Davis has $20 in his savings account, and he adds $5 every month. Based on this information, which best shows the relationship between the amount of money Davis has in his savings account, y, and the number of months that have passed, x?

Answer:

y = [tex]\frac{3}{4}[/tex] x + 8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{3}{4}[/tex] , then

y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation

to find c substitute (- 4, 5 ) into the partial equation

5 = - 3 + c ⇒ c = 5 + 3 = 8

y = [tex]\frac{3}{4}[/tex] x + 8 ← equation of line

Answer: (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 )

Step-by-step explanation:

To write a polynomial in standard form, simplify and then arrange the terms in descending order. Expand (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 ) using the FOIL Method.

Question:

Write a linear function f with f (- 1/2) = 1 and f (0) = -4

The linear function f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.

What is a linear equation?

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form

y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

We are asked to write the linear function f with f (- 1/2) = 1 and f (0) = -4

Let the equation in variables x and y can be written in the form y = mx + c

So f (- 1/2) = 1

this gives, 1 = -1/2m+c      -----------eq 1

Also f (0) = -4

This gives -4 = c.            --------------eq2

Now Putting the value of c in the equation in eq1 we get m=0.

So 1 = -1/2m+c  

1 = -1/2m - 4

m = -5

Then we get;

y = -5x -4.

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The option that Sarah should choose is option 2.

Sarah would choose the option that give her the higher amount of money at her 21st birthday.

The amount that Sarah would earn each year with option 1 would increase at a linear rate. This is because she gets the same amount of money each year.

The form of a linear equation is y = mx + b

Where:

The amount that Sarah would earn each year with option 2 would increase at an exponential rate.

The general form of exponential equation is f(x) = [tex]e^{x}[/tex]

Where:

The rate of growth with an exponential function is faster than that of a linear function. It is for this reason that option 2 is the better option.

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The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

Given data;

Here, we present the dataset from the United Nations, which contains information on the number of kilowatt-hours of wind energy generated globally. The data set provides statistics on the US for 25 years, from 1990 to 2014, in millions of kilowatt-hours.

The linear equation for the first 11 years of data, from 1990 to 2000, must be determined.

To determine how much the actual value and anticipated value for the year 2001 differ in Quantity, we must first forecast the value for the year 2001 using our fitted equation with y-intercept.

It will be written as y = m(x) + c.

where,

The dependent variable is y. (in our example is quantity)

The independent variable is x. (in our example is the year)

'm' is equal to the slope of the variable X.

'C' is a constant.

The fitted equation is provided as follows:

Quantity = 186.87 (year) - 369274.72

Now that the value for the year 2001 has been provided,

Quantity = -1868.87 -369274.72 

Quantity = 4652.15

The value that the linear equation predicts for the year 2001 is 4652.15.

The precise figure for 2001 is 6806.

For the year 2001, the discrepancy between the actual and anticipated values is

6806 - 4652.15 = 2173.85

The distinction is 2173.85.

(2173.85/6806)*100 is the percentage difference.

As a result, the difference between the actual value and the forecasted value for the year 2001 is 31.94%.

Hence,

The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

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The expression that represents the sum of the arithmetic series that has a first term of -12, a common difference of +7 and a number of terms of 5 is the option with the following;

An arithmetic series one that consists of the sum of an arithmetic sequence, such that each term of the series is obtained from the previous term by the addition or subtraction of a constant.

The series in the question is; -12 + (-5) + 2 + 9 + 16

The series in therefore a series of an arithmetic sequence

The equation of the series when the first term is -12 can therefore be presented as follows;

-12 + 7·k

Where;

-12 is the first term, 7 is the common difference, n is the number of terms, and k = n - 1

The above values for the terms of the series is obtained by using values of k that range from k = 0 to k = 4

The expression that represents the series is therefore the option;

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The value of f(-5) = -130

A cubic equation is an equation with degree three. All cubic equations have either one real root and two imaginary roots or three real roots. When polynomials have degree three, they are referred to as cubic polynomials.

A Cubic polynomial function is a polynomial function with the highest degree of exponents as 3. A cubic polynomial function has the following standard form:

Ax3 + bx2 + cx +d = 0

For the given question the cubic equation will be:

2x3 + bx2 + cx - 5 = 0

Given

Leading coefficient (a) = 2

Constant (T) = -5

f(1) = 0

f(2) = 9

Therefore the equation formed will be:

2x3 + bx2 + cx - 5 = 0

Now f(1) = 0

2(1)3 + b(1)2 + c(1) - 5 = 0

2 + b + c -5 = 0

b + c = 3  

b = 3-c -----(1)

On solving f(2) = 3

2(2)3 + b(2)2 + c(2) - 5 =3

16 + 4b + 2c – 5 =3

4b +2c = 3 – 11

4b + 2c = -8  ----(2)

Now substitute the b value in equation (2)

4(3-c) + 2c = -8  

12 – 4c +2c = -8

-2c = -20

C =10

Now substitute the c value in equation (1)

b= 3 – c

b = 3 -10

b = -7

Now substitute the b and c values in the cubic equation

2x3 - 7x2 + 10x - 5 = 0

Now calculate f(-5)

2(-5)3 - 7(-5)2 + 10(-5) - 5

= -250 + 175 – 50 -5

= -130

Therefore the value of f(-5) = -130

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Answer:

A = 0.25*j + 1

Step-by-step explanation:

Answer:

[tex]A = 18 + \frac{j}{4}[/tex]

Step-by-step explanation:

A = 18 + j/4

A = Amount in $

Starting amount is 18 and a 1/4 dollar is earned for every cup of juice sold.

the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old IS 0.24243

the complete question is:

The demographic profile of Ecuador in 2018 is • 27.08% of the population are 0–14 years old • 18.35% are 15–24 years old • 39.59 are 25–54 years old • 7.53% are 55–64 years old • 7.45% are 65 years and older. In a random sample of 20 people, what is the probability that 2 are 65 years or older, 5 are 55–64 years old, 6 are 25–54 years old, 4 are 15–24 years old and 3 are 0–14 years old?

answer:

P(x) = P(x=2) + P(x=5) +p(x=6) +p(x=4) +p(x=3)

      =20[tex]C_{2}[/tex][tex](7.45)^{2}[/tex][tex](2.55)^{18}[/tex]+20[tex]C_{5}[/tex][tex](7.53)^{5}[/tex][tex](2.47)^{15}[/tex]+20[tex]C_{6}[/tex][tex](39.59)^{6}[/tex][tex](0.41)^{14}[/tex]+20[tex]C_{4}[/tex][tex](18.35)^{4}[/tex][tex](1.65)^{16}[/tex]+20[tex]C_{3}[/tex][tex](27.08)^{3}[/tex][tex](2.92)^{17}[/tex]

P(x) = 0.2424

the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old IS 0.24243

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Answer:

Step-by-step explanation:

There is only one line of symmetry:

because the one that is vertical is not representing symmetry.

Step-by-step explanation:

using Pythagoras theorem.

37,

x² = 6² + 8²

x = √6²+8² = 10ft

38.

13²=12²+x²

169 = 144 + x²

√169 - 144 = x = 5cm

hope it helps. :)

Answer:

x = 10 and x = 5

Step-by-step explanation:

using Pythagoras' identity

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

(36)

x² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )

x = [tex]\sqrt{100}[/tex] = 10

(38)

13² = x² + 12²

169 = x² + 144 ( subtract 144 from both sides )

25 = x² ( take square root of both sides )

[tex]\sqrt{25}[/tex] = 5 = x

x = 5

Answer:

I hope this will help. Tip: reuse the formula!

The total cost of 12 printers is; $493.41

Cost of first printer; C1 = $54

Cost of second printer is; 95% × 54 = $51.3

Cost of third printer is; 0.95 × 51.3 = $48.735

Cost of fourth printer = 0.95 × 48.735 = $46.298

Now, let us apply same pattern using a calculator for the remaining costs and we will have them as follows;

Cost of 5th printer = $43.983

Cost of 6th printer = $41.784

Cost of 7th printer = $39.695

Cost of 8th printer = $37.710

Cost of 9th printer = $35.825

Cost of 10th printer = $34.033

Cost of 11th printer = $32.332

Cost of 12th printer = $30.715

Total cos is; 54 + 51.3 + 48.735 + 46.298 + 43.983 + 41.784 + 36.695 + 37.710 + 35.825 + 34.033 + 32.332 + 30.715 = $493.41

Therefore, the total cost of 12 printers is $493.41

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Yes, y=x has an inverse.

Yes, y=x passes the horizontal line test.

If it didn't pass the horizontal line test, it would not have an inverse.

Answer:

soda: 97

Hot dogs: 56

Step-by-step explanation:

S-sodas

H- hot dogs

S+H=153

41+H=S

Substitute equation

(41+H)+H=153

41+2H=153

-41.        -41

2H=112

/2.   /2
H=56

S+56=153

 -56.  -56

S=97

Hopes this helps please mark brainliest

In most of the cases airlines charges a fees for baggage weigh in excess of 50 pounds. Then about 94.06% passengers incur this fees.

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Given That,

Mean (μ) = 45 pounds and Standard Deviation (σ) = 3.2

This means that μ = 46 , σ = 3.2

Since, Most airlines charges a fee for baggage that weigh in excess of 50 pound.

Then, As a proportion this is 1 subtracted by the P - value of Z when

X =50. So,

      Z = X - μ / σ

⇒ Z = 50 -45/ 3.2

⇒ Z = 5/3.2

⇒ Z = 1.56

when Z = 1.56 has a P- value of 0.9406

Now, 0.9406 × 100%

       = 94.06%

Therefor, 94.06% of airline passengers incur this fees.

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The option that is not an isometry from the given transformations is 3). Point reflection.

An Isometry refers to a transformation that leads to the distance and length  of a shape being preserved when it is transformed.

Translations and rotations preserve the shape of a figure during transformation which means they preserve length which makes them an isometry. The same is true of line reflections.

Point reflections on the other hand, will lead to a change in dimensions for the figure being transformed.

In conclusion, `a point reflection is not an isometry.

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Answer:

1/5

Step-by-step explanation:

these fractions are proper fractions

Answer: 1/

Step-by-step explanation:

Step-by-step explanation:

AC is the combination of AB and BC.

so, AB + BC = AC

(2n - 1) + (4n + 5) = 10n - 12

2n - 1 + 4n + 5 = 10n - 12

6n + 4 = 10n - 12

4 = 4n - 12

16 = 4n

n = 4

Answer:

slope is the coefficient of x

so it is 6

good luck!!

The surface area of a triangular prism = 108cm2

The volume of the triangular prism = 48cm3

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

Given that

The Triangle legs are 3 and 4 feet long, the hypotenuse is 5 feet long, and the prism height is 8 feet tall.

We have to determine the surface area and volume of each triangular prism

here a = 3ft b = 4ft  c = 5ft and height  h = 8ft

Surface area of triangular prism = ab + h(a+b+c)

= 3x4 + 8(3+4+5)

= 12 + 8(12)

= 12 + 96

= 108cm2

Volume of triangular prism = ½(abh)

= ½ (3x4x8)

=1/2(96)

= 96/2

= 48cm3

Therefore

The surface area of a triangular prism = 108cm2

The volume of the triangular prism = 48cm3

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Answer:

-11r

Step-by-step explanation:

4r - 9r = -5r

-5r - 11r = -16r

-16r + 7r = -11r

Answer:

Step-by-step explanation:

Ok! So apparently I think you are learning about pre algebra. So the questions are saying what times 1/4=8 in that case it would be x = 32. x is just a fancy way to say you don’t know what it is.

Annie paid a total of $2.6 for 1.2 pounds of strawberries

In this question, we have the following parameters:

Unit cost per pound = $2.13 per pound

Number of pounds = 1.2 pounds

The amount paid for the number of pounds is represented by the equation

Amount paid = Unit cost per pound x Number of pounds

Substitute the known values in the above equation So, we have the following equation

Amount paid = 2.13 * 1.2

Evaluate the products

Amount paid = 2.556

Approximate

Amount paid = 2.6

Hence, the amount is $2.6

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Answer:

2.56

Step-by-step explanation:

The vertex of the function f(x) = x^2 + 12x is (-6, -36).

The concept that will be used here is the concept of Standard equation of a curve in vertex form.

The standard equation can be written as

f (x) = ax^2 + bx + c

Then the Vertex is the (h,k)

Then the X-coordinate of the vertex  can be written as (h = -b/2a) where  k = f(h)

If we compare the given equation with the standard form, then we have

a = 1, b = 12 and c = -10

Then we can input the values into the  (h = -b/2a)

h =[ -12/2(1)] = - 6

Then we can substitute the value of h in f (x) which is f(x) = x2 + 12x

k = f(h)= f (-6) =[ (-6)2 + 12 (-6)]

= [36 - 72] = -36

In conclusion the vertex is (-6, -36).

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Answer:

$90

Step-by-step explanation:

180x5 equal 00

$18x5 equals $90

Answer:

i think 2/15 of the cookies

Step-by-step explanation:

hope this helps