Answer:
x = 4.85 feet
Step-by-step explanation:
Original area of the petting farm = 10 × 14
= 140 square feet
.
New area = double the original area = 140 * 2
= 280 square feet
New area of the petting farm =
Width × length
280 = (10+x) × (14+x)
280 = 140 + 10x + 14x + x²
280 - 140 = x² + 24x
140 = x² + 24x
x² + 24x - 140 = 0
Solve the quadratic equation
x = -b ± √b² - 4ac / 2a
= -24 ± √(24)² - 4*1*-140 / 2*1
= -24 ± √ 576 - (-560) / 2
= -24 ± √ 576 + 560 / 2
= -24 ± √1,136 / 2
= -24 ± 4√71 / 2
= -24/2 ± 4√71/2
= -12 ± 2√71
x = 4.8523 or x = -28.8583
x can not be a negative value
Therefore,
x = 4.85 feet to the nearest hundredth
Ericka observed the total variation in the water level over 6.2 years to be −13.64 mm. She compared this to the average annual trend, which shows the water level rising 1.8 mm/year. Remember, she used 6.2 years as her time period. What is the difference between how much average water levels rose and how much the water level fell in the part of the river she observed?
__________millimeters
Answer:
In the area that she observed, the water level fell 13.64mm over 6.4 years, for an average annual rate of change of: -13.64 ÷ 6.2 = -2.2 mm/ year.
I need help with this proof!
Answer:
∠B ≅ ∠F ⇒ proved down
Step-by-step explanation:
In the two right triangles, if the hypotenuse and leg of the 1st right Δ ≅ the hypotenuse and leg of the 2nd right Δ, then the two triangles are congruent
Let us use this fact to solve the question
→ In Δs BCD and FED
∵ ∠C and ∠E are right angles
∴ Δs BCD and FED are right triangles ⇒ (1)
∵ D is the mid-point of CE
→ That means point D divides CE into 2 equal parts CD and ED
∴ CD = ED ⇒ (2) legs
∵ BD and DF are the opposite sides to the right angles
∴ BD and DF are the hypotenuses of the triangles
∵ BD ≅ FD ⇒ (3) hypotenuses
→ From (1), (2), (3), and the fact above
∴ Δ BCD ≅ ΔFED ⇒ by HL postulate of congruency
→ As a result of congruency
∴ BC ≅ FE
∴ ∠BDC ≅ ∠FDE
∴ ∠B ≅ ∠F ⇒ proved
Write 5.5% as a fraction in simplest form
Answer:
11/200
Step-by-step explanation:
5.5% = 5.5/100 = 0.055
0.055 1000
———- X ———
1 1000
=55/1000
=11/200
what is the measure of angle A in the triangle
Which of the following functions maps 3 to -5?
O f(x) = 4 – x2
O f(x) = x-5
O f(x) = -x + 2
O f(x) = x + 8
Answer: A
Step-by-step explanation:
write 1.054 in words
Answer:
one and fifty-four thousandths
Step-by-step explanation:
The 1 is easy.
The 4 is in the thousandths place, so the decimal part is 54/1000.
Answer: one and fifty-four thousandths
Find the equation of the line that contains the point (-5,-3) and is parallel to the line 5x+6y=11. Write the equation in slope-intercept form,if possible.
Answer:
y = -5x/6 - 33/6
Step-by-step explanation:
The standard form of equation of a line in point slope form is y - y0 = m(x - x0)
m is the slope
(x0, y0) is the point on the line
First we need the slope of the given equation 5x+6y=11.
Rewrite in standard form;
5x+6y=11
6y = -5x + 11
y = -5/6 x + 11/6
Hence the slope is -5/6
Since the unknown line is parallel to this line, they will have the same slope, hence the slope of the required line is -5/6
Substitute m = -5/6 and the point (-5,-3) into the point-slope expression;
y - y0 = m(x - x0)
y - (-3) = -5/6 (x - (-5))
y + 3 = -5/6(x+3)
6(y+3) = -5(x+3)
6y+18 = -5x - 15
6y+5x =-15 -18
6y+5x =-33
Express in slope intercept form
6y = -5x - 33
y = -5x/6 - 33/6
HELP HAVING A BAD DAY
Brandon decided to make his own hand sanitizer.
To be effective, hand sanitizer should contain 60% alcohol.
How much pure alcohol does Brandon need to make
a)150ml of hand sanitizer?
b)250ml of hand sanitizer?
I WILL AWARD BRAINLIEST FOR THE CORRECT ANSWER
Answer:
A - 90ml
B - 150ml
Step-by-step explanation:
A - 150ml ÷ 100 = 1.5 x 60 = 90ml
B - 250ml ÷ 100 = 2.5 x 60 = 150ml
Brandon needs 90 ml and 150 ml of alcohol to make 150 ml and 250 ml hand sanitizer.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Brandon decided to make his own hand sanitizer.
To be effective, hand sanitizer should contain 60% alcohol.
a) 150ml of hand sanitizer;
Use percentage formula,
Percentage of alcohol = 150 x 60 / 100
Percentage of alcohol = 90 ml
a) 250ml of hand sanitizer;
Use percentage formula,
Percentage of alcohol = 250 x 60 / 100
Percentage of alcohol = 150 ml
Therefore, he needs 90 ml and 150 ml of alcohol to make 150 ml and 250 ml hand sanitizer.
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Which function rule models the function over the domain specified in the table below?
f(x)
11
11
17
O f(x) =3x + 10
O fx) = 2x + 3
O fx)= 4x +5
O fx) =3x-10
The function with the domain is given by f ( x ) = 2x + 3
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
Let the x values be x = { -7 , -1 , 3 , 4 , 7 )
Let the y values be y = { -11, 1 , 9 , 11 , 17 }
Now , the function is given as
f ( x ) = 2x + 3 be equation (1)
when x = -7
y = 2 ( -7 ) + 3
y = -11
when x = 7
y = 2 ( 7 ) + 3
y = 17
Hence , the function is f ( x ) = 2x + 3
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Two friends are going to the mall to buy pizza. One of the friends buys 1cheese slice and 2 pepperoni slices for $8.75. Her friend purchases 2 chese slices and 3 pepperoni slices for $15.00. Find the cost of each.
Answer:
The cost of each:
1 cheese slice = c = $3.75
1 pepperoni slice = p = $2.5
Step-by-step explanation:
Let the cost:
1 cheese slice = c
1 pepperoni slice = p
Two friends are going to the mall to buy pizza.
One of the friends buys 1cheese slice and 2 pepperoni slices for $8.75.
c + 2p = $8.75.....Equation 1
c = $8.75 - 2p
Her friend purchases 2 chese slices and 3 pepperoni slices for $15.00.
2c + 3p = $15.00.....Equation 2
We substitute 8.75 - 2p for c in Equation 2
2(8.75 - 2p) + 3p = $15.00
17.5 - 4p + 3p = 15
Collect like terms
- 4p + 3p = 15 - 17.5
-p = -2.5
p = $2.5
c = $8.75 - 2p
c = $8.75 - 2(2.5)
c = $8.75 - 5.0
c = $3.75
The cost of each:
1 cheese slice = c = $3.75
1 pepperoni slice = p = $2.5
Explain, in terms of the structure of the expression for L(t) , why Lincoln's balance can never be 499.
Answer:
after 19 years, Helen's balance is still larger than Lincoln's but after 20 years, Lincoln's balance will be larger than Helen's.
Step-by-step explanation:
Find the magnitude of angle A if cos A = 0.5
Step-by-step explanation:
[tex]A = {cos}^{ - 1} 0.5 \\ \: \: A= 60[/tex]
Let f(x) = −2x 2 − 7 and g(x) = √x + 3. Find (f ∘ g)(25)
Answer:
(f О g)(25) is -135
Step-by-step explanation:
The composite function (f О g)(x) means substitute x in f by g
∵ f(x) = -2x² - 7
∵ g(x) = √3 + 3
→ To find (f О g)(25), find g(25) first, then substitute x in f by the value of g(25)
∵ x = 25
∴ g(25) = √25 + 3
∵ √25 = 5
∴ g(25) = 5 + 3
∴ g(25) = 8
→ Now substitute x in f by 8
∵ x = 8
∴ f(8) = -2(8)² - 7
∴ f(8) = -2(64) - 7
∴ f(8) = -128 - 7
∴ f(8) = -135
∴ (f О g)(25) = -135
Complete the table and then graph the function.y= -4x + 34
Answer:
Step-by-step explanation:
A national standardized test is graded on a scale from 1 to 5 the scores for a particular school are given below if a student Is chosen at random what is the possibility that they scored a 4 or a 5
Answer:
Step-by-step explanation:
The possibility of scoring a 4 is 1/5
The possibility of scoring a 5 is 1/5
The possibility of scoring either 4 or a 5 is 2/5
mark got 14 problems wrong on the test. his score was 72% correct.how many problems were on the test
9514 1404 393
Answer:
50 problems
Step-by-step explanation:
The percentage wrong was 100% -72% = 28%. Then the number n of problems on the test was ...
14 = 0.28·n
n = 14/0.28 = 50
There were 50 problems on the test.
The net of a triangular prism and its dimensions are shown in the diagram. what is the lateral surface area of the triangular prism in square centimeters
A-264 cm
B-240cm
C-225cm
D “Not here”
Answer: 120 sq in.
Step-by-step explanation:
For values of x when x + 0, which number property is shown below?
17x () = 172
O associative
0 commutative
O multiplicative identity
division property of zero
Hackensack and New York City are 12 miles apart. On a map, the two cities are 2 Inches apart. How many miles does 1 Inch represent on the map?
Answer:
6 miles
Step-by-step explanation:
From the question, we are told that 12 miles represents 2 inches on the map.
We are to calculate the amount of miles 1 inch will represent. To do this you will say:
12 miles = 2 inches
x miles = 1 in
Cross multiply;
2 * x = 12 * 1
2x = 12
x = 12/2
x = 6
Hence 1 inch will represents 6 miles on the map
Help! Thank youuuuu!!!!!
Answer:
scamming outta points
Step-by-step explanation:
Simplify 12−3l+5(4−l)
Answer:
−8+32
Step-by-step explanation:
...................
Lauren bikes 4/3 miles in 1/10 hour. How long does it take her to bike one mile?
Answer:
3/40 hours.
Step-by-step explanation:
hope this helps !
16x2 + 4x2 – 2x – 12x2 + 4x
Answer:
8x^2 + 2x
Step-by-step explanation:
I NEED HELP WITH THIS ASAP THERE IS ALSO ONE MORE QUESTION TO THIS PROBLEM PLEASE HELP
Answer:
whoa hold up there friend
Step-by-step explanation:
it will be 4,6,8,10 and the 2nd one is $10,$15,$20,$25
(50-72) 15 =
please help
Answer:
-330
Step-by-step explanation:
Trust me :)) sjsksksk
The Bryant family bought 7 bags of cookies. Each bag had 13 cookies. They have since eaten 29 of the cookies. How many cookies do they have left?
Answer:is 7x13=91-29=62
Step-by-step explanation:
i took the test on edge
91
Answer:
solution
1bag =13coikies
7bags=???
we take (7bag ×13 cookies)\1bagthen it will be 91cookiesthen we take 91COKIES-29COKIE so us to get the number of cookies left it will be 62 cokiesA real horse is 1.8 m high. A statue of the horse is 3 m high. What is the ratio of the height of the horse to the height of the statue
*BRAINIEST & 15 POINTS*
* MULTIPLE CHOICE*
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Isosceles right
Step-by-step explanation:
It's a right triangle because one of the angles is 90 degrees
It's isosceles because two sides are 5.57
find the distance for d
Answer:
320 i think
Step-by-step explanation:
Jasper and Corey have saved up a total of $78.00. Jasper has saved 6 dollars more than twice as much as
Corey. How much has Corey saved?
Answer:
24
Step-by-step explanation:
Corey has saved an amount of 24 dollars, if they have saved up a total of $78.00.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's assume that Corey has saved an amount of x dollars.
Given that Jasper and Corey have saved up a total of $78.00.
Jasper has saved 6 dollars more than twice as much as
Corey.
As per the given condition, the algebraic form is:
(6 + 2x) + x = 78.
Rearrange the terms of variables of x in the above equation,
6 + 2x + x = 78
Apply the addition operation,
6 + 3x = 78
Subtract 6 from both sides in the equation,
3x = 72
Now divide both sides by 3 in the equation,
x = 24
Therefore, Corey has saved an amount of 24 dollars.
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