The largest possible total area of the six pens is 33750 square feet.
Given:
An ostrich farmer wants to enclose a rectangular area and then divide it into six pens with fencing parallel to one side of the rectangle (see the figure below). there are 900 feet of fencing available to complete the job.
Let L and W be the length and width.
900 = L + 6W
L = 900 -6W
Area = A = LW = (900-6W)W = 900W -6W^2
A' = 990-12W = 0
W = 900/12 = 75 feet wide
L = 900 -6W = 900 - 6(75)
L = 900 - 450 = 450 feet.
Maximum area = 450 * 75
= 33750 square feet.
Therefore the largest possible total area of the six pens is 33750 square feet.
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p(x)=(x^2 -1)(x^2−5x+6)
The Playhouse Concert Hall has 523 seats. The Pink Ladies rock band is holding a concert there and charging $35.50 for each ticket. If the concert sells out, how much money will the band earn?
The total amount that the band earns when the concert sells out is $18566.50
Given,
Number of seats in The Playhouse Concert Hall = 523
The cost for one ticket charged by The Pink Ladies rock band who holds a concert = $35.50
We have to find the total amount that the band earns when the concert sells out;
Total amount = Number of seats x Cost for one ticket
Total amount = 523 x 35.50
Total amount that the band earn = $18566.5
That is,
The total amount that the band earns when the concert sells out is $18566.50
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"Seven more than the quotient of k and negative nine is seventeen. " -9k + 7 = 17 + 7 = 17 o 7+ (-9k) = 17 7+7= 1
The correct algebraic form is b. k/-9 + 7 = 17
There are four components in division namely divisor, dividend, quotient and remainder. The significance and meaning of each is evident from their name. The dividend is the number that is being divided. And the number which is used to divide the dividend is divisor. The result of dividing the dividend by divisor is termed as quotient. Remainder is the left over amount.
So, multiplying the divisor and quotient and adding the product with remainder will give us the desired algebraic expression. Seven is remainder. The quotient of k and negative nine implies k is dividend and negative nine is divisor. So, algebraic expression -> k/-9 + 7 = 17
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How can you determine which property of equality i needed to iolate a variable and olve a given equation? Explain. A. Ue invere relationhip to "undo" the operation. B. Ue the ame operation to "undo" the operation
C. Ue the Ditributive Property to iolate the variable. D. Subtitute the known value and implify
The property of the equality is a method to perform a operation both sides of the equal sign which will not affect the equation. Property of equality which is needed to isolate a variable and solve a given equation is use inverse relationships to "undo" the operation. Thus the option A is the correct option.
Property of equality
The property of the equality is a method to perform a operation both sides of the equal sign which will not affect the equation.
Inverse means to revere something which has been done earlier. An undo operation in mathematics is the operation of undoes what was done by the previous operation.
For example suppose the given expression is no 5. Then by adding 4 and again subtracting 4 keeps the system isolate.
Hence the property of equality which is needed to isolate a variable and solve a given equation is use inverse relationships to "undo" the operation. Thus the option A is the correct option.
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Which statement describes the graph of this function? f(x) =-3|x-1|+12
HELP PLEASE!!!
Answer:
This is a V-shaped function that opens downward. The vertex of the V is point (1, 12).
Step-by-step explanation:
This is a V-shaped function that opens downward. The vertex of the V is point (1, 12).
Pls Help I will give brainliest to whoever is first and correct. And answer all questions!
The operations being done in each step are:
(1) Use the distributive property
(2) Subtraction property of equality.
(3) Addition property of equality.
(4) Division property of equality.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
3(-3x-4) = 5x+2
Use distributive property:
-9x -12 = 5x + 2
Subtract 5x from both sides of the equation:
-14x -12 = 2
Add 12 to both sides of the equation:
-14x = 14
Divide both sides by -14:
x = -1
Hence, the operations being done in each step are:
(1) Use the distributive property
(2) Subtraction property of equality.
(3) Addition property of equality.
(4) Division property of equality.
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jenny charges 9.15 an hour to babysit todllers and 7.4 an hour to babysit school -aged children. if jenny babysat toddlers for 9 hours and school -aged childrenfor 6, how much did she earn in all
?
Answer:
jenny earned a total of $103.05.
Step-by-step explanation:
jenny charges 9.15 an hour to babysit todllers and 7.4 an hour to babysit school -aged children. if jenny babysat toddlers for 9 hours and school -aged childrenfor 6, she earned in all 83.55.
At a certain toy store, tiny stuffed zebras cost $3 and giant stuffed zebras cost $14. The store doesn't sell any other sizes of stuffed zebras. If the store sold
29 stuffed zebras and made $208 in revenue in one
week, how many tiny stuffed zebras were sold?
A line that intersects two or more lines in a plane at different points is called a?.
A line that intersects two or more lines at a distinct point is known as a transversal line.
A transversal is a line in geometry that connects two lines in the same plane at two different places. When determining whether two or more other lines in the Euclidean plane are parallel, transversals are important. Consecutive interior angles, consecutive exterior angles, corresponding angles, and alternate angles are only a few examples of the several pairings of angles that can be formed when a transversal intersects two lines. Euclid’s parallel postulate states that if two lines are parallel, then comparable interior angles are equal, alternate interior angles are equal, and successive interior angles are supplementary.
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A cone has a volume of 8π cubic feet and a height of 6 feet. What is the radius of the base?
Answer:
r≈1.13ft
Step-by-step explanation:
hope this helps <333
suppose we want to compute a 92% confidence interval. what excel command would compute the critical value ?
If we compute a 92% confidence interval in excel command the critical value will be 1.750686.
Level of confidence c = 0.92
level of significance α = 1 - c = 0.08
A 92% confidence interval has goes from 8/2 = 4% to 100%–(8/2)% = 96%
Leaving 92% in the middle (96%–4%) = 92 %
So look up z-score for 96% or p =0.96
The two closest value in a z-table are
P(z< 1.75) = 0.95994
P(z< 1.76) = 0.96080
Based on this online table
( https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf )
So critical value Z = 1.75 is the closest value , but just barely.
But if you want a more accurate , use the normal function on Excel or from an online calculator or interpolate
If you interpolate
1.75 + (0.96–0.959954)*0.01/ (0.9608–0.95994)
Critical value Z= 1.750535
If you round to four digits, critical value Z = 1.7505
So the interpolation isn’t that much more accurate
Excel function says critical value Z= 1.750686
=normsinv(0.96)
= 1.750686 which is probably more accurate.
By using the word interval, you have implied you are talking about a two-sided test.
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HELP PLEASE 100 POINTS
Answer: ∠1 = 90°
Step-by-step explanation:
There are a few steps we will take to solve this problem. In each step, I will write an equation to help us solve, then use inverse operations to solve.
First, we will use the exterior angles theorem to find the measurement of ∠3 (this will help us solve for ∠2, then for ∠1).
89° = 51° + ∠3
∠3 = 38°
Next, we will find the measurement of ∠2 since we know ∠2 plus ∠3 is 90 degrees, as shown by the perpendicular lines and the box.
90° = ∠3 + ∠2
90° = 38° + ∠2
∠2 = 52°
Lastly, we will solve for ∠1. We know that there are 180 degrees in a triangle.
180° = 38° + ∠1 + ∠2
180° = 38° + ∠1 + 52°
180° = 90° + ∠1
∠1 = 90°
Answer:
90
Step-by-step explanation:
I started by finding angle 5
180 - 89 = 91 Supplemental angles
Then I found angle 3
The sum of the interior angles of a triangle is 180
180-89-91 = 38
Angle2 and 3 are complementary angles
90- 38 =52
the sum of the interior angles of a triangle is 180
Angle 1
180 - 52 - 38 = 90
Line m passes through the points (2, -7) and (4, -9). Line m is parallel to which line? Responses
The line m passing through the points (2, -7) and (4, -9) is parallel to the line y = -x + 2 , the correct option is (c) .
In the question ,
it is given that ,
the Line m passes through the points (2,-7) and (4,-9),
So , the slope of the line will be = (-9 + 7)/(4 - 2)
= -2/2
= -1
We know that the if two lines are parallel then they will have same slope ,
the slope of the line should be -1,
from the given options , we can see that only option (c) has the slope = -1
on comparing equation y = -x + 2 with the general equation of the line y = mx + c , we get
slope(m) = -1
hence , the line m is parallel to y = -x + 2 .
Therefore , the line m passing through the points (2, -7) and (4, -9) is parallel to the line y = -x + 2 .
The given question is incomplete , the complete question is
Line m passes through the points (2, -7) and (4, -9). Line m is parallel to which line?
(a) 8x + 2y = -10
(b) x = 5
(c) y = -x + 2
(d) y = x - 9
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your help would be nice please I don't understand
Answer:
y=1.5x-3
Step-by-step explanation:
(0,-3) => x=0, y=-3
(2,0) => x=2, y=0
y=ax+b
-3=a*0+b
0=2*a+b
-3=b
0=2a+b
2a-3=0
2a=3
a=1.5
b=-3
y=1.5x-3
Answer:
[tex]y = \dfrac{3x}{2} -3[/tex]
Step-by-step explanation:
Before we identify the equation of the line in slope intercept form, we must identify the slope intercept form equation. The slope intercept form equation is y = (m)x + (b) ⇒ m = slope of line; b = y-intercept of line.
To identify the equation of the line shown in slope intercept form, according to the slope intercept form equation, we need to identify the slope of the line and the y-intercept of the line. The slope of a line is the rate of a line, which advances up/down/side-to-side at a constant rate. The y-intercept of a line is the intersection of the line at the y-axis.
There is a specific formula for identifying the slope:
[tex]\boxed{\text{Slope} = \dfrac{\text{y coordinate of 2nd point - y coordinate of 1st point}}{\text{x coordinate of 2nd point - x coordinate of 1st point}}}[/tex]
Some facts about slope: The slope of a line will also depend on the graph. If the graph ascends upward to somewhere in Quadrant 1 or 2, the slope of the line will be positive. If the graph descends downward to somewhere in Quadrant 3 or 4, the slope will be negative. If the line horizontal and it passes perfectly through the x-axis, the slope of the line is 0. If the slope of the line is vertical, then the slope will be undefined.
Location of plotted points: First point: (0, -3); Second point: (2, 0)
Let us now identify the x and y coordinates of the plotted points:
[tex]\boxed{\text{y-coordinate of 2nd point = 0; y-coordinate of 1st point = -3}} \\ \boxed{\text{x-coordinate of 2nd point = 2; x-coordinate of 1st point = 0 }}[/tex]
Plug the coordinates into the slope formula to determine the slope:
[tex]\implies {\text{Slope} = \dfrac{\text{0 - (-3)}}{\text{2 - 0}}} = \dfrac{0 + 3}{2} = \dfrac{3}{2}[/tex]
Plug the slope of the line into the slope intercept form equation:
[tex]\implies y = (m)x + (b)[/tex]
[tex]\implies y = \huge\text{(}\dfrac{3}{2} \huge\text{)}x + (b)[/tex]
[tex]\implies y = \dfrac{3(x)}{2} + b[/tex]
Let us plug any point (that is on the line) for x and y. This will help us find the y-intercept (b). I will plug in the first point because it is my preference.
[tex]\implies y = \dfrac{3(x)}{2} + b[/tex]
[tex]\implies -3 = \dfrac{3(0)}{2} + b \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{First point: (0, -3)} \implies x = 0; y = -3]}[/tex]
[tex]\implies -3 = 0 + b[/tex]
[tex]\implies -3 = b[/tex]
Finally, let us substitute the slope of the line and the y-intercept of the line into the slope-intercept form equation. Then, we can simplify both sides of the equation and isolate the y-variable completely on the other side.
[tex]\implies y = (m)x + (b)[/tex]
[tex]\implies y = \huge\text{(}\dfrac{3}{2} \huge\text{)}x + (-3)[/tex]
[tex]\implies y = \dfrac{3x}{2} -3[/tex]
Therefore, the equation of the line in slope intercept form is y = 3x/2 - 3.
Help!! Pls
Find the distance AB. Show work
Solve for x, round your answer to the nerest thousandth.
1.657 - 2.397 (5.968x - 0.27) = 4.193x - 3
Answer: 0.286
Step-by-step explanation:
1.657−2.397(5.968x−0.27)=4.193x−3
Use the distributive property to multiply −2.397 by 5.968x−0.27.
1.657−14.305296x+0.64719=4.193x−3
Add 1.657 and 0.64719 to get 2.30419.
2.30419−14.305296x=4.193x−3
Subtract 4.193x from both sides.
2.30419−14.305296x−4.193x=−3
Combine −14.305296x and −4.193x to get −18.498296x.
2.30419−18.498296x=−3
Subtract 2.30419 from both sides.
−18.498296x=−3−2.30419
Subtract 2.30419 from −3 to get −5.30419.
−18.498296x=−5.30419
Divide both sides by −18.498296.
x=
−18.498296
−5.30419
Expand
−18.498296
−5.30419
by multiplying both the numerator and the denominator by 1000000.
x=
−18498296
−5304190
Reduce the fraction
−18498296
−5304190
to lowest terms by extracting and canceling out −2.
x=
9249148
2652095
and then round
40% of what number is 46?
The number is 115.
What is a percentage?The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage change is also calculated using the same method.
In percentage change, we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = [tex]\frac{a}{b}[/tex] x 100
We have,
Number = M
40% of M = 46
[tex]\frac{40}{100}[/tex] x M = 46
M = (46 x 100) / 40
M = 115
Thus,
The number is 115.
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Is rectangular form a bi?.
The rectangular coordinate form of a complex number is represented by the formula z=a+bi. The real axis is the horizontal one, and the imaginary axis is the vertical one. In terms of r and, where r is the vector's length and is the angle it makes with the real axis, we determine the real and complex components.
Rectangular form;-
Rectangular form, on the other hand, is where a complex number is denoted by its respective horizontal and vertical components. In essence, the angled vector is taken to be the hypotenuse of a right triangle, described by the lengths of the adjacent and opposite sides.
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What is the simplified form of the fraction 2000 over 100
Answer:
20/1
Step-by-step explanation:
2000 divided by 100 = 20
100 divided by 100 = 1
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount Erica owed for the 6 years if 5300 dollars was loaned at the rate of 8% is $8,551.56.
How to find the amount Eric owes for 6 years?The amount Erica owes for 6 years if 5300 dollars is loaned to her at the rate of 8% compounded monthly can be computed as follow:
Therefore,
[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]
where
p = principalr = rate t = timen = number of time compoundedTherefore,
p = 5300 dollars
t = 6 years
n = 12
r = 8%
Therefore,
[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]
[tex]A = 5300(1+ \frac{0.08}{12} )^{(12)(6)}[/tex]
A = 5,300(1 + 0.0066666666666667)⁷²
Therefore,
A = $8,551.56
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help pleaseeee, i managed to get the right answer but the way i did it doesnt feel right, can somebody please answer so i can see what to do
Answer:
≈ 4,22 m
Step-by-step explanation:
volume = 20000L = 20000 dm^3 = 20 m^3
diameter = 2,4m
the volume of a cilinder is π * r^2 * h (height)
20 = π * 1,2^2 * h
h = [tex]\frac{20}{\pi * 1,44} \\[/tex] ≈ 4,42 m
What is the surface area of the given triangular prism in square inches
NEED ANSWER IMMEDIATELY!!!!
Answer:
182 [tex]in^{2}[/tex]
Step-by-step explanation:
Bottom:
12 x 4 = 48
Left side:
5x4= 20
Front:
[tex]\frac{12x5}{2}[/tex]= 30
Back
[tex]\frac{12x5}{2}[/tex] = 30
Top
13x4 =54
Add together:
48+ 20+ 30+30+54 = 182
write an ordered pair for y=1/8x-1 and -5x+4y=-3
Answer:
Step-by-step explanation:0495-46y7467-6686-745676-5
Answer:
there fore y = 1/8x-1 it can be write as 8xy+8x-1 = 0
and -5x+4y=-3 can be write it as -5x+4y+3 = 0
Step-by-step explanation:
given that
pair y = 1/8x-1 ------ equation (1)
and -5x+4y=-3 ------ equation (2)
you can write it as
you can write equation (1) as
y = 1/8x-1
y = 1-8x/8x
8xy = 1-8x
there fore
y = 1/8x-1 it can be write as 8xy+8x-1 = 0
you can write equation (2) as
-5x+4y = -3
-5x+4y+3 = 0
there fore
-5x+4y=-3 can be write it as -5x+4y+3 = 0
A right triangle has a leg length of square root of 7 and a hypotenuse length of 4. Determine the length of the other leg of the right triangle.
square root of 57
square root of 49
8
3
The length of the other leg of the right angles triangle is 3. Option D
How to determine the length of the sideThe Pythagorean theorem states that the square of the hypotenuse side is equal to the square of the other two sides in a right angled triangle.
We have;
a² = b² + c²
Where;
a is the hypotenuseb is the opposite sidec is the adjacent sideNow, substitute the values
4² = (√7)² + c²
Find the square values
16 = 7 + c ²
collect like terms
c² = 9
Find the square root of both sides
c = 3
Hence, the value is 3
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Answer:The length of the other leg of the right angles triangle is 3. Option D
Step-by-step explanation:
a class has 15 boys and 20 girls. what is the boy: girl ratio in simplest form? group of answer choices 4 to 5 10 to 13 3:5 3:4
If the a has 15 boys and 20 girls, then the boy to girls ratio in simplest form is 3 : 4
Number of boys in the class = 15 boys
Number of girls in the class = 20 girls
The ratio can be defined as the a number that can be used to express one quantity as a fraction of the other ones. That means we are comparing them by dividing those numbers
Here the ratio will be
Number of boys in the class : Number of girls in the class
Substitute the values in the ratio
= 15 : 20
Divide both numbers by 5
= (15/5) : (20/5)
= 3 : 4
Hence, if the a has 15 boys and 20 girls, then the boy to girls ratio in simplest form is 3 : 4
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The graph of the function graph (a) and the table in the figure represents the actual table of the function
How to make the table of values of the functionFrom the question, we have the following equation that can be used in our computation:
f(x) = (3/4)^x
This equation can be re-expressed as
f(x) = (3/4)ˣ
The x values on the table of values are given as: x = -2, -1, 0, 1 and 2
The next step is to substitute these values
So, we have the following equations
f(-2) = (3/4)⁻² = 16/9
f(-1) = (3/4)⁻¹ = 4/3
f(0) = (3/4)⁰ = 1
f(1) = (3/4)¹ = 3/4
f(2) = (3/4)² = 9/16
When these equations are represented on a table of values, we have the following table:
x -2 -1 0 1 2
y 16/9 4/3 1 3/4 9/16
Next, we represent the values on a graph
From the table, we have
y = 1 when x = 0
This means that it crosses the y-axis at (0, 1)
This is represented by graph (a)
So, the graph of the function is graph (a)
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The graph of y =x? was:
• reflected in the x-axis
•
• compressed vertically by a factor of ½
• translated 2 units upward (i.e. 1 2)
What is the equation after the translation?
then it becomes, [tex]y=-\frac{1}{2} x^2[/tex].
Now graph translated 2units upward so, [tex]y=-\frac{1}{4}(x+(2))^2[/tex][tex]y = -\frac{1}{4} (x+2)^2[/tex]
Hence, required equation of graph is,[tex]y = -\frac{1}{4} (x+2)^2[/tex]
What do you mean by graph?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
What do you mean by Factor?
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.
What is whole number?
The positive integers are another name for the whole numbers or the nonnegative integers, if zero is included.
What is integer?
Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
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Simplify the given expression. Show all steps. Submit your handwritten work or use the equation editor to receive credit.
The expression (√z√y√x)^8 is simplified to zyx
What is square root?Square root of a number can be defined as a value, which by multiplying itself, gives the original number.
It is represented with the symbol " √ ".
The square root of a number is the direct opposite of squaring a number.
Given the expression;
Find the square root of z
[tex]{\sqrt{z\sqrt{y\sqrt{x} } }}^8[/tex]
Square root can be expressed as the power of 1/2
Then, we have'
[tex]z\sqrt{y\sqrt{x} } ^ 4[/tex]
Find the square root of y
[tex](zy\sqrt{x} )^2[/tex]
Find the square root of x
zyz
Hence, the expression is xyz
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Quadratic formula PLEASEE help!!
Answer:
x = -0.5, -3.5
Step-by-step explanation:
You want the solution to 4x² +16x +7 = 0 using the quadratic formula.
ApplicationComparing the given equation to the standard form quadratic, you can identify the coefficients as ...
a = 4b = 16c = 7Substituting these values into the quadratic formula, you find the solutions to be ...
[tex]x=\dfrac{-16\pm\sqrt{16^2-4(4)(7)}}{2(4)}=\dfrac{-16\pm\sqrt{144}}{8}\\\\x=\dfrac{-16\pm12}{8}=\dfrac{-4\pm3}{2}\\\\x=\left\{-\dfrac{7}{2},\ -\dfrac{1}{2}\right\}[/tex]
The possible values of x are -3.5 and -0.5.
given that a=b is it ever possible to have a+a= a+b
Answer: Yes
Step-by-step explanation:
Because a=b, we can use the Substitution Property of Equality to substitute a for b. Now our equation looks like this:
a+a=a+a
Using the Reflexive Property, we know that this equation is true. We can use an example by setting a=2. This is what that would look like:
a=2
a=b transitive property
b=2
a+a=a+b substitution property
2+2=2+2
4=4 true
Therefore, yes, it is possible for a+a=a+b when a=b