An artist recreated a famous painting using a 6:1 scale. The dimensions of the scaled painting are 24 inches by 36 inches. What are the dimensions of the actual painting?

4 inches by 6 inches
18 inches by 30 inches
30 inches by 42 inches
144 inches by 216 inches

Answer:

The second answer choice represents a slope of 1/4.

Step-by-step explanation:

Using the coordinates (8,5) and (0,3) you can do point slope form (y2-y1/x2-x1). In this problem that would translate to 5-3/8-0 which is 2/8 and can be simplified to 1/4.

Answer:

Answer is A

Step-by-step explanation:

General equation of a line is given by;

[tex]{ \boxed{ \rm{y = mx + c}}}[/tex]

From the question, m = -4

[tex]{ \rm{y = - 4x + c}}[/tex]

For (-4, 6)

[tex]{ \rm{6 = ( - 4 \times - 4) + c}} \\ { \rm{6 = 16 + c}} \\ { \rm{c = - 10}}[/tex]

Therefore;

[tex]{ \rm{y = - 4x - 10}} \\ { \colorbox{silver}{subtract \: 6 \: from \: both \: sides}} \\ { \rm{y + ( - 6) = ( - 4x - 10) + ( - 6)}} \\ \\ { \rm{y - 6 = - 4x - 16}} \\ \\ { \rm{y - 6 = - 4(x + 4)}}[/tex]

The hypotenuse of the new triangle is increasing.

The Pythagorean Theorem can be used to determine the new right triangle's hypotenuse length:

[tex]c^2 = a^2 + b^2\\c^2 = 13^2 + 15^2\\c^2 = 169 + 225\\c^2 = 394\\c ≈ 19.85[/tex]

Hence, the hypotenuse of the new right triangle measures roughly 19.85 inches in length.

Let h be the height of the triangle, and let b be the base of the triangle, both as functions of time t. We know that the base and height are changing at the same rate, so we can express this as:

dh/dt = db/dt = k, where k is a constant rate of change.

We can use the Pythagorean Theorem to express the length of the hypotenuse c as a function of h and b:

[tex]c^2 = h^2 + b^2[/tex]

Taking the derivative of both sides with respect to time t using the chain rule, we get:

2c(dc/dt) = 2h(dh/dt) + 2b(db/dt)

Simplifying and substituting the values for h, b, and c at time t = 0 (when the original triangle was given):

2c(dc/dt) = 2(7)(k) + 2(x)(k)

2c(dc/dt) = 14k + 10k

2c(dc/dt) = 24k

adding 2c to both sides' sums:

(12k/c) = (dc/dt)

For the new triangle, substitute the value of c as follows:

(dc/dt) = 12k/19.85

The sign of (dc/dt) will be decided by the sign of 1/c because k is positive and constant. Since we know that 1/c is positive and that c is positive, we can infer that (dc/dt) will also be positive because it will have the same sign as k. As a result, the new triangle's hypotenuse is growing.

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Answer:

 [tex]y=\frac{5}{2} x[/tex]

Step-by-step explanation:

Notice is a line, The equation for a line can be found as the following:
[tex]y-yo=m(x-xo)[/tex]
We need to find the slope.

First take two points of the graph
(0,0) the origin and (4,10) for example. Notice i do assume the X value is 4 for Y=10, since the cropping for the picture doesn't show the exact values for X .
Then the slope is given by equation:
[tex]m=(y-yo)/(x-xo)\\[/tex]

[tex]m=\frac{10-0}{4-0} =5/2[/tex]

then the equation is

[tex]y-0=\frac{5}{2} m(x-0)[/tex]  

[tex]y=\frac{5}{2} x[/tex]

Answer:

y=5/2x or y=2.5x

Step-by-step explanation:

Pearson correlation coefficient r for the data is approximately 0.915. Since the value is positive and close to 1, we can say that there is a strong positive correlation between the number of times the commercial is run on TV and the number of car sales.

What is expression ?

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷) that represents a value or a quantity. It can be a single number or variable, or a combination of them, and can also include functions, parentheses, and other mathematical symbols. For example, 3x + 7 is an expression, where 3 and 7 are constants, x is a variable, and + is an operator. Expressions can be simplified, evaluated, or used as part of a larger mathematical statement or equation.

We can use the formula for Pearson correlation coefficient r to calculate it for the given data:

r = (nΣXY - ΣXΣY) / sqrt[(nΣX² - (ΣX)²)(nΣY² - (ΣY)²)]

where n is the number of observations, Σ represents the sum of the indicated values, and X and Y represent the two variables being correlated. Using the data from the table, we can calculate the following:

n = 5

ΣX = 25, ΣY = 25.8

ΣX² = 275, ΣY² = 288.68

ΣXY = 139.2

Substituting these values into the formula, we get:

[tex]$r = (5 * 139.2 - 25 * 25.8) \sqrt{[(5 * 275 - 25^2)(5 * 288.68 - 25.8^2)]} $[/tex]

r ≈ 0.915

Therefore, the Pearson correlation coefficient r for the data is approximately 0.915. Since the value is positive and close to 1, we can say that there is a strong positive correlation between the number of times the commercial is run on TV and the number of car sales.

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As a result the system of equation , y has a value that is roughly 4.33.

A group of two or more equations with the same variables is referred to as a system of equations. The collection of numbers that simultaneously make all the equations true is the system's solution.

For instance, take into account the equations below:

2x + y = 5

x - y = 1

There are two equations with two variables in this system (x and y). The collection of numbers that simultaneously satisfy both equations is the system's solution. The answer in this situation is x = 2 and y = 1.

We may solve for y by substituting the value of x in the system of equations, which is -4, into one of the equations.

Consider the following two equations:

axe + by = c

dx + ey = f

We can solve for y by substituting the value of x into one of the equations if we know it.

As an illustration, if x = -4, then we have:

2x + 3y = 5

4x - 3y = -16

We can change one of the equations to read x = -4:

2(-4) + 3y = 5

When we simplify this equation, we obtain:

-8 + 3y = 5

8 is added to both sides to get at:

3y = 13

When we multiply both sides by 3, we get:

y = 13/3

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Answer:

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Check the picture below.

Answer:

The numbers are -3, -2, and -1.

Step-by-step explanation:

Since -2 and -1 add up to -3, and -3+-3 = -6, and since the numbers are next to each other on your number line, well, then you got your answer. Here's how:

-3+-2+-1=-6

IS IT RIGHT??? OR I MISSED SOMETHING

The ratio as decimal is sin C = AB/BC = 8/17 = 0.4706. cos C = AC/BC = 15/17 = 0.8824 tan B = AB/AC = 8/15 = 0.5333. tan C = AB/AC = 8/15 = 0.5333. cos B = BC/AC = 17/15 = 1.1333. sin B = AC/BC = 15/17 = 0.8824.

The origin (0, 0) of a coordinate plane serves as the center of the unit circle, which has a radius of 1. It is used in trigonometry to provide the values of trigonometric functions for angles of any measure, including sine, cosine, and tangent. The x-coordinate and y-coordinate of each point on the unit circle correspond to the cosine and sine values, respectively, for that point's specific angle measure. The unit circle is a popular visual tool for teaching students about the characteristics and behaviour of trigonometric functions.

Using the right triangle we have:

sin C = opposite/hypotenuse = AB/BC = 8/17 = 0.4706

cos C = adjacent/hypotenuse = AC/BC = 15/17 = 0.8824

tan B = opposite/adjacent = AB/AC = 8/15 = 0.5333

tan C = opposite/adjacent = AB/AC = 8/15 = 0.5333

cos B = adjacent/hypotenuse = BC/AC = 17/15 = 1.1333

sin B = opposite/hypotenuse = AC/BC = 15/17 = 0.8824

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We know that the circumference (C) of a circle can be calculated using the formula:

C = 2πr, where r is the radius of the circle.

We are given that the circumference of the circle is 2.20 cm, so we can use this to solve for the radius (r):

C = 2πr

2.20 = 2πr

r = 2.20 / (2π)

r ≈ 0.350 cm

Therefore, the radius of the circle is approximately 0.350 cm.

To find the area (A) of the circle, we can use the formula:

A = πr^2

Substituting the value we found for r:

A = π(0.350)^2

A ≈ 0.385 cm^2

Therefore, the area of the circle is approximately 0.385 cm^2.

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Answer:

Step-by-step explanation:

Question :-

The circumference of the circle is 220 cm.

Find :

a) Radius

b) Area of the Circle

Solution :

a)

Circumference of circle = 2πr

[tex] \longrightarrow \: \: 220 = 2 \pi r \\ \\ \longrightarrow \: \: \frac{220}{2} = \pi r \\ \\ \longrightarrow \: \: 110 = \frac{22}{7} × r \\ \\ \longrightarrow \: \: r = 110 \times \frac{7}{22} \\ \\\longrightarrow \: \: r = \frac{770}{22} \\ \\ \longrightarrow \: \: r = 35 \: cm \\ [/tex]

b)

Area of circle = πr²

[tex]\longrightarrow \: \: \frac{22}{7} \times 35 \times 35 \\ \\ \longrightarrow \: \:22 \times 5 \times 35 \\ \\ \longrightarrow \: \:3850 \: {cm}^{2} \\ [/tex]

Hence,

a) Radius of circle is 35 cm.

b) Area of the Circle is 3850 cm²

Answer:

slope = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (8, - 2 ) and (x₂, y₂ ) = (4, - 3 )

m = [tex]\frac{-3-(-2)}{4-8}[/tex] = [tex]\frac{-3+2}{-4}[/tex] = [tex]\frac{-1}{-4}[/tex] = [tex]\frac{1}{4}[/tex]

The ordered pair that could replace the missing ordered pair to make the set not a function is given as follows:

(−7, 15).

A set of ordered pairs represents a function if every input (first component of the ordered pair) is associated with exactly one output (second component of the ordered pair). In other words, if no two ordered pairs in the set have the same first component but different second components.

Hence the ordered pair (-7,15) would make the relation not a function, as the set already has the ordered pair (-7,-15), in which the input 7 is already mapped to an output of -15, hence it cannot be mapped to an output of 15.

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The amount Jon and Ron earn are $22,000 and $ 74,000 respectively.

Word problem is a mathematical problem expressed entirely in words typically used as an educational tool.This word problem is interpreted into mathematical equation or expression.

Represent the amount Jon earn by j and Ron earn by r

j+r = 96000 equation 1

r = 8000+ 3j equation 2

from equation 1

r = 96000-j

substitute 96000-j for r in equation 2

96000-j = 8000 +3j

collect like terms

96000-8000 = 3j +j

88,000 = 4j

j = 88000/4

j = $22,000

from equation 1

22000+r = 96000

r = 96000-22000

r = 74,000

Therefore the amount Jon and Ron earn are $22,000 and $ 74,000 respectively.

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Answer: the rate of heat flow through the wall when the inside air temperature is 68 °F and the outside temperature is 5 °F is 257.42 BTU per hour.

Step-by-step explanation: The rate of heat flow through the wall can be found using the formula:

Rate of heat flow = (Temperature difference) / (Effective R-value)

The temperature difference is the difference between the inside and outside temperatures, which is:

Temperature difference = (68°F) - (5°F) = 63°F

The effective R-value of the wall is given as 15.5.

To calculate the total area of the wall, we first need to find the area of the window, which is:

Area of window = (width) x (height) = (5 ft) x (3.5 ft) = 17.5 square feet

The area of the wall without the window is:

Area of wall = (length) x (height) - Area of window

Area of wall = (14 ft) x (8 ft) - 17.5 square feet

Area of wall = 105.5 square feet

So, the rate of heat flow through the wall is:

Rate of heat flow = (Temperature difference) / (Effective R-value) x (Total area of the wall)

Rate of heat flow = (63°F) / (15.5) x (105.5 square feet)

Rate of heat flow = 257.42 BTU per hour

Answer: To calculate the hit rate metric in tons per hour, we need to first calculate how many tons of dirt the construction company can remove in one hour.

To do this, we'll convert the given time and amount of dirt into a rate of dirt removal in tons per hour:

The company takes 1 7/8 hours to remove 2 3/4 tons of dirt

We can convert 1 7/8 hours to an improper fraction: 15/8 hours

We can convert 2 3/4 tons to an improper fraction: 11/4 tons

We can calculate the rate of dirt removal as the amount of dirt divided by the time: (11/4 tons) / (15/8 hours) = (11/4) ÷ (15/8) = (11/4) x (8/15) = 22/15 tons per hour

Therefore, the construction company has a hit rate metric of 22/15 tons per hour, which simplifies to 1.47 tons per hour (rounded to two decimal places).

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve this problem, we need to find the number of acres that can be planted per pound of seed.

We know that it takes 32 pounds of seed to plant a 4-acre field. Therefore, the amount of seed needed to plant 1 acre is:

32 pounds / 4 acres = 8 pounds/acre

This means that for every pound of seed, we can plant:

1 acre / 8 pounds = 0.125 acres/pound

Therefore, we can plant 0.125 acres per pound of seed.

Step-by-step explanation:

If the stock market declined by an average of 2.5% each month during the first 6 months of Mr. Jones' investment, we can calculate the total percentage decrease using the following formula:

(1 - 0.025)^6 = 0.8938

This means that after 6 months, Mr. Jones' investment would have decreased by approximately 10.62% (1 - 0.8938 = 0.1062).

To calculate how much money Mr. Jones has remaining, we need to multiply his initial investment of $1,500 by the percentage decrease:

$1,500 x 0.1062 = $159.30

Therefore, Mr. Jones would have $1,500 - $159.30 = $1,340.70 remaining after the first 6 months of his investment in the stock market with an average decline of 2.5% each month.

The water output rate for the Rodriguez family's sprinkler was 35 L per hour, and the water output rate for the Barnes family's sprinkler was 15 L per hour (50 - 35) by solving the expression formed.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, that are written in a certain order. Expressions can be evaluated or simplified by following the rules of arithmetic or algebra. Examples of expressions include "2x + 3", "(a + b) / c", and "5^2 - 3".

According to given information :

Let's use the variable "r" to represent the water output rate for the Rodriguez family's sprinkler.

Then, the water output rate for the Barnes family's sprinkler can be represented as "50 - r", since the sum of the two rates is 50 L per hour.

Using the formula:

rate x time = amount of output, we can set up two equations:

r x 15 = amount of water output for the Rodriguez family

(50 - r) x 35 = amount of water output for the Barnes family

We also know that the total amount of water output is 1050 L, so we can set up a third equation:

r x 15 + (50 - r) x 35 = 1050

Now we can solve for "r".

First, simplify the third equation

15r + 1750 - 35r = 1050-20r = -700r = 35

Therefore, the water output rate for the Rodriguez family's sprinkler was 35 L per hour, and the water output rate for the Barnes family's sprinkler was 15 L per hour (50 - 35).

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Answer:

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Step-by-step explanation:

Medical tax credit rates and rebates are determined by the South African Revenue Service (SARS) and are subject to change from year to year. Therefore, I cannot provide you with a copy of the medical tax credit rates and rebates for the entire period of 2013 to 2023.

However, I can provide you with the following information:

The medical tax credit rate for the 2021/2022 tax year is R319 per month for the main member and the first dependent, and R215 per month for each additional dependent.

The medical tax credit rate for the 2020/2021 tax year was R310 per month for the main member and the first dependent, and R209 per month for each additional dependent.

The medical tax credit rate for the 2019/2020 tax year was R310 per month for the main member and the first dependent, and R209 per month for each additional dependent.

The medical tax credit rate for the 2018/2019 tax year was R303 per month for the main member and the first dependent, and R204 per month for each additional dependent.

The medical tax credit rate for the 2017/2018 tax year was R286 per month for the main member and the first dependent, and R192 per month for each additional dependent.

The medical tax credit rate for the 2016/2017 tax year was R286 per month for the main member and the first dependent, and R192 per month for each additional dependent.

The medical tax credit rate for the 2015/2016 tax year was R270 per month for the main member and the first dependent, and R181 per month for each additional dependent.

The medical tax credit rate for the 2014/2015 tax year was R257 per month for the main member and the first dependent, and R172 per month for each additional dependent.

As for rebates, I should note that the South African tax system works with a system of tax brackets, where the amount of tax you pay increases as your income increases. Tax rebates are a form of tax relief that is subtracted from the amount of tax you owe. The rebate amount changes annually, and for the 2021/2022 tax year, the rebate for individuals under 65 years of age is R15,714.

Again, it is important to note that these rates and rebates are subject to change from year to year, and it is recommended that you consult with a qualified tax professional for the most up-to-date information.

The value of the sum from n = 2 to n = 6 of 4n + 5 is given as follows:

b. 105.

To obtain the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression.

The expression of this problem is given as follows:

4n + 5.

The sum is the sum of the numeric values from n = 2 to n = 6, hence:

Hence the sum has the result given as follows:

13 + 17 + 21 + 25 + 29 = 105.

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{x}{6}=\cfrac{6}{8}\implies \cfrac{x}{6}=\cfrac{3}{4}\implies x=\cfrac{18}{4}\implies x=\cfrac{9}{2} \\\\[-0.35em] ~\dotfill\\\\ 8+x\implies 8+\cfrac{9}{2}\implies \cfrac{25}{2}\implies 12\frac{1}{2}=JL[/tex]

Step-by-step explanation:

geometric mean theorem :

the height of a right-angled triangle to the Hypotenuse is the square root of the product of the parts of the Hypotenuse (as the height splits the Hypotenuse into 2 parts : JM and ML).

JL = JM + ML

in short

KM = sqrt(JM × ML)

6 = sqrt(8 × ML)

36 = 8 × ML

ML = 36/8 = 9/2 = 4.5

so,

JL = JM + ML = 8 + 4.5 = 12.5

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Answer:

To find the number of boats that should be produced to incur minimum cost, we need to find the value of x that minimizes the cost function C(x).

We can do this by taking the derivative of the cost function with respect to x, setting it equal to zero, and solving for x.

C(x) = 22000 - 40x + 0.02x^2

C'(x) = -40 + 0.04x

Setting C'(x) = 0, we get:

-40 + 0.04x = 0

0.04x = 40

x = 1000

Therefore, the number of boats that should be produced to incur minimum cost is 1000.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

If they each walk in straight lines to the school Lin is closer than Elena

 so Lin walks 500 ft   and Elena walks 500 yards ( which is 1500 ft)

Answer:

Step-by-step explanation:

The common ratio of this sequence is 3.  Next 3 terms are  -81, -243, and -729.

The equation of the line of best fit is given as follows:

y = 1.5x + 4.5.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

Two points on the line for this problem are given as follows:

(1,6) and (3,9).

When x increases by 2, y increases by 3, hence the slope m of the line is given as follows:

m = 3/2

m = 1.5.

Hence:

y = 1.5x + b.

When x = 3, y = 9, hence the intercept b of the line is obtained as follows:

9 = 1.5(3) + b

b = 9 - 4.5

b = 4.5.

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The critical points for the function are [tex]x=-\frac{3+\sqrt{7}}{2},\:x=-\frac{3-\sqrt{7}}{2}[/tex]

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

f(x) = (4x + 6)/(x² + x + 1)

The critical points are the points where the derivative of f(x) equals 0 or undefined when the function is defined

When f(x) is differentiated, we have

f'(x) = 4/(x² + x + 1) - [(2x + 1)(4x + 6)/[(x² + x + 1)²]

Set to 0 and evaluate

4/(x² + x + 1) - [(2x + 1)(4x + 6)/[(x² + x + 1)²] = 0

So, we have

[(2x + 1)(4x + 6)/[(x² + x + 1)²] = 4/(x² + x + 1)

This gives

[(2x + 1)(4x + 6)/[(x² + x + 1)] = 4

Cross multiply

(2x + 1)(4x + 6) = 4x² + 4x + 4

12x² + 12x + 4x + 6 = 4x² + 4x + 4

12x² + 12x  + 6 = 4x² + 4

Evaluate

8x² + 12x + 2 = 0

So, we have

4x² + 6x + 1 = 0

Using a graphing tool, we have

[tex]x=-\frac{3+\sqrt{7}}{2},\:x=-\frac{3-\sqrt{7}}{2}[/tex]

Hence, the critical points are [tex]x=-\frac{3+\sqrt{7}}{2},\:x=-\frac{3-\sqrt{7}}{2}[/tex]

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