Answer:
The answer is 120 feet.
Step-by-step explanation:
The area of the field (A) is:
A = w · l (w - width, l - length)
It is known:
A = 12,000 ft²
l = w - 20
So, let's replace this in the formula for the area of the field:
12,000 = w · (w - 20)
12,000 = w² - 20
⇒ w² - 20w - 12,000 = 0
This is quadratic equation. Based on the quadratic formula:
ax² + bx + c = 0 ⇒
In the equation w² - 20w - 12,000 = 0, a = 1, b = -20, c = -12000
Thus:
So, width w can be either
or
Since, the width cannot be a negative number, the width of the field is 120 feet.
The length of the field is 120 feet.
Option C is the correct answer.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
Let's start by using the given information to set up two equations:
Let x be the length of the field in feet.
Then, the width of the field is x - 20 feet.
The area of the field is given as 12,000 square feet:
x (x - 20) = 12,000
Expanding the left side of the equation, we get:
x² - 20x = 12,000
Bringing all the terms to one side, we get:
x² - 20x - 12,000 = 0
Now, we can solve this quadratic equation using factoring,
Completing the square, or the quadratic formula.
Here, we will use factoring:
x² - 20x - 12,000 = 0
(x - 120) (x + 100) = 0
The solutions are x = 120 and x = -100, but a negative length doesn't make sense, so we reject that solution.
Therefore,
The length of the field is 120 feet.
To check, we can substitute x = 120 into the equation for the width:
Width = x - 20 = 100 feet
Area = Length x Width
= 120 ft x 100 ft
= 12,000 sq ft
Thus,
The length of the field is 120 feet.
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The class was given a test that had a total of 125 points possible. A student then earned an 84% on the test. What are the total points that this student earned, out of the possible 125 points?
Help me please!!
Answer:
Step-by-step explanation:
84/100 = x/125
x = 105 points
Use the Distance Formula to find the distance between each pair of points. Round to the nearest tenth if necessary.
5. P(1, 1), Q(–1, –1)
6. E(1/2,4 1/4),F(5,-1/2)
Given:
The pair of points.
5. P(1, 1), Q(–1, –1)
6. [tex]E\left(\dfrac{1}{2},4\dfrac{1}{4}\right), F\left(5,-\dfrac{1}{2}\right)[/tex]
To find:
The distance between the pair of points.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
5.
The distance between the pair of points P(1, 1) and Q(–1, –1) is:
[tex]PQ=\sqrt{(-1-1)^2+(-1-1)^2}[/tex]
[tex]PQ=\sqrt{(-2)^2+(-2)^2}[/tex]
[tex]PQ=\sqrt{4+4}[/tex]
[tex]PQ=\sqrt{8}[/tex]
[tex]PQ=2\sqrt{2}[/tex]
Therefore, the distance between P and Q is [tex]2\sqrt{2}[/tex].
6.
The distance between the pair of point [tex]E\left(\dfrac{1}{2},4\dfrac{1}{4}\right), F\left(5,-\dfrac{1}{2}\right)[/tex] is:
[tex]EF=\sqrt{\left(5-\dfrac{1}{2}\right)^2+\left(-\dfrac{1}{2}-4\dfrac{1}{4}\right)^2}[/tex]
[tex]EF=\sqrt{\left(\dfrac{10-1}{2}\right)^2+\left(-\dfrac{1}{2}-\dfrac{17}{4}\right)^2}[/tex]
[tex]EF=\sqrt{\left(\dfrac{9}{2}\right)^2+\left(\dfrac{-2-17}{4}\right)^2}[/tex]
[tex]EF=\sqrt{\dfrac{81}{4}+\left(\dfrac{-19}{4}\right)^2}[/tex]
On further simplification, we get
[tex]EF=\sqrt{\dfrac{81}{4}+\dfrac{361}{16}}[/tex]
[tex]EF=\sqrt{\dfrac{324+361}{16}}[/tex]
[tex]EF=\sqrt{\dfrac{685}{16}}[/tex]
[tex]EF=\sqrt{42.8125 }[/tex]
[tex]EF\approx 6.5[/tex]
Therefore, the distance between E and F is 6.5 units.
1 NEED HELP ASAP WILL GIVE BRAINLY
Answer:
c
Step-by-step explanation:
I believe its c I've done this last semester
please help with question 2 50 points for answer and brainliest
Answer:
b) Reflection over y = -2
Step-by-step explanation:
Reflection over y = -2
how many 0 are in 123456789123456789000012010100101010101010101010010
Answer:
19
Step-by-step explanation:
:)
help nowwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
Answer:
I beleive is is -2% because 5 is 2 more than 3
so then 5-2=3
Answer:
Error Is 100(2/3) 66.7%
how many one-digit integers are there
John says the transformation rule (x, y) Right-arrow (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the image (0, –2). What was his error?
sample response: The pre-image is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. You get (4, 5) → (4+4, 5+7). Simplify to get (4, 5) → (8, 12). This is the image. Instead the rule was applied to the image. This is the source of the error.
Answer:
The transformation rule should be applied to the pre-image. The application of the rule results in the point (8, 12). The transformation rule was applied to the wrong point.
Step-by-step explanation:
The Washington Monument is an obelisk with a square pyramid top. The slant height of the pyramid is 55.5 feet, and the square base has sides of 34.5 feet. Find the surface area of the pyramid.
Which numbers from the list below are irrational numbers?
Your answer:
fraction numerator square root of 3 over denominator 7 end fraction
square root of 2.3 end root
8.5353...
fraction numerator negative 2 over denominator 5 end fraction
Answer:
1st and 2nd option are the correct answers.
divide until the remainder is zero.
7.4 ÷ 4
Answer:
1.85
Step-by-step explanation:
Answer:
this is not possible as it is a non terminating decimal
Solve for x. Enter the solutions from least to greatest. (−5x+4)(x−3)=0
lesser x=
greater x=
Jeremiah invested
$
800
$800 in an account that pays 3% interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Jeremiah would have in the account 14 years after his initial investment. Round to the nearest tenth (if necessary).
Answer: 1210.1
Step-by-step explanation:
Over the past few years Donald made 40 trips to the amusement park. He drove 400 km in all. The distance travelled by him on each trip to the park is:
Answer:
10
Step-by-step explanation:
Answer:
10 km
Step-by-step explanation:
total no of km covered=400
total no of trips=40
distance in each trip= 400/40
=10km
Ulet rolls 2 fair dice and adds the results from each. Work out the probability of getting a total of 7.
Answer:
7/ 36
Step-by-step explanation:
Roll of 2 fair six sided die :
Sample space = 6² = 36
Sum of 7:
(1,6) ; (6,1) ; (3,4) ; (4,3) ; (2,5) ; (5,2) = 6
Probability = required outcome / Total possible outcomes
Required outcome = 7
Total possible outcomes = 36
P(obtaining a sum of 7) = 7 / 36
Jay bought 6 tubs of kutsinta at P70 per tub plus a delivery charge of P30. How much will she pay for her order?
Answer:
the total amount paid by her is P450
Step-by-step explanation:
The computation of the total amount paid by her is given below;
= Total cost + delivery charges
= 6 tubs at P70 + P 30
= P420 + P30
= P450
Hence, the total amount paid by her is P450
Y=6x-3 function rule
Answer:
f(x) = 6x - 3
Step-by-step explanation:
A recipe for beef fajitas uses 5 pounds of beef to make 20 meals. How many pounds of beef are needed to make 80 meals?
Answer: 0.25 pound of beef are needed to make 80 meals.
Step-by-step explanation:
Given : A recipe for beef fajitas uses 5 pounds of beef to make 20 meals.
Then the of beef required for 1 mesal = ( 5 pounds) ÷ 20
= [tex]\dfrac{5}{20}[/tex] pound
[tex]=\dfrac{1}{4} [\text{Divide numerator and denominator}][/tex]
=0.25 pound
Hence, 0.25 pound of beef are needed to make 80 meals.
please help i will give brainliest
How do i slove for x2 + 19 = 3
Answer:
x = ± 4i
Step-by-step explanation:
x^2 + 19 = 3
Subtract 19 from each side
x^2 +19-19 = 3-19
x^2 = -16
Take the square root of each side
sqrt(x^2) = sqrt(-16)
x = sqrt(-1*16)
x =sqrt(-1) * sqrt(16)
We know that the square root of -1 is the imaginary number i
x = ± 4i
A new Playstation game system costs $380. The tax on the system is 4%. What is the total cost of the system including tax? *
Answer:
395.2
Step-by-step explanation:
380 x 0.04 = 15.2
380 + 15.2 = 395.2
Answer:
The cost of the system including the tax is $395.20.
Step-by-step explanation:
If the tax is 4% that means that the total price will equal...
380 + (380)(0.04) = $395.20
Therefore the cost of the system including the tax will be $395.20.
does anyone know this i will give brainliest
Answer: -324.4
Step-by-step explanation:
What angle has a degrees over 180?
Right
Rex
Straight
Acute
when you Subtract: 70-(-11) what is your answer
Answer:
81
Step-by-step explanation:
What is the possible scale factor for the rectangle?
Answer:
A
Step-by-step explanation:
Which of the following expressions is equivalent to (2x)3 ?
Group of answer choices
6x4
2x3
8x3
6x3
btw the numbers on the right are exponents
Answer:
6x3
Step-by-step explanation:
....................
what is the value of x if 85 + 19x
Answer:
we dont know what the equation equals yes im using this for free points im having a compition with my friend so ty im srry if i offended you
Step-by-step explanation:
Harold is moving a 5- foot tall refrigerator. He tilts it onto its rear edge forming an angle between the back of the refrigerator and the floor; the top edge of the tilted refrigerator is exactly 4 feet above the floor as shown in the following diagram.
What is the cosine of the angle the refrigerator makes with the floor?
A, 4/5
B, 5/4
C, 4/3
D, 3/4
E, 3/5
Please help I’ll give branliest
The cosine of the angle the refrigerator makes with the floor is option (E) 3/5 is the correct answer.
What is trigonometry?Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
Harold tilted the 5 foot fridge, so the slanting height = 5 feet
The tilted refrigerator makes the height 4 feet from the floor.
From the diagram,
The three sides of the triangle according to Pythagoras theorem are
Hypotenuse side, h = 5 feet
Opposite side, o = 4 feet
Let a be the adjacent side.
By Pythagoras theorem,
[tex]Hypotenuse^{2} = Opposite^{2}+Adjacent^{2}[/tex]
⇒ [tex]5^{2} =4^{2} +a^{2}[/tex]
⇒ [tex]a^{2} = 25-16[/tex]
⇒ [tex]a=\sqrt{9}[/tex]
⇒ [tex]a=3[/tex]
Thus the trigonometric ratio cosine of the angle is
[tex]cos \theta =\frac{Adjacent}{Hypotenuse}[/tex]
⇒ [tex]cos \theta =\frac{3}{5}[/tex]
Hence we can conclude that the cosine of the angle the refrigerator makes with the floor is option (E) 3/5 is the correct answer.
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how many powers with an exponent of 2 are there between 1 and 100?
There are 10 perfect squares between 1 and 100, and 10 powers with an exponent of 2 between 1 and 100.
What is Number system?A number system is defined as a system of writing to express numbers.
Between 1 and 100, the perfect squares (numbers that can be expressed as the square of an integer) have exponents of 2.
We need to count the number of perfect squares between 1 and 100. These include:
1² = 1
2² = 4
3²= 9
4² = 16
5² = 25
6² = 36
7²= 49
8² = 64
9² = 81
10² = 100
So, there are 10 perfect squares between 1 and 100, and therefore 10 powers with an exponent of 2 between 1 and 100.
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Simplify: Square root of -16
4
4*4 = [tex]\sqrt{x}[/tex]16 not sure how it gets negative