Interest earned: $39.60

Principal: ?

Interest rate: 11%

Time: 6 months

Step-by-step explanation:

+25y + 35x = -1. × 5

+35x - 14y = -161. × 7

-. +. +

39y = 156

y=4

putting value of y in 5y + 7x =-1

5×4+7x =-1

7x = -21

x= -3

An equation which is parallel to 4x - 6y = -36 passing through points (2, 3) is y = 2x/3 + 5/9.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.

This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

Simplifying the equation, we have:

4x - 6y = -36

6y = 4x + 36

Dividing both sides by 6, we have:

y = 2x/3 + 6

m₁ = m₂ = 2/3.

Mathematically, the standard form of the equation of a straight line is given by;

y - y₁ = m(x - x₁)

At point (2, 3), we have:

y - 3 = 2/3(x - 2)

y - 3 = 2/3(x - 2)

y - 3 = 2x/3 - 4/3

y = 2x/3 - 4/3 + 3

y = 2x/3 + 5/9

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Answer: 14,825 is the answer

Step-by-step explanation:

Answer: 14,825

Step-by-step explanation:

its easy.

Moo berry can make 8 milkshakes with 1 gallon of ice cream.

Moo uses 2 cups of ice cream in each milkshake

He is using 1 gallon of ice cream

Therefore the number of milk shakes he can produce can be calculated as follows

16  cups makes 1 gallon

= 16/2

= 8

Hence 8 milkshakes can be made with one gallon of ice cream

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The degrees of the whole segment is 90 because we know that a right angle is 90 degrees and can be shown with a square in the corner. One angle inside the 90 degrees is 50 degrees and the other two values are the same. Since 90 - 50 = 40, we know that the remaining is 40 degrees. Since x is the same, we divide 40 by 2, getting 20 degrees.

ANSWER: x = 20 degrees

The required simplified value of the function is (f/g)(x) = (x - 3) / (x + 2). Option C is correct.

Given that,
f(x) = 2x² - 5x - 3

g(x) = 2x² + 5x + 2
(f / g)(x) =  To be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here.
f(x) = 2x² - 5x - 3
f(x) = (2x + 1) (x - 3 )
g(x) = 2x² + 5x + 2
g(x) = (2x + 1)(x + 2)

(f / g)(x) = (2x + 1) (x - 3 ) /  (2x + 1)(x + 2)
(f/g)(x) = (x - 3) / (x + 2)

Thus, the required simplified value of the function is (f/g)(x) = (x - 3) / (x + 2). Option C is correct.

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Answer:

0.894 is your correct answer.

Answer:

0.894 because the 0.01 will affect the hundredths so the 0 will be affected in 0.904 and the 9 will change to an 8 because there's nothing left in 0 so you have to substitute.

Answer:

X+Y=172 OE X=172-Y

X=5Y-8

5Y-8=172-Y

5Y+Y=172+8

6Y=180

Y=180/6

Y=30 ANS

X=172-30

X=142 ANS.

Step-by-step explanation:

The total time they will be driving the second day is 8 hours

The total distance they are planning to go  = 900 miles

Distance travelled on first day = 420 miles

Distance yet to be  travelled on second day = Total distance - distance covered = 900 miles- 420 miles= 480 miles

The speed of the car = 60 miles per hour

60 miles of distance covered in time = 1 hour

1 mile of distance covered in time = 1 hour /60 miles = 1 minute

This is solved using Unitary Method

1 hour = 60 minutes

480 miles can be covered in time = 1 minute × 480 miles

                                                         = 480 minute

                                                         =8 hours

Hence, The total time they will be driving the second day is 8 hours

Distance and displacement are two quantities that appear to mean the same thing but have very different meanings and definitions. Distance is defined as "how much ground an object has covered during its motion," whereas displacement is defined as "how far out of place an object is."

Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point.

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Table: x and y increments must be the same. X and y increments need not be the same.

The x and y exponents should be 1. Linear equation.

Graphs should be straight.

This is further explained below.

Generally, Based on the table, you need to ensure that the increments for the x values and the y values are the same.

It is not necessary for the increment to be the same for both the x and y values.

The following conclusion may be drawn from an equation: both the x and y exponents should be set to 1.

It seems like we need a line equation for this problem.

In conclusion, Inferred from a graph: the shape of the graph ought to be that of an unbroken line.

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Answer:

Draw a line going down from the 300, with a break in the middle and finish it out at the 6 hr mark.

Step-by-step explanation:

Start at the 300 and draw that line down to the 180 mark lined up with the 2 hour dot. Then draw a horizontal line from there to the middle of the 2 and the 4. Then draw a line from where you ended the break with the same slope as the beginning.

Hope this helps!

Answer:

The formula for scale factor is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape

To simplify the ratio just reduce it to the simplist form.

Divide each number in the ratio by the same amount to get the answer.

Step-by-step explanation:

hope this helps :)

Answer:

y= -3 or just -3

Step-by-step explanation:

The quadratic equation, x(2) + 2 =420 can be used to find x.

you can use trial and error

x(2) + 2 =420

210(2)=420 but we need to add the two so lower the [tex]120[/tex]

209(2)=418+2 = 420

so, the x value must less than 21.

A quadratic equation with variable x is written in standard form as [tex]ax2 + bx + c = 0[/tex], where a, b, and c are constants such that the value of an is non-zero but the values of b and c can both be zeros.

Let's change [tex]ax2 + bx + c = 0[/tex] from its standard form to its vertex form, which is [tex]a (x - h)2 + k = 0[/tex], where (h, k) is the vertex of the quadratic function [tex]f(x) = a (x - h)2 + k[/tex]. Keep in mind that 'a' has the same value in both equations. Just set them equal so we can determine how the variables relate to one another.

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The dimensions of the container is r = 6.828 cm and h = 13.656 cm.

Volume of the Cone:

Volume of the cone is define the space or the capacity of the cone.

The formula for the volume of the cone is,

V = πr²h

Where

r represents the radius of the cone

h represents the height of the cone

Given,

Cylindrical container must hold 2l or 2,000 cm³ of liquid.

Here we need to find the dimensions of the container which will minimize the amount of material needed.

Let height = h and radius of the base = r.

We know that the volume of the container,

V = 2000

We know the formula of volume of the cone is,

V = πr²h

2000 = πr²h

Here we need the value of h,

So,

h = 2000/πr²

and surface area of the can

S = 2πr² + 2πrh

Apply the value of h,

S = 2πr² + 2πr (2000/πr²)

S = 2πr²+ (4000/r)

S = 2πr²+ 4000 x r⁻¹

S′=(−1)(4000r⁻²)+4πr

S′=4πr−(4000/r²)

Consider,

4πr−(4000/r²) = 0

4πr³−4000 = 0

πr³−1000 = 0

πr³ = 1000

r³ = 1000 / π

r = √1000 / π

r =  6.828 cm

Apply the value of r on the equation to find the value of h,

h = 2000/(π∗(6.828)²)

h = 2000/146.46

h = 13.656

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The average speed was 60[tex]\frac{k+300}{96+t}[/tex]

We are given that a plane travelled k miles in 96 minutes. Since we need the average speed in miles per hour we can convert 96 minutes to hours.

96 minutes = 96/60 =8/5 hours

We are also given that the Plane completed the remaining 300 miles in t minutes. We must also convert t minutes to hours.

t minutes = t/60 hours

Now we can calculate the average speed for the entire trip, using the formula for average speed.

Average Speed = total distance/ total time

Average Speed = (k +300)/(8/5 + t/60)

Average speed = (k + 300) / ((96 + t)/60)

Hence, Average Speed = 60(k + 300)/ (96 + t)

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Answer:

Yes, the cube root of a negative number can be calculated.

Step-by-step explanation:

Answer:

Step-by-step explanation:

−3   (x+2)   =    −18

(−3)   (x)  +  (−3)   (2)  =  −18                                    (Distribute)

−3x    +   −6   =    −18

−3x   −6   =   −18

−3x  −6   +6    =  −18  +  6

−3x=  −12

−3x/−3     =   −12/−3

x   =   4

Answer:

Julia is 15

Step-by-step explanation:

13 + 14 + 15 = 42

Julia is the oldest and 15 is the greatest of the 3 numbers

therefore Julia is 15

Julia's age out of the three is equal to 15 years.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42.

Julia's age will be calculated as,

13 + 14 + 15 = 42

Julia is the oldest and 15 is the greatest of the 3 numbers.

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The distance between the given points P(-7,8) and J(-3,1) is √65 = 8.06225775

Given that, The points are P=(-7,8) and J = (-3,1).

A coordinate plane is a surface formed by two dimensional lines .

The distance between the points is calculated using the distance formula that is, distance between A(x1,y1) and B(x2,y2) is,

√[(x2-x1)²+(y2-y1)²], by using this formula you can find the distance between any two points on the plane.

Therefore the distance between the given points P and J is ,

  PJ = √[(-3+7)²+(1-8)²]

       = √[(4)²+(-7)²]

       = √[(16) + (49)]

       = √[16+49]

       = √[65]

       = 8.06225775

PJ = 8.06225775

Therefore the distance between the given points P(-7,8) and J(-3,1) is 8.06225775

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Answer:

$42,857.14

Step-by-step explanation:

12% = 12/100 = 0.12

If the teller's current salary is D and it increases by 12% in one year, the salary next year would be

X(1+0.12) = 1.12X

We know that salary next year is 48000

Using this fact,

1.12X = 48000

Dividing by 1.12 on both sides,

X = 48000/1.12 = 42,857.14

Answer:

3300cm² is the answer of this question i guess so

Answer:

[tex]\sf \pi = \dfrac{3V}{4r^3}[/tex]

Explanation:

Equation:

[tex]V = \dfrac{4}{3} \pi r^3[/tex]

Task: make pie the subject.

cross multiply

[tex]\sf \dfrac{3V}{4} = \pi r^3[/tex]

divide both sides by r³

[tex]\sf \dfrac{3V}{4} \div r^3= \pi r^3 \div r^3[/tex]

simplify following

[tex]\sf \dfrac{3V}{4r^3} = \pi[/tex]

Hence:

[tex]\sf \pi = \dfrac{3V}{4r^3}[/tex]

Answer:

Step-by-step explanation:

a) this graph is that of a parabola that opens up.  As is the case for all parabolas, the domain is the set of all real numbers.  The range begins with the smallest y-value, which is -4, extending upwards from there:  [-4, infinity)

b) this graph's shape most closely resembles that of a polynomial; as we move from left to right, y increases, reaches a local maximum, decreases to a local minimum, and then continues to increase with x.  As is the case for all polynomials, the domain is the set of all real numbers.  As we move from x = 0 to the left, y decreases without bound; from x ≥ 12 onward, y increases without bound; thus, the range is (-infinity, +infinity).

c) The graph represents a quarter of an ellipse for which x begins at -40 and ends at [4, -16].  Thus, the domain is [-40, 4].  By inspection we see that the smallest y value is -16 and the largest is 4; thus, the range is [-40, 4].

Answer:

A

Step-by-step explanation:

x + 4(x + 5) = 40 ← distribute parenthesis and simplify left side

x + 4x + 20 = 40

5x + 20 = 40 ( subtract 20 from both sides )

5x = 20 ( divide both sides by 5 )

x = 4

Answer:

x=-4

Step-by-step explanation:

8x+4=-28

8x=-28-4

8x=-32

x=-4