Brad has a garden with dimensions 12 feet long x 7 feet wide. He wants to enlarge the garden to an area of 119 square feet. How much farther will he need to extend the length of the garden to attain his desired area?

Answer:

x = -9

Step-by-step explanation:

find x for -3 + x = 2 (x+3)

-3 + x = 2 (x + 3) <== distribute

-3 + x = 2x + 6 <== subtract 1x from both sides

   -x     -x

-3 = x + 6 <== subtract 6 from both sides

-6       -6

-9 = x or x = -9

Hope this helps!

Given Equation :

[tex]{\longrightarrow \pmb{\sf {\qquad - \: 3+x=2(x+3)}}} \\ \\[/tex]

Solution :

[tex] \\ {\longrightarrow \pmb{\sf {\qquad - \: 3+x=2(x+3)}}} \\ \\[/tex]

Using Distributive property for the right side we get :

[tex] \\ {\longrightarrow \pmb{\sf {\qquad - \: 3+x=2x+ 6 }}} \\ \\[/tex]

Now, subtracting 2x from both sides we get :

[tex] \\ {\longrightarrow \pmb{\sf {\qquad - \: 3+x - 2x =2x - 2x + 6 }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad - \: 3- x = 6 }}} \\ \\[/tex]

Now, Adding 3 to both sides we get :

[tex] \\ {\longrightarrow \pmb{\sf {\qquad - \: 3 + 3- x = 6 + 3 }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad- \: x = 9 }}} \\ \\[/tex]

Now, Multiplying both sides by (-1) we get :

[tex] \\ {\longrightarrow \pmb{\sf {\qquad (- 1)(- x) = ( - 1)9 }}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad x = - 6 }}} \\ \\[/tex]

Therefore,

Answer:

x=4

y=1

Step-by-step explanation:

4x=7y+9

4x+y=17

7y+9+y=17

8y=17-9

8y=8

y=1

so

4x=7*1+9

4x=16

x=16/4

x=4

Step-by-step explanation:

12x - y = 1

slope of m1 = - coefficient of x / coefficient of y

                    = - 12 / -1

                    = 12

# when it is parallel;

m1 = m2

12 = m2

# when it is perpendicular;

m1 * m2 = -1

12 * m2 = -1

m2 = -1 / 12

Answer:

x < 15

Step-by-step explanation:

1)  Regroup terms.

⇒ x - 50 < - 35

2) Add 50 to both sides.

x < - 35 + 50

3) Simplify - 35 + 50 to 15.

x < 15

Answer:

x < 15

Step-by-step explanation:

-50 + x < -35

+50          +50

________________

x < 15

Hope this helps :)

Answer:

See below ↓↓↓

Step-by-step explanation:

Subquestion #1

Subquestion #2

Subquestion #3

#1

[tex]\\ \rm\Rrightarrow 2x+48=180[/tex]

[tex]\\ \rm\Rrightarrow x+24=90[/tex]

[tex]\\ \rm\Rrightarrow x=66[/tex]

#2

[tex]\\ \rm\Rrightarrow 4x+7+35=90[/tex]

[tex]\\ \rm\Rrightarrow 4x+42=90[/tex]

[tex]\\ \rm\Rrightarrow 4x=48[/tex]

[tex]\\ \rm\Rrightarrow x=12[/tex]

#3

[tex]\\ \rm\Rrightarrow 3x+54=180[/tex]

[tex]\\ \rm\Rrightarrow 3x=126[/tex]

[tex]\\ \rm\Rrightarrow x=42[/tex]

Answer:

166,649.

Step-by-step explanation:

49

∑ (2n + 1)^2 =    4∑n^2 + 4∑n + 49

0

=  (4/6)n(n +1)(2n + 1) + 4/2 n(n + 1) + 49

=  2/3 * 49* 50 *99 + 2*49*50 + 49

= 161700 + 4900 + 49

= 166649

Answer: wheres the table

Step-by-step explanation:

Answer:

1 mile = 8.5 minutes

Step-by-step explanation:

Determining the equation:

Kira ran 8 1/5 miles in 69 7/10 minutes.

⇒ Kira = 8 1/5 miles = 69 7/10 minutes

⇒ 41/5 miles = 697/10 minutes

Simplifying both sides:

⇒ 41/5 miles = 697/10 minutes

⇒ 41 miles = 697/2 minutes

Using cross multiplication:

⇒ 41 × 2 miles = 697 minutes

⇒ 82 miles = 697 minutes

Dividing 82 both sides:

⇒ 82 miles = 697 minutes

⇒ 82/82 miles = 697/82 minutes

⇒ 1 mile = 8.5 minutes

Answer:

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

Step-by-step explanation:

[tex] \frac{3}{4} \div \frac{1}{6} [/tex]

[tex] \frac{3}{4} \times \frac{6}{1} [/tex]

[tex] \frac{18}{4} [/tex]

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

Divide fractions:-

[tex]\displaystyle\frac{3}{4} :\frac{1}{6}[/tex]

Multiply the 1st fraction times the reciprocal of the 2nd fraction (flop the second fraction over) :-

[tex]\displaystyle\frac{3}{4} *\frac{6}{1} =\frac{3*6}{4*1}=\frac{18}{4}[/tex]

[If necessary, divide the top & bottom by 2, and you'll have 9/2]

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Answer:

That would be :

4x – 10 = x2 – 5x + 10  ( y = 4x - 10 is substitute for y)

PROOF:        y + 5x = x² + 10

                    (4x - 10) + 5x = x² + 10

                     4x - 10  =  x² -5x + 10

   0 = x2 – 9x + 20  (liked terms are grouped and simplified)

PROOF:      4x - 10  =  x² -5x + 10

                  4x = x² -5x + 10 + 10

                   0  = x² -5x -4x + 20

                   0  = x² - 9x + 20

Solving:

            x² - 9x + 20 = 0

            x² - 5x - 4x + 20 = 0

            (x - 5) (x - 4)  = 0

         ⇒ x = 4  (as question says) OR x = 5

Step-by-step explanation:

hope this helps

Answer:

D,E

Step-by-step explanation:

Answer:

4 4/1

Step-by-step explanation:

we know that reciprocal mans backwards. This doesn't apply to the whole number un math. only the denominational and numerator.

Answer:

4×4=16

16+1=17

=4/17

step-by-step explanation:

since that is a mixed fraction, you first change it into an improper fraction......by multiplying the denominator and the whole number then add the numerator. You will get 17 as your numerator.......then make it your denominator and 4 your numerator

Answer:

736 in^2

Step-by-step explanation:

To find the surface area of a rectangular prism, the formula is perimeter(of one base)*height + area of two bases.

If you plug in the numbers according to this problem, that is (52*8) + 160(2)

SA = 736

Answer:

6x³ - 15x² - 1

3x divided by 3x is 1

So, here we are to simplify the polynomial :

[tex] \\ \longrightarrow \sf \qquad6x^3 - 15x^2 - \frac{3x}{ 3x}\\ \\[/tex]

We can simplify it as,

[tex]\\ \longrightarrow \sf \qquad6x^3 - 15x^2 - 1 \\ \\[/tex]

Some points to know :

Answer:

Histogram (Please tell me if you disagree, Have a great day:)

Answer:

1st option

Step-by-step explanation:

Check out the attached photo

Answer:

3

Step-by-step explanation:

use the pythagoreum therory

Un diagrama de sectores se puede utilizar para todo tipo de variables, pero se usa frecuentemente para las variables cualitativas.

Los datos se representan en un círculo, de modo que el ángulo de cada sector es proporcional a la frecuencia absoluta correspondiente.

El diagrama circular se construye con la ayuda de un transportador de ángulos.

Ejemplo

En una clase de 30 alumnos, 12 juegan a baloncesto, 3 practican la natación, 4 juegan al fútbol y el resto no practica ningún deporte.

The respiratory system and the cardiovascular system are intertwined in the sense that the  respiratory system provides oxygen used in the cardiovascular system.

The respiratory system is the syetem that coordinates gaseous exchange in the body while the cardiovascular system is the system that deals with the circulation of gases in the body.

The cardiovascular system and the respiratory system work together in the following ways;

Learn more about the respiratory system: https://brainly.com/question/9904853

There are 160 students in seventh grade.  Divide the partial amount by the percentage of the partial amount to get the total amount.

A percentage is a number or ratio that is expressed as a fraction of one hundred. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement.

A total is the result of adding several numbers together or counting how many items there are in a group. The total number or cost of something is the total number or cost obtained by adding or counting all of its parts.

Percentages can also be expressed as decimals or fractions, such as 0.6%, 0.25%, and so on. Academic marks are calculated in terms of percentages for any subject.

To Find the Total Amount :

No. of student in seventh grade = 8/5 * 100 = 160

So, there are 160 students in seventh grade.

To learn more about percentage refer :

https://brainly.com/question/24877689

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Answer:

no

Step-by-step explanation:

no

Yes

since the hypotenuese will be forty

24×24=576

32×32=1024

1024+576=1600

√40=1600 which makes YES be the correct answer

Question 1 Answer:

Aunt 1 and Grandma 1 would fill gift bags.

Mom and Aunt 2 would make centerpieces.

You and Grandma 2 would blow up balloons.

Since you are pairing up to complete the tasks, these pairs each have the shortest times in their respective categories and therefore are the most logical pairing to complete tasks.

Question 2 Answer:

We use algebra and our previous pairings to determine the length of each task.

Gifts Bags --> 6/7 hours

x = time together

[tex]\frac{1}{x}[/tex] = rate of completion

Aunt 1 = [tex]\frac{1}{1.5}[/tex] Grandma 1 = [tex]\frac{1}{2}[/tex]

[tex]\frac{2}{3} +\frac{1}{2} = \frac{1}{x}[/tex]

[tex]\frac{7}{6} = \frac{1}{x}[/tex]

[tex]x = \frac{6}{7}[/tex]

Centerpieces --> 7/4 hours

x = time together    [tex]\frac{1}{x}[/tex] = rate of completion

Mom = [tex]\frac{1}{3.5}[/tex] Aunt 2 = [tex]\frac{1}{3.5}[/tex]

[tex]\frac{2}{7} + \frac{2}{7} = \frac{1}{x}[/tex]

[tex]\frac{4}{7} = \frac{1}{x}[/tex]

[tex]x = \frac{7}{4}[/tex]

Balloons --> 15/16 hours

x = time together    [tex]\frac{1}{x}[/tex] = rate of completion

You = [tex]\frac{1}{1.5}[/tex] Grandma 2 = [tex]\frac{1}{2.5}[/tex]

[tex]\frac{2}{3} + \frac{2}{5} = \frac{1}{x}[/tex]

[tex]\frac{16}{15} = \frac{1}{x}[/tex]

[tex]x = \frac{15}{16}[/tex]

Shortest amount of time to complete all tasks is:

[tex]\frac{6}{7} + \frac{7}{4} + \frac{15}{16} = \frac{397}{112}[/tex]  ≈ 3.54 hours

Converting hours to hours and minutes --> 3 hours 32 minutes

Therefore they must arrive by 5:28pm to complete the tasks in time to leave at 9:00pm.

Answer:

23/42 or 0.547619048

Steps are given below in the picture

I hope my answer helps you.

Answer:

[tex]\mathrm{1 \dfrac{ 1 }{ 6 }\:cups}[/tex]

Step-by-step explanation:

Given from the graph:

There is  [tex]\frac{1}{2}[/tex] cups of paint for one jar

There are 3 cups of paint for three jars

There is 1 [tex]\frac{1}{2}[/tex] cups of paint for one jar

There is 2 cups of paint for one jar

total amount of jars = 6

But since we need to find the amount of cups in each jar, we do:

[tex]\dfrac{ 1 }{ 2 } +3+1 \dfrac{ 1 }{ 2 } +2[/tex]

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

[tex]2+3+2[/tex]

Add 2 and 3

[tex]5+2[/tex]

Add 5 and 2

[tex]7[/tex]

total cups of paint = 7

Then we need to find how much paint could be splitted equally among the 6 jars, so we do the following:

total amount of jars = 6

total cups of paint = 7

We divide the total amount of jars by the total cups of paint

7 ÷ 6

Divide 7 by 6

[tex]\dfrac{ 7 }{ 6 }[/tex]

[tex]= 1 \dfrac{ 1 }{ 6 }[/tex]

[tex]\mathrm{Answer: 1 \dfrac{ 1 }{ 6 }\:cups}[/tex]

Answer:

sorry but I actually don't know about it sorty

Answer:

460 miles/hour

Step-by-step explanation:

Distance = Speed x Time

We want the Speed, so let's rearrange the equation:

Speed = Distance/Time

We are given Distance = 2070 miles

and Time of 4.5 hours

Speed = (2070 miles)/(4.5 hours)

Speed = 460 miles/hour

Answer:2.4 isn’t occupied, whilst 13.3 is full

Step-by-step explanation: answerrr

Answer:

D. 15(4a + 3)

Step-by-step explanation:

15 is the least possible factorisation for both sides, therefore D is the most efficient on of all of them

Using the GCF and Distributive property, the expression can be factorized as, d. 15 (4a + 3).

GCF is the abbreviated form for Greatest Common Factor.

As the name suggests, GCF of two or more numbers or expressions is the greatest of all the common factors of them.

The given expression is 60a + 45.

Distributive property for 3 numbers, a, b and c states that,

a (b + c) = ab + ac

There are two terms here 60a and 45.

We can find the GCF using Prime factorization.

60 = 2 × 30

     = 2 × 2 × 15

     = 2 × 2 × 3 × 5

45 = 3 × 15

    = 3 × 3 × 5

Common factors are 3 and 5.

GCF = 3 × 5 = 15

60a + 45 = (15 × 4a) + (15 × 3)

               = 15 (4a + 3)    [Using the distributive property]

Hence the factorized form is 15 (4a + 3)  

Learn more about GCF here :

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Step-by-step explanation:

Surface area of cone = πr ( l + r)

= 22/7 × 4 (5+4

= 88/7 × 9

= 792/7

= 113.14 cm²

Answer:

D.  113.13 cm^2.

Step-by-step explanation:

I am assumming you want the surface area of this cone.

This = area of base + area of the curved side

= π r^2 + π r L

=  4^2 π + 4*5 π

= 113.13 cm^2.