Mathematics High School

Rewrite the following alebraic expression using the distributive property.
-2a(a+b-5) + b(6a+b-8)

Answers

Answer 1
Apply the distributive property.xx+x⋅−2=8xx+x⋅-2=8Use the power rule aman=am+naman=am+n to combine exponents.x1+1+x⋅−2=8x1+1+x⋅-2=8Add 11 and 11 to get 22.x2+x⋅−2=8x2+x⋅-2=8Move −2-2 to the left of the expression x⋅−2x⋅-2.x2−2⋅x=8x2-2⋅x=8Multiply −2-2 by xx to get −2x-2x.x2−2x=8x2-2x=8Move 88 to the left side of the equation by subtracting it from both sides.x2−2x−8=0x2-2x-8=0Use the quadratic formula to find the solutions.−b±√b2−4(ac)2a-b±b2-4ac2aSubstitute the values a=1a=1, b=−2b=-2, and c=−8c=-8 into the quadratic formula and solve for xx.2±√(−2)2−4⋅(1⋅−8)2⋅12±-22-4⋅1⋅-82⋅1Simplify.Tap for fewer steps...Simplify the numerator.Tap for fewer steps...Raise −2-2 to the power of 22 to get 44.x=2±√4−4⋅(1⋅−8)2⋅1x=2±4-4⋅1⋅-82⋅1Multiply −8-8 by 11 to get −8-8.x=2±√4−4⋅−82⋅1x=2±4-4⋅-82⋅1Multiply −4-4 by −8-8 to get 3232.x=2±√4+322⋅1x=2±4+322⋅1Add 44 and 3232 to get 3636.x=2±√362⋅1x=2±362⋅1Rewrite 3636 as 6262.x=2±√622⋅1x=2±622⋅1Pull terms out from under the radical, assuming positive real numbers.x=2±62⋅1x=2±62⋅1Multiply 22 by 11 to get 22.x=2±62x=2±62Simplify 2±622±62.x=1±3x=1±3The final answer is the combination of both solutions.x=4,−2                   hope iam some help

Related Questions

Select the equation that most accurately depicts the word problem.

The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches.

68 = 9L + 2
68 = 2L + 2(9)
68 = 9(L + 2)
68 = + 2(9)
68 = +
68 = 2(L - 9)

Answers

68 = 2L + 2(9)

hope that helps, God bless!

Answer:

68 = 2L + 2(9)

Step-by-step explanation:

Find the derivative of f(x) = 7 divided by x at x = 1.

Answers

I find it best to switch everything exponents when taking derivatives.
F(x) = 7/x
Same as..
F(x) = 7x^-1
Take derivative..
F'(x) = -7x^-2
Plug in x = 1
F'(1) = -7(1)^-2
F'(1) = -7

The solution is, the derivative of f(x) = 7 divided by x at x = 1 is -7.

What is derivative?

A derivative is described as either the rate of change of a function, or the slope of the tangent line at a particular point on a function.

here, we have,

given that,

the derivative of f(x) = 7 divided by x at x = 1.

so, we get,

F(x) = 7/x

Same as..

F(x) = 7x^-1

we know that,

d/dx (x^n) = n*x^n-1

so, using this, we get,

Take derivative..

F'(x) = -7x^-2

Plug in x = 1

F'(1) = -7(1)^-2

F'(1) = -7

Hence, The solution is, the derivative of f(x) = 7 divided by x at x = 1 is -7.

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A car traveled 360 km in 6 h. A train traveled 400 km in 8 h. A boat traveled 375 km in 5 h. Which has the fastest average speed

Answers

First, it is important to know that speed is equal to distance divided by time. I took a picture of my work. Let me know if you still have questions or cannot read something I've written. Thank you!

The most Kilometers traveled per one hour was traveled by THE BOAT at 75 Km/h. Therefore, the boat had the fastestaverage speed.

Mari has a part time job. She earns $7 an hour. She makes at most $143.50 a week. What is the greatest number of hours that she works?

Answers

If Mary earns 7$ an hour, we need to multiplicate 7$ by the number of hours worked for the entire week so we can get the salary per week. And when we want to know how many hours she had worked, we have to "transform" the equation : Salary per week = salary per hours x worked hours Here, we know to informations : salary per hours and salary per week. Worked hours = salary per week / salary per day Worked hours = 143.50 / 7 Worked hours = 20.5 The greatest number of hours thats he works is 20h30.
Final answer:

Mari works at most 20 hours per week.

Explanation:

To find the greatest number of hours that Mari works, we can divide her total weekly earnings by her hourly wage. In this case, we divide $143.50 by $7. The result is approximately 20.5. Since Mari cannot work a fraction of an hour, we round down to the nearest whole number. Therefore, the greatest number of hours she works is 20 hours.

A stock market analyst observes the following for the price of two stocks that he owns, one of which is increasing at an exponential rate (geometric) and the other is increasing in a linear fashion (arithmetic).

Stock A: Equation: an = 15n + 130, where an is the value of the stock and n is the number of years.


Year Price
1 $145.00
2 $160.00
3 $175.00
4 $190.00
5 $205.00


Stock B: Equation: an = 36(1.09)n − 1, where an is the value of the stock and n is the number of years.

Year Price
1 $36.00
2 $39.24
3 $42.77
4 $46.61
5 $50.82


Assuming these stock values continue to increase in the same manner until retirement, which stock option is worth more in 50 years and how much more is this stock worth per share?


OPTIONS:
A) Stock B is worth more in 50 years, $1,575.84 more per share
B) Stock A is worth more in 50 years, $1,364.08 more per share
C) Stock B is worth more in 50 years, $1,796.87 more per share
D) Stock A is worth more in 50 years, $880.00 more per share

Answers

in 50 years  stock A realises 15*50 + 130  = $880

in 50 yeras stock B  gives  50(1.09)^50 = $2676.87

2676.87 - 880 = $ 1796.87 / share

Its C
Final answer:

Stock B is worth more in 50 years, $1,575.84 more per share.

Explanation:

To determine which stock option is worth more in 50 years, we need to find the value of each stock after 50 years.

For Stock A, we have the equation: an = 15n + 130. Plugging in n = 50, we get a50 = 15(50) + 130 = $880.

For Stock B, we have the equation: an = 36(1.09)n - 1, where n is the number of years. Plugging in n = 50, we get a50 = 36(1.09)^50 - 1 = $2,455.84.

Therefore, Stock B is worth more in 50 years, $1,575.84 more per share.

Rolando had $120,000 in a CD at Big Bucks Bank, which just failed. If the FDIC insurance limit per depositor, per bank, is $250,000, how much will Rolando get back?

Answers

I think Rolando would get back 120,000. Because the insurance limit is 250k, Rolando only put in 120k, so he should get everything back.

the answer will be 120,000


Write an equivalent expression for 5x + 2y + 3x

Answers

Well, if you combine like terms that version of this equation would be equivalent. 
5x + 2y + 3x = 8x + 2y

I'm not sure if this is the answer you're looking for but, I hope this helps!

The equivalent expression is 8x + 2y.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

5x + 2y + 3x

Add like terms.

8x + 2y

Thus,

The final expression is 8x + 2y.

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Given that 56 square equals 3,136 find the square of112

Answers

112  = 56 x 2 

so  56 square = 3136

112 squared = 56 squared x 2 squared = 3136 x 4 =12544

The length of a rectangle is 10 feet more than the width. if the perimeter of the rectangle is 180 feet, find the length and the width of the rectangle

Answers

The length would be 50 ft and the width would be 40 ft.

What geometric term does the flight path of a plane on radar represent?

A line     B plane       C angle           D point

Answers

the answer is A. Line

The Geometric Term that best approximates this reality is option A (A line).

Planes usually travel in a straight Line at constant Speed, Flight Path represents the Trajectory taken by the Plane and shown on radar, which can be either a Line or a Curve.

Hence, the Geometric Term that best approximates this reality is option A (A line).

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The petting zoo is not closed and the animals are not being fed by people.

write the statement that is logically equivalent to the statement

Answers

De Morgan's laws of distributing negation over disjunction and conjunction states that

1.) ¬ ( a ∨ b ) ≡ ( ¬ a ∧ ¬ b )
2.) ¬ ( a ∧ b ) ≡ ( ¬ a ∨ ¬ b )

Thus, given the statement "The petting zoo is not closed and the animals are not being fed by people."

The statement is the conjunction of the negation of the statement "The petting zoo is closed" and the negation of the statement "The animals are being fed by people".

Using the first of De Morgan's laws above, we have that the equivalence of the statement given above is: "It is not the case that the petting coo is closed or the animals are being fed by people".

k + k divided by 2 when k = 20

Answers

The answer would be 20 because 20 plus 20 equals 40, and 40 divided by 2 equals 20! Hope this helped!

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

1. 7, 1+i
2.

Answers

Final answer:

The polynomial function of least degree with rational coefficients, a leading coefficient of 1, and the given zeros 7, 1 + i, and 1 - i is f(x) = x^3 - 9x^2 + 21x - 14.

Explanation:

In mathematics, zeros are the x-values where a function touches or crosses the x-axis, or the values where f(x) = 0. When a polynomial has rational coefficients and you have a complex zero (a + bi), the conjugate of that zero (a - bi) also needs to be a zero of the polynomial. This is based on the Complex Conjugate Root Theorem. Hence, in this case, the other zero will be 1 - i.

Since you are given zeroes of 7, 1 + i, and 1 - i, the polynomial function of least degree is obtained by employing the Factor Theorem, which states that if k is a zero of a polynomial, then (x - k) is a factor of the polynomial.

Therefore, f(x) = (x - 7)(x - (1 + i))(x - (1 - i)) = (x - 7)(x^2 - 2x + 2). So, f(x) = x^3 - 9x^2 + 21x - 14 is the polynomial function of least degree with rational coefficients, a leading coefficient of 1, and the given zeros.

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Jean has $20 and is going shopping to buy 3 scarves and as many pairs of earrings as possible. How many pairs of earrings can she buy if scarves cost $2.55 each and earrings cost $2.99 a pair? Jean can buy at least 4 pairs of earrings. Jean can buy more than 4 pairs of earrings. Jean can buy less than 4 pairs of earrings. Jean can buy at most 4 pairs of earrings.

Answers

If scarves cost $2.55 each, and she is buying three: 2.55(3)= $7.65
20 - 7.65= $12. 35
you have $12.35 left to buy earrings 
12.35 / 2.99= 4, Jean can only buy 4 pairs of earrings

What is the circumference of the circle shown below, given that the length of ED (the minor Arc) is 6?

Answers

45' x 8 = 360

To find DE = 6 x 8 =48.
The answer is 48 because you can fit 8 45 degrees angle in the circle and since there are 8 sides, multiply the 6 with the 8 which equals to the answer

fine the distance between 8 and 32

Answers

Let d = distance between the two given numbers.

d = 32 - 8

d = 24

The difference is 24.
Do 32 minus 8
The answer is 24

3(6/8−1/2)+0.25 Please help with fractions

Answers

Parenthesis first. 6/8 - 1/2 = 1/4 or 0.25

Now we do 1/4 * 3 = 3/4 or 0.75

Finally, we do 3/4 + 0.25 [1/2] = 5/4 or 1.

Hope this helps! ☺♥
Hey Bryce!

[tex]3( \frac{6}{8} - \frac{1}{2}) + 0.25[/tex]
[tex]3( \frac{3}{4} - \frac{1}{2}) + 0.25[/tex]
[tex]3( \frac{1}{4}) + 0.25 [/tex]
[tex] \frac{3}{4} + 0.25 = 1 [/tex]


Good luck!

A squirrel is traveling at a rate of 12 miles per hour. Write the rate in miles per minute.

Answers

1 hour = 60 minutes

12/60 = 0.2 miles per minute

What is the perimeter of a polygon with vertices at (−2, 1) , ​ (−2, 4) ​, (2, 7) , ​ (6, 4) ​, and (6, 1) ​?

Enter your answer in the box. Do not round any side lengths.​

____ units

Answers

First we need the distances of the sides of the polygon, because perimeter = sum of all sides.
[tex]d = \sqrt{{(y2 - y1)}^{2} + {(x2 - x1)}^{2} } [/tex]
[tex]d1 = \sqrt{{(1 - 4)}^{2} + {( - 2 - - 2)}^{2} } \\ = \sqrt{{(- 3)}^{2} + {(0)}^{2} } = \sqrt{9} \: = 3[/tex]
[tex]d2 = \sqrt{{(4 - 7)}^{2} + {( - 2 - 2)}^{2} } \\ = \sqrt{{(- 3)}^{2} + {( -4)}^{2} } = \sqrt{9 + 16} \\ = \sqrt{25} \: = 5[/tex]
[tex]d3 \: = \sqrt{{(7 - 4)}^{2} + {(2 - 6)}^{2} } \\ = \sqrt{{(3)}^{2} + {( - 4)}^{2} } = \sqrt{9 + 16} \\ = \sqrt{25} \: = 5[/tex]
[tex]d4 = \sqrt{{(4 - 1)}^{2} + {(6 - 6)}^{2} } \\ = \sqrt{ {(3)}^{2} + {(0)}^{2} } = \sqrt{9} \: = 3[/tex]
[tex]d5 = \sqrt{{(1 - 1)}^{2} + {(-2 - 6)}^{2} } \\ = \sqrt{ {(0)}^{2} + {( - 4)}^{2}} = \sqrt{16} \: = 4 [/tex]
Now, we add all sides for the perimeter:
p = d1 + d2 + d3 + d4 + d5
p = 3+5+5+3+4 = 20 units





The other answer was using the formula correctly through most of the problem, but made a mistake when finding the last distance (#5). The person took away (-2-6 = - 4), which is incorrect. The correct answer is -8 because your adding two negatives. So, the correct answer for the whole problem is 24 units.

Good job to the person who answer they did the whole math problem - just made a little mistake at the end.

Eric is hanging a rectangle mirror that has a diagonal of 47 inches with an angle of depression of 60°. How many square inches is the mirror?

Answers

check the picture below.

make sure your calculator is in Degree mode.

the mirror is x*y square inches.

Answer:

A) 956.5 in^2

Step-by-step explanation:

took the test

Which equation exemplifies the Associative property of addition?

8+2=2+8

4+(2+1) = (4+2)+1

4+5=1+8

9(5•6)=(9•5)6

Answers

1) C(2
2) A(-4
3) B(4+(2+1)=4+2)+1
4) D(3(2x4)=(3x2)4
5) A(5+6=6+5
6) C(12x1=1x12
7) D(Exponents
8) A(addition and subtraction
9) A(55
10) B(19

Answer:

Equation which exemplifies the associative property of addition is:

4+(2+1) = (4+2)+1

Step-by-step explanation:

The associative property of addition says that:

if a,b and c are the three terms

Then,

a+(b+c)=(a+b)+c

which is given in the equation:

4+(2+1) = (4+2)+1

Hence, equation which exemplifies the associative property of addition is:

4+(2+1) = (4+2)+1

Bob runs 5 miles in 38 minutes. at the same rate, how many miles would he run in 57 minutes?

Answers

Sent a picture of the solution to the problem (s).

A survey at your school found that 792 in 1,220 students have a cell phone. what percent of the students in school has a cell phone? round to the nearest hundredth where necessary.

Answers

792/1220=0.6491...
=0.65
0.65x100=65
So 65% of the students in the school has a cell phone.

64.84% of the students in the school have a cell phone.

To find the percentage of students with cell phones, divide the number of students with cell phones by the total number of students, then multiply by 100.

Find the fraction of students with cell phones: [tex]\( \frac{792}{1220} \)[/tex].

Divide to get the decimal: [tex]\( \frac{792}{1220} = 0.6484 \)[/tex].

Multiply by 100 to get the percentage: [tex]\( 0.6484 \times 100 = 64.84\% \)[/tex].

Which is a correct expansion of (2x+3)(2x^2-5)
A. 2x•2x^2+2x•(-5)+3•2x+3•(-5)
B. 2x•2x^2+2x•(-5)+3•2x^2+3•(-5)
C. 2x•2x^2+3•2x^2+2x^2•(-5)+3•(-5)

Answers

Use distributive property.

2x * 2x^2
2x * -5
3 * 2x^2
3 * -5

2x * 2x^2 + 2x * -5 + 3 * 2x^2 + 3 * -5
Hope this helps!

Answer: B

2X.2X^2+2X.(-5)+3.2X^2+3.(-5)

Step-by-step explanation:

(2X+3) (2X^2-5)

Cross multiply (2X+3) by (2X^2-5)

2X*2X^2+

2X*(-5)+

3*2X^2+

3*(-5)

= 2X*2X^2+2X*(-5)+3*2X^2+3*(-5)

Given the statement "If Jack’s pet is a pig, then Jack’s pet cannot fly,” which statement represents the converse?

q → p, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly~q → ~p, where p = Jack’s pet cannot fly and q = Jack’s pet is a pig p → q, where p = Jack’s pet is a pig and q = Jack’s pet cannot flyq → p, where p = Jack’s pet is not a pig and q = Jack’s pet is a pig

Answers

the answer is A just had the practice quiz

Converse statement of "If Jack’s pet is a pig, then Jack’s pet cannot fly,” is given by " q → p, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly."

What is converse statement?

" Converse statement is defined as when the hypothesis and conclusion of a statement interchange or reversed."

According to the question,

Given,

p → q

Hypothesis of a statement 'p': If Jack’s pet is a pig

Conclusion of a statement 'q' : then Jack’s pet cannot fly

Converse of a statement is given by reversing hypothesis and conclusion we get,

q → p

Hypothesis of a statement 'q' : If Jack’s pet cannot fly

Conclusion of a statement  'p': then Jack’s pet is a pig

Hence, converse statement is given by  q → p, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly.

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How is 10 ounces written using apothecary abbreviations?

Answers

Apothecary abbreviations or apothecary symbols are usually found in medical recipes. For this case, we are to write 10 ounces into apothecary symbols. In this abbreviation, numbers are written in Roman Numeral and the unit precede the number, hence:

oz x

Final answer:

10 ounces can be written as 10 oz in apothecary abbreviations.

Explanation:

To write 10 ounces using apothecary abbreviations, we need to convert ounces to the appropriate apothecary unit. In the apothecary system, 1 ounce is abbreviated as oz. So, 10 ounces would be written as 10 oz in apothecary abbreviations.

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The measure of each interior angle of a regular polygon is eleven times that of an exterior angle how many sides does the polygon have

Answers

let there be x sides.
180(x-2)/x=11*360/x
   180(x-2)=11*360
            x-2=11*2
            x-2=22
                x=24

the polygon has 24 sides.

The polygon would have 24 sides.

[tex]\frac{180n -  360}{n}[/tex] ≈ [tex]\frac{360}{n}[/tex] ([tex]\frac{11}{1}[/tex])

[tex]\frac{180n -  360}{n}[/tex] = [tex]\frac{3960}{n}[/tex]

180n - 360 = 3,960

180n = 4,320

n = 24

The lengths of the sides of a triangle are 8, 15, and 17. if the longest side of a similar triangle is 51, what is the length of the shortest side?

Answers

If the longest side on the similar triangle is 51 and the longest side of the first triangle is 17, then you divide 51 and 17.

51 / 17 = 3

So the similar triangle is 3 times as big.
To find the shortest side of the similar triangle, you multiply 8 and 3.

8 * 3 = 24

The length of the shortest side of the similar triangle is 24.

Hope this helps!

he length of the shortest side is 32

Similar triangles and scale factors

Given the length if the sides of the triangle to be 8, 15 and 17. If the longest side of a similar triangle is 51, then the scale factor will be expressed as:

Scale factor  = 51/17

Scale factor = 4

For the shortest side;

Length  = 8 * scale factor

Length  = 8 * 4

Length = 32

Hence the length of the shortest side is 32

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How to find third point between two points given coordinates?

Answers

Using the midpoint formula, you can find the third point in between 2 given points. 

Put in values into the equation; (x₁+x₂)/2, (y₁+y₂)/2 

This equation will give you the coordinates for the point in the middle (x, y). 

Hope I helped :) 

at a local pizza parlor, patrons have 2 choices of cheese and 14 choices of topping. in how many different ways can a patron choose 1 type of cheese and 1 type of topping?

30

28

16

2

Answers

the answer would be 28
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