The side lengths of the fence he can build with the greatest area inside are of:
75 yards and 75 yards.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that the area and the perimeter of the rectangle are given as follows:
The area is given by the multiplication of the dimesions, that is, A = lw.The perimeter is given by twice the sum of the dimensions, that is, P = 2(l + w).A farmer has 300 yards of fencing, hence the perimeter is:
P = 300.
Then:
2(l + w) = 300
l + w = 150
l = 150 - w.
Then the equation giving the area of the fence is:
A = lw
A = w(150 - w)
A = -w² + 150w.
Which is a quadratic equation with coefficients given by:
a = -1, b = 150.
The width that will give the highest possible area is the x-coordinate of the vertex, hence:
w = -150/(2(-1)) = 75 yards.
The length is of:
l = 150 - w = 150 - 75 = 75 yards.
Which means that the third option is correct.
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Find the value of the expression (2x − 12) + (xy-10) for x = 8 and y = 2.
-
O-8
O 6
O-10
02
The value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.
According to the question,
We have the following expression:
(2x − 12) + (1/2xy-10)
Now, the values of x and y are given to be 8 and 2 respectively.
So, we will put these values of x and y in the given expression:
(2*8-12)+(1/2*8*2-10)
First, we will use multiplication:
(16-12)+(8-10)
4+(-2)
(Note that when two integers are of different signs then the integers are subtracted but the sign in the result is of the larger integer.)
4-2
2
Hence, the value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.
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9) Give the following expression in index form
a) √3
For the given expression √3, its index form is written as ( 3 )¹/² .
As given in the question,
Given expression is equal to :
√3
Standard form of writing expression in index form is given by:
√ ( square root ) will express the value in index form as 1 / 2 in the exponent.
√x = ( x ) ¹/²
Here x = 3 substitute the value of x in the standard way of index form we have:
Index form of the given expression is written as :
√3
= ( 3 )¹/²
Therefore, for the given expression √3, its index form is written as ( 3 )¹/² .
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Finn wants to buy a sweater for $29.50 and jeans for $42.50 if the sales tax rate is 8.25% what will be the amount of cell taxes on finn’s purchase
The amount of cell taxes on finn’s purchase is $5.94.
How to calculate the value of the tax?Since Finn wants to buy a sweater for $29.50 and jeans for $42.50, the total cost will be:
= $29.50 + $42.50
= $72
If the sales tax rate is 8.25%, the amount on tax will be:
= Tax rate × Total cost
= 8.25% × $72
= $5.94
The tax is $5.94.
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Nathan invested $3,500 in an account paying an interest rate of 3. 5% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 19 years?.
Amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).
As given in the question,
Amount invested by Nathan is principal 'P' = $3,500
Interest rate 'r' = 3.5% compounded quarterly
Number of compounding periods per year for given quarterly 'n' = 4
Time period 't'= 19 years
Amount of money in the account after 19 years when no deposits or withdrawals are done.
Let 'A' be the amount.
Formula used:
[tex]A = P \times ( 1+ \frac{r}{n} )^{nt}[/tex]
Substitute the value in the formula we get,
A = 3500 × [ 1 + (0.035/4) ]⁽⁴⁾⁽¹⁹⁾
= 3500 × [ 1 + 0.00875]⁽⁴⁾⁽¹⁹⁾
= 3500 × [ 1.00875]⁷⁶
= 6,786.06 (approximately)
= $6800 (nearest hundred dollars)
Therefore, amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).
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Question 12 (10 points)
If AWXY is equilateral and AWZY is isosceles, find each missing measure. Answers may be used more than once!
angle 1 =
angle 2 =
angle 3 =
angle 4 =
angle 5 =
The measure of all the angles is given below :
angle 1 = angle 2 = angle 3 = angle 4 = angle 5 = 60°
Given, ΔWXY is an equilateral triangle and ΔWZY is an isosceles triangle.
We have to find the measure of all the angles,
As, ΔWXY is an equilateral triangle
so, ∠WXY = ∠XYW = ∠YWX = 60°
Now, let ∠WZY = ∠WYZ = x and ∠ZWY = y
so, on applying angle sum property, we get
2x + y =180°
so, y = 60°
and 2x = 120°
x = 60°
Hence, angle 1 = angle 2 = angle 3 = angle 4 = angle 5 = 60°
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Hello a girl out pls
Answer:
D
Step-by-step explanation:
Find all real numbers x such that
3x - 4 > 5 or -8x - 19 > 21
Click on the correct answer.
Answer:
Option B
Step-by-step explanation:
3x - 4 > 5
3x > 9
x > 3
-8x - 19 > 21
-8x > 40
x < -5
This means that we can eliminate the first option, since it includes all real numbers. We can also eliminate the last option since it doesn't include any real numbers.
The middle option is the only graph that includes numbers from -∞ to -5, and 3 to ∞
Please help giving out max points!!
Question: Graph the polygon and its image after a dilation with the given scale factor.
See attached
Given Triangle DGF, with vertices D(- 2, 0), G(2, 0), F(2, - 2),Scale factor r = 1.5.SolutionTriangle DGF is plotted, blue figure.
Find the coordinates of the image using the rule:
(x, y) = (1.5x, 1.5y)D' = (1.5*(-2), 1.5*0) = (-3, 0),G' = (1.5*0, 1.5*2) = (0, 3),F' = (1.5*2, 1.5*(-2)) = (3, - 3).The points added to same plot, red figure.
Answer:
D' = (-3, 0)
G' = (0, 3)
F' = (3, -3)
Step-by-step explanation:
Given vertices of the polygon:
D = (-2, 0)G = (0, 2)F = (2, -2)To dilate a figure by a given scale factor, multiply the coordinates of the vertices of the figure by the scale factor:
D' = (-2 × 1.5, 0 × 1.5) = (-3, 0)G' = (0 × 1.5, 2 × 1.5) = (0, 3)F' = (2 × 1.5, -2 × 1.5) = (3, -3)Therefore, the vertices of the image after dilation are:
D' = (-3, 0)G' = (0, 3)F' = (3, -3)Complete the equation describing how
and y are related.
XOL2345
911 13 15
1
y
7
17
y = [? ]x + [ ]
Enter the answer that
belongs in [?].
The equation that describing how x and y are related is y = 2x + 7
From the given table we have to choose two points
The first point = (1, 9)
The second point = (2, 11)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (11-9) / 2 - 1
= 2 / 1
= 2
From the table
At x = 0 the value of y = 7
Therefore the y intercept = 7
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Then,
y = 2x + 7
Hence, the equation that describing how x and y are related is y = 2x + 7
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What is the value of x?
Enter your answer in the box.
x = ___
Answer:
x=32 degrees
Step-by-step explanation:
Since the triangle is equilateral, each angle is = 60 degrees. This means that 2x-4=60
=) 2x=64
=) x=32
Which expression is equivalent to -6(-3m-5)?
Answer:
18m + 30
Step-by-step explanation:
times everything in the bracket by 6
Question Write an equation of the line that passes through (4,−1) and is parallel to the line y=3x+7
Answer:
y=3x-13
Step-by-step explanation:
Since the parallel equations have equal slope.
The equation of line parallel to y=3x+7 will be y=3x+k.
(4,-1) lies in the line so it satisfies the equation amd we get the value of k as -13 and finally we substitute the value of k in the eqn and we finally get the equation as 3x-y-13=0 or you can also write it as y=3x-13
(will mark brainlist) Which of the following expressions is equivalent to 2x +37
○ 6(2)
8(2)*
2*
6
2*
8
Answer:
B) [tex]8(2)^{x}[/tex]
Step-by-step explanation:
Using the Product Property of Exponents, we know that two exponents with the same base can have their exponents added together.
Step 1 - Convert 8 to an exponent with a base of 2:
[tex]8 = 2^{3}[/tex]
Step 2 - Use the Product Property of Exponents:
[tex]2^{3} *2^{x}[/tex]
[tex]2^{x+3}[/tex]
Hope this helps and have a great day! :)
An artist charges $980 for a portrait but gives 5% discount for cash. Calculate the cash Price of the portrait
Mr. Johnson is ordering new desks and tables for the school. He has a budget of $2000, no more. Each desk is $45 and each table $75 befine your variables and write an inequality representing what Mr. Johnson can order. pls help
Answer: 45x + 75y < 2000
Step-by-step explanation:
x = # of desks
45 = cost/desk
y = # of tables
75 = cost/table
2000 = maximum dollar amount that can be spent
inequality:
45x + 75y < 2000
isaac owns a trucking company. for every truck that goes out, isaac must pay the driver $19 per hour of driving and also has an expense of $1.50 per mile driven for gas and maintenance. on one particular day, the driver drove an average of 30 miles per hour and isaac's total expenses for the driver, gas and truck maintenance were $512. write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. define the variables that you use to write the system.
8 hours the driver worked and 240 miles the truck drove.
Assume that the truck traveled y miles per hour. and that the driver worked x hours per day.
The equations describing the provided issue will be
19x + 1.50 y = 512
y = 30x
y = 19 x + 1.50 y = 30 x + 1.50 y
When we enter the second equation into the first one, we get,
19 x + 1.50 (30 x) = 512
19x+ 45x = 512
64x = 512
x = 8
y = 240
The vehicle traveled 240 miles, and the driver put in eight hours' worth of work.
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Translate this phrase into an algebraic expression.
Eight less than the product of 21 of goran’s score.
Use the variable g to represent Goran’s score.
Answer:
21g-8
Step-by-step explanation:
The product of Goran's score and 21 = 21g, then subtract 8 from that.
Answer:
lo siento no se mucho de este ap
Drag graphs to show a graph of each equation in the table.
Answer:
see screenshot
Step-by-step explanation:
the equation is always f(x) = m * x + b
with b being where the graph hits the y axis and m being how much the graph rises or drops (then m is negative) when you go 1 to the right on the x axis
At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48. Are the cost, y, in dollars and the amount of yogurt, x, proportional? explain. Write an equation to represent this relationship.
Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.
Given:
At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48.
y varies directly as x :
y = kx
k = constant of proportionality
y = 2.56 and x = 32
y = kx
k = y/x
= 2.56/32
k = 0.08
substitute k we get
y = 0.08x.
so x and y are directly proportional.
Therefore Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.
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(Pleasee hurry) Expand the expression: 1/2 (10x + 8)
5x+4 is the simplified form of expression 1/2(13x+5x-6-8x+14)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is
1/2(13x+5x-6-8x+14)
one by two times of thirteen x plus five times of x minus six minus eight times of x plus fourteen.
In the equation x is the variable
plus, minus and multiply are the operators
1/2(13x+5x-6-8x+14)
1/2(10x+8)
Now apply distributive property
1/2(10x)+1/2(8)
5x+4
Hence 5x+4 is the simplified form of expression 1/2(13x+5x-6-8x+14)
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which of the following ratios are equalvalent to 5/20
1/4
1/5
20/100
25/100
Answer:
1/4 is a equivalent ratio
Step-by-step explanation:
hope it helped :)
Can someone help me
The graph of the given table of data is attached below. And the best scale for this one is x axis 1 cm = 20 units and y axis 1 cm = 1 units. The value of A is 60 and the value of B is 140.
Graph:
Graph can be used to view the table of data in a visual manner for the easy understanding of the given range of data.
Given,
Here we have the table of data that contains the details about the length and their corresponding mass in kg.
Now, we have to plot this data on the graph and then we have to find the best scale suitable for this graph.
Finally, we have to find the value of A and B in the plotted graph.
In order to plot the graph for the given table, we have to input the values on the graphing calculator,
Then we get the graph like the following.
While we lookin into the graph we have identified then the best scale suitable for this graph is
x axis
1 cm = 20 units and
y axis
1 cm = 1 units.
Now, the value of A is 60 and the value of B is 140.
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HELP MEEEEEE PLEASEEEEE
unable to see the graph
UT
T
10. FIND THE ERROR A classmate is calculating the amount in a savings
account after 10 years. The deposit is $13,000 and the annual
simple interest rate is 2%. Describe the error. What support can
you provide to help them correct the error?
The interest when the classmate is calculating the amount in a savings account after 10 years is $2600.
How to calculate the interest?From the information, the classmate is calculating the amount in a savings account after 10 years and the deposit is $13,000 and the annual simple interest rate is 2%.
It should be noted that interest is calculated as:
= (Principal × Rate × Time) / 100
= ($13000 × 2 × 10) / 100
= $2600
The simple interest is $2600.
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Ralph hit a softball into the air with an initial upward velocity of 48 feet per
second. The height h in feet of the ball above the ground can be modeled by
h = -16t² +48t + 3, where t is the time in seconds after Ralph hit th
softball.
What is the realistic domain for this function?
Answer:
domain: [0, (6+√39)/4] ≈ [0, 3.06125]
Step-by-step explanation:
You want the realistic domain of a height function h = -16t² +48t + 3.
DomainThe given polynomial is defined for all values of t. Since it represents height above the ground, and after the ball is thrown, only function values in the first quadrant are of interest: h ≥ 0, t ≥ 0.
The height becomes zero at t = (6+√39)/4 ≈ 3.061 seconds after the ball is hit. Hence the realistic domain is [0, (6+√39)/4], the interval in which the ball is above ground.
__
Additional comment
We can solve this using the "completing the square" method.
t^2 -3t = 3/16 . . . . . . divide by -16, add 3/16
(t -3/2)^2 = 3/16 +9/4 . . . . . add 9/4 to complete the square
t = 3/2 ± √(39/16) = (6 ± √39)/4 . . . . . . take the square root, add 3/2
Only the positive value of the solution is applicable to this problem. That value is ...
h = 0 at t = (6 +√39)/4 ≈ 3.061249
Warren and Dirk are baking cookies for a charity bake sale. First they bake gingersnaps, which are Warren's favorite cookie. Then they bake 120 chocolate crinkles, which are Dirk's favorite. In all, Warren and Dirk bake 204 cookies. Use an equation to find the number of gingersnaps Warren and Dirk bake. gingersnaps Ver en españ
Answer:
g = 204 - 120
Step-by-step explanation:
T - CC = amount of gingersnaps
204 - 120 = 84
Warren and Dirk baked 84 gingersnaps
A painter can paint 15 square feet every 1/4 hour. How many square feet can they paint in one hour?
A painter can paint 60 square feet every 1 hour.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A painter can paint 15 square feet every 1/4 hour.
Now,
Since, A painter can paint 15 square feet every 1/4 hour.
Let painter can paint in every 1 hour = x square feet
So, By definition of proportional as;
⇒ 15 / (1/4) = x / 1
Solve for x as;
⇒ 15 × 4 = x
⇒ x = 60 square feet
Thus, A painter can paint 60 square feet every 1 hour.
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Find the slope (3,-20),(5,8)
Answer: 14
Explanation:
(3, -20) (5, 8)
x1 y1 x2 y2
[tex]\frac{y2 - y1}{x2 -x1}[/tex]
[tex]\frac{8 - -20}{5-3}[/tex] = [tex]\frac{8+20}{5-3} = \frac{28}{2} = 14[/tex]
The vertex angle of an isosceles triangle is 5 degrees more than 3 times the measure of one of the
base angles. Determine the measure of each angle of the triangle.
The measure of each angle of the triangle are 35°, 35°, 110°.
What is an isosceles triangle?
An isosceles triangle has two equal sides as well as two equal angles.The Greek words iso (same) and skelos are the source of the name (leg).An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.Let's Base angle =x°
Vertex angle = 5° +3x°
The sum of measure of angles of triangle are supplementary.
i.e., Sum of triangle = 180°
So,
x° + x° + 5° + 3x° =180°
5x° + 5° = 180°
5x° = 175°
x° = 175° /5°
x = 35°
Base angle = 35°
Vertex angle = 5°+ 3x°
= 5° + 3×35°
= 5° +105°
Vertex angle = 110°
Hence, the measure of each angle of the triangle are 35°, 35°, 110°.
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Write down the factors of 28 Then,write down the prme factors of 28
the factors of 28 are : 1, 2, 4, 7, 14, and 28.
the prime factors of 28 are : 2, 2, and 7.