A certain forest covers an area of 4900 km². Suppose that each year this area decreases by 7%. What will the area be after 8 years?
Use the calculator provided and round your answer to the nearest square kilometer.

Using the information in the exercise to develop the system of equations and using the substitution method, the following answers are found:

The system of the linear equations is P = F + 0.50, 2D = 3F - 0.50, and 2P + F + 3D = 7.75, where P = The price of a box of popcorn, D = The price of a drink, and F = The price of a piece of fruit. By other hand, the price of each item is: Popcorn = $1.50, Drink = $1.25, and Fruit = $1.

Solution of the system of equations by the Substitution Method.

Taking into account the information given in the exercise, we can write the next equations:

Where:

Since all equations have the variable F, we are going to use it as a key variable to represent the other variables in terms of F.

In the first equation we should not do anything, since P is in terms of F, in the second case the variable D is also in terms of F, but we need to find the value of just D, by this:

We proceed to substitute the first and second equations in the third equation:

And we solve for the variable F:

Now, we can solve for the variable D with the second equation:

Finally, we can solve for the variable P with the first equation:

So, we have the price of each item:

If you want to see another exercise solved by the substitution method, you can see this link: https://brainly.com/question/22340165?referrer=searchResults

Answer:

5 years

Step-by-step explanation:

Let x be the unknown numer of years ago when the product of the man and his child's age was 96.

》 x years ago, the man's age = 37 - x

the child's age = 8 - x

(37 - x)(8 - x) = 96

296 - 37x - 8x + x² = 96

x² - 45x - 296 - 96 = 0

x² - 45x - 200 = 0

x² - 5x - 40x - 200 = 0

x(x - 5) -40(x - 5) = 0

(x - 5)(x - 40) = 0

x = 5 years ago or x = 40 years ago

but x = 40 > son's present age.

Thus, x = 5.

Therefore, 5 years ago the product of the ages of the man and his child was 96.

[tex]\\ \sf\longmapsto 2-x\gt x-2[/tex]

[tex]\\ \sf\longmapsto 2+2\gt x+x[/tex]

[tex]\\ \sf\longmapsto 4\gt 2x[/tex]

[tex]\\ \sf\longmapsto x\lt \dfrac{4}{2}[/tex]

[tex]\\ \sf\longmapsto x\lt 2[/tex]

Answer:

-7.11111111111

Step-by-step explanation:

Answer:

y = 2x + 2

BRAINLIEST, PLEASE!

Step-by-step explanation:

(-2, -2) (-1, 0)

y = mx + b (m = slope, b = y-intercept)

m = rise/run = change in y / change in x

change in y: +2

change in x: + 1

change in y/change in x = 2/1 = 2

m = 2, y = 2x + b

We can plug -1 in for x, and 0 in for y.

0 = 2(-1) + b

0 = -2 + b

b = 2

y = 2x + 2

Answer:

y = 2x + 2

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

You would add 5 + 4.2 + 5 - 2.2 - 1 in a calculator and it would come out to be 11.

Answer:

Domain is {x|x = -2, -1, 1, 3}

Step-by-step explanation:

I. When domain is x.value and renge is y.value

Got more question or something to discuss? leave comment below

Answer:

Irrational

Step-by-step explanation:

Its irrational as it has no pattern of numbers after decimal point and the number are infinite

Answer:

irrational because it has a coma after one number

Answer:

Fred has = 9 $

Alicia has = 9 + 8 =17 $

Step-by-step explanation:

Let, Fred has = f $

Then, Alicia has = f + 8 $ ;[as Alicia has 8 more dollars than fred]

Now, the required expression is

∴[tex]f+(f+8)=26\\=>2f+8=26\\=>2f=18\\f=9[/tex]

So, Fred has = 9 $

Alicia has = 9 + 8 =17 $

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(x+3)(x^2-3x+27)

x^3-3x^2+27x+3x^2-9x+81

x^3+19x+8

Here we have a problem of reflections and of how these reflections affect lines. Here we will find that the reflection does not affect the pair of parallel lines, and in the flipped shape we still have a pair of parallel lines.

We can define two parallel lines as two lines that never meet.

And, for a given point (x, y), the simplest reflection across a horizontal line is the reflection across the x-axis (or the line y = 0) as it transforms the point into:

(x, - y)

And all the reflections across horizontal lines will only affect the y-value of the points.

Now, particularly, we have two vertical and parallel lines.

Notice that a vertical line is defined by its x-value, and the transformation we used does not affect the x-value, so a reflection across a horizontal line will not affect a vertical line.

From this, we can conclude that the reflection across a horizontal line will not affect the pair of vertical parallel lines, so at the end, we still have only one pair of parallel lines.

If you want to learn more, you can read:

https://brainly.com/question/15627170

Answer:

C. Y=2x

Step-by-step explanation:

I hope this help you

Answer:

160 cm²

Step-by-step explanation:

If the two rectangles are similar, that means they have equal scale factors.  The smaller rectangle has length of 8 cm and area of 40 cm, which means the width is 5 cm.  

The width of the larger rectangle is 10 cm, which is double the width of the smaller, similar rectangle.  So, to find the length of the larger rectangle, multiply 8 x 2, which gives you 16 cm for the length, since the scale factor is 2.

Now, just find the area of the larger rectangle by doing length x width.  16cm x 10 cm = 160 cm²

Answer:

160 cm^2

Step-by-step explanation:

Our strategy is to find the length of the larger rectangle so we can find the area. To find the length, we will rely on the fact the two rectangles are "similar": their sides are in equal proportions, or have the same "ratio."

We know that the smaller rectangle has a width of 5 cm because, when we substitute area and length into

A = lw

we get

40 = 8w

w = 5

when we divide both sides by 8.

Because of equal proportions:

Width : length of the smaller rectangle = Width : length of the larger rectangle

We can write an equation

5 / 8 = 10 / x

Cross multiply

5x = 80

x = 16

So the larger rectangle has a length of 16 cm and a width of 10 cm (given)

meaning the area is

16 * 10 = 160 cm^2

Answer:

-21

Step-by-step explanation:

h(x) = -x-18

h(3) = -(3)-18 = -21

Answer:

[tex]h(3)=-21[/tex]

Step-by-step explanation:

One is given the following:

[tex]h(x) = -x - 18[/tex]

One is asked to find the value of ([tex]h(3)[/tex]). Substitute ([tex]3[/tex]) in place of ([tex]x[/tex]) and simplify to evaluate,

[tex]h(x)=-x-18\\\\h(3)=-(3)-18\\\\h(3)=-3-18\\\\h(3)=-21[/tex]

Answer:

(14, 42)

Step-by-step explanation:

(-4, 2, 14, 34, 42) are all elements of b, and (-7. 14, 21, 42) are all elements of c. (14, 42) are the only elements that are in both sets

This value is approximate.

============================================================

Explanation:

Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.

Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.

Based on those two interior angles, angle C must be...

A+B+C = 180

107+42+C = 180

149+C = 180

C = 180-149

C = 31

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

To sum things up so far, we have these known properties of triangle ABC

Let's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).

b/sin(B) = c/sin(C)

b/sin(42) = 24/sin(31)

b = sin(42)*24/sin(31)

b = 31.1804803080182 which is approximate

b = 31.2 miles is the distance from the storm to station A

Make sure your calculator is in degree mode.

The weather station A is 31.2 miles from the storm

From the triangle shown:

m<B = 90° - 48°

m<B = 42°

m<A = 17° + 90°

m<A = 107°

m<A + m<B + m<C = 180° (Sum of angles in a triangle)

107° + 42° + m<C = 180°

m<C = 180° - 149°

m<C = 31°

The distance between the weather stations A and B = 24 miles

That is, AB = 24 miles

The storm is at point C

The length AC is found by using the rule of sines:

[tex]\frac{sinC}{AB}=\frac{sinB}{AC} \\\\\frac{sin31}{24}=\frac{sin42}{AC} \\\\\frac{0.515}{24} = \frac{0.669}{AC} \\\\0.02146=\frac{0.669}{AC}\\\\AC=\frac{0.669}{0.02146} \\\\AC=31.2 miles[/tex]

The weather station A is 31.2 miles from the storm

Learn more on sine rule here: https://brainly.com/question/4372174

Answer:

SEE THE IMAGE FOR SOLUTION .

HAVE A GREAT DAY

Answer:

11. D

12. C

13. D

14. B

15. E

Step-by-step explanation:

11.

1/3 + 1/2 = 2/6 + 3/6 = 5/6

A is 3/4

B is 2/3

C is 9/10

D is 4/5

E is 2/5

the closest to 5/6 is 4/5.

12.

this is totally easy. just simply additions and one subtraction (to see what is left).

8+10+9 = 27

so, he has

60 - 27 = 33 hours left

13.

the mean value of a series of equal weighted numbers is simply their sum divided by the amount of numbers.

so,

(2+5+3+6+4)/5 = 20/5 = 4

14.

a scale factor is always applied to all dimensions, otherwise the result will be distorted. and that would be especially bad for a map.

so, clearly the width of the larger map is 3 times the width of the smaller map. therefore, the length of the larger map has to be also 3 fine the length of the smaller map.

3×6 = 18

15.

3t - 10 = 8

3t = 18

t = 6

Answer:

n = 6

Step-by-step explanation:

To solve this you can use an equation such as:

[tex]\frac{2}{3} n+4=8\\\\[/tex]

We need to so for n. Subtract 4 from both sides to get the variable (n) alone. 4 - 4 and 8 - 4 equals:

[tex]\frac{2}{3}n=4[/tex]

So now we divide both sides by 2/3.

This now equals:

[tex]n=6[/tex]

Answer:

-8x^2 -10x + 8

Step-by-step explanation:

there is no multiplying just adding

Step-by-step explanation:

maybe I am wrong sorry for that but try to understand it

have a great day

Answer:

19/20 cups

Step-by-step explanation:

Add the amounts together

1/4 + 7/10

Get a common denominator of 20

1/4 *5/5   + 7/10 *2/2

5/20 + 14/20

19/20

Answer:

19/20

Step-by-step explanation:

find a common denominator then do the same with the numerator then add.

Answer:

It is y = x - 5

Step-by-step explanation:

General equation of a line:

[tex]{ \bf{y = mx + c}}[/tex]

m is the gradient, and c is y-intercept.

For gradient:

[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1}} [/tex]

substitute:

[tex]slope = \frac{1 - ( - 2)}{6 - 3} \\ \\ = \frac{3}{3} \\ slope \: = 1[/tex]

m = 1

for y-intercept:

consider point (6, 1):

[tex]y = mx + c \\ 1 = (6 \times 1) + c \\ 1 = 6 + c \\ c = 1 - 6 = - 5[/tex]

therefore:

[tex]{ \sf{equation \: is \: \{y = x - 5 \}}}[/tex]

Answer:

1

Step-by-step explanation:

2(k + 1) = -4(k - 2)

2k + 2 = --4k+8

2k+4k=8-2

6k=6

k=6/6

k=1

Step-by-step explanation:

the radius cuts the segment into two equal parts because it is perpendicular to the chord

Answer:

Step-by-step explanation:

As O is the mid point of the circle

Similarly, B also becomes the mid point of the line AC.

So, line OB divides AB and BC equally.

Hence, lines AB = AC, but they are asking to prove congruency of triangles.

So, u have to join OA and OC.

Same way,   line OB divides ∠OBA and ∠OBC.

So it is proved that AB = AC

Answer:

40 and 60

Step-by-step explanation:

Sum of ratio=2+3

sum of ratio=5

Share of part 2=2/5*100

share of part 2=40

Share of part 3=3/5*100

share of part 3=60

Note:if you need to know any question please let me know.

Answer:

Pantalones = $600.00 × 2

$ 1,200.00

Blusas = $350.00 × 4

$ 1,400.00

Calcetas = $120.00 × 3

$ 360.00

Par de tenis = $950.00 × 2

$ 1,900.00

Total a pagar = $4,850.00

$5,000.00

- $4,860.00

Sobrante = $140.00