The figure shows the 50 - foot side of a house and a proposed rectangular garden to be fences in on 3 sides.
The 3 sides, a,b, and x will be made of 40 feet of fencing.
Which of the following is an expression for a in terms of x?
A. 2x+40
B. 2x-40
C. 40-2x
D. 40-x+x
What is the area, in square feet, for the garden if 40 feet of fencing are used and x=15?
Answers
Option C 40-2 x
150 square feet
Step-by-step explanation:
Step 1 :
Given that the 3 sides, a,b, and x will be made of 40 feet of fencing,
we have a + b + x = 40
Since this is a rectangular garden , b= x
substituting b= x, we have a + x + x = 40
=> a+2 x = 40
=> a= 40-2 x
Step 2 :
To find the area in square feet,
when x = 15, a = 40 - 2 * 15 = 40-30 = 10 feet
The length and breadth of the rectangular garden are therefore 5 and 10 feet respectively
Hence, the area of the garden = length * breadth = 15 * 10 = 150 square feet
Related Questions
1. A clothing store is having a sale of
30% off all dresses. What is the discount
and new price of a dress that originally
cost $90?
Answers
Answer:
$63
Step-by-step explanation:
30% of 90 is 27
90-27=63
What is the circumference of a circle if the radius is 33 inches and pi is 3.14
Answers
Answer:
207.24 inches
Step-by-step explanation:
The formula for circumference is C=[tex]2[/tex][tex]\pi r[/tex]
Apply the formula here
r = 33
[tex]\pi[/tex]=3.14
C=2*3.14*33 = 207.24
Apply units!
207.24 inches
Circumference Formula with radius: c=2r*3.14
Circumference Formula with Diameter: c=d*3.14
With this you are given the radius so plug in the value and you’ll get the formula c=2(33)*3.14 next distribute and you’ll get c=66*3.14 and now solve, c=207.24
The circumference would be 207.24
What is the sign of 3x y3xy3, x, y when x>0x>0x, is greater than, 0 and y<0y<0y, is less than, 0?
Answers
Answer: It's negative! Dude, could I please have brainiest!?!
Final answer:
The sign of the expression 3x * y^3 is negative when x is positive and y is negative because a negative number raised to an odd power remains negative.
Explanation:
The question asks about the sign of a mathematical expression where the variables have specified signs based on their values. Given that x is positive (x > 0) and y is negative (y < 0), the expression 3x * y^3 encompasses multiplying a positive number by a negative number raised to an odd power. Multiplying a positive number by a negative number results in a negative number, and raising a negative number to an odd power preserves the negative sign. Therefore, the product 3x * y^3 will be negative because y^3 maintains its negative sign while 3x is positive.
20 POINTS!!!!! im stuck.
Answers
Answer:
First Option
Step-by-step explanation:
An exponent is how many times you multiply a number by its self, in this case, that's 5 times
Answer:
[tex] \frac{32}{243} \\ [/tex]
Step-by-step explanation:
[tex] = ( { \frac{2}{3})}^{5} \\ \\ = \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} [/tex]
0.599 as a percentage of 0.319
Answers
Answer: " 187. 774 % " .
_____________________________________
Step-by-step explanation:
_____________________________________
So, let's rewrite this statement as a question:
0.599 is "what percent" of: 0.319 ? ;
Set up an equation:
[tex]0.599 = (\frac{n}{100}) *0.319[/tex] ;
↔ [tex](\frac{n}{100}) * 0.319 = 0.599[/tex] ;
_____________________________________
Divide each side of the equation by: "(0.319)" ; as follows:
_____________________________________
[tex][ (\frac{n}{100}) * 0.319 ] / 0.319 = (0.599)/ (0.319)[/tex] ;
to get:
_____________________________________
[tex]\frac{n}{100} = 1.87774294671[/tex] ;
_____________________________________
Now, multiply each side of the equation by "100" ;
to isolate "n" on one side of the equation; & to solve for "n" ;
_____________________________________
[tex]100 * (\frac{n}{100)} = (1.87774294671) * 100[/tex] ;
_____________________________________
On the left-hand side of the equation; the "100's: cancel out to "1" ;
→ since: "[tex](\frac{100}{100} =1)[/tex]" ;
and we have:
→ n = 187.774294671 ;
round to three decimal places:
→ n = 187. 774 .
The answer is: 187.774 % .
_____________________________________
Min is trying to place some bookmarks inside a 10000 page book. the pages that she wants to place the bookmarks on have four digits page numbers. the digits in the thousands and units places add up to 7. How many bookmarks will she need?
Answers
Final answer:
Min will need a total of 700 bookmarks for the pages where the digits in the thousands and units places add up to 7, since there are 700 four-digit page numbers meeting the criteria.
Explanation:
To determine the number of bookmarks Min needs for the pages where the digits in the thousands and units place add up to 7, we will consider all four-digit numbers that meet this criterion. This involves taking the sum of the thousands and units digits, which can equal 7 in the following ways: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, and 7+0. Considering that for every combination of thousands and units digits, there are 10 possibilities for the hundreds digit and 10 possibilities for the tens digit, we can calculate the total number of eligible page numbers.
For 1+6 or 6+1, the number of possibilities is 2 (the two combinations) multiplied by 100 (since there are 10 choices for each of the two remaining digits), giving us 200 options.
For 2+5 or 5+2, we have another 200 options.
For 3+4 or 4+3, we get another 200 options.
For 7+0, we would only have 100 options, as there is only one combination.
Summing these up, we find Min will need 700 bookmarks: 200 + 200 + 200 + 100 = 700.
Identify an equation in point-slope form for the line perpendicular to
y=-3x+11 that passes through (4,-8).
Answers
Answer:
perp. : 1/3= m
y + 8 = 1/3(x -4): answer is c
y + 24/3 = (1/3)x - 4/3
y = (1/3)x - 28/3
Step-by-step explanation:
answer is c
To find the equation of a line perpendicular to y = -3x + 11 that passes through the point (4, -8), we first calculate the negative reciprocal of the original line's slope, which is 1/3. Then we apply this slope and the given point to the point-slope form equation to obtain y + 8 = (1/3)(x - 4).
The student has asked for an equation in point-slope form for a line that is perpendicular to y = -3x + 11 and passes through the point (4, -8). Firstly, we identify the slope of the given line, which is -3.
As we need a perpendicular line, we find the negative reciprocal of this slope, which is 1/3 (since the slope of perpendicular lines are negative reciprocals of each other). Now, using the point-slope form formula, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope, we plug in our values to get:
y - (-8) = (1/3)(x - 4)
This simplifies to:
y + 8 = (1/3)(x - 4)
Which is the equation of the line perpendicular to y = -3x + 11 that passes through the point (4, -8) in point-slope form.
a truck filled with a load of peanuts drives onto an 80-ft long ramp at a peanut factory. the front end of th ramp raised 30 degrees to empty the peanuts. what is the height of the ramp?
Answers
Answer:
Step-by-step explanation: so, u would do 80 times 30 which equals 2400. Then u would divide 2,400 by 4 which gives u ur answer which is 60ft long! :)
Answer:
if im right its 110ft
Step-by-step explanation:
which of these equations shows a proportional relationship between x and y
F. y=-1/3x
G. y=-x+1
H. y=3/2x+3/2
J. y=2x-4
Answers
Answer:
F. y= -[tex]\frac{1}{3\\}[/tex]x
Step-by-step explanation:
A proportional relationship between x and y exists if it can be expressed in the form y/x=k or y=kx. From the choices listed, F. y= -[tex]\frac{1}{3\\}[/tex]x is the only equation expressed in this form.
The correct option is J. [tex]\( y = 2x - 4 \).[/tex]
To determine which equation represents a proportional relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex], we need to look for an equation where [tex]\( y \)[/tex] is a constant multiple of [tex]\( x \)[/tex], and passes through the origin (0,0). A proportional relationship can be expressed in the form [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.
Let's analyse each option:
F. [tex]\( y = -\frac{1}{3}x \)[/tex]
This equation represents a proportional relationship with a constant of proportionality [tex]\( k = -\frac{1}{3} \)[/tex].
G. [tex]\( y = -x + 1 \)[/tex]
This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is 1).
H. [tex]\( y = \frac{3}{2}x + \frac{3}{2} \)[/tex]
This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is [tex]\( \frac{3}{2} \))[/tex].
J. [tex]\( y = 2x - 4 \)[/tex]
This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is -4).
Which expression is equivalent to 5 x + 10 y minus 15? 5 (x minus 2 y minus 3) 5 (x + 5 y minus 10) 5 (x + 2 y minus 3) 5 (x + 2 y minus 15)
Answers
You get this answer by factoring the original expression. Hope this helps!
Answer: 5 (x + 2y - 3)
Step-by-step explanation:
a field is in the shape of a rectangle 5/6 mile long and 3/4 mile wide. what is the area of the field.
Answers
Answer: 15/24
Step-by-step explanation: 6x4=24 which is the denominator and 5x3=15 which is the numerator
Answer:
15/24
Step-by-step explanation:
h(x) = x2 + 1 k(x) = x – 2
(h + k)(2) =
(h – k)(3) =
Evaluate 3h(2) + 2k(3) =
Answers
Answer:
(h + k)(2) = h(2) + k(2) = [tex]2^{2}[/tex] + 1 + 2 - 2 = 4 + 1 = 5
(h - k)(3) = h(3) - k(3) = [tex]3^{2}[/tex] + 1 - (3 - 2) = 10 - 1 = 9
Step-by-step explanation:
h(x) = [tex]x^2 + 1[/tex]
k(x) = x - 2
(h + k)(2) = h(2) + k(2) = [tex]2^{2}[/tex] + 1 + 2 - 2 = 4 + 1 = 5
(h - k)(3) = h(3) - k(3) = [tex]3^{2}[/tex] + 1 -(3 - 2) = 10 - 1 = 9
Which BEST describes the system of equations graphed on the coordinate plane?
A) Consistent
B) Inconsistent
C) Consistent and Dependent
D) Consistent and Independent
Answers
Answer:
C) Consistent and Dependent.
Step-by-step explanation:
As the system has at least ONE solution. Both lines lie over each other, which makes them dependent.
The system, therefore, is consistent and dependent.
When people leave a 15% or 20% tip they often round up to the nearest multiple of 5 or 10 cents. If Kadisha always rounds up what is a 20% tip on her bill?
Answers
To do this on your own, you round up the amount by 5¢ or 10¢, whichever is closer, and then take 20% of her bill
Remember to put 20% into the calculator as 0.2 and multiply 0.2 by her bill that has been rounded up
To calculate a 20% tip and round up, multiply the bill by 0.2, then round to the nearest 10 cents.
Explanation:To calculate a 20% tip, first, determine the total bill amount. Then, multiply the bill amount by 0.2 to find 20% of the bill. Finally, round up to the nearest multiple of 5 or 10 cents. Since Kadisha always rounds up, she should round up to the nearest 10 cents.
If the total bill is $50, to calculate a 20% tip, we multiply $50 by 0.2 to get $10, which is 20% of the bill. Then, we round up to the nearest 10 cents, making the tip $10.00.
Learn more about Calculating a 20% tip with rounding up here:https://brainly.com/question/33172213
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rewrite the equation
Answers
Explanation:
Divide y^3 by y. Subtract the exponents to get y^2. Divide 4 by -1 and you get -4.
The sum of ten and the quotient of a number xxx and 666.
Answers
Answer:
[tex]10+\dfrac{x}{6}[/tex]
Step-by-step explanation:
The wording, "the sum of A and B" translates to the math formula A+B.
The wording, "the quotient of A and B" translates to the math formula A/B.
Then "the sum of 10 and the quotient of x and 6" will translate to the math formula ...
[tex]\boxed{10+\dfrac{x}{6}}[/tex]
please help me with this
Answers
or: 5x - 8 + 43 = 180
or try this: 5x - 8 = 43
solve for x
don’t forget to plug the number back in
PLEASE HELPPP MEEEEE
Answers
Step-by-step explanation:
Given , a line passes through the points (1,-3) and (3,1)
The equation of line which passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex]y - y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Here [tex]x_1 = 1 , y_1= -3[/tex] and [tex]x_2 = 3 , y_2= 1[/tex]
The required equation of the line is
[tex]y+3=\frac{1+3}{3-1} (x-1)[/tex]
[tex]\Leftrightarrow y +3 =2(x-1)[/tex]
[tex]\Leftrightarrow y =2x-2-3[/tex]
[tex]\Leftrightarrow y =2x-5[/tex]
8.
Given, y varies directly with x and y=24 when x=8
Therefore,
[tex]y\propto x[/tex]
[tex]\Rightarrow y = kx[/tex].........(1)
y = 24 when x=8
[tex]\therefore 24 = 8k[/tex]
[tex]\Rightarrow k =3[/tex]
Equation (1) becomes
y= 3x
So, when x=10
y=3×10
⇒y=30
2x-7=-2x+9
How do you solve this?
Answers
Answer:
4
Step-by-step explanation:
2x-7=-2x+9
2x-(-2x)-7=9
2x+2x-7=9
4x-7=9
4x=9+7
4x=16
x=16/4
x=4
Explain how you found the volume of water in the fish tank if it was only 1/2 full with water.
You have a fish tank with the following dimensions:
Height: 3 feet
Width: 1.5 feet
Length: 2 feet
Answers
We found the volume of water by finding the volume of fish tank from given dimensions and dividing it by 2.
Step-by-step explanation:
Given,
Height of tank = 3 feet
Width of tank = 1.5 feet
Length of tank = 2 feet
We will first find the volume of tank;
Volume = Length * Width * Height
Volume = 3 * 1.5 * 2
Volume = 9 feet cubed
As we know the water is 1/2; therefore we will divide the volume of tank by 2.
Volume of water = [tex]\frac{9}{2} = 4.5\ ft^3[/tex]
We know that;
1 cubic feet = 7.481 gallons
4.5 cubic feet = 7.481*4.5 = 33.66 gallons
Keywords: volume, division
Learn more about volume at:
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In circle A, arc CD is congruent to arc BD. What is the measure of arc CD?
90
180
45
Answers
Check the picture below.
The measure of arc CD of circle A will be 90°. Then the correct option is A.
What is the arc length of the sector?Let r be the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be
Arc = (θ/2π) 2πr
In circle A, arc CD is congruent to arc BD. And we know that the Line segment CAD is the diameter of the circle. Then the equation is given as,
arc CD = arc BD ....1
arc CD + arc BD = 180° ....2
From equations 1 and 2, then we have
arc CD + arc CD = 180°
2 arc CD = 180°
arc CD = 90°
The measure of arc CD of circle A will be 90°. Then the correct option is A.
More about the arc length of the sector link is given below.
https://brainly.com/question/15955580
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Find the value for the following determinant.
5
-5
-11
Answers
Also manually, to solve for determinants, you do:
2*-4=-8
1*-3=-3
-8-(-3)=-5
The ratio of people to books in a classroom is 10:4 what is the unit ratio of people to per book ?
Answers
Answer:
[tex]2.5\ \frac{people}{book}[/tex]
Step-by-step explanation:
The correct question is
The ratio of people to books in a classroom is 10:4 what is the unit rate of people per book?
Let
x ----> the number of people
y ----> the number of books
we know that
To find out the unit rate of people per book , divide the total number of people by the total number of books
we have
[tex]x=10\ people\\y=4\ books[/tex]
so
[tex]\frac{x}{y}=\frac{10}{4}=2.5\ \frac{people}{book}[/tex]
Consider the figure.
What is JL?
Answers
The answer for the above mentioned problem is JL = 12.5
Step by step explanation:
Given:
JM = 8
KM = 6
To Find:
JL = ?
Formula to be used:
[tex]KM^2[/tex] = JM x ML
In order to find " JL" we must first find "ML",
[tex]KM^2[/tex] = JM x ML
[tex]6^2[/tex] = 8 x ML
36 = 8 x ML
36/8 = ML
ML = 4.5
Now JL = 4.5+8
= 12.5
Thus the value of JL = 12.5
15. The volume of a rectangular pyramid
is 10,500 cubic centimeters. It has a
length of 15 centimeters and a width of
85 centimeters. What is its height?
Answers
Answer:
Its height is 24.71 centimeters.
Step-by-step explanation:
Given:
The volume of a rectangular pyramid is 10,500 cubic centimeters.
It has a length of 15 centimeters and a width of 85 centimeters.
Now, to find the height.
Let the height be [tex]h.[/tex]
Volume of rectangular pyramid = 10,500 cubic centimeters.
Length (l) = 15 centimeters.
Width (w) = 85 centimeters.
Now, to get the height by putting formula:
[tex]Volume=\frac{l\times w\times h}{3}[/tex]
[tex]10500=\frac{15\times 85\times h}{3}[/tex]
[tex]10500=\frac{1275h}{3}[/tex]
Multiplying both sides by 3 we get:
[tex]31500=1275h[/tex]
Dividing both sides by 1275 we get:
[tex]24.71 =h\\\\h=24.71\ centimeters.[/tex]
Therefore, its height is 24.71 centimeters.
Maya spent 40% of her savings to pay for a bicycle that costs 85$. How much money was in her savings to begin with ?
Answers
Answer:
Total amount of saving = $212.5
Step-by-step explanation:
Let x be the amount of saving to begin with.
Given:
Maya spent = 40%
Bicycle cost = $85
We need to find the amount of savings Maya began with.
Solution:
From the statement, Maya spent 40% of her savings to pay for a bicycle that costs $85.
So, 40% of total amount = $85
[tex]40\%\times Total\ amount = \$85[/tex]
Substitute [tex]40\% = \frac{40}{100}[/tex] and total amount = x in above equation.
[tex]\frac{40}{100}\ties x = 85[/tex]
Using cross multiplication rule.
[tex]x=\frac{85\times 100}{40}[/tex]
[tex]x=\frac{8500}{40}[/tex]
x = $212.5
Therefore, amount of savings Maya began with (x) = $212.5
Choose the solution(s) of the following system of equations:
x² + y² = 6
x² - y=6
Answers
Answer:
see attachment
Step-by-step explanation:
Answer:
2nd 4th 6th 8th or B D F H
Step-by-step explanation:
I did it on edge
in terms of S, N, and A, what is the value of B in the equation S=n/2(a+b)
Answers
The value of B = [tex]\dfrac{2S-NA}{N}[/tex]
Step-by-step explanation:
The given equation,
[tex]S=\dfrac{N}{2}(A+B)[/tex]
To find, the value of B in terms of S, N and A = ?
∴ [tex]S=\dfrac{N}{2}(A+B)[/tex]
By crossmultiplication, we get
⇒ N(A + B) = 2S
⇒ NA + NB = 2S
⇒ NB = 2S - NA
⇒ B = [tex]\dfrac{2S-NA}{N}[/tex]
∴ The value of B = [tex]\dfrac{2S-NA}{N}[/tex]
Each side of a suspension bridge has a cable that is secured at either end of the span by two supporting towers. The cable is attached to the tops of the two towers. In the section between the two towers, the cable forms a parabolic curve. At its lowest point, the cable is 40 feet above the surface of the bridge. The towers are 450 feet apart, and the vertical distance from the surface of the bridge to the top of each tower is 500 feet. Use the left tower as the y-axis. Hint y=a(x-h)2+ k
Answers
Answer: y= 40
Step-by-step explanation:
1. The lowest point of the cable is 40 feet above the surface of the bridge.
2. The towers are 450 feet apart.
3. The vertical distance from the surface of the bridge to the top of each tower is 500 feet.
We’ll use the general form of a parabolic equation:
[ y = a(x - h)^2 + k ]
Where:
(y) represents the vertical position (height) of the cable.
(x) represents the horizontal position along the bridge.
(h) represents the horizontal position of the vertex (lowest point) of the parabola.
(k) represents the vertical position of the vertex.
Given that the lowest point of the cable is at (y = 40) feet, we have:
[ k = 40 ]
Now let’s find the vertex position ((h)). Since the towers are 450 feet apart, the midpoint between the towers corresponds to the vertex. Therefore:
[ h = \frac{{450}}{2} = 225 ]
Now we can express the equation as:
[ y = a(x - h)^2 + k ]
Next, let’s find the value of (a). At the top of each tower, the cable is at a height of 500 feet. So, when (x = 0) (left tower) or (x = 450) (right tower), we have:
At the left tower (left end of the span): [ y = 500 = a(0 - 225)^2 + 40 ] Solving for (a): [ a = \frac{{500 - 40}}{{225^2}} = \frac{{460}}{{50625}} ]
At the right tower (right end of the span): [ y = 500 = a(450 - 225)^2 + 40 ] Solving for (a): [ a = \frac{{500 - 40}}{{225^2}} = \frac{{460}}{{50625}} ]
Since the value of (a) is the same at both ends, we can use either tower to find the equation of the parabolic curve:
[ y = \frac{{460}}{{50625}}(x - 225)^2 + 40 ]
Which of the following expressions would appear farthest to the right on a number line when solved?
3-1
-2+5
4+(-2)
-4-(-2)
Answers
Answer:-2+5
Step-by-step explanation:
So basically you do simple math and you need to know that the highest number goes on the right
So basically for each one there is
3-1 that makes 2
-2+5 creates 3 because it’s a negative so you must cancel the negative out and your left with three after
And with that mind set in mind with having to cancel the negative out with the positive
4+(-2) is basically 4-2 and that makes 2
And the last one is a little bit tricky because of all the negatives involved and with this one you need to know that to negatives make a positive
So it’s -4-(-2) so because of the minus and the negative two being negatives right next to each other they cancel each other out to make the equation basically -4+2 which would ultimately make -2
So all the answers are
3-1=2
-2+5=3
4+(-2)=2
-4-(-2)=-2
And out of all those we know 3 is the highest number there so therefore it would make it the one farthest to the right on a number line when solved.