Answer:
[tex]\frac{8}{25}[/tex] square miles
Step-by-step explanation:
The relationship between the side length (let it be s) of a square and its diagonal (let it be d) is given by:
[tex]s=\frac{d}{\sqrt{2} }[/tex]
Since d is given as 4/5, we solve for s:
[tex]s=\frac{d}{\sqrt{2} }\\s=\frac{\frac{4}{5}}{\sqrt{2} }\\s=\frac{4}{5\sqrt{2} }[/tex]
NOW, area of square is s^2 where s is the side length.
Area = [tex]s^2=(\frac{4}{5\sqrt{2} })^2=\frac{16}{50}=\frac{8}{25}[/tex]
The area of the park is:[tex]\[\boxed{\frac{8}{25} \text{ square miles}}\][/tex]
To find the area of the square park given the length of the diagonal, we need to use the relationship between the side length of a square and its diagonal.
[tex]\[d = s\sqrt{2}\][/tex]
Given that the diagonal [tex]\( d \) is \(\frac{4}{5}\)[/tex] miles, we can set up the equation:
[tex]\[s\sqrt{2} = \frac{4}{5}\][/tex]
[tex]\[s = \frac{\frac{4}{5}}{\sqrt{2}} = \frac{4}{5\sqrt{2}}\][/tex]
Rationalize the denominator by multiplying the numerator and the denominator by [tex]\(\sqrt{2}\):[/tex]
[tex]\[s = \frac{4\sqrt{2}}{5 \cdot 2} = \frac{4\sqrt{2}}{10} = \frac{2\sqrt{2}}{5}\][/tex]
[tex]\[A = \left( \frac{2\sqrt{2}}{5} \right)^2\]\[A = \frac{(2\sqrt{2})^2}{5^2} = \frac{4 \cdot 2}{25} = \frac{8}{25}\][/tex]
Therefore, the area of the park is:
[tex]\[\boxed{\frac{8}{25} \text{ square miles}}\][/tex]
Answer ASAP
Which two expressions are equivalent to 6 * V * W * 1/2
A. 1 * 3 * v * w + 0
B. 3(v + w)
C. 3 * v * w
D. w * v * 1/2 * 6 + 1
E. 2 * v * w
* = multiplication
The answer is C. Hope this helps!
111 = 14g what is g??
Answer:
the answer to this is 7.9 or 7 13/14
Step-by-step explanation:
1. Divide both sides by 14
111/14 = 14g/14
2. Simplify
g = 7 13/14
Final answer:
The variable 'g' in the equation 111 = 14g is found by dividing 111 by 14, resulting in approximately 7.929 (rounded to 4 significant figures).
Explanation:
The equation given is 111 = 14g, which seems to be a simple algebra equation where you are solving for the variable g. To find g, you would divide both sides of the equation by 14 to isolate g.
This calculation yields: g = 111 / 14, which equals 7.92857142857. However, this number might need to be rounded depending on the context or instructions for significant figures. If the problem instructions mentioned 4 sig figs, the answer would be rounded to 7.929.
what number is 4.0003 x 10^7 in scientific notation
4.0003 x 10^7 is already in scientific notation. If you mean in regular notation/as a regular number, it is 40003000. Since it is 10 to the power of positive 7, you move the decimal place 7 to the right.
Answer:
40,003,000
Step-by-step explanation:
The given number is :
[tex]4.0003\times 10^{7}[/tex]
As we can see that [tex]4.0003\times 10^{7}[/tex] is already in scientific notation.
Scientific notation means writing numbers in powers of 10.
Hence, we can write this notation in regular way as:
40,003,000
What is the distance between points D and H? Round to the nearest tenth of a unit. D(1,3) H(9,8)
Answer:
9.4 units
Step-by-step explanation:
To find the distance between two points D ( 1, 3 ) and H ( 9, 8 ), we can use the distance formula:
d = √(( x₂ - x₁ )² + ( y₂ - y₁ )² )
Substituting the coordinates, we have:
d = √( ( 9 - 1 )² + ( 8 - 3 )²)
Simplifying,
d = √( 8² + 5² )
d = √( 64 + 25 )
d = √89
d ≈ 9.4 units
The distance between point D and H to the nearest tenth is 9.4 units
What is distance between two points?The distance between two points is the length of the line segment joining them. Since the length of the line segment cannot be negative, the distance between two points is always positive.
The distance between two points is expressed as
S = √ X -x)² + (Y -y)²
= √ 9-1)² + 8-3)²
= √ 8² + 5²
= √ 64 +25
= √89
= 9.4 ( nearest tenth)
Therefore the distance between point D and H to the nearest tenth is 9.4 units
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1. What is the solution to the system of equations?
3x + 4y = 12
x + 2y = 10
(a) Show how to solve the system of equations using the linear combination or elimination method.
(b) Show that you can get the same answer by using the substitution method.
Please help worth 93 points
Answer:
Step-by-step explanation:
(a) In order to use the elimination method, multiply the second equation by 2.
It becomes 2x + 4y = 20.
Subtract that from the first equation: 3x + 4y = 12
3x + 4y - 2x - 4y = 12 - 20
x = -8
Put that back in the second equation: -8 + 2y = 10
2y = 18
y = 9
(b) In order to use the substitution method, subtract 2y from the second equation.
It becomes x + 2y - 2y = 10 - 2y
x = 10 - 2y
Substitute that into the first equation:
3(10 - 2y) + 4y = 12
30 - 6y + 4y = 12
30 - 2y = 12
2y = 18
y = 9
Put back into the equation for x:
x = 10 - 2(9)
= 10 - 18
= -8
Answer:
Step-by-step explanation:
(1) 3x + 4y = 12
(2) x + 2y = 10
(2)*3: 3x+6y=30
by elimination (2)*3 - (1)
6y-4y=30-12
2y=18
y=9
x+2(9)=10
x=-8
rearrange (2): x=10-2y
substitute in (1): 3(10-2y)+4y=12
30-6y+4y=12
2y=30-12
y=9
x=10-2(9)
=-8
same ans either way
may somebody help me please
Answer:
The answer is C because when you substituted the coordinate pairs into the equation, both sides are equal which tells you that they're a solution to the equation.
Explanation:
All you do is substitute. (x,y)
A:
Substitute
1 = 4(2) - 7
Multiply the number inside the parentheses by the outside number.
1 = 8 - 7
Subtract to get your solution.
1 = 1
Both sides equal to each other so this means that this is a solution to the equation.
B:
Substitute
9 = 4(4) - 7
Multiply the number inside the parentheses by the outside number.
9 = 16 - 7
Subtract to get your solution.
9 = 9
Both sides equal to each other so this means that this is also a solution to the equation.
D:
Both ordered pair is a solution to the equation.
write the equation 2/3 of c subtracted from 2
Hello.
You would write the equation like this: [tex]\frac{2}{3} c - 2[/tex]
Let me know if that was what you were looking for.
How can x + 3 = −2x + 5 be set up as a system of equations?
Answer:
y = x+3; y = -2x +5
Step-by-step explanation:
x + 3 = -2x + 5
Let y = x + 3 = -2x + 5
If a = b = c then a=b and a=c
we can write the equation as
y = x + 3 and y = -2x + 5
Thus, this is the system of equations
y = x + 3
y = -2x + 5
Answer:
y = x + 3 and y = -2x + 5
Step-by-step explanation:
If we consider one set of equation as:
[tex] y = x + 3 [/tex]
and the other set of equation as:
[tex] y = - 2 x + 5 [/tex]
Since the left hand side for both these equations is same, therefore we can equate the right hand side and write it as:
[tex] x + 3 = - 2 x + 5 [/tex]
Determine if the numbers are parallel, perpendicular or netiher.
y=-7
y=6
Will mark brainest!!
Answer:
Parallel :)
Step-by-step explanation:
thats the tea sis.
A leaky pool loses 2 1/4 inches of water each day. Jermaine and Mildred are asked to determine the change in the amount of water in the pool over 5 days.
Mildred’s Solution
5 (-2 1/4)
5(-2- 1/4)
-10-5/4
-11 1/4
Answer: 5(-2 1/4)
Step-by-step explanation: When somethig is being taken away, it's represented as a negative number. The number needs to be displayed throug 5 days, so A would be correct. To check, a negative times a postive is a negative, and 5 times -2 1/4 is -11 1/4.
A swimming pool had 2.5 million liters of water in it. Some water evaporated, and then the pool only had 2 million liters in it.
Answer:
The swimming pool lost 500,000 liters
Step-by-step explanation:
Now it only has .5 million liters now
12y^2–5y=2
thank you!
answer Y=1 over 4 and Y= 2 over 3 that is your answer and these are the steps I'm going to put a image hope this is useful to u and have a beuty day
Answer:
f(y) = 12y^2 -5y -2 = 0
a = 12 b =-5 c=-2
Using quadratic formula:
y = [-b +-sq root (b^2 -4ac)] / 2 a
y = [--5 +-sq root (25 -4*12*-2)] / 24
y = [5 +- sq root (25 + 96) ] / 24
y = [5 +- sq root (121) ] / 24
y = [5 + 11] / 24
y1 = (2/3) = .66666666666
y2 = 5 -11 / 24
y2 = -(1/4) = -.25
Step-by-step explanation:
Identify the figure formed by the net
Answer:
cylinder
Step-by-step explanation:
g^2 +23 when. g=6 please help
Answer:
59
Step-by-step explanation:
Substitute.
6 ^ 2 = 36
36 + 23 = 59
A princess hat for a costume is shaped like a cone. The base of the cone is 12 in across and the height is 8 in. The slant height of the outside edge, which is unknown, is the hypotenuse of the right triangle formed with the radius and the height of the cone.
(a) Sketch the princess hat. Label the known lengths as described and label the unknown length as x.
(b) what is the slant height of the outside edge?
plz help!
Answer:
Part a) The drawn in the attached figure
Part b)The slant height of the outside edge is [tex]x=10\ in[/tex]
Step-by-step explanation:
Part a) The drawn in the attached figure
Part b) What is the slant height of the outside edge?
we have that
The diameter of the base of the cone is 12 in
so
[tex]r=12/2=6\ in[/tex] ----> the radius is half the diameter
[tex]h=8\ in[/tex]
Applying the Pythagoras Theorem find the slant height x
[tex]x^{2}=r^{2}+h^{2}[/tex]
substitute the values
[tex]x^{2}=6^{2}+8^{2}[/tex]
[tex]x^{2}=100[/tex]
[tex]x=10\ in[/tex]
a laptop was originally sold for $975. The laptop is now on sale for $828.75. What is the percent markdown?
so the difference is 975 - 828.75 = 146.25.
now, if we take 975 to be the 100%, what is 146.25 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 975&100\\ 146.25&x \end{array}\implies \cfrac{975}{146.25}=\cfrac{100}{x}\implies 975x=14625 \\\\\\ x=\cfrac{14625}{975}\implies x=15[/tex]
A car servicing station is running a special offer. The breakdown of the cost for different services is given below.
Membership Fee: $50 (one-time cost)
Air Freshener Cost: $4 per car per month
Washing Cost: $10 per car per month
Tire Replacement Cost: $400 per car
Tire Pressure Check Cost: $15 per month
The total cost for 12 months of this service for n cars is given by the expression below.
568n + 230
Answer:
Option C
Step-by-step explanation:
There are several types of costs in this problem:
* Unique costs
* Costs that depend on the number of cars
* Costs that depend on the number of months
* Costs that depend on the number of months and the number of cars.
The costs that depend on the number of cars represent the coefficient of the variable n.
The costs that do not depend on the number of cars represent the constant value of the equation.
Then, to solve this problem you must identify the costs that do not depend on the number of cars.
These costs are:
* Membership Fee: $ 50 (one-time cost)
* Pull Pressure Check Cost: $ 15 per month
[tex]\$50 + \$15(12\ month) = \$230[/tex]
Then the answer is option C
The current in a simple electric circuit varies inversely as the resistance. If the current is 20amps when the resistance is 5 ohms, find the current when the resistance is 8 ohms
Answer:
0.5amps
Step-by-step explanation:
I is inversely proportional to resistance
I = k/R
k = I/ R
k = 20/5
k = 4
This means that, I = 4/R
So, when R = 8ohms,
I = 4/8
=0.5amps
Using Ohm's law, the inverse relationship between current and resistance in a simple circuit allows calculation of the new current as 12.5 amps when the resistance changes from 5 ohms to 8 ohms.
Explanation:The student's question involves an application of Ohm's law, which is a fundamental principle in Physics that relates electric current (I), resistance (R), and voltage (V). According to Ohm's law, in a simple circuit, the current is inversely proportional to the resistance when the voltage is held constant. Given that the current is 20 amps when the resistance is 5 ohms, we can write the relationship as I1 * R1 = I2 * R2 where I1 and R1 are the initial current and resistance, and I2 and R2 are the final current and resistance we wish to find.
Plugging in the given values, we have:
20 amps * 5 ohms = current when resistance is 8 ohms * 8 ohms
Solving for the current when the resistance is 8 ohms:
20 amps * 5 ohms = I2 * 8 ohms
100 = I2 * 8
I2 = 100 / 8
I2 = 12.5 amps
Therefore, the current when the resistance is 8 ohms is 12.5 amps.
Talia uses 10 strawberries and 4 oranges to make 8 servings of fruit salad. how many oranges and strawberries does talia need to make 12 servings?
Answer:
25 strawberries and 10 oranges
Step-by-step explanation:
1) 12 ÷ 8 = 2.5
2)10 x 2.5= 25
3)4 x 2.5=10
Plz help !! Needed to graduate
Answer: 3x
Step-by-step explanation:
[tex]\dfrac{\sqrt[3]{54x^5}}{\sqrt[3]{2x^2}}=\dfrac{\sqrt[3]{3\cdot 3\cdot 3\cdot 2\cdot x\cdot x\cdot x\cdot x^2}}{\sqrt[3]{2x^2}}=\dfrac{3x\sqrt[3]{2x^2}}{\sqrt[3]{2x^2} }=\boxed{3x}[/tex]
Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed. x + y ≤ 6 x ≤ 4
Answer: The graph is attached.
Step-by-step explanation:
The region is limited by two lines:
[tex]x+y=6[/tex] and [tex]x=4[/tex]
You can write the first inequlity [tex]x+y\leq6[/tex] in the following form:
[tex]y\leq-x+6[/tex]
This region are all the values for which the y-axis is less than the line f(x)=x+6 (all the values under the line).
The other inequality x ≤ 4 are all the values for which the x-axis is less than the line x=4 (all the values to the left of the line).
Observe the graphs attached.
Answer:
its this one
Step-by-step explanation:
I need help on this...
Answer:
(b) 12; (a) 75%
Step-by-step explanation:
For b, convert the percentage to a SIMPLIFIED FRACTION [3⁄20 = 15%]. After you get your fraction, multiply it by 80 to get 12.
For a, it gives you your number already, but kind of turned around. This time, they want to to figure out what percentage of 48 will give you 36. Simply divide 36 by 48 to get your answer.
I am joyous to assist you anytime.
Write the point-slope form of the line's equation satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Passing through (negative 2,4) and (3,4)
Answer:
y = 4
or
y - 4 = 0(x - 3)
Step-by-step explanation:
The points (-2,4) and (3,4) have the same y-value. Because of this, the slope of the line will be 0 and the line will be horizontal. This means the line will have the equation y = b where b is the y-coordinate. The equation of the line is
y = 4.
In point slope form, the equation will have m = 0.
y - 4 = 0(x -3)
A square has a side length of 36 feet the square is dilated by a scale factor of 2/3 do you create a new square what is the side length of them is square
you would multiply 36*2/3 and get 24 which would be the new side length
Answer:
24 feet
Step-by-step explanation:
got it right on ttm :)
You have $20.43 in your wallet. You find $5.12 in your pocket before washing your clothes. How much money do you have?
20.43+5.12=25.55 so ur answer is 25.55
Answer:
$25.55
Step-by-step explanation:
43+ 12 =55
20+5=25
The answer is $25.55.
A group of students are planning a mural at a wall the rectangular wall has dimensions of (6x+7) by (8x+5) and they are planning the mural to be (x+4) by(2x+5) what is the area of the remaining wall after the mural has been Painted
Answer: [tex]46x^2+73x+15[/tex]
Step-by-step explanation:
The area of a rectangle can be calculated with the formula:
[tex]A=lw[/tex]
l: the length of the rectangle.
w: the width of the rectangle.
The area of the remaning wall after the mural has been painted, will be the difference of the area of the wall and the area of the mural.
Knowing that the dimensions of the wall are [tex](6x+7)[/tex] by [tex](8x+5)[/tex], its area is:
[tex]A_w=(6x+7)(8x+5)\\\\A_w=48x^2+30x+56x+35\\\\A_w=48x^2+86x+35[/tex]
As they are planning that the dimensions of the mural be [tex](x+4)[/tex] by [tex](2x+5)[/tex], its area is:
[tex]A_m=(x+4)(2x+5)\\\\A_m=2x^2+5x+8x+20\\\\A_m=2x^2+13x+20[/tex]
Then the area of the remaining wall after the mural has been painted is:
[tex]A_{(remaining)}=A_w-A_m\\\\A_{(remaining)}=48x^2+86x+35-(2x^2+13x+20)\\\\A_{(remaining)}=48x^2+86x+35-2x^2-13x-20\\\\A_{(remaining)}=46x^2+73x+15[/tex]
which shows a perfect square trinomial?
Answer:
THE THIRD ONE I THINK :D
Please help!! I need ASAP 10 points <3
What is the domain and range for the following function and its inverse?
f(x) = x^2+3
Answer: The first answer choice
Step-by-step explanation:
help please! which choice represents the fraction below as a single exponential expression?
Answer:
B
Step-by-step explanation:
use the exponent rule of division: you just subtract the exponents if the base is the same, so 4-8=-4
The fraction with a numerator of 3.74 x 10⁻¹⁶ and a denominator of 10⁻³⁰ represented as a single exponential expression is 3.74 x 10¹⁴, obtained by dividing the digit terms and subtracting the exponents.
Explanation:To represent the fraction as a single exponential expression, you follow the division of exponentials rule, which involves dividing the digit terms and subtracting the exponents of the exponential terms. Given the fraction with a numerator of 3.74 x 10-16 and a denominator of 10-30, you would divide 3.74 (the digit term of the numerator) by 1 (the implied digit term of the denominator) which is just 3.74, and subtract the exponents (-16 - (-30)) which equals 14. Therefore, the fraction as a single exponential expression is 3.74 x 1014.
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