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3 years ago

Translate the following sentence into math symbols. Then solve the problem. Show your work and keep the equation balanced.

Mathematics

1 answer:

adell [148]3 years ago

4 0

For this case we have to represent the following expression algebraically:

"10 less than x is -45"

So:

10 less than x is represented as: $x-10$

Then, the complete expression is represented as:

$x-10 = -45$

Adding 10 to both sides of the equation:

$x = -45 + 10\\x = -35$

Thus, the value of the variable is $x = -35$

Answer:

$x = -35$

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Where is the axis on a quadrant

dezoksy [38]

Answer:

x axis and y axis divide the coordinate plane into four quadrants.

Step-by-step explanation:

If one coordinate is zero, then the point is located on the x-axis or the y-axis. If y coordinate is zero, then the point is located on the y-axis. If both coordinates are zero, then the point represents the origin.

8 0

3 years ago

on a map the distance between two towns is 4 inches. the actual distance between the towns is 360 miles. what is the scale of th

chubhunter [2.5K]

1 in = 90 miles I believe would be the scale

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3 years ago

Arif's backyard is 24 by 37 meters. He wants to put a flower garden in the middle of the backyard, leaving a strip of grass of

Tpy6a [65]

Answer:

Length of the flower garden = 29 meters

Width of the flower garden = 16 meters

Step-by-step explanation:

I have also attached a diagram for your convenience

Now First let us see the data we are given with:

Arif's backyard length = 37 meters

Arif's backyard Width = 24 meters

Area that should be left with grass = 424 m^2

Now lets suppose the width of the stirp of grass be "a"

According the image the area of backyard will be:

Area ABCD = 24 x 37

Area ABCD = 888 m^2

The length LM will be = (37 -2a)

The Width LO will be = (24 -2a)

Area LMNO = (37 -2a) x (24 -2a)

Area LMNO = 888 -74a -48a +4a^2

Area LMNO = 4a^2 -122a + 888

Now in order the to calculate the area of the grass strip we must subtract the area LMNO from the total area ABCD and we already know that the areas the area of grass strip should be 424 m^2

hence, A = Area ABCD - Area LMNO

424 = 888 - (4a^2 -122a + 888)

424 = 888 - 4a^2 +122a - 888

424 = -4a^2 +122a

4a^2 -122a +424=0

(We can solve this quadratic equation by breaking the middle term method)

2(2x-53)(x-4) = 0

2(2x-53) = 0

2x -53 = 0

x = 53/2

x = 26.5 (Not Possible)

x-4 = 0

x = 4

Length of the flower garden = 37 -2(4)

Length of the flower garden = 29 meters

Width of the flower garden = 24 -2(4)

Width of the flower garden = 16 meters

4 0

3 years ago

A salesman keeps 20% of his sales as a commission. How much does he have to sell to earn $1,000? It is percent proportions by th

BARSIC [14]

If he wants to earn $1000, it means that $1000 must be 20% of his overall sales.

1000 = 20% * x
1000 = 20/100x
1000 = 0,2x / ÷ 0,2 (both sides)
x = 5000

Answer: A salesman must sell products for $5000 to earn $1000.

6 0

3 years ago

Your cousin has a goat in his backyard, tied with a 4 foot rope. The goat can move in a circular motion the length of the rope.

rosijanka [135]

The stake the rope is tied to is the center of the circle. If the goat pulls the rope as far as it can go and walks around like this he makes a circle and he can eat the grass anywhere within this circle.

(a) Since the area of a circle is given by $A= \pi r^{2}$ this is the formula we can use to find the area of the yard where the goat can roam/eat/reach.

(b) Since the rope is 4 feet the radius r = 4 and the area is given by $4^{2} \pi =16 \pi ^{2}$ square feet. That's the exact area. For an approximation you could substitute 3.14 for pi and get 50.24 square feet.

(c)Since the rope is 5 feet the radius r = 4 and the area is given by $5^{2} \pi =25 \pi ^{2}$ square feet. That's the exact area. For an approximation you could substitute 3.14 for pi and get 78.5 square feet.

6 0

3 years ago