Mrs. Nelson asked students in her class to translate the statement “Remy lost some of the $14 his mom gave him” into an algebraic expression. Four students’ solutions are shown below. Alice: 14 minus x He had $14, then he lost (subtraction) an unknown amount (x). Bobby: x minus 14 He had an unknown amount of money (x) and he lost (subtraction) $14. Camila: 14 greater-than x He had $14 more than (>) the unknown amount (x) he lost. Daniel: 14 less-than x He had $14 less than (<) the unknown amount (x) he lost. Which student’s solution is correct? Alice Bobby Camila Daniel

Answer:

1) 10x⁵+38x⁴-23x³-101x²- 96x+50

-x+17

(7x²-x-29)=0

3x³ -13x²-4x + 67=0

3x³ -6x²-11x+19

5x²- 20x

Step-by-step explanation:

Spanish

Agregar los polinomios:

(4x + 9) + (5x - 8) (x2 - 4x + 7) + (2x2 + 6x - 8) (5x3 + 4x2 - 7x -8) + (2x3 - 3x2 + 4x - 3)

Primero multiplicaremos los polinomios con los corchetes

= 4x ​​+ 9 + (5x³- 20x² + 35x - 16x² + 32x-56) + (10x⁵ + 8x⁴- 14x³- 16x² + 30x⁴ + 24x³- 42x²- 48x- 40x³- 32x²- 56x + 64) + (2x³- 42x² + 4x -3)

Ahora simplificaremos dentro de los corchetes agregando primero los términos similares

= 4x ​​+ 9 + (5x³- 36x² + 67x-56) + (10x⁵ + 38x⁴- 30x³- 90x²-104x + 64) + (2x³- 42x² + 4x-3)

Ahora suma o resta todos los términos similares y distintos

= 10x⁵ + 38x⁴- 30x³ + 5x³ + 2x³- 90x²- 36x²- 42x² + 67x²-104x + 4x + 4x + 64 + 9-3

= 10x⁵ + 38x⁴-23x³-101x²- 96x + 50 Ans

Restando los polinomios

(4x + 9) - (5x - 8) = - x + 17

-5x +8 + 4x + 9 = -x + 17

-x + 17 = -x + 17

(x2 - 4x + 7) - (2x2 + 6x - 8) = -20x2-13x-72

x²-2x²-4x-6x + 7 + 8 = 20x2-13x-72

-x²-10x + 15-20x² + 13x + 72 = 0

-21x² + 3x + 87 = 0

-3 (7x²-x-29) = 0

(7x²-x-29) = 0

(5x3 + 4x2 - 7x -8) - (2x3 - 3x2 + 4x - 3) = 20x2 + 32x-45x-72

5x³-2x³ + 4x² + 3x²-7x-4x-8 + 3 = 20x2 -7x-72

3x³ + 7x²-11x-5-20x² + 7x + 72 = 0

3x³ -13x²-4x + 67 = 0

(7x3 - 10x2 - 11x + 9) - (4x3 - 4x2 - 10)

Los signos negativos cambian cuando restamos

= 3x³ -6x²-11x + 19

Ahora multiplicando

5x (x-4) = 5x²- 20x

English

Adding the polynomials :

(4x + 9) + (5x – 8) (x2 – 4x + 7) + (2x2 + 6x – 8) (5x3 + 4x2 – 7x -8) + (2x3 – 3x2 + 4x – 3)

First we will multiply the polynomials  with the brackets

= 4x+9 + ( 5x³- 20x²+ 35x - 16x²+ 32x-56) + (10x⁵ + 8x⁴- 14x³- 16x²+30x⁴+ 24x³- 42x²- 48x- 40x³- 32x²- 56x+ 64) + ( 2x³- 42x²+ 4x-3)

Now we will simplify within the brackets first adding the like terms

= 4x+9 + (5x³- 36x²+67x-56) + (10x⁵ +38x⁴- 30x³- 90x²-104x+64) + ( 2x³- 42x²+ 4x-3)

Now add or subtract all the like and unlike terms

= 10x⁵+38x⁴- 30x³+5x³+2x³- 90x²- 36x²- 42x²+67x²-104x+4x+4x+64+9-3

= 10x⁵+38x⁴-23x³-101x²- 96x+50  Ans

Subtracting the Polynomials

(4x + 9) - (5x – 8)=-x+17

-5x +8 +4x+9 = -x+17

-x+17=-x+17

(x2 – 4x + 7) - (2x2 + 6x – 8)= -20x2-13x-72

x²-2x²-4x-6x+7+8=20x2-13x-72

-x²-10x+ 15-20x²+13x+72=0

-21x²+3x+87=0

-3(7x²-x-29)=0

(7x²-x-29)=0

(5x3 + 4x2 – 7x -8) - (2x3 – 3x2 + 4x – 3)=  20x2 +32x-45x-72

5x³-2x³+4x²+3x²-7x-4x-8+3= 20x2 -7x-72

3x³+7x²-11x-5-20x²+7x+72=0

3x³ -13x²-4x + 67=0

(7x3 – 10x2 – 11x + 9) - (4x3 – 4x2 – 10)

The negative signs are changed when we subtract

= 3x³ -6x²-11x+19

Now Multiplying

5x(x-4) = 5x²- 20x

Answer: 3. Natural, whole, integer, rational, real

Answer:

Answer 3: Natural, whole, integer, rational, real

Step-by-step explanation:

Answer:

If an equal number of each brand was ordered, how many dozens of each brand were ordered?

Step-by-step explanation:

in order to determine the number of balls purchased, we must first determine the difference in price between them = $2 - $0.90 = $1.10

since the total difference in price was $660 and an equal number of balls were purchased, then the number of balls purchased = $660 / $1.10 = 600 balls

to determine the number of dozens purchased of each brand we just divide 600 by 12 = 50 dozens

Answer:

875 cm^3

Step-by-step explanation:

Here, we want to calculate the volume of the pyramid.

To do this, we need to calculate the area of the base and then multiply this by the height of the pyramid in question

Mathematically since the base is a square, formula for the base area would be ;

L^2 = 5^2 = 125 cm ^2

Now

using the height to get the volume , we have 125 * 7 = 875 cm^3

Answer:

58 1/3 cm³

Step-by-step explanation:

V = 5² * 7 / 3

V = 25 * 7 / 3

V = 58 cm³

Answer:

25

Step-by-step explanation:

Here is a picture of my work. I thought it would be too tedious to type it up. I hope this helps you!! Have a great rest of your day.

Answer:

92

Step-by-step explanation:

Given

Scores: 85, 78, 81

Required

Determine the least score in 4th subject is average must be at least 84

To solve this, we'll make use of Mean formula.

Mean = Sum of observations/Number of observations

We have that; Average = 84

Number of subjects = 4

Let the 4th subject be represented by F;

So, the sum of the four Subjects is:

Sum = 85 + 78 + 81 + F

Sum = 244 + F

Substitute these values in the above formula.

84 = ¼(244 + F)

Multiply both sides by 4

4 * 84 = 4 * ¼(244 + F)

336 = 244 + F

Subtract 244 from both sides

336 - 244 = 244 - 244 + F

92 = F

F = 92

To have an average of at least 84, Su's score must be atleast 92

Answer:

4.2 days

Step-by-step explanation:

Number of Weeks during which she practiced =4 weeks

Convert from weeks to days = 4 X 7=28 days

Since she practices all of her scales 15% of her practice days.

Number of Days that she practiced all her scales

=15% X 28

=0.15 X 28

=4.2 days

Answer:

Step-by-step explanation:

8x² + 7x - 1 = 0

Rewrite 7x as a difference

That's

8x² + 8x - x - 1 = 0

Factorize

8x( x + 1) - ( x + 1) = 0

(8x - 1)( x + 1) = 0

8x - 1 = 0 x + 1 =0

8x = 1 x = - 1

x = 1/8

The solutions are

Hope this helps you

Answer:

[tex]-4x^{2} -4xy+6y^{2}[/tex]

Step-by-step explanation:

(3x2 − 8xy + y2) − (7x2 − 4xy − 5y2)

First, we remove the parenthesses. We can just remove the first parnthesses because there isn't any sign before them. When removing the second ones, we will change the sign of every term in it. It becomes:

[tex]3x^{2} -8xy+y^{2} -7x^{2} +4xy+5y^{2}[/tex]

Now we will combine the like terms. That means that we will subtract 7x2 from 3x2, add 4x to -8x etc.

[tex]-4x^{2} -4xy+6y^{2}[/tex]

Answer:

-4xy - 8x + 12y

Answer:

[tex]m\angle 1 =105^\circ\\m\angle 2 =75^\circ[/tex]

Step-by-step explanation:

The diagram is drawn and attached below.

From the diagram

[tex]m\angle 2 =75^\circ $ (Alternate Angles)[/tex]

[tex]m\angle 1+ m\angle 2 =180^\circ $ (Sum of angles on a straight line)\\m\angle 1+75^\circ =180^\circ\\m\angle 1 =180^\circ-75^\circ\\m\angle 1 =105^\circ[/tex]

Answer:

m<2: 75

m<1: 105

Step-by-step explanation: On edge 2021

Hope this helps!

Answer:

22cm

Step-by-step explanation:

take 22 mulitply by 23=506 dived by 23= to 22

Answer:

B(x) = 2x + 3

Step-by-step explanation:

Given:

Amount used = 3 GB   (constant term)

Additional amount for each stream = 2 GB  (slope)

Total bandwidth used for x streams

B(x) = 2x + 3

Answer:

x²−25

Step-by-step explanation:

CLT:

Apply the formula (a-b)(a+b) = a^2*b^2. Substitute 'x' for 'a' and y for 'b'.

(x+5)(x−5)

=(x+5)(x+−5)

=(x)(x)+(x)(−5)+(5)(x)+(5)(−5)

=x²−5x+5x−25

=x²−25

Thats a lot of x's

Hope this helps!

If it does please give me a 'thanks'

Answer:

[tex]x^{2} -25[/tex]

Step-by-step explanation:

[tex](x+5)(x-5)[/tex]

[tex](x*x)(x*-5)(5*x)(5*-5)[/tex] multiply the insides by their opposites

[tex]x^{2}-5x+5x-25[/tex] this can also be shown as [tex]x^{2}+5x-5x-25[/tex]

[tex]x^{2} -25[/tex] the [tex]5x[/tex] and [tex]-5x[/tex] cancle each other out

Answer:

2x sqrt(3)

Step-by-step explanation:

f(x) = 4x sqrt(3x+3) =4x sqrt(3  (x+1)) = 4x sqrt(3 ) * sqrt (x+1)

g(x) = 2 sqrt(x+1)

f(x) / g(x) = 4x sqrt(3 ) * sqrt (x+1)/ 2 sqrt(x+1)

     Canceling like terms

              = 4x sqrt(3) / 2

              = 2x sqrt(3)

Answer:

A and C

Step-by-step explanation:

The shapes that have 4 congruent sides are squares and rhombi.

Answer:

B. f(-4) = g(-4), and f(0) = g(0)

Step-by-step explanation:

We are given two functions that have been graphed already. The points on the coordinate plane  where the  curve of g(x) intercepts that of f(x), are the values of x for each function, that would give us the same output (y).

Thus, for f(x) intercepts g(x) at the point where x = -4, y = 4.

Also, f(x) and g(x) intercepts at the point where x = 0, y = 4.

Therefore, the correct answer is f(-4) = g(-4), and f(0) = g(0)

Answer:

(.5 , 0) (7.8 , 2.4)

Step-by-step explanation:

The solution to a system of equations is when they cross each other on a graph.

When this is graphed you case use the trace and zoom in tools to find where they are solutions at.

Answer: Jay is 2x + 4 years old

Step-by-step explanation:

May's age = M

Jay's age = J

Kay's age = x

J = M + 4

M = 2x

substitution

J = 2x + 4

Hope it helps <3

Answer:

[tex]3x^2 - 8x - 4[/tex]

Step-by-step explanation:

This is a short and simple question, but it's good!

We are given the expression [tex]\left(x^2-5x+3\right)+\left(2x^2-3x-7\right)[/tex], and simply being asked to combine like elements to simplify the expression. Take a look at the procedure below -

[tex]\left(x^2-5x+3\right)+\left(2x^2-3x-7\right)[/tex] - Remove ( ),

[tex]x^2-5x+3+2x^2-3x-7[/tex] - Add like elements,

[tex]3x^2-5x-3x+3-7,\\3x^2-8x+3-7,\\[/tex] - And further simplify to derive solution

[tex]Solution = 3x^2-8x-4[/tex]

Hope that helps!

Answer:

The total cost depends on the weight of the pacakge

Answer:

c. 38

Step-by-step explanation:

Answer:

Option C.

Step-by-step explanation:

In a linear function, the change in y-values with respect to x-values is constant.

We need to find table from the given tables which represents a non-linear function.

In option A, x is increasing by 1 unit and y is decreasing by 1 unit. So, rate of change is constant.

In option B, x is increasing by 1 unit and y is decreasing by 1 unit. So, rate of change is constant.

In option C, x is increasing by 1 unit but y is not decreasing by same units. So, rate of change is not constant.

In option D, x is increasing by 1 unit and y is increasing by 1 unit. So, rate of change is constant.

Only in option C, the rate of change is not constant. So, it represents a non-linear function.

Therefore, the correct option is C.

Answer:

The Correct Answer would be C

Step-by-step explanation:

Answer:

The answer is B. 12,34 cm .....:)

Answer:

201.06

Step-by-step explanation:

A=4πr2=4·π·42≈201.06193

Answer:

44

Step-by-step explanation:

Tan v=opp/adj 18s/19s=0.947

v=44 degrees (approximately)

angle T=180 - (90+44)

angle T= 46

Answer:

a. 17

b. 50

c. 9

Step-by-step explanation:

Simply replace the variables with the given numbers:

3(5) + 2

15 + 2

17

2(5)²

2(25)

50

(5 - 2)²

3²

9

Answer:

a) 17

b) 50

c) 9

Step-by-step explanation:

x = 5; y = 2

a) 3x + y

b) 2x^2

c) (x - y)^2

a) 3x + y = 3(5) + 2 = 15 + 2 = 17

b) 2x^2 = 2(5^2) = 2(25) = 50

c) (x - y)^2 = (5 - 2)^2 = 3^2 = 9

Answer:

810

Step-by-step explanation:

The original price of the car = 100%.

Price is decreased by 10%- price now equal 90% of original.

Let original price = x

.9x=729

x=810

Check:

810 - .1(810) = 729

True!

729 + 10%=801.90

is the answer

Answer:

6

Step-by-step explanation:

Let's call the number of red cubes that Sam has r, and the number of yellow cubes that she has y.

Since the sum of the number of cubes is 20:

r+y=20

Since she has 8 more yellow cubes than red ones:

y=r+8

You can now plug this back into the first equation:

r+(r+8)=20

2r+8=20

2r=12

r=6

Therefore, Sam has 6 red cubes. Hope this helps!

Hope this helps!

Answer:

6 red cubes

Step-by-step explanation:

Let statements: let y be the number of yellow cubes, and let r be the number of red cubes.

r+y=20

r+8=y

r+(r+8)=20

2r+8=20

2r=12

r=6

Answer:

The radicals should be negatives of each  other

Step-by-step explanation:

When we get solutions that are radicals, they have to be in the form

a+ sqrt(b) and a- sqrt(b)

His answer is a + sqrt(b) and -a - sqrt(b)