Which graph shows the solution to the system of linear inequalities? 2x -3y ≤ 12 y < -3

Logan Chivery owns her own car. Her June monthly interest was $300. The rate is 8.5 percent. Logan's principal balance at the beginning of June is: (Use 360 days-do not round the denominator.)

A. $42,353.14

B. $42,335.14

C. $2,335.14

Answer: A. $42,353.14

Step-by-step explanation:

When taking a loan, we have to pay interest. The Simple Interest Formula is:

Simple Interest (I) = Principal (P) × Interest Rate (r)

Principal (P) is the borrowed amount.

Interest Rate (r) is the percent of the principal to be paid.

Time (t) is the length of time that money is borrowed.

If Logan Chivery has the monthly interest of $300  at a rate of 8.5% per year, first, we have to convert the year rate to the month of June rate.

30 days = 8.5÷360÷30 = 0.7083333333 interest rate

Then, find the Principal by using the formula

Simple Interest (I) = Principal (P) × Interest Rate (r)

4,2352.94×0.7083333333÷100=299.99

Answer:

  False

Step-by-step explanation:

In a proportion, the two fractions are equal. Here the denominators are different for the same numerator, so the fractions are not equal. The given expression is not a proportion.

Answer:

The graph shaded outside the parabola and the curve is solid.

Step-by-step explanation:

The given inequality is  

[tex]y+4x\leq x^2+2[/tex]

It can be rewritten as

[tex]y\leq x^2-4x+2[/tex]

The sign of inequality is [tex]\leq[/tex], so the curve is a solid line.

The related equation of line is

[tex]y=x^2-4x+2[/tex]

Table of values is

x          0          2          4

y          2         -2          2

Plot these points and draw a U-shaped curve.

Check the equality for (0,0).

[tex]0\leq (0)^2-4(0)+2[/tex]

[tex]0\leq 2[/tex]

This statement is true. So, (0,0) lies in the shaded portion.

So, shade the graph outside the parabola.

Answer:

12

Step-by-step explanation:

The proper divisors of 12 are

1 2 3 4 6

Add those together you get 16

Answer:

answer is a

Step-by-step explanation:

zeros are x intercepts

Answer:

A

Step-by-step explanation:

(2x+1)(x+2)

so

2x=-1

x=-1/2

x=-2

A

Answer:

b

Step-by-step explanation:

The answer is b because we are looking for opposites

The opposite of +x is -x

While the opposite of -3 is +3

with this, we can switch them around.

this gives us the inverse of 3-x

Answer:

$3 discount

Step-by-step explanation:

If Fredo originally had the markdown as $0 (meaning no change), then he arrived at the store, seeing the markdown was $2, the current markdown is $2.

Now that he has an extra $1 off, he gets 2+1 = $3 off the bread.

Hope this helped!

Answer: There is sufficient evidence to reject the dealer's claim that the mean price is at least $20,500

Step-by-step explanation:

given that;

n = 14

mean Ж = 19,850

standard deviation S = 1,084

degree of freedom df = n - 1 = ( 14 -1 ) = 13

H₀ : ц ≥ 20,500

H₁ : ц < 20,500

Now the test statistics

t = (Ж - ц) / ( s/√n)

t = ( 19850 - 20500) / ( 1084/√14)

t = -2.244

we know that our degree of freedom df = 13

from the table, the area under the t-distribution of the left of (t=-2.244) and for (df=13) is 0.0215

so P = 0.0215

significance ∝ = 0.05

we can confidently say that since our p value is less than the significance level, we reject the null hypothesis ( H₀ : ц ≥ 20,500 )

There is sufficient evidence to reject the dealer's claim that the mean price is at least $20,500

Answer:

Below

Step-by-step explanation:

The canister has a cylindric form

The volume of a cylinder is given by the following formula :

V= r^2 * Pi *h

H is the heigth and r os the radius(half of the diameter)

Let Pi = 3.14

●●●●●●●●●●●●●●●●●●●●●●●●

V= 3.14*4.5^2 * 12

V= 763.02

V = 763 cm^3(after rounding to the nearest unit)

●●●●●●●●●●●●●●●●●●●●●●●●

The surface area of a cylinder is given by the followong formula:

Sa = 3.14*r^2*2 + Pi*d*h

r is the radius, d the diameter and h the heigth

Let Pi= 3.14

Sa= 3.14*4.5^2*2 + 3.14*9*12

Sa= 466.29 cm^2

Sa= 466 cm^2 ( after rounding to the nearest unit

●●●●●●●●●●●●●●●●●●●●●●●●

The dimensions of the second canister are the double of the first one

V= r^2*Pi*h

V= 9^2 *3.14*24

V= 6104.16 cm^3

V= 6104 cm^3 (after rounding to the neatest unit)

Sa= 2*3.14*r^2+ 3.14*d*h

Sa= 2*3.14*9^2 + 3.14*24*18

Sa= 1865.16 cm^2

Sa= 1865 cm^2 (after roundong to the nearest unit)

●●●●●●●●●●●●●●●●●●●●●●●●

The volume and the surface area of the second canister are bigger than the first one

Divide the second volume by the first one :

V2/V1= 6104/763 = 8

We deduce that the voulme of the second canister is greater 8 times than the first one

Do the same for the surface area

Sa2/Sa1 = 1865/466 = 4.002 = 4 (after rounding to the nearest unit)

The second surface area is greater 4 times than the first one

Answer:

Yeah, what they said above.

Step-by-step explanation:

Answer:

x = -5

Step-by-step explanation:

-7(x + 2) = 21​

Divide each side by -7

-7/-7(x + 2) = 21​/-7

x+2 = -3

Subtract 2 from each side

x+2-2 = -3-2

x = -5

Answer:

x = -5

Step-by-step explanation:

distribute: -7x-14 = 21

add 14 to both sides

divide by -7

x = -5

Answer:

[tex]10\sqrt{2[/tex]y²

Step-by-step explanation:

So I am not sure if the root is only on 200, but if it is not, please comment, and I will add to it.

Answer:

x = -6

Step-by-step explanation:

First write the equation.

4x + -3 = 5x + 3

The isolate x in the equation. Add -4x to both sides.

4x + -3 + -4x = 5x + 3 + -4x

-3 = x + 3

Then add -3 to both sides.

-3 + -3 = x + 3 + -3

-6 = x

Now you have the value of x = -6.

Cheers.

Answer:

Step-by-step explanation:

          +3             +3

          -5x       -5x

            ÷(-1)     ÷(-1)    

Answer:

Step-by-step explanation:

8j^3-10j^2-7-6j^3+10j^2+j-12

2j^3+j-12

Answer:

Step-by-step explanation:

A rational number are numbers that can be expressed as as fraction. They can be expressed as a ratio of two integers. An irrational is quite the opposite.  An irrational number cannot be expressed as a ratio of two integers.

Taking square root of two as an example;

√2 cannot be expressed as a ratio of two integers because the result will always be a decimal. If expressed as √2/1, it is still not a rational number because of the square root of 2 at the numerator. Square root of 2 is not an integer even though 1 is an integer.

Mark is wrong because √2 is irrational and it is irrational because it cannot be expressed as a ratio of two integers not due to the fact that he can write it as a fraction.

Answer:

8+n^2

Step-by-step explanation:

Answer:

f(n+1)=(f[n]-1)^2, where f(1)=8

Step-by-step explanation:

"it appears your explanation includes a link" so you don't get an explanation

Answer:

clay sphere gives more clay for less money

Step-by-step explanation:

Volume of cone=1/3πr^2h

=1/3*3.14*(9^2)*12

=1/3*3.14*81*12

=3,052.08/3

=1017.36 inches^3

Volume of a cyclinder=πr^2h

=3.14*(9^2)*12

=3.14*81*12

=3,052.08 inches^3

Volume of a sphere=4/3πr^3

=4/3*3.14*(9^3)

=4/3*3.14*(9^3)

=4/3*3.14*729

=9,156.24 / 3

=3,052.08 inches^3

Clay cone=$12

Clay cyclinder=$30

Clay sphere=$28

Which is the best to buy

Comparing volume

Volume of sphere=3,052.08 inches^3

Volume of cyclinder=3,052.08 inches^3

Volume of cone=1017.36 inches^3

Sphere and cyclinder both have the same volume which is 3 times more than volume of a cone

Clay sphere cost $28 which is cheaper than clay cyclinder at the same volume.

Therefore, clay sphere gives more clay for less money

Answer:

The mean number of the children is 1.2

Step-by-step explanation:

Given

Children: 0, 1, 2, 1, 2

Required

Determine the Mean number

The mean of a set is calculated as follows;

[tex]Mean = \frac{\sum x}{n}[/tex]

Where x is the given set and n is the number of sets

In this case, n = 5 children

Hence;

[tex]Mean = \frac{0 + 1 + 2 + 1 + 2}{5}[/tex]

[tex]Mean = \frac{6}{5}[/tex]

[tex]Mean = 1.2[/tex]

Hence, the mean number of the children is 1.2

Answer:y = 2/3

Step-by-step explanation:

2x + y = 10

x - y = 4

-----------------add

3x = 14

x = 14/3

x - y = 4

14/3 - y = 4

-y = 4 - 14/3

-y = 12/3 - 14/3

-y = -2/3

y = 2/3 <==

Answer:

2x + y = 10

x - y = 4

-----------------add

3x = 14

x = 14/3

x - y = 4

14/3 - y = 4

-y = 4 - 14/3

-y = 12/3 - 14/3

-y = -2/3

y = 2/3 <==

Step-by-step explanation:

Answer:

The data that we have is:

f(x) = x + 5

g(x) = x^2 + 1

p(x) = g(x) + f(x) = (x^2 + 1) + (x + 5) = x^2 + x + 6.

q(x) = g(x) - f(x) =  (x^2 + 1) - (x + 5) = x^2 - x - 4

We want to find  p(x)*q(x)

well, we can replace:

p(x)*g(x) = (g(x) + f(x))*(g(x) - f(x))

Now, you can recall the relationship:

a^2 - b^2 = (a + b)*(a - b)

then we have that:

(g(x) + f(x))*(g(x) - f(x)) = g(x)^2 - f(x)^2

now we can replace g(x) and f(x) by the expressions that we know:

g(x)^2 - f(x)^2 = (x^2 + 1)^2 - (x + 5)^2

now we can simplify this:

(x^2 + 1)^2 - (x + 5)^2 = (x^4 + 2*1*x + 1^2) - (x^2 + 2*5*x +5^2)

= x^4 + 2*x + 1 - x^2 - 10x - 25

= x^4 - x^2 - 8*x - 24

p(x)*q(x) = x^4 - x^2 - 8*x - 24

Answer:

x^4+x^2-10x-24

Step-by-step explanation:

Answer:

4/3

12

44/30

Step-by-step explanation:

2/5:3/10

=2/5*10/3

=20/15

=4/3

1/2:1/4:1/6

=1/2*4/1*6/1

=4/2*6/1

=24/2

=12

2⅕:1¼:1⅕

11/5:5/4:6/5

=11/5*4/5*5/6

=44/25*5/6

=220/150

=44/30

Hope this helps ;) ❤❤❤

Answer:

a = 7

b = 7

c = 14             [Correct option is B. 14]

Step-by-step explanation:

Since the shape is a parallelogram, to solve this problem, use some of the properties of a parallelogram:

(i) Opposite sides are parallel and congruent. Being congruent means the sides are identical. In other words, they have the same length.

From the diagram, this means that sides PQ and SR are identical. i.e

=> PQ = SR

=> 6a + 10 = 8a - 4          [collect like terms and solve]

=> 14 = 2a

=> a = 7

(ii) Opposite angles are congruent. Angles PQR and PSR are identical. i.e

<PQR = <PSR = (9b + 2)°

Also,

<SPQ = <SRQ = (18b - 11)°

(iii) Consecutive angles are supplementary. The sum of any two angles that are not opposite to each other is 180°. i.e.

<SPQ + <PQR = 180°

<PQR + <QRS = 180°

<QRS + <RSP = 180°

.

.

.

Also,

<PSR + <SPQ = 180°      

(9b + 2)° + (18b - 11)° = 180°        [expand bracket and solve for b]

9b  + 2 + 18b - 11 = 180

27b - 9 = 180

27b = 189

b = 7

Now, since a = 7 and b = 7;

c = a + b = 7 + 7 = 14

Therefore;

a = 7

b = 7

c = 14

Answer:

1. It has 5 sides.

2. It has 6 walls.

3. Octagon

4. a. Pentagon (The figure has 5 sides.) b. Triangle (The figure has 3 sides.) c. Hexagon (The figure has 6 sides.) d. Hexagon (The figure has 6 sides.)

5. a. 6 cm + 6 cm + 6 cm + 6 cm = 24 cm, or 4 × 6 cm = 24 cm, b. 7 in. + 7 in. + 7 in. = 21 in., or 3 × 7, in. = 21 in., c. 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. = 28 ft., or 7 × 4 ft. = 28 ft., d. 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. = 81 in., or 9 × 9 in. = 81 in.

6. a. 4 ft. + 3 ft. + 3 ft. + 2 ft. + 4 ft. + 5 ft. = 21 ft. b. 8 in. + 8 in. + 8 in. + 8 in. + 3 in. + 3 in. + 3 in. + 3in. = 44 in. c. 3 cm + 3 cm + 3 cm + 2 cm + 2 cm = 13 cm

7. Shelly has enough lights to decorate four windows.

8. a. 8 ft, b. 4 m, c. 24 ft, d. 7 cm

Step-by-step explanation:

PennFoster

Answer:

It has 5 sides.

It has 6 walls.

Octagon

a. Pentagon (The figure has 5 sides.)

b. Triangle (The figure has 3 sides.)

c. Hexagon (The figure has 6 sides.)

d. Hexagon (The figure has 6 sides.)

a. 6 cm + 6 cm + 6 cm + 6 cm = 24 cm, or 4 × 6 cm = 24 cm

b. 7 in. + 7 in. + 7 in. = 21 in., or 3 × 7 in. = 21 in.

c. 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. = 28 ft., or 7 × 4 ft. = 28 ft.

d. 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. = 81 in., or 9 × 9 in. = 81 in.

a. 4 ft. + 3 ft. + 3 ft. + 2 ft. + 4 ft. + 5 ft. = 21 ft.

b. 8 in. + 8 in. + 8 in. + 8 in. + 3 in. + 3 in. + 3 in. + 3in. = 44 in.

c. 3 cm + 3 cm + 3 cm + 2 cm + 2 cm = 13 cm

Let w stand for the number of windows Shelly can decorate. Each window is a square with sides measuring 5 feet. The perimeter of one window is 4 × 5 feet. Divide the total length of the light strings by the perimeter of one window.

80 ft. ÷ (4 × 5ft.) = w

80ft. ÷ 20ft. = w

4 = w

Answer: Shelly has enough lights to decorate four windows.

Step-by-step explanation:

PENN

Answer:

1.  20 tins of milk

2.  Weight of the Carton = 8,4kg ot 8400g

Step-by-step explanation:

Given

Volume of a Tin = 77cm³

Weight of a tin = 5000g

Volume of Empty Carton = 1540cm³

Weight of Empty Carton = 5000g

Calculating the number of tins of milk

To do this, we have to make use of the given volumes;

And this is done as follows;

[tex]Number = \frac{Volume\ of\ Empty\ Carton}{Volume\ of\ a\ Tin}[/tex]

Substitute  77cm³ for Volume of a Tin and 1540cm³ for Volume of an Empty Carton

[tex]Number = \frac{1540cm^3}{77cm^3}[/tex]

[tex]Number = 20[/tex]

Hence, 20 tins of milk will filled the empty carton

Calculating the weight of the Carton after filled with tins of milk

This is calculated as thus;

Total Weight = Weight of Empty Carton + Weight of Tins of Milk

Substitute 5000g for Weight of Empty Carton

Total Weight = 5000g + Weight of Tins of Milk

_________________________________________

Calculating Weight of Tins of Milk

Since 20 tins of milk will fill the empty carton, the

Weight of Tins of Milk = 20 * Weight of 1 Tin of Milk

Weight of Tins of Milk = 20 * 170g

Weight of Tins of Milk = 3400g

_________________________________________

Substitute 3400g for Weight of Tins of Milk

[tex]Total\ Weight = 5000g + 3400g[/tex]

[tex]Total\ Weight = 8400g[/tex]

In Kilograms:

[tex]Total\ Weight = 8.4kg[/tex]

Answer:

[tex]C(x) = 540x + 72120[/tex]

Step-by-step explanation:

Given

Cost = $78,600 when Printing Press = 12

Cost = $82,380 when Printing Press = 19

Required

Determine the linear equation

From the given parameters; Cost is a function of Printing Press

Represent Cost by C and Printing press by x;

This implies that C = f(x)

The given parameters can then be modeled as; [tex](x, C)[/tex]

[tex](x_1, C_1) = (12,78600)[/tex]

[tex](x_2, C_2) = (19,82380)[/tex]

The first step is to calculate the slope, m;

[tex]m = \frac{C_1 - C_2}{x_1 - x_2}[/tex]

[tex]m = \frac{78600 - 82380}{12 - 19}[/tex]

[tex]m = \frac{-3780}{-7}[/tex]

[tex]m = 540[/tex]

The linear equation can then be calculated using slope formula

[tex]m = \frac{C- C_2}{x - x_2}[/tex]

Substitute 540 for m and [tex](x_2, C_2) = (19,82380)[/tex]

[tex]540 = \frac{C- 82380}{x - 19}[/tex]

Multiply both sides by x - 19

[tex]540 * (x-19)= \frac{C- 82380}{x - 19} * (x-19)[/tex]

[tex]540 * (x-19)= C- 82380[/tex]

Open bracket

[tex]540x - 10260 = C - 82380[/tex]

Add 82380 to both sides

[tex]540x - 10260 + 82380= C - 82380 + 82380[/tex]

[tex]540x - 10260 + 82380= C[/tex]

[tex]540x + 72120= C[/tex]

[tex]C = 540x + 72120[/tex]

Hence;

[tex]C(x) = 540x + 72120[/tex]

Answer:

[tex]y\ =\ \left|\frac{1}{2}x-2.5\right|+3[/tex]

Step-by-step explanation:

Look at the image below ↓

Answer:

Check below the graph.

Step-by-step explanation:

Hi, for this function, check the graph below:

1) Note that in this function the value outside the brackets points how high the graph will be traced.

2) The value within the brackets, points since it's a negative expression how far to the right the graph will be traced.

Answer:

11

Step-by-step explanation:

6.7 / .6

Multiply top and bottom by 10

67/6

66/6 = 11 so this is close to 11

Answer:

area=17.5

Step-by-step explanation:

area=1/2(base*height)

area=1/2(3*7)

are=17.5