14. What is the equation of the line that passes through the
point (-3, -5) and has a slope of
-2/3

Answer:

[tex]\mbox{\large \textsf{Timothy bought 14 books}}[/tex]

Step-by-step explanation:

Let's use first letters of names to represent the number of books bought by that person. This makes it easier to explain.

Therefore, the books bought by each of the three persons are T(imothy), L(aurence) and M(ike)

We will now convert each of the word description into math equations and solve

We are given that the ratio of the number of books bought by Laurence and Mike were 2: 7

We can write this as:
[tex]\dfrac{L}{M} = \dfrac{2}{7}\\\\[/tex]

Multiplying both sides by M:
[tex]L = \dfrac{2}{7}M\cdots\cdots(1)[/tex]  

Timothy and Laurence bought a total of 20 books can be represented as
[tex]T + L = 20\cdots\cdots(2)[/tex]

Timothy and Mike bought a total of 35 books can be represented as
[tex]T + M = 35\cdots\cdots(3)[/tex]

Eq (3) - Eq (2):

[tex]T + M - (T + L) = 35 - 20\\\\T + M - T - L = 15\\\\M - L = 15 \cdots\cdots (4)[/tex]

Substituting for [tex]\displaystyle L = \frac{2}{7}M[/tex]  from equation (1) into equation (4) we get

[tex]M - \dfrac{2}{7}M = 15\\\\\dfrac{5}{7}M = 15\\\\M = \dfrac{7}{5} \times 15\\\\M = 21\\\\[/tex]

Given [tex]\displaystyle M = 21[/tex] using equation (3), [tex]\displaystyle T + M = 35[/tex] we get

[tex]T + 21 = 35\\\\T = 35 - 21\\\\\textrm{or}\\\\T = 14[/tex](Answer)

If we wanted to find out how many books Laurence bought use Eq(1)
[tex]L = \dfrac{2}{7}M\\\\L = \dfrac{2}{7} \times 21\\\\L = 6\\\\[/tex]

His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation

Two or more expressions with an Equal sign is called as Equation.

Sheldon wants to buy two shirts at the store.

They were each originally $14.99, but one of the shirts is on sale this week for 10% off.

A 6% sales tax is applied to the total cost of the shirts.

0.90 • 14.99 + 14.99 • 1.06 = n

The first term in the equation, 0.90 • 14.99, represents the cost of the shirt that is on sale.

The 10% discount is applied to the original price of $14.99, which is why we multiply by 0.90.

This term calculates the discounted price of the first shirt.

The second term in the equation, 14.99 • 1.06, represents the cost of the second shirt, plus the 6% sales tax that is applied to both shirts.

This term calculates the total cost of the second shirt with sales tax.

Hence, His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation

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x^2 - 2x + 1 is the required quadratic equation using the completing the square

Given the quadratic expression below

x^2 - 2x

We need to determine the constant that will make the expression a perfect square.

The constant will be the half of the square of coefficient of 'x'

Coefficient of 'x' = -2

Half of the coefficient of 'x' = -2/2 = -1

Square of the coefficient = (-2/2)^2

Square of the coefficient = 1

Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1

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The amount that should be invested in order to have $2,290 in 16 years is $929.11.

What is compound interest?

The interest on a deposit calculated using both the initial principle and the accrued interest from prior periods is known as compound interest. In other words, compound interest is interest that is earned on interest.

Here, we have

Given: Xin will invest in an account paying an interest rate of 5.8% compounded annually.

Amount to invest = Future value / (1 + r)ᵗ

Where:

r = interest rate

t = time

X = $2,290 / (1 + 0.058)¹⁶

X = 2,290 / 2.46474

X = $929.11

Hence, the amount that should be invested in order to have $2,290 in 16 years is $929.11.

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Answer:

Step-by-step explanation:

An equation to show the sequence is -25n.

When all the terms of the geometric sequence are added, than that expression is known as geometric series.

The sum of terms of a geometric sequence;

Now, lets suppose its initial term is   , multiplication factor will be r

and let it has total n terms, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

We are given that;

The first term of sequence=-25

D= -50-(-25)

=-25

Now,

an = a + (n-1)d

=-25+(n-1)-25

=-25-25n+25

=-25n

Therefore, the answer of the sequence will be -25n.

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In the equation, the number 5,000 represents the initial value of the motorcycle. The value of the motorcycle is increasing at a rate of 3% per year.

Exponential functions are functions where the independent variable, x is in the exponent.

The given exponential equation is,

V = 5,000 (1.03)^t

Here V represents the value of the motorcycle in t years.

When t = 0,

V = 5000 (1.03)⁰ = 5000

So 5000 represents the initial value of the motorcycle.

V = 5,000 (1 + 0.03)^t

At t = 0, V = 5000

At t = 1, V = 5000 (1.03)¹ = 5150

At t = 2, V = 5000 (1.03)² = 5304.5

So the value of the motorcycle is increasing.

The rate is 0.03 or 3%.

Hence, 5,000 represents the initial value of the motorcycle and the value of the motorcycle is increasing at a rate of 3% per year.

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Answer:

Standard form of the equation for the circle

(x + 3)² + (y + 5)² = 40

Step-by-step explanation:

The equation of a circle in standard form is
[tex]\boxed{(x - a)^2 + (y-b)^2= r^2}[/tex]

where (a, b) is the center of the circle and r is the radius

To find center of circle

The end points of the diameter are (-5, -11) and (-1, 1)

The center of the circle is midway between these two points

The x-coordinate of the midpoint = (-5 + -1)/2 = -6/2 = -3

The y-coordinate of the midpoint is (-11 + 1) /2 = -10/2 = -5

So the center of the circle is at (-3, -5)

To find the radius,

Calculate the distance from (-3, -5) to any of of the endpoints.

Let's take the endpoint (-1, 1) and find its distance from (-3, -5)

The distance between any two points (x₁, y₁) and (x₂, y₂) is calculated from the formula

[tex]d^2 = {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2[/tex]

Substituting
(x₁, y₁) = (-1, 1)
(x₂, y₂)  = (-3, -5)

and r for distance

we get

[tex]r^2 = {(-3 - (-1))^2 + (-5 - 1)^2[/tex]

[tex]r^2 = {(-2)^2 + (-6)^2}[/tex]

[tex]r^2 = {{4} + {36}}[/tex]

[tex]r^2 = {40}[/tex]

So the center (a, b) is (-3, -5) and r² =40

Plugging this into the circle equation:
(x - (-3))² + (y - (-5))² = 40

(x + 3)² + (y + 5)² = 40

The two integers are 5 and 10.

What do you mean by Integers?

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.

A number is positive if it is greater than zero, so it said to be positive integers

A number is negative if it is less than zero, so it said to be negative integers.

A number line is a visual representation of numbers on a straight line. This line is used for the comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.

Given:

Let x be the positive number

2x be the other positive number

Find the first integer

[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]

[tex]\frac{2x - x}{2x^2} = \frac{1}{10}[/tex]

[tex]\frac{x}{2x^2} = \frac{1}{10}[/tex]

[tex]\frac{1}{2x} = \frac{1}{10}[/tex]

2x = 10

x = 5

Therefore, the first positive integer is 5.

Find the other integer

2x = 2(5) = 10

Therefore, the other integer is 10.

To check:

[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]

[tex]\frac{1}{5} - \frac{1}{10} = \frac{1}{10}[/tex]

[tex]\frac{2}{10} - \frac{1}{10} = \frac{1}{10}[/tex]

[tex]\frac{1}{10} = \frac{1}{10}[/tex]

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300.5 ml of antihistamine is needed for a 100​-pound person to take in a​ week

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

1 day = 24 hours

1 week = 7 days = 24 hours per day * 7 days = 168 hours

A typical dose for a 100​-pound person is 22 mg every six hours. Hence for one week:

Dosage in one week = (22 mg per 6 hours) * 168 hours = 616 mg

Antihistamine also comes in a liquid form with a concentration of 12.3 ​mg/ 6 mL. For 616 mg:

Amount of antihistamine = 616 mg / (12.3 ​mg/ 6 mL) = 300.5 ml

300.5 ml of antihistamine is needed

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Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

It's the most random and produces no bias.

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

When we use the distance formula for two points ( x, y ) and ( x', y¹ ) Then formula is (distance)² = (x - x¹)² + (y - y¹)² This is quite similar to the formula used in a right angle triangle

The possible equation of the parabola is y = (x - 5)^2 - 4

from the question, we have the following parameters that can be used in our computation:

Vertex = (5, -4)

The vertex form of a parabola is given by:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola.

We are given that the vertex of the parabola is (5,-4). Substituting these values into the vertex form, we get:

y = a(x - 5)^2 - 4

Let a = 1

So, we have

y = (x - 5)^2 - 4

Hnce, the possible equation is y = (x - 5)^2 - 4

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Answer:

f(-2) = 46

f(-1) = 17

f(0) = 2

f(1) = 1

f(2) = 14

Step-by-step explanation:

F(-2) = 46

F(-1)= 17

F(0)= 2

F(1)= 1

F(2)= 14

Answer:

4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.

Step-by-step explanation:

To find the weight of 4.4 cubic feet of water in pounds, we need to find the number of gallons it contains and then multiply it by the weight of one gallon of water.

1 cubic foot = 7.48 gallons

So, 4.4 cubic feet = 4.4 * 7.48 = 32.912 gallons

And the weight of 32.912 gallons of water in pounds is:

32.912 gallons * 8.33 pounds/gallon = 273.5016 pounds

To convert this weight to tons, we divide the weight in pounds by 2000:

273.5016 pounds / 2000 = 0.13676 tons

So, 4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.

Answer: Let's follow the same steps as in the previous example:

Identify the constants and the variables.

The known constant here is 4. Shailyn read 4 fewer books than Oswaldo. Let's call the number of books Oswaldo read "o".

Identify the operations.

The phrase "four fewer" tells us we need to subtract.

Rewrite the phrase as an expression.

"Four fewer books than Oswaldo" is o - 4.

So, the expression that shows how many books Shailyn read last year is o - 4.

Step-by-step explanation:

Answer:you never asked for like in what minutes or hours?

Step-by-step explanation:

The car, traveling at a speed 5 mph faster than the truck, will take more than 4.6 hours to be more than 23 miles ahead.

This question pertains to relative speed. When the car is traveling at 55 mph and the truck at 50 mph, the car is effectively moving away from the truck at (55 mph - 50 mph) = 5 mph. To calculate the time it will take for the car to be more than 23 miles ahead, we can use the formula: Time = Distance/Speed. So the time it would take is Time = 23 miles / 5 mph = 4.6 hours. Therefore, it will take the car more than 4.6 hours to be more than 23 miles ahead.

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The vertices of the image of triangle ABC are A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4) and C''(x, y) = (- 4, 4).

Any triangle can be generated by three points that are not collinear, in this problem we need to determine the image of a triangle, which is the result of two rigid transformations: (i) Reflection over the y-axis, (ii) Dilation centered at the origin with a scale factor of 2, whose definitions are shown below:

Reflection over the y-axis:

(x, y) → (- x, y)

Dilation centered at the origin with a scale factor of 2:

(x, y) → (2 · x, 2 · y)

If we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (2, 2), then the image of the vertices are determined below:

Reflection over the y-axis

A'(x, y) = (- 3, 4), B'(x, y) = (- 4, 2), C'(x, y) = (- 2, 2)

Dilation centered at the origin with a scale factor of 2

A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4), C''(x, y) = (- 4, 4)

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The equation that represents the graph of a line passing through the points (0, -1) and (1, -4) is y = -3x - 1.

What is graph?

A graph is a visual representation of data or information that shows the relationship between different variables or quantities. Graphs can take many forms, including bar graphs, line graphs, scatterplots, and pie charts, among others. They are widely used in many fields, including mathematics, science, economics, and social sciences, to help visualize and analyze data, identify patterns, and communicate findings to others in a clear and concise manner. By representing complex information in a simple, easy-to-understand format, graphs can provide valuable insights and help us make informed decisions.

The equation that represents the graph of a line passing through the points (0,-1) and (1,-4) is:

y = -3x - 1

To find the equation of a line given two points, you can use the slope-intercept form:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the given points.

First, we can find the slope of the line:

m = (y2 - y1) / (x2 - x1)

= (-4 - (-1)) / (1 - 0)

= -3

Next, we can choose one of the given points and substitute its coordinates and the slope into the slope-intercept form:

y - (-1) = -3(x - 0)

y + 1 = -3x

y = -3x - 1

Therefore, the equation that represents the graph is y = -3x - 1.

Option A, y = -1/3x - 1, has a slope of -1/3, which is not the slope of the line passing through the given points.

Option C, y = -1/3x + 1/3, also has an incorrect slope of -1/3, and it also does not pass through the point (0,-1).

Option D, y = -3x + 1/3, has the correct slope of -3, but it does not pass through the point (0,-1).

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Answer:

9 trucks/hour

Step-by-step explanation:

If he loaded 9 trucks in one hour, his loading speed is 9 trucks per hour.

Answer:

p = x(y)(z)

Step-by-step explanation:

product is multiplication.

multiplication has no specific order.

From given quadratic equation:

Exact Cost of 31st food processor = $15.6

Approx. cost of 31st food processor  =  $15.2

What is a quadratic equation?

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

It is given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.

The given quadratic equation for the cost of producing x food processors is:

 C(x) = 2400 + 40x - 0.4x²

a) The exact cost of producing the 31st food PROCESSOR is:

cost of 31 food processors - cost of 30 food processors = C(31) - C(30)

= (2400 + 40*31 - 0.4*31²) - (2400 + 40*30 - 0.4*30²)

= 3255.6 - 3240 = $15.6

b) The marginal cost at x = 31

Differentiate the quadratic equation

C'(x) = 40 - 0.8x

Marginal cost = C'(31) = 40 - 0.8*31 = $15.2

So the cost of producing the 31st food processor is approx $15.2.

Therefore from the given quadratic equation:

Exact Cost of 31st food processor = $15.6

Approx. cost of 31st food processor  =  $15.2

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well, in 2007 it was 12000, so initially that's what it was, and in 2019 it went to 23000, so that's 12 years later, and in 2040, that'll be 33 years later.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 23000\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &12\\ \end{cases} \\\\\\ 23000 = 12000(1 + \frac{r}{100})^{12}\implies \cfrac{23000}{12000} =\left(1+ \cfrac{r}{100} \right)^{12} \\\\\\ \cfrac{23}{12}=\left(\cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{\cfrac{23}{12}}=\cfrac{100+r}{100}[/tex]

[tex]100\sqrt[12]{\cfrac{23}{12}}=100+r\implies 100\sqrt[12]{\cfrac{23}{12}}-100=r\implies \boxed{5.57\approx r} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to 5.57\%\to \frac{5.57}{100}\dotfill &0.0557\\ t=years\dotfill &\stackrel{year~2040 }{33}\\ \end{cases} \\\\\\ A \approx 12000(1 + 0.0557)^{33} \implies \boxed{A \approx 71782}[/tex]

Answer:

46.21%

Step-by-step explanation:

The area of the table top is 1.3 x 1.3 = 1.69 m²

The area of the circular tablecloth is given by πr² where r is the radius of the table cloth

Give diameter of tablecloth is 2m, radius r = 2/2 = 1 m

Area of tablecloth = π · 1² = π

So the excess area of the tablecloth which overhangs

= π - 1.69 = 1.45 m²  (taking π = 3.14)

So the fraction of the tablecloth that overhangs
= Excess area of tablecloth ÷ total area of tablecloth
= 1.45 /π

= 0.4621

As a percentage this would be
0.4621 x 100

= 46.21%

The equations of the parabolas are y = x² - 6x - 7 and y = x² - 7

Parabola 1

Given that

The points (-1,0), (7, 0) and (3,-16)

The equation is represented as

y = ax² + bx + c

So, we have

a - b + c = 0

49a + 7b + c = 0

9a + 3b + c = -16

Make c the subject in a - b + c = 0

c = b - a

So, we have

49a + 7b + b - a = 0

9a + 3b + b - a = -16

48a + 8b = 0

8a + 4b = -16

Multiply 8a + 4b = -16 by 2

48a + 8b = 0

16a + 8b = -32

Subtract

32a = 32

So, we have

a = 1

Recall that 48a + 8b = 0

So, we have

48 + 8b = 0

This gives

8b = -48

Divide

b = -6

Also, we have

c = b - a

This gives

c = -6 - 1

c = -7

So, the equation is

y = x² - 6x - 7

Parabola 2

Given that

The points (-4,9), (-3, 2) and (0,-7) and (4,9)

The equation is represented as

y = ax² + bx + c

So, we have

16a - 4b + c = 9

9a - 3b + c = 2

c = -7

16a + 4b + c = 9

The equations become

16a - 4b = 16

9a - 3b = 9

16a + 4b = 16

Add (1) and (3)

32a = 32

So, we have

a = 1

Subtract (1) and (3)

-8b = 0

So, we have

b = 0

So, the equation is

y = x² - 7

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Answer: the answer is 5/12

(a) The union set is AUB'={f, k, m, x, y}.

(b) The union set is A'UB'={q,k, x, y}.

The union of two sets is also a set. This set contains all the elements of both two sets.

The universal set is U= {f, k, m, q, x,y} and two subsets are A={f, k, m, y} and B = {f, m,q}.

(a)

B' is the complementary set of B. So, find the elements of B'=U-B.

B'= {f, k, m, q, x,y}-{f, m,q}

={k, x,y}

Now, find the union set AUB'.

AUB' ={f, k, m, y}U{k, x,y}

={f, k, m, x, y}

Therefore, the required answer is AUB'={f, k, m, x, y}.

(b)

Also, A' is the complementary set of A. So, find the elements of A'=A-B.

A'= {f, k, m, q, x,y}-{f, k,m, y}

={q,x}

Now, find the union set A'UB'.

A'UB' ={q,x}U{k, x,y}

={q,k, x, y}

Therefore, the required answer is A'UB'={q,k, x, y}.

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Answer:

16

Step-by-step explanation:

As the question states, we are counting downwards which means with every interval we are going back -1. Therefore, 17 - 1 = 16