { \bf{{y}}}}}} \\ { \tt{y = - {x}^{2} + 5x + 24 }} \\ { \tt{y = (x + 3)(x - 8)}} \\ for \: x - intercept : y = 0 \\ { \tt{(x + 3)(x - 8) = 0}} \\ { \bf{x = - 3 \: and \: 8}}[/tex]

The factors to the given expression are -1(x+3)(x-8)

The x-intercepts are -3, 8

What do we mean by factorization?

Factorization is the process in which we write an expression in its factors which when multiplied results in the original expression.

How do we factorize the given expression?

We equate the given expression to f(x)

     (-x² + 5x + 24) = f(x)

⇒ -1(x² - 5x - 24) = f(x)

⇒ -1(x² - (8-3)x - 24) = f(x)

⇒ -1(x² + 3x - 8x -24) = f(x)

⇒ -1(x(x+3) -8(x+3)) = f(x)

⇒ -1(x+3)(x-8) = f(x)

∴The factor to the given expression is -1(x+3)(x-8)

How do we find the x-intercepts?

To find the x-intercepts we equate f(x) = 0

⇒ -1(x+3)(x-8) = 0

⇒ (x+3)(x-8) = 0

x-intercepts are the roots of the above equation.

∴ The x-intercepts occur where x = -3 and x = 8

Learn more about the Factorization and x-intercepts at

https://brainly.com/question/11579257

https://brainly.com/question/3951754

#SPJ2

How many miles are equivalent to 800 meters? Round answer to the nearest hundredth.

0.50 miles

1.29 miles

2.62 miles

4.97 miles

Answers

Answer:

0.5miles

Step-by-step explanation:

800meters is 0.497097miles

Round 0.497097miles to the nearest hundredth which would be 0.5 miles.

Can someone help me with this math homework please!

Answers

Answer:

[tex]j = - 0.45[/tex]

Step-by-step explanation:

Combine like terms and apply the rules of algebra.

[tex]2.25 - 11j - 7.75 + 1.5j = 0.5j - 1[/tex]

[tex] - 5.5 - 9.5j = 0.5j - 1[/tex]

[tex] - 9.5j = 0.5j + 4.5[/tex]

[tex] - 10 j= 4.5[/tex]

[tex]j = - 0.45[/tex]

Answer: j = -0.45

Step-by-step explanation:

Step 1: Combine like terms

2.25 - 11j - 7.75 + 1.5j = 0.5j - 1

-5.5 - 9.5j = 0.5j - 1

Step 2: isolate your variable

-5.5 - 9.5j = 0.5j - 1

Subtract 0.5j from both sides

-5.5 - 10j = -1

Add 5.5 to both sides

-10j = 4.5

Divide both sides by -10

j = -0.45

PLS HELP ASAP HOW DOES THIS= THIS

f(x)=2x^3-9x^2+11x-20....

look at photo.
true or false

Answers

Answer:

false

Step-by-step explanation:

Write the equation of the line passing through the points (−2,3) and (−1,−2) in Slope-Intercept and Point-Slope Form.

Answers

Point slope form is y-3 = -5( x + 2 )

Slope intercept form is y= -5x - 7

SOMEBODY PLEASE ILL GIVE BRAINLIEST AND FREE ROUBUX

Answers

Answer:

The y-coordinate is 4. The point is (2,4)

Step-by-step explanation:

The point is 4 units above the x axis.

Answer:

y-coordinate=4

Step-by-step explanation:

A baseball league is holding registration for both a men's league and a women's league. Only a total of 400 players can register, and each team consists of exactly 10 players. If 24 women's teams have already registered, which inequality could be used to find m, the number of men's teams that can register?
A.
24(10) + 10m < 400

B.
24(10) + 10m > 400

C.
24(10 + 10m) > 400

D.
24(10 + 10m) < 400

Answers

the correct answer is b

Find the length of side xx in simplest radical form with a rational denominator.

Answers

Answer:

Solution given:

it is a right angled isosceles triangle

so

perpendicular [p]=base[b]=3

hypotenuse [h]=x

we have

by using Pythagoras law

p²+b²=h²

3²+3²=h²

18=h²

h=[tex]\sqrt{18}[/tex]

x=[tex]\bold{3\sqrt{2}}[/tex]

someone help me with my algebra homework please

Answers

Answer:

D.

Step-by-step explanation:

x = number of glasses of iced tea

y = number of glasses of lemonade

The total number of glasses is

x + y

The total number of glasses is 44

x + y = 44

This is not a choice, but the answer must be equivalent to this equation.

Solve for x by subtracting y from both sides.

x = 44 - y

Answer: D.

Solve for X.

-8x - 4(x - 4) = 88

Please show work

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]\huge x=-6[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\-8x-4(x-4)=88\\-------------\\\rightarrow -8x-4x+16=88\\\\\rightarrow -12x + 16 = 88\\\\\rightarrow -12x + 16 - 16 = 88 - 16\\\\\rightarrow -12x = 72\\\\\rightarrow \frac{-12x=72}{12}\\\\\rightarrow \boxed{x=-6}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer: x = -6

Step-by-step explanation: Start by changing the - 4 to plus a negative 4 so that you know you're distributing a -4 through the parentheses.

So we have -8x - 4x + 16 = 88.

Simplifying the left side further gives us -12x + 16 = 88.

Now subtract 16 from both sides to get -12x = 72.

From here it should be easy to find the x = -6.

Please help I don't understand this at all

Answers

Answer:

The answer is 48in

Step-by-step explanation:

I am pretty sure you add all the numbers together

Maria has 72 flowers and four vases she put the same number of flowers in each vase how many flowers are in one vase

Answers

The answer is 18. Divide 72 by four.

College national study finds that students buy coffee from a coffee shop on average 12 times a week, I believe it may be different for UML students. I collect data from a sample of 36 UML students and find that they buy coffee on average 8 times a week, with a standard deviation of 6 days. What is the T value for this data, and can you reject the null?

Answers

Answer:

The t-value for this data is -4.

The p-value of the test is 0.0003 < 0.05, which means that the null hypothesis can be rejected.

Step-by-step explanation:

College national study finds that students buy coffee from a coffee shop on average 12 times a week, I believe it may be different for UML students.

At the null hypothesis, we test if the mean is of 12, that is:

[tex]H_0: \mu = 12[/tex]

At the alternative hypothesis, we test if the mean is different of 12, that is:

[tex]H_1: \mu \neq 12[/tex]

The test statistic is:

We have the standard deviation for the sample, so the t-distribution is used to solve this question.

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

12 is tested at the null hypothesis:

This means that [tex]\mu = 12[/tex]

I collect data from a sample of 36 UML students and find that they buy coffee on average 8 times a week, with a standard deviation of 6 days.

This means that [tex]n = 36, X = 8, s = 6[/tex]

Value of the test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{8 - 12}{\frac{6}{\sqrt{36}}}[/tex]

[tex]t = -4[/tex]

The t-value for this data is -4.

P-value of the test:

Considering a standard significance level of 0.05.

Test if the mean is different from a value, so two-tailed test, with 36 - 1 = 35 df and t = -4. Using a t-distribution calculator, the p-value is of 0.0003.

The p-value of the test is 0.0003 < 0.05, which means that the null hypothesis can be rejected.

Which is a simplified form of the expression -4(n + 1) – (n + 2)?
A. 2n + 3
B. -3n - 2
C. -4n - 5
D. -5n - 6

Answers

Answer:

the answer is D

Answer:

D. - 5n - 6

Step-by-step explanation:

- 4 ( n + 1 ) - ( n + 2 )

= - 4n - 4 - n - 2

= - 4n - n - 4 - 2

= - 5n - 6

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