Your identity says ...
... sum of cubes = (sum)³ -3(product)(sum)
... = 4³ -3·1·4
... = 64 -12 = 52
_____
The two numbers are 2±√3, and the sum of their cubes is indeed 52.
A particular style of sunglasses costs the retailer $70 $70 per pair. At what price should the retailer mark them so he can sell them at a 10% 10% discount off the original price and still make 35% 35% profit on his cost?
After the 10% discount on marked price (P), the selling price is ...
... P×(100% -10%) = 0.90P
After a markup off 35% on cost, the value is
... $70×(100% +35%) = 1.35×$70 = $94.50
The retailer wants these two values to be equal:
... 0.90P = $94.50
... P = $94.50/0.90 = $105.00 . . . . . divide by the coefficient of P
The marked price should be $105.00.
To make a 35% profit on the cost, the retailer should mark the sunglasses at a price of $85.05.
Explanation:To determine the price at which the retailer should mark the sunglasses, we need to calculate the original price and then apply the discount. First, let's find the 35% profit on the cost, which is $70. 35% of $70 is 0.35 * 70 = $24.50.
To make a profit of $24.50, the original price should be $70 + $24.50 = $94.50. To sell the sunglasses at a 10% discount, the marked price will be 90% of $94.50. 90% of $94.50 is 0.90 * 94.50 = $85.05.
Therefore, the retailer should mark the sunglasses at a price of $85.05.
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Simplify -52 + 8|-1| + (-3).
A. 30
B. 14
C.-20
D. -36
Please help!
Answer:
C. -20
Step by step explanation:
It appears you want the value of the expression -5² +8|-1| +(-3).
Order of operationsThe order of operations tells us that the first step is to evaluate expressions in parentheses. Here, the absolute value symbols effectively serve as parentheses, so we start there.
|-1| signifies the absolute value of -1, its magnitude, or positive value. That simplifies to 1. So, your expression is ...
-5² +8·1 -3
The next step is to evaluate the term with an exponent: -5² = -(5·5) = -25.
= -25 +8·1 -3
Now, we perform the multiplication:
= -25 +8 -3
And finally, the addition/subtraction
= -17 -3
= -20
__
Additional comment
The expression you show in the problem statement looks like the first term is negative fifty-two. That is very different from negative five squared. An exponent is indicated using a caret (^), as -5^2, or using a superscript font, as -5². Please be careful to use appropriate math symbols where exponents are involved.
Q # 14 please . .Write the slope-intercept of the equation for the line
You can see that this line passe through the points (-4,-2) and (4,3).
The slope of the line passing through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]
Thus, the slope is
[tex]\dfrac{3-(-2)}{4-(-4)}=\dfrac{5}{8}.[/tex]
Then the equation of the line is
[tex]y-3=\dfrac{5}{8}(x-4),\\\\y=\dfrac{5}{8}x+\dfrac{1}{2}.[/tex]
Answer: correct choice is C.
P = 215 (1.005)t/3 the equation above can be used to model the population, in thousands, of a certain city t years after 2000. according to the model, the population is predicted to increase by 0.5% every n months. what is the value of n
As t/3 it means that 0.5% every 3 years.
So n will be 3 years , 36 months
Solution:
The Given model to Predict the population
[tex]P=P_{0}(1.005)^{\frac{t}{3}[/tex]
----------------------------------(1)
The population increases by 0.5 % every n months.
Initial Population = 215
Final Population
[tex]=215+215\times \frac{0.5}{100}\\\\=215+1.075\\\\=216.075[/tex]
Substituting the value of , Initial and final Population in equation 1,
[tex]216.075=215\times (1.005)^{\frac{t}{3}}\\\\ (1.005)^{\frac{t}{3}}=\frac{216.075}{215}\\\\ (1.005)^{\frac{t}{3}}=(1.005)^{1}\\\\ \frac{t}{3}=1\\\\ t=3[/tex]
t=3 years =36 months
The value of n is equal to 36 months.
Suppose the exponential regression equation for some data is y=1.923*3.772^x. When x equals 5, what is the predicted value of y? Round your anser to the nearest whole number. A. 147 B. 99 C. 992 D/ 1468
Put 5 where x is in the equation and do the arithmetic.
y = 1.923×3.772⁵ ≈ 1468.377444
The most appropriate answer is ...
... D. 1468
Answer:
the value of y when x= 5 is 1468
Step-by-step explanation:
Suppose the exponential regression equation for some data is given by y=1.923*3.772^x
We need to find out the value of y when x= 5
Plug in 5 for x and find out y
y=1.923*3.772^x
y=1.923*3.772^5=1468.37744
So the value of y when x= 5 is 1468
1000m divided by 100n can be written in the form 10z. Express z in terms of m and n
Answer:
[tex]10 ^ {3m-2n} = 10 ^ z[/tex]
Where z = 3m-2n
Step-by-step explanation:
An important mathematical property about the powers is that when powers of equal base are divided, the same base is placed and the exponents are subtracted.
Then we can write 1000m and 100n as powers of the same base:
[tex]1000 ^ m = (10 ^ 3) ^ m = 10 ^ {3m}\\ 100 ^ n = (10 ^ 2) ^ n = 10 ^ {2n}[/tex]
Now we perform the division of powers of the same base (10)
[tex]\frac{10 ^ {3m}}{10 ^ {2n}} = 10 ^ {3m-2n}[/tex]
Finally
[tex]10 ^ {3m-2n} = 10 ^ z[/tex]
Where z = 3m-2n
To express z in terms of m and n, rewrite the equation: 1000m / 100n = 10z. Then, simplify to 100m / 10n = z. So, z can be expressed as 10m/n.
Explanation:The given equation is 1000m divided by 100n equals to 10z. To express z in terms of m and n, we need to isolate z. Let's proceed step by step:
First, rewrite the equation: 1000m / 100n = 10z;Then, eliminate the 10 on the right side by dividing both sides by 10, we get: 100m / 10n = z; Then, simplify the left side, we get: 10m/n = z;So, z can be expressed as 10m/n.
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Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contraction or neither.
A) 20-4x=12-x+8-3x
B) 5x+4x-3+24+8x
C) 5x +6+2x+6+3x-15
Confusing please help
These are three equations and three answers.
Answers:
A) infinite solutions, identityB) one solution, x = 27, neither contradiction nor identiyC) x = no solutions, contradictionExplanation:
Equation A: 20 - 4x = 12 - x + 8 - 3x
The objective is clearing the unknown, which is to isolate it in one side of the equation.
These are the steps and properties that you need to use:
1. Combine like terms on right side:
20 - 4x = 20 - 4x
2. Use addition property of equality (add 4x on each side).
20 = 20 ↔ identity
Conclusion: you have gotten a condition that is always true, no matter the value of x, which means that the equation has infinite solutions and it is an identity.
Equation B: 5x + 4x - 3 = 24 + 8x (note that I placed the equal sign as it was missing)
1. Combine like terms on each side:
9x - 3 = 24 + 8x
2. Subtraction property and addition propertiy of equality (subtract 8x and add + 3 on both sides)
x = 27 ↔ solution (neither contradiction nor identity)
Conclusion: the solution is x = 27.
Equation C: 5x + 6 = 2x + 6 + 3x - 15 (note that I placed the equal signs as it was missing)
1. Comitne like terms on the right side:
5x + 6 = 5x - 9
2. Subtraction property of equality (subtract 5x from each side)
6 = - 9 ↔ contradiction
Conclusion: the equation does not have a solution since the final equality is always false (a condradiction or absurd).
For your information, when the variable (x) dissapears and fhe final equality is always true (for example 0 = 0, or 20 = 20), the equation is an identity.
A) 20-4x=12-x+8-3x
Bring all x values at one side and all numerical values to the other side of the equal sign and solve. Also, do not forget to change the sign when you change the side.
-4x + x + 3x = -20 + 12 + 8
-4x + 4x = -20 + 20
0 =0 No solution
B) 5x+4x-3+24+8x
this expression can only be simplified to 17x + 21 and not solved because there is no equal sign here
C) 5x +6+2x+6+3x-15
this expression can only be simplified to 10x - 3 and not solved because there is no equal sign here
Also, neither of these is an identity or contraction.
please answer this i dont understnad
Graph f(x)=12x+2.
Use the line tool and select two points to graph the line.
Answer:
(0,2) and (1,14)
Graph is attached.
Step-by-step explanation:
Let us find y intercept
When x=0, y = f(x) =2
Hence one point is (0,2)
Other point is let x = 1,
y =12(1)+2 =14
(1,14) (0,2) are plotted and joined.
Graph is attached.
Please Help ASAP 20 points
Find the slope of the line through the given points.
(−1, 2) and (−5,10)
(1,3) and (0,−9)
(18, 6) and (−7, 7)
(−7, 10 ) and (1, 10)
Which ordered pairs are solutions to the inequality −2x+y≥−4 ?
Select each correct answer.
(0, −5)
(3, −1)
(1, −2)
(0, 1)
(−1, 1)
Answer:
(0,-5) , (1,-2) , (0,1) and (-1,1)
Step-by-step explanation:
-2x + y ≥ -4
y ≥ 2x - 4
Taking a point (0,-5):
-5 ≥ 0 - 4 , 5 ≥ -4
This situation is true.
Taking a point (3,-1):
-1 ≥ 2(3) - 4 , -1 ≥ 2
This situation is not true.
Taking a situation (1,-2):
-2 ≥ 2(1) - 4 , -2 ≥ -2
This situation is true.
Taking a point (0,1):
1 ≥ 0 - 4 , 1 ≥ -4
This situation is true.
Taking a point (-1,1):
1 ≥ 2(-1) - 4 , 1 ≥ -6
This situation is true.
The correct answers are
(−1, −1)
(5, −12)
(0, 1)
Have a nice day!
Which expressions are polynomials? Select each correct answer. 30y^2 30y^2+x 30y2x 30y2+x12
To know which of the following expressions are polynomials, let us look at the definition of a polynomial:
Polynomial is derived from poly- (which means "many") and -nomial (meaning "term"), so it says "many terms".
For an instance: [tex]2x^2y+2y^2[/tex] is a polynomial, but [tex]4xy^2[/tex] is not a polynomial because it contains single term only.
We must keep in mind that in polynomial it can have variables, constants, and exponents but it can never have division by a variable.
Now lets, look at the
[tex]30y^2[/tex] since it has got one term it can not be a polynomial.
[tex]30y^2+x[/tex]: it has got more than one term therefore, it is a polynomial.
[tex]30y^2x[/tex]: again it has got just one term so it is not a polynomial.
[tex]30y^2+x^{12}[/tex]: Since it has got more than one term, so again it is a polynomial.
The correct polynomial expressions are 30y²+x and 30y². Option A and D is the correct answer.
Polynomials are expressions that consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and exponentiation.
30y²+x: This expression is a polynomial because it consists of a constant term (30), a variable term (y²) raised to a non-negative integer exponent, and an additional variable term (x).
30y²: This expression is a polynomial because it consists of a constant term (30) and a variable term (y²) raised to a non-negative integer exponent.
These expressions are considered polynomials because they consist of variables, constants, and non-negative integer exponents, and they involve the appropriate mathematical operations of addition and multiplication.
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The complete question is, "Which expressions are polynomials? Select each correct answer.
a. 30y²+x
b. 30y²+x (¹/²)
c. (30y²) ÷ x
d. 30y²"
What is the value of the expression (9+15) divided by 3 plus 2
Hey!
This question is super easy to me. This question is going to be used their order of operations.
Order of operations stands for
↓
P-Parenthesis
E-Exponents
M-Multiply
D-Divide
A-Add
S-Subtract
(9+15)/3+2
24/3+2
8+2
=10
Answer⇒⇒⇒⇒⇒=10
Hope this helps!
Thank you for posting your question at here on Brainly.
-Charlie
Answer:
10
Step-by-step explanation:
(9+15) ÷ 3 + 2 = 10
I just need help on learning how to do ten and eleven thank you!
How would the fraction 1/3+square root of 2 be rewritten if its denominator is rationalized using difference of squares? A. 3-square root of 2 B. 3-square root of 2/5 C. 3-square root of 2/7 D. - 3+square root of 2/7
C
given 1 /( 3 + √2 )
then rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator
the conjugate of 3 + √2 is 3 - √2
1 / (3 + √2 ) × (3 - √2 ) / (3 - √2 )
= (3 - √2 ) /( 9 - 2 ) = (3 - √2 ) / 7
The fraction [tex]\frac{1}{3+\sqrt{2}}[/tex] can be written as [tex]\frac{3-\sqrt 2}{7}[/tex]. Option C is correct.
What is a fraction simplification?Fraction simplification is a method of fraction reduction that entails making a fraction as simple as possible.
This is accomplished by dividing the numerator and denominator by the biggest integer that divides both integers exactly.
Given fraction;
[tex]\frac{1}{3+\sqrt{2}}[/tex]
Multiplying the numerator and denominator by the conjugate of the denominator will rationalize the denominator;
The conjugate of the denominator (3 + √2) is 3 - √2;
Apply the rationalization of fraction;
[tex]\frac{1}{3+\sqrt{2}} \\\ \frac{1}{3+\sqrt{2}} \times \frac{3-\sqrt2}{3-\sqrt 2} \\\\ \frac{3-\sqrt 2}{9-2} \\\\\ \frac{3-\sqrt 2}{7}[/tex]
Hence option C is correct.
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PLZ HELP ASAP GEOMETRY
Josh is building an enclosure with recycled cardboard for his collection of model cars. His design is as shown below:
What is the length of side BC in inches?
a. 14b. 42c. 49d. 63
Answer:
Option D [tex]BC=63\ in[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
In this problem
[tex]\frac{DC}{ML}=\frac{BC}{KL}[/tex]
substitute the given values and solve for BC
[tex]\frac{56}{8}=\frac{BC}{9}[/tex]
[tex]BC=56(9)/8\\BC=63\ in[/tex]
Quick!!! I need to do my homework
Solve: x - 1 < 3
x < 4
given x - 1 < 3 ( add 1 to both sides )
x < 4
or x ∈ ( - ∞, 4 ) ← in interval notation
Evaluate the following
|10| =
|-7| =
The absolute value of a number is that number with a positive sign.
|10| = 10
|-7| = 7
Choose the expressions that are perfect cubes.
–3
125a^6
8m^20
100w^24x^3
–64q^12
–c^30d^9f^18g^3
Answer:125a6
-64q12
-c^30d^9f^18g^3
Step-by-step explanation:
Got it right on edgy
Write the equation of the line parallel to the given line and passing through the given point.
y=2x−8 through (3,10)
Copy down y = 2x - 8. Note that any line parallel to this will have exactly the same form, although the constant (representing the y-intercept) may be different.
Knowing that this line passes through (3,10), all we have to do is find the value of the constant of this new, parallel line. Substitute 10 for y and 3 for x, obtaining 10 = 2(3) + b. Then 10-6 = b, or b = 4, and:
y =2x + 4 (answer). Again, note how the form of this new equation is exactly the same as the form of the given equation; only the constant (the y-intercept) is different.
Answer:
y=2x+4
Step-by-step explanation:
The equation we have is y=2x-8, so we subsitute the values and 8 is equal to b. After you substitue you solve it. b=4. So, the answer is y=2x+4
Hope this helped :) *also sorry if I spelled some words wrong*
Stephon has a square brick patio. He wants to reduce the width by 2 feet and increase the length by 2 feet.
Let x represent the length of one side of the square patio. Write expressions for the length and width of the new patio. Then find the area of the new patio if the original patio measures 10 feet by 10 feet.
A. lw = (x + 2)(x – 2); 96 square feet
B. lw = (x – 2)(x – 2); 64 square feet
C. lw = x(x – 2); 80 square feet
D. lw = (x + 2)(x + 2); 144 square feet
A
reducing one side by 2 is expressed as (x - 2) ← length
increasing the other side by 2 is expressed as (x + 2 ) ← width
the area of new patio = (10 - 2 )(10 + 2) 8 × 12 = 96 ft²
Answer: A. lw = (x + 2)(x – 2); 96 square feet
Step-by-step explanation:
Given: Stephon has a square brick patio. He wants to reduce the width by 2 feet and increase the length by 2 feet.
Let x be the side-length of the patio, then
The length of the patio after change = x+2
The width of the patio after change = x-2
Then the area of the patio is given by :-
[tex]A=lw\\\Rightarrow\ A=(x+2)(x-2)[/tex]
If the original patio measures 10 feet by 10 feet.
Then the area of the patio= [tex](10+2)(10-2)=(12)(8)=96[/tex] square feet.
Hence, A is the right answer.
72 ÷(11-3²) ÷ 3 but as a fraction
Let's evaluate the quantity within the parentheses. (11 - 3^2) becomes (2). Then we have:
(72 divided by 2) / 3, or 36/3, or 12.
How many subsets of 100 have exactly 99 elements?
How many subsets of 100 have exactly 98 elements?
How many subsets of 100 have exactly 2 elements?
The number of k-element subsets of a set of n elements is given by
... C(n, k) = n!/(k!(n-k)!)
a) C(100, 99) = 100!/(99!×1!) = 100
b) C(100, 98) = 100!/(98!×2!) = 100*99/2 = 4950
c) C(100, 2) = 100!/(2!×98!) = 4950 . . . . same as (b)
Keisha solved the following equation:
4x − 2x + 8 = 6(x + 4)
Step Work Justification
1 2x + 8 = 6(x + 4) Combine like terms
2 2x + 8 = 6x + 24 Associative property of multiplication
3 −4x + 8 = 24 Subtraction property of equality
4 −4x = 16 Addition property of equality
5 x = −4 Division property of equality
Which step has an incorrect justification?
Remark
Answer: The second one. The second step removes the brackets on the right. It uses the distributive property which puts back the common factor that was taken out of the two terms 6x and 24. Quite often the distributive property is useful when presenting a problem to be solved.
The associative property is more of an order thing and that is very useful sometimes as well what it says is that if you have three numbers a + b + c the order which you combine things does not matter.
For example 3 + 4 + 5 could be combined as 3 + 4 = 7; 7 + 5 = 12 or 3 + 5 = 8, 8 + 4 = 12.
The associative property is useful when adding fractions.
The weight of an object on the moon varies directly as its weight on earth. A person who weights 150.94lb on earth weighs 25.66lb on the moon. How much would a 218.24lb person weigh on the moon?
109.93 lbs
since the quantities vary directly, then
w(moon) = kw(earth ) ← ( k is the constant of variation )
to find k use the given condition
k = w( moon ) / w( earth ) = [tex]\frac{25.66}{150.94}[/tex]
given w(earth) = 218.24
w(moon) = [tex]\frac{25.66(218.24)}{150.94}[/tex] = 109.93
ILL GIVE MEDAL AND BRAINLIST AWNSER TO whoEVER IN THE FIRST!!!!Roland's heart beats 495 times in 6 minutes. At that rate, how many times would it beat in 20 minutes?
A.
9900
B.
2970
C.
1650
D.
615
Answer,
C. 1650
Explanation,
495/6 = 82.5
82.5 x 20 = 1650
Hope this helps :-)
Use the identity x^3+y^3+z^3−3xyz=(x+y+z)(x^2+y^2+z^2−x^y−y^z−z^x) to determine the value of the sum of three integers given:
the sum of their squares is 110,
the sum of their cubes is 684,
the product of the three integers is 210,
and the sum of any two products (xy+yz+zx) is 107.
Correctly written, your identity would tell you ...
... (sum of cubes) - 3·(product) = (sum of integers)·((sum of squares) - (sum of any two products))
Filling in the given numbers, you have ...
... 684 - 3·210 = (sum of integers)·(110 -107)
... 54 = (sum of integers)·3 . . . . . simplify
... sum of integers = 54/3 . . . . . . divide by the coefficient of the variable
... sum of integers = 18
_____
Integers 5, 6, and 7 meet these conditions.
Solve the problem using the previous balance method.
The account balance on April 1st is $60.15.
On April 15th a payment of $51.00 is made.
On April 25th a purchase of $91.27 is made.
What is the finance charge if the annual rate is 18%?
What is the new account balance?
Finance charge = $ ____
New balance = $ ____
Annual Percent Rate (APR) = 18%
Rate during the current billing cycle = 18/12 = 1.5%
Balance at the beginning of the billing cycle = 60.15
Payment 51.00
Balance 10.15
Purchase 91.27
Balance - 81.12
Finance Charge 60.15 * 0.015 = 0.90
New Balance - 82.02
maria is bringing her sick dog pedro in for a series of appointments at the veterinary clinic. Her total over the course of treatment with be $150 for tests and medidine plus $30 per appointment,a. the clinic offers Maria a 15% discount off her total cost. Write an equation to show her updated cost.
After the 15% discount, Maria pays 85% of the cost. That cost is the sum of the fixed cost and the variable (per visit) cost.
... (updated cost) = 0.85×($150 +$30×a)
... (updated cost) = 127.50 +25.50a . . . . in dollars
I need help with this one please help asap thank you