Answer:
Our two numbers are:
[tex]2+4\sqrt{2} \text{ and } 4\sqrt{2}-2[/tex]
Or, approximately 7.66 and 3.66.
Step-by-step explanation:
Let the two numbers be a and b.
One positive real number is four less than another. So, we can write that:
[tex]b=a-4[/tex]
The sum of the squares of the two numbers is 72. Therefore:
[tex]a^2+b^2=72[/tex]
Substitute:
[tex]a^2+(a-4)^2=72[/tex]
Solve for a. Expand:
[tex]a^2+(a^2-8a+16)=72[/tex]
Simplify:
[tex]2a^2-8a+16=72[/tex]
Divide both sides by two:
[tex]a^2-4a+8=36[/tex]
Subtract 36 from both sides:
[tex]a^2-4a-28=0[/tex]
The equation isn't factorable. So, we can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = -4, and c = -28. Substitute:
[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-28)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{4\pm\sqrt{128}}{2}=\frac{4\pm8\sqrt{2}}{2}=2\pm4\sqrt{2}[/tex]
So, our two solutions are:
[tex]\displaystyle x_1=2+4\sqrt{2}\approx 7.66\text{ or } x_2=2-4\sqrt{2}\approx-3.66[/tex]
Since the two numbers are positive, we can ignore the second solution.
So, our first number is:
[tex]a=2+4\sqrt{2}[/tex]
And since the second number is four less, our second number is:
[tex]b=(2+4\sqrt{2})-4=4\sqrt{2}-2\approx 3.66[/tex]
Answer:
[tex]2+4\sqrt{2}\text{ and }4\sqrt{2}-2[/tex]
Step-by-step explanation:
Let the large number be [tex]x[/tex]. We can represent the smaller number with [tex]x-4[/tex]. Since their squares add up to 72, we have the following equation:
[tex]x^2+(x-4)^2=72[/tex]
Expand [tex](x-4)^2[/tex] using the property [tex](a-b)^2=a^2-2ab+b^2[/tex]:
[tex]x^2+x^2-2(4)(x)+16=72[/tex]
Combine like terms:
[tex]2x^2-8x+16=72[/tex]
Subtract 72 from both sides:
[tex]2x^2-8x-56=0[/tex]
Use the quadratic formula to find solutions for [tex]x[/tex]:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] for [tex]ax^2+bx+c[/tex]
In [tex]2x^2-8x-56[/tex], assign:
[tex]a\implies 2[/tex] [tex]b \implies -8[/tex] [tex]c\implies -56[/tex]Solving, we get:
[tex]x=\frac{-(-8)\pm \sqrt{(-8)^2-4(2)(-56)}}{2(2)},\\x=\frac{8\pm 16\sqrt{2}}{4},\\\begin{cases}x=\frac{8+16\sqrt{2}}{4}, x=\boxed{2+4\sqrt{2}} \\x=\frac{8-16\sqrt{2}}{4}, x=\boxed{2-4\sqrt{2}}\end{cases}[/tex]
Since the question stipulates that [tex]x[/tex] is positive, we have [tex]x=\boxed{2+4\sqrt{2}}[/tex]. Therefore, the two numbers are [tex]2+4\sqrt{2}[/tex] and [tex]4\sqrt{2}-2[/tex].
Verify:
[tex](2+4\sqrt{2})^2+(4\sqrt{2}-2)^2=72\:\checkmark[/tex]
Use completing the square to solve this quadratic equation. Check all that apply.
x + 10x + 25 = 2 D
A. x = 5+ m2
B. x = 5 - 12
C. x= -5 +_2
D. x= -5-2
Answer: x= -5+ 2 squared.
Step-by-step explanation:
lol help pleas jdcbfjvbcjvdj
Answer:
C is your correct answer
Step-by-step explanation:
just multiply it together then you get 70.51
Graph the picture nes whose equation is 2y=-3x-2
Answer:
Picture Below
Step-by-step explanation:
You can simplify it by dividing it into
y = -1.5x-1
Natalie and Warren started swimming laps in the pool at 5:47. Natalie finished swimming her laps 27 minutes later. Warren finished swimming his laps 8 minutes after Natalie. What time did Warren finish his laps?
Answer:
6:22
Step-by-step explanation:
original time minutes when they both started - 47
47+ natalie's time
47+27 =74
minus 60 minutes to account for the hour (6 o'clock)
74-60=14
natalie finished at 6:14
warren finished 8 minutes after natalie's time
14+8=22
the hour did not finish so it will remain at 6
which leaves your final answer for the time that warren finished as 6:22
Which expression is equivalent to f+f+8ff+f+8f?
Answer:
8f² + 11f
Step-by-step explanation:
there are no expressions listed
This is the expression simplified
8f² + 11f
I need help with this
7/10= 28/40
5/8=25/40
0.8=4/5=32/40
32>28>25
So 0.8>7/10>5/8
I don't get how to do this.
Answer:
426 chickens
Step-by-step explanation:
let the pigs = x
the ducks = 2×x = 2x
the chickens = 3×(2x) = 6x
x +2x +6x = 639
9x=639
x = 639/9 = 71
the chickens = 6x = 6×71 = 426
Answer:
[tex]426\:\mathrm{chickens}[/tex]
Step-by-step explanation:
Since a duck has two legs, a pig has four legs, and a chicken has two legs, we can write the following system of equations:
[tex]\begin{cases}d+p+c=639,\\d=2p,\\c=3d\end{cases}[/tex], where [tex]d[/tex] is the number of ducks on the farm, [tex]c[/tex] is the number of chickens, and [tex]p[/tex] is the number of pigs.
Substituting, we get:
[tex]d+\frac{1}{2}d+3d=639,\\4.5d=639,\\d=\boxed{142}[/tex]
Now substitute [tex]d=142[/tex] into [tex]c=3d[/tex] to get the number of chickens:
[tex]c=3(142)=\boxed{426\:\mathrm{chickens}}[/tex]
A man borrows Rs. 50000 at 12% p.A., compounded half-yearly. He pays back Rs. 18000 at the end of every six months. Calculate the third payment, he has to make to clear the entire loan
Answer:
Rs. 20246
Step-by-step explanation:
According To the Question,
Given, A man borrows Rs. 50000 at 12% per Annum(compounded half-yearly). Thus the Rate of Interest for 6 months would be 6%. Now, He pays back Rs. 18000 at the end of every six months.Thus, the third payment, he has to make to clear the entire loan.
First-Payment = ( 50000 x 1.06 ) - 18000 ⇔ 35000 Rs.
Second-Payment = (35000 x 1.06) - 18000 ⇔ 19100 Rs.
Third-Payment = (19100 x 1.06 ) ⇔ 20246 Rs. the third payment, he has to make to clear the entire loan.
Substitute (2, 1) into x + 3y = 5 to get ✔ 2 + 3(1) = 5 . Simplify the equation to get . Substitute (2, 1) into y = –x + 3 to get ✔ 1 = –(2) + 3 . Simplify the equation to get .
Answer:
See explanation
Step-by-step explanation:
A
x + 3y = 5
(x, y) = (2,1)
x + 3y = 5
2 + 3(1) = 5
2 + 3 = 5
5 = 5
The equation is true
B.
y = –x + 3
(x, y) = (2, 1)
y = –x + 3
1 = -2 + 3
1 = 1
The equation is true
I have five numbers, the mean is 6, and the mode is 7 what could these numbers be?
Answer:
3, 5, 7, 7, 8
Step-by-step explanation:
3, 5, 7, 7, 8
the mean = (3+5+7+7+8)/5 = 30/5= 6
the mode = 7
Peggy had four times as many quarters as nickles. She had $2.10 in all. How many nickles and how many quarters did she have?
Which of the following equations could be used to solve the problem?
n+4n=2.10
n+4n=210
5n+100n=2.10
5n+100n=210
Answer:
the answer is the third option
Step-by-step explanation:
A ride-share company has a fee that includes a fixed cost and a cost that depends on both the time spent travelling, in minutes, and the distance travelled, in kilometres. The fixed cost of a ride is $2.55 Judy's ride costs $16.75 and took eight minutes. The distance travelled was 10 km. Pat's ride cost $30.35 and took 20 minutes. The distance travelled was 18 km. Roy's ride took 10 minutes. The distance travelled was 15 km. Find the cost of Roy's ride.
Answer:
the cost of Roy's ride is $23.05
Step-by-step explanation:
According to the Question,
Let, Cost of per minute charge is 'x' & Cost Of Per Kilometre charge is y .
Given, A ride-share company has a fee of the fixed cost of a ride is $2.55 .And, The Total cost of the Ride depends on both the time spent on travelling(in minutes), and the distance travelled(in kilometres) .⇒ Judy's ride costs $16.75 . but the actual cost after deducting the fixed charge is 16.75-2.55 = $14.20, took 8 minutes & The distance travelled was 10 km. Thus, the equation for the journey is 8x+10y=14.20 ⇒ Equ. 1
⇒ Pat's ride costs $30.35 . but the actual cost after deducting the fixed charge is 30.35-2.55 = $27.80, took 20 minutes & The distance travelled was 18 km. Thus, the equation for the journey is 20x+18y=27.80 ⇒ Equ. 2
Now, on Solving Equation 1 & 2, We get
x=0.4(Cost of per minute charge) & y=1.1(Cost Of Per Kilometre charge)
Now, Roy's ride took 10 minutes & The distance travelled was 15 km . Thus, the cost of Roy's Ride is 10x+15y ⇔ 10×0.4 + 15×1.1 ⇔ $20.5
Hence, the total cost of Roy's ride is 20.5 + 2.55(fixed cost) = $23.05
Multiply the polynomials.
(8x2 + 6x + 8)(6x-5)
A. 48x3 - 4x2 + 18x + 40
B. 48x3 - 76x2 + 18% - 40
C. 48x3 - 4x2 + 78x - 40
D. 48x3 - 4x2 + 18x- 40
18⅔ ÷ ⅔
how many children are there?
Solve for x. Round to one decimal place.
I keep messing this one up and im timed
Answer:
x ≈ 16.5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 70°
Opposite Leg = x
Adjacent Leg = 6
Step 2: Solve for x
Substitute in variables [tangent]: tan70° = x/6[Multiplication Property of Equality] Multiply 6 on both sides: 6tan70° = xRewrite: x = 6tan70°Evaluate: x = 16.4849Round: x ≈ 16.5Find the product.
-1/2 y(2y^3-8)
Answer:
Its the last one
Step-by-step explanation:
-1/2 y(2y^3+8) is
-1 y^4 + 4 y
What is the domain of this function?
O {x|x>0}
O {xlx<8}
O {x|0 < x <8)
O {xlx<0x 8)
Given:
Consider the below figure attached with this question.
To find:
The domain of the graphed function.
Solution:
Domain is the set of input values or x-values.
From the given graph it is clear that the function has one end point at (0,9) and an arrow at (8,1). It means it is not a line because it is a ray that moves further from point (8,1) in the downward direction.
The minimum value of x is 0 and their is no maximum value of x because graph of the function is a ray. So, the domain of the given function is:
[tex]\text{Domain}=\{x|x\geq 0\}[/tex]
Therefore, the correct option is A.
Find the difference of the numbers. Express your answer in scientific notation.
(9.84 x 100)-(7.99x109)
1.85 x 10^9
9.041x 10^
1.85 x 10^10
9.041x 10^10
Answer:
D: 9.041 × 10^(10)
Step-by-step explanation:
The correct expression is;
(9.84 × 10^(10)) - (7.99 × 10^(9))
To subtract this, we need to ensure that both terms have the same powers.
Thus, (7.99 × 10^(9)) = (0.799 × 10^(10))
Lets now solve;
>> (9.84 × 10^(10)) - (0.799 × 10^(10))
Collecting like terms we have;
(9.84 - 0.799) × 10^(10)
>> 9.041 × 10^(10)
I kinda need help
What is the fraction 1/4 in decimal form?
I need help with this one to
Solve 3^3
Answer: easy
Step-by-step explanation: 0.25 there
What is the value of y ?
Answer:
67
Step-by-step explanation:
Answer.
67°
Step-by-step explanation:
the two lines are parallel so,
angle on line XY 67° is alternate angle on BD so, angle will be opposite angle y.
therefore, angle y= 67°
i got help from an awesome app called Gauthmath you can check it out on play store and app store. in my opinion avery good app with tutors and concept videos.
Write down in terms of n, an expression for the nth term
of the following sequences:
a) 4 1 -2 -5 -8
b) -7 -12 -17 -22 -27
ASAP!!!!!! Factor the trinomial x^2 + 7x + 12
What is a name for the marked angle?
Picture given
Answer:
L DAC
Step-by-step explanation:
__________________
Help ASAP please!!!!!!!!!
Answer:
1/4
Step-by-step explanation:
pitches >3
pitches=4,5
P=(15+10)/(15+20+40+15+10)=1/4
MATH HELP PLEASE DUE SOON
Answer:
a. Alternate exterior angles.
b. <A and <B are congruent. This diagram involves a line intersecting two parallel lines, forming the congruent angles <A and <B on opposite sides of the transversal.
c. They are alternate exterior angles like <A and <B, but because it is not guaranteed that the transversal is intersecting parallel lines in this case, we cannot prove that <C and <D are congruent alternate exterior angles.
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction
The number b varies directly with the number a. For example b= 2 when a = -2
-2. Which equation represents this
direct variation between a and b?
Obra
O b = a
Ob-a= 0
Ob(-a) = 0
Answer:
b = -a
Step-by-step explanation:
We know that:
On a number line, the distance between 0 and b is the same distance that between 0 and a (but b and a are in opposite sides of zero).
And we know that, for example, when:
b = 2, a = -2
Remember that the distance between two values is given by:
|n - m|
Then the distance between 0 and b is:
|0 - b|
and the distance between 0 and a is:
|0 - a|
we have:
|-b| = |-a|
|b| = |a|
But the numbers are in opposite sides of the zero, so one must be positive and the other negative, then we can conclude that:
b = -a
or
-b = a
(these are equivalent)
Then the correct option is the first option:
b = -a
add the following decimals
Answer:
148.91
Step-by-step explanation:
hope it helps<333
Edmund and Lucy go to a toy shop. Edmund does not have enough money to buy the toy he wants. He says to Lucy, 'If you give me ₹ 40, I can buy my toy. But you will have ₹ 10 less to buy your toy." How much money does Lucy have?
Answer and explanation:
Assuming Edmund has $0
From Edmund, we know the toy costs $40(assuming it's in dollars)
Lucy gives him $40 and has $10 less($40-$10) to buy her own toy
Therefore Lucy had $40+$30= $70 before giving Edmund $40 for his toy.
Lucy currently has $70-$40 =$30, therefore needs $10 more to buy her own toy
The difference between the interest for first and second year on a sum of money compounded annually is rs 30 if the rate of interest is 5% what was the sum of money deposited
Answer:
$600.00
Step-by-step explanation:
The difference between the interest for first and second year on a sum of money compounded annually is rs 30 if the rate of interest is 5% what was the sum of money deposited
We solve using Compound Interest formula which is given as:
First, convert R as a percent to r as a decimal
r = R/100
r = 5/100
r = 0.05 per year,
Then, solve the equation for P
P = I / ((1 + r/n)^nt - 1)
P = 30 / ((1 + 0.05/1)^(1×1) - 1)
P = 30 / ((1 + 0.05)^(1) - 1)
P = $600.00
Why did the framers of the Constitution include the concept of limited government?
to promote business
to help the legislative branch
to help the judicial branch
to prevent tyranny
Answer:
to prevent tyranny
Step-by-step explanation:
the government was weak so the founding fathers decided to write it.