The length of a vegetable garden is 6 feet longer than it’s width if the area of the garden is 55 square feet , find its dimensions.
Answers
Answer:
Width is 5.
Length is 11.
Step-by-step explanation:
Let the width be x.
x = width
The length is 6 feet longer.
x + 6 = length
Area is
length × width
Area is 55 (given)
55 = x(x+6)
Use distributive property.
55 = x^2 + 6x
Set equal to 0 and factor to solve. See image.
We have to toss out a solution that doesn't make sense. A measure of a side of a rectangle cannot be negative.
see image.
Related Questions
A school club visits. a museum, Students tickets cost $ 6. Non- student ticket’s cost $12. The club paid $240 for tickets. (1) Define variables (1) Create an equation that models this situation (2) Rewrite equations slope intercept form.
Answers
"Define variables"
→ The number of student's tickets = a
→ The number of non-student tickets = b
→ the total cost represented = y
"Create an equation that models this situation"
→ y = $5 × a + $10 × b
"Rewrite the equation in slope intercept form"
→ y = $5 × a + $10 × b
→ y = 5a + 10b
→ 250 = 5a + 10b
Use the formula A=(1+r/n)^nt to solve the compound interest problem.
Find how long it takes for 900$ to double if it is invested at 6% interest compounded monthly.
The money will double in value in approximately ? years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answers
The total years taken to double the money according to Compounding will be 12.5 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 6%
amount = $900
Total amount = $1800
Compounded monthly,
so formula becomes,
Total amount = amount (1+r/1200)^12t
T = A[tex](1+r/1200)^{12t}[/tex]
1800 = 900 (1+6/1200)^12t
2 = (1+1/200)^12t
2 = 1.005^12t
taking log on both sides
log 2 = 12t *log 1.005
0.3/0.002 = 12t
t = 12.5 years
Hence the time taken to double the money is 12.5 years.
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Simplify the expression using properties of operations 7 1/3t-(10 2/3t-6)
Answers
The result is 6-13/3×t after simplification by multiplying first and added the like term.
What do you mean by properties of operation?The procedure of calculation which we use in arithmetic. We perform our mathematical calculation by using particular operational properties such as addition, subtraction, multiplication and division.
How do we simplify mathematical terms?we can simplify any expression by using the properties of addition, subtraction, multiplication or division depending on the statement given.
in the above expression 7×(1/3)t- [10×(2/3)t-6]
we simplify it (7/3)t- (20/3)t+6
-(13/3)t+6
hence, 6-13/3t
hence, the result is 6-13/3×t
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42 minus blank equals 29
Answers
Answer: 13
Step-by-step explanation:
Minus 29 from 42 to get 13
Answer:
13
Step-by-step explanation:
If you subtract 20 from 42, you will get your answer. Then you plug it into the equation to make sure it's correct.
42-29=13
29+13=42
42-13=29.
-Hope this helped
On Kate's reading app, she eams one star for every six books she reads. So far she has read 1.590 booksHow many stars has she earned?
Answers
Answer:
265
Step-by-step explanation:
1590/6=265
265x1=265
Write an equation in slope intercept form
Answers
Answer:
y = 2x - 5
Step-by-step explanation:
slope = 1-(-3)/3-1
4/2 = 2
this is the m value, or value before x.
So far, this is what we have: y = 2x + b
To find b, we plug in one of the points we have, into the equation.
(in this case ill use (3, 1), where 3 is the x and 1 is the y)
So,
1 = 2(3) + b
1 = 6 + b
1 - 6 = b
-5 = b
Finally,
y = 2x - 5
The sequence negative one fifth comma two sixths comma negative three sevenths comma four eighths and so on is given.
Part A: Assuming the pattern continues, list the next four terms in the sequence. Show all necessary math work. (4 points)
Part B: Write the explicit equation for f (n) to represent the sequence. Show all necessary math work. (4 points)
Part C: Is the sign of f (56) positive or negative? Justify your reasoning mathematically without determining the value of f (56). (2 points)
PLEASE ANSWER IN THE FORMAT AS
A;
B;
C;
Answers
The answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.
What is a sequence?
A sequence is defined as an arrangement of numbers in a particular order.
A sequence is given ; -1/5, 2/6, -3/7, 4/8.....
Part A
From inspection of the sequence, the pattern is:
i) Add 1 to the numerator of the previous term.
ii) Add 1 to the denominator of the previous term.
iii) Make every other term negative.
Therefore, The next four terms are -5/9, 6/10, -7/11, 8/12
Part B
From inspection of the sequence, we can see that the numerator is the position of the term (n) in the sequence. So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.
The denominator is 5 more than the position of the term in the sequence. So when n = 2 the denominator is 2 + 4 = 6, and when n = 4 the denominator is 4 + 4= 8.
Hence, the rule can be,
f(n) = n/(n+4)
If n is even, then f(n) is positive.
If n is odd, then f(n) is negative.
Part C
56 is an even number.
As the function f(n) is positive when n is even, the sign of f(56) is positive.
Therefore, the answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.
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Each marble bag sold by Ashley's Marble Company contains 3 green marbles for every 5 yellow marbles. If a bag has 18 green marbles, how many yellow marbles does it contain
Answers
Number of yellow marbles for every 18 green marbles = 30 yellow marbles
What is unitary method ?The unitary method entails figuring out the value of a single unit from which we can extrapolate the values of all the required units.
According to the given information
Applying the unitary method
Number of yellow marbles for every 3 green marbles = 5
Number of yellow marbles for every One green marbles = [tex]\frac{5}{3}[/tex]
Number of yellow marbles for every 18 green marbles = [tex]\frac{5}{3}[/tex] × 18
So
Number of yellow marbles for every 18 green marbles = 30 yellow marbles
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What is 6 3/5-2 7/10
Answers
The value of the given expression 6 3/5-2 7/10 is 39/10.
What is an expression?
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
Here, we have
Given: 6 3/5-2 7/10
We have to solve this expression and find the value of the given expression.
6 3/5-2 7/10 = 33/5 - 27/10
6 3/5-2 7/10 = (66-27)/10
6 3/5-2 7/10 = 39/10
Hence, the value of the given expression is 39/10.
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Solve the compound inequality and graph on the number lines provided.
7) -2 x ≤ 4 AND 10>-2 x
8) 10<3 x-2 or -3 x-2>14
Answers
The compound inequality solved are:
x ≤ 2 and x > -5
x > 4 or x < -5.3
The graph of the number line is given above.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
-2 x ≤ 4 and 10 > -2x
x ≤ 4/-2 and 10/2 > -x
x ≤ -2 and 5 > -x
x ≤ 2 and x > -5
This means.
-5 < x ≤ 2
The number line can be graphed as,
<----__-5__-4__-3__-2__-1__0__1__2__3__4__5----->
o---------------------------------------- o
10 < 3x - 2 or -3x - 2 > 14
10 + 2 < 3x or -3x > 14 + 2
12 < 3x or -3x > 16
x > 4 or -x > 16/3
x > 4 or x < -16/3
x > 4 or x < -5.3
x > 4 can be represented on a line graph as,
__-1__0__1__2__3__4__5__6__7--------->
o----------------------->
x < -5.3 can be represented on a number graph as,
<---------8__-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4---------->
<--------------------------o
Thus,
The compound inequality solved are:
x ≤ 2 and x > -5
x > 4 or x < -5.3
The graph of the number line is given above.
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Evaluate the absolute of w if w = -8 -5
Answers
Answer:
13
Step-by-step explanation:
w = -8 -5 =-13=13
w=-(8+5)
w=-13
Answer: -13
the least common multiple of the two numbers is 40 the ratio of the greater number is the to the lessor number is 5, 4
Answers
if 40 is the least frequent multiple of two whole numbers. The higher number to lesser number ratio is 4:5. The two digits after that are 8 and 10.
What is Least Common Multiple (LCM)?Least Common Multiple is the meaning of the abbreviation LCM.
The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.
It can also be computed using two or more numbers.
Finding the LCM of a given collection of numbers can be done in a variety of ways.
Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple.
The smallest number among all numbers is called the least common multiple of two or more numbers.
According to our question-
The number LCM is equal to 40.
4 × 5 × x = 40
20 × x = 40
20x=40
x=2
The larger number is equal to 4 x=4(2)=8.
The smaller value is =5x=5(2)=10.
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Complete question-
The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 4:5. What are the two numbers?
Which expression is equivalent to (36−y2)
(
36
−
y
2
)
?
Responses
(36+12y+y2)
(
36
+
12
y
+
y
2
)
( 36 + 12 y + y 2 )
(36−12y+y2)
(
36
−
12
y
+
y
2
)
( 36 − − 12 y + y 2 )
(6−y)(6+y)
Answers
The equivalent expression to (36 - y²) is (6 - y) (6 + y).
The correct answer option is option C
Which is the equivalent expression?(36 - y²)
Check all options
A. (36 + 12y + y²)
No
B. (36 - 12y + y²)
No
C. (6 - y) (6 + y)
open parenthesis
= 36 + 6y - 6y - y²
= 36 - y²
Yes
D. (6 - y) (6 - y)
= 36 - 6y - 6y + y²
= 36 - 12y + y²
No
In conclusion, the expression (6 - y) (6 + y) is equivalent to (36 - y²)
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Jenny has five exam scores of 100 , 83 , 96 , 84 , and 98 in her biology class. What score does she need on the final exam to have a mean grade of 90 90 ? Round your answer to two decimal places, if necessary. (All exams have a maximum of 100 100 points.)
Answers
Jenny needs to score 79 on final exam.
How to add decimal places?A decimal separator is a symbol that separates the integer and fractional parts of a decimal number. Different countries have officially designated various symbols to be used as separators. The symbol chosen also influences the symbol used for the thousands separator in digit grouping. Rounding to two decimal places is the same as rounding to the hundredths place, which is the second place to the right of the decimal point. 2.83620364, for example, can be rounded to two decimal places as 2.84, and 0.7035, to two decimal places as 0.70.
Total marks divide by total number subjects=Average
100+88+96+84+98+x=90*6
461+x=540
x=79
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How can fossils tell us about Earth's past?
A. Fossils give clues about environmental changes where the organisms lived.
B. Fossils can be used to date the time period of rocks and rock layers when the organisms lived.
C. Fossils can give clues of changes in the organism's body structure over time.
D. All of these are true.
E. None of these are true.
Answers
Choose the letter of the correct equation for the graph
Answers
Using translation concepts, the equation for the graph is b.
y = cos(x + π/2) + 1
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Suppose that we've got:
f(x) = a cos (bx - c) + d
Then, this function has:
Amplitude (the maximum distance of the graph from the middle line) = a
Period =[tex]\dfrac{2\pi}{b}[/tex]
Phase shift = [tex]\dfrac{c}{b}[/tex]
Maximum value: a + d
Minimum value: -a + d
In this problem, we have a cosine function
(zero at π/2, this is zero at the origin), shifted π/2 units to the right and 1 unit up.
Since the standard amplitude is between -1 and 1, here is between 0 and 2).
Hence the rule is given as follows:
b. y = cos(x + π/2) + 1
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evaluate: x2 - y2 by replacing x with 1/2 and y with 1/4
Answers
[tex]x^2 - y^2[/tex] when x = 1/2 and y = 1/4
[tex]\frac{1}{2} ^2 - \frac{1}{4} ^2\\\\=\frac{1}{4}-\frac{1}{16} \\\\= \frac{4}{16}-\frac{1}{16}\\ \\= 3/16[/tex]
Suppose you have just obtained a 30-year home mortgage for $120,000 at an APR of 5%. Find the required monthly payment.
Answers
The required monthly payment is given as follows:
$644.22.
What is the monthly payment formula?The monthly payment is defined by the equation presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
The parameters are listed as follows:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the values of these parameters are given as follows:
P = 120000, r = 0.05, n = 30 x 12 = 360.
Then:
r/12 = 0.05/12 = 0.004167.
Hence the monthly payment is obtained as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 120000\frac{0.004167(1.004167)^{360}}{(1.004167)^{360} - 1}[/tex]
A = $644.22.
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please help me mickey and how do I do brainlest your so smart
Answers
Answer:
second option or B
And to mark brainliest on answers when 2 people answer a crown button will appear on the bottom right and you click that
Step-by-step explanation:
-7+4x>-3
+7. +7
4x>4
/4. /4
x>1
So second option is correct
Hopes this helps sorry for late response I was eating
How many unit cubes would you need to create a tower that was 7 units tall and 3 units deep?
Answers
7+3 right? Or am I wrong
find the center and radius from the equation (x - 2)^2 + (y + 1)^2 = 16
Answers
Answer:
Center: (2,-1)
Radius: 4
Step-by-step explanation:
Circle equation: (x-h)^2 + (y-k)^2 = r^2
Finding the center:
Set to equaling 0 and solve for x and y
(x - 2)^2=0
(y + 1)^2=0
Finding the radius:
In the equation, because it's set to r^2, you would undo the square.
[tex]\sqrt{16}[/tex]=4
allison uses of a bag of horse feed per day. she feeds 2 quarter horses and 3 paint horses the same amount each day. draw a model to show a whole bag of horse feed below.
Answers
Allison feeds 11 horses in a day.
Horses are herbivores and, as such, they need a very specific diet. They must consume lots of fiber to keep their extremely long and sensitive digestive tract working and they must eat little and often, almost all day long.
A horse's feed should consist primarily of grass or roughage. However, hay is insufficient to provide a complete nutritional profile. Important minerals and nutrients will be added by adding grains and concentrates, but calories will also be added. Roughage, feeds, and concentration types are listed below, from least to most "complete."
Given,
Allison feeds 2 quarter horses and 3 paint horses the same amount each day.
Therefore, she feeds 2*4+3 = 11 horses in a day.
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Graph the function f(x) = 14(0.87). Does this function show growth or decay? What is the equation of the asymptote?
Growth; y = 0
Growth; y = 14
Decay; y = 0
Decay; y = 14
Answers
The function f(x) = 14(0.87) has is a constant function has no growth or decay.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given a function f(x) = 14(0.87) Now it is a constant function as for every different values of x the function f(x) has same value and has no growth or decay.
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Kelly wants to fill 2 punch bowls for a birthday party. Each punch bowl holds 7 2/5 quarts of punch. How much punch will Kelly need?
Answers
Answer:
14 4/5
Step-by-step explanation: 7 2/5 x 2 or 7 2/5
+7 2/5
-------
14 4/5
Which could be the first step in solving the equation represented by the model below?
Add 4 positwe unt tles to each side.
Remove 4 unit ties from each side.
Add 6 positive unit tiles to each side.
Remove 6 unit tiles from each side.
Answers
To each side, add 4 positive unit tiles.
What is a one-variable linear equation and what does it look like?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.
The initial formula is:
3x - 4 = 2x + 5
Four positive unit tiles are added to each side, giving us:
3x - 4 + 4 = 2x + 5 + 4
3x = 2x + 9
which removes the independent elements off both sides of the equal sign and places them all on the right side (the +9 term), simplifying the initial equation. You'll see that the other choices don't produce this outcome.
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Subtract 2w + 4 from 3w - 6
Answers
Answer:
w-10
Step-by-step explanation:
(3w-6)-(2w+4)
Take out the brackets:
3w-6-2w-4
Group the like terms:
3w-2w-6-4
Simplify:
w-10
Find an equation for the parabola that has its vertex at the origin and satisfies the given condition. Directrix y=1/2
Answers
Required equation of the parabola with origin as its vertex and directrix
y = 1/2 is equal to x² = -2y.
As given in the question,
Let vertex of the parabola be ( h, k )
Vertex of the given parabola be at origin
⇒ ( h , k ) = ( 0 , 0 )
Directrix is y =1/2 above the vertex.
Focus is ( 0, -1/2)
Equation of the parabola is given by
Distance between focus to the vertex = distance between vertex to the directrix
( y - (1/2) )² = ( x - 0)² + ( y - (-1/2) )²
⇒ y² - y + 1/4 = x² + y² + y + 1/4
⇒ -y = x² + y
⇒x² = -y - y
⇒ x² = -2y
Therefore, the equation of the parabola with vertex at origin and directrix y =1/2 is equal to x² = -2y .
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Simplify please!
Sqrt(-256x^8)
Answers
find the 16th term of the arithmetic sequence whose common difference is d=7 and whose first term is a↓1=-2
Answers
The 16th term of the arithmetic sequence value is 103.
How to find 16th term of the arithmetic sequence?The 16th term of the arithmetic sequence whose common difference is d=7 and whose first term is a↓1=-2
An arithmetic sequence is defined as an=a1+d (n-1). In essence, this indicates that the term you're looking for, an, is equal to the first term, a1, plus the term difference, d, times the number of terms, n, minus one. For this issue, that essentially means that
an=a1+d(n-1)
The value of an at term sixteen is equal to -2 + 7*. (16-1)
PEDMAS is used to
a16= -2+7*15
a16= -2+105
a16= 103
Therefore, 103 will be the 16th term's value.
The 16th term of the arithmetic sequence value is 103.
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Gwen and Max had breakfast at a cafe. Muffins cost $2 each, and fruit cups cost $4 each. Gwen had 2 muffins and 1 fruit cup. Max had 2 muffins and 1 fruit cup. How much did their breakfast cost?
Answers
Answer: Gwen's breakfast in total was $8. Max's Breakfast in total is $8 as well. so their breakfast together is $16 in total
Answer:
their breakfast cost 16 dollars
Step-by-step explanation:
because you would do 2 times 2 which is 4 and 1 times 4 which is also 4 add those two together to get 8 and the double it because max got the same thing