Find x.
Please help me with this

The area of the rectangular garden that has a 70-meter path surrounding it is: 1,176 m².

Area = length × width

Perimeter of a rectangle = length surrounding a rectangular shape = 2(length + width).

Give the following:

Perimeter of the rectangular garden = 70 meter

Length = l

Width = 2/3l

Therefore:

l + 2/3l = 70

5/3l = 70

5l = 3(70)

5l = 210

5l/5 = 210/5

l = 42

Length = l = 42

Width = 2/3l = 2/3(42) = 28

Area of rectangular garden = 42 × 28 = 1,176 m².

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[tex](7.8*10^5)+(2.4 * 10^5)[/tex]

[tex](7.8 * 100,000) + (2.4 * 100,000)[/tex]

[tex]780,000 + 240,000[/tex]

= 1,020,000

Answer:

1020000

Step-by-step explanation:

(7.8 x 10^5) + (2.4 x 10^5)

780000+240000

1020000

Hopes this helps please mark brainliest

The area of the final polygon is 8x² + 4x - 16

From the question, we are to determine the area of the final polygon.

From the given information,

"A polygon with an area of (4x^2 + 2x - 16) square units is combined with a rectangle that has a width of (6x + 2) units and a length of (x - 5) units."

First, we will determine the area of the rectangle.

Area of the rectangle = (6x + 2)(x - 5)

Area of the rectangle = 6x² - 30x + 2x - 10

Area of the rectangle = 6x² - 28x - 10

Now, we will add it to the area of the polygon

4x² + 2x - 16 + 6x² - 28x - 10

= 4x² + 6x² - 28x + 2x - 10 - 16  

= 10x² - 26x -26

Also,

From the given information,

"a polygon with an area of (2x^2 - 30x - 10) square units is removed"

Then,

The area of the final polygon = 10x² - 26x - 26 - (2x² - 30x - 10)

Area of the final polygon = 10x² - 26x - 26 - 2x² + 30x + 10

Area of the final polygon = 10x² - 2x² + 30x - 26x + 10 - 26

Area of the final polygon = 8x² + 4x - 16

Hence, the area is 8x² + 4x - 16

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The solution to the differentiation dy/dx =(1+x/1-x)^1/3 is  [tex]\frac{dy}{dx} = 1^\frac{1}{3}[/tex]

What is differentiation?

Differentiation is a method of finding the derivative of a function.

To find the derivation of the function Simplify

[tex]\frac{dy}{dx} = ( 1+ \frac{x}{1} - x)^ \frac{1}{3}[/tex]

Any expression divided by one remains the same

[tex]\frac{dy}{dx}= ( 1+ x-x) ^\frac{1}{3}[/tex]

Eliminate x

[tex]\frac{dy}{dx} =[/tex] 1 [tex]\frac{1}{3}[/tex]

Therefore, the solution to the differentiation is  [tex]\frac{dy}{dx} =[/tex] 1 [tex]\frac{1}{3}[/tex]

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Answer:

-7/3

Step-by-step explanation:

(-2-5)/(5-2)

-7/3

Answer:

C.

Step-by-step explanation:

Using Slope formula (y2-y1/x2-x1), we can plug these 2 coordinates in. -2-5/5-2= -7/3.

Or even by simply using rise over run, we can get the slope. Up 7 over 3, and we know that the slope is negative, so we add a negative sign in front.

-Hope this helped

The rules for transformation of first graph is (x + 4, y + 6).

The rules for transformation of second graph is (x + 4, y + 6).

Transform the forms on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century. In geometry, object transformations are the foundation for the majority of proofs.

In first graph it is clear that the graph is translated and the rule for first graph is (x + 4, y + 6).

Similarly, the second graph is also translated and the rule is (x+3, y).

Therefore, the rule for first graph is (x + 4, y + 6) and the rule for second graph is (x + 4, y + 6).

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The equation of circle (x-4)² + (y+11)² = 64

What is a Circle?

All points in a plane that are at a specific distance from a specific point, the center, form a circle. Alternatively, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Here we know that (h,k)=(4,-11) but we are not given the radius.

However, we can find the radius by using the distance formula.

Therefore,

r = √[(x2 - x1)² + (y2 - y1)²]

r = √[(4 - 4)² + (-3 + 11)²]

r = √[(0)² + (8)²]

r = √(8²)

r = 64

An equation of the circle with center (h,k) and radius r is

(x−h)^2 +(y−k)^2=r^2

Substitute the values in the equation of circle as follows:

(x-4)² + (y+11)² = 8²

(x-4)² + (y+11)² = 64

Therefore, the equation of the circle is (x-4)² + (y+11)² = 64

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Solution to the questions are: (1) 3.95      

                                                  (2)19.92      

                                                  (3) 5.45

                                                  (4) 42.18

                                                  (5) 21.77  

                                                  (6) 57.84

What is Simplify?

Simplify in mathematics is a simple way of bringing down a problem, fraction or word expression into an easier from

1. ( 1.8 + 3.44 ) x 0.75

Simplify the equation using

=(5.24) x 0.75

=3.95

2. (8.29 - 0.32) ÷ 0.4

Rewrite the equation and simplify

=[tex]\frac{8.29 -0.32}{0.4}[/tex]

=[tex]\frac{7.97}{0.4}[/tex]

=19.92

3. 7.58 (1.5 x 0.24) ÷ 0.5

Rewrite the equation and simplify

=[tex]\frac{7.58(1.5 * 0.24) }{0.5}[/tex]

= [tex]\frac{7.58 (0.36)}{0.5}[/tex]

= [tex]\frac{2.728}{0.5}[/tex]

= 5.45

4. (16.45-5.05) x (2.46 + 1.24)

Simplify the equation

=(11.4)x (3.7)

=42.18

5. (7.1 x 2.3) ÷ (1.25 x 0.6)

Rewrite the equation and simplify

= [tex]\frac{7.1 * 2.3}{1.25 * 0.6}[/tex]

= [tex]\frac{16.33}{0.75}[/tex]

= 21.77

6. (4.19 + 6.8) ÷ (0.34-0.15)

Rewrite the equation and simplify

= [tex]\frac{4.19 + 6.8 }{0.34 - 0.15}[/tex]

= [tex]\frac{10.99}{0.19}[/tex]

= 57.84

Therefore, the solution to the equations are ;(1) 3.95      

                                                  (2)19.92      

                                                  (3) 5.45

                                                  (4) 42.18

                                                  (5) 21.77  

                                                  (6) 57.84

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The population of Springfield in 2046, given the growth rate, can be found to be  251, 940 people

When given the starting population, and the population growth rate, the growth in population can be found by the formula:

= Starting population x ( 1 + population growth rate ) ^ number of years

The number of years would be:
= 2046 - 2019

= 27 years

The population in 2046 would be:

= 202, 628 x ( 1 + 0.81 % ) ²⁷

= 251, 940 people

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The linear regression equation for the profit in x years after 1997 is of:

y = 20.5x + 142.

Using this equation, the estimate for the profit in 2006, is of: $326,500.

The linear regression equation is obtained inserting the points of the data, represented either in a table or in a scatter plot, into a linear regression calculator.

In the context of this problem, these points are given as follows:

(0, 131), (1, 168), (2, 202), (3, 193), (4, 221).

Inserting these points into a calculator, the equation is:

y = 20.5x + 142.

The estimate for the profit in 2006, that is, 9 years after 1997, is of:

y = 20.5(9) + 142 = 326.5 thousand dollars = $326,500.

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The missing values in the ratios are 2/3 and 16/3 in the set of 1, _ , _.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given are two sets of ratios 2, _, _ and 3, 1, 8.

If we observe the first value of the first and second ratio we see that

The second set of ratios is (3/2) or 1.5 times larger than the first set of ratios.

So the second and the third value of the first set of ratios are (1/3/2) = 2/3 and 8/(3/2) = 16/3.

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An equation 7x+3x+10= -2[-5x +(-5)] has infinite solutions and an equation 7x+3x+10= -2[-5x + (-4)] has no solution.

Given that:

7x+3x+10 = -2 (_x + _)

=> 10x + 10 = -2 (_x + _)

Putting in the blank -5 so as to satisfy the equation that has an infinite solution.

=> 10x + 10 = -2(-5x + -5)

This is the equation that shows that it has infinite solutions and they are in the same line.

For no solutions

7x+3x+10 = -2 (_x + _)

In no solution, the value of b is not equal to -5.

For equation:

7x+3x+10 = -2 (-5x + b) [If putting value in first blank = -5]

Therefore, -2 (-5x + b) is parallel to 10x+10 for any value of b not equal to -5. Parallel lines never intersect. So solutions are no solution.

Putting the value of b = -4

7x+3x+10 = -2 [-5x + (-4)]

This is the equation that shows that it has infinite solutions and they are in the same line.

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The volume of the cylindrical water tank that has a length of 20 feet and a radius of 12 feet is about 9,048 cubic feet.

The correct option is option d;

d. 9,048

The volume of a solid indicates the amount of space the solid takes at a location.

The formula for finding the volume of the cylindrical tank is presented as follows;

V = π·r²·L

Where;

r = The radius of the tank

L = The length of the tank

From a similar question on the website, we have;

The length of the tank, L = 20 feet

Therefore;

The volume of the tank, V = π × 12² × 20 ≈ 9048

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For the z-score = 1, the percentile = 84.13%

In this question, we need to find the percentile when z-score is 1

We know that a Z-scores is a normalized score that used to compare values relative to their population. z-score represents a specific location in the normal distribution, so that there is a certain area that is to the left of that z-score. The percentile associated to a z-score is nothing but the area to the left of that z-score.

When z = 1 then the percentile would be 84.13%

Therefore, for the z-score = 1, the percentile is 84.13%

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1. Triangle ABC with the vertices, A(0, 2), B(6, 4), and C(4, -2) is drawn and attached below.

2. The midsegment is EF. This is verified using the triangle midsegment theorem which states that EF = 1/2(AC).

The midsegment of a triangle is the line segment that joins the midpoints of two sides of a triangle together. Every triangle typically has three midsegments.

According to the triangle midsegment theorem, the length of the midsegment is half the length of the third side of the triangle that it is parallel to.

The midpoint of a line is its middle, which can be calculate using the formula:

M(x, y) = [tex](\frac{x_2 - x_1}{2}, \frac{y_2 - y_1}{2})[/tex].

1. The coordinate of the three vertices that is used to draw a triangle are:

A(0, 2), B(6, 4), and C(4, -2).

The triangle is in the attachment below.

2. To plot the midsegment of the triangle, determine the midpoints of AB and BC, then plot the coordinate where both midpoints would be joined.

Midpoint of AB = (x, y) = (0+6)/2, (2+4)/2

= (6/2, 6/2)

= (3, 3) (let this be point E)

Midpoint of AB = (x, y) = (4+6)/2, (−2+4)/2

F = (5, 1)

The midsegment will have the endpoints, E(3, 3) and F(5, 1).

To verify the segment draw is the midsegment according to the triangle midsegment theorem, find the length of the midsegment, EF, and the length of the third side, AC using the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

EF = √[(5−3)² + (1−3)²]

EF = √8 units

AC = √[(4−0)² + (−2−2)²]

AC = √32 units

Based on the triangle midsegment theorem:

EF = 1/2(AC)

Plug in the values:

√8 = 1/2(√32)

√8 = 1/2(4√2)

√8 = 2√2

2√2 = 2√2 (true)

This means that EF is a midsegment of triangle ABC.

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Answer:

a=34π

b=64π

c=39π

d=25π

Step-by-step explanation:

Answer:

Step-by-step explanation:

x= a. 60

y = I. 15

angle c = b. 45

angle DBC = h. 105

angle CBA = g. 75

Answer:

x=60° y=15° m∠c=45° ∠DBC=105° ∠CBA=75°

Step-by-step explanation:

Since it shows that 7y and 5y make 180 degrees, 12y=180 and y=15

So m∠c=45 degrees and ∠CBA is 75 degrees.

180-(45+75)=60 degrees.

So ∠DBC is 105 degrees. :D

The solution to the questions are:

From the question, we have the following parameters that can be used in our computation:

Length = 350 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

A = (350 - 2x) * x

Evaluate

A = 350x - 2x²

Differentiate and set to 0

350 - 4x = 0

So, we have

4x = 350

Divide by 4

x = 87.5

Recall that

Length = 350 - 2x

So, we have

Length = 350 - 2 x 87.5

Evaluate

Length = 175

The area is then calculated as

Area = Length x Width

So, we have

Area = 175 x 87.5

Evaluate

Area = 15312.5 square meters

Hence, the area is 15312.5 square meters

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Step-by-step explanation:

a² - 3x - 10

a(a -3) (x - 10)

Answer:

$8

Step-by-step explanation:

Mary and Tom bought a gift for their mother for Mother's Day. Tom paid $28.00, and Mary paid $12.00. If they wanted to share the cost of the gift equally, how much money does Mary owe Tom?

total paid: 28 + 12 = $40

if they split equally: $40/2 = $20 each

because Mary only paid $12 she owes Tom: 20-12 = $8

The number of stuffed animals Lakeview shipped to each store is 31

The Lakeview Toy Factory produced 180 stuffed animal

It donated 25 of the stuffed animals to a local e

After donation the number of stuffed toys left = 180 - 25 = 155

Lakeview shipped the rest to 5 store

Each of the stores received the same number of stuffed animals

Number of stuffed animals each store recieved = total toys/ number of store

= 155/ 5 = 31

Therefore,  the number of stuffed animals Lakeview shipped to each store is 31

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Answer:

- 4x3=12

12x2=24

so, 24 = 24

The smallest number of bags the groundskeeper must buy to cover the circular field is 4.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

The longest line which can be drawn inside the circle will be the diameter.

The perimeter of the circle = 2πr where r is the radius of the circle.

As per the given,

Diameter of the circular field = 290 feet

Radius = 290/2 = 145

Area of circle = πr² = π(145)²

⇒ 66051.985 feet²

In one bag = 50 pounds

Area cover in one bag = 50 × 400 = 20000

Number of bags needed to cover the whole area

⇒ 66051.985/20000 = 3.3025

Since the number of bags is a whole quantity thus it will round up to 4.

Hence "The smallest number of bags the groundskeeper must buy to cover the circular field is 4".

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Answer:

The [tex]x[/tex]-intercept

Step-by-step explanation:

The equation of line A is [tex]y=\frac{1}{3}x+1[/tex].

The equation of line B is [tex]y=x+3[/tex].

The lines share the same [tex]x[/tex] intercept, since when [tex]x=-3[/tex], [tex]y=0[/tex] for both lines.

Answer:

∴ Samantha ate [tex]\frac{1}{3}[/tex] of the pizza on Saturday.

Step-by-step explanation:

Fraction of pizza left on Friday = [tex]1-\frac{1}{2}[/tex]

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

∴ Fraction of pizza eaten on Saturday = [tex]\frac{2}{3}[/tex] × [tex]\frac{1}{2}[/tex]

                                                               = [tex]\frac{1}{3}[/tex]

The completion of the inventory table is as follows:

A = $48

B = $264

C = $420

D = $304.

What methods are used for inventory?

Utilizing some of the inventory procedures, the aforementioned inventory table is finished.

The First-in, First-out (FIFO) principle presupposes that the physical flow of products sold corresponds to the order in which they were acquired.

The Last-in, First-out method (LIFO) bases the cost of products sold on the most recent inventory acquisitions.

The weighted-average technique calculates the ending inventory and cost of goods sold using the average cost of goods.

Allocating the expenses of products sold and ending inventory are not based on any presumptions in Specification Identification. It substitutes specified expenses instead.

Inventory Table:

                                    Units    Unit Cost    Total Cost

Jan. 1      Beg. Inventory   8        $6.00            $48 ($6 x 8)

April 11    Purchases        24       $11.00          $264 ($11 x 24)

May 17    Purchases        30      $14.00          $420 ($14 x 30)

Dec. 5    Purchases         19      $16.00          $304 ($16 x 19)

Total                                 81                         $1,036

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Answer:

30 gallons of gas is left

Step-by-step explanation:

1680 is what we start with

25 filled with 24

25*24=600

35 filled with 30

35*30= 1050

So we take away what we used

600+1050= 1650

We started with 1680

1650 got taken away so

1680-1650= 30

30 gallons are left

Answer:

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

Initial volume of gas in the storage tank is 1680 gallons.

Cars took:

Trucks took:

Gas left in the storage tank:

"The population of the culture 6 days after inoculation is 1,000(1.15)^6 ; 2313 bacteria"

Initial inoculated bacteria = 1000

Growing rate of bacteria = 15%

we have to find the population of the culture after 6 days

y = 1000 ( 1 + 15/100)^6

y= 1000 (1.15)^6

y = 1000(2.313060)

y = 2313.06 ≈ 2313

The population of the culture 6 days after inoculation is 2313.

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The simplified form of the expression will be 1 / [2(x - 5)] and [(x - 4) / [x (x - 2)].

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The expression is given below.

⇒ [(3x) / (x² - 25)] · [(x² + 6x + 5) / (6x² + 6x)]

Simplify the expression, then we have

⇒ [(3x) / (x² - 25)] · [(x² + 6x + 5) / (6x² + 6x)]

⇒ [(3x) / (x² - 5²)] · [(x² + 5x + x + 5) / (6x² + 6x)]

⇒ {3x / [(x - 5)(x + 5)]} · {[(x + 5)(x + 1)] / [(6x)(x + 1)]}

⇒ 1 / [2(x - 5)]

The expression is given below.

⇒ [(x² - 2x - 3) / (x² + 2x + 1)] ÷ [(x³ - 5x² + 6x ) / (x² - 3x - 4)]

Simplify the expression, then we have

⇒ [(x² - 2x - 3) / (x² + 2x + 1)] ÷ [(x³ - 5x² + 6x ) / (x² - 3x - 4)]

⇒ {[(x - 3)(x + 1)] / [(x + 2)(x + 1)]} · {[(x - 4)(x + 1)] / [x(x - 3)(x - 2)]}

⇒ [(x - 4) / [x (x - 2)]

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3 kg of an alloy with 90% copper must be added to 6 kg of another alloy with 15% copper to obtain an alloy that is 40% copper.

Given, we are asked to determine:

How many kg of an alloy with 90% copper must be added to 6 kg of another alloy with 15% copper to obtain an alloy that is 40% copper = ?

convert kg to ounces.

6kg = 211.644 ounces.

90%x+15%(211.644)=40%(211.64+x)

0.9x+0.15(211.64)=0.4(211.64+x)

0.9x+31.7466 = 84.6576 + 0.4x

0.9x - 0.4x = 84.6576 - 31.7466

0.5x = 52.911

x = 52.911/0.5

x = 105.822

now convert ounces to kg.

= 3kg

Hence approximately 3 kg of an alloy with 90% copper must be added to 6 kg of another alloy with 15% copper to obtain an alloy that is 40% copper.

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