Answer:
The largest area she can enclose for her garden with this fencing is [tex]56 ft^2[/tex]
Step-by-step explanation:
Suppose the rectangular space Mrs. Greene wants to plant has dimensions x feet and y feet.
Since each section of fencing is 1-foot long, both x and y must be integer numbers.
The perimeter of the rectangular space is calculated as:
P = 2x + 2y
And we know she uses all 30 sections of fencing, thus:
2x + 2y = 30, where x, y are integers and positive.
Simplifying by 2:
x + y = 15
Solve for x:
x = 15 - y
This equation doesn't have infinitely many solutions, since both numbers must be integers and positive. Suppose we start by setting y=1, then x=14. That is a possible arrangement for the garden.
Another valid option is for y=2, x=13
Continuing with these patterns, we find the maximum value for y is 7, x=8, because if we set y=8, x=7, this is the same condition as y=7, x=8.
Thus, from y=1 to y=7, there are 8 possible combinations for the arrangement of the garden.
The area of a rectangle is
[tex]A=x\cdot y[/tex]
Testing some possible arrangements:
y=1, x=14
[tex]A=1\cdot 14= 14 ft^2[/tex]
y=2, x=13
[tex]A=2\cdot 13= 26 ft^2[/tex]
y=3, x=12
[tex]A=3\cdot 12= 36 ft^2[/tex]
We can notice the combination y=7, x=8 has an area of:
[tex]A=7\cdot 8= 56 ft^2[/tex]
This is the largest possible area of all combinations, thus:
The largest area she can enclose for her garden with this fencing is [tex]56 ft^2[/tex]
Which of the following inequalities are equivalent to the inequality x-b<3, where b is a constant? Select all that apply.
Answer:
x - b - 3 < 0
Step-by-step explanation:
o
The inequality that is equivalent to x-b < 3 will be x - b - 3 < 0. The correct option is A.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Given inequality is x-b<3. Solve the inequality and match it with the options.
x - b < 3
x - b - 3 < 0
From the options, we can see that the inequality x-b<3 is equivalent to the inequality x - b - 3 < 0.
Therefore, the inequality that is equivalent to x-b < 3 will be x - b - 3 < 0. The correct option is A.
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Which shows the scale factor used to dilate triangle XYZ to form triangle X'Y'Z'?
A( 1/2 x, 1/2 y)
B (1/3 x, 1/3 y)
Answer:
B
Step-by-step explanation:
A is wrong lol, trust me.
HELP ASAP!! pleaseeeee
solve each equation using the quadratic formula. 4x^2-13x+3
Answer:
( 4 x − 1 ) ( x − 3 )
Step-by-step explanation:
Factor by grouping.
Answer:
Your answer is: x = 3 , 1/4
Solve the equation for x by finding a , b , and c of the quadratic then applying the quadratic formula.
Step-by-step explanation:
Hope this helped : )
-0.8 x +40 - 8x -35 i need help ASAP
Answer:
-8.8x + 5
Step-by-step explanation:
See the attached picture.
Hope this helps!!!
The value of x is 0.57 in the given expression -0.8 x +40 - 8x -35
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is -0.8 x +40 - 8x -35
Minus zero point eight times of x plus forty minus eight times of x minus thirty five
-0.8 x +40 - 8x -35
Add the like terms
-0.8x-8x+40-35
-8.8x+5
Isolate the variable x
-8.8x=-5
Divide both sides by 8.8
x=5/8.8
x=0.57
Hence, the value of x is 0.57 in the given expression -0.8 x +40 - 8x -35
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An animal shelter has $2500 in its reserve fund. The shelter charges $40 per animal placement and would like to have at least $4000 in its reserve fund. Write an inequality to represent this situation.
Answer:
Step 1
Write and solve the inequality:
2,500 + 40a ≥ 4,000, or 40a ≥ 1,500
a ≥ 37.5
Step 2
If the shelter places 30 cats and 10 dogs,
or 40 animals, that will be enough to meet
its goal, because a = 40 is a solution to the
inequality a ≥ 37.5.
Which of the following forms a proportion?
5/9 = 14/18 3/5 = 21/35 6/12 = 18/34 1/8 = 2/24
Answer:
3/5 = 21/35
Step-by-step explanation:
if you reduce 21/35 it is 3/5 so it is the same thing
For the following right triangle, find the side length x.
Answer: 37
Step-by-step explanation:
Use A squared plus b squared equals c squared.
1. 35 squared is 1,225.
2. 12 squared is 144.
3. 144 plus 1,225 is 1,369. Now is 1,369 a square number?
Well the square root of 1,369, that's 37.
Write the inequality. Lawyers work up to 80 hours a week. (Use x for your variable)
Evaluate x/y when x=9/4 and y=3/5
Answer:
[tex]\displaystyle x/y=\frac{15}{4}[/tex]
Step-by-step explanation:
Division of fractions
To calculate the division of fractions a/b and c/d, it's usually easier to multiply a/b by the reciprocal of the denominator, that is:
[tex]\displaystyle \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\cdot \frac{d}{c}[/tex]
We will evaluate x/y when x=9/4 and y=3/5:
[tex]\displaystyle \frac{\frac{9}{4}}{\frac{3}{5}}=\frac{9}{4}\cdot \frac{5}{3}[/tex]
[tex]\displaystyle=\frac{45}{12}[/tex]
Simplifying:
[tex]\displaystyle \boxed{x/y=\frac{15}{4}}[/tex]
Which set of side lengths form a right triangle?
a.) 2 inches, 3 inches, 4 inches
b.) 6 inches, 8 inches, 10 inches
c.) 8 inches, 9 inches, 11 inches
d.) 10 inches, 12 inches, 13 inches
A group of 80 ants went to collect some honey. 1/2 lost their way and 1/4 got eaten by a passing anteater. How many ants came back?
Answer:
23
Step-by-step explanation:
Matthew is going to drive from Salt Lake City, Utah, to Las Vegas, Nevada. His car travels a consistent
number of miles
per gallon of gasoline and he has some gasoline in his tank already. Matthew writes the
equation 25(x + 3) = 424, where x represents the number of gallons of gasoline he will need to purchase to
complete the trip.
Identify the meaning of each of the constants in Matthew's equation in the context of the problem, then solve
the equation to determine how many gallons of gasoline he must purchase.
Answer: 14 gallons of gasoline.
Step-by-step explanation:
given data:
25(x + 3) = 424
where x is the number of gallon of gasoline needed to purchase.
Solution.
25(x + 3) = 424
first we open the bracket
25x + 75 = 424
collect like terms
25x = 424 – 75
25x = 349
divide both sides by 25
25x/25 = 349/25
x = 13.96
x = 14
mathew needs to get 14 gallons of gasoline.
expand (2x+3) (2x-5)
Answer:
4x^2−4x−15
Split using the sum and difference of the formula, the simplify
A disadvantage of privately owned media is its __________.
Answer:
Its D
Step-by-step explanation:
Suppose y varies directly as x. To solve you will need to find the constant of the
variation, write the equation so you can answer the question. If y = 4 when x = 2,
find y when x = 16.*
Answer:
32
Step-by-step explanation:
Given, y varies directly as x. So, y=kx, where k is the constant of proportionality.
Given, x=2, y=4. plug in the values in the equation.
4=k*2
k=4/2
k=2
x=16
y=2*16
y=32
Write a complex number where the real component is 7 and the imaginary component is -13i
Answer:
z = 7 - 13i
Step-by-step explanation:
A complex number has the form
z = a + bi ( where a is the real part and bi the imaginary part )
Here a = 7 and bi = - 13i, thus
z = 7 - 13i
A glacier is moving at a rate of 0.3 inches every hour. The table below represents this relationship.
Glacial Movement
Distance Moved (inches)
Time
(hours)
0.3
1
0.6
2
0.9
3
x
4
What value of x completes the table?
Answer:1.2
Step-by-step explanation:
Answer:
1.2 Inches, It moves 0.3 inches in 1 hour so if in 1 hour it moves 0.3 and in 2 0.6 and in 3 0.9 so in 4 hours it will move 1.2 inches
Step-by-step explanation:
You type 4500 words per hour. How many words do you type
per minute?
Answer:
you type 75 words per minute.
Step-by-step explanation:
since there are 60 minutes in an hour, simply divide 4,500 by 60 to get 75. i hope this helps you! good luck and have a great day. :)
See attachment for math work and answer.
let f(x)=2x and g(x)=x-4, what is the range of (f o g)(x)?
a. y>0
b. all real numbers except y=0
c. y <= 0
d. all real numbers
Answer:
c
Step-by-step explanation:
Answer:the answer is c
Step-by-step explanation:
this is the picture that goes with my question.
Answer:
first u should make your equation: y= -1/5 (x-5) - 3
y= -1/5x +1 -3
y= -1/5 x -2
then u should setting some number like 1 ,2 ..... instead of *x* and when u done this u should dissolve it (now your *y* is came out too) so you have your x,y now
According to the points you get, you put it on the chart and connect it
if you do not understand something, tell me to draw on paper so you can understand better
Find the slope of the line described by:
X -6y= -9
write answer as a fraction
Is the statement true or false? If false, give a counterexample.
For all real numbers a, b and c, a(b + c) = ab + bc.
A. true
B. false; a(b + c) = ab − ac
C. false; if a = b = c = 1, then 1(1 + 1) ≠ 1(1) + 1(1)
D. false; if a = 1, b = 2, and c = 3, then 1(2 + 3) ≠ 1(2) + 2(3)
Answer:
D. false; if a = 1, b = 2, and c = 3, then 1(2 + 3) ≠ 1(2) + 2(3)
Step-by-step explanation:
A is false, because the a is being distributed/ being multiplied to all terms inside the parenthesis, and not the term b.
B is also false. There is no indicated negative signs.
C is also false because 1(1 + 1) is EQUAL to 1(1) + 1(1)
D is true.
Find m2 KLM ifm/NLM = 950
and mKIN = 46°.
Answer:
46
Step-by-step explanation:
Which function corresponds to the table?
A) y = 3x - 2
B) y = 2x + 3
C) y = -2x + 3
D) y = -3x + 2
Answer:
c is the correct answer
Pls help hurry I need to find the slope
Answer:
a. -1
Hope this helps!
Find the value of X
(5x+4)°+(8x-71)°
Answer:
x = -4/5
Step-by-step explanation:
Solve for x:
(5 x + 4) (8 x - 71) = 0
Split into two equations:
5 x + 4 = 0 or 8 x - 71 = 0
Subtract 4 from both sides:
5 x = -4 or 8 x - 71 = 0
Divide both sides by 5:
x = -4/5 or 8 x - 71 = 0
Add 71 to both sides:
x = -4/5 or 8 x = 71
Divide both sides by 8:
Answer: x = -4/5 or x = 71/8
Write the slope intercept form (y = mx + b) of the equation of the line through the given points with the given slope. Through:(2,-4), slope =-1
y = mx +c
Substitute the values,
-4 = -1(2) + c
c = -2
Thus, the equation is y= -x -2
1. Escreva na forma fatorada: a. 51 b. 56 c. 65 d. 77 e. 48 f. 50 g. 80 h. 99 i. 108 j. 132 k. 210 l. 180 m. 234
Answer:
por favor, verifique a explicação
Step-by-step explanation:
Queremos escrever cada um dos números como uma multiplicação de seus fatores; Procedemos da seguinte maneira;
a. 51 = 3 * 17
b. 56 = 2 * 2 * 2 * 7
c. 65 = 5 * 13
d. 77 = 7 * 11
e. 48 = 2 * 2 * 2 * 2 * 3
f. 50 = 2 * 5 * 5
g. 80 = 2 * 2 * 2 * 2 * 5
h. 99 = 3 * 3 * 11
i. 108 = 2 * 2 * 3 * 3 * 3
j. 132 = 2 * 2 * 3 * 11
k. 210 = 2 * 3 * 5 * 7
l. 180 = 2 * 2 * 3 * 3 * 5
m. 234 = 2 * 3 * 3 * 13
is 54/35 a rational number?
Answer:
54/35 is a rational number!
Have a great rest of your day!
Answer:
Yes and no
Step-by-step explanation:
The number 54 is a rational number if 54 can be expressed as a ratio, as in Rational. A quotient is the result you get when you divide one number by another number. Although the 54 is good the 35 is not due to it if you had to choose if it was or not you can say yes but it determines the question.