9. Read the following word problem, then create a linear equation to model the problem. Provide work to show how your linear equation models the problem, such as a brief description, a picture, or a table. Finally, use the linear equation you created to solve the problem.

$2400 is divided between two accounts. One account pays 2% interest, while the other account pays 3.5% interest. At the end of one interest period, the interest earned is $81. How much was invested in each account?

Answer:

[tex]1\frac{3}{20}[/tex]

Step-by-step explanation:

'23' fits into '20' one time. So, '1' would be the whole number. We would be left over with  '[tex]\frac{3}{20}[/tex]'  as the remainder, so  '[tex]\frac{3}{20}[/tex]' would be the fraction of the mixed number.  

Put them together, and you get: [tex]1\frac{3}{20}[/tex]

The fraction is already in it's simplest form.

Brainilest Appreciated.

The solution for mixed fraction of number 23 / 20 is,

⇒ 23/20 = 1 3/20

We have to given that,

A number is,

⇒ 23 / 20

We can divide it for the mixed fraction as,

⇒ 23 / 20

20 ) 23 ( 1

    - 20

  --------------

          3

Therefore, It can be written as,

⇒ 23 / 20 = 1 3/20

Thus, The solution for mixed fraction of number 23 / 20 is,

⇒ 23/20 = 1 3/20

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Answer:

Please find the attached the required inequality graph

Step-by-step explanation:

Given that inequality is 2.5 ≤ x ≤ 4.5, we have;

The region in the given inequality is the region between 2.5 and 4.5 inclusive

Therefore, to represent 2.5 ≤ x ≤ 4.5 on the number line, we have;

A closed circle (representing the less than or equal to inequality symbol, showing inclusiveness) at 2.5, another closed circle at 4.5 (representing the less than or equal to inequality symbol, showing inclusiveness) and the region between 4.5 and 2.5 shaded.

Answer:

Jesse

Step-by-step explanation:

Everyone except for Jesse and Trey asked other grades but Jesse and Trey was the only one that asked 6th graders. The reason why I thought Trey might be biased is he asked HIS class while Jesse asked random people.

Hope this helped! :)

Answer:

1. 677 inches = 18.056 yards

677 inches  = 56.416 feet

677 inches = 677 inches

2. QP = 23.5 cm

3. The perimeter = 53.5 cm

Step-by-step explanation:

1. To convert, 677 inches to yards, we have;

1 inch = 0.0277778 yards

677 inches = 677*0.0277778 = 18.056 yards

To convert, 677 inches to feet, we have;

1 inch = 0.083333 feet

677 inches = 677*0.083333  = 56.416 feet

To convert, 677 inches to inches, we have;

1 inch = 1 inch

677 inches = 677*1  = 677 inches

2. We have that ∠PRQ and ∠PRS are supplementary angles (angles on a straight line

Given that ∠PRS = 90°, ∠PRQ = 180° - 90° = 90°;

∠PRQ + ∠PQR + ∠RPQ = 180°, sum of angles in a triangle

∠PQR = 24° given

∠PRQ = 90°

∴  ∠RPQ = 180° - 90° - 24° = 66°

∴∠SPQ = ∠SPR + ∠RPQ = 36° + 66° = 102°

∠QSP + ∠SPQ + ∠PQS = 180° (sum of angles in a triangle)

∠QSP = 180° -∠SPQ - ∠PQS = 180° -102° - 24 = 54°

By sine rule, we have;

a/(sin(A)) = b/(sin(B))

Therefore, we have;

11.8/(sin(24)) = QP/(sin(54°))

QP = (11.8/(sin(24))) × (sin(54°)) = 23.5 cm

3. From trigonometric ratios, we have;

tan(43°) = BC/CA = BC/(16.2 cm)

BC = 16.2 cm × tan(43°) = 15.1

By Pythagoras theorem, we have;

AB = √(15.1² + 16.2²) = 22.2

The perimeter = 15.1 + 16.2 + 22.2 = 53.5 cm

Answer:

Y= -1/5x + 1

Step-by-step explanation:

Just type it on a graphing calculator an click graph

Answer:

Step-by-step explanation:

2)

a) elimination method

b) substitution method

c) substitution method

For the first part we can elimate the y variable by subtracting the equations. We can then find the value of x.

For the second part we can substitute y as 2x+5 in the second equation and solve for x.

For the third part we can substitute y as 4x+3 in the first equation and solve for x.

3)

Answer:

Step-by-step explanation:

   +4x+6         +4x+6

     ÷5.5       ÷5.5

Answer:

Left table: y= 1.5x - 6

Right table : y= -4x + 6.1

Solution : (2.2 , -2.7)

Step-by-step explanation:

:)

Answer:

D = - 13/19

Step-by-step explanation:

Slope = (y2 - y1)/(x2 - x1) = (6- (-7))/(-5-14) = -  13/19

Answer:

-61/4

Step-by-step explanation:

-1/2 + x = - 21/4 - 23/4 - 19/4

-1/2 + x = -(21+23+19)/4

x = -63/4 + 1/2

x= -63/4 + 2/4

x = -61/4

Hope that helps, tell me if you need further explanation. =)

Answer:

B. -19/4

Step-by-step explanation:

-1/2 + x = -21/4

x = -21/4 + 2/4

x = -19/4

Answer: B. -19/4

Answer: no solution

Step-by-step explanation:

-2(x-7)+3(x+5)=x+9

Distribute

-2x+14+3(x+5)=x+9

Distribute

-2x+14+3x+15=x+9

Combine like terms

x+29=x+9

Subtract(x)

29=9

Because 29 does not equal 9, the equation has no solutions

Hope it helps <3

Answer:

There is no solution.

Step-by-step explanation:

[tex] - 2(x - 7) + 3(x + 5) = x + 9[/tex]

Distribute -2 through the parentheses

[tex] - 2x + 14 + 3(x + 5) = x + 9[/tex]

Distribute -3 through the parentheses

[tex] - 2x + 14 + 3x + 15 = x + 9[/tex]

Collect like terms

[tex]x + 14 + 15 = x + 9[/tex]

Add the numbers

[tex]x + 29 = x + 9[/tex]

Cancel equal terms on both sides of the equation

[tex]29 = 9[/tex]

The statement is false for any value of x

Hope this helps..

Best regards!!

Answer:  8 days

Step-by-step explanation:

Given, At Sami's Shoe Warehouse, it takes 4 over 5 of a day to complete 1 over 10 of an order of sneakers.

i.e. [tex]\dfrac{4}{5}[/tex] x  (1 day) = [tex]\dfrac{1}{10}[/tex] x (an order of sneakers)

Multiply 10 on both the sides , we get

[tex]\dfrac{4}{5}\times10[/tex] x  (1 day) = [tex]\dfrac{1}{10}\times10[/tex] x (an order of sneakers)

⇒[tex]4\times2[/tex] x  (1 day) = an order of sneakers

⇒[tex]8[/tex] x  (1 day) = an order of sneakers

i.e. Time to complete an order of sneakers = 8 days

Hence, it will take 8 days to complete the entire order of sneakers.

Answer: 8 days total

Step-by-step explanation:

Answer:

(-2, 5/3)

Step-by-step explanation:

Step 1: Write out systems of equations

y = 2/3x + 3

x = -2

Step 2: Substitution

y = 2/3(-2) + 3

y = -4/3 + 3

y = 5/3

Step 3: Write solution

(-2, 5/3)

Answer:

[tex]\boxed{(-2, \frac{5}{3} )}[/tex]

Step-by-step explanation:

y = 2/3x+3

x = -2

Plug x as -2 in the first equation.

y = 2/3(-2) + 3

Solve for y.

y = -4/3 + 3

y = -4/3 + 3/1

y = -4/3 + 9/3

y = 5/3

The value of x is given already as -2.

The value of y is 5/3.

The solution to the system of equations is (-2, 5/3).

Answer:

A= 2

B=28

C=0

Step-by-step explanation:

ax2 + bx + c=0

so x = minus 9

then

7 × (-9) - 2y = 35

-63 - 2y = 35

-2y = 35 plus 63

-2y = 98

- y = 49

y = -49

Answer:

[tex]\boxed{y = -49}[/tex]

Step-by-step explanation:

=> [tex]7x-2y = 35[/tex]

Given that x = -9

=> [tex]7(-9) -2y = 35[/tex]

=> [tex]-63-2y = 35[/tex]

Adding 63 to both sides

=> [tex]-2y = 35+63[/tex]

=> [tex]-2y = 98[/tex]

Dividing both sides by -2

=> [tex]y = -49[/tex]

Answer:

(i) The increase expected in the share price between the first year and the third year is $0.90

(ii) The 10th year

Step-by-step explanation:

(i) The given relation is [tex]V = 2.95+2\cdot log_{10}\left (10\cdot t + 1 \right )[/tex]

In the first year, we have t = 1, which gives;

[tex]V = 2.95+2\cdot log_{10}\left (10\times 1 + 1 \right ) = 2.95+2\cdot log_{10}\left (1 1 \right ) = \$5.03[/tex]

In the third year, we have t= 3 which gives;

[tex]V = 2.95+2\cdot log_{10}\left (10\times 3 + 1 \right ) = 2.95+2\cdot log_{10}\left (31 \right ) = \$5.93[/tex]

Therefore, the increase expected in the share price between the first year and the third year is $5.93 - $5.03 = $0.90

(ii) When the share price value becomes >$7.00, we have;

[tex]7 = 2.95+2\cdot log_{10}\left (10\cdot t + 1 \right )[/tex]

Which gives;

7 - 2.95 = 2·㏒(10·t + 1)

4.05/2 = ㏒(10·t + 1)

2.025 = ㏒(10·t + 1)

[tex]10^{2.025} = 10 \cdot t + 1[/tex]

105.93 = 10·t + 1

104.93 = 10·t

t = 104.93/10 = 10.493 ≈ 10.5 years which is within the 10th year.

Answer:

[tex]x >4[/tex]

Step-by-step explanation:

[tex]x+3>19-3x[/tex]

Add 3x and -3 on both parts.

[tex]x+3+3x-3>19-3x+3x-3[/tex]

Combine like terms.

[tex]x+3x>16[/tex]

[tex]4x >16[/tex]

Divide 4 on both parts.

[tex]\frac{4x}{4} > \frac{16}{4}[/tex]

[tex]x >4[/tex]

Answer:

32-(7-17)+11

32-(-10)+11

32+11-(-10)

43-(-10)

53

Answer:

Yes

Step-by-step explanation:

This graph represents a continuous function. That means that the line can be drawn without lifting your pen/pencil from the graph. You can tell that it is a function by doing the vertical line test. Since there is only one output for every input on the graph, it would be a function.

(Thanks to the users who caught my previous error :)

Answer:

The answer is C addition property of equality.

Step-by-step explanation:

In step 1, 7x − 25 = 4x − 1 there are the numbers -25 and -1

In step 2, 7x = 4x + 24 The -25 is removed and -1 is replaced with 24

Meaning that in step 2 25 was added to those numbers meaning the answer C addition property of equality.

Answer:

C

Step-by-step explanation:

Answer:

500cm or 5 meters

Step-by-step explanation:

The ratio of drawing and field is 1:90.

So we have to make 450 m into cm.

450 -> is 45,000

Now we can make 2 fractions,

[tex]\frac{1}{90}=\frac{x}{45000}[/tex]

Cross multiply

90*x = 90x

1*45000 = 45000

90x = 45000

Divide 90 to both sides

x = 500cm

Thus,

the drawing's field is 500cm or 5m long.

Hope this helps :)

Answer:

Add equations A + B to eliminate y

Then add equations A and C to eliminate y

Step-by-step explanation:

Since all the equations have y with a coefficient of 2, I would eliminate y

Add equations A + B to eliminate y

Then add equations A and C to eliminate y

Answer:

the 3rd choice

Answer:

1/3

Step-by-step explanation:

Let's say you picked the blue one first. You have a 2/3 chance of doing that, and now you're left with 2. Now, to pick the green one, you have a 1/2 chance. Multiply that and you  see that you have a 1/3 chance of picking it last.

Answer:

1/3.

Step-by-step explanation:

The probability that the red cube WON'T be picked on the first draw is 2/3. This is because there is a 1/3 probability of picking a green cube, added to a 1/3 probability of picking a blue cube.

The probability that the red cube WON'T be picked on the second draw is 1/2.  This is because one cube has already been picked, so there are two remaining. You can only pick one of the two.

(2/3) * (1/2) = (2 * 1) / (3 * 2) = 2 / 6 = 1/3.

Hope this helps!

Answer:

9/13

Step-by-step explanation:

rise = y₂ - y₁ = -1 - (-10) = -1 + 10 =   9

run = x₂ - x₁ =   9 - (-4)   =   9 +   4 = 13

Step-by-step explanation:

Answer:

348 7gb93c9 good morning to you all right place on my bed right now iam not geting the best way u are gonna be in this situation is it was not Halloween but gug batson vocal vox's John b bucko and my dear loving n love u soo hapy that u can go ahead with it is my beauty grl for the kichen and u will not cm to ur 2AM to go to Gangtok and my 7th anniversary of the 4588th 468inches I will not be the 6th of God Amen n and 93feet

Step-by-step explanation:

Queremos encontrar el valor de x que maximiza la expresión dada.

Veremos que el valor de x que maximiza la producción es x = 4.

Tenemos la expresión:

F(x) = -2*x^2 + 16*x + 25

Y queremos maximizarla.

Notar que es una función cuadratica cuyo coeficiente principal es negativo, es decir, el máximo de la función esta en el vertice.

Para una cuadratica generica:

y = a*x^2 + b*x + c

El vertice está en:

x = -b/2a

Entonces en nuestro caso, el vertice va a estar en:

x = -16/(2*-2) = 4

x = 4

Es decir, la producción de cacao será máxima cuando se utilicen 4 toneladas de fertilizante.

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Answer:

25.4 degrees

Step-by-step explanation:

Use the inverse sine function to calculate

Answer:

? = 4.41

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos A = adj / hyp

cos 25 = 4/?

? = 4/ cos 25

? =4.413511676

To the nearest hundredth

? = 4.41

Answer:

1) 33.11 m

2) 58.1°

3) 35·√2

4) 491.925 m²

Step-by-step explanation:

Side length of the pyramid = 35 m

The height of the pyramid = 22 m

The slant height = √(Height² + (1/2 Side length)²)

The slant height = √(22² + (1/2×35)² = 28.11 m

1) The slant edge length = √((Slant height)² + (1/2 Side length)²

The slant edge length = √(28.11² + (1/2×35)²) = 33.11 m

2) The base angle = tan⁻¹((Slant height)/(1/2 Side length))

The base angle = tan⁻¹(28.11/(1/2×35)) = 58.1°

3) The distance between the center pf the base and the corner of the pyramid is half the length of the base diagonal

The length of the base diagonal = √((Side length)² + (Side length)²)

The length of the base diagonal = √(35² + 35²) = 35·√2

The distance between the center pf the base and the corner of the pyramid = 35·√2/2 = 24.75 cm

4) The area of the side of the pyramid = 1/2×(Side length)× (slant height)

The area of the side of the pyramid = 1/2*35*28.11 = 491.925 m²

Answer:

slope of the line containing the given points (6,-1) AND (5,-7) is 6

point- slope form of the equation is

(y+1)= 6(x-6)  ( because, i'm choosing the point (6,-1)

Step-by-step explanation:

slope = (-7 + 1) / (5 - 6 ) = -6/-1 = 6

(y-y1) = m ( x - x1)

(y+1 ) = 6 ( x-6)

Answer: 4cm

Step-by-step explanation:

Ok so no matter the orientation of the carton, it will contain the same volume of milk. We can use the fact it's volume of milk will stay constant to find out it's new depth.

Before being turned over the milk volume is:

5 * 8 * 12 = 480. This is because the volume of a cuboid is length * width * height (depth).

Therefore the volume of the milk once turned over is 480

When on it's side, the volume of the milk equals

8 * 15 (the base) * depth

120 * depth

120 * depth = 480

so the depth = 4cm

Answer:

900

Step-by-step explanation:

a heptagon has 7 sides, so we take the hexagon's sum of interior angles an and add 180 to it's getting us, 720 + 180 = 900 degrees